The perimeter of a rectangle i 80 inche. The length of the rectangle i 12 inche. Which equation could repreent the width of the rectangle, w? Repone w = 2(80 – 12) w, = 2(80 – 12) w = (80 – 12) ÷ ÷ 2 w, = (80 – 12) divided by 2 w = 2(80 – 24) w , = 2(80 – 24) w = (80 – 24) ÷ ÷ 2

If the polygon is a square the other 2 coordinates are

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points  (0, 0) and (3, 2) is the diagonal of the polygon calculated as follows

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

d =√{(3 - 0)² + (2 - 0)²}

d =√{9 + 4}

d = √13 units

this is the hypotenuse

from Pythagoras theorem

let length of one side be x

√13² = x² + x²

13 = 2x²

6.5 = x²

x = 2.5495

x = 2.55 units

In ordered pair this is 2.55 units from the origin in the x and y direction

(0, 2.55) and (2.55, 0)

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Answer:

Okay so what we need to do is prove that they are not the same.

Step-by-step explanation:

So first we need to find out what 6*2 is which practically is 6 x 6.

Its so because the exponent 2 means you multiply that by that many times. So it would look like 6 x 6 which is different from 2 x 6.

2 x 6 is just multiplying the two different numbers together, and they are not expenentiol so that's your answer.

Hope this helped :P

Lisa bowling score is 100.

John bowling score is 282.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

Lisa and John are bowling.

Johns score is three times the difference of Lisa's score and 6.

The sum of their scores is 382.

Now, Let Lisa bowling score = x

Then, John bowling score = 3 (x - 6)

Since, The sum of their scores is 382.

Hence,

x + 3 ( x - 6 ) = 382

After solving,

x + 3x - 18 = 382

4x = 382 + 18

4x = 400

x = 100

Hence, Lisa bowling score = x = 100

And, John bowling score = 3 (x - 6)

                                       = 3 (100 - 6)

                                       = 3 × 94

                                       = 282

Therefore, Lisa bowling score is 100.

And, John bowling score is 282.

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a.) The probability that Ben is ruined is 0.07776, or approximately 7.78%

b.) The probability that Jerry is ruined is 0.064, or approximately 6.4%

a. To find the probability that Ben is ruined, we need to calculate the probability of Jerry winning all the remaining games.
Ben starts with $9 and Jerry starts with $6. In order for Jerry to wipe out Ben, he needs to win at least $9 from Ben.
Let's consider the scenario where Ben loses all his remaining money, one game at a time.
For Ben to lose $9, Jerry needs to win at least 5 games in a row.
The probability of Jerry winning a game is 0.6. So, the probability of Jerry winning 5 games in a row is 0.6^5 = 0.07776.
Therefore, the probability that Ben is ruined is 0.07776, or approximately 7.78%.

b. To find the probability that Jerry is ruined, we need to calculate the probability of Ben winning all the remaining games.
For Jerry to be ruined, Ben needs to win at least $6 from Jerry.
Let's consider the scenario where Jerry loses all his remaining money, one game at a time.
For Jerry to lose $6, Ben needs to win at least 3 games in a row.
The probability of Ben winning a game is 0.4 (since Jerry wins with a probability of 0.6). So, the probability of Ben winning 3 games in a row is 0.4^3 = 0.064.
Therefore, the probability that Jerry is ruined is 0.064, or approximately 6.4%.

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Answer:

1.2x10^-1 seconds

Step-by-step explanation:

Answer:

0.12 seconds

Step-by-step explanation:

just think - how long does it take you to travel for example 30 km, if you are going 60 km/h ?

you have to divide 30 by 60 and get 0.5 or 1/2. meaning it takes you (logically) 30 minutes or half an hour to do so.

it is the same principle for all these kinds of questions.

we only need to keep an eye on the dimension of what we are talking about. is it hours or seconds ? meters or kilometers ? and do in

we need here to focus on seconds and to calculate

3.6×10⁷ / 3×10⁸ = 3.6 / 3×10¹ = 1.2 / 10 = 0.12 seconds

or

\(1.2 \times {10}^{ - 1} \)

seconds

Answer:

Step-by-step explanation:

sun cos

Answer:

The mean will be 420 without round of and after round of it will be 400

The value of mean absolute deviation of the numbers is,

⇒ 4.3

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

The numbers below represent the speeds of the last 6 vehicles that a police officer recorded:

⇒ 68, 72, 78, 59, 73, 70

Hence, Mean of data set is,

= (68 + 72 + 78 + 59 + 73 + 70)/ 6

= 70

So, The value of mean absolute deviation of the numbers is,

⇒ |68- 70| + |72 - 70| + |59 - 70| + |73 - 70| + |70 - 70| / 6

⇒ 13 / 3

⇒ 4.3

Thus, The value of mean absolute deviation of the numbers is,

⇒ 4.3

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There are 13,992 integers between 1 and 1,000,000 with a sum of digits equal to 15.

To find the number of integers between 1 and 1,000,000 with a sum of digits equal to 15, we can use a combinatorial approach.

We need to distribute the sum of 15 among the digits of the number. We can think of this as placing 15 indistinguishable balls into 6 distinct boxes (corresponding to the digits).

Using the stars and bars method, the number of ways to distribute the sum of 15 among 6 boxes is given by the combination formula:

C(n + r - 1, r - 1)

where n is the sum (15) and r is the number of boxes (6).

Plugging in the values, we have:

C(15 + 6 - 1, 6 - 1) = C(20, 5)

Calculating this combination, we find:

C(20, 5) = 13,992

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Answer:

47.5cm^2

Step-by-step explanation:

A=a+b /2h

A=a+b

2h=6+13

2·5=47.5

to find the area of a trapezoid, use the equation A = \(\frac{a+b}{2}\)h

a = 6 cm, b = 13 cm, and h = 5 cm.

\(\frac{6+13}{2}\)x 5 = 47.5

The area of the trapezoid should be 47.5 cm.

Hope this helped! :D

Answer:

128 pizzas

Step-by-step explanation:

Y = 3.4x + 43

Substitute 25 for x

y = 3.4(25) + 43

y = 128

So the model predicts that  128 pizzas will be sold if 25 coupons are issued.

Answer:

\(-16\)

Step-by-step explanation:

\(f(5)=4(5)-1=19 \\ \\ g(5)=2^5+3=35 \\ \\ (f-g)(5)=f(5)-g(5)=19-35=-16\)

The correct order to draw the angle bearing of 55° at a point is as follows:

Draw a vertical line from point X to represent North. Option D.

Place the centre of the protractor on point X and 0° on the North line. Option B.

Make a mark at 55°. Option C

Draw a line from point X through the mark. Option A.

An angles can be drawn from a point using a protractor to measure the angle of its bearing before joining the formed angle.

The correct steps that should be used include the following;

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To find the area of a quadrilateral with given coordinates, you can use the Shoelace Formula.

The Shoelace Formula, also known as Gauss's area formula, provides a method to calculate the area of any polygon given its coordinates. Here's how it works for a quadrilateral:

Let's say you have the coordinates of the four vertices of the quadrilateral: (x1, y1), (x2, y2), (x3, y3), and (x4, y4).

1. Write down the coordinates in a clockwise order:

  (x1, y1), (x2, y2), (x3, y3), (x4, y4), (x1, y1).

2. Multiply each x-coordinate by the y-coordinate of the next vertex.

  For example, for the first vertex (x1, y1), multiply x1 by y2, and for the second vertex (x2, y2), multiply x2 by y3, and so on.

3. Multiply each y-coordinate by the x-coordinate of the next vertex.

  For example, for the first vertex (x1, y1), multiply y1 by x2, and for the second vertex (x2, y2), multiply y2 by x3, and so on.

4. Add up all the results from Steps 2 and 3.

5. Take the absolute value of the sum calculated in Step 4 and divide it by 2.

By following the steps of the Shoelace Formula, you can calculate the area of a quadrilateral given its coordinates. Remember to ensure that the coordinates are listed in a clockwise or counterclockwise order to obtain the correct result. This method can be applied to any quadrilateral shape and provides an efficient way to find its area without requiring complex calculations or trigonometric functions.

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Based on the information, we can determine convergence or divergence of series.The given options do not provide a clear representation of potential outcomes.It is not possible to select correct option.

The given series is "nvž enn |||-) En=12 100 1-) Σπίο 3* 2"-1 ||-) En=2 n". In the series, we have the characters "nvž enn |||-)" which indicate the series notation. The characters "En=12 100 1-" suggest that there is a summation of terms starting from n = 12, with 100 as the first term and a common difference of 1. The characters "Σπίο 3* 2"-1 ||-) En=2 n" indicate another summation, starting from n = 2, with a pattern involving the operation of multiplying the previous term by 3 and subtracting 1.

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The mass of the radioactive sample at the beginning of the 11th day of the experiment is approximately 286 grams.

Since the mass is decreasing by 14% per day, we can find the mass at the beginning of each day by multiplying the previous day's mass by 0.86 (which is 100% - 14%).

At the beginning of the first day, the mass was 1300 grams.

At the beginning of the second day, the mass is:

1300 grams x 0.86 = 1118 grams (rounded to the nearest gram)

At the beginning of the third day, the mass is:

1118 grams x 0.86 = 962 grams (rounded to the nearest gram)

We can continue this pattern to find the mass at the beginning of the 11th day:

Mass at the beginning of the fourth day: 962 grams x 0.86 = 828 grams

Mass at the beginning of the fifth day: 828 grams x 0.86 = 711 grams

Mass at the beginning of the sixth day: 711 grams x 0.86 = 612 grams

Mass at the beginning of the seventh day: 612 grams x 0.86 = 526 grams

Mass at the beginning of the eighth day: 526 grams x 0.86 = 452 grams

Mass at the beginning of the ninth day: 452 grams x 0.86 = 388 grams

Mass at the beginning of the tenth day: 388 grams x 0.86 = 333 grams

Mass at the beginning of the eleventh day: 333 grams x 0.86 = 286 grams (rounded to the nearest gram)

Therefore, the mass of the radioactive sample at the beginning of the 11th day of the experiment is approximately 286 grams.

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Answer:

x = -2/5 or x = -28/5

Step-by-step explanation:

Let's solve your equation step-by-step.

5(|2x+6|)=26

Step 1: Divide both sides by 5.

5(|2x+6|)/5 = 26/5

|2x+6|=26/5

Step 2: Solve Absolute Value.

|2x+6|=26/5

We know either2x+6= 26/5 r2x+6=−26/5

2x + 6 = 26/5(Possibility 1)

2x+6−6= 26/5 - 6 (Subtract 6 from both sides)

2x = -4/5

2x/2 = -4/5/2 (Divide both sides by 2)

x = -2/5

2x + 6=-26/5 (Possibility 2)

2x+6= -26/5 (Simplify both sides of the equation)

2x + 6 - 6 = -26/5  - 6 (Subtract 6 from both sides)

2x = -56/5

2x/2 = -56/5/2(Divide both sides by 2)
x = -28/5

Answer:

x = -2/5 or x = -28/5

The profit margins (return on sales) for each division are approximately :Division A = 10.85%,Division B = 9.11% and The calculations for the year would be:Net Income = $85,428,Return on Assets = 18.9%.

To compute the profit margins (return on sales) for each division, we divide the profit by the sales and multiply by 100 to express the result as a percentage.

For Division A:

Profit Margin = (Profit / Sales) * 100

Profit Margin = ($230,000 / $2,120,000) * 100

Profit Margin ≈ 10.85%

For Division B:

Profit Margin = (Profit / Sales) * 100

Profit Margin = ($34,700 / $381,000) * 100

Profit Margin ≈ 9.11%

To calculate the net income and return on assets for Polly Esther Dress Shops Inc., we use the given information.

Net Income = Profit Margin * Sales

Net Income = 7% * $1,220,400

Net Income = $85,428

Return on Assets = Profit Margin * Asset Turnover

Return on Assets = 7% * 2.7

Return on Assets = 18.9%

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Answer:

8 inches

Step-by-step explanation:

The volume of a hemisphere is half the volume of a sphere.

Therefore, the sum of the volumes of the two hemisphere-shaped scoops of ice cream (with diameters of 4 inches), is equal to the volume of a sphere with diameter of 4 inches.

If the melted ice cream fills the cone exactly to the top without overflowing, the volume of the cone with diameter of 4 inches must be equal to the volume of a sphere with diameter of 4 inches.

As the diameter of a circle is twice its radius, then the radius of the sphere and cone is r = 2 inches.

The formulas for the volume of a cone and the volume of a sphere are:

\(\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}\)   \(\boxed{\begin{minipage}{4 cm}\underline{Volume of a sphere}\\\\$V=\dfrac{4}{3} \pi r^3$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\\\end{minipage}}\)

The depth of the cone is its height.

Therefore, to calculate how deep the cone must be so that the melted ice cream will fill the cone exactly to the top without overflowing, set the two equations equal to each other, substitute r = 2, and solve for h (the depth of the cone).

\(\begin{aligned}\textsf{Volume of a cone}&=\textsf{Volume of a sphere}\\\\\dfrac{1}{3} \pi (2)^2 h & = \dfrac{4}{3} \pi (2)^3\\\\\dfrac{1}{3} \pi \cdot 4 h & = \dfrac{4}{3} \pi \cdot 8\\\\\dfrac{4}{3} \pi h& = \dfrac{32}{3} \pi \\\\\dfrac{4}{3} h& = \dfrac{32}{3} \\\\4 h& = 32 \\\\h&=\dfrac{32}{4}\\\\h&=8\; \sf inches\end{aligned}\)

Therefore, the depth of the cone must be 8 inches.

The cone must be at least 8 inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing.

1. The opening of the ice cream cone has a diameter of 4 inches. This means that the radius of the cone's opening is 4/2 = 2 inches.

2. The two hemisphere-shaped scoops of ice cream have diameters of 4 inches each. This means that the radius of each scoop is 4/2 = 2 inches.

3. When the ice cream melts, it will take up the space between the scoops and fill the cone. In order for the melted ice cream to fill the cone exactly to the top without overflowing, the depth of the cone must be equal to the combined height of the two ice cream scoops.

4. The height of each hemisphere-shaped scoop can be calculated using the formula for the volume of a sphere, which is (4/3)πr³, where r is the radius.

  - For each scoop, the radius is 2 inches, so the height of each scoop is (4/3)π(2)³ = (4/3)π(8) = (32/3)π.

5. Since there are two scoops, the combined height of the two scoops is 2 * (32/3)π = (64/3)π.

6. Therefore, the cone must be at least (64/3)π inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing. This is approximately equal to 67.03 inches.

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Answer:

Reflection on y=1

Dilation by 2 (Enlargement)

Translation 1 to the right

Step-by-step explanation:

Im not that sure tho sorry

Answer:

Dilate ABCD by a scale factor of 2. Then reflect the image.

Step-by-step explanation:

Answer:

185

Step-by-step explanation:

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,2021.22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40

I give up

The 185th digit in the pattern is 5.

It is a sequence where the difference between each consecutive term is the same.

We have,

To find the 185th digit in the pattern, we can first calculate the total number of digits in the pattern up to and including the 16th number.

We can do this by noticing that the first nine numbers each have one digit, the next 90 numbers each have two digits, and the final 7 numbers each have three digits.

So, the total number of digits in the pattern is:

9 x 1 + 90 x 2 + 7 x 3

= 9 + 180 + 21

= 210

Since 210 is greater than 185, we know that the 185th digit must be one of the first 16 numbers.

To figure out which number it is, we can subtract the total number of digits in the first 15 numbers from 185, which gives us:

185 - (9 x 1 + 90 x 2 + 6 x 3)

= 185 - (9 + 180 + 18)

= 185 - 207

= -22

Since the result is negative, we know that the 185th digit must be the 3rd digit from the end of the 15th number, which is 1 5.

Therefore,

The 185th digit in the pattern is 5.

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Answer:

The value of x is 20 ft

Step-by-step explanation:

15/6 = 2.5

8 x 2.5 = 20

Answer: 65 - $39 = $26 >> amount you save

26 / 65 = 0.4 = 40% >> discount rate

Step-by-step explanation:

A LOD score is the ratio of probabilities that two genes are linked to the probability that they are not linked, expressed as a log10. This measure is commonly used in linkage analysis, a statistical method used to determine whether genes are located on the same chromosome and thus tend to be inherited together.

In linkage analysis, the LOD score is used to determine the likelihood that two genes are linked, based on the observation of familial inheritance patterns. A LOD score of 3 or higher is generally considered to be strong evidence for linkage, indicating that the likelihood of observing the observed inheritance pattern by chance is less than 1 in 1000.

The LOD score is also used to estimate the distance between two linked genes, with higher LOD scores indicating that the two genes are closer together on the chromosome. In general, the LOD score is a useful tool for identifying genetic loci that contribute to complex diseases or traits.

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Answer:

x=46

Step-by-step explanation:

hope this helps

6 Students can arrange themselves in 720 different ways to sit in the front row of an auditorium.

To determine the number of ways 6 students can arrange themselves to sit in the 6 seats in the front row, you can use

the concept of permutations.

There are 6 seats, so for the first seat, there are 6 choices of students who can sit there.

For the second seat, 5 students remain, so there are 5 choices.

For the third seat, 4 students remain, so there are 4 choices.

For the fourth seat, 3 students remain, so there are 3 choices.

For the fifth seat, 2 students remain, so there are 2 choices.

For the last seat, only 1 student remains, so there is 1 choice.

Now, multiply the number of choices for each seat together to find the total number of arrangements:

6 × 5 × 4 × 3 × 2 × 1 = 720 ways.

So, 6 students can arrange themselves in 720 different ways to sit in the front row of an auditorium.

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Step-by-step explanation:

Given equation of line: y = 5x/4 - 5

To graph the line, we need to identify the x and y intercepts. This can be done by setting the x and y values to 0 and solving for each variable.

Setting the y-variable to 0 and solving for x (x-intercept):

Adding 5 both sides of the equation:

Smart Tip: If the x-variable is being multiplied by a fraction, simply multiply the fraction by its reciprocal to isolate the x-variable. Here, 5/4 is being multiplied to the x-variable. Since the reciprocal of 5/4 is 4/5, we will multiply 4/5 on both sides of the equation to isolate the x-variable.

Therefore, the x-intercept is located at (4, 0).

Side note: It is not required to plug x = 0 to solve for the y-intercept since we are given b = -5 in the slope intercept form equation, where b is known as the y-intercept. But if you want to show evidence that -5 is the y-intercept is the correct y-intercept, you are free to do that task!

Plotting the points on the coordinate plane:

Now, it is time to plot the x and y intercepts on the graph so that we can draw the line with the help of the two "plotted" points on the graph.

After plotting these points, your graph should look like the attachment.

Graphing the line on the coordinate plane:

This is the last and final step to finish the problem. Take a ruler and with the help of the two points plotted, draw the line.

And you are done!

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Answer:

To graph a linear equation, find at least two points on the line, plot them on a coordinate plane, then draw a straight line through them.

Step-by-step explanation:

Given linear equation:

\(y=\dfrac{5}{4}x-5\)

To graph a linear equation, find at least two points on the line, plot them on a coordinate plane, then draw a straight line through them.

To find points on the line, substitute values of x into the given equation.

Note:  As the slope of the given line is 5/4, substitute multiples of 4 as values of x to eliminate the fraction and ensure the points contain integers only.  This will make the points easier to plot.

\(\begin{aligned}x=0 \implies y&=\dfrac{5}{4}(0)-5\\y&=0-5\\y&=-5\end{aligned}\)

\(\begin{aligned}x=4 \implies y&=\dfrac{5}{4}(4)-5\\y&=5-5\\y&=0\end{aligned}\)

\(\begin{aligned}x=8 \implies y&=\dfrac{5}{4}(8)-5\\y&=10-5\\y&=5\end{aligned}\)

Therefore, to graph the given equation: