A study considered the question, "Are you a registered voter?" Accuracy of response was confirmed by a check of city voting records. Two methods of survey were used: a face-to-face interview and a telephone interview. A random sample of 93 people were asked the voter registration question face to face. Of those sampled, seventy-six respondents gave accurate answers (as verified by city records). Another random sample of 83 people were asked the same question during a telephone interview. Of those sampled,seventy-two respondents gave accurate answers. Assume the samples are representative of the general population.
Let p1 be the population proportion of all people who answer the voter registration question accurately during a face-to-face interview. Let p2 be the population proportion of all people who answer the question accurately during a telephone interview. Find a 95% confidence interval for p1 – p2. (Use 3 decimal places.)

Answer:

When x/9 - 1 = 2, x = 27.

Step-by-step explanation:

x/9 - 1 = 2

Add 1 to both sides.

x/9 = 3

Multiply both sides by 9.

x = 27.

Proof:

x/9 - 1 = 2

Substitute variable.

27/9 - 1 = 2

Divide 27 by 9.

3 - 1 = 2

Subtract 1 from 3.

2 = 2.

Answer:

B. Multiply both sides of the top equation by 3

Step-by-step explanation:

Given:

4x+2y = 4

12x+y = 22

For the equations to have equal x-coefficients, you'll multiply both sides of (1) by 3

4x+2y = 4 (1)

12x+y = 22 (2)

B. Multiply both sides of the top equation by 3

3(4x+2y=4)

We have,

12x+6y=12 (3)

12x+y=22 (2)

Subtract (2) from (3)

5y=12-22

5y=-10

y= -10/5

y=-2

Substitute y=-2 into (1)

4x+2y = 4

4x+2(-2)=4

4x-4=4

4x=4+4

4x=8

x=8/4

x=2

Therefore, y= -2 and x=2

Answer:

its B

Step-by-step explanation:

A pex:)

Answer:

BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB

Step-by-step explanation:

Ok...so we have this........

y = ax2 + 4      ....... and we need to find "a"

So we have

-1 = a(-10)2 + 4

-5 = a (100)

(-1/20) = a      .......  So we have ..........

y = (-1/20)(x- 0)2 + 4   or just  (-1/20)x2 + 4

Note that this parabola opens downward...That makes sense since the vertex is above the x axis and the parabola passes through a point below the x axis.

Hope This Helped!

I couldn't copy paste the equation on here, so i attached it in pictures.

The total area of the spheres are: 5. 952.85 m²; 6. 1,519.76 cm²; 7. 1,231.01 mm²; 8. 791.28 cm²; 9. 235.5 cm²; 10. 94.985 km².

The formula to find the total area of a sphere is:

TA = 4πr², where r is the radius of the sphere.

5. r = 8.71

TA = 4 * 3.14 * 8.71²

Total area = 952.85 m²

6. r = 11

TA = 4 * 3.14 * 11²

Total area = 1,519.76 cm²

7. r = 9.9

TA = 4 * 3.14 * 9.9²

TA = 1,231.01 mm²

8. r = 3√7

TA = 4 * 3.14 * (3√7)²

TA = 791.28 cm²

9. r = 5√13/2

TA = 4 * 3.14 * (5√13/2)²

TA = 235.5 cm²

10. r = 2.75

TA = 4 * 3.14 * 2.75²

TA = 94.985 km²

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3514 1404 393

Answer:

  (d)  8 cm and 9 cm

Step-by-step explanation:

The sum of the short sides must exceed (not equal) the long side. The only proposed measures that do that are ...

  8 cm and 9 cm

Answer:

Step-by-step explanation:

#CARRYONLEARNING

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Answer:

0.60

Step-by-step explanation:

becouse of two probability within added gives the above answer

(a) g'(π/3)  = 12. This can be found using the product rule, which states that the derivative of f(x) g(x) is f'(x) g(x) + f(x) g'(x). In this case, f(x) = sin x and g(x) = f(x), so the product rule gives us: g'(x) = f'(x) g(x) + f(x) g'(x)

Plugging in x = π/3 and using the fact that f(π/3) = 4 and f'(π/3) = −3, we get g'(π/3) = (-3) 4 + 4 g'(π/3)

Solving for g'(π/3), we get g'(π/3) = 12.

(b) h'(π/3)

The h'(π/3) = −3/4, this can be found using the quotient rule, which states that the derivative of f(x)/g(x) is (g'(x) f(x) - f'(x) g(x)) / [g(x)]^2. In this case, f(x) = cos x and g(x) = f(x), so the quotient rule gives us h'(x) = (f'(x) g(x) - f(x) g'(x)) / [g(x)]^2

Plugging in x = π/3 and using the fact that f(π/3) = 4 and f'(π/3) = −3, we get: h'(π/3) = ((-3) 4 - 4 (-3)) / (4)^2 = -3/4

The product rule and quotient rule are two important differentiation rules that can be used to find the derivatives of composite functions. The product rule states that the derivative of f(x) g(x) is f'(x) g(x) + f(x) g'(x). The quotient rule states that the derivative of f(x)/g(x) is (g'(x) f(x) - f'(x) g(x)) / [g(x)]^2.

In this problem, we were given that f(π/3) = 4 and f'(π/3) = −3. We were then asked to find g'(π/3) and h'(π/3). To find g'(π/3), we used the product rule. To find h'(π/3), we used the quotient rule.

The product rule and quotient rule are powerful tools that can be used to find the derivatives of a wide variety of functions. They are essential for anyone who wants to understand calculus.

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                                       "complete question"

Suppose f(π/3) = 4 and f '(π/3) = −3, and let g(x) = f(x) sin x and h(x) = (cos x)/f(x). Find the following.

(a) g'(π/3)

(b) h'(π/3)

The transformation of System A into System B is:

Equation [A2]+ Equation [A 1] → Equation [B 1]"

The correct answer choice is option D

How can we transform System A into System B?

To transform System A into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

System A:

-3x + 4y = -23 [A1]

7x - 2y = -5 [A2]

Multiply equation [A2] by 2

14x - 4y = -10

Add the equation to equation [A1]

14x - 4y = -10

-3x + 4y = -23 [A1]

11x = -33 [B1]

Multiply equation [A2] by 1

7x - 2y = -5 ....[B2]

So therefore, it can be deduced from the step-by-step explanation above that System A is ultimately transformed into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

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Answer:

-3

Step-by-step explanation:

Let the number be x.

x^2 - 21 = 4x

x^2 - 4x - 21 = 0

(x - 7)(x + 3) = 0

x - 7 = 0 or x + 3 = 0

x = 7 or x = -3

Answer: -3

Answer:

-3

Step-by-step explanation:

I got it right

Answer:

Step-by-step explanation:

negative

According to the solving the area of the square is 68.0625.

As is common knowledge, a square is a four-sided, two-dimensional figure. It is also referred to as a quadrilateral. The total quantity of unit squares forming a square is referred to as the square's area. In other words, it is described as the area that the square takes up.

The box formed after cutting the square from each corner will have the dimensions as,

length = 104 - 2x, width = 39 - 2x, height = x.

∴ volume of the box = length × width × height

∴ v = (104 - 2x)(39 - 2x)(x) -----(i)

∴ v = (104 - 2x) (39x - 2\(x^{2}\))

∴ v = 104(39x - 2\(x^{2}\)) -2x(39x - 2\(x^{2}\))

∴ v = 4056x - 208\(x^{2}\) - 78\(x^{2}\) + 4\(x^{3}\)

∴ v = 4\(x^{3}\) - 286\(x^{2}\)  + 4056x

let f(x) =  4\(x^{3}\) - 286\(x^{2}\)  + 4056x  -----(ii)

To, find x for which f(x) is maximum,

⇒we should apply second derivative test ,

According to this test, first we should find critical points at which f'(x) = 0.

then if f''(x) < 0 for that critical point then f(x) is maximum at that critical point.

∴ let us consider, f'(x) = 0.

now, f(x) =  4\(x^{3}\) - 286\(x^{2}\)  + 4056x

⇒ f'(x) = 12\(x^{2}\) - 572x + 4056.  -----(iii)

⇒ f'(x) = 4(3\(x^{2}\) - 143x + 1014)

⇒ f'(x) = 0.

⇒  f'(x) = 4(3\(x^{2}\) - 143x + 1014) = 0

⇒ x = (-b ± \(\sqrt{b^{2} - 4ac }\))/2a    ; where a = 3, b = -143, c = 1014.

∴ x = (-(-143) ± \(\sqrt{(-143)^{2} -4(3)(1014)}\))/2×3

∴ x = (143 ± \(\sqrt{8281}\))/6.

∴ x = \(\frac{143 + 91}{6}\)  , x = \(\frac{143 - 91}{6}\)

⇒ x = 39, 8.25

the square of length 8.25 inch should be cut from each side to det contained with the maximum volume.

Area of the square is = \(x^{2}\) = \(8.25^{2}\)

∴ Area = 68.0625

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Answer:

y = 19

Step-by-step explanation:

2y + 2 + 20° = 60 because the sum of interior angles in a triangle is equal to 180°

2y + 22 = 60

2y = 38 divide both sides by 2

y = 19

Answer:

142 506

Step-by-step explanation:

here the order does not matter

Then

we the number of sets is equal to the number of combinations.

Using the formula :

the number of sets is 30C5

\(C{}^{5}_{30}=\frac{30!}{5!\left( 30-5\right) !}\)

      \(=142506\)

There are 142506 ways in which 5 students can be selected out of 30 students.

The selection of 5 students out of 30 students can be achieved with the use of combination since the order of selection is not required to be put into consideration.

By using the formula:

\(\mathbf{^nC_r = \dfrac{n!}{r!(n-r)!}}\)

where;

\(\mathbf{^nC_r = \dfrac{30!}{5!(30-5)!}}\)

\(\mathbf{^nC_r = \dfrac{30!}{5!(25)!}}\)

\(\mathbf{^nC_r = 142506}\)

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Answer:  \(9\sqrt{15}\)

Work Shown:

\(x = 3\sqrt{135}\\\\x = 3\sqrt{9*15}\\\\x = 3\sqrt{9}*\sqrt{15}\\\\x = 3*3*\sqrt{15}\\\\x = 9\sqrt{15}\\\\\)

In the second step, I factored 135 into 9*15 so that I could pull out the perfect square 9. This is the largest perfect square factor of 135. In the next step, I used the rule \(\sqrt{A*B}=\sqrt{A}*\sqrt{B}\\\\\)

Answer:

D- 3 (3) StartRoot 5 (3) EndRoot = 9 StartRoot 15 EndRoot

Answer:

that is the simplest form

Step-by-step explanation:

We are required to express the ratio below in its simplest form. 1 : 1.5

Given:

1 : 1.5

= 1 ÷ 1.5

= 1 / 1.5

The ratio is already in it's simplest form. We can only find an equivalent form of the ratio

Equivalent of 1 : 1.5

2 : 3

4 : 6

6 : 9

8 : 12

10 : 15

Therefore, the ratio 1 : 1.5 is already in it's simplest form

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The probability of guessing the correct answer for each question is 1/4, while the probability of guessing incorrectly is 3/4.

To calculate the probability of answering at most one correct answer, we need to consider two cases: answering zero correct answers and answering one correct answer.

For the case of answering zero correct answers, the probability can be calculated as (3/4)^5, as there are five independent attempts to answer incorrectly.

For the case of answering one correct answer, we have to consider the probability of guessing the correct answer on one question and incorrectly guessing the rest. Since there are five questions, the probability for this case is 5 * (1/4) * (3/4)^4.

To obtain the probability of answering at most one correct answer, we sum up the probabilities of the two cases:

Probability = (3/4)^5 + 5 * (1/4) * (3/4)^4.

Therefore, by calculating this expression, you can determine the probability of answering at most one correct answer among five questions when guessing randomly.

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Answer:

6%- 457 Million

Step-by-step explanation:

w=241(1.06)^11=457 million

We can say that the value of k will be equal to the y-coordinate of the center of the circle (since k represents the y-coordinate of the center).

To answer this question, we need to use the equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

Where h and k represent the coordinates of the center of the circle, and r represents the radius. In this case, we are given that the circle has center (h, k) and radius 10. So we can write:

(x - h)^2 + (y - k)^2 = 10^2

We are asked to find the value of k. To do this, we need to look at the equation of the circle and notice that the y-coordinate is paired with k. This means that we can isolate k by rearranging the equation as follows:

(y - k)^2 = 10^2 - (x - h)^2

y - k = ±√(10^2 - (x - h)^2)

k = y ±√(10^2 - (x - h)^2)

Since we don't have any information about the x-coordinate, we can't solve for a specific value of k. However, we can say that the value of k will be equal to the y-coordinate of the center of the circle (since k represents the y-coordinate of the center). Therefore, the answer is:

k = y

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Answer:

4/5 is the slope

Step-by-step explanation:

The line is written in the form

y = mx+b where m is the slope and b is the y intercept

y = 4/5x -3

4/5 is the slope and -3 is the y intercept

Answer:

7 6

Step-by-step explanation:

Answer:

i think it 7 6

Step-by-step explanation:

There are 2300 workers in all in the company.

Let the number of all workers in company be = 100x

95% workers are female then (100-95) = 5% of workers are not female.

So, the number of workers who are not female = 5x

According to the condition, the suitable equation is

5x = 115

x = 115/5

x = 23

So, the total number of workers in the company is = 100*23 = 2300.

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Answer:

$1,489.88 (nearest cent)

Step-by-step explanation:

To calculate gross pay, multiply the number of hours worked by the pay per hour.

Warren worked 36.5 hours one week and 32 hours the week before.

Therefore, the total number of hours Warren worked was:

Multiply the total number of hours worked by Warren's rate of pay of $21.75 per hour:

Therefore, Warren's gross pay for the two weeks was $1,489.88 (nearest cent).

Answer:

$1489.875

Step-by-step explanation:

Warren's gross pay for 36.5 hours last week can be calculated as follows:

Gross pay for 36.5 hours = $21.75/hour * 36.5 hours = $793.875

Similarly, Warren's gross pay for 32 hours the week before can be calculated as follows:

Gross pay for 32 hours = $21.75/hour * 32 hours = $696

Adding the gross pay for the two weeks, we get:

Gross pay for 2 weeks = $793.875 + $696 = $1489.875

The value of the place occupied by the digit 2 (hundreds place) is 10 times greater than the value of the place occupied by the digit 5 (thousandths place).

To determine the value of the place occupied by the digit 2 compared to the value of the place occupied by the digit 5 in the number 823.4956, we need to examine the place value of each digit.

In the given number, 823.4956, the digit 2 is in the hundreds place, while the digit 5 is in the thousandths place.

The place value of a digit is determined by its position relative to the decimal point. Moving one place to the left or right of the decimal point represents a tenfold increase or decrease in value, respectively.

Therefore, the value of the place occupied by the digit 2 (hundreds place) is 10 times greater than the value of the place occupied by the digit 5 (thousandths place).

In other words, the digit 2 represents a value that is 10 times greater than the value represented by the digit 5 in the given number.

Hence, the value of the place occupied by the digit 2 is 10 times as great as the value of the place occupied by the digit 5.

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Lowes Depot uses a (Q, R) policy to manage its stock levels for a popular mini drill with a replacement lead time of 14 weeks. Historical demand during the replacement lead time is normally distributed with a mean of 90.4616 and a standard deviation of 14.3795. Each drill costs $6, and backorders result in a loss of goodwill of $10. The supplier charges $15 per order, and holding costs are based on a 30% annual interest rate.

To determine the optimal order quantity Q and reorder point R, we need to use the (Q, R) policy. The policy specifies that when the inventory level reaches the reorder point R, an order of size Q is placed. We need to determine Q and R such that the total annual cost is minimized.

The total annual cost consists of three components: ordering costs, holding costs, and shortage costs. Ordering costs are the costs associated with placing an order, which is given by (number of orders per year) x (ordering cost per order). The number of orders per year is the annual demand divided by the order quantity, which is Q. The ordering cost per order is $15. Therefore, the ordering cost is 15 X (Demand rate/Q).

Holding costs are the costs associated with holding inventory, which is given by (inventory level) x (holding cost per unit per year). The holding cost per unit per year is 30% of the unit cost, which is 0.3 x $6 = $1.8.

Shortage costs are the costs associated with backordering, which is given by (expected shortage per year) x (shortage cost per unit). The expected shortage per year is the probability of a stockout during the lead time multiplied by the expected demand

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Answer:

8.2

Step-by-step explanation:

-7.2 to -7.2 is 0

-9.3 to -1.1 is 8.2

Pythagorean theorem is a^2+b^2=c^2

0^2=0

8.2^2=67.24

0+67.24=0

√67.24=8.2

The distance between the to points is 8.2

To evaluate the integral ∫2 tan^3(x) sec(x) dx, we can use the substitution method and trigonometric identities. By making suitable substitutions and applying trigonometric identities, we can simplify the integral and find its antiderivative.

Let's start by making the substitution u = tan(x). This substitution helps simplify the expression involving tangent and secant functions.

Differentiating both sides with respect to x, we get du/dx = sec^2(x).

Rearranging the equation, we have dx = du/sec^2(x).

Now, let's substitute the values in the integral:

∫2 tan^3(x) sec(x) dx = ∫2 u^3 du/sec^2(x)

                     = ∫2 u^3 du/(1 + tan^2(x))

Using the identity 1 + tan^2(x) = sec^2(x), we can simplify further:

∫2 u^3 du/(1 + tan^2(x)) = ∫2 u^3 du/sec^2(x)

                         = ∫2 u^3 du/((1 + u^2)/1)

                         = ∫2 u^3 du/(1 + u^2)

Integrating with respect to u, we have:

= (1/4) u^4 + C

= (1/4) tan^4(x) + C

Therefore, the antiderivative of 2 tan^3(x) sec(x) dx is (1/4) tan^4(x) + C, where C is the constant of integration.

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