The estimated probability of getting at least 10 correct answers by random guessing is approximately 0.023, or about 2.3%.
To solve this problem, we need to use the binomial distribution. Let X be the number of correct answers out of 27, with each question having 4 possible choices, so the probability of guessing correctly is 1/4.
Let p = 1/4 be the probability of guessing a question correctly, and q = 1-p = 3/4 be the probability of guessing incorrectly.
The probability of getting at least 10 correct answers out of 27 is:
P(X >= 10) = 1 - P(X < 10)
We can use the binomial probability formula to calculate P(X < 10) as follows:
P(X < 10) = Σ_{k=0}^{9} (27 choose [tex]k) * p^k * q^(27-k)[/tex]
where (27 choose k) = 27! / (k! * (27-k)!) is the number of ways to choose k correct answers out of 27.
We can use a calculator or a computer program to evaluate this sum, or we can use a normal approximation to the binomial distribution.
Using the normal approximation, we can approximate the binomial distribution with a normal distribution with mean μ = np = 27*(1/4) = 6.75 and standard deviation σ = sqrt(npq) = sqrt(27*(1/4)*(3/4)) = 1.64.
Then, we can standardize the random variable X as follows:
Z = (X - μ) / σ
The probability of getting at least 10 correct answers is equivalent to the probability of Z being greater than or equal to:
Z' = (10 - 6.75) / 1.64 = 1.99
Using a standard normal distribution table or a calculator with a normal cumulative distribution function, we can find:
P(Z >= 1.99) = 0.023
Therefore, the estimated probability of getting at least 10 correct answers by random guessing is approximately 0.023, or about 2.3%.
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A publishing company prints 5 science fiction comic books per month and 8 super hero comic books per month. The total number of pages in all the science fiction comic books for one month is 7 more than the total number of pages in all the super hero comic books for one month. Each science fiction comic book has 6 fewer pages than each super hero comic book. Which system of equations can be used to find f, the number of pages in each science fiction comic book and h, the number of pages in each super hero comic book?
f = h - 6 and 5f = 8h + 7 are the system of equations to find f and h
How to dfind the system of equationsWe have to form a system of equations
Let F be no of pages in each science fiction comic book
Let h h be the no of pages in each super hero comic
To find f,
5f = 8h + 7
this is because no of pages in all science fiction is 7 times more than total in super hero bopks
Then f = h - 6
this is because the science fiction has fewer pages than 6 compared to supoer heroes
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T/F : In a 5 by 5. If A has three pivots, then ColA is a (two-dimensional) plane
True.
If A is a 5 by 5 matrix and has three pivots, then its row reduced echelon form will have three leading 1's, and the other two rows will be zero rows.
If A is a 5 by 5 matrix and has three pivots, then its row reduced echelon form will have three leading 1's, and the other two rows will be zero rows. This means that the three pivot columns of A are linearly independent, and they span a three-dimensional subspace of R^5.
Since the pivot columns of A are the columns of ColA, we can say that ColA is a subspace of R^5 that is spanned by three linearly independent vectors. Since the dimension of this subspace is three, it is a three-dimensional subspace of R^5. Geometrically, a three-dimensional subspace of R^5 is a (two-dimensional) plane, sincsincesincsinceee it is the intersection of two three-dimensional spaces. Therefore, we can conclude that ColA is a (two-dimensional) plane in R^5.
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For every 4 goals Anthony scored, Kyree scored 11 goals. How many goals will Kyree score if Anthony scored 60 goals?
Kyree would score 165 goals if Anthony scored 60 goals, given that for every 4 goals Anthony scores, Kyree scores 11 goals. This means Kyree scores at a faster rate than Anthony.
If Anthony scored 60 goals and for every 4 goals Anthony scored, Kyree scored 11 goals, we can set up a proportion to find out how many goals Kyree scored. We can use the fact that the ratio of goals scored by Anthony and Kyree is the same as the ratio of 4 to 11. We can express this as:
4/11 = 60/x
Solving for x, we can cross-multiply to get:
4x = 11 * 60
Dividing both sides by 4, we get:
x = 165
Therefore, Kyree would have scored 165 goals if Anthony scored 60 goals. This means that Kyree scores at a faster rate than Anthony, since for every 4 goals Anthony scores, Kyree scores 11 goals.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The only equation that met the condition is x² + (y + 8)² = 36
What is Analytics Geometry?Analytic Geometry is a branch of mathematics that deals with the study of geometry using algebraic methods. It involves using coordinate systems to describe geometric figures and to express geometric properties in terms of algebraic equations.
In particular, the study of equations of circles is a fundamental topic in analytic geometry. A circle is a set of points in a plane that are equidistant from a fixed point called the center. In the coordinate plane, a circle with center (a, b) and radius r can be described by the equation:
(x - a)² + (y - b)² = r²
where x and y are the coordinates of any point on the circle.
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Y=^2+6x+8 and y=(x+2)(x+4)
The two equations y=x²+6x+8 and y=(x+2)(x+4) are equal.
The given two equations are y=x²+6x+8 and y=(x+2)(x+4)
We have to check whether the two equations are equal or not
y=x²+6x+8 ----(1)
y=(x+2)(x+4) ---(2)
y=x² + 4x+2x+8
y=x² + 6x+8 ....(2)
From equation (1) and (2), y=x²+6x+8 and y=(x+2)(x+4) are equal.
Hence, the two equations y=x²+6x+8 and y=(x+2)(x+4) are equal.
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The weight of football players is normally distributed with a mean of 205 pounds and a standard deviation of 10 pounds. What is the minimum weight of the middle 95% of the players? a. 185.4 b. 221 O c. 189 d. 224.6
The minimum weight of the middle 95% of the players is 185.4 pounds.
To find the minimum weight of the middle 95% of the players, we need to find the weight that separates the bottom 2.5% of the distribution from the top 2.5%.
We can use the z-score formula:
z = (x - μ) / σ
Where:
x = the weight we're looking for
μ = the mean weight of 205 pounds
σ = the standard deviation of 10 pounds
To find the z-score that corresponds to the bottom 2.5%, we can use a z-table or calculator and look up the z-score that has an area of 0.025 to its left. This value is -1.96.
Plugging this into the z-score formula:
-1.96 = (x - 205) / 10
Solving for x:
x = (-1.96 * 10) + 205
x = 185.4
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run a multiple regression of price versus home size, lot size, rooms, and bathrooms. what is the 95% confidence interval for the coefficient of rooms now? why you think it can be so different from the one in part (b)? based on this regression, can you reject the null hypothesis that the population regression coefficient of room is zero versus a two-tailed alternative? what does this mean?
The reason why the confidence interval for the coefficient of rooms in the multiple regression model can be different from the one in part (b) is that in the multiple regression, we are controlling for the effects of other variables (home size, lot size, and bathrooms) on the dependent variable. This can lead to changes in the null hypothesis and their standard errors compared to a simple linear regression model that only considers one independent variable (rooms).
To calculate the 95% confidence interval for the coefficient of rooms in the multiple regression model, we need to use the t-distribution and the standard error of the estimate. The formula is:
Coefficient of rooms ± t_(α/2,n-k-1) x SE
Where t_(α/2,n-k-1) is the critical value of the t-distribution with n-k-1 degrees of freedom and α/2 significance level (α/2 = 0.025 for a 95% confidence interval), n is the sample size, and k is the number of independent variables in the regression model. SE is the standard error of the estimate, which measures the variability of the data around the regression line.
If the confidence interval does not include zero, we can conclude that the coefficient of rooms is statistically significant at the 0.05 level and has a non-zero effect on the dependent variable (price). If the confidence interval includes zero, we cannot reject the null hypothesis that the population regression coefficient of room is zero, meaning that there is no evidence of a significant relationship between rooms and price.
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Please help me with this homework
The slope between the points, (2, -4) and (-1, -12), is calculated as:
m = 8/3.
What is the Slope between Two Points on a Line?To find the slope between two points that lie on a line, we would apply the slope formula below:
Slope of a line (m) = change in y / change in x = (y2 - y1) / (x2 - x1) = rise / run.
Given the following points:
(2, -4) = (x1, y1)
(-1, -12) = (x2, y2)
Plug in the values:
Slope of the line (m) = change in y / change in x = (-12 -(-4)) / (-1 - 2)
m = -12 + 4 / -3
m = -8/-3
Slope between the two points (m) = 8/3
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What is the yield on a corporate bond with a $1000
face value purchased at a discount price of $875, if
it pays 7% fixed interest for the duration of the
bond?
yield = [?] %
Give your answer as a percent rounded to the nearest
hundredth.
Answer: yield = ($70 / $875) x 100% = 8% (rounded to the nearest hundredth)
Step-by-step explanation:
To calculate the yield on a corporate bond, we need to use the following formula:
yield = (annual coupon payment / bond price) x 100%
In this case, the bond has a face value of $1000 and pays a fixed interest rate of 7%. The bond was purchased at a discount price of $875. The annual coupon payment can be calculated as:
annual coupon payment = face value x coupon rate = $1000 x 7% = $70
Using the formula above, we can calculate the yield as:
yield = ($70 / $875) x 100% = 8%
Therefore, the yield on this corporate bond is 8% rounded to the nearest hundredth.
What is the Volume of this cube
Answer: 27
Step-by-step explanation:
This is a cube so all of the lengths have the same lengths.
3x3x3=27
3x3=9
9x3=27
A sorted list of numbers contains 128 elements, Which of the following is closest to the maximum number of list elements that can be examined when performing a binary search for a value in the list? A. 2
B. 8 C. 64 D. 128
8 is closest to the maximum number of list elements that can be examined when performing a binary search for the value in the list.Therefore option B is correct.
To find the maximum number of list elements:
When performing a binary search on a sorted list of 128 elements, you would repeatedly divide the list in half until you find the target value or the list cannot be divided further.
In this case, you can divide the list a maximum of 7 times (2^7 = 128) before you reach a single element.
However, since the options provided do not include 7, the closest option is 8 (option B).
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The number line below represents the solution to which inequality? F. -2x+7>8
H. 6x-9<-21 G. 7x+11 < 4 J. -3x-15<-27
x < -1/2 is the solution of the inequality -2x+7>8
The given inequality is -2x+7>8
We have to find the solution
Subtract seven from both sides
-2x>8-7
-2x>1
Divide both sides by 2
-x>1/2
so x<-1/2 is the solution
Hence, x < -1/2 is the solution of the inequality -2x+7>8
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What is solution of inequality -2x+7>8?
Use the graph to solve x^2+8x+16=0. Select all solutions that apply.
We can see from the graph that the parabola intersects the x-axis at -4 (where the vertex touches the x-axis).
Since the equation is in the form of ax^2 + bx + c = 0, we can identify that a = 1, b = 8, and c = 16.
Using the quadratic formula, we get:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
x = (-8 ± sqrt(8^2 - 4(1)(16))) / 2(1)
x = (-8 ± sqrt(0)) / 2
x = -4
Therefore, the only solution is x = -4.
Show that the differential form in the integral below is exact. Then evaluate the integral. (2,2,4) s 10x dx + 18y dy + 8z dz (0,0,0) Select the correct choice below and fill in any answer boxes within your choice. A. (2,2,4) | 10x dx + 18y dy +8z dz = 1 (0,0,0) (Simplify your answer. Type an exact answer.) B. The differential form is not exact.
The correct choice is A: (2,2,4) | 10x dx + 18y dy + 8z dz = 21 (0,0,0)
To check whether the differential form is exact, we need to calculate its curl:
curl(F) = (∂Q/∂y - ∂P/∂z)i + (∂R/∂z - ∂Q/∂x)j + (∂P/∂x - ∂R/∂y)k
Here, P = 10x, Q = 18y, and R = 8z. Substituting these values, we get:
curl(F) = (0 - 0)i + (0 - 0)j + (0 - 0)k = 0
Since the curl of F is zero, the differential form is exact. We can find a potential function f such that F = ∇f.
To find f, we integrate the differential form along any path from (0,0,0) to (2,2,4)
f(2,2,4) - f(0,0,0) = ∫CF · dr
where CF is the given differential form and the integral is taken along the path C. We can choose a simple path, such as a straight line from (0,0,0) to (2,2,4):
r(t) = ti + tj + 2tk, 0 ≤ t ≤ 1
Then CF · dr = 10x dx + 18y dy + 8z dz = (10t)i + (18t)j + (16t)k dt
Substituting for x, y, and z in terms of t, we get:
CF · dr = 10ti dt + 18tj dt + 16tk dt = d(5t^2 + 9t^2 + 8t^2/2)
Therefore, f(2,2,4) - f(0,0,0) = (5(1)^2 + 9(1)^2 + 8(1)^2/2) - (5(0)^2 + 9(0)^2 + 8(0)^2/2) = 21
Hence, the value of the integral is:
∫CF · dr = f(2,2,4) - f(0,0,0) = 21
Therefore, the correct choice is A: (2,2,4) | 10x dx + 18y dy + 8z dz = 21 (0,0,0)
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In this question, you will compute the variance of a geometric distribution with parameter p. (1) Recall the following Taylor expansion. "=1+r+ ir -1
To compute the variance of a geometric distribution with parameter p, we first need to understand the geometric distribution itself.
The geometric distribution represents the number of trials required for the first success in a sequence of Bernoulli trials, where each trial has a success probability of p.
The variance of a geometric distribution with parameter p can be calculated using the formula:
Variance = (1 - p) / p^2
Please note that the Taylor expansion "=1+r+ ir -1" you mentioned does not seem to be relevant to the calculation of the variance of a geometric distribution. The correct formula for the variance is provided above.
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For his phone service, Austin pays a monthly fee of 29$, and he pays an additional 0.5$ per minute of use. The least he has been charged in a month is $80.25 . What are the possible numbers of minutes he has used his phone in a month? Use m for the number of minutes, and solve your inequality for m.
PLEASE PLEASE PLEASE HELP ME!!!!!!!!!!!!!!!!!!!
a) Based on the least amount that Austin has been charged in a month as $80.25, the possible numbers of minutes he has used his phone in a month are 102 and 103 minutes.
b) Using m for the number of minutes Austin has used his phone in a month, and solving the inequality for m, m ≥ 102.5.
What is inequality?Inequality is a mathematical statement that two or more algebraic expressions are unequal.
Inequalities can be represented by:
Greater than (>)Less than (<)Greater than or equal to (≥)Less than or equal to (≤)Not equal to (≠).The monthly fee that Austin pays for his phone service = $29
The charge per minute of use (variable cost) = $0.5
The least amount charged Austin per month = $80.25
Let the number of minutes = m
Inequality:29 + 0.5m ≥ 80.25
Solving the inequality:
29 + 0.5m ≥ 80.25
0.5m ≥ 80.25 - 29
0.5m ≥ 51.25
m ≥ 102.5
m = 102, 103
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The human resources department of the Mean Corporation would like to estimate the size of the annual salary that they should offer to university graduates. The CEO of the Mean Corporation has suggested that the salary offered (W) should be calculated based on the Grade Point Average (G) of a student. Based on a random sample of university graduates, the human resources department has calculated the mean salary offered to university graduates to be /W and the mean Grade Point Average of university graduates to be /G. The Mean Corporation will carry out a regression analysis to investigate the relationship between salary and Grade Point Average.
Write down the independent variable in the regression analysis that will be conducted.
The independent variable in the regression analysis that will be conducted is the Grade Point Average (G) of university graduates.
It is considered the independent variable because it is the predictor or explanatory variable that is believed to have an effect on the dependent variable, which is the salary offered (W). The regression analysis will help to estimate the relationship between the two variables and provide a mathematical equation that can be used to predict the expected salary for a given Grade Point Average.
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Find the area of the figure. Round to the nearest hundredth.
11 cm
The area of the figure is 47.67 [tex]cm^2[/tex] round to the nearest hundredth.
We can find the area of the half circle with a diameter of 11 cm.
The formula for the area of a circle is A = πr^2, where r is the radius.
Since the diameter is 11 cm, the radius is half of that, which is 5.5 cm.
Substituting the value of r, we get:
A = π(5.5)^2
A = 30.25π
The area of figure is half of the area of the full circle, so we divide by 2:
A = 15.125π
Rounding to the nearest hundredth, we get:
A ≈ 47.67 [tex]cm^2[/tex]
Thus, the answer is 47.67 [tex]cm^2[/tex].
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A national television network took an exit poll of 1490 voters after each had cast a vote in a state gubernatorial election. Of them, 680 said they voted for the Democratic candidate and 810 said they voted for the Republican candidate. Treating the sample as a random sample from the population of all voters, a 95% confidence interval for the proportion of all voters voting for the Republican candidate was (0.518,0.569). Suppose the same proportions resulted from n = 149 (instead of 1490), with counts of 68 and 81, and that there are only two candidates. Complete parts a and b below. a. Does a 95% confidence interval using the smaller sample size allow you to predict the winner? Explain. The 95% confidence interval for the proportion of all voters voting for the Republican candidate is (OD). Now a 95% confidence interval allow you to predict the winner, since this interval (Round to three decimal places as needed.)
a. No, a 95% confidence interval using the smaller sample size does not allow us to predict the winner., b) We cannot use the confidence interval to predict the winner with certainty, but we can say that there is a higher probability of the Republican candidate winning since the lower bound of the interval is 0.407.
The 95% confidence interval for the proportion of all voters voting for the Republican candidate with n=149 and counts of 68 and 81 is (0.407,0.573). This interval is wider than the interval with n=1490, which makes sense since a smaller sample size leads to more variability in the estimates.
b. We cannot use the confidence interval to predict the winner with certainty, but we can say that there is a higher probability of the Republican candidate winning since the lower bound of the interval is 0.407, which is higher than the proportion of Democratic voters. However, there is still a possibility that the Democratic candidate may win since the upper bound of the interval is 0.573.
a. To determine whether a 95% confidence interval using the smaller sample size (n=149) allows you to predict the winner, we first need to calculate the confidence interval.
Here, we have 68 voters for the Democratic candidate and 81 voters for the Republican candidate.
1. Calculate the sample proportion for the Republican candidate (p):
p = 81/149 = 0.543
2. Calculate the standard error (SE) for the sample proportion:
SE = √(p(1-p)/n) = √(0.543(1-0.543)/149) = 0.040
3. Find the margin of error (ME) for a 95% confidence interval using a Z-score of 1.96:
ME = 1.96 × SE = 1.96 × 0.040 = 0.078
4. Calculate the 95% confidence interval (CI) for the proportion of all voters voting for the Republican candidate:
CI = (p - ME, p + ME) = (0.543 - 0.078, 0.543 + 0.078) = (0.465, 0.621)
The 95% confidence interval for the proportion of all voters voting for the Republican candidate is (0.465, 0.621).
Since this interval includes values both below and above 0.5, we cannot predict the winner with 95% confidence using the smaller sample size. The interval shows that the proportion of voters supporting the Republican candidate could range from 46.5% to 62.1%, making it unclear whether the Republican or Democratic candidate would win.
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Which are the appropriate measures to describe the center and spread of the distribution?
Responses
A median and modemedian and mode
B mean and medianmean and median
C mode and interquartile rangemode and interquartile range
D median and interquartile rangemedian and interquartile range
Symmetrical data has an approximate line of symmetry. In this case, however, the data is skewed by an unusually high value w/out a corresponding low value to balance it out. The data set is NOT symmetrical. The MEAN & standard deviation are the most often-used measures of center & spread. Unfortunately, the mean's value can be greatly affected by the presence of even a single outlier. When outliers are present, the MEDIAN & iqr provide more appropriate measures of center & spread
D) Median and interquartile rangemedian and interquartile range
Symmetrical data has an approximate line of symmetry.
When describing a distribution, it's important to use applicable measures of center and spread that reflect the shape and nature of the data. For symmetrical data, the mean and standard divagation are generally used as measures of center and spread, independently. still, when the data is disposed or contains outliers, these measures may not be applicable.
In similar cases, the standard and interquartile range( IQR) are more robust measures of center and spread. The standard is the value that separates the lower 50 of the data from the upper 50, and is thus innocent by outliers. The IQR is the difference between the 75th percentile and the 25th percentile, and represents the range of the middle 50 of the data. It's also less sensitive to outliers than the range or standard divagation.
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suppose the number of cell phone calls made or received per day by cell phone users follows a normal distribution with a mean of 13.1 and a standard deviation of 4.3. use this information to answer questions 6 - 9.
The probability that a cell phone user makes or receives less than 12 calls per day is 0.3971.
What is probability that user makes or receives less than 12 calls?To find P(x < 12), we need to standardize the value of 12 using the formula: z = (x - μ) / σ where z = z-score, x = value of interest, μ = mean, and σ = standard deviation.
Substituting the values, we get:
z = (12 - 13.1) / 4.3
z = -0.25581
Using a calculator, we can find the probability that z is less than -0.25581, which is:
P(z < -0.25581) = 0.3971
P(z < -0.25581) = 39.71%.
Full question "Suppose the number of cell phone calls made or received per day by cell phone users follows a normal distribution with a mean of 13.1 and a standard deviation of 4.3. Find P (x <12)".
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1 1/2 + ___ = 4
please help really confused.
Answer:
Step-by-step explanation:
2 and 1/2
Answer:
2 1/2 or 2.5
Step-by-step explanation:
1. Rewrite:
1 1/2 + x = 4
2. Subtract 1 1/2 from both sides:
4 - 1 1/2 = 2 1/2
x = 2 1/2 or 2.5
Chloe has enough sand to fill a rectangular sandbox with an area of
36 square units. She wants the outer edges of the sandbox to use as little material as possible.
Answer: If Chloe wants to minimize the amount of material used for the outer edges of the sandbox, she should make the sandbox a square shape.
Here's why:
- The area of a rectangle is given by the formula A = l x w, where A is the area, l is the length, and w is the width.
- For a square, the length and width are equal, so we can write A = s^2, where s is the length of a side.
- We know that the area of Chloe's sandbox is 36 square units, so we can write s^2 = 36.
- Solving for s, we get s = 6.
- Therefore, Chloe should make the sandbox a square with sides of length 6 units.
- This will minimize the amount of material used for the outer edges of the sandbox, since all sides will be the same length.
Step-by-step explanation:
On June 1, 2013 the number of hours of daylight in Anchorage, Alaska was18.4 hours what was the number of hours without daylight
The number of hours without daylight will be 5.6 hours.
On June 1, 2013, the number of hours of daylight in Anchorage, Alaska was 18.4 hours.
There are 24 hours a day. Then the number of hours without daylight is calculated as,
⇒ 24 - 18.4
⇒ 5.6 hours
The number of hours without daylight is 5.6 hours.
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1. Find the area of the parallelogram. Explain or show your reasoning.
2. Was there a length measurement you did not use to find the area? If so, explain why it was not used.
1. The area of the parallelogram is 54 cm².
2. The length measurement that 7.5 cm did not use to find the area.
1. As per the shown figure, it is given that:
Base (B) = 9 cm
Height (h) = 6 cm
The area of the parallelogram can be calculated as:
= B × h square units
Substitute the given values in the above formula,
The area of the parallelogram = 9 × 6
The area of the parallelogram = 54 cm².
2. Here, we did not use a length measurement of 7.5 cm to find the area of the given parallelogram because it is irrelevant to the formula.
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The diameter of a circular cookie cake is 16 inches. How many square inches make up half of the cookie cake? Approximate using π = 3.14.
100.48 square inches
200.96 square inches
401.92 square inches
803.84 square inches
The circular cookie cake have an area of 200.96 in², and thus 100.48 square inches will make up its half.
What is area of a circleThe area of a circle is π multiplied by the square of the radius. The area of a circle when the radius 'r' is given is πr².
Area of circle = πr²
π = 3.14
radius = 2 m {half the diameter}
Area of the circular cookie = 3.14 × 8 in × 8 in
Area of the circular cookie = 200.96 in²
square inches to make up half the cookie = 200.96 in²/2
square inches to make up half the cookie = 100.48 in²
Therefore, the circular cookie cake have an area of 200.96 in², and thus 100.48 square inches will make up its half.
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Suppose the scores x on a college entrance examination are normally distributed with a mean of 550 and standard deviation of 100. A certain prestigious university will consider for admission only those applicants whose scores exceed the 90th percentile of the distribution. Find the minimum score an applicant must achieve in order to receive consideration for admission to the university. Helpful Hints: The Normal Table in Reverse
The minimum score an applicant must achieve in order to receive consideration for admission to the university is 678.
To solve this problem, we need to find the score x such that the area to the right of x under the standard normal curve is 0.1 (since the 90th percentile corresponds to the top 10% of scores).
Using a standard normal table (also known as a Z-table), we can find the z-score that corresponds to the area of 0.1. The closest value we can find in the table is 1.28. This means that 10% of the scores fall above a z-score of 1.28.
Now we can use the formula for converting a z-score to an x-score:
z = (x - mu) / sigma
where mu is the mean and sigma is the standard deviation of the distribution. Substituting the given values, we have:
1.28 = (x - 550) / 100
Solving for x, we get:
x = 100(1.28) + 550 = 678
Therefore, the minimum score an applicant must achieve in order to receive consideration for admission to the university is 678.
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What is the best probability distribution to use for simulating the outcome of flipping a single coin? uniform binomial exponential normal poisson none of the other answers is correct
The best probability distribution to use for simulating the outcome of flipping a single coin is the binomial distribution. The binomial distribution is used to model the number of successes in a fixed number of independent trials, where each trial has the same probability of success (in this case, 0.5 for heads or tails).
It is a discrete distribution and is often used in situations where there are only two possible outcomes. The other distributions mentioned (uniform, exponential, normal, and Poisson) are not appropriate for this scenario.
The best probability distribution to use for simulating the outcome of flipping a single coin is the binomial distribution. The binomial distribution is appropriate because it models the number of successes (e.g., heads).
In a fixed number of independent Bernoulli trials (e.g., coin flips) with the same probability of success on each trial. In this case, there are two possible outcomes (heads or tails) and each flip is independent with an equal probability of success (0.5).
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Points (-3,6 ) (-2,9 ) the equation in point slope form step by step
The equation of line passing through points (-3,6 ) (-2,9 ) in point slope form is y-6=3(x+3)
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The slope of line passing through (-3,6 ) and (-2,9 )
m=9-6/-2+3
=3
Point slope form equation is y-y₁=m(x-x₁)
y-6=3(x-(-3))
y-6=3(x+3)
Hence, the equation of line passing through points (-3,6 ) (-2,9 ) in point slope form is y-6=3(x+3)
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Test for the best ~ A major financial services company uses a set of pre-employment tests to evaluate potential employees before they are hired. All applicants sign a confidentiality agreement not to divulge any content from the tests, which has allowed the company to use the same tests over many years. The test scores are known to be normally distributed with a mean of 75.2.
In an effort to hire more talented employees, the company recently hired a recruiting firm to find better qualified applicants. A random sample of 24 applicants provided by the recruiting firm had a mean test score of 76.85 and a standard deviation of 9.3.
The company wants to determine if the mean test score for all applicants supplied by the recruiting firm is higher than the historical mean of 75.2.Round all calculated values to 4 decimal places as appropriate.
1. Which inference procedure should the company use?
A. Z confidence interval for a population proportion
B. Z test for one population proportion
C. Randomization test for the difference of two population proportions
D. 2 test of independence
E. t test for a population mean
2. Which set of hypotheses should the company use to answer the research question?
A. H0:x¯=76.85 vs. H:x¯>76.85
B. H0:=75.2 vs. H:≠75.2
C. H0:=75.2 vs. H:<75.2
D. H0:=75.2 vs. H:>75.2
1. The company should use a t-test for the population mean, as we are comparing the mean test score for the sample of applicants supplied by the recruiting firm to the historical mean of 75.2.
2. The set of hypotheses the company should use to answer the research question is: D. H0: μ = 75.2 vs. H1: μ > 75.2
1. The appropriate inference procedure for this scenario is the t-test for a population mean. This is because we are comparing a sample mean (76.85) to a known population mean (75.2) with a known sample standard deviation (9.3). So the correct answer is:
E. t-test for a population mean
2. The company wants to determine if the mean test score for applicants provided by the recruiting firm is higher than the historical mean of 75.2. Therefore, the null hypothesis (H0) should be that the mean test score is equal to 75.2, and the alternative hypothesis (H1) should be that the mean test score is greater than 75.2. The correct set of hypotheses is:
H0: μ = 75.2 (the historical mean)
Ha: μ > 75.2 (the mean for the sample of applicants supplied by the recruiting firm is higher).
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