1. The side opposite the 30° angle measures 6 cm. What is the measurement of the side
opposite the 60° angle

Answer:

(-1,-2) is the correct one but they all are the same

The images of points B and C are B'(x, y) = (- 2, 6) and C'(x, y) = (- 1, 7), respectively.

In this problem we find must determine the image of two points by translation, whose formula is introduced below:

T(x, y) = P'(x, y) - P(x, y)

Where:

First, determine the translation vector:

T(x, y) = (1, 4) - (0, 0)

T(x, y) = (1, 4)

Second, determine the images of points B and C:

B'(x, y) = (- 3, 2) + (1, 4)

B'(x, y) = (- 2, 6)

C'(x, y) = (- 2, 3) + (1, 4)

C'(x, y) = (- 1, 7)

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The economic impact of fishing for nearly all great lakes states varies, but according to a report by the U.S. Fish and Wildlife Service, it falls within the range of $1 to $8 billion (in millions of dollars).

This impact includes the economic contributions of recreational fishing, commercial fishing, and related industries such as tourism and boat manufacturing. The exact amount varies from state to state and from year to year depending on factors such as weather, fish populations, and fishing regulations.

The Great Lakes region of the United States is home to some of the largest freshwater bodies in the world and boasts a rich variety of fish species. Fishing is an important economic activity in the region, contributing billions of dollars to the local and national economy. The economic impact of fishing in the Great Lakes region includes not only the direct revenue generated by commercial and recreational fishing, but also the indirect and induced effects of fishing-related industries such as tourism and boat manufacturing.

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Answer:

7?

Step-by-step explanation:

Note that the proof that ΔABC ≅ ΔEDC is given as follows:

According to the ASA rule, if any two angles and sides included between the angles of one triangle are comparable to the corresponding two angles and sides included between the angles of the second triangle, the two triangles are said to be congruent.

Thus, given the above statements, it is clear that ΔABC ≅ ΔEDC

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Full Question:

Angle BAC is congruent to Angle DEC: Given

C is the midpoint of AE: Given

Prove triangle ABC is congruent to triangle EDC

What are the statements and reasons for this proof?

To eliminate the unknown variable a1 from the system of equations, we need to select two equations that can be combined in a way that eliminates a1 when the equations are subtracted or added. The specific choice of equations depends on the structure of the system and the coefficients of a1 in each equation.

To determine which equations can be used to eliminate a1, we need to examine the coefficients of a1 in each equation. If the coefficients are of equal magnitude but opposite signs, subtracting the equations will result in the elimination of a1. Conversely, if the coefficients have the same sign, adding the equations can eliminate a1.

Given the system of equations, eq.2, eq.3, and eq.4*, we should analyze the coefficients of a1 in these equations. By comparing the coefficients, we can determine which combination of equations can be used to eliminate a1. It is essential to select two equations where the coefficients of a1 have opposite signs or equal signs, depending on whether we are subtracting or adding the equations, respectively.

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(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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Answer: A) AC=DF

Step-by-step explanation:

Angle-Side-Angle (ASA) Postulate: If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent.

Answer A is the only one that wouldn’t help you prove that these triangles are congruent.

Answer:

y = -4

x = 6

Solution:

7x + 11y = -2 [1]

7x + 3y = 30 [2]

[1] - [2],

8y = -32

y = -4

(use substitution method to find x)

substitute y = -4 into [2],

7x + 3y = 30

7x + 3(-4) = 30

7x - 12 = 30

7x = 30 +12

7x = 42

x = 6

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

\(y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{7}{4}}x+2\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{7}{4}} ~\hfill \stackrel{reciprocal}{\cfrac{4}{7}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{4}{7} }}\)

so we're really looking for the equation of a line whose slope is -4/7 and it passes through (2 , -2)

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{4}{7} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{- \cfrac{4}{7}}(x-\stackrel{x_1}{2}) \implies y +2 = - \cfrac{4}{7} ( x -2) \\\\\\ y+2=- \cfrac{4}{7}x+\cfrac{8}{7}\implies y=- \cfrac{4}{7}x+\cfrac{8}{7}-2\implies {\Large \begin{array}{llll} y=- \cfrac{4}{7}x-\cfrac{6}{7} \end{array}}\)

The probability that no letters are repeated is 0.4121.

Divide the total number of outcomes by the entire number of different ways an event could happen to arrive at the probability. There are differences between probability and odds. The possibility of an event happening divided by the likelihood that it won't happen yields the odds. Probability is a metric used to assess the likelihood that a specific event will occur. The likelihood that the coin will land with the heads side up is measured using the probability concept when we toss it in the air. Here is an example of how probability is used in everyday life that you probably already know about. Prior to a major outing, we always consult the weather prediction.

So, the probability

Given, Number of letters=8

N\(=26*25*24*23*22*21*20*19\)

P\(=\frac{25}{26}*\frac{24}{26}*\frac{23}{26}*\frac{22}{26}*\frac{21}{26}*\frac{20}{26}\\=0.96*0.92*0.88*0.85*0.81*0.77\\=0.4121\)

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True. Strings can be concatenated (joined together) using the plus sign in programming languages like Python, JavaScript, and Java.

In most programming languages, strings can be concatenated or added together using the "+" operator. When the "+" operator is used with two string operands, it combines the two strings into a single string by appending the second string to the end of the first string.

It's important to note that the "+" operator behaves differently when used with other types of operands, such as numbers or lists, and can perform addition or concatenation depending on the context.

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The probability that exactly 5 black cars and exactly 10 non-black cars drive by in a particular afternoon is approximately 0.00167.

The probability that exactly 5 black cars and exactly 10 non-black cars drive by on a particular afternoon is

, where \($X_b$\) are the number of black cars and \($X_{nb}$\) the number of non-black cars passing by the playground in the afternoon. Since the color of the cars is independent of the number of cars that drive by, we can model the number of black and non-black cars using two separate Poisson distributions with means

\($\lambda_b = \frac{1}{5}\cdot25=5$ and $\lambda_{nb}=25-5=20$\), respectively.

Plugging in the values and simplifying, we get:

\($$P(X_b=5,X_{nb}=10)=\frac{e^{-5}5^{5}}{5!}\cdot\frac{e^{-20}20^{10}}{10!}\cdot\frac{1}{5^{5}}\cdot\frac{4^{10}}{5^{10}}\approx 0.00167$$\)

Therefore, the probability that exactly 5 black cars and exactly 10 non-black cars drive by in a particular afternoon is approximately 0.00167.

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If the diameter of the circle is 18 feet, the circumference of the circle is 56.55 feet.

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc.

The diameter of a circle is 18 feet.

D = 18 feet

Now, the radius of the circle is half the diameter of the circle.

Therefore,

Diameter = 2 × Radius

Radius = Diameter / 2

D = 2r

r = D / 2

r = 18 feet / 2

r = 9 feet

Now, the circumference of a circle is given as:

Circumference = π × diameter

Circumference = π × 2r

Circumference = 2πr

Circumference = 2 × π × 9 feet

Circumference = 2 × 3.14159 × 9

Circumference = 56.55 feet

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Answer: The odds in favor of a horse winning a race are given as 8:9, which means that the probability of the horse winning is 8/(8+9) = 8/17. Therefore, the probability of the horse winning the race is 8/17.

Step-by-step explanation:

The probability of the horse winning the race is 8/17.

The odds in favor of a horse winning a race is 8:9. To find: The probability of the horse winning the race. The odds are defined as: The odds in favor of an event = Number of ways an event can occur : Number of ways the event cannot occur.

Here, the odds in favor of a horse winning a race = 8 : 9. That means, the horse can win in 8 ways and lose in 9 ways. Therefore, the probability of the horse winning the race can be calculated as follows:

Probability of horse winning the race = Number of ways the horse can win / Total number of possible outcomes
= 8 / (8 + 9) [As total outcomes = winning outcomes + losing outcomes]
= 8 / 17
Therefore, the probability of the horse winning the race is 8/17.

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Answer: \(\frac{2(x-7)}{5(x-3)(x-2)}\)

Step-by-step explanation:

I'll do the fraction on the left, then the one on the right. Follow the screenshots below to help you out.

1. Use distributive property. The first of the images is me distributing all the values on the fraction on the left. Now I will do the ones on the left.

2. I used the same method. Now I will multiply the two.

3. \(\frac{2(x-7)}{5(x-3)(x-2)}\)

Answer:

7

Step-by-step explanation:

Answer:

7 units north

Step-by-step explanation:

Count from 3,4 to 10,4 and there are seven units

The probability of choosing a red ball out of the total number of balls (blue, green, pink, and red) is 1/4 or 0.25. Since the 80 selections are made with replacement, the probability of choosing a red ball on each selection remains constant at 0.25. To predict the number of times the ball would be the color red, we can multiply the probability of selecting a red ball by the total number of selections: 0.25 x 80 = 20. Therefore, the answer is A. The color red would be chosen exactly 20 times.
B. The color red would be chosen roughly 20 times, but probably not exactly 20 times.

Explanation: Since there are an equal number of blue, green, pink, and red balls, the probability of choosing a red ball is 1/4. With 80 random selections and replacement, we can predict the number of times a red ball would be chosen using the following calculation:

(Number of selections) x (Probability of choosing red) = 80 x (1/4) = 20

However, since the selections are random, it's likely that the actual number of red balls chosen may vary slightly from the predicted 20 times.

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The linearized equation for the non-linear equation z = x² + 4xy + 6xy² in the region defined by 8 ≤ x ≤ 10, 2 ≤ y ≤ 4 is given by :

z ≈ 244 + 20(x - 8) + 128(y - 2).

When using the linearized equation to calculate the value of z at x = 8, y = 2, the error is 0.

1.1. To linearize the equation in the given region, we need to find the partial derivatives of z with respect to x and y:

∂z/∂x = 2x + 4y

∂z/∂y = 4x + 6xy

At the point (x₀, y₀) = (8, 2), we substitute these values:

∂z/∂x = 2(8) + 4(2) = 16 + 8 = 24

∂z/∂y = 4(8) + 6(8)(2) = 32 + 96 = 128

The linearized equation is given by:

z ≈ z₀ + ∂z/∂x * (x - x₀) + ∂z/∂y * (y - y₀)

Substituting the values, we get:

z ≈ z₀ + 24 * (x - 8) + 128 * (y - 2)

1.2. To find the error when using the linearized equation to calculate the value of z at x = 8, y = 2, we substitute these values:

z ≈ z₀ + 24 * (8 - 8) + 128 * (2 - 2)

= z₀

Therefore, the linearized equation gives the exact value of z at x = 8, y = 2, and the error is 0.

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The standard normal distribution  becomes smaller.

What is standard deviation?

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

becomes smaller.

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In circle, Value of  x = 3.8 degrees.

To solve for x, we can use the fact that the sum of angles in a triangle is 180 degrees.

First, we know that angle XWY + angle YWX + angle YWZ = 180 degrees. Since we know that angle YWX is 59 degrees, we can substitute that in and simplify:

angle XWY + 59 + angle YWZ = 180

Next, we know that angle XWY is equal to angle YWZ, since they both intercept the same arc. So we can substitute (7x + 34) for both angles:

2(7x + 34) + 59 = 180

Simplifying:

14x + 68 + 59 = 180

14x + 127 = 180

14x = 53

x = 3.8 (rounded to the nearest tenth)

Therefore, x = 3.8 degrees.

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The researcher should use a sample size of approximately 312 middle school students to conduct the research.

To determine the sample size needed for the researcher to create a 95% confidence interval with a margin of error of 0.5 days, we can use the formula:

\(\[ n = \left(\frac{Z \cdot \sigma}{E}\right)^2 \]\)

Where:

- \(\( n \)\) is the sample size

- \(\( Z \)\) is the z-score corresponding to the desired confidence level (for 95% confidence, Z is approximately 1.96)

- \(\( \sigma \)\) is the known standard deviation of the population

- \(\( E \)\) is the desired margin of error

Plugging in the values, we get:

\(\[ n = \left(\frac{1.96 \cdot 4.5}{0.5}\right)^2 \]\)

To solve the equation for the required sample size, we can substitute the given values into the formula:

\(\[ n = \left(\frac{1.96 \cdot 4.5}{0.5}\right)^2 \]\)

Calculating this expression gives us:

\(\[ n = \left(\frac{8.82}{0.5}\right)^2 \]\)

\(\[ n = (17.64)^2 \]\)

\(\[ n \approx 311.1696 \]\)

Therefore, the researcher should use a sample size of approximately 312 middle school students to conduct the research.

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Step-by-step explanation: The solution to this system of equations will be where the two lines on the graph intersect with each other.

Notice that both of them intersect to the left of the y-axis which means our x - coordinate must be negative.

They also intersect above the x-axis so our y-coordinate must be positive.

So the only option with a negative x-coordinate

and a positive y-coordinate is (-1/4, 3/4).

Answer:

\(36.35 - 2.41 \\ = 33.94\)

Answer:

33.94

Step-by-step explanation:

Just subtract 2.41 from 36.35 and you get the answer. Easy!

Answer:

b=sqrt7

Step-by-step explanation:

16=9+b^2

A pole  feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Avery measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.

The number of engines that must be made to minimize the unit cost are 180

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

C(x) = −0.5x² + 180x + 25,609.

Differentiate the above equation

So, we have the following representation

C'(x) = -x + 180

Set the equation to 0

So, we have the following representation

-x + 180 = 0

This gives

x = 180

Substitute x = 180 in the above equation, so, we have the following representation

C(180) = −0.5(180)² + 180(180) + 25,609

Evaluate

C(180) = 41809

Hence, the engines that must be made to minimize the unit cost are 180

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Answer:

C. The reciprocal

I hope this helps!

Answer:

C the reciprocal I used process of elimination honestly

Step-by-step explanation:

The absolute minimum value of f(x) on the interval [-5, 1] is -1125, which occurs at x = -5, and the absolute maximum value is 19, which occurs at x = 1.

To find the absolute extreme values of the function f(x) = x^4 + 8x^3 + 10x^2 on the interval [-5, 1], we need to evaluate the function at its critical points and endpoints.

First, we find the critical points by taking the derivative of f(x) and setting it equal to zero:

f'(x) = 4x^3 + 24x^2 + 20x = 0

Factoring out common terms, we get:

4x(x^2 + 6x + 5) = 0

Setting each factor equal to zero, we find the critical points:

x = 0, x = -5, x = -1

Next, we evaluate the function f(x) at these critical points and the endpoints of the interval:

f(-5) = (-5)^4 + 8(-5)^3 + 10(-5)^2 = 625 - 2000 + 250 = -1125

f(-1) = (-1)^4 + 8(-1)^3 + 10(-1)^2 = 1 - 8 + 10 = 3

f(0) = (0)^4 + 8(0)^3 + 10(0)^2 = 0

Finally, we evaluate the function at the endpoints of the interval:

f(-5) = (-5)^4 + 8(-5)^3 + 10(-5)^2 = -1125

f(1) = (1)^4 + 8(1)^3 + 10(1)^2 = 19

From these evaluations, we can see that the absolute minimum value of f(x) on the interval [-5, 1] is -1125, which occurs at x = -5, and the absolute maximum value is 19, which occurs at x = 1.

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Answer:

7 hours

Step-by-step explanation:

As you can see it costs 22.75 dollars for 3 and a half hours, which means that 45.50 dollars will allow you to park for 7 hours.