A library association plans to take an SRS of 150150150 adults from the population of adults in the US to see what proportion of adults sampled believe that public libraries help them learn new things. Suppose that 76\vv, percent of adults in the US believe that public libraries help them learn new things. What are the mean and standard deviation of the sampling distribution of the proportion of US adults who believe that public libraries help them learn new things

Answer:

Equation 1:   x + 3y = 17

Equation 2:  -x + 2y = 8

Add Equation 2 to Equation 1:

     x + 3y = 17

+   -x + 2y = 8

           5y = 25

Divide both sides by 5:

\(\sf \implies \dfrac{5y}{5}=\dfrac{25}{5}\)

\(\sf \implies y=5\)

Answer:Q = 26(52-26) = 26*26 = 676

Step-by-step explanation:

Answer:

Domain: (-∞, -4) U (-4,∞)

range: (0,∞)

The possible rectangle's length and width are A) 1 cm and 15 cm and C) 3 cm and 5 cm

The given parameters are

Area = 15 square cm

The area is given as

Area = 15 square cm

The formula of area is

Area = Length x Width

Using the above formula, we have:

A) 1 cm and 15 cm ⇒ 15 square cm

B) 2 cm and 7 cm ⇒ 14 square cm

C) 3 cm and 5 cm ⇒ 15 square cm

D) 4 cm and 4 cm ⇒ 16 square cm

Hence, the possible rectangle's length and width are A) 1 cm and 15 cm and C) 3 cm and 5 cm

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Possible question

The area of a rectangle is 15 square cm

Which of the following could be the rectangle's length and width?

(Area = length x width)

Choose all answers that apply:

A) 1 cm and 15 cm

B) 2 cm and 7 cm

C) 3 cm and 5 cm

D) 4 cm and 4 cm

Answer: Domain x<7 Range y<0 In this case I think it would be D

Step-by-step explanation: The domain is x<7 and the range is y<0

54 grams of aluminium is present in aluminium sulphate Al₂(SO₄)₃.

A substance's molecular mass is the sum of the atomic masses of all of the atoms in the molecule of a substance.

For the given question, the expression is;

aluminium sulphate Al₂(SO₄)₃

As three of aluminium is present in the aluminium sulphate.

And, molecular mass of one aluminium atom is 27 grams;

Thus, for 2 aluminium atoms = 2×27 = 54  grams.

Therefore, the compound aluminium sulphate contains 54 gram of aluminium in it.

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M = 270,000 * (0.5833% * (1 + 0.5833%)^240) / ((1 + 0.5833%)^240 - 1).  Calculating this equation will give us the monthly mortgage payment for Abigail and Curtis Siebert.

Abigail and Curtis Siebert have a $270,000 mortgage at an interest rate of 7% for a term of 20 years.

To calculate the monthly mortgage payment, we can use the formula for an amortizing mortgage:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1),

where M is the monthly mortgage payment, P is the principal amount (loan amount), r is the monthly interest rate, and n is the total number of monthly payments.

First, we need to convert the annual interest rate to a monthly interest rate. Since there are 12 months in a year, the monthly interest rate is 7% divided by 12, which is approximately 0.5833%.

The total number of monthly payments is the term of the mortgage multiplied by 12. In this case, it's 20 years * 12 months, which equals 240 months.

Now, we can substitute the values into the formula:

M = 270,000 * (0.5833% * (1 + 0.5833%)^240) / ((1 + 0.5833%)^240 - 1).

Calculating this equation will give us the monthly mortgage payment for Abigail and Curtis Siebert.

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The volume of the cone is 314cm³

A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex, to all the points of a circular base(which does not contain the apex). The distance from the vertex of the cone to the base is the height of the cone.

The volume of the cone is 1/3πr²h

h²= 13²-5²

h = √169 - 25

h = √144

h = 12 cm

V = 1/3πr²h

V = 1/3 ×3.14 × 5² × 12

V = 942/3

V = 314 cm³

therefore the volume of the cone is 314cm³

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A multiplication equation to show an equivalent fraction of 15 using fifteenths would gives 10/75

A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.

We have to write an equivalent fraction of 15 using fifteenths.

2/15

So let multiply by 5 .

2 / 15 x  5/ 5 = 10/75

Thus, 10/75 is equivalent expression.

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Answer:

4,7025 (kJ).

Step-by-step explanation:

1) according to the condition: m=25 gr.; t₂=90; t₁=45; c=4.18 J/(g°C);

2) the formula of required heat is

Q=c*m*(t₂- t₁);

3) according to the formula of heat:

Q=4.18*25*45=4702.5 (J).

Answer:

First option pays $480.60 in interest and the second option pays $442.84 in interest

Step-by-step explanation:

Answer:

In mathematics, the extrema of a function refer to the maximum and minimum values that the function can take on. These values can be local extrema, which occur within a certain range of the function, or global extrema, which are the maximum and minimum values over the entire domain of the function.

To find the extrema of a function, one can use a variety of techniques, such as taking the derivative of the function and setting it equal to zero to find the points of stationary values, or using the second derivative test to determine whether a stationary point is a local maximum or minimum.

Interpreting the extrema of a function can provide valuable information about the behavior of the function. For example, the global maximum of a function might represent the highest possible value that the function can attain, while the global minimum might represent the lowest possible value. Local extrema can also be important, as they can indicate changes in the slope or concavity of the function, which can have important implications for applications such as optimization or modeling real-world phenomena.

The statement that correctly compares the centers of the distributions is this:

D. The mean of East Hills HS is greater than the mean of Southview HS.

Since, The statement that correctly describes the centers of the distributions is option D. To find out, we will calculate the mean of the two distributions as follows:

For East Hills HS

25 * 1 + 29 * 1 + 31 * 2 + 33 * 4 + 35 * 5 + 37 * 8 + 39 * 4

= 875

And, Frequency = 1 + 1 + 2 + 4 + 5 + 8 + 4 = 25

Hence,

Mean = 875/25

Mean = 35

For Southview

25 * 2 + 27 * 6 + 29 * 9 + 31 * 6 + 33 * 2

= 725

Frequency = 2 + 6 + 9 + 6 + 2 =25

Hence, Mean = 29

So, from our calculation, the mean of East Hills HS is greater than the mean of Southview HS.

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Answer:  36

Step-by-step explanation: If the coach wants to divide the team by the ratio of 1 to 3, then we will take 48 and divide by 4.

This leaves us with 12 x 4 = 48. Then we calculate 48 - 12 = 36

Now you have your 1 to 3 ratio with the teams being split into team 1 with 12 and team 2 with 36.

Answer:

The answer is 20

Step-by-step explanation:

Now, we know that their ages are consecutive integers.

Let their ages be (x), (x + 1), (x + 2) and (x + 3). Where, Mariana's age is x.

Here, The sum of their ages is 86.

(x) + (x + 1) + (x + 2) + (x + 3) = 86

x + x + 1 + x + 2 + x + 3 = 86

4x + 6 = 86

4x + 6 – 6 = 86 – 6

4x = 80

4x/4 = 80/4

x = 20

We assumed that Mariana's age is x and the value of x is 20.

Thus, The age of Mariana is 20.

Using the binomial distribution, it is found that there is a 0.0008 = 0.08% probability that she will get a passing score.

For each question, there are only two possible outcomes, either she answers it correctly, or she does not. The probability of answering a question correctly is independent of any other question, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

A passing score is at least 13 correct, thus, the probability is:

\(P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18)\)

Then

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 13) = C_{18,13}.(0.3333)^{13}.(0.6667)^{5} = 0.0007\)

\(P(X = 14) = C_{18,14}.(0.3333)^{14}.(0.6667)^{4} = 0.0001\)

The others, until P(X = 18), will be approximately 0, thus:

\(P(X \geq 13) = P(X = 13) + P(X = 14) = 0.0007 + 0.0001 = 0.0008\)

0.0008 = 0.08% probability that she will get a passing score.

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The average profit of this group is B. -$100.

The average represents the total profits and losses generated by the group of friends, divided by the number in the group.

The average is the data set's mean after performing the mathematical operations of addition and division on the data values.

Friends    Profits

A                $120

B              -$230

C               $670

D              -$1020

E               $250

F               -$430

G               -$60

Total      -$700

Average profit = -$100 (-$700/7)

Thus, we can conclude that the friends generated an average profit of B. -$100 from gambling or a total loss of $700.

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Answer:

The length of AB is 18

Step-by-step explanation:

Do the pygotham theorem

24^2 + 7^2 = 625

Square root the answer

\(\sqrt{625}\) = 25

Line BO equals 7 because CO is 7 and they are both radiuses

Subtract the answer to the length BO

25 - 7 = 18

18 is the length of AB bro

It would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

To calculate the time it would take to drive from Statesville, NC to Washington, DC, we can divide the distance of 389 miles by the average speed of 65 mph.

Time = Distance / Speed

Time = 389 miles / 65 mph

Time ≈ 5.98 hours

Therefore, it would take approximately 5.98 hours to drive from Statesville, NC to Washington, DC on interstates with an average speed of 65 mph.

To calculate the cost of driving to Washington, DC, we need to know the number of gallons of gas required for the trip. We can find this by dividing the distance by the car's mileage, which is 29 miles per gallon.

Number of gallons = Distance / Mileage

Number of gallons = 389 miles / 29 miles per gallon

Number of gallons ≈ 13.41 gallons

The cost of gas can be calculated by multiplying the number of gallons by the cost per gallon, which is $3.89.

Cost = Number of gallons * Cost per gallon

Cost ≈ 13.41 gallons * $3.89/gallon

Cost ≈ $52.18

Therefore, it would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

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Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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The girl which is correct between kate and her friend Margo is Margo.

The correct answer option is option B

If each friend gets the same number of pens;

Number of pens each friend get = Number of pens Kate has / Number of Kate's friends

= 63 / 9

= 7

Check:

Number of pens each friend get × Number of Kate's friends = Number of pens Kate has

7 × 9 = 63

Therefore, Kate's friend, Margo is correct.

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Using L'hopital we can see that the limit is equal to 1/22

Here we want to take the limit of x tending to zero for x/sin(22x)

Notice that when x = 0, both numerator and denominator are zero, so we need to take the limit of the first derivatives, for:

y = x

y' = 1

And for:

y = sin(22x)

y' = 22*cos(22x)

Now taking the limit we will get:

\(\lim_{x \to 0} \frac{1}{22cos(22x)} = \frac{1}{22cos(0)} = 1/22\)

That is the value of the limit.

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Answer:

50

Step-by-step explanation:

40 plus 90 equals 130 and triangle must be 180 so we need 50 degree

50°

Let x be the missing angle.

90°(right angle) + 40°(given) + x = 180° ( the sum of degrees of interior angles of triangle)

x = 180°-130°

x = 50°

The equation of the possible way to begin solving for x is 2/5x - 7/20x = 3/4 - 1/2

From the question, we have the following parameters that can be used in our computation:

-3/4 + 2/5x = 7/20x -1/2

The first step is to collect the like terms

So, we have

2/5x - 7/20x = 3/4 - 1/2

This represents an equation of the possible way to begin solving for x

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The only possible value of "a" that satisfies the given equations is a = 5.

The possible values of "a" that satisfy the given equations, let's solve the system of equations:

a + ab = 250 ---(1)

a - ab = -240 ---(2)

We can solve this system by using the method of substitution. Rearranging equation (2), we get:

a = ab - 240 ---(3)

Substituting equation (3) into equation (1), we have:

(ab - 240) + ab = 250

2ab - 240 = 250

2ab = 250 + 240

2ab = 490

ab = 490/2

ab = 245

Now we have the value of "ab."

We can substitute this back into equation (3) to solve for "a":

a = (245) - 240

a = 5

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Answer:

Step-by-step explanation:

x=shirt

y=pants

a) First week 4x+3y=85.50

b)3x+5y=115.00

C)

D) This point represent when the price is the same but the number of shirt are different for the first and second week.

Part#1: 425L + 125S ≥ 4500 (David wants to earn at least $4500)

Part#2: David can reach his goal of making at least $4500 by selling 8 laptops and 10 smartphones.

Part#3: The maximum number of smartphones he can sell is 18 - 1 = 17, and the minimum number of smartphones he needs to sell is 18 - 8 = 10

What is linear inequalities?

Linear inequalities are used to model the constraints on the number of devices that can be sold (L + S ≤ 18, L ≥ 0, and S ≥ 0) and the minimum amount of money that must be earned (425L + 125S ≥ 4500).

Part #1:

Let L be the number of laptops sold and S be the number of smartphones sold.

To represent the number of laptops L and smartphones S that David can sell, we have the following inequalities:

L + S ≤ 18 (David can sell up to 18 devices)

L ≥ 0 (The number of laptops sold cannot be negative)

S ≥ 0 (The number of smartphones sold cannot be negative)

To represent the amount of money David can earn, we have the following inequality:

425L + 125S ≥ 4500 (David wants to earn at least $4500)

Part #2:

If David sells 8 laptops, he has 10 devices left to sell (18 - 8 = 10). Let's assume he sells all of these devices as smartphones. Then, the total amount he earns from the smartphones would be:

125 x 10 = 1250

The total amount he earns from the laptops and smartphones would be:

425 x 8 + 125 x 10 = 3400 + 1250 = 4650

Hence, he can reach his goal of making at least $4500 by selling 8 laptops and 10 smartphones.

Part #3:

If David sells only smartphones, the maximum number he can sell is given by the inequality:

125S ≥ 4500

S ≥ 36

So, David needs to sell at least 36 smartphones to reach his goal of making at least $4500. However, he cannot sell more than 18 devices, so he needs to sell a combination of laptops and smartphones that adds up to 18 devices.

Let's assume he sells x laptops and (18 - x) smartphones. Then, the total amount he earns from the laptops and smartphones would be:

425x + 125(18 - x) = 2125x + 2250

To earn at least $4500, we need:

2125x + 2250 ≥ 4500

2125x ≥ 2250

x ≥ 1.06

Since x represents the number of laptops sold, David can sell at most 1 laptop (since he can only sell whole numbers of laptops), and the remaining devices must be smartphones.

Hence, the maximum number of smartphones he can sell is 18 - 1 = 17, and the minimum number of smartphones he needs to sell is 18 - 8 = 10 (as found in part #2).

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