A Norman window is a window with a semicircle on top of a regular rectangular window as shown in the diagram. What should the dimensions of the rectangular part of a Norman window be to allow in as much light as possible if there is only 12 ft of the framing material available?

Answer:

150%

Step-by-step explanation:

Answer:

66.7%

Step-by-step explanation:

\( \frac{16}{24} \times 100 = 66.67\)

The linear equation we need to solve is:

$27.50*w = $309.99 - $144.99

And the solution is w = 6.

How to write and solve the equation?

We know that the cost of the gaming chair is $309.99.

To buy this, you already have saved $144.99, and save another $27.50 per week, then the amount you have after w weeks is:

f(w) = $144.99 + $27.50*w

So the linear equation we need to solve is:

$144.99 + $27.50*w = $309.99

To solve this we need to isolate w.

$144.99 + $27.50*w = $309.99

$27.50*w = $309.99 - $144.99

w = ($309.99 - $144.99)/$27.50 = 6

So they can buy the chair after 6 weeks.

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Answer:

5x(8-1)=(5x10)-(5x4)

Answer: 16,200,000

Step-by-step explanation: divide both numbers

The future value of her deposit would be in 5 years.

The total amount needed to start a cupcake cafe venture

= $9,000

Deposit per year = $1,800

Therefore, if $1,800 = 1 year

$9,000 = X

\(x = \frac{9000}{1800} \)

\(x = 5\)

Therefore in 5 years, Jamie Lee would be able to start her cupcake café venture.

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An expression for the area of △KNM is = 1/2 x 2b x a

Given,

In the question:

In triangle KNM ;

The length of the base (MK) = 2b

and, height of the triangle is= a

To write an expression  for the area of △KNM .

Now, According to the question:

We know that :

Area of triangle is = 1/2 x base x height

The length of the base (MK) = 2b

and, height of the triangle is= a

Plug all the values in the area of triangle :

Here, Area of triangle is = 1/2 x 2b x a

Hence, An expression for the area of △KNM is = 1/2 x 2b x a.

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The domain of the function shown in the graph is (-∞, ∞), so option B is correct.

The collection of possible input values is referred to as the domain, and the domain of a graph is made up of all the input values displayed on the x-axis. The collection of potential output values that make up the range is represented by the y-axis.

As you can see from the graph, the function is defined at every set of values,

Therefore, the domain of the function shown in the graph is (-∞, ∞).

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Answer:

arc a = 64°

arc b = 112°

Step-by-step explanation:

inscribed angles = 1/2 their arc

arc of 102° = 204° arc

arc a = 204° - 140° = 64°

arc of 92° = 184°

arc b = 360° - 184° - 64° = 112°

The probability of randomly picking a school or library-related issue from the ballot is 9/19 or approximately 0.474 (rounded to three decimal places).

To determine the probability of a randomly picked issue being school or library related, you'll need to consider the total number of issues and the number of school and library issues combined.

There are 7 school-related issues, 10 ordinance-related issues, and 2 library-related issues, making a total of 19 issues on the ballot. To find the probability of picking a school or library issue, combine the number of school and library issues: 7 + 2 = 9.

Now, divide the number of school and library issues (9) by the total number of issues (19): 9/19.

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Answer:

32778

Step-by-step explanation:

76543-43765=32778

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer:

Yes that a good answer...

Answer:

\(g(x) = 30\cdot x +40\); \(a \approx 1.898\), \(k = 40\).

Step-by-step explanation:

The resultant function is obtained by multiplying \(f(x)\) by a real number \(k\). That is:

\(g(x) = k \cdot f (x)\)

If \(k = 5\) and \(f(x) = 6\cdot x + 8\), then \(g(x)\) is:

\(g(x) = 5\cdot (6\cdot x + 8)\)

\(g(x) = 30\cdot x +40\)

Given that presence of the expression \(g(x) = 6^{a}\cdot x + k\), then:

\(6^{a} = 30\) and \(k = 40\)

The value of a is obtained by applying the definition of logarithms:

\(a = \log_{6}30\)

\(a \approx 1.898\)

Finally, the value of k is found by direct comparison:

\(k = 40\)

Answer: 1/5 and 8

Step-by-step explanation:

Answer:

Therefore, there are 10 nickels in the coin purse.

Step-by-step explanation:

Let's call the number of dimes in the coin purse "D" and the number of nickels "N".

We know the total value of the coins in the purse is $0.70, which we can express in cents as 70 cents:

5N + 10D = 70

We also know that the number of nickels is two less than six times the number of dimes:

N = 6D - 2

We can substitute the second equation into the first equation to get an equation with only one variable:

5(6D - 2) + 10D = 70

Simplifying this equation, we get:

30D - 10 + 10D = 70

Combining like terms, we get:

40D = 80

Dividing both sides by 40, we get:

D = 2

So there are 2 dimes in the coin purse.

Using the equation N = 6D - 2, we can find the number of nickels:

N = 6(2) - 2 = 10

Therefore, there are 10 nickels in the coin purse.

Using the height and radius given, the surface area of the cylinder is 408.2m²

The surface area of a cylinder is the combined area of its curved surface (lateral surface) and its two circular bases. The formula for the surface area of a cylinder is:

A = 2πrh + 2πr²

where:

In the given question, the data are;

Substituting the value into the formula

A = 2π(5 * 8) + 2π(5)²

A = 408.2m²

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Answer:

the fourth box (parabola)

Step-by-step explanation:

yeah

To have the same price, 40 stickers will have to be ordered and the equation is 16 = 0.40p.

What is the equivalent equation?

Equivalent equations are algebraic equations with identical solutions or roots. Adding or subtracting the same number or expression from both sides of an equation yields an equivalent equation. An equivalent equation is created by multiplying or dividing both sides of an equation by the same non-zero number.

We have,

for company A :

Design Fee = $30

Costvper sticker = $0.80

for company B :

Design Fee = $14

Cost per sticker = $1.20

Let the number of stickers = p

Total cost of company A = 30 + 0.80p

Total cost of company B = 14 + 1.20p

For the cost to be the same :

Company A = Company B

30 + 0.80p = 14 + 1.20p

Collect like terms :

30 - 14 = 1.20p - 0.80p

16 = 0.40p

p = 16/0.40

p = 40 stickers

Therefore, to have the same price, 40 stickers will have to be ordered and the equation would be 16 = 0.40p.

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Answer:

a.) 3x+2y=34 is the equation. 2 pairs could be 10,2 and 8,5.

b.) .5x+2y=14

c.) 8,5

Step-by-step explanation:

because both 8 and 5 work in both equations 3(8)+2(5)=34

.5(8)+2(5)=14

Answer:

Step-by-step explanation:

In 2017, California led the nation with 858 pedestrian fatalities. Arizona had only 216. The 2017 population of California was 39,536,653 and of Arizona was 7,016,270. Compute and compare the rate of pedestrian fatalities per 100,000 residents.

Solution

The pedestrian fatality rate for California per 100,000 residents

= pedestrian fatality in California / total population in California × 100,000

= (858 / 39,536,653) × 100,000

= 2.17 people per 100,000

The pedestrian fatality rate for Arizona per 100,000 residents

= pedestrian fatality in Arizona / total population in Arizona × 100,000

= (216 / 7,016,270) * 100,000

= 3.08 people per 100,000

This means that, though California may have a higher number of pedestrian fatalities compared to Arizona, the rate of pedestrian fatalities per 100,000 residents in California is lower compared to Arizona.

Answer:

30.85

Step-by-step explanation:

1. Put the 12.34 on top to make things simpler

then just multiply each number as if the decimals weren't there to begin with.

Your answer should look way too big, but when you finish multiplying count how many decimal places were in the two numbers, for this it would be 3 since there is a 5, 3, and 4 behind the decimal places.

You have to count 3 decimal places in your final answer to get the right solution! Any 0's trailing behind can be removed as well.

Hope this helps!!!

Answer: 30.85

Step-by-step explanation:

This is the answer because you have to straight up your decimal so you can multiply your numbers up right and every time you get ready to add you suppose to add a extra zero.

Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

Answer:

D

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

(-5,4)

To get from B to A, the x value increases 5 and the y value increases 5, for every one unit increase in x, y also increases by 1. 1/5 of the way is 1/5 times 5 = 1. Just increase both x and y by 1 to get (-5, 4)

-6+1 = -5 = x and 3 + 1 = 4 = y (-5,4) is the point 1/5 of the way from B to A

Point B is in coordinates (1,6):

The first coordinate is for vertical lines and correspond to coordinates in x: x=1 and the second coordinate is for horizontal lines and correspond to coordinates in y: y=6

Then, the answer is: V: x=1; H: y=6

Answer:

17. a  18. c   19. d   20. b

Step-by-step explanation:

Hello, for the first question, you just take the person with the largest number and the person with the smallest number. Kenny (5) and Sammy (0).

For question 18, you just add up all the numbers like this:

0+1+3+5+4+1+1+2+1= 18

And then you divide it by the number of people there which is 9:

18/9=2

For question 19, you arrange all the numbers from least to greatest like this:

0,1,1,1,1,2,3,4,5

And then you count on both ends until it meets the middle. 1 is the middle.

For the last question, you just find the number that appears the most, which is one.

step 1

Adds the total yards that Rick walked

1,280+920+589+856=3,645 yards

step 2

Divide 3,645 by 125 yards

3.645/125=29.16

step 3

Multiply 29.16 by $15

29.16*15=$437.40

The number 5 is closest to the mean of the distribution, option (B) is correct.

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

From the histogram:

2, 6, 4, 2, 0, 1, 6, 4, 2, 1

The sum of the above data = 28

= 2×1+6×2+4×3+2×4+0×5+1×6+6×7+4×8+2×9+1×10

= 2+12+12+8+6+42+32+18+10

= 142

Mean = 142/28

= 5.07

Thus, the number 5 is closest to the mean of the distribution option (B) is correct.

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Answer:4

Step-by-step explanation:jus done this question

Answer: what unit is this?

Step-by-step explanation:yeah I’ll need the unit to solve this question

The scale factor of dilation from WY to W'Y' is 2.75

From the question, we have the following parameters that can be used in our computation:

The length of WY is 1.5

The length of W'Y' is 4.125

From the complete question, we understand that:

Dilation changes the size of the shape that is being dilated.

This means that

Scale factor = The length of W'Y'/The length of WY

Substitute the known values in the above equation, so, we have the following representation

Scale factor = 4.125/1.5

Evaluate the quotient

Scale factor = 2.75

Hence, the scale factor is 2.75

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Complete question

Line WY is dilated to create line W'Y' using point Q as the center of dilation.

What is the scale factor?

Given that The length of WY is 1.5 and the length of W'Y' is 4.125

Answer:

3

Step-by-step explanation:

Every minute a 3 pointer was scored as 24/8 is 3