a political candidate has asked you to conduct a poll to determine what percentage of people support her. a) suppose the candidate believes that the percentage that support her is approximately 73%. if we want a 6% margin of error at a 94% confidence level, what size sample is needed?

To construct the graph of the hyperbola, the procedure is as follows:

The equation of a vertical hyperbola with center (x*, y*) is given according to the following equation:

(y - y*)²/a² - (x - x*)²/b² = 1.

A vertical hyperbola opens up and down.

In this problem, the equation is:

(y + 2)²/36 - (x + 5)²/64 = 1.

Hence the center is:

(-5, 2).

The value of coefficient a is:

a² = 36 -> a = 6.

Then the vertices of the hyperbola are:

The slopes of the asymptotes of the parabola are given as follows:

±a/b.

Hence:

Since the asymptotes pass through the center, the equation is:

y - 2 = ± 3/4(x + 5).

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The coordinates of the vertices after the reflection over the x-axis are A' (2, -3) B' (4, 5) and C' (-1, -2)

Given,

A triangle ABC with vertices A(2,3) , B(4,-5), and C(-1,2)

To find the coordinates of the vertices of each figure after a reflection over the given axis.

Now, According to the question:

We should know that:

You should know that you can predict changes in coordinates after translations without a graph or anything like that.

(x, y) reflected over the x axis = (x, -y)

(x, y) reflected over the y axis = (-x, y)

(x, y) rotated 90 degrees around the origin = (y, -x)

(x, y) rotated 180 degrees around the origin = (-x, -y)

(x, y) rotated 270 degrees around the origin = (-x, y)

So here's our set of points.

A(2,3) , B(4,-5), and C(-1,2)

Here's those points reflected over the x axis.

A' (2, -3) B' (4, 5) and C' (-1, -2)

Hence, The coordinates of the vertices after the reflection over the x-axis are A' (2, -3) B' (4, 5) and C' (-1, -2)

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Answer:

[tex]\\ y = \frac{1}{3} x - 4[/tex]

Step-by-step explanation:

Hope this helps! :))

The length of the diagonal of the Triangle is 14.86 units

What is Diagonal?

When two polygonal vertices are not on the same edge, a diagonal is a line segment connecting them. Any sloping line is known as a diagonal informally.

Given,

Area of Rectangle = 110square units

Length = 11units

Breadth = ?

Area of Rectangle = length x breadth

Breadth = Area of Rectangle / length

Breadth = 110 / 11

Breadth = 10units

Length of diagonal (Pythagoras Theorem)

H^2 = P^2 + B^2

H^2 = (11)^2 + (10)^2

H^2 = 121 + 100

H^2 = 221

H = [tex]\sqrt{221}[/tex]

H = 14.86 units

Hence, The length of its diagonal is 14.86 units

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Answer:

Let's break down the given information.

Car A

Speed - 30 mph

Hence the distance traveled per minute would 30/60 mph which is 0.5 Miles every minute.

Car B

Speed - 36 mph

The distance traveled per minute would 36/60 mph which is 0.6 Miles every minute.

Initial distance between the cars is 10 Miles

Car A travels 1 miles in 2 minutes and Car B travels 1.2 miles in 2 minutes.

Hence to calculate the distance between the 2 cars we need to calculate

Initial distance - Distance travelled by Car A - Distance traveled by Car B

Which is

10 - 1 - 1.2

7.8 Miles distance between the 2 cars

Plotted Answers:

12.) See attached for my work

13.) See attached for my work

14.) See attached for my work

Simplified Answers:

12.) y > –24

13.) x ≥ –12

14.) x > –7

Hope that helps! Have an amazing rest of your day! Please consider giving me the Brainliest! :)

Answer:

(g o f)(8)

Step-by-step explanation:

First we find f(8).

f(8) = 8 - 1 or 7.

We now find g(f(8)), which means g(7).

g(7) = 7^3 or 343

Based on the distance walked by Nadia when she took her break, the statement that explains the distance already walked is C. The distance Nadia already walked is less because 3.4 - 1.6 = 1.8, and 1.6 < 1.8.

Nadia had already walked 1.6 miles by the time she took her break. This means that the distance she was still left to walk in the mile trail was:

= 3.4 - 1.6

= 1.8 miles

The distance that Nadia had already walked was 1.6 miles and yet she was left to walk 1.8 miles.

We can therefore conclude that the distance that Nadia already walked is less than the distance still to be walked.

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The distance Nadia already walked is less because 3.4 - 1.6 = 1.8, and 1.6 < 1.8 which is the correct answer would be an option (C).

Distance is calculated as the product of a person's movement and time.

Nadia took a rest after covering 1.6 miles of walking.

This indicates that she had the following distance to cover on the mile trail:

⇒ 3.4 - 1.6 = 1.8 miles

Nadia had already walked 1.6 miles, but she still had another 1.8 miles to go.

Therefore, the distance Nadia has already traveled is less than the distance that needs to be covered.

Hence, the correct answer would be an option (C).

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Given:

Amount Marty spent per day = $3

Number of days = 14

Remaining amount = $68

Since the amount left depends on the number

Answer:

B) x > 8

Step-by-step explanation:

1-Step: Combine like terms by subtracting 9 on both sides : 17-9 < X

8 < X

2- Step: flip the signs (Since 8 is less than X, Then X is greater than X)

X > 8

The two inequalities are (option c) y > x - 2 and2y + x < 4

Given,

Let's start by locating the red-hued area.

If the shadow is visible to be over the line, then the situation will be as follows:

y > ax + b

Hence the equation for the line is ax + b.

The slope is a, and the y-intercept is b.

The line in the graph intersects the y-axis at y = -2, which results in:

b = -2

Two points on the line are required to determine the slope; these points are (0, -2), and (2, 0)

We are aware of the slope for a line passing through the points (x1, y1) and (x2, y2) as follows:

a = (y2 - y1)/(x2 - x1) (x2 - x1)

The slope for this line will then be:

a = (0 - (-2))/(2 - 0) = 2/2 = 1

Then this line's equation is:

1x - 2

And here's the inequality:

y > x - 2.

The shaded area of the blue one is below the line, thus we will have:

y < ax + b

The y-intercept in this situation is y = 2.

This line crosses through the points (0, 2) and, as can be seen (4, 0)

The slope is then:

a = (0 - 2)/(4 - 0) (4 - 0) = -2/4 = -1/2

This inequality is then:

y < (-1/2)x + 2

If we rewrite this using the choices, we get the following:

y < (-1/2)x + 2

2y < -x + 2 ×2

2y + x < 4

The two inequalities are (option c) y > x - 2 and2y + x < 4

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Answer: C

Step-by-step explanation:

Based on the ratios of water consumed to the fruit juice consumed, the missing figures in the completed table would be:

The ratio of water gallons consumed to fruit juice gallons is equivalent which means that at their simplest, they will always have the ratio of 6 : 7 as is the case in the 5th grade.

The missing ratio for Juice in 6th grade is:

= (Water gallons x Juice gallons in 5th grade) / water gallons in 5th grade

= (24 x 7) / 6

= 28 gallons of fruit juice

The missing ratio for water in 6th grade is:

= (18 x 7) / 6

= 21 gallons of fruit juice

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Answer:

pretty sure its WZX

Step-by-step explanation:

Answer:

  (c)  see attached

Step-by-step explanation:

You want the number line that shows the solutions to |-2x| = 4.

The absolute value equation resolves to two equations:

The solution will be plotted on the number line as solid dots at -2 and 2, as shown in the attachment.

Answer:

C

Step-by-step explanation:

If there is a negative number in "I  I", then it becomes positive but if it is a positive number, then it remains positive

Answer: it

Step-by-step explanation:

!!!

The percent equation is = 2600/ 4000 × 100/1

The percentage of books that are fiction is 65%

Percentage can be described as the ratio, quotient or number that is being expressed as a fraction of 100.

It is also described as the given part or amount in every hundred.

It is expressed as a fraction with 100 as the denominator of the fraction

It is represented with the symbol "%".

Given the information ;

Total number = 4000 books

Fiction books = 2600

The percentage is represented as;

= 2600/ 4000 × 100/1

Find the ratio

= 0. 65 × 100/1

Multiply through

= 65%

Hence,  the value is 65%

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The slope of the line that is perpendicular 6y=−7x+4 is: 6/7.

If one line has a slope of a/b, the slope of the line that is perpendicular to the line would be the negative reciprocal of a/b, which is -b/a.

If the slopes of perpendicular lines are multiplied together, for example (a/b)(-b/a), we would always have a result of -1.

Rewrite the equation 6y = −7x + 4 in slope-intercept form as y = mx + b, in other to determine the value of m = slope.

6y/6 = −7x/6 + 4/6

y = −7/6x + 2/3

The slope of 6y = −7x + 4 is -7/6. 6/7 is the negative reciprocal of -7/6. Therefore, the slope of the perpendicular line is: 6/7.

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The solutions are x = -1,  y = 1 and z = 5  

In Mathematics, the equation which has highest degree 1 is known as a Linear equation. Linear equations are used to calculate unknown values. Here to represent unknown values we will use variables like x, y, z  or a, b, c .. etc.  

According to the number of variables in given equations, the given equations will be called a Linear equation in one variable or Linear equation in two variables and so on. To solve linear equations we will use Elimination method

Here, we have three linear equations with 3 and 2 variables

4x - 2y + 3z = 9 ----(1)

x - 2y = -3 -----(2)

2x + 3y = 1​ -----(3)

Here, to find x, y and z we will use Elimination method

First of all solve (2) and (3) as given below

2 × (2) ⇒  2x - 4y = - 6 -----(4)

1 × (3) ⇒  2x + 3y = 1​  

Now subtract (3) from (4)

(4) - (3) ⇒ 2x - 4y -2x - 3y  = - 6 - 1

⇒ - 7y = -7

⇒   y = 1

Substitute y = 1 in (2)

(2) ⇒ x - 2(1) = -3

x - 2 = -3

x = -1    

Now substitute x = -1 and y = 1 in (1)

(1) ⇒ 4(-1) - 2(1) + 3z = 9  

- 6 + 3z = 9

3z = 15

z = 5

From above calculations

The values of x = -1,  y = 1 and  z = 5

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The translation moves 5 units to the left and 2 units down, so we have:

c = -5

d = -2

To identify the translation, let's follow a single vertex of the triangle.

The top vertex of triangle A is at (2, -3)

After a reflection about the x-axis only the y-value changes, so after the reflection the coordinates of that vertex will be:

(2, 3).

In now we apply the given translation, the new coordinates will be:

(2 + c, 3+ d)

And the coordinates of this vertex on triangle B is (-3, 1), so we have:

(2 + c, 3+ d) = (-3, 1)

2 + c = -3

c = -3 - 2 = -5

3 + d = 1

d = 1 - 3

d = -2

So the translation is defined by the values:

c = -5

d = -2

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Answer:

slope = -1/9

Step-by-step explanation:

Hope this helps!!!

Remember that

The y-intercept is the value of y when the value of x=0

In this problem

we have the equation

y=7x^2+4

For x=0

substitute

y=7(0)^2+4

y=4

8.27 is the normally distributed value of the shelf life which falls under 16% of the battery shelf life.

Because the shelf life of a battery manufactured by one big business is known to be regularly distributed, we would use the normal distribution formula, which is stated as

z = (x - µ) ÷ σ

Where

x = shelf life of a battery in years.

µ = mean shell life

σ = standard deviation

Based on the facts provided,

µ = 8 years

σ = 0.3 years

The z score corresponds to a p-value of 16% in the normal distribution table,

(16 ÷ 100 = 0.16) is - 0.9.

Therefore,

- 0.9 = (x - 9) ÷ 0.3

0.3 × (- 0.9) = x - 8

0.27 = x - 8

x = 0.27 + 8

x = 8.27

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All the x-values that bring a polynomial, p(x), to zero are referred to as its zeros. They are intriguing to us for a variety of reasons, one of which is that they provide information on the graph's x-intercepts for the polynomial.

We will also observe that they have a direct connection to the polynomial's factors.

What are polynomial zeros with an example?

Real number k is referred to as the zero of a polynomial P(x) if P(k) = 0. As a result, the polynomial x2 - 3x + 2 has a zero at 1 and a zero at 2.

The equation p(x)=(x-1) (x-3)

Although it is a polynomial of third degree, 2, only has two different zeros. This is due to the zero x=3 having a connection to the factor.

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The absolute value equation to represent the definition of betweenness is

AB + BC = AC ↔ B ∈ A,C  

Absolute value equation:

An absolute value equation is a function that contains an algebraic expression within absolute value symbols.

Given,

Here we have the statement "If three points a, b, and c lie on the same line, then b is between a and c if and only if the distance from a to c is equal to the sum of the distances from a to b and from b to c.".

Here we need to find the absolute value function for this statement.

In order to find the absolute value equation,

First we have to identify the symbols for the terms mentioned in the statement they are,

between = ∈

if and only if = ↔

sum = +

Now, we have to divide the statement as two parts.

First one is, "c lie on the same line, then b is between a and c"

It can be written as,

B ∈ A,C

Then the second part is, "the distance from a to c is equal to the sum of the distances from a to b and from b to c."

Which can be written as

AB + BC = AC

When we combine it, the we get the absolute value equation as,

B ∈ A,C ↔  AB +BC = AC

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Answer:

I've included a visual representation

Step-by-step explanation:

i did the assigment yesterday

To find the volume of the given prism, first, we have to transform each mixed number into a fraction

Then, we multiply the dimensions to find the volume

But, we know that 1 foot is equivalent to 30.48 centimeters, so let's transform it

Given:

Total number of hamburgers and cheeseburgers sold = 439

There were 61 fewer cheeseburgers than hamburgers sold.

Let's determine the number of hamburgers sold.

Let C represent the number of cheeseburgers

Let H represent the number of hamburgers sold.

We have the system of equations:

• H + C = 439

• C = H - 61

Now, let's solve the equations simultaneously using the substitution method.

Substitute (H - 61) for C in the first equation.

We have:

H + (H - 61) = 439

H + H - 61 = 439

2H - 61 = 439

Add 61 to both sides:

2H - 61 + 61 = 439 + 61

2H = 500

Divide both sides by 2:

Therefore, they sold 250 hamburgers on Friday.

ANSWER:

250 hamburgers

If I'm not mistaken, the answer is 43.17

Let:

L = length of the road

D = Days of construction

We can write a linear equation in the slope-intercept form:

Where:

m = Slope = rate = 1 mile per day

b = y-intercept = Initial value = 10 miles

Therefore:

The graph is: