This scale drawing shows a parking lot with an actual length of 315 meters. What is the width of the actual parking lot?

The 95% confidence interval for the true proportion of people who favored candidate a is 0.419, 0.481

How to calculate confidence interval?

First, calculate sample proportion by divide number people who favored candidate by number of sample. So:
[tex]\pi[/tex] = 450 / 1,000 = 0.45

Then we use the formula for confidence interval

[tex]\pi[/tex] ± [tex]z\sqrt{\frac{\pi (1-\pi )}{n}}[/tex]

In which z is z score that has a p value of [tex]1 - \frac{\alpha }{2}[/tex]

For 95% confidence interval z is the value of Z that has a p value of [tex]1 - \frac{0.05}{2}[/tex] = 0.975, so z = 1.96

After we have [tex]\pi[/tex] value and z value then put it in the formula. So:

= 0.45 ± [tex]1.96\sqrt{\frac{0.45(1-0.45)}{1000} }[/tex]

= 0.45 ± 0.0308

= 0.419, 0.481

Thus, the 95% confidence interval for the true proportion of people who favored candidate a is 0.419, 0.481

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The unit rate for this problem is how much Alyssa  earns per hour

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Alyssa works 6.4-hour shifts at the donut shop each day.

Last week she earned $480 for working 32 hours.

Now, To determine her earnings per hour we have to divide her total earnings by the total no. of hours she worked which is,

= $(480/32).

= $15 per hour.

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The equation of the line that is parallel to the given line, through the given point is y = -5x - 7

Given equation,

y = -5x + 1

Slope = m

          = -5

For two lines to be parallel, slope is equal.

Therefore, m = -5 for another line.

Let the equation of the line be y = mx + c

This line passes through A(-2,3)

Therefore, 3 = -5(-2) + c

                  3 = 10 + c

                  c = 3 - 10

                     = -7

Hence, equation of line is y = -5x - 7.

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Answer:

She sent 111 texts that month

Step-by-step explanation:

The values of x in the given equation are x = -9 and x = 3. The solution set is [-9, 3]

From the question, we are to determine the value of x in the given equation.

The given equation is

|x + 3|= 6

Then, we can write that

x + 3 = 6 and -(x + 3) = 6

Solving the first equation

x + 3 = 6

Subtract 3 from both sides of the equation

x + 3 - 3 = 6 - 3

x = 3

Solving the second equation

-(x + 3) = 6

-x - 3 = 6

Add 3 to both sides of the equation

-x - 3 + 3 = 6 + 3

-x = 9

Multiply both sides of the equation by -1

-1 × -x = -1 × 9

x = -9

Hence, the solutions are x = -9 and x = 3

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Answer:

22ft

Step-by-step explanation:

2+2+5+4+4+2+2= 22

The percent of times the machine will dispense less than 7.75 oz. is 69.15%.

In the given question we have to find the percent of time the machine will dispene less than 7.75 oz.

A vending machine we deigned to dipene a mean of 7.5 oz of coffee into an​ 8-oz cup.

If the standard deviation of the amount of coffee dipened is 0.5 oz and the amount is normally​ ditributed.

Mean = 7.5 ,

Standard Deviation = 0.5

P(z< 7.5) = P(z<(X-Mean)/Standard Deviation)

P(z< 7.5) = P(z<(7.75-7.5)/0.5)

P(z< 7.5) = P(z<0.25/0.5)

P(z< 7.5) = P(z< 0.5)

P(z< 7.5) = 0.6915

P(z< 7.5) = 69.15%

Hence, the percent of times the machine will dispense less than 7.75 oz. is 69.15%.

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Using the t test statistic, the value of the test statistic is 1.25.

In the given question we have to find the value of the test statistic.

A manufacturer of chocolate potato chips would like to know whether its bag filling machine works correctly at the 400 gram setting.

= 400

A 25 bag sample had a mean of 399 grams and the variance is 400.

There is sufficient evidence at the 0.025 level that the bags are underfilled.

Sample size(n) = 25

sample Mean = 399

Sample Variance = 400

Standard Deviation = √Sample Variance

Standard Deviation = √400

Standard Deviation = 20

Population Mean = 400

So , the null and alternative hypothesis are

H0 : μ = 400

Ha : μ < 400

Using the sample t test statistic

t = (Population Mean - Sample Mean)/(Standard Deviation/Sample size)

t = (400 - 399)/(20/25)

t = 1*25/20

t = 1.25

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Answer: 12 small t-shirts and 18 large t-shirts

Step-by-step explanation:

24÷4=6

2×6=12 small t-shirts

3×6=18 large t-shirts

Answer:

8

Step-by-step explanation:

Price : %

  [tex]x[/tex]    :  100

 6.4  :  80     (Got 80 by 100 - 20)

Cross multiply

100*6.4 = 80[tex]x[/tex]

640 = 80[tex]x[/tex]

640/80 = [tex]x[/tex]

[tex]x[/tex] = 8

The interest rate for one month is 2.42% and the interest amount is $40 approximately.

Given,

The penalty APR rate = 28.99%

Balance amount = $1800

We have to find the interest for one month;

Here,

The APR of 28.99% is the yearly interest. To find the monthly rate:

= Rate / 12 months

= 28.99% / 12

= 2.42%

The amount owed is therefore;

= 1,800 x 2.42%

= $43.56

= $40.00 approximately

That is,

The interest rate for one month is 2.42% and the interest amount is $40 approximately.

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Since triangle P'Q'R' is the result of a transformation of triangle PQR, an algebraic representation which best describes this transformation is: C. (x, y) → (5x/2, 5y/2).

In Mathematics, a transformation can be defined as the movement of a point from its original (initial) position to a final (new) location. This ultimately implies that, when an object is transformed, all of its points would be transformed as well.

From the information provided above, we can logically deduce the following coordinates:

Therefore, the transformation rule is given by:

P (x, y)                      →               P' (x, y)

Point P = (-1, 1)      →  Point P' = ((5/2 × -1), (5/2 × 1)) = Point P' = (-5/2, 5/2).

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Answer:

It is the first option

Step-by-step explanation:

The values of the function when x = 3 are -10. -1 and -3, respectively

Function 1

The equation of the function is given as

y = -4x + 2

We have the value of x to be 3

So, we have

y = -4 x 3 + 2

Evaluate

y = -10

Function 2

The graph represents the notation of the function

On the graph, we have the value of y to be -1, when x = 3

This means that

y = -1

Function 3

The table represents the notation of the function

On the table, we have the value of y to be -3, when x = 3

This means that

y = -3

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-1 39/45

that is the answer

Answer:

130°

Step-by-step explanation:

Triangle JKL is an isosceles triangle and leg angles are equal :

m<J = m<L

The sum of interior angles in a triangle is equal to 180.

m<J + m<L + m<K = 180

25 + 25 + m<K = 180

50 + m<K = 180 subtract 50 from both sides

m<K = 130°

The value of x is -6 or 0 which is obtained by solving the giving equation using factoring.

Given equation: 2x³ + 12x² = 0

Solving this equation by factoring as follows:

2x³ + 12x² = 0

= 2x²(x+6) = 0

So, x + 6 = 0 or 2x² = 0

x = -6 or x = 0

Therefore, the value of x is -6 or 0 which is obtained by solving the giving equation using factoring.

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There is no definite formula for calculation of circumcenter of a triangle but a process for calculation of circumcenter has been described here.

What is circumcenter of a triangle?

Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.

Let the coordinate of A, B, C [tex]\Delta[/tex] ABC be ([tex]x_1, y_1[/tex]), [tex](x_2, y_2)[/tex] and [tex](x_3, y_3)[/tex] respectively and let the coordinate of circumcenter of [tex]\Delta ABC[/tex] is (x, y)

We need to find the length of AB, BC and AC

The length will be obtained in terms of x and y

On solving the equations, we will obtain the value of x and y

The value of x and y is the required coordinate of the circumcenter.

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Answer:

5h+35y=390$

20h+20y=360$

Step-by-step explanation:

there are many answers possible.

The following are just examples:

5h+35y=390$

20h+20y=360$

The picture for the condition is attached below.

What is factors of number?

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor in mathematics. As an illustration, 3 and 6 are factors of 12 because 12 3 = 4 and 12 6 = 2, respectively. 1, 2, 4, and 12 are the other components that make up 12.

Let, the factors of 72 are

72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24 36, 72.

When we divide 72 by 6 we get 12.

⇒ [tex]\frac{72}{6} = 12[/tex]

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-2 - 10 + (-3)^3

= -12 - 27

= -39

Answer:

-39

Step-by-step explanation:

Substitute v and k

v - 10 + k³

-2 - 10 -3³

Multiply the 3 and the power of thirds together

-2 -10 + 27

Combine like terms

It will take 1.5 minutes for printer to print 12 papers.

Given,

Time taken to print 40 papers=5 minutes

then,

Time taken to print 1 paper =[tex]\frac{5}{40}=\frac{1}{8}[/tex] minutes

then to find time taken to print 12 papers, multiply 12

Time taken to print 12 paper,

[tex]Time=\frac{1}{8}*12\\\\Time=1.5\ minutes[/tex]

Thus, it will take 1.5 minutes for printer to print 12 papers.

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Angles 1 and 5 constitutes one of the pairs

Step-by-step explanation:

Answer:

There are 13 small rooms and 9 large rooms reserved.

Step-by-step explanation:

First, we can make a system of equations. We can use s to represent the number of small rooms and l to represent the number of large rooms.

2 guests per small room added to 3 guests per large room equals 53 guests total, so 2s + 3l = 53.

The number of small rooms (s) plus the number of large rooms (l) equals the total number of rooms, so s + l = 22 or s = 22 - l.

We can substitute the first second equation into the first equation.

2 (22 - l) + 3l = 53

44 - 2l + 3l = 53

l = 9

So, the number of large rooms is 9. Then, to find the number of small rooms, we can substitute l into the second equation.

s = 22 - 9

s = 13

So, the number of small rooms is 13.

Answer:

[tex]y=\frac{1}{2}x-8[/tex]

Step-by-step explanation:

Perpendicular lines have the same slope. So, the slope of the line we need to find is 1/2.

Thus, the equation is

[tex]y+5=\frac{1}{2}(x-6) \\ \\ y+5=\frac{1}{2}x-3 \\ \\ y=\frac{1}{2}x-8[/tex]

Answer:

x = 30

y = 15

z = 150

Step-by-step explanation:

90°, 2x°, and x and supplementary.

Using this knowledge, we can form the equation:

2x° + 90° + x° = 180°

and solve for x.

3x°+ 90° = 180°

3x° = 90°

x° = 30°

x = 30

x and z are same side interior angles. Therefore, they are supplementary.

Using this knowledge, we can form the equation:

x° + z° = 180°

30° + z° = 180°

z° = 150°

z = 150

z° and 2y° are supplementary.

Using this knowledge, we can form the equation:

z° + 2y° = 180°

150° + 2y° = 180°

2y° = 30°

y° = 15°

y = 15

Answer:

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