PLEASE ANSWER AND EXPLAIN WHY THE ANSWER IS CORRECT!

Answer:

Yes, you did solve it correctly, and the way you did it is fine

Step-by-step explanation:

You correctly applied the formula for the Law of Cosines to solve for the unknown side length c of a triangle, given the values of the other two side lengths and the angle opposite the unknown side. Specifically, you plugged in the given values of a, b, and C into the formula c^2 = a^2 + b^2 - 2ab cos(C) and then solved for c by taking the square root of both sides of the equation. Finally, you simplified the expression for c by calculating the square root of 25 to obtain a numerical value of c=5

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The area of ACD based on the information given will be 54 units².

The area of a trapezoid is calculated as follows:

(base1 + base2) height / 2 = Area

where base1 and base2 are the lengths of the trapezoid's two parallel sides, and height is the perpendicular distance between them.

So, assuming you have the measurements for base1, base2, and height, you can use the formula above to compute the area of the trapezoid.

Area = 1/2 × (10 + 8) × 6

Area = 1/2 × 18 × 6

Area = 54 units ²

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Along with proof of (a.) and (d.), (b.) Power tower: one level is a, (k + 1) levels is a raised to the power of a power tower with k levels, (c.) A(2, n) <= 2 ↑↑ n for all positive integers n, where ↑↑ denotes power tower notation.

The idea of a fully computable function that is not primitive recursive is illustrated by the recursively constructed mathematical function known as the Ackermann function. Since m and n are non-negative integers, it is commonly written as A(m, n).

a.) Prove using regular induction that [tex]A(1, n) \leq 2^n[/tex] for all positive integers n:

Base Case: For n = 1, A(1, 1) = 2, which is equal to [tex]2^1[/tex].

Inductive Hypothesis: Assume that [tex]A(1, k) \leq 2^k[/tex] for some positive integer k.

Inductive Step: We need to show that [tex]A(1, k + 1) \leq 2^{(k + 1)}[/tex]. Using the recursive definition of A(m, n), we have [tex]A(1, k + 1) = A(0, A(1, k)) = 2^{(A(1, k))}\leq 2^{(2^k)}[/tex] (by inductive hypothesis)[tex]< = 2^{(2^{(k + 1)})}[/tex].

Therefore, by regular induction, we have proved that [tex]A(1, n) \leq 2^n[/tex] for all positive integers n.

b.) A power tower with one level is defined as a, and a power tower with (k + 1) levels is defined as a raised to the power of a power tower with k levels.

c.) [tex]A(2, n) \leq 2[/tex] ↑↑ n for all positive integers n, where ↑↑ denotes power tower notation.

d.) The recursive definition of a triple arrow-up notation for power towers is:

a ↑↑↑ 1 = a (base case)

a ↑↑↑ (k + 1) = a ↑↑ (a ↑↑↑ k) (recursive step)

This definition states that a triple arrow-up notation with one level is equal to the base value "a", and a triple arrow-up notation with (k + 1) levels is equal to "a" raised to the power of a triple arrow-up notation with "k" levels.

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Complete Question: ( Refer to image)

The approximate z-score that corresponds to a right tail area of 1.50 is 0.066807

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

P(Z > 1.5)

This means that we calculate the z-score right tail area of 1.50

This is represented as

Probability = (z > 1.50)

Using a graphing calculator, we have

Probability =  0.066807

Hence, the probability value is 0.066807

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The most common amount of sleep is 8 1/2 hours.

There is no outlier in the data.

The difference in hours between the longest night's sleep and the longest night's sleep is 3.5 hours.

The number of people who slept longer than 8 hours is 15 people.

In Mathematics and Statistics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of crosses or dots.

Based on the information provided about the number of hours Molly's friends slept last night, we can reasonably infer and logically deduce that all of the data points would be between 6 and 11, without any outlier.

In this scenario, we would use an online graphing calculator to construct a dot plot with respect to a number line that accurately fit Molly's data set, with a scale of 0 < x < 11.

Difference in hours = 10 - 6.5 = 3.5 hours.

In conclusion, the dot plot would be titled "Hours of sleep."

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Plot the points on the graphing calculator, and then determine the linear regression function: y = -1.16786x + 8.82857

You may obtain a slightly different linear regression equation.

1) -1 (g)

2) 8 (not one of the choices)

3) graph (i)

4) approximately -1/strong negative trend (not one of the choices)

5) y = -x + 8 (h)

The better statistics to use to compare the distributions includes mean and standard deviation. The Option C is correct.

Mean represents the central tendency of the distribution, while standard deviation reflects the spread of the data around the mean. Comparing mean & standard deviation of 2 or more distributions can provide insights into similarities and differences.

If the means of two distributions are similar, it suggests the data points in each distribution are centered around similar value. But if standard deviations are also similar, it indicates that the spread of the data points around the mean is also similar.

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Okay, let's analyze the linearized data options to determine which equation best models it:

a. log y = 0.116315x+0.249114

This has a positive slope coefficient of 0.116315, so it will model increasing data. But the y-intercept term 0.249114 is negative, so the model line would start below the origin. This does not seem to match the typical linear relationship we would expect.

b. log y = 0.249114x+0.116315

This also has a positive slope coefficient, but now the y-intercept term 0.116315 is positive. This could potentially model increasing data that starts above the origin. However, without seeing the data it's hard to definitively say if this is the best fit.

c. log y = 0.0288761x+0.435269

This has a positive but much smaller slope coefficient of 0.0288761. This would model increasing data at a much shallower rate. Again, without seeing the data we can't rule this out, but it seems less likely.

d. log y = 0.435269x+0.0288761

This has a larger positive slope coefficient of 0.435269, so it would model increasing data at a steeper rate. And the positive y-intercept term of 0.0288761 ensures the model line starts above the origin.

Of these 4 options, choice d (log y = 0.435269x+0.0288761) seems the most likely to best model increasing linear data that starts above the origin. However, without seeing the actual data points, we can't say that with certainty. The slope and intercept values would need to give the closest fit to the data for that to be the definitive choice.

Let me know if this helps explain the options, or if you have any other questions!

Where the above information about right triangles are given, the asnswer is

A. x = 3, y = 2 (Option A)

The hypotenuse and the length of one leg of one right triangle must be equal to the hypotenuse and corresponding length of the one leg of the other ∆ for both triangles to be equal by the HL Congruence Theorem.

Thus, let's find x and y by setting the corresponding lengths of the two right ∆s equal to each other.

Therefore:

x = y + 1 ----› eqn. 1

2x + 3 = 3y + 3 ----› eqn. 2

Substitute x = (y + 1) into eqn. 2, and solve for y.

2x + 3 = 3y + 3 ----› eqn. 2

2(y + 1) + 3 = 3y + 3

2y + 2 + 3 = 3y + 3

2y + 5 = 3y + 3

Collect like terms

2y - 3y = -5 + 3

-y = -2

Divide both sides by -1

y = 2

Substitute y = 2 into eqn. 1.

x = y + 1 ----› eqn. 1

x = 2 + 1

x = 3

Thus,

x = 3, and y = 2 (Option A)

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Full Question:

See attached image

The solution to the equations for y are y = 9, y = 8 and y = 7

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

y²- 1 = 80

(y - 4)÷ 4 = 1

10 - 63 ÷ y = 1​

Solving the equations, we have

y²- 1 = 80

y² = 81

y = 9

Next, we have

(y - 4)÷ 4 = 1

(y - 4) = 4

y = 8

Lastly, we have

10 - 63 ÷ y = 1​

-63 ÷ y = -9

-9y = -63

y = 7

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Answer:

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

The range of the given function has one restriction, its denominator can't be zero, hence:

Therefore the function can get any value but zero:

The matching answer choice is D.

Linear function is f(x) = mx + b.

Reciprocal of a function f(x)  is 1/f(x).

So the reciprocal of linear function has a form of f(x) = 1 / (mx + b).

The only answer choice in same form is D.

Substitute x = - 5/3 into function to get:

This is undefined value, therefore it represents the vertical asymptote.

The function gets close to - ∞ when x → - 5/3 from left and gets close to +∞ when x → - 5/3 from right (see attached graph).

Therefore the correct choice is B.

The maximum price you should be willing to pay for the annuity, given the cash flow and the interest rates, would be 2. R 39, 272

The maximum price to be paid for the annuity would be the present value of the annuity which can be found by the formula :

= Annuity x Present value interest factor of annuity, 20 years, 8 %

The annuity = R 4, 000

Present value interest factor of annuity, 20 years, 8 %  = 9. 81815

The maximum you should pay for the annuity is therefore:

= 4, 000 x 9. 81815

=  R 39, 272 . 60

= R 39, 272

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Answer:

9

Step-by-step explanation:

All you have to do is replace the letters with numbers

= ( x - y) + z

= ( 4 - 5) +  10

= -1 + 10

= 10 - 1

= 9

2. 28 goldfish was what was given away before noon than in the afternoon

3. 108 goldfish were given away all day

4. Yes the owner have enough goldfish for the entire day

5. 16 goldfish were left over

2. Before noon, gold fish = 30 + 36 + 40 = 106

after noon gold fish = 28 + 30 + 10 + 2 + 8 = 78

diference = 106 - 78

= 28

3. Gold fish given away all day = 106 + 78

= 184

4. The owner had enough fish because the total fist he had was 200 and the amount that was given away is 184

5. The left over fish = 200 - 184

= 16

6. The owner was nervous because the customers were increasing between 9 to 11 and she had given away more than half in the first three hours

7. A reason no one came at noon could be because a resstaurant was having a lunch special

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Answer: To find the area of the ring-shaped path, we need to subtract the area of the inner circle (the pool) from the area of the outer circle. The radius of the pool is half the diameter, so it is 11 yards. The radius of the outer circle is the sum of the radius of the pool and the width of the path, so it is 11 + 5 = 16 yards.

The area of the pool is:

A_pool = pi * r^2 = pi * 11^2 ≈ 380.13 square yards

The area of the outer circle is:

A_outer = pi * R^2 = pi * 16^2 ≈ 804.25 square yards

The area of the ring-shaped path is:

A_path = A_outer - A_pool ≈ 804.25 - 380.13 ≈ 424.12 square yards

Since one gallon of coating can cover 5 square yards, we need:

Gallons = A_path / 5 ≈ 424.12 / 5 ≈ 84.82

Therefore, we need approximately 85 gallons of coating to cover the ring-shaped path.

Step-by-step explanation:

the speed of the train in km/h is 40.32 whereas the speed of the train in m/s is 11.2.

(i) To find the speed of the train in km/h, we can use the formula:

speed = distance/time

Here, the distance travelled by the train is 16.8 km, and the time taken is 25 minutes, which is equivalent to 0.4167 hours (since 1 hour = 60 minutes). Substituting these values in the formula, we get:

speed = 16.8 km/0.4167 hours

speed = 40.32 km/h (rounded to two decimal places)

Therefore, the speed of the train in km/h is 40.32.

(ii) To find the speed of the train in m/s, we can convert the speed in km/h to m/s by multiplying by 1000/3600 (since 1 km/h = 1000 m/3600 s). Using the speed of 40.32 km/h from part (i), we get:

speed = 40.32 km/h * 1000 m/km / 3600 s/h

speed = 11.2 m/s (rounded to one decimal place)

Therefore, the speed of the train in m/s is 11.2.

If the speed limit is 55 km/h, we cannot directly determine the distance travelled by the train without additional information. The distance travelled by the train would depend on the time it took to travel at the given speed limit.

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The probabilities will be :

P(none) = 0.018

P(at least one) =  0.982

P(at most one) = 0.187

Pretty Betty share  is 15%, the probability that any one household is tuned to the show will be:  0.15.

To find the probability that none of the households are tuned to Pretty Betty will be:

P(none) = 0.85¹¹

            ≈ 0.018

So, to find the probability that at least one household is tuned to Pretty Betty,  i use the complement rule as well as subtract the probability of none of the households being tuned to the show from 1:

P(at least one)

= 1 - P(none)

≈ 1 - 0.018

≈ 0.982

So, to find the probability that at most one household is tuned to Pretty Betty:

P(at most one) = P(none) + P(one)

= 0.85^11 + 11(0.15)(0.85^10)

≈ 0.187

Hence, the probabilities will be :

P(none) = 0.018

P(at least one) =  0.982

P(at most one) = 0.187

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This means that the coordinates of P are (a, b), where a is the value for which f'(a) = 0, and b = f(a).

The term "coordinate" generally refers to a value or set of values that describe the position or location of a point or object in a particular system or space. In mathematics, coordinates are typically used to describe the position of a point on a graph or in a geometric plane, and they usually consist of a set of numerical values that indicate the distance or direction of the point from a specified origin or reference point. In geographic or cartographic contexts, coordinates might refer to latitude and longitude values that indicate a specific location on the Earth's surface. Other systems may use different types of coordinates, but the underlying idea is usually the same: a set of values that describe the position of an object or point in a given space or system.

if the graph of f has a horizontal tangent at point P, this means that the slope of the tangent line at P is zero.

Let (a, b) be the coordinates of P. Then the equation of the tangent line at P is:

[tex]y - b = f'(a)(x - a)[/tex]

Since the slope of the tangent line at P is zero, we have:

f'(a) = 0

This means that the derivative of f at x = a is zero. So, we need to find the value of a for which f'(a) = 0.

Once we find the value of a, we can substitute it into the equation of the tangent line to find the value of b.

So, let's find f'(x) first:

f(x) = ... (the function is not given, so we cannot find f'(x) explicitly)

We know that f'(a) = 0, so we have:

[tex]f'(a) = lim h- > 0 [f(a+h) - f(a)]/h = 0[/tex]

This means that:

[tex]lim h- > 0 [f(a+h) - f(a)]/h = 0[/tex]

Multiplying both sides by h, we get:

[tex]lim h- > 0 [f(a+h) - f(a)] = 0[/tex]

Taking the limit as h approaches 0, we get:

[tex]f(a) - f(a) = 0[/tex]

So, we have:

[tex]f(a) = b[/tex]

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Answer:

(-1, 2)

Step-by-step explanation:

When an equation is formatted like this, you can just reverse the operators (in this case +1 and -2) and you'll get your coordinates.

Elsa has a 5:7 an odd of getting an extra-large stuffed animal against her.

Elsa has a 7:5 chance in her favor of getting an extra-large stuffed animal.

(a) The total number of balloons is 1 + 2 + 2 + 7 = 12. The number of balloons that are not extra-large is 1 + 2 + 2 = 5. So the odds against Elsa winning an extra-large stuffed animal are 5:7.

(b) The odds in favor of Elsa winning an extra-large stuffed animal are the opposite of the odds against winning an extra-large stuffed animal. So the odds in favor of Elsa winning an extra-large stuffed animal are 7:5.

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A loan of $595 borrowed on June 15 and repaid on Dec 17 at an exact interest rate of 6%. The exact time between the two dates is 170 days, and the maturity value is $611.69 rounded to the nearest cent.

Using the Days in a year table, we can find the exact time between June 15 and December 17 as follows

June has 30 days in the table and July through November have 31 days each. December has 17 days until the loan is repaid. Therefore, the exact time is

30 + 31 + 31 + 30 + 31 + 17 = 170 days

Next, we can calculate the interest using the formula

interest = principal x rate x time / 365

where the principal is $595, the rate is 6%, and the time is 170 days.

Substituting these values, we get

interest = 595 x 0.06 x 170 / 365

interest = $16.69

Therefore, the exact interest is $16.69.

Finally, we can calculate the maturity value by adding the principal and the interest

maturity value = principal + interest

maturity value = $595 + $16.69

maturity value = $611.69

Therefore, the maturity value is $611.69 rounded to the nearest cent.

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The distance between Eilat and Jerusalem is 181.4 miles.

To convert kilometers to miles, we need to multiply the number of kilometers by 0.621371, which is the conversion factor from kilometers to miles. Therefore, to convert the distance between Eilat and Jerusalem from kilometers to miles, we can use the following formula:

distance in miles = distance in kilometers × 0.621371

Substituting the given distance of 292 kilometers into the formula, we get:

distance in miles = 292 km × 0.621371 = 181.417852 miles

Rounding this answer to the nearest tenth, we get:

distance in miles ≈ 181.4 miles

Therefore, the distance between Eilat and Jerusalem is approximately 181.4 miles.

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Step-by-step explanation:

(3h - 5)(5h + 4) =   3h * 5h    +   3h * 4     - 5*5h    - 5 *4

                              =    15h^2        - 13h    -20

[tex](3h-5)(5h+4)[/tex]

[tex]=(3h+-5)(5h+4)[/tex]

[tex]=(3h)(5h)+(3h)(4)+(-5)(5h)+(-5)(4)[/tex]

[tex]=15h^2+12h-25h-20[/tex]

Answer:

The distance, 27 ft 10  in, is equivalent to 8.48 meters.

1. Convert 27 ft first to inches by multiplying it by a conversion factor.

2. Add the converted value to 10 inches.

3. Convert the inch measure by multiplying it by a conversion factor.

4. Round to the nearest hundredth.

Convert the factor 12 inch/ 1 ft.

since 1 foot is equivalent to 12 inches.

= 27 ft × [tex]\frac{12inch}{1ft}[/tex] + 10 inch = 324 inch + 10 inch = 334 inch

This means that 27 ft 10 in is equivalent to 47/2 inches.

Again, The conversion factor 0.0254 m/ 1 inch

since there are 0.0254 meters in an inch.

[tex]334 inches[/tex] × [tex]\frac{0.00254 meters}{1 inch}[/tex]

= 334  × 0.00254 meters

= 8.4836 meters

Thus, distance, 25 ft and 20 inches, is equivalent to approximately 8.48 meters.

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The factored form of        [tex]8x^{2} 4 - 27y^{6}[/tex] 8x²4 - 27y⁶

To factor this expression, that it is in the form of a difference of two squares.

Specifically, 8x²4 is equal to (2x²)³ and 27y⁶ is equal to (3y²)³.

the formula for the difference between two cubes, states that:

              [tex]a^3 - b^3 = (a - b)(a^2 + ab + b^2)[/tex]  (a³ - b³ = (a - b)(a² + ab + b²)

Substituting [tex]a = 2x^2[/tex] a = 2x² and [tex]b = 3y^2[/tex] b = 3y², gives

[tex]8x^24 - 27y^6 = (2x^2)^3 - (3y^2)^3= (2x^2 - 3y^2)(4x^2 + 6x^2y^2 + 9y^4)[/tex]

8x²4 - 27y⁶ = (2x²)³ - (3y²)³ = (2x² - 3y²)(4x⁴ + 6x²y² + 9y⁴)

Therefore, the factored form of [tex]8x^{2} 4 - 27y^{6}[/tex] 8x²4 - 27y⁶ is [tex](2x^2 - 3y^2)(4x^4 + 6x^2y^2 + 9y^4).[/tex](2x² - 3y²)(4x⁴ + 6x²y² + 9y⁴).

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Answer:

the answer is E

Step-by-step explanation:

Answer:

y = [tex]\sqrt{11}[/tex]

Step-by-step explanation:

Substitute -4 for x and solve for y

[tex]y^{2}[/tex] = -2x + 3

[tex]y^{2}[/tex] = -2(-4) + 3

[tex]y^{2}[/tex] = 8 + 3

[tex]y^{2}[/tex] = 11

[tex]\sqrt{y^{2} }[/tex] = [tex]\sqrt{11}[/tex]

y = [tex]\sqrt{11}[/tex]

Helping in the name of Jesus.

Answer:

If I am not mistaken a=3;b=10;c=23;d=39

Step-by-step explanation: