What is an equivalent expression for (x + 7)(x + 1).

Grant is painting a rectangular board that has a width of į foot. He has enough

andrezito [222]

Answer:

how you convert feet to square feet

length X width = square feet

if the board is 3ft long and 1 foot wide

3ft X 1ft = 3square feet

so the length is 3 feet

7 0

3 years ago

Suppose that a local TV station conducts a survey of a random sample of 120 registered voters in order to predict the winner of

forsale [732]

Answer:

a) The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).

b) The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

Sample of 120 registered voters in order to predict the winner of a local election. The Democrat candidate was favored by 62 of the respondents.

So 120 - 62 = 58 favored the Republican candidate, so:

$n = 120, \pi = \frac{58}{120} = 0.4833$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a p-value of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 - 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.3658$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 + 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.6001$

The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).

b. If a candidate needs a simple majority of the votes to win the election, can the Republican candidate be confident of victory? Justify your response with an appropriate statistical argument.

The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.

8 0

3 years ago

The graph of which function has a minimum located at (4, –3)?

valentinak56 [21]

Answer:

None of the options is the answer to the question

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

$f(x)=a(x-h)^{2}+k$

where

(h,k) is the vertex of the parabola

case A) we have

$f(x)=x^{2}+4x-11$

In this case the x-coordinate of the vertex will be negative

therefore

case A is not the solution

case B) we have

$f(x)=-2x^{2}+16x-35$

This case is a vertical parabola open downward (the vertex is a maximum)

The vertex is the point $(4,-3)$ <u>but is not a minimum</u>

see the attached figure

therefore

case B is not the solution

case C) we have

$f(x)=x^{2}-4x+5$

Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-5=x^{2}-4x$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)-5+4=(x^{2}-4x+4)$

$f(x)-1=(x^{2}-4x+4)$

Rewrite as perfect squares

$f(x)-1=(x-2)^{2}$

$f(x)=(x-2)^{2}+1$ --------> vertex form

The vertex is the point $(2,1)$

therefore

case C is not the solution

case D) we have

$f(x)=2x^{2}-16x+35$

Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-35=2x^{2}-16x$

Factor the leading coefficient

$f(x)-35=2(x^{2}-8x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)-35+32=2(x^{2}-8x+16)$

$f(x)-3=2(x^{2}-8x+16)$

Rewrite as perfect squares

$f(x)-3=2(x-4)^{2}$

$f(x)=2(x-4)^{2}+3$ --------> vertex form

The vertex is the point $(4,3)$

therefore

case D is not the solution

The answer to the question will be the function

$f(x)=2x^{2}-16x+29$

7 0

4 years ago

Read 2 more answers

On Saturday, 1164 people saw a movie at Upcity Theater. There were a total of 4 movie screens with the same number of people in

valkas [14]

1164/4 =291 saw the movie at once

3 0

3 years ago

Read 2 more answers

Find the cosine of L

aleksandr82 [10.1K]

Answer:

0.42

Step-by-step explanation:

use the attached as reference

recall that for a right (90°) triangle, with any acute angle θ,

cos θ = length of adjacent side / length of hypotenuse

in our case, for angle I, the adjacent side is HI = 36 units and the hypotenuse is IJ = 85 units

by the above formula,

cos I = length of adjacent side / length of hypotenuse

= 36 / 85

= 0.42353

= 0.42 (rounded to nearest hundredth)

4 0

3 years ago