A controversial bill is being debated in the state legislature. Representative Williams wants to estimate within 2 percentage points and with 95% confidence the difference in the proportion of her male and female constituents who favor the bill. What sample size should she obtain?

Answer: 57

Step-by-step explanation:

Given: a is a multiple of 456

Let [tex]a = 456 x[/tex]

Then, expression [tex]3a^3+a^2+4a+57 =3(456x)^3+(456x)^2+4(456x)+57[/tex]

Since 456 = 57 x 8

Then, [tex]3(456x)^3+(456x)^2+4(456x)+57=3(57\times 8x)^3+(57\times 8x)^2+4(57\times 8x)+57[/tex]

[tex]=3(57)^3\times (8x)^3+(57)^2\times (8x)^2+4(57)\times (8x)+57[/tex]

Taking 57 out as common

[tex]=57[3(57)^2\times (8x)^3+(57)\times (8x)^2+4\times (8x)+1][/tex]

Now, the greatest common divisor of [tex]a = 456 x[/tex] and [tex]3a^3+a^2+4a+57=57[3(57)^2\times (8x)^3+(57)\times (8x)^2+4\times (8x)+1][/tex] is 57.

Hence, the greatest common divisor of 3a^3+a^2+4a+57 and a is 57.

Answer:

[tex]\huge\boxed{x+y=-2}[/tex]

Step-by-step explanation:

The standard form of an equation of a line:

[tex]Ax+By=C[/tex]

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

where

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have two points (-2, 0) and (1, -3).

Substitute:

[tex]x_1=-2;\ y_1=0;\ x_2=1;\ y_2=-3[/tex]

[tex]m=\dfrac{-3-0}{1-(-2)}=\dfrac{-3}{1+2}=\dfrac{-3}{3}=-1\\\\y-0=-1(x-(-2))\\\\y=-(x+2)[/tex]

[tex]y=-x-2[/tex]         add x to both sides

[tex]x+y=-2[/tex]

Answer:

Hey there!

(2x+1)(x+1)

2x^2+1x+2x+1

2x^2+3x+1

The answer would be A.

Let me know if this helps :)

Answer:

The mean, variance, and standard deviation of the binomial distribution are 10, 8, and 2.83 respectively.

Step-by-step explanation:

We have to find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p, i.e; n = 50 p = 0.2.

Let X = binomial random variable

So, X ~ Binom(n = 50, p = 0.2)

Now, the mean of the binomial distribution is given by;

         Mean of X, E(X) = n [tex]\times[/tex] p

                                    = 50 [tex]\times[/tex] 0.2 = 10

Now, the variance of the binomial distribution is given by;

        Variance of X, V(X) = n [tex]\times[/tex] p [tex]\times[/tex] (1 - p)

                                         = 50 [tex]\times[/tex] 0.2 [tex]\times[/tex] (1 - 0.2)

                                         = 10 [tex]\times[/tex] 0.8 = 8

Also, the standard deviation of the binomial distribution is given by;

        Standard deviation of X, S.D.(X) = [tex]\sqrt{\text{n} \times \text{p} \times (1 - \text{p})}[/tex]

                                                              = [tex]\sqrt{\text{50} \times \text{0.2} \times (1 - \text{0.2})}[/tex]

                                                              = [tex]\sqrt{8}[/tex] = 2.83

Answer:

Total hours that Jenny ran = 3.63 hours.

Step-by-step explanation:

Jenny ran on Tuesday for = 2/5 hours or 0.4 hours.

Time consumed to run on Thursday = 11/6 hours or 1.83 hours.

Time consumed to run on Saturday = 21/ 15 hours or 1.4 hours.

Here, the total hours can be calculated by just adding all the running hours. So the running hours of Tuesday, Thursday, and Saturday will be added to find the total hours.

Total hours that Jenny ran = 0.4 + 1.83 + 1.4 = 3.63 hours.

Answer:

14.13 cubic feet of lake water can fill the given balloon.

Step-by-step explanation:

concept used:

volume of sphere = 4/3 [tex]\pi r^3[/tex]

where r is the radius of sphere

we take [tex]\pi[/tex] = 3.14

_____________________________________

shape of balloon can be taken as spherical.

Amount water filled in the balloon will be equal to capacity of balloon which is equal to volume of spherical balloon.

Given radius of balloon = 1.5 feet

Thus, volume of balloon = 4/3 [tex]\pi[/tex] 1.5^3 = 4/3*3.14*1.5^3

volume of balloon = 42.39/3 = 14.13 cubic feet

Thus, 14.13 cubic feet of lake water can fill the given balloon.

Answer:

12

Step-by-step explanation:

Perimeter of a square:

4(L)

L = Length

=> 4(L) = 48

=> 4L = 48

=> 4L/4 = 48/4

=> L = 12

The length of the square is 12 cm.

Answer:

12

Step-by-step explanation:

Since the lengths of the sides of a square are equal, divide the perimeter by 4

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          Hi my lil bunny!

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When dividing polynomials using factorization, cancelling identical factors in the denominator and the numerator will give the remainder.

A. remainder

B. dividend

C. quotient

D. divisor

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

a. remainder

Step-by-step explanation:

took the test

dont leave your house without a vest

or you will get hit in the vital organs in your chest

Answer:

40.5

Step-by-step explanation:

diameter^2 = (3 +6)^2 + (5+4)^2

or, d^2 = 9^2 + 9^2

or, d^2 = 81 +81

or,d^2 =162

or d=√ 162

• d= 81

then radius = d/2

r = 81/2

•r= 40.5 ans

Answer: a. 0.4 × 0.15 = 0.060

Step-by-step explanation: Probability of the complement of an event is the one that is not part of the event.

For P(A):

P(A') = 1 - 0.6

P(A') = 0.4

For P(B):

P(B') = 1 - 0.85

P(B') = 0.15

To determine probability of A' and B':

P(A' and B') = P(A')*P(B')

P(A' and B') = 0.4*0.15

P(A' and B') = 0.06

Probability of the complement of the event is 0.060

Answer:

The average score of 6 tests is 19.

Step-by-step explanation:

Given that the average score of 5 tests is 18. So first, we have to find the total number of scores for 5 tests :

[tex]let \: x = total \: no. \: of \: scores[/tex]

[tex] \frac{x}{5} = 18[/tex]

[tex]x = 18 \times 5[/tex]

[tex]x = 90[/tex]

We have found out that the total scores for 5 tests is 90. So we have to find the average of 6 scores :

[tex] \frac{x + 24}{5 + 1} = \frac{90 + 24}{6} = \frac{114}{6} = 19[/tex]

[tex] \LARGE{ \boxed{ \rm{ \pink{Solution : )}}}}[/tex]

We need to know how to find the average

☄ For this case, We are gonna find average score...!

[tex] \large{ \boxed{ \sf{Avg. \: score = \frac{Total \: score}{No. \: of \: tests} }}}[/tex]

So, Let's proceed further towards solution....

We have,

Finding total score in 5 tests,

⇛ Total score = Avg. score × No. of tests

⇛ Total score = 18 × 5

⇛ Total score = 90

According to question,

⇛ Total score now = 90 + 24 = 114

Finding the average score of 6 tests,

⇛ Avg. score = 114 / 6

⇛ Avg. score = 19 points

☄ Avg. score of lynette in 6 tests = 19

━━━━━━━━━━━━━━━━━━━━

Answer:

.02

Step-by-step explanation:

2 is in "Hundredths' place in .826

So, the number is multiplied with 1/100 or .01

=> 2 x 1/100

=> 2/100

=> .02

=> 2 x .01

=> .02

The value of 2 in .826 is .02

Answer:

2.8 < x < 5.4

Step-by-step explanation:

Given the triangle with two known sides, 4.1 and 1.3, the range of possible values of the third side, x, can be ascertained by considering the triangle inequality theorem.

According to the theorem, when you add any two of the angles in a triangle, it should give you a value greater than the third side.

If a, b, and c are 3 sides of a triangle, the theorem implies that:

a + b > c.

Therefore, a - b < c < a + b

We can use this logic to find the possibly values of x in the given triangle above.

Thus,

4.1 - 1.3 < x < 4.1 + 1.3

2.8 < x < 5.4

Range of possible sizes of x is 2.8 < x < 5.4

Answer:18.5

Step-by-step explanation:

10+8=18

18*5=90

90/4

22.5-4=18.5

Answer:

shown below..I can't see..

Answer:

93.5 for area

Step-by-step explanation:

there is no picture so that's  a simple guess

Complete Question

I = prt is an example of

• a variable

• an expression

• a constant

• a formula

Answer:

A formula

Step-by-step explanation:

I = prt is an example of a formula called Simple Interest.

Simple Interest can be defined as the formula that is used to calculate the interest that is accumulated on a particular amount of money which was saved in a financial institution or loaned out to a person at a given interest rate for a particular period of time.

The formula for Simple Interest is Expressed as:

I = PRT

Where :

I = Simple Interest

P = Principal = Amount saved, or loaned out

R = Interest rate that is given in percentage form

T = Time that has elapsed in Years.

Answer:

D. A Formula

Step-by-step explanation:

A formula is an equation that uses variables to state a rule.

Hope I was able to help you!

Answer :

[tex] \frac{2 {x}^{3} + 7 {x}^{2} + 3x - 4}{ {x}^{3} + 3 {x}^{2} + x - 1} [/tex]

Step-by-step-explanation :

I did the explanation in the picture.

Answer:

b = -9.

Step-by-step explanation:

The line passes through (4, 3) and (7, 12). First, we need to find the slope: the rise over the run.

(12 - 3) / (7 - 4) = 9 / 3 = 3.

Now that we have the slope, we can say that m = 3. So, we have an equation of y = 3x + b. To find b, we can use M(4, 3) and say that y = 3 and x = 4.

3 = 3 * 4 + b

b + 12 = 3

b = -9.

Hope this helps!

The value of b in the equation is -9

The points are given as:

M(4, 3) and N(7, 12)

The equation is then calculated using:

[tex]y = \frac{y_2 -y_1}{x_2 -x_1} * (x - x_1) + y_1[/tex]

This gives

[tex]y = \frac{12 -3}{7 -4} * (x - 4) + 3[/tex]

Evaluate the quotient

y = 3 * (x - 4) + 3

Open the bracket

y = 3x - 12 + 3

Evaluate the difference

y = 3x - 9

Hence, the value of b is -9

Read more about linear equations at:

https://brainly.com/question/14323743

#SPJ9

Here is the complete question:

a. Statistically significant at 0.01

b. Not statistically significant

Answer:

The test is significant

Step-by-step explanation:

When a p value is smaller than or less than alpha we say it is statistically significant.

We are testing the p value or likelihood of 0005 against a significant level of 0.01

P value = 0.005 < 0.01

0.005 is less than 0.01 which shows the test to be significant.

The decision rule would be to reject the null hypothesis and say the result is statistically significant.

Answer:

67.5p.

Step-by-step explanation:

315p in total.

- Baseball has 55p.

- Soccer teams points = 55x2 = 110p.

-  Football team points = 110 x 0.5 = 55 x 1.5 = 82.5p.

So then you just do 315p - 82.5p - 55p - 110p = 67.5p

Answer:

Step-by-step explanation:

The summary of the statistics given include:

population mean [tex]\mu[/tex] = 15

sample mean [tex]\oerline x[/tex] = 13.5

sample size n = 16

standard deviation s = 6

The level of significance ∝ = 0.10

The  null and the alternative hypothesis can be computed as follows:

[tex]\mathtt{H_o: \mu = 15} \\ \\ \mathtt{H_1 : \mu \neq 15}[/tex]

Since this test is two tailed, the t- test can be calculated by using the formula:

[tex]t = \dfrac{\overline x - \mu}{\dfrac{\sigma }{\sqrt{n}}}[/tex]

[tex]t = \dfrac{13.5 - 15}{\dfrac{6}{\sqrt{16}}}[/tex]

[tex]t = \dfrac{- 1.5}{\dfrac{6}{4}}[/tex]

[tex]t = \dfrac{- 1.5\times 4}{6}}[/tex]

[tex]t = \dfrac{- 6.0}{6}}[/tex]

t = - 1

degree of freedom = n - 1

degree of freedom = 16 - 1

degree of freedom = 15

From the standard normal t probability distribution table, the p value when t = -1 at  0.10 level of significance, the p - value = 0.3332

Decision Rule: We fail to reject the null hypothesis since the p-value is greater than the level of significance at 0.10

Conclusion: Therefore, we can conclude that  there is insufficient evidence at the 0.10 level of significance to conclude that the population  mean μ is different than 15.

Answer:

Step-by-step explanation:

Distance walked by Arthur = 5/8 miles

Distance ride  by Jonathan = 8 times that of Arthur

it means that Distance rode on bus by Jonathan is 8 multiplied by Distance walked by Arthur

Distance rode on bus by Jonathan = 8 * Distance walked by Arthur

Distance rode on bus by Jonathan = 8 * 5/8 = 5 Miles Answer

Answer: 4

Step-by-step explanation:

Since this inequality gives us a list, we want to choose the greatest number shown because x≤?. Because x has to be less than or equal to a number, it makes the most sense to put the greatest number there. In the list, 4 is the greatest number.

Answer:

Ordinary Least Square (OLS) for the multiple regression model involves selecting parameters of a straight line function that will minimize the sum of the squares of the variance in the given dataset and those forecasted by the straight-line function.

Cheers

Answer:

Desmos could come in handy

Answer: Hi!

Let's solve your equation step-by-step.

12x^2 + 54x = −42

Step 1: Subtract -42 from both sides.

12x^2 + 54x − (−42) = − 42 − (−42)

12x^2 + 54x + 42 = 0

Step 2: Factor left side of equation.

6(2x + 7)(x + 1) = 0

Step 3: Set factors equal to 0.

2x + 7 = 0 or x + 1 = 0

You have two answers.

x = −7/2 or x = −1

Hope this helps!

Answer:

[tex] Area = 240 m^2 [/tex]

Step-by-step explanation:

The area of the right triangle above = [tex] \frac{1}{2}*base*height [/tex].

Where,

base = 16 m

height = 30 m

Plug in the above values into the area formula:

[tex] Area = \frac{1}{2}*16*30 [/tex]

[tex] Area = 8*30 [/tex]

[tex] Area = 240 m^2 [/tex]

Refer to the attachment for solution.

Answer:

[tex]\dfrac{-14}{9}[/tex].

Step-by-step explanation:

The given number is [tex]-1.\overline{5}[/tex].

We need to find a rational number in fraction form that is equivalent to given number.

Let [tex]x=-1.\overline{5}[/tex]

[tex]x=-1.555...[/tex]     ...(1)

Multiply both sides by 10.

[tex]10x=-15.555...[/tex]  ...(2)

Subtracting (1) from (2), we get

[tex]10x-x=-15.555...-(-1.555...)[/tex]

[tex]9x=-14[/tex]

Divide both sides by 9.

[tex]x=\dfrac{-14}{9}[/tex]

Therefore, the required rational number is [tex]\dfrac{-14}{9}[/tex].

Answer:

5/12

Step-by-step explanation:

3/4-1/3=

9/12-4/12=

5/12

Answer:

16 yard line

Step-by-step explanation:

The football team is starting on the 10 yard line. In the first play, they move up to the 24 yard line. Then in the second play, they go back to the 12 yard line since they lost 12 yards. Then in the third play, they gain 4 yards so you add 4 to 12. They end up at the 16 yard line after the third play. This means that they're going to start their fourth play at the 16 yard line.

Answer:

16 yards.

Step-by-step explanation:

They start at 10 yards. They are moving towards the 50 yard line, so gaining yards will add to the 10 yards instead of subtract from the 10 yards.

In the first play, they gain 14 yards. 10 + 14 = 24 yards.

In the second play, they lose 12 yards. 24 - 12 = 12 yards.

In the third play, they gain 4 yards. 12 + 4 = 16 yards, which is where they start their fourth play.

Hope this helps!