Marts is solving the equation S=2nrh+2nr2 for h. Which should be the result?

Answers

Answer 1

Step-by-step explanation:

Hope you understand this

Marts Is Solving The Equation S=2nrh+2nr2 For H. Which Should Be The Result?

Related Questions

For the following hypothesis​ test, determine the null and alternative hypotheses.​ Also, classify the hypothesis test as two​ tailed, left​ tailed, or right tailed. The mean local monthly bill for cell phone users in this country was ​$47.79 in 2001. A hypothesis test is to be performed to determine whether last​ year's mean local monthly bill for cell phone users has decreased from the 2001 mean of ​$47.79.

Answers

Answer:

The null and alternative hypothesis are:

[tex]H_0: \mu=47.79\\\\H_a:\mu< 47.79[/tex]

This is a left tailed test.

Step-by-step explanation:

A hypothesis test is to be performed to determine whether last​ year's mean local monthly bill for cell phone users has decreased from the 2001 mean of ​$47.79.

Then, the claim that will be expressed in the alternative hypothesis is that the monthly bill is lower than $47.79.

The null hypothesis will state that the monthly bill does not differ significantly from $47.79.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=47.79\\\\H_a:\mu< 47.79[/tex]

As we only want to test if its lower, we are interested only in the left tail of the distribution. We want to know if the test statistic is below the critical value to conclude if we have evidence for our claim. This is then a left tailed test.

A road crew can pave 2/5 km in 1 1/2 hours.how many km of road can they pave in 10 hours?

Answers

Answer:

8/3 km

Step-by-step explanation:

we can represent the given information on a table:

Kilometers        time (hours)

      2/5           ⇔         1 1/2

and since we want to know how many kilometers (x) will be paved on 10 hours:

Kilometers        time (hours)

      2/5           ⇔         1 1/2

        x             ⇔         10

The relationship these 3 numbers have can be described by using the rule of three, which is to multiply the cross quantities on the table (2/5 by 10) and then divide by the remaining amount (1 1/2):

x = [tex]\frac{2}{5}*10[/tex] ÷ [tex]1\frac{1}{2}[/tex]

x = [tex]\frac{20}{5}[/tex] ÷ [tex]1\frac{1}{2}[/tex]

we use [tex]1\frac{1}{2}=\frac{3}{2}[/tex]

x = [tex]\frac{20}{5}[/tex] ÷ [tex]\frac{3}{2}[/tex]

and we make the division:

x = [tex]\frac{20}{5}[/tex] ÷ [tex]\frac{3}{2}[/tex] = [tex]\frac{20*2}{5*3}=\frac{40}{15}[/tex]

we simplify the fraction by dividing the numerator and denominator both by 5, and we get the result:

x = [tex]\frac{8}{3}[/tex]

thus, in 10 hours the crew will pave 8/3 km. Which is about 2.66 km.

Write an algebraic expression for the phrase.

the sum of f and 6

Answers

Answer:

f+6

f+6 =(f+6)

What is Three-fourths divided by one-half?

Answers

Answer:

3/2

Step-by-step explanation:

(3/4) / (1/2) is equivalent to (3/4)*(2/1), or 6/4, or 3/2.

To divide by a fraction, invert the fraction and multiply instead.

Answer:

the answer is 1 and 1/2

The bottom of a deposit, of 300l of capacity, is cover by a layer of salt. Assuming that the velocity at which the salt is disolved is proportional to the difference between the concentration at this time and the concentration of the saturated solution ( 1 kg of salt for 3 liters of water), and also take into account that the amount of pure water disolve 1/3 de Kg of salt per minute. Find the ODE giving the amount of salt x(t), as a function of time, integrate it, and determine the amount of salt in the solution after one hour.Find the solutions of the ODE that satisfy the indicated conditions when x → ±[infinity]

Answers

Answer:

Step-by-step explanation:

Assuming x(t) to be the number of salt

The maximum bottom of deposits =300 Litre

Initial Concentration of the saturated salt solution = 1 kg of salt for 3 liters of water

[tex]x_ic_i= \dfrac{1}3[/tex]

⇒x = 0

The  differential equation is :

[tex]\dfrac{dx(t)}{dt}[/tex] [tex]={x_ic_i}-{x_oc_o}[/tex]

       [tex]= \dfrac{1}{3} - \dfrac{x(t)}{300}[/tex]

[tex]\dfrac{dx(t)}{dt} + \dfrac{x(t)}{300} = \dfrac{1}{3}[/tex]

Using the first order differential equation of the form :

x' + p(t) x = q(t)

where

[tex]p(t) = \dfrac{1}{300}[/tex]   ;   [tex]q(t) = \dfrac{1}{3}[/tex]

By integrating the factor:

[tex]\mu = e^{\int\limitsP(t)dt } \\ \\ =e^{\int\limits \dfrac{1}{300}dt } \\ \\ = e^{\frac{t}{300} }[/tex]

[tex]x(t) = \dfrac{1}{\mu(t) }\int\limits \mu (t) * q(t) dt \\ \\ = e ^{- t/300} \ \ [\int\limits e ^{+ t/300} * \dfrac{1}{3}dt ][/tex]

[tex]= e ^{- t/300} \ \ [\dfrac{1}{3} * \dfrac{e^{t/300}}{1/300} + C ][/tex]

[tex]x(t) = 100 + Ce ^{-t/300[/tex]

Thus the differential equation solution  is : [tex]x(t) = 100 + Ce ^{-t/300[/tex]

However; we have initial concentration   x(0) = 0

SO;

[tex]0 = 100 + Ce^{-0/300}[/tex]

C = -100

[tex]x(t) = 100 -100e ^{-t/300[/tex]

when x → ±[infinity]

[tex]\infty = 100 + Ce^{- \infty /300}[/tex]

[tex]x(t) = 100 -100e ^{-t/300[/tex]

Now;  the amount of salt after an hour is as follows:

1 hour = 60  minutes

t = 60 min

[tex]x(60) = 100 -100e ^{-60/300[/tex]

= 100 -100 (0.818)

= 100 - 81.8

= 18.2

x(60) = 18.2 kg

how much does 757 go into 68

Answers

Answer:

Divide 757 by 68 so:

Step-by-step explanation:

757 / 68 = 11.9 so 757 can go into 68 11.9 times.

Hope this helps, have a good day! :)

(Brainliest would be appreciated?)

The ideal mass for a piece of chocolate is 2.5 ounces. The actual mass for a production can vary by, at most, 0.08
ounces. Create an absolute value inequality and solve it to determine the range of chocolate masses.

Answers

9514 1404 393

Answer:

  |m-2.5| ≤ 0.08

  2.42 ≤ m ≤ 2.58

Step-by-step explanation:

The equation of interest is the one that says the positive difference from the ideal mass is at most 0.08 ounces:

  |m -2.5| ≤ 0.08 . . . an absolute value inequality

The solution is found by solving the equivalent compound inequality:

  -0.08 ≤ m -2.5 ≤ 0.08

  2.42 ≤ m ≤ 2.58 . . . . the range of masses

A researcher wanted to see if giving a selective serotonin reuptake inhibitor (anti-depressant) would decrease the number of self-injurious behaviors (SIB’s) found in adolescents. They gave the anti-depressant to a group of 8 participants and counted the numbers of SIBs a person performed for a month after taking the drug for 6 months. Here are the number of SIB’S performed by the 8 people, 27, 25, 32, 40, 43, 37, 35, 38.
a. Find the mean variance, and standard deviation of this group.
b. Suppose the u=45, what is the z score?
c. What is the SEM for this particular group?

Answers

Answer:

a. The mean of the sample is M=35.

The variance of the sample is s^2=39.125.

The standard deviation of the sample is s=6.255.

b. z=-1.6

c. SEM = 2.212

Step-by-step explanation:

The mean of the sample is M=35.

The variance of the sample is s^2=39.125.

The standard deviation of the sample is s=6.255.

Sample mean

[tex]M=\dfrac{1}{8}\sum_{i=1}^{8}(27+25+32+40+43+37+35+38)\\\\\\ M=\dfrac{277}{8}=35[/tex]

Sample variance and standard deviation

[tex]s^2=\dfrac{1}{(n-1)}\sum_{i=1}^{8}(x_i-M)^2\\\\\\s^2=\dfrac{1}{7}\cdot [(27-(35))^2+(25-(35))^2+(32-(35))^2+(40-(35))^2+(43-(35))^2+(37-(35))^2+(35-(35))^2+(38-(35))^2]\\\\\\[/tex]

[tex]s^2=\dfrac{1}{7}\cdot [(58.141)+(92.641)+(6.891)+(28.891)+(70.141)+(5.64)+(0.14)+(11.39)]\\\\\ s^2=\dfrac{273.875}{7}=39.125\\\\\\s=\sqrt{39.125}=6.255[/tex]

b. If the population mean is 45, the z-score for M=35 would be:

[tex]z=\dfrac{M-\mu}{\sigma}=\dfrac{35-45}{6.255}=\dfrac{-10}{6.255}=-1.6[/tex]

c. The standard error of the mean (SEM) of this group is calculated as:

[tex]SEM=\dfrac{s}{\sqrt{n}}=\dfrac{6.255}{\sqrt{8}}=\dfrac{6.255}{2.828}=2.212[/tex]

Select the equivalent expression.

A, B or C?

Answers

Answer:

  A

Step-by-step explanation:

The relevant rules of exponents are ...

  (a^b)^c = a^(bc)

  a^-b = 1/a^b

__

  [tex]\left(\dfrac{2^{-10}}{4^2}\right)^7=\dfrac{2^{(-10)(7)}}{4^{(2)(7)}}=\dfrac{2^{-70}}{4^{14}}\\\\=\boxed{\dfrac{1}{2^{70}\cdot 4^{14}}}[/tex]

The average of four numbers is 38, and the average of the first two numbers is 42, and the average of the last three numbers is 36. What is the second number?

Answers

Answer:

40

Step-by-step explanation:

let the numbers be a+b+c+d.

the average of 4 numbers is 38

; (a+b+c+d)/4 = 38

(a+b+c+d) = 152 ......equ1

the average of the first two numbers is 42

; (a+b)/2 = 42

(a+b) = 84 ...... equ2

the average of the last three numbers is 36

; (b+c+d)/3 = 36

(b+c+d) = 108 .....equ3

substitute equ3 into equ1

a + 108 = 152

a= 152 - 108

a = 44

input the value of a into equ2

44 + b = 84

b = 40

the second number is 40.

I hope this helps.

Types of bonds are divided into three categories: good risk, medium risk, and poor risk. Assume that of a total of 11, 332 bonds, 7,311 are good risk, 1,182 are medium risk, and the rest are poor risk. One bond is chosen at random. What is the probability that the bond is not a poor ? Write only a number as your answer. Round to two decimal places (for example : 0.43). Do not write as a percentage .

Answers

Answer:

Probabilty of not poor= 0.75

Step-by-step explanation:

total of 11332 bonds.

7311 are good risk.

1182 are medium risk.

Poor risk

= total risk-(good risk+ medium risk)

= 11332-(7311+1182)

= 11332-8493

= 2839.

Poor risk = 2839

Probabilty that the ball choosen at random is not poor= 1 - probability that the ball is poor

Probability of poor = 2839/11332

Probabilty of poor= 0.2505

Probabilty that the ball choosen at random is not poor= 1- 0.2505

= 0.7495

To two decimal place= 0.75

Use the formula above to find the Celsius temperature equivalent to 185°F. A. 85°C B. 153°C C. 102°C D. 68°C

Answers

Answer: A. 85ᴼC

Step-by-step explanation:

0 degrees Celsius is at 32 degrees Fahrenheit.

100 degrees Celsius is at 212 degrees Fahrenheit.

212 - 32 = 180

180 / 100 = 1.8

So, every degree Celsius is 1.8 degrees Fahrenheit, starting at 32 of course.

1.8 * 85 = 153

153 + 32 = 185

Answer:

The correct answer is 85°C.

Step-by-step explanation:

I use the equation 9C = 5F - 160 to solve for temperatures.

Therefore, we just insert values for each variable except for the one that we want to solve for. In this case, we are doing Fahrenheit → Celsius, so we are solving for the unknown variable of C. We are given a value for F, 185°.

Therefore, just insert these into the equation and solve for C.

[tex]9C = 5(185)-160[/tex]

[tex]9C = 925 - 160[/tex]

[tex]9C = 765[/tex]

[tex]\frac{765}{9} = 85[/tex]

C = 85°C

Which of the following are valid names for the given triangle? Check all that
apply
T
A
A. ATAY
B. AMAY
C. AMAX
D. AAXM
Ε. ΔΧΜΑ
F. AXMT​

Answers

Answer:

I think it's just E.

Step-by-step explanation:

When you name triangles, you would often put a Δ and then the letters of the 3 angles. The only answer that fits that criteria is E.

The valid name for the given triangle is ΔΧΜΑ.

What is a triangle?

A triangle is a 3-sided polygon that consists of three edges and 3 vertices. The most vital asset of a triangle is that the sum of the inner angles of a triangle is identical to a hundred and eighty tiers. This belonging is called the attitude sum property of the triangle.

What are the types of triangles?

equilateral, isosceles, scalene, right triangles.

Learn more about triangle here https://brainly.com/question/2938476

#SPJ2

The value of homes sold in Hampton VA are normally distributed with a mean of $200,000

and a standard deviation of $10,000. If 1216 houses were sold in 2012, how many houses would

have a value greater than one standard deviation above the mean?

Answers

Answer:

[tex]X \sim N(200000,100000)[/tex]  

Where [tex]\mu=200000[/tex] and [tex]\sigma=10000[/tex]

From the empirical rule we know that within one deviation from the mean we have 68% of the values so then 1 deviation above the mean we will have (100-68)/2 = 16% and then the number of houses that are greater than one deviation above the mean are:

[tex] Number = 1216*0.16 = 194.56[/tex]

And the answer woud be between 194 and 195 houses

Step-by-step explanation:

Let X the random variable that represent the value of homes in Hampton VA of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(200000,100000)[/tex]  

Where [tex]\mu=200000[/tex] and [tex]\sigma=10000[/tex]

From the empirical rule we know that within one deviation from the mean we have 68% of the values so then 1 deviation above the mean we will have (100-68)/2 = 16% and then the number of houses that are greater than one deviation above the mean are:

[tex] Number = 1216*0.16 = 194.56[/tex]

And the answer woud be between 194 and 195 houses

This diagram to the right represents a small stage in the shape of a SEMIcircle (half of a circle). Find the area of the stage. ***Diameter of the semi circle is 10 yards

Answers

Answer:

above is the answer

Step-by-step explanation:

Area of a circle=

[tex]\pi {r}^{2} [/tex]

but this Is a semicircle so you divide it by 2 as in

[tex] a = \frac{\pi {r}^{2} }{2} [/tex]

so d=2r so r=5yd

A=5×5 pie/2

=25 pie/2=12.5 yards

Any help would be greatly appreciated

Answers

Answer:

0.927

Step-by-step explanation:

Hope this helps.

Answer:

I think it would just be 0.927

Step-by-step explanation:

with 0.9267, 6 is in the thousandth spot. 2 is in the hundredth spot, and 9 is in the tenth spot. Since the number behind 6 is larger than five, you'd round your number 6 in the thousandth spot to a 7. Therefore, you should have 0.927.

4. Calculate the volume of material used in making 100 ft of 4-in. type M, copper tubing.

Answers

Answer:

1443.3 in³ or 0.835 ft³

Step-by-step explanation:

Let's begin by listing out the given variables:

length (l) = 100 ft = 1200 in, nominal size = 4 in

From the copper tube of industry standard guide of the design and the installation of piping system, the dimension and physical characteristics of type M copper tubing of nominal size 4 inch is given as

Outer diameter (Do) = 4.125 in ⇒ ro = Do ÷ 2 = 2.0625 in, Inner diameter (Di) = 3.935 in ⇒ ri = Di ÷ 2 = 1.9675 in

calculate the volume of the pipe, we use the formula

V = π(ro² - ri²) * l

V = π(2.0625² - 1.9675²) * 1200

V = 1443.3 in³ or 0.835 ft³

1. Considere as funções f e g, ambas com domínio Z, dadas por f(x) = x²- 2x e g(x) = x³-1. Associe as colunas e assinale a alternativa que apresenta a sequência correta: *
1 ponto
a) f (-2) ( )29
b) g(-2) ( )15/7
c) f(-1) + g(3) ( )8
d) f(5) : g(2) ( )-9

a) C, D, A, B
b) A, B, D, C
c) D, C, A, B
d) A, C, D, B



ajuuuuuda

Answers

Answer:

(A)C,D,A,B

Step-by-step explanation:

[tex]f(x) = x^2- 2x\\g(x) = x^3-1[/tex]

a)

[tex]f(-2) = (-2)^2- 2(-2)\\=4-(-4)\\=4+4\\=8$ (C)[/tex]

b)

[tex]g(-2) = (-2)^3-1\\\=-8-1\\=-9 $(D)[/tex]

c)

[tex]f(-1) = (-1)^2- 2(-1)=1+2=3\\g(3) = (3)^3-1=27-1=26\\f(-1) + g(3)=3+26\\=29$ (A)[/tex]

d) f(5) : g(2)

[tex]f(5) = (5)^2- 2(5)=25-10=15\\g(2) = (2)^3-1=8-1=7\\f(5) :g(2)=15/7$ (B)[/tex]

find the arc length of a partial circle

Answers

Answer:

23.55 or [tex]\frac{15}{2}[/tex]π

Step-by-step explanation:

The arc is 75% of the full circumference, as the cut away angle is 90º.

To find the arc length, you multiply the ratio of the whole circle that remains by the circumference: [tex]\frac{270}{360}[/tex]×π×2(5)=[tex]\frac{15}{2}[/tex]π, or 23.55 if you round pi to 3.14.

Answer:

7.85

Step-by-step explanation:

Solve this by using the formula for arc length with central angle in degrees.

Do this by identifying the formula and plugging in the given values. The formula for arc length is [tex]arc length = 2\pi r (\frac{theta}{360} )[/tex] , where the theta is represented by the central angle and r is the radius

The radius is shown on the circle is 5 and the theta (angle in degrees) is 90, represented by the tiny square in the middle.

Plug it all into the formula. Your equation should now look like this: arc length = 2 (3.14 or [tex]\pi[/tex]) (5) ([tex]\frac{90}{360}[/tex])

Solve for arc length and enter your answer as a decimal or in terms of pi

It is known that the highest weekly average price for gasoline in California during 2005 was $3.15 per gallon and the lowest weekly average price for gasoline in California during 2005 was $2.56. Use this information to estimate the standard deviation of the weekly average price for gasoline in California during 2005. The standard deviation is ($3.15-2.56) / 6. I was wondering why you divide by 6?

Answers

Answer:

$0.15

Step-by-step explanation:

To solve this problem, we apply the Range rule for estimating Standard deviation.

By the Range Rule:

Standard Deviation

Highest weekly average price for gasoline= $3.15 per gallon.

Lowest weekly average price for gasoline =$2.56 per gallon.

Therefore:

[tex]\text{Standard Deviation}\approx \dfrac{3.15-2.56}{4} \\=\dfrac{0.59}{4} \\\\=\$0.15 $(correct to the nearest cent).[/tex]

The standard deviation of the weekly average price for gasoline is approximately $0.15.

NOTE: You divide by 4 not 6.

Base of building 180 meters

Answers

Step-by-step explanation:

please give me full question

9. What is the scale factor of the dilation?

Answers

Answer:

D

Step-by-step explanation:

The scale factor is the ratio of the corresponding sides, image to original, that is

scale factor = [tex]\frac{P'S'}{PS}[/tex] = [tex]\frac{6}{3}[/tex] = 2 → D

The Grand canyon national park has a new parking lot.the perimeter is 84feet the shape of the parking lot is a square what is the length of each sides

Answers

Answer:

21 feet

Step-by-step Explanation:

Given that the new parking lot of the Grand Canyon National park has a square shape, which means all the lengths of the 4 sides of the parking lot are equal and the same, the perimeter of the parking lot = 4(L) = 84feet.

L = length of 1 side of the parking lot; perimeter = 84feet,

Therefore, solving for L (length of each side) would be:

84 = 4(L)

84/4 = L

L = 21ft

The length of each sides are all equal and each would be 21 feet long.

Use the GCF and the distributive property to find the expression that is
equivalent to 36 + 60.
18 (2+4)
3(12 + 20)
6(6+10)
12 (3+5)

Answers

Answer:

[tex]D[/tex]

Step-by-step explanation:

[tex]36 + 60[/tex]

[tex]12(3)+12(5)[/tex]

[tex]12(3+5)[/tex]

Answer:

12( 3+5)

Step-by-step explanation:

Five cards are drawn from a standard 52-card playing deck. A gambler has been dealt five cards—two aces, one king, one 3, and one 6. He discards the 3 and the 6 and is dealt two more cards. What is the probability that he ends up with a full house (3 cards of one kind, 2 cards of another kind)? (Round your answer to four decimal places.)

Answers

Answer:

The probability that he ends up with a full house is 0.0083.

Step-by-step explanation:

We are given that a gambler has been dealt five cards—two aces, one king, one 3, and one 6. He discards the 3 and the 6 and is dealt two more cards.

We have to find the probability that he ends up with a full house (3 cards of one kind, 2 cards of another kind).

We know that gambler will end up with a full house in two different ways (knowing that he has given two more cards);

If he is given with two kings.If he is given one king and one ace.

Only in these two situations, he will end up with a full house.

Now, there are three kings and two aces left which means at the time of drawing cards from the deck, the available cards will be 47.

So, the ways in which we can draw two kings from available three kings is given by =  [tex]\frac{^{3}C_2 }{^{47}C_2}[/tex]   {∵ one king is already there}

              =  [tex]\frac{3!}{2! \times 1!}\times \frac{2! \times 45!}{47!}[/tex]           {∵ [tex]^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }

              =  [tex]\frac{3}{1081}[/tex]  =  0.0028

Similarly, the ways in which one king and one ace can be drawn from available 3 kings and 2 aces is given by =  [tex]\frac{^{3}C_1 \times ^{2}C_1 }{^{47}C_2}[/tex]

                                                                   =  [tex]\frac{3!}{1! \times 2!}\times \frac{2!}{1! \times 1!} \times \frac{2! \times 45!}{47!}[/tex]

                                                                   =  [tex]\frac{6}{1081}[/tex]  =  0.0055

Now, probability that he ends up with a full house = [tex]\frac{3}{1081} + \frac{6}{1081}[/tex]

                                                                                    =  [tex]\frac{9}{1081}[/tex] = 0.0083.

Answer:

0.0083

Step-by-step explanation:

The gambler will have full house if he is dealt two kings or ace and a king.Now, there are 47 cards left in the deck and two which are aces and three are king.

The probability of these event are [tex]\frac{3C_2}{47C_2}[/tex]

and  [tex]\frac{3C_1\times 2C_1}{47C_2}[/tex]  respectively. So, the probability of a full house is given as:

[tex]\frac{3C_2}{47C_2}+\frac{3C_1\times 2C_1}{47C_2}[/tex]

=0.0083

After shopping, it took Manuel 87 seconds to push a shopping cart directly to his car. In one-

third of that time, Manuel had moved 58 meters at a constant velocity. What was the cart's

velocity?

Answers

Answer:

The carts velocity= 2m/s

Step-by-step explanation:

It took Manuel 87 seconds to push a shopping cart directly to his car.

One third of 87 = 87/3 = 29

In 29 seconds the carts moved 58 meter's.

The carts velocity = distance/time

The carts velocity = 58/29

The carts velocity= 2m/s

Which of the x-values are solutions to both of the following inequalities? 60 > X and x > 57. Also, Please hurry I will give brainliest to whoever answers 1st.

Answers

Answer:

B

Step-by-step explanation:

x must be a number between 60 and 57 and those numbers are 58 or 59

60 is greater than 59, and 59 is greater than 57

Answer:

x = 59

Step-by-step explanation:

The number must be less than 60 from the first inequality and greater than 57 from the second inequality

so the integers allowed are 58,59

If f(x) = 6x - 4, what is f(x) when x = 8?
2.
16
044
52

Answers

Answer:

44

Step-by-step explanation:

f(x) = 6x - 4

f(8) = 6(8) - 4

f(8) = 48 - 4

f(8)= 44

Out of 25 students taking a midterm psychology exam, 15 answered the first of two bonus questions, 11 answered the second bonus question, and 1 didn't bother with either one. Round your answer to the nearest percent. What percentage of students tried both questions? What percentage tried at least one question?

Answers

Answer:

Percentage of students who tried both questions = [tex]8\%[/tex]

Percentage of students who tried at least one question = [tex]96\%[/tex]

Step-by-step explanation:

Given: 25 students take a midterm psychology exam, 15 answered the first of two bonus questions, 11 answered the second bonus question, and 1 didn't bother with either one.

To find: percentage of students who tried both questions and percentage of students who tried at least one question

Solution:

Let A denotes students who answered the first of two bonus questions and B denotes students who answered the second bonus question.

Let U denotes the universal set denoting students who take a midterm psychology exam.

[tex]n(A)=15\,,\,n(B)=11\,,\,n(U)=25[/tex]

[tex]n\left ( A'\cap B' \right )=1[/tex]

[tex]n\left ( A'\cap B' \right )=n\left ( A\cup B \right )'\\=n(U)-n\left ( A\cup B \right )\\\Rightarrow 1=25-n\left ( A\cup B \right )\\n\left ( A\cup B \right )=25-1=24[/tex]

[tex]n\left ( A\cup B \right )=n(A)+n(B)-n\left ( A\cap B \right )\\24=15+11-n\left ( A\cap B \right )\\n\left ( A\cap B \right )=15+11-24=2[/tex]

Percentage of students who tried both questions = [tex]\frac{2}{25}\times 100=8\%[/tex]

Percentage of students who tried at least one question = [tex]\frac{24}{25}\times 100=96\%[/tex]

You are planning a sample survey that involves selecting 11 of the 100 counties in North Carolina. Your sample will be a stratified sample consisting of the 6 most populous counties in the state and 5 counties randomly selected from the remaining 94 counties. Obtain your stratified sample from the US Census Bureau North Carolina county populations in this Excel file. The Excel worksheet has an alphabetical listing of all 100 North Carolina counties in column A and population estimates for July 1, 2011 and July 1, 2012 in columns D and E, respectively. We will use the population values for July 1, 2012 in column E. To simplify the selection of the 11 counties, we will order the counties according to their July 1, 2012 populations.Order the counties by July 1, 2012 population as follows:
Excel 2003
highlight the cell range A5:E105
in the Excel menu bar click on "Data"; in the drop-down menu click "Sort"
near the bottom of the Sort dialogue box click the radio button next to "Header row"
in the first "Sort by" window choose "2012" and make sure that the "Ascending" radio button is selected
click OK
Excel 2010 and Excel 2007
highlight the cell range A5:E105
Click the "Home" tab at the upper left of the Excel window
at the far right of the menu ribbon click on the "Sort and Filter" icon
In the drop-down menu click on "Custom Sort..."
In the upper right-hand corner of the Sort window make sure the box next to "My data has headers" has a check mark; if it does not have a check mark, click in the box to make a check mark appear.
In the Sort window, under Column, sort by "2012"
In the Sort window, under Sort On, choose "values"
In the Sort window, under Order, choose "A to Z"
Click OKThe counties should now be listed in increasing order according to their July 1, 2012 populations. Tyrell County should be listed first (in row 6) with July 1, 2012 population 4,338.
Question 1. Scroll down to the bottom of the worksheet to see the most populous counties. List below the 6 most populous counties and their populations. List the most populous county first and use commas in your population answers.

Answers

Answer: The answer is given below

Step-by-step explanation:

In statistics, a stratified sampling is a method of sampling that is gotten from a population that can be divided into subpopulations.

Based on th information provided in n the question, the 6 most populous counties and their populations are provided below

Mecklenburg County, North Carolina 969,031

Wake County, North Carolina 952,151

Guilford County, North Carolina 500,879

Forsyth County, North Carolina 358,137

Cumberland County, North Carolina 324,049

Durham County, North Carolina 279,64

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