Answer: The resulting P-value is 0.923, which is greater than 0.05. Therefore, we do not reject the null hypotheses.
Step-by-step explanation:
(a) The appropriate hypotheses for this study would be:
Null hypothesis: There is no difference in intelligence scores between first-born and second-born monozygotic twins.
Alternative hypothesis: There is a significant difference in intelligence scores between first-born and second-born monozygotic twins.
(b) In Minitab, we can conduct a Paired-T test using the following steps:
1. Enter the data into two columns, one for first-born twins and one for second-born twins.
2. Select "Stat > T Tests > Paired T" from the menu.
3. In the "Paired-T Test" dialog box, select the two columns of data as the "Pairs" and specify the significance level as 0.05.
4. Click "OK" to run the test.
The P-value obtained from this test is 0.752, which is greater than the specified significance level of 0.05. Therefore, we do not reject the null hypotheses.
Why is it appropriate to use a Paired-T test in this study?
It is appropriate to use a Paired-T test in this study because the data consists of paired samples (first-born and second-born monozygotic twins) and we are comparing the mean difference between the two groups. The Paired-T test is specifically designed to compare the means of paired samples and allows for the correction of any inherent dependency between the two groups.
The P-value of 0.752 indicates that there is a 75.2% chance of obtaining the observed difference in intelligence scores between first-born and second-born twins if the null hypothesis is true.
Since this probability is relatively high, we cannot conclude that there is a significant difference in intelligence scores between the two groups. This means that the intelligence scores of first-born and second-born twins are not significantly different.
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P-value = 0.29, which is higher than 0.05. Therefore, we don't reject the null hypotheses.
a)The proper hypotheses for this investigation would be:
Null hypotheses: First-born and second-born monozygotic twins do not differ in their cognitive ratings.
Appropriate hypotheses: First-born and second-born monozygotic twins' IQ scores differ significantly.
(b)The steps listed below can be used to do a Paired-T test in Minitab:
1. Separate the data into first-born twins and second-born twins columns.
2. "Stat > T Tests > Paired T" can be selected from the menu.
3. Choose the two data columns as the "Pairs" in the "Paired-T Test" dialogue box, and enter 0.05 for the significance level.
4. To launch the test, click "OK".
This test yielded a P-value of 0.752, which is higher than the 0.05 designated threshold of significance. Therefore, we don't reject the null hypotheses.
Why is a Paired-T test useful for this study?
The first-born and second-born monozygotic twins in this study are paired samples, and we are comparing the mean difference between the two groups, therefore a Paired-T test is acceptable. The Paired-T test allows for the correction of any inherent dependencies between the two groups and is specifically created to compare the means of paired samples.
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Write 28 as a product of its prime factors, write factors in order from smallest to largest
Answer:
2 × 2 × 7
Step-by-step explanation:
start dividing by the lowest prime and work up until 1 is reached
28 ÷ 2 = 14
14 ÷ 2 = 7
7 ÷ 7 = 1
then
28 = 2 × 2 × 7 = 2² × 7
the temperature in summit green land was -29'F in Fairbanks Alaska the temperature was 23'F in barrels Brazil the temperature was 81'F which two cities had a difference in temperature of 58'F
Answer: Brazil and Alaska
Step-by-step explanation
Take away Brazil's temperature from Alaska's to get your answer
81 - 23 = 58'F
A city has 4 voting districts. Records from previous years show what proportion of residents live in each district. A political analyst wondered if those proportions still held true, so they took a random sample of 120 residents. Here are their results along with a chi-square goodness-of-fit test:District A B C DHypothesized 0.39 0.27 0.15 0.19 Observed 58 22 12 28 Expected 46.80 32.40 18.00 22.80 Components 2.68 3.34 2.001.19 x² = 9.20, DF = 3 P-value = 0.027 Which voting district contributed the most to the test statistic?
Answer: The voting district that contributed the most to the test statistic is District B.
Step-by-step explanation:
How do you calculate the contribution of each voting district to the test statistic?
The contribution of each voting district to the test statistic is calculated by taking the difference between the observed and expected values for that district, squaring it, and then dividing it by the expected value. In this case, the contribution for District A is (58-46.80)^2/46.80 = 2.68, the contribution for District B is (22-32.40)^2/32.40 = 3.34, the contribution for District C is (12-18)^2/18 = 2.00, and the contribution for District D is (28-22.80)^2/22.80 = 1.19. Therefore, District B contributed the most to the test statistic.
The chi-square goodness-of-fit test compares observed and expected values to determine if they are significantly different from each other. The test statistic is calculated by summing the squared differences between the observed and expected values, divided by the expected values. The larger the difference between the observed and expected values, the larger the contribution to the test statistic. In this case, District B had the largest difference between the observed and expected values, therefore it had the greatest impact on the overall test statistic.
District B contributed the most to the test statistic because it had the highest value in the "Components" column. The formula for the chi-square goodness-of-fit test is (Observed - Expected)^2 / Expected, and the resulting value for District B is 3.34, which is the highest of the four districts. Therefore, District B had the biggest deviation from the hypothesized proportions.
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Answer: Voting district B contributed the most to the test statistic.
Step-by-step explanation:
How do you determine each voting district's contribution to the test statistic?
By subtracting the observed value from the predicted value for each voting district, square rooting the result, and then dividing the result by the expected value, the contribution of each voting district to the test statistic is determined. In this instance, the contributions for Districts A, B, C, and D are as follows:
District A's contribution is (58-46.80)²/46.80 = 2.68; District B's contribution is (22-32.40)²/32.40 = 3.34; District C's contribution is (12-18)²/18 = 2.00; and District D's contribution is (28-22.80)²/22.80 = 1.19. As a result, District B was most responsible for the test statistic.
In order to assess if actual and expected values differ significantly from one another, the chi-square goodness-of-fit test compares observed and expected values. The test statistic is determined by multiplying the expected values by the total of the squared discrepancies between the actual and predicted values. The contribution to the test statistic increases as the gap between observed and predicted values widens. In this instance, District B's largest disparity between actual and predicted values had the biggest effect on the test statistic as a whole.
Due to having the highest value in the "Components" column, District B had the greatest impact on the test statistic. (Observed - Expected)² / Expected is the formula for the chi-square goodness-of-fit test, and the result for District B, which is the highest of the four districts, is 3.34.
District B therefore, showed the greatest departure from the predicted proportions.
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Attending Class The following data represent the number of days absent, x, and the final grade, y, for a sample of college students in a general education course at a large state University
No. of Absensense, x 0 1 2 3 4 5 6 7 8 9
Final grade, y 89.2 86.4 83.5 81.1 78.2 73.9 64.3 71.8 65.5 66.2
A) Find the least-sqaures regresssion line treating number of absenses as the explanatory variable and final grade as a response variable.
B) Interpret the slope and y-intercept , if appropriate.
C) Predict the final grade for a student who misses five class periods and compute the residual. Is the final grade abover or below average for this number of absenses.
D) Draw a least-sqaures regression line on the scatter diagram of the data.
E) Would it be reasonable to to use the least-sqaures regression line to predict the final grade for a student who has missed 15 class periods? why or why not?
We get the following answers:
A) The least square regression line is:
yi = 88.73 - 2.827(xi)
B) The slope is β₁ = -2.827 and The intercept is β₀ = 88.73.
C) e*₆ = -0.6964, final grade is below average grade.
E) It would not be reasonable since no of absence increases the score decreases, it works well for small no of absences but will not work for large number of absences since it may give absurd final grade.
we have Xi = No of absences
Yi = Final grade
The regression model is
Yi = β₀ + β₁Xi + i
β₀ = y - β₁x
we have n = 10, x bar = 4.5 , y bar = 76.01
cov(x,y) = -23.325 and var(x) = 9.1667
therefore, β₀ = 88.73 and β₁ = -2.827
A) Least square regression line is given by:
yi = β₀+ β₁Xi
yi = 88.73 - 2.827(xi)
B) The slope β₁ = -2.827 which means when no of absence is increased by 1 duty then the final grade will decrease by 2.827
The intercept β₀ = 88.73 when there are 0 days absence the average grade is 88.73
C) Predicted graph for student who misses five class periods is
x = 5
y*5 = 88.73 - 2.827(5) = 74.5964
Hence for corresponding residual is:
e*₆ = 73.9 - 74.5964
e*₆ = -0.6964, final grade is below average grade.
D) please see graph
E) when student miss 15 class periods the final grade will be
X = 5
y* = 88.73 - 2.827(15)
= 46
It would not be reasonable since no of absence increases the score decreases, it works well for small no of absences but will not work for large number of absences since it may give absurd final grade.
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3. A rectangle is 8cm longer than it is wide. If its width is x cm and its area is 84cm², form an equation in x and solve it. Hence find the dimensions of the rectangle.
Answer:
x = 6
Step-by-step explanation:
let x = the width
let x + 8 = the length
Area = w times l
84 = 14 x 6
width = 6
length = 6+8
= 14
33% of millennials rely on blogs before making a purchase and eight out of 10 millennials never buy anything without reading a review first. In a sample size of 75 Millennials, how many people use blogs to make a purchase? In a sample size of 75 Millennials, how many people never buy anything without reading a review first?
Number of people that use blogs to make a purchase are 24.75= 25 and number of people that never buy anything without reading a review first are 60.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given, 33% of millennials rely on blogs before making a purchase.
Eight out of 10 millennials never buy anything without reading a review first.
That means,
8 out of 10 is 80%.
In a sample size of 75 millennials:
To find the number of people that never buy anything without reading a review first:
80% of 75
80 x 75 / 100
= 6000/ 100
= 60
To find the number of people that use blogs to make a purchase:
33% of 75
33 x 75 / 100
= 2475/ 100
= 24.75
Therefore, the number of people are 24.75 and 60.
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Find the function represented by the following series and find the interval of convergence of the series. Sigma Infinity k=0[x^2+3/4]^k. The function represented by the series Sigma Infinity k=0[x^2+3/4]^k is f(x)= The interval of convergence is (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed.)
The function represented by the series is [tex]$\quad f(x)=\frac{4}{1-x^2}$[/tex]
The interval of convergence of the series is ( - 1, 1 )
As per the question the given function is:
[tex]$$\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k$$[/tex]
[tex]$$\sum_{n=0}^{\infty} a r^n=\frac{1}{1-r}$$[/tex]
[tex]$$\sum_{n=0}^{\infty} x^n=\frac{1}{1-x}$$[/tex]
[tex]$$\begin{aligned}\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k & =\frac{1}{1-\frac{x^2+3}{4}} \\& =\frac{1}{\frac{4-x^2-3}{4}} \\& =\frac{4}{1-x^2}\end{aligned}$$[/tex]
Thus, [tex]$\quad f(x)=\frac{4}{1-x^2}$[/tex]
[tex]$$\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k=\sum_{k=0}^{\infty} \frac{\left(x^2+3\right)^k}{4^k}$$[/tex]
[tex]$$\begin{aligned}L & =\lim _{k \rightarrow \infty}\left|\frac{\left(x^2+3\right)^{k+1}}{4^{k+1}} \frac{4^k}{\left(x^2+3\right)^k}\right| \\& =\lim _{k \rightarrow \infty}\left|\frac{\left(x^2+3\right)}{4}\right| \\& =\left|\frac{\left(x^2+3\right)}{4}\right|\end{aligned}$$[/tex]
The series will converge, if L<1
[tex]$$\begin{array}{ll} & \left|\frac{\left(x^2+3\right)}{4}\right| < 1 \\ & \frac{\left(x^2+3\right)}{4} < 1 \\ & x^2+3 < 4 \\\end{array}[/tex]
[tex]& x^2 < 1 \\[/tex]
|x| < 1
-1 < x < 1
Substitute the values of 'x' in the given function
At, x = - 1
[tex]\begin{aligned} \\\qquad \begin{aligned}\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k & =\sum_{k=0}^{\infty}\left(\frac{(-1)^2+3}{4}\right)^k \\& =\sum_{k=0}^{\infty}\left(\frac{4}{4}\right)^k \\& =\sum_{k=0}^{\infty} 1^k\end{aligned}\end{aligned}$$[/tex]
Also, at x = 1
[tex]$$\begin{aligned}\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k & =\sum_{k=0}^{\infty}\left(\frac{(1)^2+3}{4}\right)^k \\& =\sum_{k=0}^{\infty}\left(\frac{4}{4}\right)^k \\& =\sum_{k=0}^{\infty} 1^k\end{aligned}$$[/tex]
Thus, the interval of convergence is ( - 1, 1 )
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1. Computer Depot is a large store that sells and repairs computers. A random sample of 110 computer repair jobs took technicians an average of = 93.2 minutes per computer. Assume that is known to be 16.9 minutes.
(a) Find a 99% confidence interval for the population mean time for computer repairs.
(b) Write a brief explanation of the meaning of the confidence interval in the context of this problem.
Confidence interval for the population mean time σ for computer repairs is [98.05 , 89.850].
What is confidence interval?
A confidence interval, in statistics, refers to the chance that a population parameter can fall between a collection of values for an exact proportion of times.
Main body:
According to question:
N = 110
X bar = 93.9 minutes
σ = 16.9 minutes
value for 99% confidence interval = 2.576
C.I. = x bar ± z*s/√n
C.I. = 93.9 ± 2.576 *16.9 /√110
C.I. = 93.9 ± 4.150
C.I. = [98.05 , 89.850]
Hence , confidence interval for the population mean time σ for computer repairs is [98.05 , 89.850].
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Write the equation in exponential form. Assume that all constants are positive and not equal to 1. logz(w) = p ________
Write the equation in exponential form. Assume that all constants are positive and not equal to 1. log(s) =r ________
Write the equation in logarithmic form. Assume that all constants are positive and not equal to 1. 7m = a ________
To write the equation in exponential form we must follow certain rules:
1. Logarithm product rule - log b ( x ∙ y) = log b ( x) + log b ( y)
2. Logarithm quotient rule - log b ( x / y) = log b ( x) - log b ( y)
3. Logarithm power rule - log b ( x y) = y ∙ log b ( x)
4. Logarithm base switch rule - log b ( c) = 1 / log c ( b)
1. ㏒z(w) = p
Here all constants are taken to be positive and not equal to 1
z = base of the logarithmic function
z^p = w --------> (1)
This z^p = w is the exponential form of ㏒z(w) = p
2. ㏒(s) = r
Here all constants are taken to be positive and not equal to 1
e = base of the logarithmic function
e^r = s --------> (2)
This e^r = s is the exponential form of ㏒(s) = r
3. 7m = a
Here we have to write the equation in logarithmic form
㏒(7m) = log r
log(7m) - log r = 0
We know quotient rule :-
log b ( x / y) = log b ( x) - log b ( y) --------(A)
Applying that same principle to our question by using this equation we have:
log (7m/r)
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I don’t know why I’m finding this so hard but I’ve tried so many attempts
Check the picture below.
Enter the ordered pair for the vertices for (Ry-axis T(2, 0))(QRST).
I need help with this please help me
The ordered pair for the vertices after the transformation will be:
Q' = (3, 5)
R' = (5, -1)
S'= (2, 0)
T' = (0, 3)
How to find the ordered pair for the vertices for (Ry-axis T(2, 0))(QRST)?
A geometric transformation is a function that maps points in a plane or space to other points in the same plane or space. Geometric transformations can be used to change the size, shape, orientation, or position of an object or image.
Given: (Ry-axis T(2, 0))(QRST). That means we have a translation T(2, 0). This implies (x,y) → (x + 2, y + 0). Thus, the ordered pair for the vertices will be:
Q (x = 1, y = 5)
Q' = Q(x+2, y + 0) = (1+2, 5+0) = (3, 5)
R (x = 3, y = -1)
R' = R(x+2, y + 0) = (3+2, -1+0) = (5, -1)
S (x = 0, y = 0)
S' = S(x+2, y + 0) = (0+2, 0+0) = (2, 0)
T (x = -2, y = 3)
T' = T(x+2, y + 0) = (-2+2, 3+0) = (0, 3)
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Solve the equation.
-1/6x-5=2/3x
A. x= - 6.
B. x = -5.
C. x = 3.
D. x = 6.
Answer:
A. x = -6
Step-by-step explanation:
-1/6x - 5 = 2/3x
add 1/6x to both sides:
-1/6x - 5 + 1/6x = 2/3x + 1/6x
-5 = 2/3x + 1/6x
common denominator on right side:
-5 = 4/6x + 1/6x
combine right side:
-5 = 5/6x
multiply both sides by 6/5:
(-5)(6/5) = (5/6x)(6/5)
-30/5 = x
reduce left side:
-6 = x
x = -6 (option a)
Answer: A) x=-6
Step by step explanation:
[tex]\boldsymbol{\sf{\dfrac{-1}{6}x-5=\dfrac{2}{3}x }}[/tex]
We calculate the multiplication expression.
[tex]\boldsymbol{\sf{\dfrac{-1}{6}x-5=\dfrac{2}{3}x \iff \ -\dfrac{x}{6}-5=\dfrac{2}{3} x \iff -\dfrac{x}{6}-5=\dfrac{2x}{3} }}[/tex]
Eliminate the fractions by multiplying by the least common multiple of the denominators of both sides.
[tex]\boldsymbol{\sf{ -\dfrac{x}{6}-5=\dfrac{2x}{3} \iff \ -x-30=4x}}[/tex]
The variable is moved to the left and the symbol is changed.
[tex]\boldsymbol{\sf{-x-30=4x \iff -x-30-4x=0}}[/tex]
We move the constant to the right side and change the sign.
[tex]\boldsymbol{\sf{-x-30-4x=0 \iff -x-4x=30}}[/tex]
[tex]\boldsymbol{\sf{-x-4x=30 \ < == We \ organize \ the \ equation== > \ -5x=30 }}[/tex]
[tex]\bf{\underline{Change \ the \ sign \ on \ both \ sides \ of \ the \ equation.}}[/tex]
[tex]\boldsymbol{\sf{-5x=30 \iff \ 5x=-30 \ < ==Split== > \ x=-\dfrac{30}{5}=\boxed{\boxed{\boldsymbol{\sf{-6}}}} }}[/tex]
A college admissions officer for an MBA program has determined that historically
applicants have undergraduate grade point averages that are normally distributed with
standard deviation 0.45. From a random sample of 25 applications from the current year,
the sample mean grade point average is 2.90.
Required: Find the confidence interval foe the population mean at the 5% significance level.
(10marks)
B. An educational study was designed to investigate the effectiveness of a reading program
of elementary age children. Each child was given a pre-test and post-test. Higher posttest scores would indicate reading improvement. From a very large population, a random
sample of scores for the pre-test and post-test are as follows:
The confidence interval for the population mean at significance level is
2.724<μ<30.76 .
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Population standard deviation: σ = 0.45
Sample size: n = 25
Sample Mean: x= 2.90
Х=2.90 represent the sample mean for the sample
μ population mean (variable of interest)
σ = 0.45 represent the population standard deviation
n=25 represent the sample size
We have the following distribution for the random variable:
X≈N(μ,σ =0.45)
And by the central theorem we know that the distribution for the sample mean is given by:
X≈N( μ, [tex]\frac{σ}{\sqrt{n} }[/tex])
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha =0.05[/tex] and[tex]\frac{\alpha }{2} =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)" and we see that
Z₁ =±1.96
Now we have everything in order to replace into formula:
[tex]2.90-1.96\frac{0.45}{\sqrt{25} }=2.724[/tex]
[tex]2.90+1.96\frac{0.45}{\sqrt{25} }=3.076[/tex]
So on this case the 95% confidence interval would be given by (2.724:3.076) .
At a significance level, the population mean's confidence interval is 2.724–30.76.
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Two random number generators each generate a number from 1 to 10. What is the probability that both number generators generated the number 5
Hello,
The probability that both number generators generate the number 5 is (1/10) * (1/10) = 1/100 = 0.01 or 1%.
This is because the probability of an event occurring is the product of the probabilities of each event occurring independently. In this case, the probability of the first generator generating the number 5 is 1/10 and the probability of the second generator generating the number 5 is also 1/10, so the probability of both events occurring is (1/10) * (1/10) = 1/100.
----
Assume that the distributions for the following scenarios are normal. Use the normal standard table to find the following probabilities. Round z-scores to the nearest hundredth.
1. The average score on a math test is 75 with a standard deviation of 8. What is the probability that a randomly selected test has a score of 90 or higher?
2. The life of a gas grill is 3.5 years with a standard deviation 0.35 years. What is the probability that the grill will last less than 3 years?
3. Ambulance response times average 7.5 minutes with a standard deviation of 2.5. What is the probability that an ambulance will respond within 6 to 8 minutes.
Answer:
1. To find the probability that a randomly selected test has a score of 90 or higher, we need to find the z-score corresponding to a score of 90 and then use the standard normal table to find the probability that a score is greater than or equal to this value. To find the z-score, we can use the formula:
z = (x - mean) / standard deviation
where x is the score we are interested in, mean is the average score, and standard deviation is the standard deviation of the distribution. Plugging in the values from the problem, we get:
z = (90 - 75) / 8 = 1.875
Rounding this value to the nearest hundredth, we get z = 1.88. Looking up this value in the standard normal table, we find that the probability that a score is greater than or equal to 1.88 is 0.9637. Therefore, the probability that a randomly selected test has a score of 90 or higher is 0.9637.
2. To find the probability that the grill will last less than 3 years, we need to find the z-score corresponding to a life of 3 years and then use the standard normal table to find the probability that a life is less than this value. To find the z-score, we can use the formula:
z = (x - mean) / standard deviation
where x is the value we are interested in, mean is the average value, and standard deviation is the standard deviation of the distribution. Plugging in the values from the problem, we get:
z = (3 - 3.5) / 0.35 = -1.43
Rounding this value to the nearest hundredth, we get z = -1.43. Looking up this value in the standard normal table, we find that the probability that a life is less than -1.43 is 0.0747. Therefore, the probability that the grill will last less than 3 years is 0.0747.
3. To find the probability that the ambulance will respond within 6 to 8 minutes, we need to find the z-scores corresponding to a response time of 6 and 8 minutes, respectively, and then use the standard normal table to find the probability that a response time is between these two values. To find the z-score, we can use the formula:
z = (x - mean) / standard deviation
where x is the value we are interested in, mean is the average value, and standard deviation is the standard deviation of the distribution. Plugging in the values from the problem, we get:
z1 = (6 - 7.5) / 2.5 = -0.6
z2 = (8 - 7.5) / 2.5 = 0.2
Rounding these values to the nearest hundredth, we get z1 = -0.6 and z2 = 0.2. Looking up these values in the standard normal table, we find that the probability that a response time is less than -0.6 is 0.2743 and the probability that a response time is less than 0.2 is 0.5398. Therefore, the probability that a response time is between -0.6 and 0.2 is 0.5398 - 0.2743 = 0.2655. Therefore, the probability that the ambulance will respond within 6 to 8 minutes is 0.2655.
1. The probability that a randomly selected test has a score of 90 or higher is 0.0301.
2. The probability that the grill will last less than 3 years is 0.0764.
3. The probability that an ambulance will respond within 6 to 8 minutes is 0.1465.
How to determine the required probabilities?In Mathematics and Statistics, the z-score of a given sample size or data set can be calculated by using the following formula:
Z-score, z = (x - μ)/σ
Where:
σ represents the standard deviation.x represents the sample score.μ represents the mean score.Part 1.
By substituting the given parameters, we have the following:
Z-score, z = (90 - 75)/8
Z-score, z = 1.88
Based on the standardized normal distribution table, the required probability is given by:
P(Z ≥ 1.88) = 1 - P(x < Z)
P(Z ≥ 1.88) = 1 - 0.9699
Probability = 0.0301.
Part 2.
By substituting the given parameters, we have the following:
Z-score, z = (3 - 3.5)/0.35
Z-score, z = -1.43
Based on the standardized normal distribution table, the required probability is given by:
P(Z < -1.43) = 1 - P(x > Z)
P(Z < -1.43) = 1 - 0.9236
Probability = 0.0764.
Part 3.
At 6 minutes, we have:
Z-score, z = (6 - 7.5)/2.5
Z-score, z = -0.6
At 8 minutes, we have:
Z-score, z = (8 - 7.5)/2.5
Z-score, z = 0.2
Based on the standardized normal distribution table, the required probability is given by:
P(6 < x < 8) = P(-0.6 < z < 0.2)
P(-0.6 < z < 0.2) = P(z < 0.2) - P(z < -0.6)
P(-0.6 < z < 0.2) = 0.42074 - 0.27425
P(-0.6 < z < 0.2) = 0.1465.
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Mackenzie's car used 4 gallons to travel 108 miles. How many gallons of gas would she need to travel 162 miles?
The gallons of gas that she would need to travel 162 miles will be 4374 gallons.
How to illustrate the ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
Since Mackenzie's car used 4 gallons to travel 108 miles. The rate will be:
= 108 / 4
= 27 miles per gallon
The gallons of gas that she would need to travel 162 miles will be:
= 162 × 27
= 4374 gallons.
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g. find polar coordinates of the following points given in cartesian coordinates (x, y): (2,5), (3,-6), (-4,9), (-8,-1
The polar coordinates of the points are: A(√29,68.1°),B(√45,-63.4°),C(√97,66.0°),D(√65,7.12°)
consider A=(2,5)
To find the polar coordinates we have the formula:
[tex]r=\sqrt{x^2+y^2} and tan^{-1} (\frac{y}{x} )----------(1)[/tex]
Assume that x=2,y=5 and substitute in equation(1)
r=√2^2+5^2 and tan^-1(5/2)
r=√4+25 and tan^-1(2.5)
r=(√29,68.1°)
For point B =(3,-6)
Assume that x=3,y=-6 and substitute in equation(1)
r=√3^3+(-6)^2 and tan^-1(-6/2)
r=√9+36 and tan^-1(-2)
r=(√45,-63.9°)
For point C=(-4,9)
Assume that x=-4,y=9 and substitute in equation(1)
r=√(-4)^2+9^2 and tan^-1(9/-4)
r=√16+81 and tan^-1(2.25)
r=(√97,66.0°)
For the point D=(-8,-1)
Assume that x=-8,y=-1 and substitute in equation(1)
r=√(-8)^2+(-1)^2 and tan^-1(-1/-8)
r=√64+1 ,7.12°
r=(√65,7.12°)
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What is the result of 6+
3/8?
1/8
1/4
16
48
Answer:
C) 16------------------------------
Simplify:
6 ÷ 3/8 = Given6 × 8/3 = Flip the fraction2 × 8 = Cancel the denominator 16 AnswerAnswer:
[tex] \sf \red{c) \: 16} \: is \: the \: answer.[/tex]
Step-by-step explanation:
Given problem,
[tex] \sf →6 + \frac{3}{8} [/tex]
Changing error in problem,
[tex] \sf →6 \div \frac{3}{8} [/tex]
Let's solve the problem,
[tex] \sf →6 \div \frac{3}{8} [/tex]
[tex] \sf →6 \times \frac{8}{3} [/tex]
[tex] \sf → \frac{(6 \times 8)}{3} [/tex]
[tex] \sf → \frac{48}{3} [/tex]
[tex] \sf \: →16 \:[/tex]
Hence, the answer is 16.
Calculate the difference and enter it in the box below.
-7 - 9
Answer:
Step-by-step explanation:
-7-9=-16
in triangle abc, lines ad and bd are the angle bisectors of angle a and b and line de is parallel to line ab find the length of line de if perimeter of abde is 30 cm and ab is 12 cm
If the circumference of ABDE is 30 cm, then the length of the line DE is 6 cm.
The answer to the query is
ABDE's perimeter is 30 cm.
AB length is 12 cm.
Let DE ne length be "x"
Since DE and AB are parallel, the alternate interior angles theorem states that
∠ABE = ∠DEB and ∠BAD = ∠ADE.
Since AD is the angle that bisects ∠A,
∠DAB = ∠EAD
BE is the angle bisector of B, therefore
∠EBD = ∠ABE.
∠EAD = ∠ADE and ∠EBD = ∠BED as a result.
If AE = ED and ED = DB, the triangles ADE and EDB are therefore isosceles. AE = DE = DB = x, then.
Given that ABDE's perimeter is 30 cm,
therefore 12 + 3x = 30,
By finding the x,
=> 3x = 30 -12
=> 3x = 18
=> x = 6 cm.
Consequently, DE has a length of 6 cm.
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In a normal distribution, a data value located 1.1 standard deviations below the mean has Standard Score: z = In a normal distribution, a data value located 2.5 standard deviations above the mean has Standard Score: z = In a normal distribution, the mean has Standard Score: z =
In a normal distribution, a data value located 1.1 standard deviations below the mean has Standard Score: z = -1.1
What is standard deviation?
In statistics, the quality deviation could be a live of the quantity of variation or dispersion of a group of values. an occasional variance indicates that the values tend to be about to the mean of the set, whereas a high variance indicates that the values area unit opened up over a wider vary
Main body:
The z score tells us the distance, in terms of standard deviation, the raw score is from the mean. Negative z values are below the mean, while positive ones are above the mean.
Something like z = 2.5 indicates we're 2.5 standard deviation units above the mean.
Something like z = -1.1 indicates we're 1.1 standard deviation units below the mean.
The value z = 0 itself is the center of the standard normal distribution (it's the mean mu).
The sigma value for the standard normal Z distribution is sigma = 1
sigma = population standard deviation
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consider the set of students enrolled in a college and the set of faculty members at that college. suppose we define a one to one correspondence between the two sets by saying that a student corresponds to a faculty member if the student is currently enrolled in a course taught by that faculty member. is this correspondence a function? briefly discuss. a simple yes or no needs reasoning so please answer thoughtfully.
We state that a student correlates to a faculty member if somehow the student gets currently enrolled in some kind of a course taught by such faculty member in order to define a one to one relationship between the two sets. The correspondence a function.
Define the term one-to-one relation in function?The symbol for an ordered pair is (INPUT, OUTPUT): The relation denotes the connection between the input and output.
A function, on the other hand, is a relation that yields one Outcome for each input Data.A is a relationship that states that there should only be one outputs for each input. Alternatively, we could say that a function is a special sort of relation (a collection of ordered pairs) that adheres to the rule that every X-value should only be connected with one y-value.A function f: A → B is one-to-one if there is only one instance of a ∈ A with f(a) = b for each instance of b B. It is onto if it has least one a A with f(a) = b for each b B. If it is simultaneously one-to-one and onto, it is a one-to-one correlation or bijection.For the stated question-
We state that a student correlates to a faculty member if somehow the student gets currently enrolled in some kind of a course taught by such faculty member in order to define a one to one relationship between the two sets.
One student is related to one facility.
Thus, correspondence given forms a function.
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Please Help will mark Brainly
Answer:
A, B, C
Step-by-step explanation:
You want to know the correct descriptors of the given graph.
SolutionThe solution to a system of equations is the set of points that satisfy all of the equations at once. On a graph, it will be the set of points where the graphs of the equations intersect.
Here the two lines cross at one point, hence there is one solution.
The point where the lines cross is approximately (3, -0.5). That makes (3, -0.5) a reasonable estimate of the solution of the system.
for a study cvaluating the difference among three treatments with a separate sample of n-10 for cach treatment,the kruska-walis test statistic would have df -
for a study cvaluating the difference among three treatments with a separate sample of n-10 for cach treatment,the kruska-walis test statistic would have df - 2(3-1)=2
The Kruskal-Wallis test statistic has a degrees of freedom (df) equal to the number of groups minus one. In this case, there are three groups, so the df is 2 (3-1).The Kruskal-Wallis test statistic is a non-parametric test used to compare the means of a set of independent samples. In this case, we have three separate samples of n-10 for each treatment. To calculate the Kruskal-Wallis test statistic, we need to first calculate the sum of the ranks for each sample and then subtract the expected sum of ranks for each sample. The df for the Kruskal-Wallis test statistic is equal to the number of groups minus one. In this case, there are three groups, so the df is 2 (3-1). Finally, the Kruskal-Wallis test statistic is calculated by dividing the calculated sum of ranks by the expected sum of ranks and multiplying by the df. This will give us the Kruskal-Wallis test statistic for the data set.
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Use Taylor's Theorem to obtain an upper bound for the error of the approximation. Then calculate the exact value of the error. Round your answers to three significant figures.)
cos(0.3)=1−(0.3)22!+(0.3)44!
R4≤ .
R4=.
Answer:
Step-by-step explanation:
According to Tylor theorem,
f(x)=f(a)+f′(a)/1!×(x−a)+f′′(a)/2!×(x−a)2+......+fn(a)/n!×(x−a)n
Tylor series for cosx is
1 - x^2/2! + x^4/4! + x^6/6! + ……
cos (0.3) = 1 - 〖(0.3)〗^2/2! + 〖(0.3)〗^4/4!
The R4 valur is fourth derivative of cosx
f’(x) = -sinx
f’’ (x) = -cosx
f’’’ (x) = sinx
f’’’’ (x) = cosx
Here, a = 0, n = 3, x = 0.3
max l f^4l = cos (0.3)
= 0.9999
lR_4 (x)l ≤ |0.3-0|^(4+1)/4! × 0.9999
≤ 0.00015186
= 1.51786 × 10^(-4)
R_n (x) = cos (0.3) – (1 - 〖(0.3)〗^2/2!-(0.3)^4/4!)
= 0.0446
The error of approximation R_4 (x) ≤ 1.2 × 10^(-2) and exact value of error R_4 = 0.0446
0.1 recurring as a fraction
Answer:
1/9
Step-by-step explanation:
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Which sequence explains a geometric method of determining
● Plot 2 + 2i. Scale by 2. Rotate 45° clockwise.
4
Plot 3-17i. Scale by ✓2.Rotate 45° clockwise.
O Plot 2 + 2i. Scale by 2√2. Rotate 45° clockwise.
Plot 3-17i. Scale by 2√2. Rotate 45° clockwise.
3-171 ?
2 + 2i
Answer:
Second option (Plot 3-17i. Scale by ✓2/4 .Rotate 45° clockwise.)
Step-by-step explanation:
Given below in the picture.
I hope my answer helps you.
In each case below find an equation for the line with the given information about the linear equation and
give the slope of each line.
a) Vertical line through point (2, -65)
b) Horizontal line through point (-2, 4)
a) The equation of a vertical line is x = k, where k is the x-coordinate of the point where the line intersects the y-axis. In this case, the point where the line intersects the y-axis is (2, -65), so the equation of the line is x = 2. The slope of a vertical line is undefined, since it has no slope.
b) The equation of a horizontal line is y = k, where k is the y-coordinate of the point where the line intersects the x-axis. In this case, the point where the line intersects the x-axis is (-2, 4), so the equation of the line is y = 4. The slope of a horizontal line is 0, since it has no slope.
If the probability that a person will die in the next year is
probability that the person will not die in the next year?
OA. 99%
B. 99548
C. 0.00452
OD. 0.99548
452
100,000
what is the
SUBMIT
The probability that the person will not die will be D. 0.99548
How to illustrate the probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.
Since the probability that the person will die is 814/1000000, the probability that the person will not die will be:
= 1 - 452/100000
= 99548/100000
= 0.99548
The correct option is D.
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If the probability that a person will die in the next year is 452/100000, the probability that the person will not die in the next year?
A. 99%
B. 0.99548
C. 0.00452
D. 0.99548
When students are admitted to a specific university, they are given a seven (7) digit identification number (NNNNNNN). If the first digit must be either a 0 or 1, how many identification numbers are possible?
Step-by-step explanation:
so, we have 1 position with 2 options (0 or 1).
and 6 positions with 10 options (0 to 9).
so, we have
2×10×10×10×10×10×10 = 2×10⁶ = 2,000,000
different identification numbers possible.