Which of the following similarity statements about the triangles in the figure is true?

Right triangle P Q R has angle Q marked as a right angle. A segment is drawn from point Q to side P R. The point where the segment intersects side PR is point S. Angle P S Q is marked as a right angle.

A. Triangle P Q R is similar to triangle P S Q, which is similar to triangle Q S R.
B. Triangle R Q P is similar to triangle S Q P, which is similar to triangle R S Q.
C. Triangle Q R P is similar to triangle Q S P, which is similar to triangle Q S R.
D. Triangle P R Q is similar to triangle Q P S, which is similar to triangle R Q S.

Answer:

Using the t-distribution, the critical value needed is: t = 2.2622.

The critical value is found using a calculator, with two parameters:

For this problem, we have a confidence level of 95% and 10 - 1 = 9 df, hence the critical value is t = 2.2622.

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please send a picture of it

the equation seems a lil bit complicated

Using the hypergeometric distribution, the probabilities are given as follows:

a) 0.2 = 20%.

b) 0.5539 = 55.39%.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

Researching this problem on the internet, it is found that the council has 15 members, of which 7 are Democrats and 8 are Republicans.

Item a:

The parameters are:

N = 15, n = 2, k = 7.

The probability is P(X = 2), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,15,2,7) = \frac{C_{7,2}C_{8,0}}{C_{15,2}} = 0.2[/tex]

Item b:

At most one Democrat, with n = 3, hence:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

In which:

[tex]P(X = 0) = h(0,15,3,7) = \frac{C_{3,0}C_{8,3}}{C_{15,3}} = 0.1231[/tex]

[tex]P(X = 1) = h(1,15,3,7) = \frac{C_{3,1}C_{8,2}}{C_{15,3}} = 0.4308[/tex]

Then:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1231 + 0.4308 = 0.5539[/tex]

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Answer:

a.$4165

b.$4956.35

Step-by-step explanation:

a)19% × 3500 = 665.

3500+665 =4165

b)19% × 4165 = 791.35

4165+791.35= 4956.35

Answer:7 people

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Using the monthly payment formula, he needs to deposit A = $1,342.12 a month to reach his goal.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

For this problem, the parameters are:

P = 250000, r = 0.05, n = 12 x 30 = 360.

Then:

r/12 = 0.05/12 = 0.004167.

Then:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 250000\frac{0.004167(1+0.004167)^{360}}{(1+0.004167)^{360} - 1}[/tex]

A = $1,342.12

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Answer:

Step-by-step explanation:

i didnt do anything bro why u delete my answer

See below for how the domain and the range are calculated

Function, y = -x^4 + 4

The function is given as:

y = -x^4 + 4

See attachment for the graph

From the attached graph, we have:

Function, y = 2x^3 - 1

The function is given as:

y = 2x^3 - 1

See attachment for the graph

From the attached graph, we have:

Function, y = ∛(2x + 8)

The function is given as:

y = ∛(2x + 8)

See attachment for the graph

From the attached graph, we have:

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Answer: False

Step-by-step explanation:

The only number that makes this impossible to solve is x = 0

1. The solution to the first percent puzzle is as follows:

                              75%         66²/₃         11¹/₉

          33¹/₃%        25%          22¹/₅%      3⁷/₁₀%

         50%         37¹/₂%          33¹/₃%      5¹/₂%

        50%          37¹/₂%          33¹/₃%      5¹/₂%

2. The solution to the second percent puzzle is as follows:

                           10%             90%

         50%           5%              45%

         50%           5%              45%

A percent puzzle is a puzzle that engages students to practice working with percentages.

The percent puzzle involves a matrix format, in which students multiply the column percent by the row percent to find the percent they must put in the missing boxes to complete the puzzle.

The multiplication results for the missing boxes can be either stated in decimals, fractions, or a combination.

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The equation that can be used to find the height of the tree is as follows:

[tex]\frac{h}{sin 29} =\frac{40}{sin147}[/tex]

The height of the tree is 35.6 m

Th equation that can be used to find the height of the tree uses the principle of sine rule.

Therefore,

[tex]\frac{h}{sin 29} =\frac{40}{sin(180-4-29)}[/tex]

[tex]\frac{h}{sin 29} =\frac{40}{sin147}[/tex]

Therefore,

[tex]\frac{h}{sin 29} =\frac{40}{sin147}[/tex]

cross multiply

h sin 147 = 40 sin 29°

h = 40 sin 29° / sin 147

h = 19.3923848099 / 0.54463903501

h = 35.6015636045

h = 35.6 m

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The expressions are illustrated below.

3x = 12

x = 12/3

x = 4

x + 4 = 17

x = 17 - 4

x = 13

9y + 3 = 21

9y = 21 - 3

9y = 18

y = 18/9

y = 2

x ÷ 2 = 4

x = 4 × 2

x = 8

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Answer: B

Step-by-step explanation:

1: 5 × 1.25 = 6.25

 2 × 1.25 = 2.5

 1.7 × 1.25 = 2.125

2: L × W × H = 6.25 × 2.5 × 2.125 = 33.20 cubic

Answer:

C

Step-by-step explanation:

x²-9x<-8

x²-9x+(-9/2)²<-8+(-9/2)²

(x-9/2)²<-8+81/4

(x-9/2)²<(-32+81)/4

(x-9/2)²<49/4

|x-9/2|<7/2

-7/2<x-9/2<7/2

add 9/2

9/2-7/2<x-9/2+9/2<7/2+9/2

2/2<x<16/2

1<x<8

Using the z-distribution, the 95% confidence interval of the population mean is: (17.5, 24.5).

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

For this problem, the other parameters are:

[tex]\overline{x} = 21, \sigma = 26.8, n = 225[/tex]

Hence the bounds of the interval are:

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 21 - 1.96\frac{26.8}{\sqrt{225}} = 17.5[/tex]

[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 21 + 1.96\frac{26.8}{\sqrt{225}} = 24.5[/tex]

The interval is: (17.5, 24.5).

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Answer:

log(a^x^2-27(radicalx))

Step-by-step explanation:

Assuming you have written your question correctly, this is it.

The number of board game sorted is 14

The games have been sorted into video games and board games.

The number of video games is 28 less than 6 times the number of board games.

Therefore,

the number of board games = x

number of video game = 6x - 28

The games are 80% video games. Hence,

80 / 100 × x + 6x - 28 = 6x - 28

4 / 5 × 7x - 28 = 6x - 28

4 / 5 (7x - 28) = 6x -28

28 / 5 x - 112 / 5  = 6x - 28

28 / 5 x  - 6x = -28 + 112 / 5

28x - 30x / 5 =  - 28 + 112 / 5

-2x / 5  = -28 / 5

-10x = -140

x = 14

Therefore, the number of board game sorted is 14.

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Answer:

14

Step-by-step explanation:

80 / 100 × x + 6x - 28 = 6x - 28

4 / 5 × 7x - 28 = 6x - 28

4 / 5 (7x - 28) = 6x -28

28 / 5 x - 112 / 5  = 6x - 28

28 / 5 x  - 6x = -28 + 112 / 5

28x - 30x / 5 =  - 28 + 112 / 5

-2x / 5  = -28 / 5

-10x = -140

x = 14

The value for x that is a double root of this function is x = -1

The function is given as:

f(x) = x^3 - 3x - 2

From the graph of the above function (see attachment), we have the following highlights:

The point that it touches the x-axis is the double root point

Hence, the value for x that is a double root of this function is x = -1

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The function is illustrated below based on the information.

When x <= 8000

The cost remains constant at 0.35 when x increases from 0 to 8000. The slope of the cost function over this part is 0

When 8000 < x <= 20000

The cost remains constant at 0.75 when x increases from 8000 to 20000 and the slope of the cost function over this part is 0.

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Using a system of equations, it is found that there were 100 students at the bus stop.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Considering the first paragraph, the equation is:

[tex]\frac{x}{y - 25} = \frac{3}{2}[/tex]

Considering the second paragraph, the equation is:

y - 25 = x - 15.

Hence:

y = x + 10.

Replacing on the first equation:

[tex]\frac{x}{x - 15} = \frac{3}{2}[/tex]

3x - 45 = 2x

x = 45.

y = x + 10 = 55.

The total number was:

45 + 55 = 100.

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If the value of a is negative, the line is reflected across any of the axis

The equation is given as:

y = ax

The new line is given as

y = -ax

The above implies that y = ax is transformed to y = -ax

The transformation can be any of:

Hence, if the value of a is negative, the line is reflected across any of the axis

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The matrix [tex]\vec C[/tex] resulting from the multiplication between matrices [tex]\vec B[/tex] and [tex]\vec A[/tex] is equal to the matrix [tex]\left[\begin{array}{ccc}37&55&- 20\\23&11&- 20\\25&28&-9\end{array}\right][/tex]. (Correct choice: C)

In this question we must apply the operation of multiplication of two matrices, whose definition is shown below:

[tex]\vec B\, \cdot \, \vec A[/tex], where [tex]\vec B \in \mathbb {R}_{n \times p}[/tex] and [tex]\vec A \in \mathbb{R}_{p \times n}[/tex]     (1)

Where each element of the resulting matrix is equal to the following expression:

[tex]c_{(i, j)} = b_{(i, p)} \,\bullet\, a_{(p, j)}[/tex]     (2)

Where the operator "[tex]\bullet[/tex]" represents a dot product.

Now we proceed to calculate each element of the matrix:

[tex]c_{(1, 1)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]

5 · 1 + 7 · 5 + 3 · (- 1)

37

[tex]c_{(1, 2)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]

5 · 7 + 7 · 2 + 3 · 2

55

[tex]c_{(1, 3)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]

5 · (- 3) + 7 · 1 + 3 · (- 4)

- 20

[tex]c_{(2, 1)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]

(- 3) · 1 + 7 · 5 + 9 · (- 1)

23

[tex]c_{(2, 2)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]

(- 3) · 7 + 7 · 2 + 9 · 2

11

[tex]c_{(2, 3)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]

(- 3) · (- 3) + 7 · 1 + 9 · (- 4)

- 20

[tex]c_{(3, 1)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]

2 · 1 + 5 · 5 + 2 · (- 1)

25

[tex]c_{(3, 2)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]

2 · 7 + 5 · 2 + 2 · 2

28

[tex]c_{(3, 3)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]

2 · (- 3) + 5 · 1 + 2 · (- 4)

- 9

The matrix [tex]\vec C[/tex] resulting from the multiplication between matrices [tex]\vec B[/tex] and [tex]\vec A[/tex] is equal to the matrix [tex]\left[\begin{array}{ccc}37&55&- 20\\23&11&- 20\\25&28&-9\end{array}\right][/tex]. (Correct choice: C)

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The value of bh for b =12 and h = 2 is 24

The expression is given as:

bh

Where

b = 12 and h = 2

So, we have:

bh = 12 * 2

Evaluate

bh = 24

Hence, the value of bh for b =12 and h = 2 is 24

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Answer:

B is correct

Answer:

Step-by-step explanation:

2x+3y=15

multiply by 2

4x+6y=30   ...(1)

6y=-4x+12

4x+6y=12    ...(2)

(1) and (2) represent parallel lines.

Hence no solution.