A rectangular park is 40 yards wide. Then a city planner designs a path that is 1 yard wide to run all the way around the park. Now the area of the park plus the path is 4200 yd.² how long is the park not counting the path?

Answer: $2.96

Step-by-step explanation:

$18.75 - $3.95 = $14.80

$14.80 / 5 = $2.96

The equation of a line in the slope-intercept form is:

Where m is the slope and b is the y-intercept. These values are given, then the equation of the line is:

To graph it, we need to know the coordinates of at least two points on the line.

Whan x=0, then y is:

Thus, the first point is (0,-4).

When x=1, then y is:

The second point on the line is (1,0).

If we draw these points in the coordinate plane, we can draw a line that passes through them, and this will be the graph of the line.

It looks like this:

The null hypothesis should not be rejected. There is insufficient evidence that the true diameter differs from 0.5 inches.

We are given that,

n = 15

t-value = 1.66

Significance level;α = 0.05

So, DF = n - 1 = 15 - 1 = 14

In the attached one-sample t-table, we can see that the p-value of 0.06

corresponds to a t-value of 1.66 and a DF of 14

Due to the P-value of 0.06, it is greater than the significance level of 0.05. Based on the results, we are not rejecting the null hypothesis. There is insufficient evidence to conclude that the true diameter in active attachment is different from 0.5

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1. The width of the rectangle is 3.1cm

2. The number of games in Lanie's phone is 10

The formula for calculating the perimeter of a rectangle is expressed as;

Perimeter = 2(l + w)

Where;

Given the values as length = 4.3cm and perimeter = 14. 8cm

Substitute the values into the formula

14. 8 = 2(4.3) + 2w

expand the bracket

14. 8 = 8. 6 + 2w

collect like terms

2w = 14. 8 - 8.6

2w = 6. 2

Divide through by the coefficient of w

w = 6.2/2

w = 3.1 cm

Let the number of games in Lanie's phone be x

x + 3x - 7 = 33

collect like terms

4x = 33 + 7

4x = 40

Divide both sides by 4

x = 40/4

x = 10 games

Hence, the width is 3.1cm

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Based on the gross pay for Melika Yasin, and the fact she claims no allowances and is married, the amount withheld from her pay for Federal Income Tax is $43.

Melika Yasin had a gross pay of $355.00 for the week. This amount is more than $350 but less than $360.

Melika Yasin therefore falls into the bracket of "At least $350 but less than $360."

She also claims no allowances in this bracket. This means that the amount that would be withheld for Federal Income Tax according to the table would be $43.

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Answer:

x = - 1 / 24

Step-by-step explanation:

-6 ( 6x - 1 ) + 9 = 36x + 18

First, solve the brackets.

-36x + 6 + 9 = 36x + 18

Then, subtract 36x by both sides.

-36x - 36x + 6 + 9 = 18

-72x + 15 = 18

Now, Subtract 15 by both sides.

-72x = 18 - 15

-72x = 3

Now divide both sides -72 by both sides.

x = - 3 / 72

x = - 1 / 24

Answer:

Step-by-step explanation:

To find the cost of the apples, simply multiply the cost by how much Derek buys. So: 3.8 * 1.35= 5.13.

So, For Part A the answer is  A.

For Part B: We need to find the total cost of both apples and oranges. We already know the total cost of apples is 5.13. We need to find the cost of oranges.

We multiply:

5.2* 1.45= 7.54

Now, add the totals together: 7.54+5.13

The total is 12.67.

If Derek payed with a 20 dollar bill, we would subtract 20 with 12.67.

The answer is 7.33. So the answer is A.

The number of green marbles in the bag is 10

From the question, we have the following parameters:

The given parameters can be represented using the following ratio

Ratio = Green marble : Orange marble

So, we have

Green marble : Orange marble = 2 : 3

When there are a total number of 15 orange marbles in a bag, then we have

Green marble : 15 = 2 : 3

Multiply ratio by 5

Green marble : 15 = 10 : 15

By comparison, we have

Green marble = 10

Hence, there are 10 green marbles in the bag

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Answer:

118 miles

Step-by-step explanation:

Explanation in photo attached

The absolute value of (-8) would be 8 on number line.

The absolute value of any number represented on number line is given as the distance of the number from zero on a number line, when counted on whichever side it is present that is either negative or positive. In mathematical notation, absolute value is defined as the modulus of the number, enclosed in two straight lines. For example: |-8| or |8| would have absolute value 8 even though both the numbers are represented on negative and positive side of zero respectively on the number line. The absolute value of any number which is also a real number is the non-negative value of that number irrespective of its sign. Number line figure is attached below.

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Answer:

400

Step-by-step explanation:

yw

Answer:

1. 26 2/3

2. 13/5

3. 2000,3000,4000

Answer:

the answer is 196

63^2-49^2

(7×9)^2 -(7×7)^2

7^2 (9-7)

7^2 ×2^2

49 × 4

196

Answer:

1568

Step-by-step explanation:

i simplified the expression

Before taxes, the tie will cost $11.25

Discounts are price cuts made by store owners on goods or services that would otherwise be sold for the indicated price. Usually, this portion of the rebate is given to increase sales or get rid of extra inventory. The List Price, sometimes referred to as the Marked Price, is the cost of a product as declared by the seller or manufacturer, excluding any discounts.

The final price at which a product is actually sold is the selling price, which includes any discounts or price drops from the list price. Off or reductions are frequent terms used to describe discounts. Note that the marked price of the item is always used to calculate the discount (list price).

Discount = List Price - Selling Price

Discount (%) = (Discount/List Price) × 100

According to the question,

List price = $15.00

Discount % = 25 %

Cost of the tie before taxes = [tex]List \: price \:\frac{ (100 - Discount \%)}{100}[/tex]

⇒ [tex]\text{\$15.00}\: \frac{(100-25)}{100}[/tex]

⇒ [tex]\text{\$15.00}\: \frac{75}{100}[/tex]

⇒ [tex]\text{\$15.00}\: \frac{3}{4} = \text\:{\$15.00 \times 0.75}[/tex]

⇒ $11.25

Therefore, before taxes, the tie will cost $11.25

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The expanded form of this number 14.702 will be  (1 × 10) + (4 × 1) + (7/10) + (2/1000)

It should be noted that expanded form simply means breaking down of the number given into different units.

Therefore, based on the information illustrated. This will be:

14.702 will be:

= (1 × 10) + (4 × 1) + (7/10) + (2/1000)

= 10 + 4 + 0.7 + 0.002

Note that your options aren't written well.

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Answer: the y-intercept of this equation is (0,4)

Step-by-step explanation:

Answer: 2/3

Step-by-step explanation:

1) First locate two points.

First, locate two points on the graph. For this example, I will choose (-2,0) and (1,2)

2) Find the distance between these two points.

We can find that from starting from (-2,0), we go right 3 and up 2. You can easily do this on paper by drawing a triangle.

3) Using the numbers we have before, find the rate.

To find the rate, we can use rise/run. Which will become 2/3.

Hello!

To find the slope of the line:

 ==> must find two points on the line

    (x₁, y₁): (-2,0)

    (x₂, y₂):(1,2)

 [tex]Slope = \dfrac{2-0}{1--2} =\dfrac{2}{3}[/tex]    <== Answer

Hope that helps!

The transformation has a horizontal shift right by 4 units and vertical shift upwards by 3 units.

What do you mean by transformation of a function ?

The modification of a graphed function to create a different version of the parent function is known as transformation.

For the given condition :

The function is y = (x - 4)² + 3.

The above function is transformed from the parent function which is y = x².

We know that , the horizontal shift depends on the value of h. The horizontal shift and it is described as:

y = f (x + h)

Then , the graph of function will be shifted to left by h units.

and

y = f (x - h)

Then , the graph of function will be shifted to right by h units.

If we compare both functions i.e., y = (x - 4)² and y = f (x - h), their is a difference of -1 , it meant shift is right by 4 units.

Now , we know that , the vertical shift depends on the value of k. The vertical shift is described as:

y = f(x) + k

Then , the graph of function will be shifted up by k units.

and

y = f(x) - k

Then , the graph of function will be shifted down by k units.

Here , if we compare functions i.e., y = (x - 4)² + 3 and y = y = f(x) - k ,  we find out that the graph of function will be shifted upwards by 3 units.

Therefore , the transformation has a horizontal shift right by 4 units and vertical shift upwards by 3 units.

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Answer:

12^4

Step-by-step explanation:

because dividing exponent divide when the number in this case 12 don’t change so 8-4=4 so 12^4 or 20736

Answer:

1.) 88 cones were sold

2.) $17.00 per gal of paint; $5.50 per brush

Step-by-step explanation:

1.) ($1.10(88)= $96.80) + ($2.35(84)= $197.40)= $294.20

2.) I have a really complicated process, and it's really late at night where I am

Answer:

For the first question, 88 cones were sold

For the second question, a gallon of paint costs 17 dollars and a brush costs 5.5 dollars (that is, 5 dollars and 50 cents).

Step-by-step explanation:

For the first question,

Let the number of ice cream cones be represented by the letter 'x'

And the number of sundaes be represented by the letter 'y'

[tex](1.10x + 2.35y) = 294.20 \: \: \: equ.2 \\ (x + y) = 172 \: \: \: equ.1[/tex]

Solving it simultaneously, subtract equ. 2 from equ. 1

[tex]0.10x - 1.35y = 122.20[/tex]

Making x the subject,

[tex]x = \frac{122.20 + 1.35y}{0.10} [/tex]

Substitute the value of x above in equ. 1

[tex] \frac{122.20 + 1.35y}{0.10} + y = 172[/tex]

L. C. M = 0.10

Multiply through by the L. C. M

[tex]122.20 + 1.35y + 0.10y = 17.2[/tex]

Collect like terms

122.20 - 17.2 = - 1.35y - 0.10y

105 = - 1.25y

[tex]y = \frac{105}{1.25} = 84[/tex]

Substituting the value of y in equ. 1

[tex]x + 84 = 172 \\ x = 172 - 84 \\ x = 88[/tex]

Therefore, 84 sundaes were sold and 88 ice-cream cones were sold.

For the second question, let paint represent 'p' and brush represent 'b'

[tex]8p + 3b = 152.5 \: \: \: equ2 \\ 6p + 2b = 113 \: \: \: equ1[/tex]

Solving simultaneously,

Subtract equ2 from equ 1

[tex]2p + b = 39.5 \\ b = 39.5 - 2p[/tex]

Substituting the value of b in equ1

[tex]6p + 2(39.5 - 2p) = 113 \\ 6p + 79 - 4p = 113[/tex]

Collect like terms

[tex]2p = 113 - 79 \\ 2p = 34 \\ p = 17[/tex]

Substituting the value of p in equ1

[tex]6(17) + 2b = 113 \\ 102 + 2b = 113[/tex]

Collect like terms

[tex]2b = 113 - 102 \\ 2b = 11 \\ b = 11 \div 2 \\ b = 5.5[/tex]

Therefore, a gallon of paint costs 17 dollars and a brush costs 5.5 dollars (i.e 5 dollars, 50 cents)

The correct decision and summary based on the excel output below is  Standard Error =5.389361. and P-value=0.5364.

Two sample T summary hypothesis test:

[tex]u_{1[/tex] : Mean of Population 1

[tex]u_{2}[/tex] : Mean of Population 2

[tex]u_{1} -u_{2}[/tex] : Difference between two means

[tex]H_{0}[/tex] : [tex]u_{1} -u_{2}[/tex] = 0

[tex]H_{a}[/tex] : [tex]u_{1} -u_{2}[/tex]

 0

(without pooled variances)

Hypothesis test results:

Difference = u1-u2

Sample Diff=3.34725

Standard Error =5.389361.

DF=77.988073

T-Stat=0.62108476

P-value=0.5364

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SOLUTION

We are told to translate; (x, y) to (x -8, y). This means we have to add - 8 to each value of x in P(-5,1), Q(-4,6), and R(-2,3).

In P(-5,1), x = -5 and y = 1

In Q(-4,6), x = -4 and y = 6 and

In R(-2,3), x = -2 and y = 3

For the dilation centered at the origin k =2, simply multiply the value of k, which is 2 into the translations.

The approximate age of the bone is 22920

The half-life of an isotope is characterized as the sum of time it takes for there to be half the beginning sum of the radioactive isotope present.

since we know for half time

N = N₀(1/2) n     ..........1

where n is the new amount whereas N₀ is the initial amount  and n is the number of half time

since the ratio of  14c:12c  is 1/16

so the equation 1 gets converted  to

N/No =(1/2)n

=>1/16 = (1/2)n

=>(1/2)4 = (1/2)n

=> n= 4

So the age of the bone will be 4*  5730 =22920

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You find a piece of bone that has a 14c/12c ratio that is 1/16 that of the atmospheric 14c/12c ratio. If the half-life of 14C is 57305730 years what is the approximate age of the bone?

Answer:

x = 50° , y = 40°

Step-by-step explanation:

x and 40° form a right angle and sum to 90° , that is

x + 40° = 90° ( subtract 40° from both sides )

x = 50°

x and y form a right angle and sum to 90° , then

x + y = 90°

50° + y = 90° ( subtract 50° from both sides )

y = 40°

Based on the ratios given of 0.3 : 4 = 9 : y, the value of y can be found to be 120

From the given ratios of 0.3 : 4 = 9 : y, we can infer that these are equivalent ratios.

This means that y is to 9, what 4 is to 0.3.

The value of y can therefore be found by direct proportion:

0.3 : 4

9 : y

Cross multiplying gives:

0.3 y = 36

y = 36 / 0.3

y = 120

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(i) When sinФ=2/3 → It lies in Ist and IInd quadrants and the suitable graph is not provided here.

(ii) when cosФ=-1/2 → It lies in IInd and IIIrd quadrants and the suitable graph is A and D.

(iii) when cotФ=3/4 → It lies in Ist and IIIrd quadrants and the suitable graph is E.

(iv) when cosecФ=3/2 → It lies in the Ist quadrant and the suitable graph is not provided here.

What is Quadrant?

(i) When sinФ=2/3

Ф=sin^(-1)(2/3)

Ф=41.81°,138.18°

So it lies in Ist and IInd quadrant.

A suitable graph is not provided here.

(ii) when cosФ=-1/2

Ф=cos^(-1)(-1/2)

Ф=120°,240°

So it lies in IInd and IIIrd quadrant.

A suitable graph is A and D.

(iii) when cotФ=3/4

Ф=cot^(-1)(3/4)

Ф=53.13°,233,13°

So it lies in Ist and IIIrd quadrant.

A suitable graph is E.

(iv) when cosecФ=3/2 or sinФ=2/3

Ф=sin^(-1)(2/3)

Ф=0.729°

So it lies in Ist quadrant.

A suitable graph is not provided here.

(i) When sinФ=2/3 → It lies in Ist and IInd quadrants and the suitable graph is not provided here.

(ii) when cosФ=-1/2 → It lies in IInd and IIIrd quadrants and the suitable graph is A and D.

(iii) when cotФ=3/4 → It lies in Ist and IIIrd quadrants and the suitable graph is E.

(iv) when cosecФ=3/2 → It lies in the Ist quadrant and the suitable graph is not provided here.

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Considering Justin's serve, it is found that:

a) The ball traveled 21.4 feet, which means that Justin's estimate is correct.

b) An assumption regarding the angle of Justin's serve was made.

c) The Pythagorean Theorem was used to solve this mathematical problem.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle(triangle which has an angle of 90º between the two legs) with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following rule:

[tex]h^2 = l_1^2 + l_2^2[/tex]

Assuming that the ball was served at an angle of 90º, the situation can be summarized as follows:

Hence the Pythagorean Theorem is applied and the distance is calculated as follows:

d² = 7.5² + 20²

d = sqrt(7.5² + 20²)

d = 21.4 feet.

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