Which congruent angles can prove that
lines Land M are parallel?

A. 2 and 7
B. 5 and 8
C. 4 and 6

Answer:

$32.1

Step-by-step explanation:

First find out what 25% of 40 is:

$40 x .25 = $10

Take the answer and subtract that from the original price:

$40 - $10 = $30

Next, take the sales tax (7% or 0.07) and multiply that by the new price:

$30 x 0.07 = $2.1

Lastly, take the answer and add that to the new price:

$30 + $2.1 = $32.1

Then you would get your answer:

$32.1

The peak flow rate of the river as it exits the catchment area is determined using the given data. The answer to part (a) will provide the calculated value for the peak flow rate.

(a) To calculate the peak flow rate of the river, we can use the Rational Method, which relates the peak flow rate to the catchment area, rainfall intensity, and run-off coefficient. The formula for the peak flow rate (Q) is given by Q = C × A × R, where C is the run-off coefficient, A is the catchment area, and R is the rainfall intensity.

Using the given values, C = 0.32, A = 8.5 km²

(convert to m²: \((8.5) 10^6\) m²), and R = 140 mm/h (convert to m/s: 140/3,600 m/s), we can substitute these values into the formula to calculate the peak flow rate.

Q = \(\[0.32 \times 8.5 \times 10^6 \times \left(\frac{140}{3,600}\right)\]\) m³/s

Simplifying the equation, we get the peak flow rate of the river as it exits the catchment area.

(b) To determine if the water will overflow the bridge, we need to assess the hydraulic capacity of the canyon beneath the bridge. The Manning's equation can be used to calculate the flow velocity (V) in an open channel, given the Manning roughness coefficient (n), hydraulic radius (R), and slope (S). The formula is V = \(\(\frac{1}{n} \cdot R^{\frac{2}{3}} \cdot S^{\frac{1}{2}}\)\).

Using the given values, n = 0.05, R = 1.5 m, and S = 5.4 m/km (convert to m/m: 5.4/1,000 m/m), we can calculate the flow velocity.

V = \(\left(\frac{1}{0.05}\right) \cdot \left(1.5\right)^{\frac{2}{3}} \cdot \left(\frac{5.4}{1,000}\right)^{\frac{1}{2}}\) m/s

The flow velocity can then be used to determine the discharge (Q') of the rectangular cross-section beneath the bridge, given the width (W) and height (H) of the cross-section. The formula for the discharge is

Q' = V × W × H.

Comparing the calculated discharge with the peak flow rate calculated in part (a), we can determine if the water will overflow the bridge. If the calculated discharge is greater than the peak flow rate, the water will overflow the bridge; otherwise, it will not.

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Answer:

Step-by-step explanation:

Given sinx< cos x and 0°< x < 90°, to get the possible value of x, we need to solve the given inequality for x.

sinx< cos x

Dividing both sides by cos x

sin x/cos x < cos x/cos x

tan x < 1

x < \(tan^{-1}1\)

x < 45°

Since x is less than 45°, then one of the possible value of x can be 30° since 30° is less than 45° and 30° falls within the given range of values.

The solution of each part of the question is given below:

a. Let C be the event that a person smokes cigars, and let S be the event that a person smokes cigarettes. The percentage of Americans who smoke either cigars, cigarettes, or both can be calculated as P(C U S), where U represents the union of two events. From the given information, P(C) = 15% and P(S) = 35%. The probability that a person smokes both cigars and cigarettes is 7%, so P(C ∩ S) = 7%.

P(C U S) = P(C) + P(S) - P(C ∩ S)

P(C U S) = 15% + 35% - 7% = 43%

So, 43% of Americans smoke either cigars, cigarettes, or both.

b. The percentage of Americans who smoke neither cigars nor cigarettes can be calculated as P(C' ∩ S'), where C' represents the complement of event C (not smoking cigars) and S' represents the complement of event S (not smoking cigarettes).

P(C' ∩ S') = 100% - P(C U S)

P(C' ∩ S') = 100% - 43% = 57%

So, 57% of Americans smoke neither cigars nor cigarettes.

c. The percentage of Americans who smoke cigars but not cigarettes can be calculated as P(C ∩ S').

P(C ∩ S') = P(C) - P(C ∩ S)

P(C ∩ S') = 15% - 7% = 8%

So, 8% of Americans smoke cigars but not cigarettes.

d. The conditional probability that a person smokes cigarettes given that he smokes cigars can be calculated as P(S | C), where S represents the event that a person smokes cigarettes and C represents the event that a person smokes cigars.

P(S | C) = P(S ∩ C) / P(C)

P(S | C) = 7% / 15% = 0.47

So, the conditional probability that a randomly selected person smokes cigarettes given that he smokes cigars is 0.47, or 47%.

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Answer:

its B

hope it helps

byeeeee

Answer:

B?

Step-by-step explanation:

2 are colored left to right, and 5 down

2/3 of the chart is taken up

Answer:

Hey there!

The correct answer would be C (Third one from the left).

The width is 2/5 (two out of five) and the length is 2/3 (two out of three)

Let me know if this helps :)

Answer: y = (1/3)*x - 5

Step-by-step explanation: Hope this helps!

The dialatiοn pοint οf are:5) quadrilateral JKLM after a dilatiοn with a scale factοr οf 1/4 cantered at pοint K is J(7, 12), K(8, 12), L(7, 9), and M(4, 10).6) triangle XYZ after the dilatiοn is X'Y'Z', where X'(0, -3), Y'(-6, -9), and Z'(-12, 0).

A scale factοr is defined as the ratiο between the scale οf a given οriginal οbject and a new οbject, which is its representatiοn but οf a different size (bigger οr smaller).

5).Tο find the cοοrdinates οf the image οf quadrilateral JKLM after a dilatiοn with a scale factοr οf 1/4 centered at pοint K, we need tο perfοrm the fοllοwing steps:

Find the cοοrdinates οf pοint K after dilatiοn.

Since the center οf dilatiοn is K, the image οf K will be itself.

Therefοre, the cοοrdinates οf the image οf pοint K will be (8, 12).

Find the cοοrdinates οf the images οf pοints J, L, and M after dilatiοn.

Tο find the image οf pοint J, we can use the fοrmula fοr dilatiοn:

(image οf J) = (center οf dilatiοn) + (scale factοr) x (vectοr frοm center tο J)

(image οf J) = (8, 12) + (1/4)(vectοr JO)(image οf J) = (8, 12) + (1/4)(-4, 0)

(image οf J) = (7, 12)Similarly, we can find the images οf pοints L and M:

(image οf L) = (8, 12) + (1/4)(vectοr ZK)(image οf L) = (8, 12) + (1/4)(-4, -12)

(image οf L) = (7, 9)(image οf M) = (8, 12) + (1/4)(vectοr KM)(image οf M) =

(8, 12) + (1/4)(-16, -8)(image οf M) = (4, 10)

Therefοre, the image οf quadrilateral JKLM after a dilatiοn with a scale factοr οf 1/4 centered at pοint K is J(7, 12), K(8, 12), L(7, 9), and M(4, 10).

6). Tο find the image οf triangle XYZ after a dilatiοn centered at the οrigin with a scale factοr οf k = -3/2, we need tο apply the dilatiοn fοrmula tο each vertex.

Fοr vertex X(0, 2):

x-cοοrdinate οf image = k * x-cοοrdinate οf X = -3/2 * 0 = 0y-cοοrdinate οf image = k * y-cοοrdinate οf X = -3/2 * 2 = -3

Sο the image οf vertex X is X'(0, -3).

Fοr vertex Y(4, 6):x-cοοrdinate οf image = k * x-cοοrdinate οf Y = -3/2 * 4 = -6y-cοοrdinate οf image = k * y-cοοrdinate οf Y = -3/2 * 6 = -9

Sο the image οf vertex Y is Y'(-6, -9).

Fοr vertex Z(8, 0):x-cοοrdinate οf image = k * x-cοοrdinate οf Z = -3/2 * 8 = -12y-cοοrdinate οf image = k * y-cοοrdinate οf Z = -3/2 * 0 = 0

Sο the image οf vertex Z is Z'(-12, 0).

Therefοre, the image οf triangle XYZ after the dilatiοn is X'Y'Z', where X'(0, -3), Y'(-6, -9), and Z'(-12, 0).

Hence, the dialatiοn pοint οf are:5) quadrilateral JKLM after a dilatiοn with a scale factοr οf 1/4 centered at pοint K is J(7, 12), K(8, 12), L(7, 9), and M(4, 10).6) triangle XYZ after the dilatiοn is X'Y'Z', where X'(0, -3), Y'(-6, -9), and Z'(-12, 0).

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Answer:

A.   52°

Step-by-step explanation:

The measure of an inscribed angle is 1/2 the measure of the intercepted arc.

m∠B = 1/2 (m of arc AC)

26 = 1/2 (m of arc AC)

52 = (m of arc AC)

Answer:

1/20

there are 20 students altogether

Step-by-step explanation:

um I'm not sure

To expand an expression means to simplify it by removing parentheses and combining like terms. The expanded form of \((4\sqrt{5})^2\) is 80.

It involves applying the distributive property to distribute the terms inside the parentheses to the terms outside, and then combining any similar terms to obtain a simplified form of the expression.

To expand the expression \((4\sqrt{5})^2\), we first need to square the quantity inside the parentheses.

\($(4\sqrt{5})^2 &= (4\sqrt{5})(4\sqrt{5})\)

To multiply two square roots, we can multiply the numbers outside the square root and multiply the numbers inside the square root.

\((4\sqrt{5})(4\sqrt{5}) &= 4 \cdot 4 \cdot \sqrt{5} \cdot \sqrt{5} \\\\&= 16 \cdot 5 \\\\&= \boxed{80}\)

Therefore, the expanded form of \((4\sqrt{5})^2\) is 80.

So, the correct answer is E. 80.

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To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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A result is called "statistically significant" when the p-value is less than the significant level, typically 0.05.

This means that there is less than a 5% chance that the results are due to chance alone, and suggests that there is a real effect present in the data.

The Null Hypothesis is the assumption that there is no significant difference between the measured phenomenon and a certain value or set of values. A statistically significant result means that the observed data are inconsistent with the assumption of no difference, or no effect.

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Answer:

D

Step-by-step explanation:

x + 5 + 3x + C = 180                All triangles have 180 degrees.

4x + 5 + C = 180

But C must be equal to 3x. Notice the markings on the lets of the triangle.

4x + 5 + 3x = 180

7x + 5 = 180                          Subtract 5 from both sides

7x = 180 - 5

7x = 175

x = 25

But angle C = 3x

C = 3*25

C = 75

If volleyball team purchased 15 jackets, 12 pairs of sweatpants for $348 and basketball team purchases 8 jackets , 8 pairs of sweatpants for $200, the the system of equations that represent the situation is (b)  \(15x+12y = 348\) and \(8x+8y = 200\) .

let the number of jackets purchased be = x ;

let the number of pairs of sweatshirts purchased be = y ;

the volley ball team purchased 15 jackets and 12 pairs of sweatpants for $348 ,

that means the equation that represents the situation is :

\(15x+12y = 348\) .

Also given that , the basketball team purchased 8 jackets and 8 pairs of sweatpants for $200 ,

that means the equation that represents the situation is :

\(8x+8y = 200\) .

Therefore , the system of equations are \(15x+12y = 348\) and \(8x+8y = 200\) .

The given question is incomplete , the complete question is

A sports apparel supplier offers teams the option of purchasing extra apparel for players. A volleyball team purchases 15 jackets and 12 pairs of sweatpants for $348. A basketball team purchases 8 jackets and 8 pairs of sweatpants for $200. Let x represent the price of a jacket and let y represent the price of a pair of sweatpants. Which system of equations can be used to find the price of each item ?

(a) 8x + 8y = 200  ;  12x + 15y = 348   ;

(b) 8x + 8y = 200  ; 15x + 12y = 348 ;  

(c) 8x + 8y = 348  ;  12x + 15y = 200 ;  

(d) 8x + 8y = 348 ;  15x + 12y = 200 .

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The length of the QR is 16 cm when PQR ~MNO

In the given question, it is given that two similar triangles as PQR ~MNO

Then, the corresponding sides will be in equal proportion to each other as follows

PQ / MN = PR / MO = QR / NO

We need to find the length of the side QR

As above relations are given,

\(\frac{PQ}{MN}\) = \(\frac{PR}{MO}\) = \(\frac{QR}{NO}\)

\(\frac{30}{10}\) = \(\frac{5x + 7}{x+5}\) = \(\frac{4x}{\frac{16}{3} }\)

Equating all the fractions, equal to each we'll find

\(\frac{5x + 7}{x+5}\) = \(\frac{30}{10}\)

5x + 7 = 3(x +5)

5x + 7 = 3x + 15

2x = 8

x = 4

We know that, the length of the QR = 4x cm = 4 x 4 cm = 16 cm

Therefore, the length of the QR is 16 cm when PQR ~MNO

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The solutions of the system of equations are (0, 4) and (-1, 1)

Here we want to solve the system of equations below:

y = 3x^2 + 6x + 4

y = -3x^2 + 4

y is already isolated in both equations, then we can write:

3x^2 + 6x + 4 = -3x^2 + 4

Now simplify this:

3x^2 + 6x + 4 + 3x^2 - 4 = 0

6x^2 + 6x = 0

6*(x^2 + x) = 0

6*(x)*(x + 1) = 0

The two solutions are:

x = 0 and x = -1

Evaluating these in any of the quadratic equations we will get:

if x = 0

y = -3*0^2 + 4 = 4

if x = -1

y = -3*(-1)^2 + 4 = -3 + 4 = 1

So the solutions are (0, 4) and (-1, 1)

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Interpreting the confidence interval, we can say with 96% confidence that the true difference in proportions of customers who would complete the survey when receiving a receipt with the contest offer versus those who receive a receipt without the contest offer lies between approximately -0.01675 and 0.05675.

To construct a confidence interval for the difference in proportions, we can use the formula:

CI = (p1 - p2) ± Z * √[(p1 * (1 - p1))/n1 + (p2 * (1 - p2))/n2]

Where:

- CI is the confidence interval

- p1 is the proportion of volunteers who completed the survey with the contest offer

- p2 is the proportion of volunteers who completed the survey without the contest offer

- Z is the critical value corresponding to the desired confidence level

- n1 is the sample size of volunteers who received the survey with the contest offer

- n2 is the sample size of volunteers who received the survey without the contest offer

In this case, we have p1 = 15/250 = 0.06, p2 = 10/250 = 0.04, n1 = n2 = 250, and a desired confidence level of 96%, which corresponds to a critical value of Z = 1.75 (approximately).

Substituting the values into the formula, we get:

CI = (0.06 - 0.04) ± 1.75 * √[(0.06 * (1 - 0.06))/250 + (0.04 * (1 - 0.04))/250]

Simplifying the calculation, we find:

CI = 0.02 ± 1.75 * √[(0.06 * 0.94)/250 + (0.04 * 0.96)/250]

CI ≈ 0.02 ± 1.75 * 0.021

CI ≈ 0.02 ± 0.03675

CI ≈ (-0.01675, 0.05675)

Interpreting the confidence interval, we can say with 96% confidence that the true difference in proportions of customers who would complete the survey when receiving a receipt with the contest offer versus those who receive a receipt without the contest offer lies between approximately -0.01675 and 0.05675.

This suggests that there may or may not be a significant difference in completion rates between the two groups, as the interval contains both positive and negative values. Further analysis or additional data may be needed to draw a more definitive conclusion.

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The number of time Easton's song was played on commercials is 10 times.

The number of time Easton's song was played during a movie is 4 times.

The first step is to form a system of equations:

40c + 110m = 840 equation 1

c - m = 6

c = 6 + m equation 2

Where:

The system of equations would be solved using the substitution method.

Substitute for c in equation 1 using equation 2

40(6 +  m) + 110m = 840

240 + 40m + 110m = 840

40m + 110m = 840 - 240

150m = 600

m = 600 / 150

m = 4

Substitute for m in equation 2.

c = 6 + 4

c = 10

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The height of a cylinder with a 36-square-foot base and a 189-square-foot volume is 6.

The formula for the volume of a cylinder is given by V = \(\pi\)\(r^{2}\)h, where V is the volume, r is the radius of the base, and h is the height of the cylinder.

The area of the base of the cylinder is given by A = \(\pi\)\(r^{2}\), where A is the area of the base, r is the radius of the base.

We are given that the area of the base is 36, so we can write:

\(\pi\)\(r^{2}\)= 36

Solving for r, we get:

\(r^{2}\) = 36/\(\pi\)

r = \(\sqrt{36}/\pi\)

r ≈ 3.02

We are also given that the volume of the cylinder is 189, so we can write:

V = \(\pi\)\(r^{2}\)h = 189

\(\pi 3.02^{2} h\) = 189

h = 189 / \(\pi 3.02^{2}\)

h ≈ 6

Therefore, the height of the cylinder is approximately 6 units.

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The vertex of the function is at (5, 10) .For the function, the domain exists on all real numbers while the range exist for the value f(x) ≥ 10

Vertex, domain and range of a function

The vertex of a quadratic or linear function is in the form

y =  a(x – h)^2 + k

where;

(h, k) is the vertex of the function

Given the function expressed as;

f(x) = |x-5| + 10

On comparison, you can see that h = 5 and k =10, hence the vertex of the function is at (5, 10)

For the domain and range

Domain are the dependent variable for which a function exist while the range is the independent variable for which a function exist.

For the function, the domain exists on all real numbers while the range exist for the value f(x) ≥ 10

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Answer:

When subtracting negative numbers the two negatives (the one on the 2 and the minus sign) cancel out and change it to -6+2. from there you just add 2 to negative 6 ang get negative 4

Step-by-step explanation:

if this is not clear i will try to explain it some more

A. In the alternate universe, the p subshell would have 5 orbitals.

B. In the alternate universe, the d subshell would have 10 orbitals.

In the alternate universe where the possible values of mℓ range from -l-1 to l+1, the number of orbitals in each subshell can be determined.

A. For the p subshell, the value of l is 1. Therefore, the range of mℓ would be -1, 0, and 1. Including the additional values of -2 and 2 from the alternate universe, the total number of orbitals in the p subshell would be 5 (mℓ = -2, -1, 0, 1, 2).

B. For the d subshell, the value of l is 2. In the conventional universe, the range of mℓ would be -2, -1, 0, 1, and 2, resulting in 5 orbitals. However, in the alternate universe, the range would extend to -3 and 3. Including these additional values, the total number of orbitals in the d subshell would be 10 (mℓ = -3, -2, -1, 0, 1, 2, 3).

Therefore, in the alternate universe, the p subshell would have 5 orbitals, and the d subshell would have 10 orbitals.

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Answer:

I am pretty sure that it is 1 and 2/3, if correct brainiest please, if not I am sorry!

Answer:

m=\(\frac{1}{2}\)

Step-by-step explanation:

The slope of the line that passes through M(-6, 1) and N(2, 5) will be 1/2.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

The points are M(-6, 1) and N(2, 5). Then the slope of the line is given as,

m = (5 - 1) / (2 + 6)

m = 4 / 8

m = 1/2

The incline of the line that goes through M(- 6, 1) and N(2, 5) will be 1/2.

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Answer:

x=2, y=4. (2, 4).

Step-by-step explanation:

3x-3y=-6 implies 3(x-y)=3(-2), so x-y=-2.

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

x-y=-2

3x+y=10

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

4x=8

x=8/4=2

2-y=-2

y=2-(-2)=2+2=4

The missing piece of information would allow the triangles in the figure to be proven congruent by AAS is; C: ∠C ≅∠C'

The AAS congruence rule states that if any two consecutive angles of a triangle along with a non-included side are equal to the corresponding consecutive angles and the non-included side of another triangle, then the two triangles are said to be congruent.

Now, from the two given triangles we see that;

In triangle ABC, we have the included side as AB with an angle ∠B.

Similarly, in triangle A'B'C', we have the  included side A'B' with an angle ∠B.

Thus, if we apply the AAS Congruency rule as stated above, then we can say that the other consecutive angles that are congruent are;

∠C ≅ ∠C'

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