Need help with top problem. Maybe bottom too

Answer:

The answers are

y=9

x≈16

Step-by-step explanation:

90+60+z=180

z+150=180

z=180-150

z=30°

sin30=y/18

y=18sin30

y=9

hyp²=opp²+adj²

adj²=hyp²-opp²

x²=18²-9²

x²=324-81

x²=243

take the square root of both sides

x≈16

A randomized experiment with order, replacement, and no repetition is one in which the order of the outcomes matters, the same outcome can occur multiple times, and no outcome can occur more than once.

For example, drawing a card from a deck and then flipping a coin would be a random experiment with order, replacement, and no repetition. The order of the results is important because the outcome of the coin toss will depend on the outcome of the card draw.

The same result can occur multiple times because the same card can be drawn twice, and no result can occur more than once because the coin can only land heads or tails once.

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Random experiment with order, replacement and without repetition

The area of the sector is approximately 36.0 ft²

To find the area of the sector formed by a central angle of 260° in a circle with a radius of 4 ft, you can use the formula:

Area of sector = (θ/360°) * π * r²

where θ is the central angle in degrees, π is the value of pi, and r is the radius.

Plugging in the values:

θ = 260°

r = 4 ft

π = 3.14

Area of sector = (260/360) * 3.14 * 4²

Area of sector = (0.7222) * 3.14 * 16 = 36.3 square feet

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The given quadrilaterals, 1 and 2,  are parallelograms because the pair of opposite sides are parallel and the other pairs are congruent.

3. According to Theorem 7.9, quadrilateral ABCD is a parallelogram.

4. According to Theorem 7.12, quadrilateral PQRS is a parallelogram.

3. Quadrilateral ABCD with vertices A(0,0), B(7,1), C(5,6), D(-2,5), and Theorem 7.9:

Theorem 7.9 states that if the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Using the distance formula, we can calculate the lengths of the sides of quadrilateral ABCD:

AB = √((7 - 0)² + (1 - 0)²) = √50

BC = √((5 - 7)² + (6 - 1)²) = √29

CD = √((-2 - 5)² + (5 - 6)²) =√50

DA = √((0 - (-2))² + (0 - 5)²) = √29

We can see that AB = CD and BC = DA, indicating that the opposite sides are congruent.

Quadrilateral PQRS with vertices P(-2,0), Q(3,1), R(4,4), S(-1,3), and Theorem 7.12:

Theorem 7.12 states that if both pairs of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.

Using the slope formula, we can calculate the slopes of the sides of quadrilateral PQRS:

Slope of PQ = (1 - 0) / (3 - (-2)) = 1/5

Slope of RS = (4 - 3) / (4 - (-1)) = 1/5

Slope of QR = (4 - 1) / (4 - 3) = 3

Slope of SP = (3 - 0) / (-1 - (-2)) = 3

The lengths of opposite sides can be calculated using the distance formula:

PQ = √((3 - (-2))² + (1 - 0)²) = √(25 + 1) = √26

RS = √((4 - 4)² + (4 - 1)²) = √(9) = 3

QR = √((4 - 3)² + (4 - 1)²) = √(1 + 9) = √10

SP = √((-1 - (-2))² + (3 - 0)²) = √(1 + 9) = √10

We can see that PQ = RS and QR = SP, indicate that the opposite sides are parallel and congruent.

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Answer:

[tex]6[/tex]

Step-by-step explanation:

[tex]\mathrm{Solution: }\\\\\mathrm{sin30^o=\frac{p}{h}=\frac{a}{12}}\\\\\mathrm{or,\ \frac{1}{2}=\frac{a}{12}}\\\\\mathrm{or,\ 2a=12}\\\\\mathrm{\therefore a=6}[/tex]

Answer:

F(4) = -256

Step-by-step explanation:

f(1)=4

f(2)= -4* f(1) = -4 *4 = -16             F(2 ) = -16

f(3) = -4* f(2) = -4* (-16) = 64       F(3) = 64  

f(4) = -4* f(3)  = -4* 64 = -256     F(4) = -256

Answer:

f(4) = -256

Step-by-step explanation:

A recursive formula defines the nth term of a sequence based on the values of earlier terms.

To find the value of f(4) using the given recursive formula, we can work our way up from f(1) using the formula repeatedly.

Given recursive rule:

[tex]\begin{cases}f(1)=4\\f(n)=-4f(n-1)\end{cases}[/tex]

To find f(2):

[tex]\begin{aligned}f(2)&=-4f(2-1)\\&=-4f(1)\\&=-4 \cdot 4\\&=-16\end{aligned}[/tex]

To find f(3):

[tex]\begin{aligned}f(3)&=-4f(3-1)\\&=-4f(2)\\&=-4 \cdot -16\\&=64\end{aligned}[/tex]

To find f(4):

[tex]\begin{aligned}f(4)&=-4f(4-1)\\&=-4f(3)\\&=-4 \cdot 64\\&=-256\end{aligned}[/tex]

Therefore, the value of f(4) is -256.

The Probability of guessing the right combination in one try is approximately 0.0007716, or 0.07716%.This probability is extremely low, indicating that it is highly unlikely to guess the correct combination by chance in a single attempt.

The probability of guessing the right combination in one try, we need to calculate the total number of possible combinations and the number of successful outcomes.

In this case, we have 4 dials, each with 6 letters. Since each dial can be set to one of the 6 letters, the number of possible combinations for each dial is 6.

To calculate the total number of possible combinations for the lock, we need to multiply the number of options for each dial. In this case, since we have 4 dials, the total number of combinations is:

6 * 6 * 6 * 6 = 6^4 = 1,296

So, there are 1,296 possible combinations in total.

Now, to calculate the probability of guessing the right combination in one try, we divide the number of successful outcomes (which is 1, as there is only one correct combination) by the total number of possible outcomes:

Probability = Number of successful outcomes / Total number of possible outcomes

Probability = 1 / 1,296

Simplifying this fraction, we get:

Probability = 1 / 1,296 ≈ 0.0007716

Therefore, the probability of guessing the right combination in one try is approximately 0.0007716, or 0.07716%.

This probability is extremely low, indicating that it is highly unlikely to guess the correct combination by chance in a single attempt. Locks with multiple dials and options are designed to provide a high level of security by creating a vast number of possible combinations, making it difficult to guess the correct one.

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Answer:

[tex]\$17181.86[/tex]

Step-by-step explanation:

[tex]A=P(1+r)^t\\A=10000(1+0.07)^8\\A=10000(1.07)^8\\A\approx\$17181.86[/tex]

Answer: $17182.

This is an example of an exponential growth function, which looks like f(x)=a(1+r)^x, where r is the growth rate, a is the initial value, and x is the time. 10000 is the initial value, 7% is the growth rate, and 8 years is the time. 7% can become 0.07. f(x)=10000(1+0.07)^8. f(x)=10000(1.07)^8. First simplify the exponent. f(x)=10000(1.71818618). f(x)≈17182.

Answer: The function rule is f(x) = 5(10)^x. Using this rule, we can find f(0) by substituting x with 0: f(0) = 5(10)^0 = 5 * 1 = 5. So f(0) = 5.

Here are the steps to find f(0) using the function rule f(x) = 5(10)^x:

1. Substitute x with 0 in the function rule: f(0) = 5(10)^0

2. Any non-zero number raised to the power of 0 is equal to 1: f(0) = 5 * 1

3. Multiply 5 by 1: f(0) = 5

4. So f(0) = 5.

Answer:

f(0) = 5

Step-by-step explanation:

The given function is:

[tex]f(x)=5(10)^x[/tex]

To find f(0), substitute x = 0 into the given function:

[tex]f(0)=5(10)^0[/tex]

According to the zero exponent property, any non-zero number raised to the power of zero is equal to 1. Therefore, 10⁰ = 1:

[tex]f(0)=5 \cdot 1[/tex]

According to the multiplicative identity property, when any number is multiplied by 1, the result is equal to the original number. Therefore:

[tex]f(0)=5[/tex]

The equation of the line in slope-intercept form is y = (3/4)x.

To write the equation of a line in slope-intercept form, we need to use the slope-intercept form equation: y = mx + b,

where m is the slope and b is the y-intercept.

Given that the line passes through the point (-8, 5) and has a slope of 3/4, we can substitute the values into the equation to find the y-intercept (b).

First, let's find the value of b using the point-slope form equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Using (-8, 5) as the point and 3/4 as the slope, we have:

5 - 5 = (3/4)(-8 - x)

0 = (3/4)(-8 - x)

0 = (-3/4)(8 + x)

0 = -6 - (3/4)x

Next, we can solve for x:

(3/4)x = -6

x = -6 [tex]\times[/tex] (4/3)

x = -8

Now that we have the value of x, we can substitute it back into the equation to find the value of b:

0 = -6 - (3/4)(-8)

0 = -6 + 6

0 = 0

So, the value of b is 0.

Finally, we can write the equation of the line in slope-intercept form:

y = (3/4)x + 0

y = (3/4)x.

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Answer:

19.2

Step-by-step explanation:

(32) 3/5

= 32 multiple 3/5

= 96/5 [ explanation: 32 multiple 3 = 96 ]

= 19.2 [ explanation: 96 divided by 5 = 19.2 ]

[tex]\Huge \boxed{\Florin f(x) = 2x^{3} - 8x^{2} + 6x}[/tex]

The given zeros are 0, 1, and 3.

Since the zeros are the values of [tex]\bold{x}[/tex] that make the polynomial equal to zero, we can write the factors corresponding to each zero as [tex](x - 0)[/tex], [tex](x - 1)[/tex], and [tex](x - 3)[/tex].

Simplifying the first factor, we get [tex](x)[/tex], [tex](x - 1)[/tex], and [tex](x - 3)[/tex].

Now, multiply the factors together to form the polynomial:

                             [tex]\Large \boxed{(x)(x - 1)(x - 3)}[/tex]

Expanding this expression, we get:

                             [tex]\Large \boxed{x^{3} - 4x^{2} + 3x }[/tex]

The leading coefficient is 2, so we need to multiply the entire polynomial by 2:

                           [tex]\Large \boxed{2(x^{3} - 4x^{2} + 3x)}[/tex]

Expanding this expression, we get:

                          [tex]\Large \boxed{2x^{3} - 8x^{2} + 6x}[/tex]

So, the polynomial function in standard form with a leading coefficient of 2 and zeros at 0, 1, and 3 is:

                        [tex]\large \boxed{\Florin f(x) = 2x^{3} - 8x^{2} + 6x}[/tex]

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If a pattern is observed in a residual plot, such as non-linearity, heteroscedasticity, outliers, or systematic deviations, it indicates that a linear model may not be a good fit for the data.

A residual plot is a graphical representation that shows the difference between the observed values of the dependent variable and the predicted values by a linear regression model. It is useful for assessing the goodness of fit of the model to the data.

When examining a residual plot, if a clear pattern or structure is observed, it suggests that the linear model may not be an appropriate fit for the data. Here's why:

In summary, It suggests the need for alternative models or adjustments to better capture the underlying relationships in the dataset.

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The given equation is y = x + 31 + 7,the Values of x and y  the correct answer is: O(-3, 7); - O(-3,7): y ≥ -∞.

The given equation is y = x + 31 + 7.

The vertex of the equation, we need to determine the values of x and y when the equation reaches its maximum or minimum point. In this case, since the coefficient of x is positive, the graph of the equation will be an upward-sloping line, and there is no minimum point. Therefore, the vertex is not applicable in this scenario.

The range of the equation represents the set of all possible y-values that the equation can take. In this case, since the equation is y = x + 31 + 7, there is no restriction on the y-values. The graph of the equation extends indefinitely in the positive y-direction. Thus, the range can be represented as y ≥ -∞.

Therefore, the correct answer is: O(-3, 7); - O(-3,7): y ≥ -∞.

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The graph of the function y = -√(x - 5) - 2 is added as an attachment

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

y = -√(x - 5) - 2

The above function is a square root function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Answer:

A= 180-41=  

A= 139 degrees

B= 180-41

B = 139 degrees

Step-by-step explanation:

On a straight line its 180 degrees

A is separating a straight line with a 41-degree angle so.  

A= 180-41  

A= 139 degrees

B is also separating a straight line with a 41-degree angle so.

B= 180-41

B = 139 degrees

Answer:

Hi

Please mark brainliest

The coordinates in the solution to the systems of inequalities graphically is (6, 2)

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

x + y > 3

x - 3y < 2

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities graphically is (6, 2)

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Answer: See attached image.

Questions 1-4 is answered and furthered explained below.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

Now, let's answer these questions about whether it is a equation or an expression.

1. Equations have an equal sign, but expressions do not which is true.

Hence, this have been proved.

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The expected value of the game to you is approximately $0.39.

To calculate the expected value of the game, we need to the probability of winning and losing and the corresponding payoffs.

The probability of drawing two hearts with replacement can be calculated as the product of the probabilities of drawing a heart on the first and second draws.

The probability of drawing a heart from a standard deck of 52 cards is 13/52, as there are 13 hearts out of 52 cards. Since the first card is replaced before the second draw, the probability remains the same for both draws.

Thus, the probability of drawing two hearts is (13/52) * (13/52) = 169/2704.

The payoff for winning is $12, and the payoff for losing is -$1.

To calculate the expected value, we multiply the probability of winning by the payoff for winning and subtract the probability of losing multiplied by the payoff for losing.

Expected Value = (169/2704) * $12 - (2535/2704) * $1 ≈ $0.39.

This means that on average, you can expect to win about 39 cents per game in the long run.

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Using the fact that ∠A is congruent to ∠B and ∠C is a complement of ∠A, we determined that the measure of ∠B is 65° based on the given measure of ∠C as 25°.

If ∠A is congruent (≅) to ∠B and ∠C is a complement of ∠A, we can use the properties of complementary angles to find the measure of ∠B.

Given that m∠C = 25° and ∠C is a complement of ∠A, we know that ∠A + ∠C = 90°.

Since ∠A is congruent to ∠B, we can replace ∠A with ∠B in the equation:

∠B + ∠C = 90°.

Substituting the given value, we have:

∠B + 25° = 90°.

To isolate ∠B, we subtract 25° from both sides of the equation:

∠B = 90° - 25°.

Simplifying, we get:

∠B = 65°.

Therefore, the measure of ∠B is 65°.

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The WACC for A-Rod Manufacturing Company is 11.2%.

how to get A-Rod Manufacturing Company's weighted average cost of capital (WACC):

Determine the debt's cost. The yield on the company's outstanding bonds is the cost of debt. In this instance, the company's bond yield is 11.8%.

Determine the preferred stock's price. The dividend yield on the company's preferred stock is the cost of preferred stock. In this instance, the preferred stock of the corporation has a dividend yield of 8.5 percent.

Determine the equity cost. The anticipated return that investors expect on the company's common shares is known as the cost of equity. The dividend discount model is one popular way to determine the cost of equity among the many other approaches. The cost of this model's

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33a^2 is the greatest common factor of 66a^2b^3 and 33a^4c.

To find the greatest common factor (GCF) of [tex]66a^2b^3 and 33a^4c[/tex], we need to find the largest term that divides both expressions without leaving a remainder.

First, we can find the prime factorization of each term:

[tex]66a^2b^3[/tex] = 2 * 3 * 11 * a * a * b * b * b

[tex]33a^4c[/tex] = 3 * 11 * a * a * a * a * c

Next, we can identify the common factors between the two expressions:

- Both have a 3 and an 11 as factors

- Both have at least two factors of a

The GCF must include all common factors, so we can write:

GCF = 3 * 11 * a * a = [tex]33a^2[/tex]

We can check that this is indeed the GCF by dividing both original expressions by[tex]33a^2[/tex]:

[tex]66a^2b^3 / 33a^2 = 2b^3[/tex]

[tex]33a^4c / 33a^2 = a^2c[/tex]

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Answer:

Given:

Area of the sector (A) = 104π/9 square inches

Central angle (θ) = 65 degrees

The formula for the area of a sector of a circle is:

A = (θ/360) * π * r^2

We can rearrange this formula to solve for the radius (r):

r^2 = (A * 360) / (θ * π)

Plugging in the given values:

r^2 = (104π/9 * 360) / (65 * π)

r^2 = (104 * 40) / 9

r^2 = 4160 / 9

r^2 ≈ 462.22

Taking the square root of both sides:

r ≈ √462.22

r ≈ 21.49

Therefore, the radius of the circle is approximately 21.49 inches.

Answer: 8 inches

Step-by-step explanation:

Answer:

[tex]x=-\frac{4}{5}[/tex]

Step-by-step explanation:

[tex]6=\frac{3}{4}(10x+16)\\\mathrm{or,\ }6\times 4=3(10x+16)\\\\\mathrm{or,\ }24=30x+48\\\\\mathrm{or,\ }-24=30x\\\\\mathrm{\therefore}\ x=-\frac{4}{5}[/tex]

Answer:

Step-by-step explanation:

U={x|x∈N and x<10}

or U={1,2,3,4,5,6,7,8,9}

B={x|x∈N and x is even and x<10}

or

B={2,4,6,8}

C={x|x∈N and x<10}

or

C={1,2,3,4,5,6,7,8,9}

(B∩C)={2,4,6,8}

(B∩C)'={1,3,5,7,9}

The completed sequence is: 3/k, 3/k, 3/k, 9/2k.To complete the sequence of numbers with a constant difference between adjacent numbers, we can calculate the common difference by subtracting the first term from the second term.

Let's denote the missing terms as A and B.

The given sequence is: 3/k, A, B, 9/2k.

The common difference can be found by subtracting 3/k from A or B. Therefore:

A - 3/k = B - A = 9/2k - B.

To simplify, we can equate the two expressions for the                     common difference:

A - 3/k = 9/2k - B.

Next, we can solve for A and B using this equation.

Adding 3/k to both sides gives:

A = 3/k + 9/2k - B.

Now, we can substitute the value of A into the equation:

3/k + 9/2k - B - 3/k = 9/2k - B.

Simplifying further, we have:

9/2k - 3/k = 9/2k - B.

Cancelling out the common terms, we find:

-3/k = -B.

Multiplying both sides by -1, we get:

3/k = B.

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No, the conditions for inference are not met. The Large Counts Condition is not satisfied because the number of successes (6) is less than 10.

To determine if the conditions for inference are met in this scenario, we need to consider a few key conditions: the 10% condition, the randomness condition, and the Large Counts Condition.

The 10% condition: This condition states that the sample size should be no more than 10% of the population size. In this case, the sample size is 10 (the number of times the penny was spun), and we don't have information about the population size. However, since the proportion of times the penny lands tails up is not likely to be affected by the sample size of 10, we can assume that the 10% condition is met.

The randomness condition: This condition requires that the sample is randomly selected from the population. If the student followed the instructions and spun the penny 10 times, recording the number of times it landed tails side up, and there was no bias in the way the spins were performed, we can assume that the randomness condition is met.

The Large Counts Condition: This condition is related to the number of successes and failures in the sample. It states that both the number of successes and failures should be at least 10. In this case, the student recorded 6 tails side up out of 10 spins. Since 6 is less than 10, the Large Counts Condition is not met.

Based on these conditions, we can conclude that the conditions for inference are not fully met. The 10% condition and the randomness condition are likely met, but the Large Counts Condition is not satisfied. This means that we should be cautious when making inferences about the true proportion of tails up based on this sample. It may not be appropriate to construct a confidence interval or perform statistical inference in this case due to the violation of the Large Counts Condition.

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19. The calculated value of x in the triangles is 5

21. The calculated value of x in the triangles is 4

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

The similar figures

The value of x can then be calculated using the following ratio

x : 4 = 15 : 12

Express the ratio as fraction

So, we have

x/4 = 15/12

Solving for x, we have

x = 4 * 15/12

Evaluate

x = 5

Hence, the value of x is 5

For the second pair of triangles, we have the following ratio

x : 2 = 12 : 6

Express the ratio as fraction

So, we have

x/2 = 12/6

Solving for x, we have

x = 2 * 12/6

Evaluate

x = 4

Hence, the value of x is 4

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