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Part 1
The length of a rectangular park is six times its width. The park is surrounded by a ​3-foot-wide path. Let x denote the width of the park. Write a quadratic function to represent the total area of the park and the path.

Step-by-step explanation:

the volume of a sphere is

4/3 × pi × r³

the original sphere had a radius of 3.

now, after a dilation of factor 4 the radius is 3×4 = 12.

the volume of that sphere is then

4/3 × pi × 12³ = 4/3 × pi × 1728 = 2304pi

The perimeter of the shape above is 22.22 units

the area of the shape above is 26 square units

We can see from the diagram shown, that the shape is made up of a semicircle below and a triangle above.

Now, the formula for calculating the area of a triangle is expressed as;

A = 1/2bh

Such that the parameters are;

Now, substitute the values

Area = 1/2 × 7 ×6

Multiply the values

Area = 42/2

Area = 26 square units

The formula for perimeter of a triangle is;

Perimeter = (a + b + c)

Perimeter = 6 + 7 + 9. 22

Add the values

Perimeter = 22. 22 units

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According to the line plot, the statement that best describes the spread and distribution of the data is "The data is bimodal with an approximate range of 24. The most frequent number of activities was either 16 or 28, which might show that the entire class needed to choose an activity.". (option c).

The horizontal number line starts at 0 and increases by units of two up to 30. The dots above the numbers represent the number of schools that offer a certain number of activities. For instance, there is one dot above 4, 6, 14, and 28, which means that only one school offers four activities, one school offers six activities, one school offers 14 activities, and one school offers 28 activities.

Based on this line plot, we can conclude that the data is not symmetric because there is not an equal number of dots on either side of the plot. Therefore, we can rule out the first and fourth options.

We can observe that there are more dots on the left-hand side of the plot, indicating that there are more schools that offer fewer activities. Additionally, the most frequent number of activities is 16, which means that about half of the schools offer this number of activities.

Furthermore, we can estimate the range of the data to be approximately 24, as the number line goes up to 30, and the highest number of activities offered by any school is 28.

Hence the correct option is (c).

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The height of this parallelogram include the following: B. 12 cm.

In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:

Area of a parallelogram, A = b × h

Where:

By substituting the given parameters into the formula for the area of a parallelogram, we have the following;

Area of a parallelogram = 10 × 12

Area of a parallelogram = 120 cm².

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Step-by-step explanation:

A = length x width = (2w + 5)(w) = 2w² + 5w

P = 2(2w + 5) + 2w = 6w + 10

To graph:  sorry, Brainly doesn't have graphing tools so I'll just have to describe it

A:  parabola, opens up, vertex at (-1.25, -3,124), crosses x axis at (-2.5, 0) and (0,0)

P:  straight line, slants up, with a slope of 6, y-intercept of 10, crosses x axis at (-1.667, 0)

FYI, the 2 graphs intersect at 2 points:  (-2, 2) and (2.5, 25)

The figure that has two more faces than a rectangular prism is a Square pyramid.

There are precisely six faces that a rectangular prism contains, which consists of a pair of identical rectangles for its top and bottom planes as well as four lateral faces consisting of corresponding right-angled, congruent rectangles. Hence, a solid figure that has two more sides than the aforementioned rectangular prism could only have eight total faces without exception.

An example of such an entity is a square pyramid whose base constitutes of four equal-length sides with four corresponding triangular surfaces converging at one single vertex on the summit's tip. Within this context, it possesses five faces (one square and four isosceles triangles), thus exceeding by two faces compared to the former geometric model.

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The correct statement regarding the relations in this problem is given as follows:

Only relation A could represent a linear relationship.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

From the first bullet point, we have that what classifies a linear relation is a constant rate of change.

For relation K, we have that it is not linear, as:

For relation R, we have that it is linear, as it has a constant rate of change.

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The total gain at the end of the second year for both accounts combined is $509.09.

We have,

Amount saved = $8500

40% of 8500 is saved in saving account = 0.4 x 8500 = $3400

Remainder amount in stock plan = 8500 - 3400 = 5100

Working for savings plan

A = P(1 + r/n[tex])^{nt[/tex]

A = 3400(1 + 0.042/1)²

A = $3691.60

So, we gain = 3691.6 - 3400 = $291.6

Working for stock plan:  

The stock plan decreases 3% in the first year

= 5100 x 0.97

= $4947

and increases 7.5% in the second year.

= 4947 x 1.75

= $5318.03

So, we gain = 5318.03 - 5100 = $218.03

Thus, the total gain is

= 291.06 + 218.03

= $509.09

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The radius of the diameter X is 6cm. Option D

To determine the radius of the circle, we have;

It is important to that the formula for diameter

The formula for calculating the diameter is given as;

d = r/2

Such that the parameters are given as;

From the information given, we have that;

Diameter, d = 12cm

Now, we have to substitute the values

Radius =diameter/2

Radius = 12/2

Radius = 6cm

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Answer:

12 - 6n

Step-by-step explanation:

As this sequence decreases, rather than increases, this tell us that the nth term of this sequence will be minus. The difference from 6 and 0 is 6, telling us that the decrease is by 6 each time. So now we know the nth term of this sequence; -6n, but the sequence of -6n is -6,-12,-18 and so on. We need 6,0,-6. To find out the second part of the nth term find the difference from the sequence given and the sequence of -6n. The difference is 12 because the 6--6 = 12. So now we get the nth term of the sequence -6n + 12 which is written as 12-6n.  

This interval is wider than the confidence interval in part (a) and the prediction interval in part (b) because it is based on the entire population of metal pieces, not just a sample.

(a) To find a 99% confidence interval on the mean diameter, we can use the t-distribution with n-1 degrees of freedom since the population standard deviation is not known. The formula for the confidence interval is:

CI = x ± tα/2,s/√n

where x is the sample mean, s is the sample standard deviation, n is the sample size, and tα/2 is the t-value with (n-1) degrees of freedom for the desired level of confidence α.

Plugging in the values, we get:

CI = 1.0056 ± t0.005/2,0.0246/√9

= 1.0056 ± 0.025

= (0.9806, 1.0306)

Therefore, we can be 99% confident that the true mean diameter of the metal pieces produced by the machine is between 0.9806 and 1.0306 centimeters.

(b) To compute a 99% prediction interval on a measured diameter of a single metal piece taken from the machine, we can use the formula:

PI = x ± tα/2,s(1 + 1/n)√(1 + 1/n)

where x is the point estimate of the diameter (in this case, the sample mean), s is the sample standard deviation, n is the sample size, and tα/2 is the t-value with (n-1) degrees of freedom for the desired level of confidence α.

Plugging in the values, we get:

PI = 1.0056 ± t0.005/2,0.0246(1 + 1/9)√(1 + 1/9)

= 1.0056 ± 0.052

= (0.9536, 1.0576)

Therefore, we can be 99% confident that a single metal piece produced by the machine will have a diameter between 0.9536 and 1.0576 centimeters.

(c) To find the 99% tolerance limits that will contain 95% of the metal pieces produced by this machine, we can use the formula:

TL = x ± kσ

where x is the sample mean, σ is the population standard deviation (which is estimated by the sample standard deviation s), k is the number of standard deviations from the mean that will contain the desired percentage of the population (in this case, 95% or 1.96 standard deviations for a normal distribution).

Plugging in the values, we get:

TL = 1.0056 ± 1.96(0.0246)

= (0.9573, 1.0539)

Therefore, we can be 99% confident that 95% of the metal pieces produced by the machine will have diameters between 0.9573 and 1.0539 centimeters. This interval is wider than the confidence interval in part (a) and the prediction interval in part (b) because it is based on the entire population of metal pieces, not just a sample.

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The missing values are 60, 100 and 40 if the Median and Mode of the  wage distribution are known to be $33.5 and $34 respectively

Wages (in Rs)_freq____        CF

0-10________4___________4

10-20_______16________20

20-30_______x________20+x

30-40______y_________20+x+y

40-50______z________20+x+y+z

50-60______6_______26+x+y+z

60-70______4______30+x+y+z

Since total 230

So, 30+x+y+z=230

x+y+z=200

Mode =34

Median = 33.5

By solving the equations we get x=60, y=100 and z=40

Hence, the missing values are 60, 100 and 40

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Let's assume the price of a citron is "x" units and the price of a fragrant wood apple is "y" units.

From the given information, we can form two equations:

7x + 9y = 135 ...(1)

9x + 7y = 137 ...(2)

We can solve this system of equations using the elimination method. Multiplying equation (1) by 9 and equation (2) by 7, we get:

63x + 81y = 1215 ...(3)

63x + 49y = 959 ...(4)

Subtracting equation (4) from equation (3), we get:

32y = 256

y = 8

Substituting the value of y in equation (1), we get:

7x + 9(8) = 135

7x + 72 = 135

7x = 63

x = 9

Therefore, the price of a citron is 9 units and the price of a fragrant wood apple is 8 units.

To complete the proof below, we have;

<EFC is right angle; definition of a right angle

m<EFC = 90 degrees; definition of a tangent line

m<EFC + m<FEC + m<ECF = 180; Triangle sum theorem

90° + m<FEC + m<ECF = 180; Substitution property of equality

m<FEC + m<ECF = 90; Subtraction property of equality

<FEC + <ECF are complementary angles; definition of complementary angles

To match the statement with their corresponding equations, we need to know the following;

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Answer:

0.375

Step-by-step explanation:

namely, what is "t" when f(t) = 2000

[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{f(t)}{2000}=500e^{0.195t}\implies \cfrac{2000}{500}=e^{0.195t}\implies 4=e^{0.195t} \\\\\\ \log_e(4)=\log_e\left( e^{0.195t}\right)\implies \log_e(4)=0.195t\implies \ln(4)=0.195t \\\\\\ \cfrac{\ln(4)}{0.195}=t\implies 7.11\approx t[/tex]

This capital gain  problem that can be modelled using this equation is one that relates to the price of a stock or share.

It can be writen as follows.....

Suppose that one purchased 900 shares of a stock at a price of $  12.55 per share .

After a year, the stock price rose to $ 13.25 per share, but you sold the shares at a price of $8. 14 per share due to financial difficulties.

You also incurred a transaction cost of $25.

What is the capital gain or loss made on the stock?

given the above question, if we solved for for the problem, we would get....

Solving for x, we get:

((900 )(x )-(900 )(x)(.01))-(900) (x-4)  +25)

= 15,740

Simplifying this expression, we get:

(0.99900x) - (36 x 900) + 25

= 15,740

0.99900 x = 15,655

x = 17.39

Therefore, the current stock price is $17.39

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Full Question:

1. Examine the equation below used for determining the capital gain made on a stock. Look through this chapter and your notes to help you write a problem that could be modeled by this equation.

.((900)(12.55)-(900)(12.55)(.01))-(900)(8.14)+25)=3,831.05

When we create a budget for television purchase as a technique, this can help you avoid overspending and ensure that you stay within your means.

It is best to ensure we you are purchasing a television that meets your needs and is within your budget. We can look for reviews, compare prices and features of different models to make an informed decision.

One can also try to purchase during sales, holidays and special events which is when retailers offer discounts and promotions.

Finally, when we create a budget, this can help you avoid overspending and ensure that you stay within your means. By setting a limit on how much you're willing to spend, you can focus on finding the best deal within your budget.

Full question "The discussion above offers a third tip for saving money on purchases which is create a budget. Write a short paragraph, consisting of 125 words or more, that applies these techniques to purchasing a television".

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Answer:60, 6.75

Step-by-step explanation:

To solve the first prompt, we must create an equality statement.

[tex]\frac{10}{45}=\frac{x}{270}[/tex] X being the distance he can go in 4.5 hours.

In order to have came up with 270, we needed to take 4.5 hours and turn it into a measure of minutes to correspond to the minute value of 45.

This is found by multiplying 4.5 by 60.

Now that we have this done, we can cross multiply the equality statement.

[tex]10\cdot270=45x[/tex]

Simplify the first side

[tex]2700=45x[/tex]

Divide both sides by 45

[tex]\frac{2700}{45}=\frac{45x}{45}[/tex]

[tex]60=x[/tex]

This means that Jacob can bike 60 miles in 4.5 hours.

For the second prompt, we need to find how long it would take for him to bike 90 miles given the amount of time it took for him to bike 10 miles.

We can use an equality statement like this:

[tex]\frac{45}{10}=\frac{x}{90}[/tex]

Now we cross multiply:

[tex]45\cdot90=10\cdot x[/tex]

Simplify:

[tex]4050=10x[/tex]

Now we can divide both sides by 10.

[tex]\frac{4050}{10}=\frac{10x}{10}[/tex]

[tex]405=x[/tex]

This means that it would take Jacob 405 MINUTES to bike 90 miles.

To turn this into a measure of hours, we need to divide 405 by 60, which comes out to 6.75.

It would take Jacob 6.75 hours to bike 90 miles.

The point that satisfies y = -3-x is (0,-3), the point that satisfies y = x-3 is (0,-3), the point that satisfies y = 3x+2 is (0,2), the point that satisfies y = 3x -2 is (0,-2), the point that satisfies y = -3x+2 is (0,2). The graph is shown below.

To find the points that satisfy the equation y = -3 - x, we can substitute different values of x and solve for y.

When x = 0, y = -3 - 0 = -3, so one point is (0, -3).

When x = 1, y = -3 - 1 = -4, so another point is (1, -4).

When x = -1, y = -3 - (-1) = -2, so another point is (-1, -2).

By repeating this process for different values of x, we can find more points that satisfy the equation.

To find the points that satisfy the equation y = x - 3, we can again substitute different values of x and solve for y.

When x = 0, y = 0 - 3 = -3, so one point is (0, -3).

When x = 1, y = 1 - 3 = -2, so another point is (1, -2).

When x = -1, y = -1 - 3 = -4, so another point is (-1, -4).

To find the points that satisfy the equation y = 3x + 2, we can once again substitute different values of x and solve for y.

When x = 0, y = 3(0) + 2 = 2, so one point is (0, 2).

When x = 1, y = 3(1) + 2 = 5, so another point is (1, 5).

When x = -1, y = 3(-1) + 2 = -1, so another point is (-1, -1).

To find the points that satisfy the equation y = 3x - 2, we can once again substitute different values of x and solve for y.

When x = 0, y = 3(0) - 2 = -2, so one point is (0, -2).

When x = 1, y = 3(1) - 2 = 1, so another point is (1, 1).

When x = -1, y = 3(-1) - 2 = -5, so another point is (-1, -5).

To find the points that satisfy the equation y = -3x + 2, we can once again substitute different values of x and solve for y.

When x = 0, y = -3(0) + 2 = 2, so one point is (0, 2).

When x = 1, y = -3(1) + 2 = -1, so another point is (1, -1).

When x = -1, y = -3(-1) + 2 = 5, so another point is (-1, 5).

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Answer:

Since the triangles are similar, their corresponding sides are in proportion. The ratio of sides AB to DE is 9:13.5, which simplifies to 2:3. Therefore, the ratio of their areas is the square of the ratio of their sides, which is 4:9.

If the area of triangle ABC is 34 cm, then the area of triangle DEF is:

Area of DEF = (Area of ABC) x (DE^2/AB^2) = 34 x (13.5^2/9^2) = 34 x 1.5^2 = 34 x 2.25 = 76.5 cm^2

Therefore, the area of triangle DEF is 76.5 cm^2.

Step-by-step explanation:

The missing length is 11.0818 unit.

We have,

Angle = 52 degree

H = 18

Using Trigonometry

cos 52 = B/H

cos 52 = x / 18

0.615661 = x  /18

x = 11.0818 unit

Thus, the missing length is 11.0818 unit.

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A linear equation which shows a proportional relationship include the following: A. y = 2x.

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 2/1 = 4/2 = 6/3 = 8/4

Constant of proportionality, k = 2.

Therefore, the required linear equation is given by;

y = kx

y = 2x

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Answer: 9

Step-by-step explanation: volume is l x w x h, so 9 x 9 x height = 729

9 x 9 = 81, so 81 x height = 729

by dividing 729 / 81, you get 9

Answer: The answer is H=9.

The reason of this is because the branch of mathematics concerned with the shape of individual objects, spatial relationships among various objects, and the properties of surrounding space.

Hence,

We can see that thats the answer because volume is l x w x h, so 9 x 9 x height = 7299 x 9 = 81, so 81 x height = 729by divide 729 / 81, you get 9

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Step-by-step explanation: Please give Brainliest.

Hope this helps!!!!

I can answer more questions if you want.

The data value corresponding to z = 0.55 is approximately 87.6075.

To find the data value corresponding to a given z-score, we need to use the formula:

z = (x - μ) / σ

where z is the standard score, x is the data value, μ is the mean, and σ is the standard deviation.

Rearranging this formula, we get:

x = z * σ + μ

Substituting the given values, we get:

x = 0.55 * 4.85 + 85.3

x = 87.6075

Therefore, the data value corresponding to z = 0.55 is approximately 87.6075.

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A normal distribution has a mean of 85.3 and a standard deviation of 4.85. Find the data value corresponding to the value of z given. (Enter your answer to four decimal places.) z = 0.55

The interest on the loan using the Banker's Rule is $139.20.

The formula for calculating interest using the Banker's Rule is:

Interest = Principal x Rate x Time / 360

where:

Principal is the amount of the loan

Rate is the interest rate as a decimal

Time is the time period in days

Using this formula, we can calculate the interest on the loan as:

Interest = 4800 x 0.088 x 105 / 360

Interest = 139.20

Therefore, the interest on the loan using the Banker's Rule is $139.20.

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∠ AFE is supplementary to ∠ AFB and the measure of ∠ AFE = 102⁰.

option A.

Supplementary angles are the two angles that sum up to 180 degrees.

That is, if the sum of two angles is equal to 180 degrees, then the two angles are supplementary.

From the given diagram we can form the following equation;

∠ AFE + ∠ AFB = 180 (sum of angles on a straight line is equal to 180⁰ )

∠ AFE = 180 - ∠ AFB

∠ AFE = 180 - 78

∠ AFE = 102⁰.

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The x-intercepts represent a zero profit.

The maximum value of the graph represents the maximum profit.

The function increases up till the vertex and decreases after it.

This means that the profit increases as it reaches the peak at the vertex.

It decreases after the vertex up till it reaches zero.

On the left of the first zero and on the right of the second zero, the profits are negative.

An approximate average rate of change of the graph from x = 3 to x =5 represents the reduction in profit from 3 to 5

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