The standard error measures the variability of the sample mean from the true population mean. It represents the standard deviation of the sampling distribution of the mean and gives an estimate of how much the sample means will vary from one sample to another.
b. When calculating the standard error of the mean, we assume that the sample was randomly selected from the population, and that the sample size is large enough (usually, n > 30) for the central limit theorem to apply.
c. To reduce the standard error of their estimate of the mean home range size, researchers could increase the sample size, which will decrease the standard error by reducing the variability of the sampling distribution of the mean.
Alternatively, they could improve the precision of their measurements or reduce measurement errors to decrease the standard deviation of the sample, which will also decrease the standard error.
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You may need to use the appropriate appendix table or technology to answer this question. The following results come from two independent random samples taken of two populations. Sample 1 Sample 2 ni = 50 n2 = 35 = X1 13.6 x2 = 11.6 0 1 = 2.4 02 3 (a) What is the point estimate of the difference between the two population means? (Use x1 - xz.) 2 (b) Provide a 90% confidence interval for the difference between the two population means. (Use X2 Round your answers to two decimal places.) 0.98 X to 3.02 x - X2. Round your answers to two decimal places.) (C) Provide a 95% confidence interval for the difference between the two population means. (Use X X to 3.21 x 0.79
The appendix table the point estimate of the difference between the two population means is 2
The difference between the two population means, we need to find the standard error of the difference and use the t-distribution with (n1 + n2 - 2) degrees of freedom. The formula for the standard error of the difference is:
SE = sqrt[ (s1 / n1) + (s2 / n2) ]
Substituting the given values, we get:
SE = sqrt[ (2.4 / 50) + (3 / 35) ] = 0.617
Using a t-distribution with 83 degrees of freedom (50 + 35 - 2), and a 90% confidence level, we find the t-value to be 1.66 (from the t-table or calculator). Therefore, the 90% confidence interval is:
x1 - x2 ± t(α/2) * SE
= 2 ± 1.66 * 0.617
= 0.98 to 3.02
So, we can say with 90% confidence that the true difference between the two population means lies between 0.98 and 3.02.
To calculate the 95% confidence interval:
x1 - x2 ± t(α/2) * SE
= 2 ± 2.00 * 0.617
= 0.79 to 3.21
So, we can say with 95% confidence that the true difference between the two population means lies between 0.79 and 3.21.
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Nicholas splits 27 green markers equally into 9 cups. He then splits 18 yellow markers equally into the same 9 cups. How many markers are in each cup?
There are 5 markers in each cup
How to calculate the number of markers in each cup?Nicholas splits 27 green markers equally into 9 cups
Hence the number of green markers in one cup is
= 27/9
= 3
He then spilt 18 yellow markers equally into the same 9 cups
The number of yellow markers in one cup is
= 18/9
= 2
The total number of markers in each cup is
= 3 + 2
= 5
Hence there are 5 markers in each cup
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It's a math problem about graphing. thank you
The interval for which the ball's height is increasing on the graph, would be 0 seconds to 1.5 seconds.
What is the interval the ball's height increases ?The interval for which the ball's height is increasing is when the slope of the graph is positive, or when the height is increasing with respect to time.
Looking at the graph, we can see that the ball starts at a height of 0 meters and reaches a peak of 11.025 meters at 1.5 seconds. After 1.5 seconds, the ball begins to fall back to the ground.
Therefore, the interval for which the ball's height is increasing is from 0 seconds to 1.5 seconds. During this interval, the height of the ball is increasing as it travels upwards, reaching its peak at 1.5 seconds. After 1.5 seconds, the height of the ball starts decreasing as it falls back down to the ground.
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a random sample of 50 medical school applicants at a university has a mean raw score of 31 on the multiple choice portions of the medical college admission test (mcat). a student says that the mean raw score for the school's applicants is more than 30. assume the population standard deviation is 2.5. use a 1% level of significance. is there enough evidence to support the student's claim?
There is enough proof that the mean raw score for the school's applicants is more than 30 at a significance level of α = 0.01, therefore we reject the null hypothesis.
The null hypothesis H0: μ ≤ 30 mean raw score for the school's applicants is less than or equal to 30 and the alternative hypothesis Ha: μ > 30
We can utilize a one-tailed t-test since we don't know the population standard deviation and our sample size is less than 30. The test statistic is evaluated
t = (x' - μ) / (s / √n)
here
x'= sample mean = 31,
μ = hypothesized population mean = 30,
s = standard deviation = 2.5,
n = sample size = 50.
t = (31 - 30) / (2.5 / √50)
= 3.16
Applying t-distribution table with degrees of freedom (df) = n - 1 = 49 and a significance level of α = 0.01, we find that the critical value is
t-critical = 2.404.
The calculated t-value (3.16) is greater than our critical value (2.404), we reject the null hypothesis since there is enough evidence to support the student's claim that the mean raw score for the school's applicants is more than 30 at a significance level of α = 0.01.
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6. Suppose the object hits the top of a tree that is 44 feet above the
ground. Write and solve an equation that allows you to find how many
seconds after being dropped that this occurs.
According to the Equation, the provided question's conclusion is that the object strikes the top of the tree in roughly 4 seconds.
What is Equation?An equation is a mathematical statement that demonstrates the equality of two expressions and is typically denoted by the equals symbol (=). Equations can be used to solve issues and make predictions as well as to express a wide variety of mathematical relationships.
The formula for the distance travelled by an object under constant acceleration can be used to solve this issue:
d = 1/2 * g * t²
where:
The distance travelled is d.
Gravitational acceleration (g) is around 32.2 feet per second squared.
T is the passing of time
Since the object is being dropped in this scenario, we know that its initial height is 0 feet and its ending height is 44 feet. For the duration of the trip, we may construct the following equation:
The required time is t seconds.
h(t) = 44
Simplifying:
-16t² + 300 = 44
16t² = 300 - 44
t² = 256/16
t² = 16
When both sides are squared:
t = 4 seconds
The time it takes for the object to strike the tree's top is therefore 4 seconds.
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The complete question is,
Let's say the object lands 44 feet above the ground, at the top of a tree. You may calculate the number of seconds after being dropped by writing and solving an equation.
In the figure below, <1 measures (3x + 20) and <2 measures x. what is the measure of <4?
After solving the given angles we can conclude that ∠4 is (D) 140° respectively.
What are angles?Two rays that have a common terminal and are referred to as the angle's sides and vertices, respectively, make up an angle in Euclidean geometry.
Two rays can form angles in the plane where they are positioned.
Angles are also produced when two planes intersect.
These are what are known as dihedral angles.
Acute, obtuse, right, straight, reflex and full rotation are examples of basic angles.
So, according to the given image, we know that:
∠ 1 + ∠ 2 = 180
Then,
(3x + 20) + x = 180
4x + 20 = 180
4x = 180 - 20
4x = 160
x = 160 / 4
x = 40
We got that:
∠ 1 = ∠ 4
∠ 2 = ∠ 3
Simply substitute for x and solve if ∠1 = ∠4:
3x + 20 = 3(40) + 20 = 120 + 20 = 140
Therefore, after solving the given angles we can conclude that ∠4 is (D) 140° respectively.
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Question 12(Multiple Choice Worth 2 points)
(Making Predictions MC)
A recent conference had 750 people in attendance. In one exhibit room of 70 people, there were 18 teachers and 52 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 193 principals in attendance.
There were about 260 principals in attendance.
There were about 557 principals in attendance.
There were about 680 principals in attendance.
Thus, we may estimate that there were 557 principals present at the meeting.
Explain about the Proportion:A mathematical comparison of two numbers is called a percentage. These figures frequently serve as a comparison between various objects or individuals. Take the scenario where you entered a crowded room as an example.
We can forecast how many principals will attend the conference according to the data supplied.In a room with 70 individuals in total and 52 principals, the ratio of principals to attendees would be as follows:52/70 = 0.743 or 74.3%
Applying this ratio to the total number of attendees, we can extrapolate the proportion of principals at the conference, assuming that it is reflective of the conference as a whole:
Total principals at conference = Proportion of principals x Total number of attendees
Total principals at conference = 0.743 x 750
Total principals at conference ≈ 557
As a result, we may estimate that there were 557 principals present at the meeting.
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Question 14(Multiple Choice Worth 2 points)
(Creating Graphical Representations MC)
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
The correct graph for the given data is given by option The bar graph x axis labeled sport and the y axis labeled number of students, with each having value as basketball -17, baseball-12, soccer - 27, and tennis - 44.
Which graph represents the given data?Because the data shows discrete categories (sports) and their related frequencies, the correct graph is a bar graph (number of students).
The x-axis is to be named "Sports" to represent the various sports (Basketball, Baseball, Soccer, and Tennis), and the y-axis has to be labelled "Number of Students" to reflect the frequency. The graph's bars will show the frequency of each sport, with the heights of the bars giving the number of students who identified each sport as their favourite. The right values for the bars should be based on the data provided:
[tex]Basketball: 17\\Baseball: 12\\Soccer: 27\\Tennis: 44[/tex]
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In March in Austin, Texas, the temperatures for 7 consecutive days were 20°C, 22°C, 20°C, 24°C, 21°C, 26°C, and 23°C. What was the median of the temperatures for these days?
Answer:
21.5
Step-by-step explanation:
1. Line the numbers from least to greatest:
20, 20, 21, 22, 23, 26
2. cross off one from one side then the other
(ex: 20, 20, 21, 22, 23, 26 --> 20, 21, 22, 23 --> 21, 22)
3. the number left is the median, but if there are 2 numbers left do step 4 and 5
4. find the middle of the 2 numbers (ex: 21 and 22's middle is 21.5)
5. The middle of the those 2 numbers is the median (which in this case is 21.5)
suppose that one customer who participated in the study is chosen at random. what is the probability that the customer did not have a high level of satisfaction with the company?
Answer: Without additional information about the study and the definition of "high level of satisfaction," we cannot determine the probability that a randomly chosen customer did not have a high level of satisfaction with the company.
The probability would depend on the specific criteria used to define a high level of satisfaction, as well as the distribution of satisfaction levels among the customers in the study.
If we have access to this information, we could use it to calculate the probability that a randomly chosen customer did not have a high level of satisfaction using the appropriate formulas or statistical techniques.
Step-by-step explanation:
Tasha has a gift card to buy tickets to the movie theater. The initial value of the gift card is $120 . The function M(x)=120-12x represents the amount of money, M , in dollars, that is still left on the gift card after purchasing x movie tickets at a cost of $12 each.
Complete the statements.
The value of is 60/-60 which is viable/not viable in terms of the given context.
The solution to the linear function M(x) = 180 is of x = -5.
What is a Linear Function Equation?The linear function equation is the slope-intercept form. Thus, it is expressed as f(x) = mx + b where m is the slope and b is the y-intercept of the line.
In this problem, the function is defined as follows:
M(x) = 120 - 12x.
M(x) represents the balance remaining on the gift card after x movie tickets priced at $12 are purchased.
The domain of the situation is given as follows:
x ≥ 0. {discrete}
As the number of tickets cannot assume negative neither decimal values.
The equation is:
M(x) = 180.
The solution is calculated as:
120 - 12x = 180
12x = -60
x = -60/12
x = -5.
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A woman decides to have children until she has her first girl or until she has four children, whichever comes first. Let X = number of children she has. For simplicity, assume that the probability of a girl is .5 for each birth.a. Write the simple events in the sample space. Use B for boy and G for girl. For instance, one simple event is BG, because the woman would stop having children once she has a girl.b. Find the probability for each of the simple events in the sample space.c. Find the probability distribution function for X.d. Draw a picture of the probability distribution function for X.
For the experiment of birth of children,
a) Sample space is S = { G, BG, BBG, BBBG, BBBB}.
b) The probability for each of the simple events in the sample space, 0.5, 0.25, 0.125, 0.0625 and 0.0625.
c) The probability distribution function for X is 0.5, 0.25, 0.125, 0.0625 and 0.0625.
d) The table form of probability density function is present in above figure.
We have a woman who decides to have children until she has first a baby girl or until she has four children, which event occurred.
a) Sample space is S = { G, BG, BBG, BBBG, BBBB} where G and B represents the birth of baby boy and baby girl.
b) Since, birth become independent so P( B) = P( G) = 0.5. Using multiplcation rule, the probability for each of the simple events, P( G) = 0.5
P( BG) = P( B) P(G) = 0.25
P( BBG) = P(B)× P(B)× P(G) = 0.125
P( BBBG) = P(B)× P(B)× P(B) ×P(G)
= 0.0625
P( BBBB) = P(B)× P(B)× P(B) ×P(B)= 0.0625
c) Let X be a variable such that it denotes number of children. So, X can take value from set { 1,2,3,4}.
The probability of a girl child is for each birth = 0.5
Therefore, P( X = 1) = { only 1 girl} = P( G)
= 0.5
P(X = 2) = { one boy and one girl } = P( BG) = P(B) P(G) = 0.25
P( X = 3) = { two boys one girl } = P( BBG) = 0.125
P( X = 4) = { three boys one girl or four all boys } = P( BBBG) + P( BBBB) = 0.0625 + 0.0625
= 0.125
So, the above values of probability distribution function for random variable X.
d) A table form picture of the probability distribution function for X is present in above figure. Hence, the required table is known.
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a) option 4-t test for one mean.
b) Null hypothesis: μ_Shadyside - μ_Oakland <= 0 (Mean monthly rent of apartments in Shadyside is not higher than in Oakland).
Alternative hypothesis: μ_Shadyside - μ_Oakland > 0 (Mean monthly rent of apartments in Shadyside is higher than in Oakland).
a) The most appropriate statistical test for this scenario would be (vi) test for two independent means, also known as two-sample t-test. This test is used to compare the means of two independent samples to determine if they are significantly different from each other. In this case, we are comparing the mean monthly rent of apartments in Shadyside and Oakland, and we have two independent samples.
b) The appropriate hypotheses for the two-sample t-test are as follows:
Null hypothesis: The mean monthly rent of apartments in Shadyside is equal to the mean monthly rent of apartments in Oakland.
Alternative hypothesis: The mean monthly rent of apartments in Shadyside is greater than the mean monthly rent of apartments in Oakland.
Symbolically, the null hypothesis can be represented as H0: µ1 = µ2, where µ1 and µ2 represent the population means of monthly rent in Shadyside and Oakland, respectively.
The alternative hypothesis can be represented as Ha: µ1 > µ2, indicating that the population mean of monthly rent in Shadyside is greater than the population mean of monthly rent in Oakland
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Question 2
Mike deposited $3,000 in the first year of a retirement account, and then increased the deposits by $300 each year. The account earned 8.35%. What was the account value after forty years?
The account value after forty (40) years is approximately $2,789,525.
Here is how to solve for the account valueWe can use the formula for future value of an annuity to solve this problem:
FV = PMT * ((1 + r)^n - 1) / r
where FV is the future value, PMT is the annual deposit amount, r is the annual interest rate, and n is the number of periods (years in this case).
For the first year, the deposit amount is $3,000, so:
FV1 = 3000 * (1 + 0.0835)^40 = $65,470.22
For the subsequent years, the deposit amount increases by $300, so:
PMT = 3000 + 300 + 300 + ... = 3000 + 300 * 39 = $15,300
Using this value for PMT, we can calculate the future value for the remaining 39 years:
FV2 = 15300 * ((1 + 0.0835)^39 - 1) / 0.0835 = $2,724,054.54
Adding the two future values together, we get the total account value after forty years:
FV = FV1 + FV2 = $2,789,524.76
Therefore, the account value after forty years is approximately $2,789,525.
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perry como fans fifty-six percent of respondents to an online poll said that they were perry como fans. if 982 randomly selected people responded to this poll, what is the true proportion of all local residents who are perry como fans? estimate at the 95% confidence level.
Perry como fans fifty-six percent of respondents to an online poll said that they were perry como fans. if 982 randomly selected people responded to this poll.
By use the sample proportion to estimate the true proportion of all local residents who are Perry Como fans.
Let p be the true proportion of all local residents who are Perry Como fans. Then, the sample proportion is 0.56 and the sample size is n = 982.
We construct a 95% confidence interval for p by using the formula
Sample proportion ± z*standard error
Where z is the critical value from the standard normal distribution for a 95% confidence level, which is 1.96. The standard error is the estimated standard deviation of the sample proportion which is defined as
[tex]\sqrt{p*(1-p)/n} \\}[/tex]
By putting the values we get
Standard error = [tex]\sqrt{0.56*(1-0.56)/982)[/tex] = 0.018.
95% confidence interval = 0.56 ± 1.96*0.018 = (0.525, 0.595).
Hence, we can say with 95% confidence that the true proportion of all local residents who are Perry Como fans is between 0.525 and 0.595.
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Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−15, −15), B′(15, 15), C′(0, 15). Determine the scale factor used.
5
one fifth
12
one twelfth
1.572 × 108 troy oz of silver were used in the United States in 1980. How manykilograms is this? (1 troy oz = 31.1 g)A) 4.89 × 106 kg D) 4.89 x 1012 kgB) 4.89 kg E) 5.05 × 10 3 kgC) 5.05 × 10 6 kg
Part A: Is the probability of hitting the black circle inside the target closer to 0 or 1? Explain your answer and show your work. (5 points)
Part B: Is the probability of hitting the white portion of the target closer to 0 or 1? Explain your answer and show your work. (5 points)
The probability of hitting the black circle inside the target is approximately 0.0314.
The probability of hitting the white portion of the target is approximately 0.686.
What is the probability?Part A:
The black circle has a diameter of 2 units, which means it has a radius of 1 unit. The area of the circle is πr^2, which is π(1)^2 or π square units. The area of the white square is 10 x 10 or 100 square units.
The probability of hitting the black circle inside the target is the ratio of the area of the circle to the area of the square, which is π/100 or approximately 0.0314. This probability is closer to 0 because the circle is much smaller than the square, and the likelihood of hitting the exact center of the circle is low.
Part B:
The white portion of the target is the area of the square minus the area of the black circle, which is 100 - π square units.
The probability of hitting the white portion of the target is the ratio of the area of the white portion to the area of the square, which is (100-π)/100 or approximately 0.686.
This probability is closer to 1 because the white portion of the target is much larger than the black circle, and there are many possible areas of the square that could be hit.
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Let's take a collection of any three 'high mountains of Nepal' and answer following questions. a) Is it a well-defined collection? Give reason. b) Is it a set? Give reason. c) Let's express it as a well-defined collection.
The collection of "high mountains of Nepal" is subjective and not well-defined, it may or may not be a set depending on the criteria specified, and to express it as a well-defined collection.
a) It is not a well-defined collection because the term "high mountains of Nepal" is subjective and does not have a clear definition. What one person considers high might be different from what another person considers high.
b) It is not necessarily a set, depending on how the collection is specified. If the collection is specified using clear criteria (such as mountains over a certain height), then it could be a set.
However, if the collection is just described using vague language like "high mountains of Nepal," then it is not necessarily a set.
c) In order to articulate it as a precise collection, we may define a precise standard for what constitutes a "high mountain of Nepal." As an illustration, we could say that any peak in Nepal that rises higher than 7,000 meters qualifies as a high mountain there.
With this precise definition, we could then pinpoint a trio of Nepalese mountains.
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A method of assigning probabilities based on historical data is called the
A method of assigning probabilities based on historical data is called the Empirical Probability method.
Empirical probability refers to the probability of an event based on observed data or past experience.
It is also known as experimental probability because it is determined through experimentation or observation.
This approach involves analyzing past events and their outcomes to calculate the probability of a particular event happening in the future.
To calculate empirical probability, you can use the formula:
Empirical Probability = (Number of successful outcomes) / (Total number of outcomes)
In this method, you collect and analyze historical data to make predictions about future events.
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Divide the sum of 13/5 and -12/7 by their difference
Answer to these fraction is 31/151
Describe fraction.
Any numerical value that is not a whole number is referred to as a fraction. It symbolizes a portion of something or several portions of something. The numerator and the denominator are the two components of a fraction. The denominator indicates how many equally sized pieces make up a whole, whereas the numerator indicates how many equally sized parts are picked from the whole or collection.
To divide a fraction, all you need to do is flip its numerator and denominator, multiply the outcome by the other fraction, and simplify1.
In light of this, we have:
SUM:
(13/5) + (-12/7) = (13× 7 + -12 ×5) / (5 ×7)
= (91 - 60) / 35 = 31/35
DIFFERENCE:
(13/5) - (-12/7) = (13× 7 - -12× 5) / (5× 7)
= (91 + 60) / 35 = 151/35
Dividing these two fractions:
(31/35) ÷ (151/35) = (31/35)×(35/151) = 31/151
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Farm joe ordered 3 bags of soil last month. Each bag weighed 4 2/5 kilograms. He used the first bag in a week. At the end of this month, there were 2 3/4 kilograms of soil left in the second bag and 7/8 kilograms of soil left in the third bag. How much soil was used in this month?
Farm Joe used [tex]7\frac{6}{15}[/tex] kg of soil in this month.
How Farm Joe uses his weightThe total weight of soil that Farm Joe ordered was:
3 bags x 4 2/5 kg/bag = 12 6/15 kg = 12 2/5 kg
The weight of the first bag used was 4 2/5 kg.
The weight of the second bag remaining is 2 3/4 kg.
The weight of the third bag remaining is 7/8 kg.
The total weight of soil used in this month can be found by subtracting the weight of the second and third bags remaining from the total weight of soil ordered:
12 2/5 kg - 2 3/4 kg - 7/8 kg
Converting all fractions to fifteenths:
12 8/15 kg - 5 1/15 kg - 1/15 kg = 7 6/15 kg
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monthly sales are independent normal random variables with mean and standard deviation a. find the probability that exactly of the next months have sales greater than 100. b. find the probability that the total of the sales in the next
Answer: We can use the properties of the normal distribution to solve both parts of this problem.
a) The number of months with sales greater than 100 is a binomial random variable with parameters n = the number of months and p = the probability of a single month having sales greater than 100. Since each month is an independent normal random variable, we can use the standard normal distribution to find this probability. Let X be the number of months with sales greater than 100. Then:
X ~ Binomial(n, p)
where n is the number of months and p is given by:
p = P(X_i > 100) = P(Z > (100 - a) / a)
where Z is a standard normal random variable.
Using the binomial probability formula, the probability of exactly k months having sales greater than 100 is:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
So the probability of exactly 3 months having sales greater than 100 is:
P(X = 3) = (n choose 3) * p^3 * (1 - p)^(n - 3)
= (12 choose 3) * P(Z > (100 - a) / a)^3 * [1 - P(Z > (100 - a) / a)]^(12 - 3)
b) The total sales in the next 12 months is a normal random variable with mean 12a and standard deviation sqrt(12)a. Let Y be the total sales in the next 12 months. Then:
Y ~ Normal(12a, sqrt(12)a)
The probability of the total sales being greater than some value x can be found by standardizing Y and using the standard normal distribution:
P(Y > x) = P((Y - 12a) / (sqrt(12)a) > (x - 12a) / (sqrt(12)a))
= P(Z > (x - 12a) / (sqrt(12)a))
where Z is a standard normal random variable. So the probability of the total sales in the next 12 months being greater than 1500 is:
P(Y > 1500) = P(Z > (1500 - 12a) / (sqrt(12)a))
Step-by-step explanation:
What is the solution to the following graph? PLEASE HELP ITS URGENT!!!
The solution shown in the graph is (-4, 0)
What is the solution of the graph?Here we have a system of equations graphed, the solutions of the system are all the points where the graphs of the functions (lines in this case) do intercept.
Then, in this case the solution is where the lines red and blue intercept, that happens at the point (-4, 0).
So that is the solution of the system of equations.
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Estimate the difference. 9 1/2 - 1 6/7
8 1/2
7 1/2
7
8
Answer:
1 6/7 is about 2, so 9 1/2 - 1 6/7 is about
7 1/2.
a circle is centered at the vertex of an angle, and the angle's rays subtend an arc that is 79 cm long. 1/360th of the circumference of the circle is 0.5 cm long. what is the measure of this angle in degrees?
The measure of the angle in degrees is approximately 713 degrees. Note that this result is greater than 360 degrees because the angle is not a standard angle in a plane but a measure in three-dimensional space.
Since 1/360th of the circumference of the circle is 0.5 cm long, the circumference of the circle is 360 times longer, or 180 cm long.
The arc subtended by the angle is 79 cm long, which is a fraction of the entire circumference. To find the angle in degrees, we need to convert the arc length to an angle measure using the formula:
angle measure = (arc length / circumference) x 360 degrees
Substituting the values we know, we get:
angle measure = (79 cm / 180 cm) x 360 degrees
Simplifying the fraction, we get:
angle measure = 1.9833 x 360 degrees
Rounding to the nearest degree, we get:
angle measure ≈ 713 degrees
Therefore, the measure of the angle in degrees is approximately 713 degrees. Note that this result is greater than 360 degrees because the angle is not a standard angle in a plane but a measure in three-dimensional space.
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E. Which number line represents the solution to the inequality 3x-8≥7?
A
B
с
D
-10 -8 -6
-4-2
-10 -8
0 2 4 6 8
-8 -6 -4 -2 0 2 4
-6 -4 -2 0 2
+44
6 8
4 6 8
-10 -8 -6 -4 -2 0 2 4 6 8
10
10
10
10
The number line that represents the solution to the inequality 3x-8≥7 is shown on the attached image.
how to find which number line represents the solution to the inequality 3x-8≥7?The inequality: 3x - 8 ≥ 7
Add 8 to both sides
3x ≥ 7 + 8
Add 7 and 8 to get 15
3x ≥ 15
Divide both sides by 3
3x/3 ≥ 15/3
x ≥ 5
What is an inequality?An inequality is a mathematical statement that compares two values or expressions, indicating whether they are equal or not. Unlike equations, which are true only if the two sides are equal, inequalities may be true for different values on either side of the inequality sign.
Inequalities are often represented using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).
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What is the domain of h?
A coordinate plane. The x- and y-axes both scale by one. The graph of the function h starts at the point negative seven, negative three and has a line segment to negative four, zero. Then it increases at a non linear rate to zero, four and decreases at a non linear rate to four, zero. A line segment connects four, zero to seven, negative three, which is plotted on the graph.
Choose 1 answer:
Choice A: -7 ≤ x ≤ 7
Choice B: -3 ≤ x ≤ 4
Choice C: The x-values -7, -4, 0, 4, and 7
Choice D: The x-values -3, 0, and 4
Answer:
The domain of h is
[tex] - 7 \leqslant x \leqslant 7[/tex]
Choice A is correct.
Answer:
c
Step-by-step explanation:
The bases of a right prism are parallelograms with sides a=10 cm, b=6 cm. The altitude of the parallelogram towards side a is ha = 3 cm. Find the surface area of the parallelepiped if the height of the prism is h=12 cm.
The solution is, the surface area of the parallelepiped is:444 cm²
Here, we have,
Area of parallelogram = a*h
= 10*3
= 30 ,
there are 2 such parallelograms in the prism
2 faces are rectangles with sides 12 and 6 ,
Area of this face is 12*6=72, there are 2 such faces
we have,
2 faces are rectangles with sides 12 and 10
Area of this face is 12*10=120,
there are 2 such faces
the surface area of the parallelepiped is:
2*30+2*72+2*120
= 444 cm²
Hence, The solution is, the surface area of the parallelepiped is:444 cm²
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Consider the sequence -3, -10, -17, -24, -31, ...
(ii) Find, in terms of n, a formula for the nth term of the sequence.
Answer:
-60
Step-by-step explanation:
Mehnaj has a set of blocks that are all the same hight the cone-shaped block has a volume of 125 cubic inches the sphere--shaaped block has a volume of 250 cubic inches what do you know about the raduis of the base of the cone-shaped block explain?
The radius of the base of the cone-shaped block is approximately 10.69 inches.
To solve this problemWe can use the formula for the volume of a cone to find the radius of its base. The volume of a cone is given by the formula :
V = (1/3)πr^2h
Where
V is the volume r is the radius of the baseh is the heightWe know that the volume of the cone-shaped block is 125 cubic inches, and we know the height is the same for all blocks. So we can solve for the radius:
125 = (1/3)πr^2h
125 = (1/3)πr^2h
375 = πr^2h
r^2 = 375/π
r ≈ 10.69
So we can conclude that the radius of the base of the cone-shaped block is approximately 10.69 inches.
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