Match each radius to the exact area of the circle with the radius

Answer: 66.5 inches

Step-by-step explanation:

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\(p = 2 \times (( - 3x - 5) + (3 - 4x)) \\ \)

Collect like terms

\(p = 2 \times ( - 7x - 2)\)

\(p = - 14x - 4\)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\(p = 66\)

Thus ;

\( - 14x - 4 = 66\)

Add sides 4

\( - 14x - 4 + 4 = 66 + 4\)

\( - 14x = 70\)

Divide sides by -14

\( \frac{ - 14x}{ - 14} = \frac{70}{ - 14} \\ \)

\(x = - \frac{7 \times 10}{7 \times 2} \\ \)

\(x = - \frac{5 \times 2}{2} \\ \)

\(x = - 5\)

Done...

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Answer:

152

Step-by-step explanation:

All segments in a triangle add to 180. 1

8+10+x=180

x=152

The length x using Pythagoras theorem is 15 unit.

According to the Pythagorean theorem, the square of the hypotenuse of a right triangle equals the sum of the squares of the other two sides.

Given:

Hypotenuse = 18 unit

Perpendicular = 10 unit

using Pythagoras theorem

H² = P² + B²

18² = 10² + B²

324 = 100 + B²

324 - 100 = B²

B² = 224

B= 14.966 unit

B= 15 unit

Thus, the measure for x is 15 unit.

Learn more about Pythagoras theorem here:

https://brainly.com/question/343682

#SPJ7

Step-by-step explanation:

When we say sum we are referring to addition.

And a number and a variable(letter) can't be added. So the sum of 8 and t can't be added.

The sum of 8 and t is;

8+t

When we talk about product or finding the product of a number we are referring to the number we get after multiplying two or more numbers.

And note that with multiplication, a number and a variable(letter) can be multiplied.

The product of 5 and b is;

5×b=5b

The new coordinates of points M and O is determined as;

M = (0.5, - 1)

O = (2.5, -2).

The new coordinate of points M and O after applying the scale factor is calculated as follows;

The given scale factor = 1/2

The current coordinates of point M and O is;

M = (1, - 2)

O = (5, - 4)

A scale factor can be used to either enlarge a figure or decrease a figure.

When the scale factor is less than 1, it means the new figure will be smaller than the original figure.

However, if the scale factor is greater than 1, the new figure will be greater than the original figure.

The new coordinates of points M and O is determined as follows;

M = (1 x 1/2,  -2 x 1/2) = (0.5, - 1)

O = (5 x 1/2, -4 x 1/2) = (2.5, -2)

Learn more about scale factor here: https://brainly.com/question/2826496

#SPJ1

a.) Suppose you have 500 feet of fencing to enclose a rectangular plot of land that borders on a river. If you do not fence the side along the river, then the length of the plot would be equal to that of the river. Suppose the length of the rectangular plot is x and the width is y.

So, the fencing required would be 2x + y = 500. y = 500 − 2x. The area of the rectangular plot would be xy.

Substitute y = 500 − 2x into the equation for the area.

A = x(500 − 2x) = 500x − 2x²

Now, differentiate the above equation with respect to x.

A = 500x − 2x²

dA/dx = 500 − 4x

Set dA/dx = 0 to get the value of x.500 − 4x = 0or, 500 = 4x

So, x = 125

Substitute x = 125 into y = 500 − 2x to get the value of y.y = 500 − 2x = 250 ft

The maximum area is A = xy = 125 × 250 = 31,250 sq. ft.

b.) Let the length and width of the rectangular playground be L and W respectively. Then, the perimeter of the playground is L + 3W. Given that 900 feet of fencing is used, we have:

L + 3W = 900 => L = 900 − 3W

Area = A = LW = (900 − 3W)W = 900W − 3W²

dA/dW = 900 − 6W = 0W = 150

Substitute the value of W into L = 900 − 3W to get:

L = 900 − 3(150) = 450 feet

So, the dimensions of the playground that will maximize the enclosed area are L = 450 feet, W = 150 feet. The maximum area is A = LW = 450 × 150 = 67,500 square feet.c.)

Let x be the number of $1 increments. Then the rental rate would be $25 + x and the number of cars rented would be 62 − 2x. Hence, the revenue would be (25 + x)(62 − 2x) = 1550 − 38x − 2x²

Differentiating with respect to x, we get dR/dx = −38 − 4x = 0or, x = −9.5. This value of x is not meaningful as rental rates cannot be negative. Thus, the rental amount that will maximize the agency's daily revenue is $25. The maximum daily revenue is R = (25)(62) = $1550.

To know more about Area of rectangle visit-

brainly.com/question/31822659

#SPJ11

According to the information we can conclude that the maximum area for the plot is 15,625 square feet (part a). Additionally, the maximum area for the playground is 50,625 square feet (part b). Finally the maximum daily revenue is $975 (part c).

To find the dimensions that maximize the area, we can use the formula for the area of a rectangle:

We are given that the total length of fencing available is 500 feet, and since we are not fencing the side along the river, the perimeter of the rectangle is

Solving for L, we have

Substituting this into the area formula, we get

To find the maximum area, we can take the derivative of A with respect to w, set it equal to zero, and solve for w. The resulting width is 125 feet, and the length is also 125 feet. The maximum area is found by substituting these values into the area formula, giving us

Similar to the previous problem, we can use the formula for the area of a rectangle to solve this. Let the width of the playground be w, and the length be L. We have

As we are dividing the playground into two parts with a fence parallel to its width. Solving for L, we get

Substituting this into the area formula, we have

To find the maximum area, we can take the derivative of A with respect to w, set it equal to zero, and solve for w. The resulting width is 225 feet, and the length is also 225 feet. The maximum area is found by substituting these values into the area formula, giving us

Let x be the rental rate in dollars. The number of cars rented can be expressed as

Since for each $1 increase in rate, two fewer cars are rented. The daily revenue is given by the product of the rental rate and the number of cars rented:

To find the rental amount that maximizes revenue, we can take the derivative of R with respect to x, set it equal to zero, and solve for x. The resulting rental rate is $22. Substituting this into the revenue formula, we find the maximum daily revenue to be

Learn more about revenue in: https://brainly.com/question/14952769
#SPJ4

Answer:

140°

Step-by-step explanation:

\( \because m\widehat{BG} = 360\degree - m\widehat{GCB} \\

\therefore m\widehat{BG} = 360\degree - 300\degree \\

\therefore m\widehat{BG} = 60\degree \\

\because m\widehat{BGD} = m\widehat{BG}

+m\widehat{GD}\\

\therefore m\widehat{BGD} = 80\degree+60\degree\\

\therefore m\widehat{BGD} = 140\degree\\

\because m\angle BAD = m\widehat{BGD} \\

\huge\purple {\boxed {\therefore m\angle BAD =140\degree}} \)

When m2 = m3, it implies that the slopes of line segments 2 and 3 are equal. This condition indicates that line segments 2 and 3 are parallel.

In geometry, the slope of a line represents its steepness or inclination. When two lines have the same slope, it means that they have the same steepness or inclination, and therefore, they are parallel.

In the given context, the statement "m2 = m3" suggests that the slopes of line segments 2 and 3 are equal. This implies that both line segments have the same steepness and direction, indicating that they are parallel to each other.

The slope of a line can be determined by comparing the ratio of the vertical change (change in y-coordinates) to the horizontal change (change in x-coordinates). If two lines have the same ratio of vertical change to horizontal change, their slopes will be equal, and they will be parallel.

Therefore, when m2 = m3, we can conclude that the line segments corresponding to m2 and m3 are parallel to each other.

The correct question should be :

Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none.

When m2 = m3

To learn more about line segments visit : https://brainly.com/question/2437195

#SPJ11

For k = - 3 and n = - 2, the expression evaluates to - 6.

We have the following expression -

- \(k^{2}\) - (9k - 7n) + 5n

We have to evaluate the above expression for k = - 3 and n = - 2.

The expression ax + b for x = - 2 can be evaluated as follows -

Substituting the value of x = - 2, we get :  - 2a + b

We can similarly solve the expression given to us -

- \(k^{2}\) - (9k - 7n) + 5n

Substitute k = - 3 and n = - 2 in the equation, we get -

\(-(-3)^{2} - (9\times -3 \;\;-\;\;7\times -2) + 5\times -2\)

- 9 - (- 27 + 14) - 10

- 9 + 27 - 14 - 10

18 - 14 - 10

18 - 24

- 6

Hence, for k = - 3 and n = - 2, the expression evaluates to  - 6.

To solve more questions on evaluating the expression, visit the link below -

https://brainly.com/question/15964396

#SPJ1

Answer:

10,000

Step-by-step explanation:

the 4 means to multiply the 10 4 times.

Answer:

10,000

Step-by-step explanation:

Answer: 15 feet

Step-by-step explanation:

The probability that the random variable will take on a value between 31 and 35 is 0.2620 or 26.20%.

To solve this problem, we need to standardize the values of 31 and 35 using the formula:

z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

For x = 31:

z = (31 - 30) / 5 = 0.2

For x = 35:

z = (35 - 30) / 5 = 1

Now, we can use a standard normal distribution table or calculator to find the probabilities corresponding to these z-values. The probability of getting a value between 31 and 35 is the difference between the probability of getting a z-value less than 1 and the probability of getting a z-value less than 0.2:

P(31 ≤ x ≤ 35) = P(z ≤ 1) - P(z ≤ 0.2)
= 0.8413 - 0.5793
= 0.2620

Therefore, the probability that the random variable will take on a value between 31 and 35 is 0.2620 or 26.20%.

To learn more about probability here:

brainly.com/question/30034780#

#SPJ11

Answer:

(150-36π) ft^2

Step-by-step explanation:

we need to subtract the area of the circle from the area of the trapezoid to find the area of the shaded region.

area of circle=πr^2=π6^2=36π ft^2

area of trapezoid=(1/2)(a+b)h=(1/2)(12+13)12=150 ft^2

so, the area of trapezoid-area of circle=(150-36π) ft^2

Answer:

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

Correct choice is D

Answer:

0.36 × 15

Step-by-step explanation:

To find a percentage of a number, convert the percentage to its decimal equivalent, then multiply it by the number.

\(\begin{aligned}\implies 36\% \;\textsf{of}\; $15&=\dfrac{36}{100} \times 15\\&=0.36 \times 15\\&=5.4\end{aligned}\)

Therefore, the correct expression to find 36% of $15 is:

1. I based my decision on allocating points to maximize my own score, while also considering the potential benefits of contributing to the group fund.

2. The best outcome for me would be allocating the minimum points required to the GIVE account, while putting the majority in the KEEP account. This would ensure I receive the most points for myself.

3. The best outcome for the group would be if both participants maximized their contributions to the GIVE account. This would create the largest group fund, resulting in the most redistributed points and highest average score.

4. There are parallels with risk management strategies. Individuals may act in their own self-interest, but a larger group benefit could be achieved if more participants contributed to "group" risk management strategies like vaccination, safety protocols, insurance policies, etc. However, some individuals may free ride on others' contributions while benefiting from the overall results. Incentivizing group participation can help align individual and group interests.

Answer:

2 × 10⁵

Step-by-step explanation:

The following data were obtained from the question:

6×10⁹/ 3×10⁴ =?

The above expression can be simplified as follow:

6×10⁹/ 3×10⁴ = 6×10⁹ ÷ 3×10⁴

Recall:

Aᵐ ÷ Aⁿ = Aᵐ ¯ ⁿ

Therefore,

6×10⁹ ÷ 3×10⁴ = (6/3) × 10⁹ ¯ ⁴

6×10⁹ ÷ 3×10⁴ = 2 × 10⁵

Thus, 6×10⁹/ 3×10⁴ is equal to 2 × 10⁵

Answer:

57 1/10

(14× 3/4)+(4× 1/2)+(8× 1/2)+(10× 2/5)+(10× 2/5)+(12× 4/5)= 571/10 or 57× 1/10

Answer:

8x

Step-by-step explanation:

Combine Like Terms:

= x+2x+5x

= (x+2x+5x)

= 8x

Answer: Not a solution of the System

Step-by-step explanation:

Plug in 0 for x and 2 for y for both equations.

Note, if only one of the equations is a true statement

(0.2) is not a solution. If either one of the equation is not true, the ordered pair is not a solution.

0+3(2)=4

3*2=6

0+6=6

6≠4

This was only the first equation but it was not true.

The equation is not true, so (0, 2) is not a solution of the second equation.  Therefore, (0, 2) is not a solution of the system of equations.

To determine graphically whether the ordered pair (0, 2) is a solution of the system of equations, we can plot the two equations on a graph. If the point (0, 2) lies on both lines, then it is a solution of the system.

The first equation is x + 3y = 4.  To plot this equation, we can first solve for y:

y = -(1/3)x + 4/3

This equation has a slope of -1/3 and a y-intercept of 4/3.  So, the line will rise 1 unit for every 3 units it moves to the left.  The y-intercept is 4/3, so the line will pass through the point (0, 4/3).  Three units to the left of (0, 4/3) is (-3, 7/3), so the line will also pass through this point.

The second equation is 3x + y = -2.  To plot this equation, we can first solve for y:

y = -3x - 2

This equation has a slope of -3 and a y-intercept of -2.  So, the line will fall 3 units for every 1 unit it moves to the right.  The y-intercept is -2, so the line will pass through the point (0, -2).  One unit to the right of (0, -2) is (1, -5), so the line will also pass through this point.

We can  check this algebraically.  Substituting (0, 2) into the first equation, we get:

0 + 3× 2 = 4

6 ≠ 4

This equation is not true, so (0, 2) is not a solution of the first equation.  Substituting (0, 2) into the second equation, we get:

3  × 0 + 2 = -2

2 = -2

This equation is also not true, so (0, 2) is not a solution of the second equation.  Therefore, (0, 2) is not a solution of the system of equations.

Learn more about equation here: brainly.com/question/10724260

#SPJ2

Answer:

To estimate the number of pentagons in the tub, we can use the proportion of pentagons in the sample of geometric shapes that Mrs. Chen selected and apply it to the total number of geometric shapes in the tub.

The proportion of pentagons in the sample is:

4 / (3 + 2 + 2 + 4 + 2) = 4 / 13 ≈ 0.31

We can assume that this proportion is representative of the entire tub of geometric shapes, and we can apply it to the total number of geometric shapes in the tub:

0.31 x 250 ≈ 77.5

Rounding to the nearest whole number, we can estimate that there are approximately 78 pentagons in the tub.

Therefore, the estimated number of pentagons in the tub is 78.

Answer:

$165

Step-by-step explanation:

Rachel works for a clothing store. She is paid $150 every week plus a 10% commission on any clothes that she sells.

Let's find the total amount she is being paid per week

Amount paid originally = $150

Percentage Commission = 10%

Commission = 10% of 150

Commission = 0.1×150

Commission = $15

Total amount paid = originally amount + Commission

Total amount paid = $150+$15

Total amount paid =$165

Hence the amount paid to Rachel okus Commission is $165

Downsizing refers to the process of reducing the size and workforce of a company to cut costs, increase efficiency, or adapt to changing market conditions. It involves eliminating positions, reducing staff numbers, or even closing down certain business units or branches.

Downsizing can occur for various reasons, such as financial difficulties, mergers and acquisitions, technological advancements, or strategic reorganization. Companies often assess their operational costs and decide to downsize to improve their financial performance.

During the downsizing process, companies may calculate the potential cost savings by considering factors such as salaries, benefits, severance packages, and operational expenses. For example, if a company decides to eliminate 100 positions with an average salary of $50,000 per year, it could result in annual savings of $5 million.

While downsizing can help companies achieve short-term cost reductions, it often has significant implications for the affected employees, including layoffs, reduced morale, and increased workload for remaining staff. It is crucial for organizations to handle the downsizing process with sensitivity and transparency, providing support to affected employees and communicating the rationale behind the decisions.

It is important to note that downsizing should not be seen as a long-term solution, but rather as a strategic measure to address specific challenges. Companies should also explore alternatives to downsizing, such as retraining and redeploying employees, implementing productivity improvements, or seeking new business opportunities, to ensure sustainable growth and success in the long run.

To know more about workforce, visit;
https://brainly.com/question/28843491
#SPJ11

1609.34 meters (M).

To determine this, we first need to convert the 7.0-minute mile to seconds, since we need to use the same units for time in our calculations.

7.0 minutes x 60 seconds/minute = 420 seconds

Next, we need to convert the distance of one mile to meters, since we need to use the same units for distance in our calculations.

1 mile = 1609.34 meters

Finally, we can use the formula for speed to find the content loaded of the athlete running a 7.0-minute mile:

Speed = Distance / Time

Speed = 1609.34 meters / 420 seconds

Speed = 3.83 meters/second

Therefore, the content loaded of a 75 kg athlete running a 7.0-minute mile is equal to 1609.34 meters (M).

Learn more about formula for speed

brainly.com/question/3004254

#SPJ11

(Hey, angles rock!)

Answer:

45 + 60 = 105

Step-by-step explanation:

ABC consists of two angles, angle ABD and angle DBC. Therefore, the sum of the measures of angles ABD and DBC is the measure of ABC.

45 + 60 = 105

The degree of freedom would be 36.

What is the degree of freedom in statistics?

It is a mathematical equation that tells how many values can vary and can aid in determining whether or not the results are statistically significant. In statistics, the most commonly encountered equation for determining degrees of freedom is df = N-1.

Que.16)

It is a statistic. Because it gives information about the sample.

Que.17)

Because 35 is close to 36.

Que.18)

degrees of freedom = n -1 = 37-1 = 36

Que .19)

\(C.I. = \bar{X} \ \pm \ t_{\alpha/2, n-1} \ \frac{s}{\sqrt{n}} \\ \\ \\ C.I. = 5.2 \pm 2.160 \ \frac{1.9}{\sqrt{14}} \\\\\\ C.I. = (4.1032, 6.2968)\)

\(t_{\alpha/2, n-1} = t_{0.05/2, 14-1} = 2.16\) it is obtained using t table.

Que. 20)

\(\\ C.I. = \bar{X} \pm z_{\alpha /2} \ \frac{\sigma }{\sqrt{n}} \\ \\ \\ C.I. = 93.2 \pm 2.58 \frac{16.9}{\sqrt{110}} \\\\\\ C.I. = (89.0427, 97.3573)\)

Hence, the degree of freedom would be 36.

To learn more about the degree of freedom, visit:

https://brainly.com/question/17284745

#SPJ4

The number of tiles needed to cover the floor is 60 tiles.

Given Information,

The floor area of the passage = 2.4 m²

Length of a side of square tile = 200mm

Length of the side is in mm which needs to be converted in its standard form which is meters.

Therefore, the length of side = 200/1000 m

                                                = 0.2 m

Area of the square tile = 0.2 x 0.2

                                      =  0.04 m²

Let the number of tiles be x.

∴ Number of tiles = \(\frac{Area of passage}{Area of each tile}\)

 x = 2.4/0.04

 x = 60

∴ The number of tiles needed to cover the floor is 60 tiles.

Let's check similar questions on Area : https://brainly.com/question/25092270

Mike Sullivan recently retired as Professor of Mathematics at Chicago State University, having taught there for more than 30 years. He received his PhD in mathematics from Illinois Institute of Technology.

He is a native of Chicago’s South Side and currently resides in Oak Lawn, Illinois. Mike has 4 children; the 2 oldest have degrees in mathematics and assisted in proofing, checking examples and exercises, and writing solutions manuals for this project. His son Mike Sullivan, III co-authored the Sullivan Graphing with Data Analysis series as well as this series. Mike has authored or co-authored more than 10 books. He owns a travel agency and splits his time between a condo in Naples, Florida and a home in Oak Lawn, where he enjoys gardening.

Michael Sullivan, III has training in mathematics, statistics and economics, with a varied teaching background that includes 27 years of instruction in both high school and college-level mathematics. He is currently a full-time professor of mathematics at Joliet Junior College. Michael has numerous textbooks in publication, including an Introductory Statistics series and a Precalculus series which he writes with his father, Michael Sullivan.

Michael believes that his experiences writing texts for college-level math and statistics courses give him a unique perspective as to where students are headed once they leave the developmental mathematics tract. This experience is reflected in the philosophy and presentation of his developmental text series. When not in the classroom or writing, Michael enjoys spending time with his 3 children, Michael, Kevin and Marissa, and playing golf. Now that his 2 sons are getting older, he has the opportunity to do both at the same time!

Product details

Publisher ‏ : ‎ Pearson; 4th edition (8 January 2018)

Language ‏ : ‎ English

Hardcover ‏ : ‎ 1224 pages

To know more about developmental visit-

brainly.com/question/29203588

#SPJ11

There are 4 possible answers for the first question and 5 possible answers for the second question, so there are a total of 4 x 5 = 20 possible outcomes.

A set of potential outcomes from a random experiment is known as a sample space. The sample space is identified by the letter "S." Events are the subset of possible experiment results.The results in a sample area could vary depending on the experiment. Discrete or finite sample spaces are those that have a finite number of outcomes.

The sample space showing all possible outcomes of the two questions is the Cartesian product of the two sets of answer choices, which is:

{(A, A), "(A, B), "(A, C), "(A, D), "(A, E), "(C, A), "(C, B), "(C, C), "(C, D), "(C, E")," "(D, A), "(D, B), "(D, C), "(D, D), "(D, E)}.

There are 4 possible answers for the first question and 5 possible answers for the second question, so there are a total of 4 x 5 = 20 possible outcomes. Each outcome is a pair of answers, where the first element of the pair is the answer to the first question and the second element of the pair is the answer to the second question.

Learn more about sample space , visit:

https://brainly.com/question/30206035

#SPJ1

In her presentation, Alaina can use a pie chart to show information about how the typical college student spends their day.

A circular chart that has been divided into sectors or "pie slices" to represent numerical proportions is known as a pie chart. Each pie slice symbolises a percentage, and each slice's size is proportional to the percentage it represents.

In this instance, Alaina can separate the pie chart into four segments that stand in for the various activities that college students engage in throughout the day: sleeping, attending classes, studying, and participating in extracurricular activities. She can give each slice a unique colour and a label indicating the proportion it represents.

The pie chart, for instance, might have the following slices:

-30% of people are sleeping (blue).

- 20% of the class (in green)

20% of study time (coloured)

30% of time for socializing

Know more about pie chart here:

https://brainly.com/question/1109099

#SPJ11

Answer:

y=36.25

Step-by-step explanation:

substitute x

y=7.25(5)

y=36.25

Answer:

y=36.25

Step-by-step explanation:

We are given

y= 7.25x

and

x=5

We know that x is equal to 5, therefore we can substitute 5 in for x.

y= 7.25x

y=7.25(5)

Multiply 7.25 and 5

y=36.25