Midsegments:RZTriangle Midsegment Theorem:A midsegment of a triangle is parallel to a side of the triangle, and its length is half the length of that side.B

Answer:

Step-by-step explanation:

Assuming that the given dimensions of 13, 13, 13 refer to the base of the rectangular pyramid, we can calculate the surface area of the pyramid as follows:

First, we need to calculate the area of the rectangular base, which is simply length x width:

Area of rectangular base = 13 x 13 = 169 square units

Next, we need to calculate the area of each triangular face of the pyramid. Since the rectangular base has two sets of parallel sides, there are two types of triangular faces: the isosceles triangles on the sides and the right triangles on the front and back.

To calculate the area of the isosceles triangles, we need to first find the length of the slant height, which can be found using the Pythagorean theorem:

a² + b² = c²

where a and b are the base and height of the triangle (both equal to 13 in this case), and c is the slant height.

13² + 13² = c²

338 = c²

c ≈ 18.38

Now that we have the slant height, we can calculate the area of each isosceles triangle using the formula:

Area of isosceles triangle = (1/2) x base x height

Area of isosceles triangle = (1/2) x 13 x 18.38

Area of isosceles triangle ≈ 119.14 square units

To calculate the area of each right triangle, we need to use the same slant height of 18.38, along with the height of the pyramid, which is also 13. Then we can use the formula:

Area of right triangle = (1/2) x base x height

Area of right triangle = (1/2) x 13 x 18.38

Area of right triangle ≈ 119.14 square units

Since there are two of each type of triangular face, the total surface area of the pyramid is:

Surface area = area of rectangular base + 2 x area of isosceles triangle + 2 x area of right triangle

Surface area = 169 + 2 x 119.14 + 2 x 119.14

Surface area = 546.28 square units

Therefore, the surface area of the rectangular pyramid with base dimensions of 13 x 13 and height of 13 is approximately 546.28 square units.

Answer:

3n+6

Step-by-step explanation:

"3 times the quantity n" = 3 * n = 3n

3n+6

(a) The mean of the relevant distribution is 2.4 defective pistons.

(b) The standard deviation of the distribution is 1.539.

The mean of the relevant distribution is the expected number of defective pistons that we would expect to get from a sample of 80 pistons produced by this machine. The mean is calculated by multiplying the probability of a defective piston (3%) with the number of pistons in the sample (80). In this case, the mean is 2.4 defective pistons. The standard deviation of the distribution quantifies the uncertainty of our estimate. It is calculated by taking the square root of the variance, which is the expected value of the squared differences between the number of defective pistons in the sample and the mean. In this case, the standard deviation is 1.539. This means that, in theory, we would expect 68% of the samples to contain between 0.861 and 4.139 defective pistons.

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Rounding to the nearest cent, the estimated value of the vehicle after 4 years is approximately $23,726.20..

To estimate the value of the vehicle after 4 years, we can use the given equation A = 39500(0.86)^t, where A represents the value of the vehicle and t represents the number of years.

Substituting t = 4 into the equation:

A = 39500(0.86)^4

A ≈ 39500(0.5996)

A ≈ 23726.20

Rounding to the nearest cent, the estimated value of the vehicle after 4 years is approximately $23,726.20.

This estimation is based on the assumption that the vehicle's value decreases by 14% each year. The equation A = 39500(0.86)^t models the exponential decay of the vehicle's value over time. By raising the decay factor of 0.86 to the power of 4, we account for the 4-year period. The final result suggests that the value of the vehicle would be around $23,726.20 after 4 years of ownership.

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\(-9x + y = 3\implies y = \stackrel{\stackrel{m}{\downarrow }}{9} x +3 \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so then

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {9\implies \stackrel{slope}{\cfrac{9}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{9}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{9}}}\)

so we're really looking for the equation of a line whose slope is -1/9 and passes through (-9 , -1)

\((\stackrel{x_1}{-9}~,~\stackrel{y_1}{-1})\qquad \qquad \stackrel{slope}{m}\implies -\cfrac{1}{9} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{-\cfrac{1}{9}}(x-\stackrel{x_1}{(-9)}) \\\\\\ y+1=-\cfrac{1}{9}(x+9)\implies y+1=-\cfrac{1}{9}x-1\implies y=-\cfrac{1}{9}x-2\)

Answer:

−15x2+23x−6

Step-by-step explanation:

(3x−1)(−5x+6)

=(3x+−1)(−5x+6)

=(3x)(−5x)+(3x)(6)+(−1)(−5x)+(−1)(6)

=−15x2+18x+5x−6

=−15x2+23x−6

Answer:

The answer is 300

Answer:

300 students

Step-by-step explanation:

hope this helps!

3. The factored polynomial is p(x) = (x - 1)(x - 5)

4. The factored polynomial is p(x) = (x + 3)²

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.

This implies that its factors are (x - 1) and (x - 5)

So, the factored polynomial is p(x) = (x - 1)(x - 5)

4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots

This implies that its factors are (x - (-3)) = (x + 3) twice

So, the factored polynomial is p(x) = (x + 3)²

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Answer:

$9.24 for 12 lbs.

Step-by-step explanation:

To solve, divide the cost with the amount of pounds you get:

$4.80 for 5 lbs:

Divide 4.80 with 5:

4.80/5 = 0.96

If you were to buy 5 lbs for $4.80, each pound will cost $0.96.

$9.24 for 12 lbs:

Divide 9.24 with 12:

9.24/12 = 0.77

If you were to buy 12 lbs for $9.24, each pound will cost $0.77.

∴ Purchasing 12 lbs of flour for $9.24 will be cheaper by $0.19 per pound.

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The sales tax rate of the cocktail table is 0.055

A sales tax is a consumption tax imposed by the government on the sale of goods and services

The cocktail table sold for $250 and the sales tax amount was $13.75. The sales tax rate can be calculated as follows:

Sales tax = list price * sales tax rate

Therefore,

sale tax rate = sales tax / list price

sales tax = $13.75

list price = $250

sale tax rate = 13.75 / 250

sales tax rate = 0.055

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In the context of this problem all the solutions to the polynomial equation is correct because they all make sense.

The given polynomial equation  can be expressed as ;

x³ + 6x² - 40x = 192 and the given solutions can be written as ; x = -8, x = -4, and x = 6

We can test if the solution is the best for the given euation because this will help us to know if these valueas are the solution for the equation

x = -8

[(-8)³ + 6(-8)² - 40(-8)]

= 192

[-512 + 384 + 320]

= 192

x = -4,

[(-4)³ + 6(-4)² - 40(-4)]

[-64 + 96 + 160 ]

= 192

x = 6

[(6)³ + 6(6)² - 40(6) ]

216 + 216 - 240

= 192

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Answer:

Step-by-step explanation:

A,B

x = –8

x = –4

all work should be in the picture, lmk if theres anything confusing

Answer:

x = 10/243

Step-by-step explanation:

3^5x = 10

243x = 10

Divide 243 on both sides

10/243

Step-by-step explanation:

2-×^2

t(×)=3×

(s o t )(x)=st(×)=s(t(x))=2-(3×)^2=2-9x^2

(s o t)(-7) =2-9(-7)^2=2-9(49)= 2-441= -439

Answer:

16 ounces = 1 pound

Step-by-step explanation:

You would just do 18/16 = 1.125 pounds. There are always 16 ounces in a pound, so it always works like this

Answer:

The correct answer will be 18

Step-by-step explanation:

First mutiply your object of the question which is 9 times 16 then make sure you have the right answer then divide it by 8 and 144 the answer you got, and you get 18

Answer:

The equation of the parallel line will be y = -2.5x - 8.

Step-by-step explanation:

First things first, let's rearrange the line equation provided into a more standard form:

\(5x + 2y = 14\)

\(5x - 14 = -2y\)

\(\frac{5x - 14}{-2} = y\)

\(y = -2.5x + 7\)

Therefore, we can see that this line has a slope (the coefficient preceding x) of -2.5. The parallel line must therefore also have a slope of -2.5.

Now, let us set the y-intercept of the parallel line to be (0, a) (since it must be on the y-axis).

If we factor in all of this, we get the equation:

\(\frac{a-(-3)}{0-(-2)} = -2.5\)

Remember, the slope is found by dividing the vertical difference with the horizontal difference.

\(a - (-3) = -2.5(0+2)\)

\(a + 3 = -5\)

\(a = -8\)

Hence, the equation of the parallel line will be y = -2.5x - 8.

Hope this helped!

Answer:

7/30

Step-by-step explanation:

The difference means subtracting so 14/15 - 7/10 = 7/30 or decimal form is 0.23

By Pythagorean theorem, the maze is solved in the following way: x = 6√5 → x = 2√5 → x = 13√5 → x = 2√41 → x = 18√2 → x = 4√6 → x = 4√41 → x = 8√3 → x = 8√5

In this problem we need to complete a maze by means of Pythagorean theorem, whose definition is now introduced:

r² = x² + y²

Where:

Now we proceed to solve the maze:

Step 1:

x = √(12² + 6²)

x = 6√5

Step 2:

x = √(6² - 4²)

x = 2√5

Step 3

x = √(22² + 19²)

x = 13√5

Step 4

x = √(8² + 10²)

x = 2√41

Step 5

x = √(27² - 9²)

x = 18√2

Step 6

x = √(14² - 10²)

x = 4√6

Step 7

x = √(16² + 20²)

x = 4√41

Step 8

x = √(16² - 8²)

x = 8√3

Step 9

x = √(24²- 16²)

x = 8√5

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Answer:

Im just as lost

Step-by-step explanation:

srry I couldnt help bc I am not whatever grade that is

we could expect any standard fair die over and over 11, 22, 33, …, 66 in 258÷6 = 43 consecutive rolls.

Given a fair die, what is the expected number of rolls required in order to get three of the same consecutive outcomes e.g. 11, 22, 33, etc.?

Let E be the expected dice roll to get 3 consecutive 1’s.

Consider 4 cases.

Case 1: We roll a non-1 in our first roll (probability of 5/6). So, one trial has been done and we are yet to get 2 consecutive 1’s. So the expected rolls would be E+1.

Case 2: We roll 1 in our first roll and then a non-1 in the next (probability of 1/6*5/6). So we wind back to the start and the expected rolls would be E+2.

Case 3: We roll two consecutive 1’s at the start and a non-1 after that (probability of 1/6*1/6*5/6). So the expected rolls would be E+3.

Case 4: We roll three 1’s consecutively at the start (probability of 1/6*1/6*1/6) and we are done. So the expected rolls here are just 3.

So the recurrence relation follows.

So we could expect a sequence of 11 in 258 rolls.

Therefore we could expect any of 11, 22, 33, …, 66 in 258/6 = 43 rolls.

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The medians are about the same.

Option C is the correct answer.

The median, in statistical terms, refers to the value in the center of a dataset that has been sorted either in ascending or descending order, and it is a commonly used measure of central tendency. This contrasts with the mean, which calculates the total value of all figures, then divides by the number of figures.

We have,

Movie theater 1.

From the box plot given,

The median is 995.

Movie theater 2.

From the box plot given,

The median is 995.

Thus,

The median in both the box plot is the same.

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Answer:

x = 47

Step-by-step explanation:

x + 121 = 4x - 20

-3x + 121 = - 20

-3x = -141

x = 47

So, the answer is x = 47

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Answer:

Step 1: Make sure the polynomial is written in descending order. If any terms are missing, use a zero to fill in the missing term

Answer:

  $142.32, profit on sale of the policy

Step-by-step explanation:

You want to know the expected value of a $280,000 life insurance policy sold for $270, if the probability the insured will live for the year is 0.999544.

The insurance company expects to have to pay the $280,000 death benefit for 0.000456 of the policies issued. That means their expected payout on any one policy is ...

  0.000456 × $280,000 = $127.68

The company gets a premium of $270 for the policy, so the expected value of the policy to the company is ...

  $270 -127.68 = $142.32

The expected value of the policy to the company is $142.32.

This represents its profit from sale of the policy.

__

Additional comment

Of course, the company has expenses related to the policy, perhaps including a commission to the agent selling it, and expenses related to handling claims. That is to say that not all of the difference between the premium and the average death benefit is actually profit. It is what might be called "contribution margin."

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First, let us locate the coordinates of the original triangle:

A(-3, 1)

B(1, 2)

C(-2, 4)

We are given the point about which the dilation would take place as:

(-1, 1)

The rule for dilation is :

The coordinates of the triangle after transformation(dilation) is:

Let us subtract the coordinates (-1,1) from each point and then multiply by the scale factor, and then add back the point (-1,1)

The plot of the original triangle and triangle after transformation is shown below:

The coordinates of the triangle after transformation is:

A'(-5,1)

B'(3,3)

C'(-3,7)

Answer:

The score on the remaining test is x = 61

Hence, option D is correct.      

Step-by-step explanation:

Let 'x' be the score of the remaining test

The average score of Nadine's six tests = 77

so

Average score = (88+65+75+83+90+x) / 6

substituting average score = 77 in the equation to find 'x'

                  77   = (401 + x) / 6

              401 + x = 77 × 6

                        x = 462 - 401

                        x = 61

Therefore, the score on the remaining test is x = 61

Hence, option D is correct.                              

Answer:

To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:

8x = x + 9

Solving for x, we get:

x = 1.5

Therefore, AB = 8x = 8(1.5) = 12.

To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:

AB^2 + BD^2 = AD^2

Substituting the values, we get:

12^2 + BD^2 = (1.5 + 9)^2

Simplifying, we get:

BD^2 = 56.25

Taking the square root of both sides, we get:

BD = 7.5

Hence, the length of AB is 12 and the length of BD is 7.5.

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