A researcher wants to use a confidence interval to estimate the proportion of college students in his state who plan to vote in the 2020 presidential election. He plans to randomly sample 120 college students, and plans to construct a 95% or 99% confidence interval. Which of these confidence intervals will be wider, and why

5 cm or 29 cm

Step-by-step explanation:

Let x length is cut off from each measurements.

Thus, the new measurements would be: 20 - x, 41 - x, 44 - x, which forms the sides of a right triangle.

Here, (44 - x) will be hypotenuse and (20 - x) and (41 - x) will be perpendicular legs of the triangle.

Therefore, by Pythagoras theorem:

[tex] {(41 - x)}^{2} + {(20 - x)}^{2} = {(44 - x)}^{2} \\ \\ \therefore \: {(41)}^{2} - 82x + {x}^{2} + {(20)}^{2} - 40x + {x}^{2} \\ = {(44)}^{2} - 88x + {x}^{2} \\ \\ \therefore \: 1681 - 122x + 2 {x}^{2} + 400 \\ = 1936 - 88x + {x}^{2} \\ \\ \therefore \: 2081 - 122x + {x}^{2} = 1936 - 88x \\ \\ \therefore \: {x}^{2} - 122x + 88x + 2081 - 1936 = 0 \\ \\ \therefore \: {x}^{2} - 34x + 145 = 0 \\ \\ \therefore \: {x}^{2} - 29x - 5x+ 145 = 0 \\ \\ \therefore \: x(x - 29) - 5(x - 29) = 0 \\ (x - 5)(x - 29) = 0 \\ x - 5 = 0 \: or \: x - 29 = 0 \\ \\ \therefore \: x = 5, \: 29[/tex]

So, the length that is cut off will be either 5 cm or 29 cm.

Answer:

increasing spread epidemics your outlook

Hey there! I'm happy to help!

SYSTEM #1

-4x+2y=22

-y=-3x-9

We can multiply both sides of the second equation by -1 to see what y equals.

y=3x+9

We can substitute this value for y into the first equation and solve for x.

-4x+2(3x+9)=22

We use distributive property to undo the parentheses.

-4x+6x+18=22

We combine like terms.

2x+18=22

Subtract 18 from both sides.

2x=4

Divide both sides by 2.

x=2

Our x has to be -4 to be the correct answer, so this option is incorrect.

SYSTEM #2

-4x+2y=22

y=-3x-9

We plug this y value into the first equation to solve for x.

-4x+2(-3x-9)=22

We use distributive property to undo the parentheses.

-4x-6x-18=22

We combine like terms.

-10x-18=22

Add 18 to both sides.

-10x=40

x=-4

We have the correct x-value to be the answer, so let's find the y-value by plugging our x-value into one of the equations.

y=-3(-4)-9

y=12-9

y=3

So, the solution of this system of equations is (-4,3), so the correct answer is 2. -4x+2y=22, y=-3x-9

Have a wonderful day! :D

Answer:

C

Step-by-step explanation:

(4/6) : (1/3), multiply by 3 both sides

(4/2) : 1 = 2:1

Answer:

A. 12:6

Step-by-step explA. 2

SE MULTIPLICA 4X3 Y 6X1

Answer:

C) C < 4

Step-bay-step explanation:

> means "greather than"

< means "less than"

The only statement that is true:

C) C< 4

Answer:

Hey there!

2/3 of 90 cm would be 60 cm.

Hope this helps :)

Answer

[tex] \boxed{60}[/tex]

Step by step explanation

To multiply one fraction by another, multiply the numerators for the numerator and multiply the denominators for its denominator and reduce the fraction obtained after multiplication into lowest term :

[tex] \mathsf{ \frac{2}{3} \times 90}[/tex]

⇒[tex] \mathsf{ \frac{2 \times 90}{3 \times 1} }[/tex]

⇒[tex] \mathsf{ \frac{180}{3} }[/tex]

⇒[tex]60[/tex]

Hope I helped!

Best regards!!

Answer:

[tex]W= 4700+0.02S[/tex]

Step-by-step explanation:

Given that

W is the monthly wage

S is the monthly sales

According to the problem statement, salesperson receives a monthly salary of $4700 (sales or no sales made he/she gets that amount)

Also plus 2%  commission of sales made for the month added to the wage

we can model his/her wage as follows

[tex]W= 4700+ (2/100)S\\\\ W= 4700+0.02S[/tex]

Hence the model for the monthly wage is [tex]W= 4700+0.02S[/tex]

Answer:

it is - 15 please mark me brainliest

Answer:

[tex]\huge \boxed{x=30}[/tex]

Step-by-step explanation:

[tex]\sf We \ can \ use \ ratios \ to \ solve.[/tex]

[tex]\displaystyle \frac{45}{27} =\frac{x}{18}[/tex]

[tex]\sf Multiply \ both \ sides \ by \ 18.[/tex]

[tex]\displaystyle \frac{45}{27}(18) =\frac{x}{18}(18)[/tex]

[tex]\sf Simplify \ the \ equation.[/tex]

[tex]\displaystyle \frac{810}{27} =x[/tex]

[tex]30=x[/tex]

If [tex]x-a[/tex] is a factor of a polynomial [tex]P(x)[/tex] then, [tex]a[/tex] is its root.

So [tex]-2[/tex] is a root of [tex]x^3-19x-p[/tex]

[tex](-2)^3-19\cdot(-2)-p=0\\-8+38-p=0\\p=30[/tex]

Answer:

(n^(2)+6n-4)(2n-4)

=============================================================

Explanation:

Let's square both sides and do a bit of algebra to get the following.

[tex]\sin(x) + \cos(x) = 1/5\\\\\left(\sin(x) + \cos(x)\right)^2 = \left(1/5\right)^2\\\\\sin^2(x) + 2\sin(x)\cos(x) + \cos^2(x) = 1/25\\\\\sin^2(x) + \cos^2(x) + 2\sin(x)\cos(x) = 1/25\\\\1 + 2\sin(x)\cos(x) = 1/25\\\\\sin(2x) = 1/25 - 1\\\\\sin(2x) = 1/25 - 25/25\\\\\sin(2x) = -24/25\\\\[/tex]

Now apply the pythagorean trig identity to determine cos(2x) based on this. You should find that cos(2x) = -7/25

This then means tan(2x) = sin(2x)/cos(2x) = 24/7.

From here, you'll use this trig identity

[tex]\tan(2x) = \frac{2\tan(x)}{1-\tan^2(x)}\\\\[/tex]

which is the same as solving

[tex]\tan(2x) = \frac{2w}{1-w^2}\\\\[/tex]

where w = tan(x)

Plug in tan(2x) = 24/7 and solve for w to get w = -4/3 or w = 3/4

So either tan(x) = -4/3 or tan(x) = 3/4.

If we were to numerically solve the original equation for x, then we'd get roughly x = 2.21; then notice how tan(2.21) = -1.345 approximately when your calculator is in radian mode.

Since tan(x) < 0 in this case, we go for tan(x) = -4/3

Answer:

1.) (2,1) is a solution

2.) (4,3) is NOT a solution

Step-by-step explanation:

1.) (2,1)

These are these mean (x,y)

2=x and 1=y

You want to substitute the numbers for the letters in the equation.

so.

2(2)+1=5

4+1=5

5=5, This statement is true so (2,1) is a solution.

2.) Same as above. 4=x and 3=y

4(4)-3(3)=10

16-9=10

7 Does Not Equal 10, Therefore, (4,3) is Not a solution to the equation.

Answer:

so the division of a number and -9 or

x/-9+10=11 or

(x/-9)+10=11

subtract 10 from both sides

x/-9=1

multiply both sides by -9

x=-9

Answer:

29.17 feet

Step-by-step explanation:

10 x 35 = 350 in. / 12 in/ft = 29.17 feet

The length of the actual wall is 29.17 feet. The correct answer is option B.

The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.

It is given that the blueprint for a house has a scale factor of n = 35. A wall in the blueprint is 10 in.

The length of the actual wall is calculated as:-

L = 10 x 35

L = 350 in. / 12 in/ft

L= 29.17 feet

Therefore, the length of the actual wall is 29.17 feet. The correct answer is option B.

To know more about scale factors follow

https://brainly.com/question/25722260

#SPJ2

Answer:

6 quarts

Step-by-step explanation:

8 bags

--------

2 quarts

Multiply top and bottom by 3

8*3 bags

--------

2*3 quarts

24 bags

--------------

6 quarts

Answer:

6

Step-by-step explanation:

2 quarts of iced tea = 8 tea bags.

x quarts of Iced tea = 24 tea bags

=> 2/8 = x/24

=> Multiply the extremes and means

=> 8x = 48

=> 8x / 8 = 48 / 8

=> x = 6

6 quarts of iced tea can be made with 24 tea bags.

sine and cosecant.

you can see the graph or on unit circle, as the for these ratios, (which depend on y coordinate) 1st and 2nd quadrant have positive y coordinate

Answer:

Step-by-step explanation:

Sin (90 - ∅) = Cos ∅

90 -54 = 36

Sin 36 = Sin (90 - 54)

            = Cos 54      --------->(I)

Now, Sin (36) - Cos (54) = Cos 54 - Cos 54   {From 1}

                                        = 0

2) tan (90-∅) = Cot ∅

Tan 80 = Tan (90 - 10)

            = Cot 10  ----------(II)

Tan 80 - Cot 10 = Cot 10 - cot 10   -----------(from (II)}

                         = 0

Are you korean?

≧∇≦

ฅ'ω'ฅ

Answer:

No, the above polynomials aren't similar as they don't have a constant scale factor

The following polygons given in the question are not similar .

Similar polygons are those polygon which have the similar shapes but with different size and dimensions.  Similar polygons have also the scaling factor ration equal.

There are two polygons given in the question LMNO and WXYZ .

For both of the polygons, we are checking the adjacent sides of the polygons.

The value of LM = 35 but for the other polygon , its adjacent side WX = 18.

Similar LO = 63 and WZ = 10 .

Also the adjacent angles are not equal as ∠MNO = 50° and ∠ZWX = 50° .

Therefore, the polygons given have different scaling factor.

Thus, the following polygons given in the question are not similar .

To learn more about similar polygons, refer -

https://brainly.com/question/16058229

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Step-by-step explanation:

the measure of the segment YZ

[tex] \sin(30) = \frac{yz}{50} \\ yz = 50 \times \sin(30) = 25[/tex]

YZ= 25 m

Answer:

-4 -5x

Step-by-step explanation:

4(1 – 3x) + 7x – 8.

Distribute

4 -12x +7x -8

Combine like terms

-4 -5x

Answer:

The simplified answer of this expression is -5x - 4

Step-by-step explanation:

4(1 - 3x) + 7x - 8

Distribute 4 to (1 - 3x)

4 - 12x + 7x - 8

Rearrange the terms so it'll be easier to combine them.

4 - 8 - 12x + 7x

Combine like terms.

-4 - 5x

Put the equation in standard form.

-5x - 4

Answer:

x = s/2

Step-by-step explanation:

● s states have joined the union in 1788

● half of s have joined in 1889

Let x be the number of states that have joined in 1889

● x = (1/2)× s

● x = s/2

Answer:

rational

Step-by-step explanation:

according to google the definition of RATIONAL is

(of a number, quantity, or expression) expressible, or containing quantities that are expressible, as a ratio of whole numbers. When expressed as a decimal, a rational number has a finite or recurring expansion. Examples of rational numbers are 4 3 and 9

AND THE DEFINITION OF IRRATIONAL IS

(of a number, quantity, or expression) not expressible as a ratio of two integers, and having an infinite and nonrecurring expansion when expressed as a decimal. Examples of irrational numbers are the number π and the square root of 2.

so 101 is a whole number and whole numbers are always rational

HOPE I HELPED

PLS MARK BRAINLIEST  

DESPERATELY TRYING TO LEVEL UP

✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                       PEACE!

Answer:

An integer is any rational number without a decimal or fraction. This includes negative numbers, and 0. But decimals and fractions are not integers.

Step-by-step explanation:

Brainliest, please!

[tex]\it R=circle's \ radius;\ \ D=diameter;\ \ D=2R\\ \\ \mathcal{C}=2\pi R\\ \\ \mathcal{A}=\pi R^2\\ \\ \mathcal{C}=\dfrac{2}{5}\cdot\mathcal{A} \Rightarrow 2\pi R=\dfrac{2}{5}\pi R^2|_{\cdot\frac{5}{2}} \Rightarrow 5\pi R=\pi R^2|_{:(\pi R)} \Rightarrow 5=R|_{\cdot2} \Rightarrow 10=2R\\ \\ But,\ 2R=D,\ so\ \ D=10\ in[/tex]

Answer:

x = - 3 ± [tex]\sqrt{10}[/tex]

Step-by-step explanation:

Given

4x² + 24x = 4 ( divide through by 4 )

x² + 6x = 1

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(3)x + 9 = 1 + 9

(x + 3)² = 10 ( take the square root of both sides )

x + 3 = ± [tex]\sqrt{10}[/tex] ( subtract 3 from both sides )

x = - 3 ± [tex]\sqrt{10}[/tex]

Answer:

X=1/8

Step-by-step explanation:

Calculate the product 4x×2 + 24x = 4

Collect like terms 8x + 24x = 4

Divide both sides of the equation by "32" 32x = 4

Solution x = 1/8

Answer:

197 pounds of cans

Step-by-step explanation:

Find how many pounds of cans they have collected by subtracting 8 from both of their barrel weights:

115 - 8

= 107

98 - 8

= 90

Add these two weights together:

107 + 90

= 197

So, they collected 197 pounds of cans