The p - value of the given hypothesis is P(2<x<6.75) is 0.49974
How to calculate p - value?
In statistics, p-value is calculated using integral calculus from the area under the probability distribution curve for all values of statistics that are at least as far from the reference value as the observed value is, relative to the total area under the probability distribution curve.
Here we have given that an article in neurology (1998, vol. 50, pp. 1246-1252) discussed that monozygotic twins share numerous physical, psychological, and pathological traits. the investigators measured an intelligence score of 10 pairs of twins, and the data.
And we need to find the value of p from it.
Here we have the following sample data,
=>2,5.73,5.80,6.08,6.22,7.99,7.44,6.48,7.99,6.32,7.60,6.03,7.52,8.42,6.84,6.43,8.76,6.32,7.62,6.59,7.67
Through the sample data we ahve identified the following values,
Standard Deviation, σ: 1.3737491940207
Count, N: 21
Sum, Σx: 141.85
Mean, μ: 6.7547619047619
Variance, σ2: 1.8871868480726
in order to find the p-value, we have to calculate the z score for the given data,
Z score = (x - μ)/σ
=> (2 - 6.75)/ 1.37
=> -3.46715
P-value from Z-Table:
=> P(x<2) = 0.000263
=> P(x>2) = 1 - P(x<2) = 0.99974
=> P(2<x<6.75) = 0.5 - P(x<2) = 0.49974
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Experience has shown that a certain lie detector will show a positive reading (indicates a lie) 10% of the time when a person is telling the truth and 95% of the time when a person is lying. Suppose that a random sample of 5 suspects is subjected to a lie detector test regarding a recent crime. The probability of observing no positive reading if all suspects are telling the truth is: (a) 0.00 (b) 0.23 (c) 0.41 (d) 0.59 (e) 0.77
The probability of observing no positive reading if all suspects are telling the truth is d. 0.59. Probability theory is a branch of mathematics that is used to model and analyze random events.
Probability can be used to predict the likelihood of different outcomes in a wide range of situations, from games of chance to scientific experiments to everyday events. Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.
To solve this problem, we need to calculate the probability of observing no positive readings given that all suspects are telling the truth, which is equal to the probability that all 5 suspects receive a negative reading on the lie detector test. Since the lie detector will show a positive reading 10% of the time when a person is telling the truth, the probability that a suspect will receive a negative reading when telling the truth is 1 - 10% = 90%. Therefore, the probability that all 5 suspects will receive a negative reading when telling the truth is:
(90%)^5 = (0.9)^5 = 0.59049.
The correct answer is therefore (d) 0.59.
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what is the simplify to 80√
Answer:
Square Root of 80 in Radical Form: 4√5.
Step-by-step explanation:
√80 = 4√5. Meaning that the square root of 80 in radical form 4 √ 5.
OR Decimal form: 8.944
(Not sure if you wanted it in radical form... I also included it in decimal form)
find the critical values for a 99% confidence interval using the chi-square distribution with 10 degrees of freedom.
The critical values for a 99% confidence interval using the chi-square distribution with 10 degrees of freedom are 18.3278 and 28.3092.
The chi-square distribution is a continuous probability distribution that is used to determine the probability of a statistic being greater than or less than a certain value. The chi-square distribution with 10 degrees of freedom is used to calculate critical values for a 99% confidence interval.
To find the critical values, we need to use the chi-square distribution calculator. In the calculator, we should enter the degrees of freedom, which is 10 in this case, and the confidence level, which is 99% in this case. The calculator will then return the critical values for the 99% confidence interval for a chi-square distribution with 10 degrees of freedom, which are 18.3278 and 28.3092.
Step 1: Go to the chi-square distribution calculator.
Step 2: Enter the degrees of freedom, which is 10 in this case.
Step 3: Enter the confidence level, which is 99% in this case.
Step 4: Click the “Calculate” button.
Step 5: The calculator will return the critical values for a 99% confidence interval for a chi-square distribution with 10 degrees of freedom, which are 18.3278 and 28.3092.
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the probability of heads of a coin is , and this bias is itself the realization of a random variable which is uniformly distributed on the interval . to estimate the bias of this coin. we flip it times, and define the (observed) random variable as the number of heads in this experiment. throughout this problem, you may find the following formula useful: for every positive integers , given the observation , calculate the posterior distribution of the bias . that is, find the conditional distribution of , given . for ,
The resulting conditional mean squared error of the LMS estimator, given N=3 is 0.0383746
What is conditional distribution formula?In general, the conditional distribution of X given Y does not equal the conditional distribution of Y given X, i.e., pX|Y(x|y)≠pY|X(y|x). If X and Y are independent, discrete random variables, then the following are true: pX|Y(x|y)=pX(x)pY|X(y|x)=pY(y)
What is full conditional distribution?The full conditional for a given node (parameter) is simply the product of the probability model (likelihood or prior) for that node and its parent node (at least up to a constant of proportionality).
1) fY|N(y∣N=3)=84 y^6 (1-y)^3
2)0.0636363
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A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally, 65 seniors reported using drugs or alcohol within the past month, while 61 national seniors reported using them. Conduct a hypothesis test at the 5% level.
NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
There is evidence to claim that the proportion of drug and alcohol use is higher locally than nationally.
Given that a recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent.
Let p1 be the proportion of local seniors and p2 national seniors.
H₀ : p₁ = p₂
Hₐ : p₁ > p₂
(right tailed test at 5% significance level)
Group I II
Success 69 60 129
Total 100 100 200
p 0.69 0.6 0.645
q 0.31 0.4 0.355
se 0.046249324 0.048989795 0.033836002
p diff 0.09
Std error 0.03384
Z 2.659574468 0
p 0.00391
we find that p value is 0.00391 < 0.05
Hence we reject null hypothesis. There is evidence to claim that the proportion of drug and alcohol use is higher locally than nationally.
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Find the x-intercept of the line 3x + 19y = -18
Answer:
Step-by-step explanation:
Sarai wants to make latkes for
the Hanukkah party. The recipe
says she will need 6 potatoes to
make 16 latkes. Sarai wants to
make 40 latkes. How many
potatoes will she need?
Answer:
The correct answer is 15 potatoes.
Step-by-step explanation:
To solve this problem, we can determine the unit rate and use proportions. We know that Sarai needs 6 potatoes for 16 latkes. We want to know how many potatoes she will need to make 40 latkes. Let's call this unknown value x. We can set up the following equation:
6 potatoes/16 latkes = x potatoes/40 latkes
To solve this equation, we can first simplify the left side to find the unit rate.
3 potatoes/8 latkes = x potatoes/40 latkes
To solve, we can recognize that 40 latkes is 5 times the amount shown in the unit rate (8 latkes), which means that we need 5 times the amount of potatoes.
3 potatoes * 5 = 15 potatoes
Therefore, the correct answer is 15 potatoes. Note that you could have also just solved the equation for x to find your answer as well.
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Mark got a new job with a starting salary of $32,000. If he gets a yearly raise
of 2%. find Marks salary after 25 years
Answer:
Mark's salary after 25 years is $52,499.39
Step-by-step explanation:
This situation can be modelled exponentially. We are given the starting amount, 32000, and the annual growth rate, 2%. This means that, for every year that passes, we'd have [tex][(32000)(1.02)][/tex] $ as the salary. As such, the model would be [tex]S(t) = 32000(1.02)^t[/tex]. We want to find Mark's salary 25 years from the starting point, t=25. Having developed a model for this situation, we can simply plug in 25 for t:
[tex]S(25) = 32000(1.02)^{(25)}[/tex]
[tex]S(25) = 52499.39[/tex]
If f(x) = -3x-2, find f(3)
Answer:
-11
Step-by-step explanation:
To find f(3), we simply need to plug 3 in for x in the function f(x) = -3x-2. This gives us:
f(3) = -3(3) - 2 = -9 - 2 = -11
Therefore, the value of f(3) is -11.
Suppose the diameter of a circle is 16 units. What is its circumference?
Use 3.14 for π and enter your answer as a decimal.
Answer: 50.24
Step-by-step explanation:
The formula to find the circumference of a circle is two pi r. So we just have substituted value into our formula. So we have To multiply by pi, so let's use 3.14 multiplied by our sequence to eight, so this is equal to 16, multiply by 3.14, which is equal to 50.24.
Solve:
3250/156 = y/40
Answer:
y = 833.(3) .3 repeatingStep-by-step explanation:
the fraction is a division, we solve with an equation
3250 : 156 = y : 40
y = 3250 × 40 : 156
y = 833.(3) 3 repeating
--------------------------
check
3250 : 156 = 833.(3) : 40
20,83333333333333 = 20,83333333333333
the answer is good
The data below consist of 25 samples of 4 observations each on the lengths of particular bolts manufactured for use in a large aircraft. The target length of these bolts is 37 centimeters. Answer the below questions and show all hand written, SPSS (screenshots) or excel work.
a) Is the process in statistical control?
b) If not in statistical control, why? Explain.
c) Given that the tolerance of these bolts is + .01 centimeters, determine the
i. Cp
ii. CpK values of this process and the
iii. Sigma level Samples
Samples
Sub 1
Sub 2
Sub 3
Sub 4
1
36.99
37.02
37.04
37.01
2
37.01
37.04
37.03
36.98
3
36.98
37.03
37.03
36.99
4
37.00
37.00
37.00
36.98
5
36.98
36.99
36.99
36.96
6
36.99
36.96
36.94
36.97
7
36.98
36.97
37.01
36.96
8
36.93
36.96
36.96
36.93
9
36.91
36.99
36.95
36.92
10
36.97
36.99
36.95
36.94
11
37.05
37.05
37.05
37.05
12
37.00
37.04
37.11
37.05
13
37.05
37.04
37.06
37.04
14
37.08
37.08
37.03
37.08
15
37.08
36.99
37.07
37.06
16
36.93
36.99
37.03
37.03
17
37.06
36.94
37.06
36.98
18
36.94
36.96
36.96
37.01
19
37.01
36.98
37.03
37.00
20
37.03
37.07
36.99
37.03
21
36.99
36.99
37.01
37.00
22
37.01
37.00
37.00
36.99
23
37.02
37.00
37.00
37.00
24
37.01
37.01
37.00
37.03
25
36.99
37.00
37.00
36.99
Using the properties of confidence interval and probability we can conclude from the observations that the process is not a statistical control process.
(a) The process is not a statistical process .
b) The control & chart is not in control because there some false alarm at 8-15. There are some special causes in the clata (may be in manufacturing) exist.
(c) (i) Given that Target length = 37 USL + LSL = 37 USL+2SL= 74
and Tolerance = 0.01 USL LSL = 0.01
After Solving equation 1 & 2 we get VSL = 37.005, LSL = 36.995
cp =2 × 0.01 6/0.05 × 2.059 = 0.01 ×0.1457 = 0.0686
(ii) Cp = min (Cpu, CP).
Cpu = 37.005-37 0.073 = 0.06849
CPL = 0.06859
Срк = 2 × 0.06849 = 0.024
The application of statistical methods to monitor and regulate the quality of a manufacturing process is known as SPC (statistical process control) or SQC (statistical quality control).
This increases the efficiency of the process, resulting in more specification-conforming goods with less waste (rework or scrap). SPC can be used to any process that can measure the output of a "compliant product" (a product that fulfils standards).
The primary tools of SPC are run charts, control charts, a focus on continuous improvement, and experiment design. Manufacturing lines are one example of a process that employs SPC.
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10. Which of the following sets of ordered pairs does not describe a function?
A
((7,-2), (5, 0), (3, 3), (1, -2)}
B
((7, 2), (5, 4), (3, 6), (1, 8))
C ((7, 2), (7, 0), (3,-2), (1,4)}
D ((7, 7),(5, 5), (3, 3), (1, 1))
Answer:
C {(7, 2), (7, 0), (3,-2), (1,4)}
Step-by-step explanation:
In a function, x = 7 can't be at both 2 and 0 because it would not pass the vertical line test.
18. In a sample of seven cars, each car was tested for nitrogen-oxide emissions (in grams per mile)
and the following results were obtained: 0.06, 0.11, 0.16, 0.15, 0.14, 0.08, 0.15. Assuming that
this sample is representative of the cars in use, construct a 98% confidence interval estimate of
the mean amount of nitrogen-oxide emissions for all cars. If the EPA requires that nitrogen-oxide
emissions be less than 0.165 g/mi, can we safely conclude that this requirement is being met?
Assume the population is normally distributed.
We cannot safely conclude that this requirement is being met because 0.165 is contained in the confidence interval.
What is Normally distribution?
A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.
results obtained are 0.06, 0.11, 0.16, 0.15, 0.14, 0.08, 0.15
[tex]\overline {X} = \frac{0.06 + 0.11 + 0.16 + 0.15 + 0.14 + 0.08 + 0.15}{7}\\\\ \overline {X} = 0.1214\\[/tex]
[tex]S=\sqrt[2]{\frac{0.0091}{n-1} } \\\\S= \sqrt[2]{\frac{0.0091}{7-1} }\\\\S=0.039\\\\n-1 = 6\\\\E= 3.143 * \frac{0.039}{\sqrt[2]{7} } \\\\E= 0.0462\\\\[/tex]
The confidence interval ⇾ 0.0752 < µ < 0.1676
We cannot safely conclude that this requirement is being met because 0.165 is contained in the confidence interval.
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what is 70x+10=200 pretty pls help
Answer: 19/7
Step-by-step explanation:
Your goal is to isolate x or get x by itself.
Move all other variables to the opposite side.
70x+10-10=200-10
70x=190
Divide both sides by 70
x= 19/7
Answer:
[tex]x= \frac{19}{7}[/tex] OR [tex]2 \frac{5}{7}[/tex]
Step-by-step explanation:
To do this you need to:
1. Subtract 10 from both sides {As shown below}
[tex]70x+10-10=200-10[/tex]
2. Simplify {As shown below}
[tex]70x=190[/tex]
3. Divide both sides by the same factor {As shown below}
[tex]\frac{70x}{70} = \frac{190}{70}[/tex]
4. Simplify {As shown below}
{a. Cancel terms that are in both the numerator and the denominator}
{b. Divide the numbers}
[tex]x= \frac{19}{7}[/tex] OR [tex]2 \frac{5}{7}[/tex]
{Please give Brainliest}
10. use a taylor series to approximate the value of the defnite integral. use as many terms as needed to ensure that the error is less than show at least 8 decimal places in your answer.
∛8.1 = 2.00829885025 it has accuracy up to 6 places which means the error is less than at least 8 decimal places .
For example ,
Using the first three terms of the Taylor series expansion of
f(x)=∛x centered at
x = 8, approximate inmate ∛8.1 :
f(x) = ∛x≈2 + (x-8) / 12 - (x-8)² / 288
the first three terms shown will be sufficient to provide a good approximation for ∛x . Evaluating this sum at x = 8.1 gives an approximation for ∛8.1
f(8.1) = ∛8.1 ≈2 + (8.1 -8)/ 12 - (8.1 - 8 )² / 288
= 2.00829861111
∛8.1 = 2.00829885025
With just three terms, the formula above was able to find the approximate accuracy in ∛8.1 to six decimal places .
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Which polynomial is the product of (4x−3)(x2+2x−6)?
The polynomial that is the product of (4x−3)(x²+2x−6) is 4x³ + 5x² - 30x + 18
Which polynomial is the product of (4x − 3)(x² + 2x − 6)?A polynomial simply refers to the expression that is composed of constant, variables, and exponents that are combined by mathematical operations.
The product of the polynomial will be:
= (4x −3)(x² + 2x − 6)
= 4x³ + 8x² - 24x - 3x² - 6x + 18
= 4x³ + 5x² - 30x + 18
The product is 4x³ + 5x² - 30x + 18.
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What is the x-intercept of 4x+2y=6?
a) If 6^x = 216’
find the value of x.
Answer: x=3
Step-by-step explanation:
6*6=36
36*6=216
6*6*6=216
6*6*6=[tex]6^{2}[/tex]
[tex]6^{x} =6^{3}[/tex]
x=3
Answer:
Step-by-step explanation:
we need to find a base for 216 that is equal to 6.
216 / 6 = 36
36 / 6 = 6,
So 6 * 6 = 36 and 36 * 6 = 216.
From this we know that 216 = 6^3
6^x = 6^3
x=3
The playing time X of classical CDs has the normal distribution with a mean of 54 and a standard deviation of 5; the N(54, 5) distribution. What is the relative frequency of classical CDs with a playing time X between 44 and 54 minutes? (2 points)
a)47.5%
b)52.5%
c)50%
d)81.5%
Using the normal distribution, it is found that the relative frequency of classical CDs with playing time X between 44 and 54 minutes is 0.8150= 81.5%.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean and standard deviation is given by:
The z-score measures how many standard deviations the measure is above or below the mean.
Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given, respectively, by:
The relative frequency of classical CDs with playing time X between 44 and 54 minutes is the p-value of Z when X = 69 subtracted by the p-value of Z when X = 44, hence:
X = 54:
Z = 3
Z = 3 has a p-value of 0.9987.
X = 54:
Z = -1
Z = -1 has a p-value of 0.1584.
0.9987 - 0.1584 = 0.8150
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a box contains ten sealed envelopes numbered 1, . . . , 10. the first six contain no money, the next two each contains $5, and there is a $10 bill in each of the last two. a sample of size 3 is selected with replacement (so we have a random sample), and you get the largest amount in any of the envelopes selected. if x1, x2, and x3 denote the amounts in the selected envelopes, the statistic of interest is m
When the expected value and variance are 3.5 and 15.25, the statistic probability distribution will be 5/10, 3/10, and 2/10.
Given that,
A box contains ten sealed envelopes labelled 1, 2, 3, and 10. Six of them are empty, two have $5 apiece, and the remaining two each contain a $10 bill. You obtain the most money in any chosen envelope when replacement is used; a sample of size 3 is selected (forming a random sample). The statistic of interest is m if the quantities in the selected envelopes are represented by x1, x2, and x3.
We know that,
The probability distribution will be
P(X=0) = 5/10
P(X=5) = 3/10
P(X=10) = 2/10
In probability theory, the expected value is a development of the weighted average. The arithmetic mean of a sizable number of outcomes of a random variable that were independently selected is, informally, the expected value.
The expected value is
E =0(5/10)+5(3/10)+10(2/10) = 3.5
The variance is
V = 0² x (5/10) + 5² ( 3/10 ) + 10² x (2/10) - 3.5² = 15.25
Therefore, the statistic probability distribution will be 5/10, 3/10, and 2/10 when the expected value and variance are 3.5 and 15.25.
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Simplify ( 7x+5y)^3–(7x–5y)^3–30y(7x+5y)(7x–5y)^3
Answer:
-72030x⁴y +18750y⁵ +102900x³y² -52500xy⁴ +1470x²y +250y³
Step-by-step explanation:
You want to simplify (7x+5y)^3–(7x–5y)^3–30y(7x+5y)(7x–5y)^3.
SubstitutionsWe recognize that there are some repeated expressions here that may make it easier to simplify this without multiplying it all out.
Let a = 7x+5y, b = 7x -5y. Then the expression becomes ...
a³ -b³ -30y·a·b³
= (a³ -b³) -30yb²(ab)
= (a -b)(a² +ab +b²) -30yb²·ab
Now ...
a -b = (7x +5y) -(7x -5y) = 10y
a² +b² +ab = (7x +5y)² +(7x -5y)² +(7x +5y)(7x -5y)
= (7x)² +2(7x)(5y) +(5y)² +(7x)² -2(7x)(5y) +(5y)² +(7x)² -(5y)²
= 3(7x)² +(5y)² = 147x² +25y²
So the first pair of terms expands to ...
a³ -b³ = 10y(147x² +25y²) = 1470x²y +250y³
The last term becomes (with a positive sign) ...
30yb²(ab) = 30y(7x -5y)²((7x)² -(5y)²)
= 30y((7x)² -2(7x)(5y) +(5y)²)((7x)² -(5y)²) . . . . see comment below
= 30y((7x)⁴ -(5y)⁴ -70xy((7x)² -(5y)²))
= 72030x⁴y -18750y⁵ -102900x³y² +52500xy⁴
Simplified expression
Putting it all together gives ...
= -72030x⁴y +18750y⁵ +102900x³y² -52500xy⁴ +1470x²y +250y³
__
Additional comment
The difference of squares form is used several times here:
p² -q² = (p -q)(p +q)
The expression ((7x)² -2(7x)(5y) +(5y)²)((7x)² -(5y)²) is decomposed to ...
((7x)² +(5y)²)·((7x)² -(5y)²) - 2(7x)(5y)((7x)² -(5y)²)
This lets us use the difference of squares form to simplify at least part of the expression. This whole thing gets multiplied by -30y.
1. What is the volume of a rectangular prism with a length of 15 yards, a width of 8 yards, and a height of 5 yards?
2. A teacher purchased a fish tank for her classroom. The dimensions of the tank are 36 inches by 60 inches by 48 inches. What is the maximum amount of water that the tank can hold?
Answer:
1. 600 yd^3
2. 103,680 in^3
Step-by-step explanation:
1. To find volume we do l*w*h
(15)(8)(5)
120(5)
600 yards^3
2. We also find the volume for this
(36)(60)(48)
2160(48)
103680 in^3
Hopes this helps
Trina is 54 3 4 inches tall. Morgan is 1 1 2 inches taller than Trina and Jane is 1 1 5 inches taller than Morgan. How tall is Jane? Label the names on the tape diagram to represent this problem. Three tape diagrams, one below the other. The first tape diagram is the shortest. The third tape diagram is the longest. Trina Morgan Jane Great job! Label the tape diagram to represent this problem. Three tape diagrams, one below the other. The first tape diagram is the shortest. The third tape diagram is the longest. The second tape diagram is longer than the first and shorter than the third tape diagram. A bracket covers the length of the first tape diagram. A bracket covers the increased length of the second tape diagram compared to the first tape diagram. A bracket covers the increased length of the third tape diagram compared to the second tape diagram. A bracket covers the entire length of the third tape diagram. 54 3 4 1 1 2 1 1 5 ? TrinaMorganJane Good work!
The height of Jane will be 38 9/30 inches.
What is Addition?The process of combining two or more numbers is called the Addition.
Given that;
Trina is 54 3/4 inches tall. Morgan is 1 1/2 inches taller than Trina and Jane is 1 1/5 inches taller than Morgan.
Now,
Since, Trina is 54 3/4 inches tall.
And, Morgan is 1 1/2 inches taller than Trina.
Hence, The height of Morgan = 54 3/4 + 1 1/2
= 219/4 + 3/2
= 219/4 + 6/4
= 225/4
And, Jane is 1 1/5 inches taller than Morgan.
Hence, The height of Jane = 225/4 + 1 1/5
= 225/4 + 6/5
= (1125 + 24)/30
= 1149/30
Thus, The height of Jane = 38 9/30 inches
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The following equation was solved incorrectly by a student
-2 (am + 4) = 22
The solution for the given equation is am = -15.
What is an equation?An equation is formed by equating an expression with another expression or a constant. An equation consists of variables, coefficients, and constants.Depending upon the degree of the variable, the equation is defined.Calculation:The given equation is -2(am + 4) = 22
On simplifying the given equation for its solution, we get
-2(am + 4) = 22
⇒ -2am - 8 = 22
⇒ -2am = 22 + 8
⇒ -2am = 30
∴ am = -30/2 = -15
So, the solution for the given equation is -15.
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If Cadence earns $66.50 washing cars for 7 hours, how much would she make washing cars for 9 hours?
Answer:$85.5
Step-by-step explanation:
So divide 66.50 by 7 and that will get you 9.5 then multiply that by 9 which is then 85.5
decide if the events are mutually exclusive. explain your reasoning based on a venn diagram. event a: randomly rolling greater than 3 with a six-sided die. event b: randomly rolling less than 5 with a six-sided die.
Analyzing the events a and b given in the question , the events are not mutually exclusive events, which are also called intersecting events in terms of venn diagram.
What is mutually exclusive event?Events that do not take place at the same time are said to be mutually exclusive. For instance, if a coin is tossed, the outcome will either be head or tail; we cannot obtain both outcomes. Since they do not occur at the same time, such occurrences are also known as disjunct events. The probability of an occurrence if A and B are mutually exclusive is indicated by P(A Or B) or P. (A U B).
What is mutually inclusive or intersecting event?Mutually inclusive events permit the occurrence of both occurrences simultaneously or inside a single trial. It refers to events that are required to take place simultaneously by a rule or a natural law. When two occurrences are mutually inclusive, they cannot happen separately.
Here, the events a and b can occur simultaneously, since we can get a number greater than 3 and less than 5 at the same time while rolling a dice randomly.
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Which inequality matches the graph?
Answer:
2n + 5 ≤ 7 The first choice
Step-by-step explanation:
2n + 5 ≤ 7 Subtract 5 from both sides.
2n + 5 - 5 ≤ 7 - 5
2n ≤ 2 Divide both sides by 2
[tex]\frac{2n}{2}[/tex] ≤ [tex]\frac{2}{2}[/tex]
n [tex]\leq[/tex] 1
Answer:
2x +5 ≤ 7
I hope my answer helps you.
Mr. Martinez has a 16-ounce Starbucks drink. He drinks 10 ounces. What is the percent of ounces Mr. Martinez has left of his drink?
well, he has left only 6 oz.
now, if we take the 16(origin amount) to be the 100%, what is 6 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 16 & 100\\ 6& x \end{array} \implies \cfrac{16}{6}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 8 }{ 3 } ~~=~~ \cfrac{ 100 }{ x }\implies 8x=300\implies x=\cfrac{300}{8}\implies x=\cfrac{75}{2}\implies x=37.5[/tex]
Fill in the blank. Given O below, you can conclude that DF is congruent to ____.
In the given circle with center O, DF is congruent to BC.
What is congruent?
When it comes to geometry, two figures or objects are said to be congruent if they are the same size and shape, or if one is the mirror image of the other.
Consider the given circle with center O.
We have to find DF is congruent to which line.
Let point E and A are the midpoints of chord DF and BC.
There is angle 90 degrees on both the points.
The chords DF and chord BC are on the same distance from the center of the circle which is 3.09.
So, the chords DF and BC are of same measure.
Therefore, the chord BC is congruent to DF.
Hence, in the given circle with center O, DF is congruent to BC.
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