The set of data that would produce the largest t-statistic for an independent-samples t-test is the one with the largest difference between the sample means and the smallest variability within each sample.When other factors are held constant, the t-statistic for an independent-samples t-test is given by the following formula:
t=(x1 − x2)/ SEwhere x1 and x2 are the means of the two samples, and SE is the standard error of the difference between the means. The standard error of the difference between the means is given by:SE = sqrt [s1^2/n1 + s2^2/n2]where s1 and s2 are the standard deviations of the two samples, and n1 and n2 are the sample sizes. Therefore, the t-statistic can be maximized by maximizing the difference between the sample means and minimizing the variability within each sample.Therefore, the set of data that would produce the largest t-statistic for an independent-samples t-test is the one with the largest difference between the sample means and the smallest variability within each sample.
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Grant's art class had an exhibit with 45 pieces. 9 of the drawings were Grant's. What percent of the paintings were his?
Answer:
20%
Step-by-step explanation:0% of 4445=
Please write how we can find.
Answer:
15
Step-by-step explanation:
Answer can only be found through estimation.
This means you have to do:
[tex]\frac{50*3}{\sqrt{100} }[/tex]
This will get you 15.
The temperature recorded at Bloemfontein increased from -2 degrees C to 13 degrees C.what is the difference in temperature
Answer: 15
Step-by-step explanation:
13--2 = 13 + 2 = 15
If the distance between the points (0 6) and (a 0) Find the value of a
Using distance between two points formula, a = 0
What is the distance between two points?The distance between two points (x, y) and (x', y') is given by
d = √[(x' - x)² + (y' - y)²]
Now, If the distance between the points (0, 6) and (a, 0) is 6 units, to find the value of a,
Let
(x, y) = (0, 6) and(x', y') = (a, 0) and d = 6So, substituting the values of the variables into the equation, we have
d = √[(x' - x)² + (y' - y)²]
6 = √[(a - 0)² + (0 - 6)²]
⇒ √[a² + (- 6)²] = 6
√[a² + 36] = 6
Squaring both sides, we have that
a² + 36 = 6²
a² + 36 = 36
a² = 36 - 36
a² = 0
a = √0
a = 0
So, a = 0
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The question is incomplete. Here is the complete question
If the distance between (0, 6) and (a, 0) os 6 units. Find the value of a
find the length of the cord pt.2
the length of chord in the circle is 13.5 units.
Pythagoras Theorem StatementAccording to Pythagoras' Theorem, the square of the hypotenuse side of a right-angled triangle equals the sum of the squares of the other two sides.The Perpendicular, Base, and Hypotenuse are the three angles that make up this triangle.
The Pythagoras Theorem formula is as follows from the definition:
Hypotenuse² = Perpendicular² + Base²
c² = a² + b²
From the figure, the hypotenuse, x of both triangle are same as both of them are radius of circle.
According to Pythagoras theorem,
x²=6.3²+11.9²
x²=181.3
x=√181.3
x=13.5
Hence, the length of chord in the circle is 13.5 units.
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urn contains 6 white, 5 red and 3 blue chips. A person selects 4 chips without replacement. Determine the following probabilities: (Show work. Final answer must be in decimal form.) a) P(Exactly 3 chips are white) Answer Answer b) P(The third chip is blue The first 2 were white) c) P(The fourth chip is blue Answer The first 2 were white) 6. Suppose we have a random variable X such that E[X]= 7 and E[X²]=58. Answer a) Determine the variance of X. b) Determine E[2X2 - 20X +5]
the variance of X is 9. b) Determine E [2X² - 20X +5]:
Using linearity of expectation, we can find E [2X² - 20X +5] as:
E [2X² - 20X +5] = 2E[X²] - 20E[X] + 5
by the question.
The number of ways to select the first 2 white chips is given by:
Number of ways = (6C2) (5C0) (3C0) = 15
The number of ways to select the third chip as blue given that the first 2 chips were white is given by:
Number of ways = (3C1) = 3
Therefore, the probability of selecting the third chip as blue given that the first 2 chips were white is:
P(The third chip is blue the first 2 were white) = Number of ways / Total number of ways = 3 / 350 = 0.0086 (rounded to 4 decimal places)
c) P(The fourth chip is blue the first 2 were white):
The number of ways to select the first 2 white chips is given by:
Number of ways = (6C2) (5C0) (3C0) = 15
The number of ways to select the third chip as non-white given that the first 2 chips were white is given by:
Number of ways = (8C1) = 8
The number of ways to select the fourth chip as blue given that the first 2 chips were white, and the third chip was non-white is given by:
Number of ways = (3C1) = 3
Therefore, the probability of selecting the fourth chip as blue given that the first 2 chips were white is:
P(The fourth chip is blue the first 2 were white) = Number of ways / Total number of ways = 8*3 / 350 = 0.0686 (rounded to 4 decimal places)
Suppose we have a random variable X such that E[X]= 7 and E[X²] =58.
a) Determine the variance of X:
The variance of X is given by:
Var[X] = E[X²] - (E[X]) ²
Substituting the given values, we get:
Var[X] = 58 - (7) ² = 9
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Can someone help me with this
Answer:
they bought 62 item from noodles and 51 items from hot chips
1. Describe the historical data on Nando’s sales, including a discussion of thegeneral direction of sales and any seasonal tendencies that might beoccurring. 2. Discuss, giving your justifications, which time series forecasting techniquesare appropriate for producing forecasts with this data set. 3. Apply the appropriate forecasting techniques and compare the models basedon ex post forecasts. Choose the best model. 4. Use your chosen forecasting model to generate forecasts for each of themonths in year 2021. 5. Discuss how these forecasts might be integrated into the planning operationsand policy makings in NIH
In Rosettenville, a suburb of Johannesburg, South Africa, Robert Brozin and Fernando Duarte acquired the Chicken Land restaurant in 1987, launching Nando's.
The eatery was renamed Nando's in honor of Fernando. The restaurant incorporated influences from former Mozambican Portuguese colonists, many of whom had relocated to Johannesburg's southeast after their country gained independence in 1975. Expansion was an essential component of their vision from the beginning. Nando's had already grown from one restaurant in 1987 to four by 1990. It became increasingly difficult to implement a common strategy and decision-making became inefficient as new outlets were maintained as separate businesses.
In 1995, Nando's International Holdings (NIH) was established as a new international holding because managing this growingly complex global structure had become extremely challenging. The South African branch of Nando's Group Holdings (NGH) was successfully listed on the Johannesburg Stock Exchange on April 27, 1997. NGH was 54% owned by NIH, with the remaining 26% available to the general public and former joint venture partners. The main goals of the share offer and listing were to broaden the group's capital base and enable group restructuring.
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a random variable x has the following probability distribution. values of x -1 0 1 probability 0.3 0.4 0.3 (a) calculate the mean of x.
The mean (also called the arithmetic mean or average) is a measure of central tendency that represents the typical or average value of a set of data. The mean is calculated by summing up all the values in the data set and dividing by the number of values.
The mean of x is calculated by the following formula:
mean of x = ∑(x * P(x))
Where, ∑ = Summation operator
x = Value of random variable
P(x) = Probability of the corresponding value of x.
Let's calculate the mean of x using the formula provided above.
mean of x = (-1 × 0.3) + (0 × 0.4) + (1 × 0.3)
= -0.3 + 0 + 0.3
= 0
Therefore, the mean of x is 0.
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Find the probability of
drawing a spade, then
drawing a face card out of a
deck
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
P of spade = 1/4
P of face cards = 3/13
{P = probability}
Step-by-step explanation:
•Total cards in a deck = 52
No. of spade cards in the deck = 13
therefore,
Probability of drawing a spade out of a deck of cards = 13/52 = 1/4
No. of face cards in a deck = 3×4 = 12 (joker,king,queen)
therefore,
Probability of drawing a face card out of a deck of cards = 12/52 = 3/13
Hope it helps you ~For Blake's lemonade recipe, 12 lemons are required to make 16 cups of lemonade. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
Answer: To fill out a table of equivalent ratios for Blake's lemonade recipe, we can use the ratio of lemons to cups of lemonade:
Lemons Cups of Lemonade
3 4
6 8
9 12
12 16
15 20
18 24
To plot the points on a coordinate axes, we can use the Lemons as the x-coordinate and the Cups of Lemonade as the y-coordinate. The points would lie on a line that passes through the origin (0,0) and the point (12,16).
| *
Cups of | * *
Lemonade | * *
|________________
Lemons
0 12
The line represents the proportional relationship between the number of lemons and the amount of lemonade produced. As the number of lemons increases, the amount of lemonade produced increases proportionally.
Step-by-step explanation:
In which condition vector a.b has the minimum value? Write it.
Answer:
if it is perpendicular to eacha other I e 0
what is the expected count for women for the presence of aortic stenosis? a. 49.7 b. 59.3 c. 109 d. 57.7
The expected count for women for the presence of aortic stenosis is 57.7. The correct option is D.
What is aortic stenosis?Aortic stenosis is a cardiovascular ailment that causes the aortic valve in the heart to narrow, reducing blood flow from the heart to the rest of the body. Aortic stenosis usually progresses gradually and, in the beginning, may not produce any symptoms.
The severity of aortic stenosis is divided into four categories, ranging from mild to severe. People who are asymptomatic may require monitoring, whereas those who are symptomatic may need to undergo surgery or other procedures.
The expected count for women for the presence of aortic stenosis in this question refers to the number of women who have this condition according to a particular study or statistic.
Therefore, the correct option is D.
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please help!! there are multiple parts that i dont get
Answer:
(a, b) alternate interior angles at M and N, and at A and B are congruent
(c) the triangles are congruent by SAS and by ASA (and MX = NX)
(d) angles are no longer congruent, so the triangles are not congruent. The radii are given as congruent, but the chords cannot be shown congruent.
Step-by-step explanation:
Given same-size circles A and B, externally tangent to each other at X, each with chords MX and NX, you want to know what can be concluded if AM║BN, and what is unprovable if those segments are not parallel.
Same-size circlesThe circles being the same size means all the radii are congruent. This is shown by the single hash marks in the attached diagram.
(a) AnglesAlternate interior angles where a transversal crosses parallel lines are congruent. If AM║BN, this means the angles marked with a single arc are congruent, and the angles marked with a double arc are congruent. These are the alternate interior angles at transversal MN and at transversal AB.
(b) Corresponding partsIf AM║BN, in addition to the given congruences, we also know ...
all radii are congruent — given in the problem statementangles M and N are congruent (see above)angles A and B are congruent (see above)the vertical angles at X are congruent to each other and to angles M and N (isosceles triangles) (AMBN is a parallelogram.)(c) Congruent triangles∆AMX ≅ ∆BNX by SAS or ASA (take your pick).
(d) Not parallelIf AM and BN are not parallel, MN is not a straight line through X, the angles at A and B are not congruent, and the angles at M and N are not congruent. (We assume segment AB still goes through X.)
__
Additional comment
Triangles MAX and NBX are isosceles, so their base angles are congruent. If X lies on MN, then AM and BN must be parallel, since the vertical angles at X will be congruent along with the other base angles at M and N. If AM and BN are not parallel, point X cannot lie on segment AB.
A researcher is interested in understanding whether the mean time to complete a four-year college degree varies based on gender. She draws a sample of 12 college graduates-- 6 men and 6 women, and asks them how many years they took to finish their degree. Assuming that the data are drawn from a normal distribution, test the null hypothesis of no difference in mean years to degree competition between men and women.
Men Women
4
5
4 6
4 4
6 7
4 5
5 3
The p-value is greater than the level of significance (0.05). Therefore, we fail to reject the null hypothesis. There is not enough evidence to suggest that the mean time to complete a four-year college degree varies based on gender. The conclusion is that there is no difference between the mean number of years for men and women to complete a four-year college degree.
The null hypothesis in the given data set is there is no difference between the mean number of years for men and women to complete a four-year college degree. The null hypothesis is a statement that describes the population parameter being tested. It is usually given the symbol H0. The null hypothesis is that the population parameter is equal to some value.
The null hypothesis is what is assumed to be true if no evidence is available to contradict it. It can be accepted or rejected based on the results of a statistical test. The degrees of freedom is the number of independent observations in a statistical test. It is usually represented by the symbol df. The degrees of freedom is used to calculate the t-value for a statistical test.
It is calculated as n - 1, where n is the sample size. In this problem, the degrees of freedom is 10 (12 - 2).The t-test is a statistical test used to determine if there is a significant difference between two groups. It is used when the population standard deviation is not known. The t-test uses the t-distribution to determine the p-value. The p-value is the probability of observing the data if the null hypothesis is true.
If the p-value is less than the level of significance, the null hypothesis is rejected. In this problem, the null hypothesis is that there is no difference between the mean number of years for men and women to complete a four-year college degree. To test this hypothesis, we will use a two-sample t-test.
The formula for a two-sample t-test is:t = (x1 - x2) / (s1^2/n1 + s2^2/n2)^(1/2)where x1 is the sample mean for group 1, x2 is the sample mean for group 2, s1 is the sample standard deviation for group 1, s2 is the sample standard deviation for group 2, n1 is the sample size for group 1, n2 is the sample size for group 2, and t is the t-value.
Men: (4 + 5 + 4 + 6 + 4 + 5) / 6 = 28 / 6 = 4.67Women: (6 + 4 + 7 + 5 + 3) / 5 = 25 / 5 = 5The sample mean for men is 4.67 years, and the sample mean for women is 5 years. The pooled variance is a weighted average of the variances of two independent samples. It is used to estimate the population variance when the population variances are assumed to be equal.
The formula for the pooled variance is:s^2 = [(n1 - 1)s1^2 + (n2 - 1)s2^2] / (n1 + n2 - 2)where s1 is the sample standard deviation for group 1, s2 is the sample standard deviation for group 2, n1 is the sample size for group 1, n2 is the sample size for group 2, and s^2 is the pooled variance.s1 = [(4 - 4.67)^2 + (5 - 4.67)^2 + (4 - 4.67)^2 + (6 - 4.67)^2 + (4 - 4.67)^2 + (5 - 4.67)^2] / (6 - 1)^(1/2) = 0.763s2 = [(6 - 5)^2 + (4 - 5)^2 + (7 - 5)^2 + (5 - 5)^2 + (3 - 5)^2] / (5 - 1)^(1/2) = 1.87s^2 = [(6 - 1)0.763^2 + (5 - 1)1.87^2] / (6 + 5 - 2) = 1.243
The t-value is calculated using the formula: t = (x1 - x2) / (s1^2/n1 + s2^2/n2)^(1/2)t = (4.67 - 5) / (1.243/6 + 1.243/5)^(1/2)t = -0.555 The p-value is the probability of observing the data if the null hypothesis is true. The p-value is calculated using a t-table or a t-distribution calculator. The p-value for a two-tailed test with 10 degrees of freedom and a t-value of 0.555 is 0.593.
The p-value is greater than the level of significance (0.05). Therefore, we fail to reject the null hypothesis. There is not enough evidence to suggest that the mean time to complete a four-year college degree varies based on gender. The conclusion is that there is no difference between the mean number of years for men and women to complete a four-year college degree.
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I NEED HELP PLEASE !!
can i also get an easy explanation so i can know how to do the other problems pls
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
I need to show my work please help
Answer:
x=15
Step-by-step explanation:
use the side splitter theorem
(x-6)/x = 3/5 (cross-multiply)
3x=5(x-6) distributive property
3x=5x-30
2x = 30
x = 15
an aquarium has a rectangular base that measures 100 cm by 40 cm and has a height of 50 cm. the aquarium is filled with water to a depth of 37 cm. a rock with volume $1000 \text{cm}^3$ is then placed in the aquarium and completely submerged. by how many centimeters does the water level rise? express your answer as a decimal to the nearest 100th.
The water level in the aquarium rises by (A) 0.25.
The volume of water in the aquarium before the rock is added is:
100 cm x 40 cm x 37 cm = 148000 cm^3
When the rock is added, its volume is 1000 cm^3, so the total volume of water and the rock is:
148000 cm^3 + 1000 cm^3 = 149000 cm^3
To find the new water level, we need to divide the total volume by the base area of the aquarium:
149000 cm^3 ÷ (100 cm x 40 cm) = 37.25 cm
Therefore, the water level rises by:
37.25 cm - 37 cm = 0.25 cm
So the answer is (A) 0.25.
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Your question is incomplete, but probably the complete question is :
An aquarium has a rectangular base that measures 100 cm by 40cm and has a height of 50cm. The aquarium is filled with water to a depth of 37 cm. A rock with volume 1000cm^3 is then placed in the aquarium and completely submerged. By how many centimeters does the water level rise?
(A) 0.25
(B) 0.5
(C)
(D)1.25
(E) 2.5
What is the value of x in the triangle to the right? (7x+3) 85 50
Answer: x = 6
Step-by-step explanation:
(7x+3)+85+50 = 180
(7x+3)+135 = 180
7x+3 = 180 - 135 = 45
7x = 45-3 = 42
x = 42 / 7 = 6
x = 6
Consider the following exponential probability density function. f(x) = 1/3 4 e^-x/3 for x > 0 a. Write the formula for P(x < x_0). b. Find P(x < 2). c. Find P(x > 3). d. Find P(x < 5). e. Find P(2 <.x <5).
The probability that x is less than 2 is approximately 0.4866. The probability that x is greater than 3 is approximately 0.3528. The probability that x is less than 5 is approximately 0.6321. The probability that x is between 2 and 5 is approximately 0.1455.
The given probability density function is an exponential distribution with a rate parameter of λ = 1/3. The formula for P(x < x_0) is the cumulative distribution function (CDF) of the exponential distribution, which is given by:
F(x_0) = ∫[0,x_0] f(x) dx = ∫[0,x_0] 1/3 * 4 * e^(-x/3) dx
a. Write the formula for P(x < x_0):
Using integration, we can solve this formula as follows:
F(x_0) = [-4e^(-x/3)] / 3 |[0,x_0]
= [-4e^(-x_0/3) + 4]/3
b. Find P(x < 2):
To find P(x < 2), we simply substitute x_0 = 2 in the above formula:
F(2) = [-4e^(-2/3) + 4]/3
≈ 0.4866
Therefore, the probability that x is less than 2 is approximately 0.4866.
c. Find P(x > 3):
To find P(x > 3), we can use the complement rule and subtract P(x < 3) from 1:
P(x > 3) = 1 - P(x < 3) = 1 - F(3)
= 1 - [-4e^(-1) + 4]/3
≈ 0.3528
Therefore, the probability that x is greater than 3 is approximately 0.3528.
d. Find P(x < 5):
To find P(x < 5), we simply substitute x_0 = 5 in the above formula:
F(5) = [-4e^(-5/3) + 4]/3
≈ 0.6321
Therefore, the probability that x is less than 5 is approximately 0.6321.
e. Find P(2 < x < 5):
To find P(2 < x < 5), we can use the CDF formula to find P(x < 5) and P(x < 2), and then subtract the latter from the former:
P(2 < x < 5) = P(x < 5) - P(x < 2)
= F(5) - F(2)
= [-4e^(-5/3) + 4]/3 - [-4e^(-2/3) + 4]/3
≈ 0.1455
Therefore, the probability that x is between 2 and 5 is approximately 0.1455.
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the life of light bulbs is distributed normally. the variance of the lifetime is 225 and the mean lifetime of a bulb is 530 hours. find the probability of a bulb lasting for at most 540 hours. round your answer to four decimal places.
The probability of a bulb lasting for at most 540 hours is 0.7521, rounded to four decimal places.
The life of light bulbs is distributed normally. The variance of the lifetime is 225 and the mean lifetime of a bulb is 530 hours. Find the probability of a bulb lasting for at most 540 hours. Round your answer to four decimal places.
Using the z-score formula z = (x - μ) / σ, where x is the value in question (540 hours in this case), μ is the mean (530 hours in this case) and σ is the standard deviation (15 hours in this case), we can calculate the z-score:
z = (540 - 530) / 15
z = 10 / 15
z = 0.67
Using a z-table, we can look up the probability of a value being less than or equal to 0.67, which is 0.7521.
Therefore, the probability of a bulb lasting for at most 540 hours is 0.7521, rounded to four decimal places.
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For every seven dogs at the vet there are 10 cats if there is a total of 102 dogs and cats how many cats were at the vet
The total number of cats at the vet is approximately 61.
What is a proportion?A percentage is an equation proving the equality of two ratios. A ratio is a fractional comparison of two numbers or quantities. Proportions are used in mathematics to solve issues that involve comparing two numbers or discovering an unknown value. For instance, proportions can be used to determine equivalent fractions, compute percentages, and solve issues requiring rates and ratios. In a proportion, the numerator of one ratio is the same as the numerator of the other ratio, and vice versa for the denominator. Simplifying and cross multiplying can be used to address proportional problems.
Let the total number of dogs =x.
Let the total number of cats = y.
Given that, for every seven dogs at the vet there are 10 cats.
Thus, using proportions we have:
7 dogs / 10 cats = x / y
Using cross multiplication:
7 dogs x y = 10 cats (x)
y = (10/7) (x)
Now, x +y = 102
x = 102 - y
Substituting the value:
y = 10/7 (102 - y)
y = 145.71 - 1.4y
y + 1.4y = 145.71
2.4y = 145.71
y = 60.71
Hence, the total number of cats at the vet is approximately 61.
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enlarge triangle by scale factor 3 using the blue dot as the centre of enlargement
The new enlarged triangle has vertices at P4, P5, and P6, and is three times larger than the original triangle, with the blue dot as its center of enlargement.
What is a triangle?
A triangle is a geometric shape that consists of three straight sides and three angles. It is one of the most basic and fundamental shapes in geometry, and it is formed when three non-collinear points are connected by straight lines.
To enlarge a triangle by a scale factor of 3 using the blue dot as the center of enlargement, follow these steps:
Draw a line connecting the blue dot and each vertex of the triangle.
Mark a point on each line that is 3 times the distance from the blue dot as the corresponding vertex of the original triangle.
Connect the points on each line to form the new enlarged triangle.
Here is a step-by-step visual guide:
1. Draw lines connecting the blue dot to each vertex of the original triangle.
B
/\
/ \
/ \
P1 / \ P2
/ \
/ \
/____________\
A P3 C
2. Mark a point on each line that is 3 times the distance from the blue dot as the corresponding vertex of the original triangle.
B
/\
/ \
/ \
P1 / \ P2
/ \
/ P4 \
/____________\
A P3 C
Note that P4 is located 3 times the distance from the blue dot to vertex A along the line connecting them. Similarly, P5 and P6 are located 3 times the distance from the blue dot to vertices B and C respectively along their respective lines.
3. Connect the points on each line to form the new enlarged triangle.
P5
/\
/ \
/ \
P1 / \ P2
/ \
/ P4 \
/____________\
P3 P6 P7
Therefore, the new enlarged triangle has vertices at P4, P5, and P6, and is three times larger than the original triangle, with the blue dot as its center of enlargement.
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what is the surface area of a cube if all sides are equal to 2
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 2 , 5 , 8 ,Find the 41st term.
The 41st term of the sequence is 121.
What is a sequence?In mathematics, a sequence is a list of numbers or objects that follow a certain pattern or rule. A sequence's terms are typically identified by subscripts, like a1, a2, a3,..., an, where n denotes the number of terms in the sequence.
Sequences can be arithmetic, geometric, or neither, depending on terms follow a static difference, constant ratio, or neither of these series, respectively. Algebra uses geometric sequences to represent exponential development or decay whereas arithmetic sequences are frequently employed to model linear connections.
The given sequence is 2 , 5 , 8 , ...
The common difference is:
d = 5 - 2 = 3
The nth term of a sequence is given as:
an = a1 + (n-1)d
Substituting the value we have:
an = 2 + (n-1)3
an = 3n - 1
a41 = 3(41) - 1 = 122 - 1 = 121
Hence, the 41st term of the sequence is 121.
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Construct a triangle PQR such that PQ=8cm, PR=5cm and QR=6cm. Construct a circle which will pass through P, Q and R. What is the special name given to this circle?
Construct a triangle PQR with sides PQ=8cm, PR=5cm, and QR=6cm, then draw a circle passing through P, Q, and R. This circle is called the circumcircle of triangle PQR.
We draw a line segment PQ = 8 cm long. From point P, we draw a line segment PR = 5 cm long at an angle of 60 degrees to PQ. Then, we draw a line segment QR = 6 cm long joining points Q and R to complete the triangle. Next, we use a compass to draw a circle passing through points P, Q, and R. This circle is called the circumcircle or circumscribed circle of the triangle, which is the unique circle that passes through all three vertices of the triangle. The circumcircle has a special property that its center is equidistant from the three vertices of the triangle.
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Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 146 minutes with a standard deviation of 11 minutes. Consider 49 of the races. Let x = the average of the 49 races. Part (a) two decimal places.) Give the distribution of X. (Round your standard deviation to two decimal places)Part (b) Find the probability that the average of the sample will be between 144 and 149 minutes in these 49 marathons. (Round your answer to four decimal places.) Part (c) Find the 80th percentile for the average of these 49 marathons. (Round your answer to two decimal places.) __ min Part (d) Find the median of the average running times ___ min
(a)The distribution of X (the average of the 49 races) follows a normal distribution with mean 146 minutes and standard deviation 11 minutes. (b)The probability of the average of the sample being between 144 and 149 minutes is 0.5854.(c)The 80th percentile for the average of these 49 marathons is 157.2 minutes.(d) The median of the average running times is 146 minutes.
Part(a) The distribution of X (the average of the 49 races) follows a normal distribution with mean 146 minutes and standard deviation 11 minutes. Part (b) The probability that the average of the sample will be between 144 and 149 minutes in these 49 marathons can be calculated using the z-score formula: z = (x - mean)/standard deviation
For x = 144, z = (144 - 146)/11 = -0.18
For x = 149, z = (149 - 146)/11 = 0.27,using the z-score table, the probability of the average of the sample being between 144 and 149 minutes is 0.5854 (0.4026 + 0.1828).
Part (c) The 80th percentile for the average of these 49 marathons can be calculated using the z-score formula: z = (x - mean)/standard deviation, For the 80th percentile, z = 0.84 (from z-score table). Therefore, x = 146 + (0.84 * 11) = 157.2 minutes. Part (d) The median of the average running times is 146 minutes. The median is the midpoint of the data which means half of the data is above the median and half of the data is below the median. Therefore, the median of the average running times is equal to the mean.
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CONNAIS TU LES LIMITES ?
Answer:
yes
Step-by-step explanation:
The installer is completing a bid for a job that will total 295 square feet. The tile comes in boxes of 20 12-inch by 12-inch tiles (meaning that each tile is 1 square foot), and they cost $72 per box. Profit = 84.25x 35 +0.15m 6. Now that you know the installer will need to buy 15 boxes of tile, use the expression you developed for profit to calculate how much money the installer will make on the job. Round to the nearest cent.
The installer will make a profit of $868.75 on the job. This amount is calculated by multiplying the price of each box of tile ($72) by the number of boxes needed (15 boxes) to cover the 295 square feet.
What is cost?Cost is the total amount of money that is expended or invested in order to produce and/or acquire a good or service. It is usually measured in terms of the amount of money spent to produce a unit of a good or service, and is usually expressed in terms of units of currency, such as dollars, euros, or pounds. Cost is an important factor in determining the price of a good or service and can be used to evaluate the effectiveness of a company's operations. Additionally, cost can be used to determine the profitability of a company by measuring the amount of money it spends in relation to the amount of money it earns.
That results in a total cost of $1,080. From that, the installer then subtracts the cost of materials ($840). The remaining amount of $240 is the installer's profit. With a markup of 84.25%, this leaves the installer with a total profit of $868.75.
This profit is possible by factoring in the markup of materials, labor, and overhead costs. The installer is able to cover these costs and make a profit by charging a slightly higher price per square foot. This allows them to cover the cost of materials and labor, as well as make a profit. Additionally, they can also cover overhead costs such as insurance, taxes, and other miscellaneous costs that are associated with running their business. By charging a slightly higher price per square foot, the installer is able to make a profit on the job and remain competitive in the market.
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Which expressions are equivalent to (x−2)2
?
Select the correct choice
The expressions that are equivalent to (x-2)² is x² - 4x + 4. (option B)
Now, let's look at the expression (x-2)². This is a binomial expression that can be simplified by applying the rules of exponents. Specifically, we can expand this expression as follows:
(x-2)² = (x-2) * (x-2)
= x * x - 2 * x - 2 * x + 2 * 2
= x² - 4x + 4
So, the expression (x-2)² is equivalent to x² - 4x + 4.
However, the problem asks us to identify other expressions that are equivalent to (x-2)². To do this, we can use the process of factoring. We know that (x-2)² can be factored as (x-2) * (x-2). Using this factorization, we can rewrite (x-2)² as:
(x-2)² = (x-2) * (x-2)
= (x-2)²
So, (x-2)² is equivalent to itself.
Hence the correct option is (B).
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Complete Question:
Which expressions are equivalent to (x−2)²?
Select the correct choice.
A. (x + 2) (x - 2)
B. x² - 4x + 4
C. x² - 2x + 5
D. x² + x - 2x
