The results of a History test and Calculus test are normally distributed. The History test had a mean score of 68 with a standard deviation of 8. The Calculus test had a mean score of 70 with a standard deviation of 7.2. Joseph scored 82 on the Calculus test and Zoe scored 82 on the History test. Which student had a higher percentile rank in their class?

Answer:

Yogurt: $0.50 Sandwich: $6

Step-by-step explanation:

Because if you make the combos equations it would be Y+Y+X=7 and X+X+Y=12.5 so you would solve with those and for it to work with both, 0.50 for yogurt, and 6 for sand which would work.

Answer:

Jenny = 23 | Nancy = 11

Step-by-step explanation:

Answer: Std = 6.0

Step-by-step explanation:

Let us take a step by step process to solve this problem.

We have from the question that;

Population 1:   76   77   66  71    55   63  83   58

Population 2:   78  71   71   65   61    71   77    62

where n is no of occurrence = 8

taking the difference of P1 - P2 we have;

Difference (d) :    -2    6    -5    6    -6   -8    6    -4

Total value of difference = -7

Difference squared (d₁ -d)² =  4    36  25   36   36   64    36   16  

Total value of difference squared (d₁ -d)² = 253

The mean Σ  = sum of values (d)/total value = -7/8 = -0.875

⇒ We are asked to find the value of the standard deviation of the paired difference.

Standard deviation is given as;

Std = √(Σ (Δd)² / n-1

Std = √[(253) / 8-1]

Std = √(253/7) = 6.0

Std = 6.0

cheers i hope this helped!!!!!!

Answer:

We can deduce that the elasticity of the labor supply is greater than 1 the labor supply is considered elastic

Step-by-step explanation:

The formula to use is the following:

Elasticity = (Change in working hours / Average working hours) / (Change in wage rate / Average wage rate)

we replace the data

Elasticity = [(7 - 3) / (7 + 3) / 2] / [(50 - 30) / (50 + 30) / 2]

Elasticity = [4 / (10/2)] / [20 / (80/2)]

Elasticity = (4/5) / (20/40)

Elasticity = 0.8 / 0.5

OUTCOME

Elasticity = 1.6

We can deduce that the elasticity of the labor supply is greater than 1 the labor supply is considered elastic

The elasticity of Poornima's labor supply between the wages of $30 and $50 per hour is approximately 1.5. This shows that Poornima's supply of labor in this wage range is elastic, indicating responsiveness to wage changes.

The elasticity of labor supply can be calculated using the midpoint method. This method measures elasticity as the percent change in quantity supplied divided by the percent change in wage. The percent change in quantity supplied is calculated as (Q2-Q1)/[(Q1+Q2)/2], where Q1 = 3 and Q2 = 7. That gives us (7-3)/[(3+7)/2] = 1. The percent change in wage is calculated similarly as (P2-P1)/[(P1+P2)/2], where P1 = $30 and P2 = $50, giving us (50-30)/[(30+50)/2] = 0.67. By dividing the percent change in quantity supplied by the percent change in wage, we get the elasticity of labor supply: 1/0.67 = 1.5 (rounded).

Therefore, the elasticity of Poornima's labor supply between wages of $30 and $50 per hour is approximately 1.5. Because the elasticity is greater than 1, Poornima's supply of labor over this wage range is elastic, meaning she is responsive to wage changes.

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Answer:

60 combinations

Step-by-step explanation:

3 × 4 × 5 = 60

Hope i helped!

Tina can choose from 60 different combinations of hat, scarf, and jacket for her doll.

To find the total number of combinations Tina can choose for her doll's outfit, you can use the multiplication principle.

Tina has 3 choices for the hat, 4 choices for the scarf, and 5 choices for the jacket.

To find the total number of combinations, multiply the number of choices for each item together:

3 (choices for the hat) × 4 (choices for the scarf) × 5 (choices for the jacket) = 60

Tina can choose from 60 different combinations of hat, scarf, and jacket for her doll.

for such more question on combinations

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To ensure Anna has two matching pairs of socks, she will need to draw out five socks. This illustrates a principle in probability known as the Pigeonhole Principle.

In this mathematics question, we are dealing with an example of the Pigeonhole Principle. Anna has 3 different types of socks: yellow, red, and blue. In the worst-case scenario, she picks one of each color for the first three socks- this doesn't give her a pair. To ensure she gets a pair, she would need to take out a fourth sock. Since we only have three different types, this fourth sock will have to be either a yellow, red or blue one, thus ensuring at least one pair. However, the question asks for two pairs. This would involve picking out a fifth sock, in the worst-case scenario this fifth sock could match with the second pair. Hence, to guarantee that there are two matching pairs, she would need to draw out a total of five socks.

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Answer:

Part I: C. statistic

Part II: 95% confidence interval = (0.130, 0.270)

Step-by-step explanation:

Part I: The proportion of the 125 people who are living below the poverty line, 25/125, is which of the following: statistic, as it is a measure taken from the sample.

Part II:

We have to calculate a 95% confidence interval for the proportion.

The sample proportion is p=0.2.

[tex]p=X/n=25/125=0.2[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.2*0.8}{125}}\\\\\\ \sigma_p=\sqrt{0.00128}=0.035777[/tex]

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.96 \cdot 0.035777=0.070122[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sisgma_p = 0.2-0.070122=0.129878\\\\UL=p+z \cdot \sisgma_p = 0.2+0.070122=0.270122[/tex]

The 95% confidence interval for the population proportion is (0.130, 0.270).

Answer:7 inches

Step-by-step explanation:

Volume of cube=343

volume of cube=length x length x length

length =L

Volume of cube=LxLxL

343=L^3

L^3=343

Taking the cube root of both sides we get

L=cube root of 343

L=7

Length =7 inches

Answer: 29 cans.

Step-by-step explanation:

20 can survive 24 days with 15 cans.

If X is the number of days that a man can survive with one can of rations.

so X is in the units can/day

then we have that:

24/15*X = 20

X = 20*15/24 = 12.5

This means that a man can live 12.5 days with a can of food.

then, for 16 men and 36 days we have:

(36/C)*12.5 = 16

C = (36/16)*12.5 = 28.1215

And we can not have a 0.1215 of a can, so we should round it up to 29 cans.

Answer:

There is not enough evidence to support the claim that the longevity of the two brand of batteries differs.

Step-by-step explanation:

The question is incomplete:

The sample data for each battery is:

Battery 1: 106 111 109 105

Battery 2: 125 103 121 118

The mean and STD for the sample of battery 1 are:

[tex]M_1=\dfrac{1}{4}\sum_{i=1}^{4}(106+111+109+105)\\\\\\ M_1=\dfrac{431}{4}=107.75[/tex]

[tex]s_1=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{4}(x_i-M)^2}\\\\\\s_1=\sqrt{\dfrac{1}{3}\cdot [(106-(107.75))^2+(111-(107.75))^2+(109-(107.75))^2+(105-(107.75))^2]}\\\\\\ s_1=\sqrt{\dfrac{1}{3}\cdot [(3.06)+(10.56)+(1.56)+(7.56)]}\\\\\\ s_1=\sqrt{\dfrac{22.75}{3}}=\sqrt{7.58333333333333}\\\\\\s_1=2.754[/tex]

The mean and STD for the sample of battery 2 are:

[tex]M_2=\dfrac{1}{4}\sum_{i=1}^{4}(125+103+121+118)\\\\\\ M_2=\dfrac{467}{4}=116.75[/tex]

[tex]s_2=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{4}(x_i-M)^2}\\\\\\s_2=\sqrt{\dfrac{1}{3}\cdot [(125-(116.75))^2+(103-(116.75))^2+(121-(116.75))^2+(118-(116.75))^2]}\\\\\\ s_2=\sqrt{\dfrac{1}{3}\cdot [(68.06)+(189.06)+(18.06)+(1.56)]}\\\\\\ s_2=\sqrt{\dfrac{276.75}{3}}=\sqrt{92.25}\\\\\\s_2=9.605[/tex]

This is a hypothesis test for the difference between populations means.

The claim is that the longevity of the two brand of batteries differs.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]

The significance level is α=0.05.

The sample 1, of size n1=4 has a mean of 107.75 and a standard deviation of 2.754.

The sample 2, of size n2=4 has a mean of 116.75 and a standard deviation of 9.605.

The difference between sample means is Md=-9.

[tex]M_d=M_1-M_2=107.75-116.75=-9[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{2.754^2+9.605^2}{4}}\\\\\\s_{M_d}=\sqrt{\dfrac{99.841}{4}}=\sqrt{24.96}=4.996[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-9-0}{4.996}=\dfrac{-9}{4.996}=-1.8014[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-1=4+4-2=6[/tex]

This test is a two-tailed test, with 6 degrees of freedom and t=-1.8014, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=2\cdot P(t<-1.8014)=0.122[/tex]

As the P-value (0.122) is greater than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the longevity of the two brand of batteries differs.

Answer:

Radius, r = 6 inches

Step-by-step explanation:

We have,

Volume of a cone is 565.2 cubic inches

Height of the cone is 15 inches

It is required to find the radius of the cone. Volume of a cone is given by :

[tex]V=\dfrac{1}{3}\pi r^2 h[/tex]

r is radius of cone

[tex]r=\sqrt{\dfrac{3V}{\pi h}} \\\\r=\sqrt{\dfrac{3\times 565.2}{3.14\times 15}} \\\\r=6\ \text{inch}[/tex]

So, the radius of the cone is 6 inches. The correct option is (b).

Answer:

X=-3

Step-by-step explanation:

Answer:

13824 cubic inches

Step-by-step explanation:

So all we need to do is:

1) Find the volume of 1 cube of the 8

2) Multiply that by 8, because 8 of them make the prism.

SO 1)

the volume of cube = side * side * side = 12*12*12 = 1728

SO 2)

the volume of prism = vol(cube) * 8 = 1728 * 8 = 13824

ANSWER: 13824 cubic inches ;)

Answer:

17 inches

Step-by-step explanation:

Answer:

356

Step-by-step explanation:

3 hundreds = 3 * 100 = 300

4 tens = 4 * 10 = 40

16 ones = 16 * 1 = 16

Combine the terms: 300 + 40 + 16 = 356

356 is your answer.

~

Answer:

P(H/A) = 0.6716

Step-by-step explanation:

Let's call H the event that Joe flipped heads, T the event that Joe flipped tails and A the event that Joe wear one read and one black sock.

So, the probability that he flipped heads given that Joe wears one read and one black sock is calculated as:

P(H/A) = P(H∩A)/P(A)

Where P(A) = P(H∩A) + P(T∩A)

On the other hand, nCx gives the number of combinations in which we can select x elements from a group of n elements. nCx is calculated as:

[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]

So, the probability that Joe wear one red and one black sock given that he picks the socks from the first drawer is:

[tex]\frac{6C1*4C1*2C0}{12C2}=0.3636[/tex]

Because he need to choose one red sock from the 6 that are in the first drawer, one black sock from the 4 that are in the first drawer and 0 white socks. Additionally there are 12C2 ways to choose a pair of socks.

Therefore the probability P(H∩A) that that Joe flipped heads and Joe wear one read and one black sock is:

P(H∩A) = 0.5*0.3636 = 0.1818

Because there is a probability of 0.5 to flipped heads and the probability that Joe wear one red and one black sock given that he flipped heads is 0.3636.

At the same way, the probability that Joe wear one red and one black sock given that he picks the socks from the second drawer is:

[tex]\frac{4C1*2C1*4C0}{10C2}=0.1778[/tex]

Therefore the probability P(T∩A) that that Joe flipped tails and Joe wear one read and one black sock is:

P(T∩A) = 0.5 * 0.1778 = 0.0889

Finally, P(A) and P(H/A) is equal to:

P(A) = 0.1818 + 0.0889 = 0.2707

P(H/A) = 0.1818/0.2707 = 0.6716

Answer:

80%

Step-by-step explanation:

20000. take out 3 zeros from both numbers and you get 20 and 16. 20 is 4 times 5 and 16 is 4 times 4 if 20 is 100% then 4 over 5 is 80%

Answer:

36x² - 9y²

Step-by-step explanation:

We see that the given expression (6x + 3y)(6x - 3y) looks just like the expression (a + b)(a - b). When multiplied out, this is a difference of squares identity that I highly recommend you memorise:

(a + b)(a - b) = a² - b²

Here, a = 6x and b = 3y, so plug these in:

(6x + 3y)(6x - 3y) = (6x)² - (3y)² = 36x² - 9y²

Answer:

36x² - 9y²

Step-by-step explanation:

(6x + 3y)(6x − 3y)

(6x)² - (3y)²

36x² - 9y²

[tex] \sqrt{ {q}^{3} } [/tex]

Step-by-step explanation:

[tex] {q}^{ \frac{3}{2} } = ( {q}^{3} )^{ \frac{1}{2} } = \sqrt{ {q}^{3} } \\ [/tex]

Answer:

4

Step-by-step explanation:

Im not completely sure

Answer:

a) The price that maximizes profit is p =$43.

b) The utility shouldn't pass all this increase on the consumers because this would mean a decrease in the profits. They should pass only $7 to consumers price.

Step-by-step explanation:

We have an electric utility company which has a demand function defined by:

[tex]p=59-10^{-5}x[/tex]

where p is the price and x is the the energy in thousands of kWh.

The cost of the company is defined as:

[tex]C(x)=3\cdot 10^6+27x[/tex]

We have to calculate the price that maximizes the utility's profit R(x).

We can define the profit as:

[tex]R(x)=p\cdot x-C=(59-10^{-5}x)\cdot x-(3\cdot 10^6+27x)\\\\R(x)=-10^{-5}x^2+(59-27)x-3\cdot10^6\\\\R(x)=-10^{-5}x^2+32x-3\cdot10^6[/tex].

To maximize R, we have to derive it and equal to zero

[tex]\dfrac{dR}{dx}=0\\\\\\\dfrac{dR}{dx}=-2\cdot10^{-5}x+32=0\\\\\\x=(32/2)\cdot 10^5=16\cdot 10^5=1.6\cdot 10^6[/tex]

The price that maximizes the profit is then:

[tex]p=59-10^{-5}x=59-10^{-5}(16\cdot 10^5)=59-16=43[/tex]

b) When the unit cost rise from $27 to $41, the utility profit function changes.

We have to calculate the new price that maximizes profit, and then we will know if the rise in cost was transferred to price completely.

The new profit function is:

[tex]R(x)=p\cdot x-C=(59-10^{-5}x)\cdot x-(3\cdot 10^6+41x)\\\\R(x)=-10^{-5}x^2+(59-41)x-3\cdot10^6\\\\R(x)=-10^{-5}x^2+18x-3\cdot10^6[/tex]

To maximize R, we have to derive it and equal to zero

[tex]\dfrac{dR}{dx}=0\\\\\\\dfrac{dR}{dx}=-2\cdot10^{-5}x+18=0\\\\\\x=(18/2)\cdot 10^5=9\cdot 10^5[/tex]

We calculate the new price as:

[tex]p=59-10^{-5}x=59-10^{-5}(9\cdot 10^5)=59-9=50[/tex]

The new price is $7 dollars above the previous maximizing price, so the rise in unit cost is only transferred 50% to the price.

The utility shouldn't pass all this increase on the consumers because this would mean a decrease in the profits. They should pass only $7 to consumers price.

Answer:

[tex]\mu_{\hat p} = 0.25[/tex]

[tex]\sigma_{\hat p}= \sqrt{\frac{0.25*(1-0.25)}{40}}= 0.0685[/tex]

[tex] z = \frac{0.2-0.25}{0.0685}= -0.730[/tex]

And we can use the normal standard distribution or excel to find this probability and we got:

[tex] P(\hat p <0.2) = P(z<-0.730)= 0.233[/tex]

Step-by-step explanation:

We define the parameter as the proportion of students at a college who study abroad and this value is known [tex]p =0.25[/tex], we select a sample size of n =40 and we are interested in the probability associated to the sample proportion, but we know that the distirbution for the sample proportion is given by:

[tex]\hat p \sim N(p , \sqrt{\frac{p(1-p)}{n}}[/tex]

And the paramters for this case are:

[tex]\mu_{\hat p} = 0.25[/tex]

[tex]\sigma_{\hat p}= \sqrt{\frac{0.25*(1-0.25)}{40}}= 0.0685[/tex]

We want to find the following probability:

[tex]P(\hat p< 0.2)[/tex]

For this case since we know the distribution for the sample proportion we can use the z score formula given by:

[tex] z = \frac{\hat p -\mu_{\hat p}}{\sigma_{\hat p}}[/tex]

Replacing the info given we got:

[tex] z = \frac{0.2-0.25}{0.0685}= -0.730[/tex]

And we can use the normal standard distribution or excel to find this probability and we got:

[tex] P(\hat p <0.2) = P(z<-0.730)= 0.233[/tex]

To find the probability that the proportion of students in your sample who have studied abroad is less than 0.2, you can use the normal distribution approximation for sampling proportions.

To find the probability that the proportion of students in your sample who have studied abroad is less than 0.2, you can use the normal distribution approximation for sampling proportions. First, find the mean of the sampling distribution, which is equal to the true proportion (0.25) multiplied by the sample size (40), giving a mean of 10.

Next, find the standard deviation of the sampling distribution, which is calculated as the square root of (p(1-p)/n), where p is the true proportion (0.25) and n is the sample size (40). The standard deviation is approximately 0.071.

Finally, use the normal distribution to find the probability that the proportion is less than 0.2. Using the z-score formula, calculate the z-score as (sample proportion - mean)/(standard deviation). In this case, the z-score is approximately -1.41. Use a standard normal distribution table or calculator to find the corresponding probability, which is approximately 0.079.

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Answer:

The three equivalent options are: [tex]\frac{1}{6}x+47[/tex], [tex]\frac{5}{3}x+35-\frac{3}{2}x+12[/tex], and [tex]5(\frac{1}{3} x+(5)(7)-(3)(\frac{1}{2}x)+(3)(4)[/tex]

Step-by-step explanation:

Expand [tex]5(\frac{1}{3}x+7)-3(\frac{1}{2}x-4)[/tex] to get [tex]\frac{5}{3}x+35-\frac{3}{2}x+12[/tex].

Simplifying this gets you [tex]\frac{1}{6}x+47[/tex].

Answer:

475  milliliters  of oil

Step-by-step explanation:

1 liter =1000 milliliters

1 deciliter =100 milliliters

To make it easier, we convert all our units to milliliters.

Volume of the water bottle =0.6 liter

=0.6 X 1000 =600 milliliters

Volume of colored water = 1.25 deciliters

=1.25 X 100 =125 milliliters

Therefore:

Volume of oil needed to fill the bottle = 600-125

=475  milliliters

Sam will need to add 475 milliliters of oil to the 0.6-liter bottle after adding 1.25 deciliters of colored water to create his homemade lava lamp.

The question involves calculating the volume of oil needed to fill the remainder of a 0.6-liter bottle after adding some colored water. To solve this, we need to convert the measurements into the same units and perform subtraction. In this case, we convert deciliters to milliliters, as we know that 1 deciliter is equivalent to 100 milliliters. The student has filled the bottle with 1.25 deciliters of colored water, which is 1.25 × 100 milliliters = 125 milliliters of water.

Since the bottle can hold 0.6 liters, which is equal to 600 milliliters, the amount of oil required will be the total bottle capacity minus the volume of colored water already added. Thus, we calculate 600 milliliters (bottle capacity) – 125 milliliters (water added) to find the volume of oil needed.

So, Sam will need 600 mL – 125 mL = 475 milliliters of oil to fill the rest of his homemade lava lamp.

Answer:36

Step-by-step explanation:u

6^7/6^5

6^(7-5)

6^2

6x6=36

Answer:

  375

Step-by-step explanation:

  b : r = 15 : 24

  r : y = 9 : 15 = 3 : 5 = 24 : 40

Then ...

  b : r : y = 15 : 24 : 40

The number of bahs equivalent to 1000 yahs is ...

  bahs = (15/40)(1000) = 375

375 bahs are equal in value to 1000 yahs.

Answer:

See Explanation

Step-by-step explanation:

The W-2 form is a form which an employer must send to an employee and the Internal Revenue Service (IRS) at the end of each year.  Every January, the employee should receive a Form W-2 Wage and Tax Statement from his/her employer. The contents of this form are the amount of money made by the employee during the previous year and how much was paid as tax.

When a citizen gets their W-2 form for the previous year, they can use it to decide if they qualify for a tax refund which could be in cash or used towards the next years' tax.

Finally,

Answer:

1. refund

2. w-2

3. online

Answer:120

Step-by-step explanation:

Volume=length x width x height

volume of box=4x2.5x1.5

Volume of box=15

Length of side of cube=1/2=0.5

Volume of cube=0.5x0.5x0.5

Volume of cube=0.125

Number of cube that can pack inside there box=15 ➗ 0.125=120

Answer:

12+ 8.2n

Step-by-step explanation:

12 more than 8.2 times a number n is:

First, 12 more indicates that whatever we get has to add 12 on since it is 12 more.

Second, 8.2 times a number is multiplication and that number is filled in by a variable (n).

Therefore, the equation is 8.2n + 12