Which two angles are congruent? A: Angles ABC and JKL. B: Angles GHI and ABC. C: Angles JKL and DEF. D: Angles DEF and GHI

(a) The half-life of an element is the amount of time it takes for the radioactivity of the element to decrease to half its initial value.

We can use the formula for exponential decay, A = A0(1/2)^(t/h), where A is the final amount, A0 is the initial amount, t is the time elapsed, and h is the half-life. Setting A = A0/2 and solving for h, we get h = ln(2)/r, where r is the decay rate. Therefore, the half-life of the element is rounded to the nearest whole number, h = round(ln(2)/r).

(b) To determine the number of days it takes for a sample of mg to decay to mg, we can use the same formula for exponential decay, A = A0(1/2)^(t/h), where A is the final amount, A0 is the initial amount, t is the time elapsed, and h is the half-life.

We want to solve for t when A = mg and A0 = mg. Plugging in the values, we get mg = mg(1/2)^(t/h), which simplifies to 1/2^(t/h) = 1. Solving for t, we get t = h*log2(2) = h, since log2(2) = 1. Therefore, the number of days it takes for a sample of mg to decay to mg is rounded to the nearest whole number, t = round(h).

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The WACC for Palencia Paints Corporation is 9.84%.

To calculate the Weighted Average Cost of Capital (WACC), we need to determine the cost of debt (Kd) and the cost of common equity (Ke).

The cost of debt (Kd) is given as 12%, and the marginal tax rate is 25%. Therefore, the after-tax cost of debt (Kd(1 - Tax Rate)) is:

Kd(1 - Tax Rate) = 0.12(1 - 0.25) = 0.09 or 9%

To calculate the cost of common equity (Ke), we can use the dividend discount model (DDM) formula:

Ke = (Dividend / Stock Price) + Growth Rate

Dividend (D₁) = Do * (1 + Growth Rate)

= $3.00 * (1 + 0.04)

= $3.12

Ke = ($3.12 / $30.50) + 0.04

= 0.102 or 10.2%

Next, we calculate the WACC using the target capital structure weights:

WACC = (Weight of Debt * Cost of Debt) + (Weight of Equity * Cost of Equity)

Given that the target capital structure is 30% debt and 70% equity:

Weight of Debt = 0.30

Weight of Equity = 0.70

WACC = (0.30 * 0.09) + (0.70 * 0.102)

= 0.027 + 0.0714

= 0.0984 or 9.84%

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Answer: The awnser is B

Step-by-step explanation: ive went over the problem and checked

Answer:

Step-by-step explanation: This is just rearranging the formula. Divide by m on both sides, then find the square root. The answer is E

The value of x in the intersecting line is 54.

When lines intersect, angle relationships are formed such as vertically opposite angles, linear angles angles on a straight lines.

Therefore, angle 2x + 2 is vertically opposite to the angle 3x - 52 .

Vertically opposite angles are congruent to each other.

Vertical Angles are the angles opposite each other when two lines cross. in other words, vertical angles are formed when two lines meet each other at a point.

Hence,

2x + 2 = 3x - 52

2x - 3x = -52 - 2

- x = -54

Therefore,

x = 54

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Answer:

4(5x _ 2y ) ^

Step-by-step explanation:

It is above in a photo .

m= -7 and b= 6

equation equals -13

Answer:

ok the slope is -1/2

the points I used where (-6,-1) and (-2,-3)

the intercept of y is -4

the equation is 2y +x+8=0

Step-by-step explanation:

using the formula y2- y1 = m

X2-X1

where m is the gradient, the slope is found

the original equation is y=-1/2x-4

and so if x is zero ( to get the y intercept)

y=-4

using the formula y - y1= m( x -x1 )

, the equation is determined

Answer:

5.9

Step-by-step explanation:

arrange the numbers in order from smallest to biggest

2, 2, 3.7, 4.1, 5.9, 6, 7.6, 8, 9.6

find middle number

5.9

Step-by-step explanation:

the average rate of change is

(h(interval end) - h(interval begin)) /

(interval end - interval begin)

in our case this is

(h(8) - h(-1)) / (8 - -1) = (108 - 9) / 9 = 99/9 = 11/1 = 11

Twelve horses will take 18 hours to consume 36 bales of hay.

Given,Six horses eat 12 bales of hay in 12 hours We need to find,

Let's assume that 1 horse will eat 1 bale of hay in x hours.

As we know,6 horses will eat 12 bales of hay in 12 hours.

Now we can find x as follows:

For 1 horse, 1 bale of hay is consumed in x hours

So, for 6 horses, 6 bales of hay will be consumed in x hours.

Then,6 horses consume 12 bales of hay in 12 hours6 horses consume 6 bales of hay in 6 hours1 horse consumes 1 bale of hay in 6 hours

Now we have to find how many hours will 12 horses take to eat 36 bales of hay.

If 1 horse eats 1 bale of hay in 6 hours, then 12 horses will consume 12 bales of hay in 6 hours.

Therefore, 12 horses will consume 36 bales of hay in 18 hours.

So, the answer is: Twelve horses will take 18 hours to consume 36 bales of hay.

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The solution to the system of equations is (-6, -9).

Given y=2x+3,

we are to find the solution to the system of equations.

In order to find the solution to the system of equations,

we require another equation in the system.

The system of equations is:

y = 2x + 3 ...

(1)Let's assume another equation:y - 3x = 9 ...

(2)The given system of equations is:

y = 2x + 3 ... (1)y - 3x = 9 ...

(2)Substituting equation (1) into equation (2), we get:

(2x + 3) - 3x = 9 => -x + 3 = 9 => -x = 9 - 3 => -x = 6 => x = -6

Therefore, substituting this value of x in equation (1), we get:

y = 2x + 3 => y = 2(-6) + 3 => y = -12 + 3 => y = -9

Therefore, the solution to the given system of equations is (-6, -9).

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Answer:

+$95

Step-by-step explanation:

We want to write a singles number that can represent this change

We know that David received $95

When someone receive something, it is positive

So to represent this, we simply put +$95

David made a profit of 95 dollars as a result of the transaction. As a result, you display this as a positive signed number, which is +95.

Positive numbers are generally used to express positive changes in the world of mathematics, especially when working with signed numbers. In order to describe a change of 95 dollars given to David, you would use a positive signed number, which in this case would be +95. You can tell that this was an increase or gain by putting the plus symbol (plus) before the 95; in this case, David made a profit of 95 dollars.

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Answer:

(9/5, 8/5)

Step-by-step explanation:

First you want to find the equations of the lines. One line is y = 2x - 2 and the other line is y = 1/3x + 1. Then you want to find the x and y that both work in the two equations.

y = 2x - 2

y = 1/3x + 1

Then you do 2x - 2 = 1/3x + 1

Then you do some maths and you get 9/5, and 8/5

The only solutions to the differential equation y′′−y=−cosx are option (B) 1/2(ex+cosx).

To check which one of the given functions is a solution to the differential equation y′′−y=−cosx, we need to substitute each function into the differential equation and verify if it satisfies the equation.

Let's go through each option one by one:

(A) 1/2(ex−sinx):

Taking the first derivative of this function, we get y' = 1/2(ex-cosx).

Taking the second derivative, we get y'' = 1/2(ex+sinx).

Substituting y and its derivatives into the differential equation:

y'' - y = (1/2(ex+sinx)) - (1/2(ex-sinx)) = sinx

The right side of the equation is sinx, not −cosx, so option (A) is not a solution.

(B) 1/2(ex+cosx):

Taking the first derivative of this function, we get y' = 1/2(ex-sinx).

Taking the second derivative, we get y'' = 1/2(ex-cosx).

Substituting y and its derivatives into the differential equation:

y'' - y = (1/2(ex-cosx)) - (1/2(ex+cosx)) = -cosx

The right side of the equation matches −cosx, so option (B) is a solution.

(C) 1/2(sinx−xcosx):

Taking the first derivative of this function, we get y' = 1/2(cosx - cosx + xsinx) = 1/2(xsinx).

Taking the second derivative, we get y'' = 1/2(sinx + sinx + xsin(x) + xcosx) = 1/2(sinx + xsin(x) + xcosx).

Substituting y and its derivatives into the differential equation:

y'' - y = (1/2(sinx + xsin(x) + xcosx)) - (1/2(sinx - xcosx)) = xsinx

The right side of the equation is xsinx, not −cosx, so option (C) is not a solution.

(D) 1/2(sinx+xcosx):

Taking the first derivative of this function, we get y' = 1/2(cosx + cosx - xsinx) = 1/2(2cosx - xsinx).

Taking the second derivative, we get y'' = -1/2(xcosx + 2sinx - xsinx) = -1/2(xcosx - xsinx + 2sinx).

Substituting y and its derivatives into the differential equation:

y'' - y = (-1/2(xcosx - xsinx + 2sinx)) - (1/2(sinx + xcosx)) = -cosx

The right side of the equation matches −cosx, so option (D) is a solution.

(E) 1/2(cosx+xsinx):

Taking the first derivative of this function, we get y' = -1/2(sinx + xcosx).

Taking the second derivative, we get y'' = -1/2(cosx - xsinx).

Substituting y and its derivatives into the differential equation:

y'' - y = (-1/2(cosx - xsinx)) - (1/2(cosx + xsinx)) = -xsinx

The right side of the equation is -xsinx, not −cosx, so option (E) is not a solution.

(F) 21(ex−cosx):

Taking the first derivative of this function, we get y' = 21(ex+sinx).

Taking the second derivative, we get y'' = 21(ex+cosx).

Substituting y and its derivatives into the differential equation:

y'' - y = 21(ex+cosx) - 21(ex-cosx) = 42cosx

The right side of the equation is 42cosx, not −cosx, so option (F) is not a solution.

Therefore, the only solutions to the differential equation y′′−y=−cosx are option (B) 1/2(ex+cosx).

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Answer:

44398.84

Step-by-step explanation:

17,000e^(0.06)(16)

it helps to use a desmos scientific calculator

90 + x + 3x = 180

4x = 90

x = 22.5

Your answer: 22.5

Answer:

7y + 4

Step-by-step explanation:

2y + 5y+4

add 2y and 5y

7y+ 4

Answer:

7y +4

Step-by-step explanation:

Open up the brackets ans collect your like terms and simplify the expression.

The sum of the expression ∑(X+Y)(2X-3Y) for the given data set is [insert calculated value].

To calculate the sum of the expression ∑(X+Y)(2X-3Y), we substitute the given values for X and Y into the expression for each pair of values, and then sum up the resulting values. Let's perform the calculations step by step for the given data:

For the pair (X=4, Y=2):

(4+2)(2(4)-3(2)) = (6)(8-6) = (6)(2) = 12.

For the pair (X=3, Y=-3):

(3+(-3))(2(3)-3(-3)) = (0)(6+9) = 0.

For the pair (X=5, Y=1):

(5+1)(2(5)-3(1)) = (6)(10-3) = (6)(7) = 42.

For the pair (X=1, Y=6):

(1+6)(2(1)-3(6)) = (7)(2-18) = (7)(-16) = -112.

For the pair (X=2, Y=0):

(2+0)(2(2)-3(0)) = (2)(4-0) = (2)(4) = 8.

For the pair (X=0, Y=8):

(0+8)(2(0)-3(8)) = (8)(0-24) = (8)(-24) = -192.

For the pair (X=5, Y=4):

(5+4)(2(5)-3(4)) = (9)(10-12) = (9)(-2) = -18.

For the pair (X=2, Y=-4):

(2+(-4))(2(2)-3(-4)) = (-2)(4+12) = (-2)(16) = -32.

Now, we sum up all the calculated values:

12 + 0 + 42 + (-112) + 8 + (-192) + (-18) + (-32) = -292.

Therefore, the sum of the expression ∑(X+Y)(2X-3Y) for the given data set is -292.

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Answer:

Step-by-step explanation:

METHOD 1

in centre it is split by 4, each angle is equal.

in a square angles add up to 360°

360/4=90°

∴∠DOC=90°

if you have to do more work or have toexplain more, or you dont get that way there is another method:

METHOD 2

since ABCD is a square it alladds up to 360°

so ∠A=B=C=D=90°

in triangle DOC anles add up to 180°

each diagonal cuts angleA,B,C and D in half

so in triangle DOC, ∠ODC=∠CDO=45

∠DOC=180-∠DOC-∠CDO       (or 180-(∠DOC+∠CDO)

∠DOC=180-45-45

∠DOC=90

Based on the given information, the calculated z-score (-2.78) is less than the critical z-score (1.96) for a one-tailed test with the alternative hypothesis stating that the population mean (mu) is less than the hypothesized mean (mu0), and the sample mean (xbar) is also less than mu0. Therefore, the conclusion would be to reject the null hypothesis.

In hypothesis testing, the z-score is used to determine the distance between the sample mean and the hypothesized mean in terms of standard deviations. The critical z-score is the value that separates the rejection region from the non-rejection region.

In this case, the calculated z-score (-2.78) is in the rejection region, which is determined by comparing it to the critical z-score (1.96) for the given significance level. Since the calculated z-score is significantly smaller than the critical z-score, it indicates strong evidence against the null hypothesis. Thus, the conclusion would be to reject the null hypothesis and accept the alternative hypothesis, which suggests that the population mean is less than the hypothesized mean.

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The forest fires in southern Mexico and Guatemala consumed forest land at a rate of 28,600 acres per week.

During May 1998, forest fires in southern Mexico and Guatemala were burning at a significant rate, resulting in the spread of smoke all the way to Austin. The fires were consuming forest land at a rate of 28,600 acres per week. This indicates the amount of forest area that was destroyed or affected by the fires within a span of one week.

The figure of 28,600 acres per week provides an understanding of the magnitude and impact of the forest fires. It highlights the rapid rate at which the fires were spreading and consuming the forested areas. Forest fires are known to have severe ecological and environmental consequences, including loss of biodiversity, destruction of habitats, and degradation of air quality due to the smoke generated. The fact that the smoke from these fires reached Austin suggests the vast distance covered by the smoke plume, indicating the scale and intensity of the fires.

Forest fires are a significant concern as they pose risks to both human lives and natural ecosystems. They can have long-lasting effects on the affected regions, requiring extensive recovery and rehabilitation efforts. Monitoring and managing forest fires, along with implementing preventive measures, are crucial for minimizing their impact and protecting valuable forest resources.

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Answer:

O.8 is greater than 7/10

Step-by-step explanation:

0.8 is in the tenths Place So you know that equals 80 ones Out of one hundred. So you have 80/100 if you divide 80 and 100 by ten it reduces to 8/10. You know that 8/10 is greater than 7/10. Hope this helped .

Answer:

Step-by-step explanation:

600 times

and

6 sides to said dice

100≠(Not equal sign)200

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

I would recommend writing/typing all of this as your answer.

Hope I helped!!

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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Step-by-step explanation:

37 and 1/2 divided by 3/16 =

75/2 divided by 3/16 =

75/2 * 16/3 =

25*8 = 200 <--- 75 cancels 3; 16 cancels 2

Answer:

13

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

1/8 = .125

2/4 = .5

therefore 1/8 does not = 2/4