Triangle ABC shown below has m∠B=36∘, a=5, and c=13. Find the area of the triangle.

The area of triangle LMN is 49.61 square units.

We have,

To find the area of triangle LMN.

Area = (1/2) x base x height

where the base and height are the sides of the triangle perpendicular to each other.

First, we need to find the length of side L.

We can use the Law of Cosines.

L² = M² + N² - 2MNcos(132°)

L² = 6² + 8.3² - 268.3cos(132°)

L² = 36 + 68.89 + 99.36

L² = 204.25

L = √204.25

L = 14.28

Now that we know the length of the base of the triangle, we can find the height by dropping a perpendicular from vertex M to side LN.

Since triangle LMN is obtuse, the perpendicular will fall outside of the triangle.

Let's call the foot of the perpendicular point P.

Since M∠M is 132°, we can find the measure of the acute angle ∠LMP:

M∠LMP = 180° - M∠M

M∠LMP = 180° - 132°

M∠LMP = 48°

We can use trigonometry to find the length of MP:

tan(48°) = h/6

h = 6 x tan(48°)

h = 6.93

The area of triangle LMN is:

Area = (1/2) x base x height

Area = (1/2) x 14.28 x 6.93

Area ≈ 49.61

Thus,

The area of triangle LMN is 49.61 square units.

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When p = 9 and w = 225, the value of m is 94.5

We know that m varies jointly as p and the square root of w, then we can write.

m = k*p*√w

Where k is a constant.

We know that m=21 when p=5 and w=36, replacing that we will get:

21 = k*5*√46

21 = k*30

21/30 = k

7/10 = k

Then the equation is:

m = (7/10)*p*√w

Then when p = 9 and w = 225 we will have:

m = (7/10)*9*√225

m = 94.5

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Answer:

1/60

Step-by-step explanation:

For each cake, there is a 1/20 chance to find the gold ring since it is in one of the 20 slices. The probability for each cake is independent of each other, so we multiply

1/20 x 1/20 x 1/20

=1/60

Answer:

7

Step-by-step explanation:

a= a+b/2*h

Where the information relating to the circle and its diameter are given, the equation of the circle would be: "(x  5)²  + y2 = 81" (Option B)

The above is determined by the standard form equation of a circle which is:

(x- h) ² + (y - k)² = r²

Here,

(h, k)  is the center of the circle and r   is the radius

In this case, the center is (-5 , 0) and the diameter is 18, so the radius is half the diameter, whic is 18/ 2 = 9

So making the required substitutions, the expression becomes:

(x-(-5))² + (y-(0))² = 9²

Which becomes

(x  5)²  + y2 = 81

Thus, it is correct to state that Option B is the equation of the circle.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

The center of a circle is at (-5, 0), and the diameter of the circle is 18. Which of the following is the equation of the circle?

A. (x  5)²  + y = 9

B. (x  5)²  + y2 = 81

C. (x  5)²  + y2 = 9

D. (x  5)²  + y2  81

The equation that represents the number of credits the student has earned after t semesters is C(t) = 12t + 15.

Let x be the number of credits the student had before starting college, and let y be the number of credits the student takes each semester. We can use this information to write an equation that represents the number of credits the student has earned after t semesters.

After 2 semesters, the student had 39 credits, which means the student earned 2y + x credits in those two semesters. Similarly, after 5 semesters, the student had 75 credits, which means the student earned 5y + x credits in those five semesters.

Using this information, we can write the following equation:

C(t) = yt + x

where C(t) represents the number of credits the student has earned after t semesters.

We know that C(2) = 2y + x = 39 and C(5) = 5y + x = 75. We can use these two equations to solve for x and y:

2y + x = 39

5y + x = 75

Subtracting the first equation from the second equation gives:

3y = 36

Therefore, y = 12, which means the student takes 12 credits each semester. Substituting y = 12 into either of the two equations above gives x = 15, which means the student had 15 credits before starting college.

Thus, the equation that represents the number of credits the student has earned after t semesters is C(t) = 12t + 15.

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Based on the rate of change, the total charge will be $ 12.60 in 4 days

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

Rate of change of investment = $3.15

Value of the investment = $12.60

Using the above as a guide, we have the following:

Number of days = Value of the investment/Rate of change of investment

Substitute the known values in the above equation, so, we have the following representation

Number of days = 12.60/3.15

Evaluate

Number of days = 4

Hence, the number of days is 4

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If Lois is retiring from her job after 27 years, then if she waited for 4 years, her pension will be $38 higher than if she retires this year.

If Lois retires this year, the flat-amount is $52, So, her monthly pension can be calculated as follows;

⇒ Monthly pension = (52 × 27)/12,

⇒ Monthly pension = $117,

If Lois works for another 4 years, the flat amount used to calculate her monthly pension will increase to $60 for each year of service.

So, her monthly pension will be calculated as follows:

⇒ Monthly pension = (60 × 31)/12,

⇒ Monthly pension = $155,

So, The difference in monthly pension between retiring this year and retiring after working another 4 years can be calculated as follows:

⇒ Difference in monthly pension = $155 - $117,

⇒ Difference in monthly pension = $38,

Therefore, if Lois waits another 4 years before retiring, her monthly pension will be $38 higher than if she retires this year.

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Krell's equity cost of capital, or expected total return, is 5.57%.

We have,

The dividend yield is the annual dividend divided by the current share price:

Dividend yield

= Annual dividend / Share price

= $0.98 / $22.08 = 0.0444 = 4.44%

The equity cost of capital is the expected total return on the stock, which includes both the dividend yield and the expected capital appreciation:

Equity cost of capital = Dividend yield + Capital Appreciation

= 4.44% + [(24.98 - 22.08) / 22.08]

= 4.44% + 0.1314

= 5.57%

Therefore,

Krell's equity cost of capital, or expected total return, is 5.57%.

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The resultant of the two vectors or the sum of the two vector is equal to the diagonal of parallelogram.

Parallelogram law of vector addition states that if two vectors are represented in magnitude and direction by the adjacent sides of a parallelogram, the diagonal of the parallelogram drawn from the point of intersection of the vectors represents the resultant vector in magnitude and direction.

For the given vector a, and vector, the resultant of the two vector is calculated as;

-----------> a  and --------------->b = a + b

The diagram represents the addition of the two vectors, a and b;

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Answer:

260

Step-by-step explanation:

The z score for a normal distribution is given by the formula
[tex]z = \dfrac{X-\mu}{\sigma}[/tex]

where
X is the data point, μ is the mean and  σ is the standard deviation

Given

Mean μ = 500
Standard deviation σ = 80
z-score = -3

and plugging in these values for z-score formula we get

[tex]-3 = \dfrac{X -500}{80}[/tex]

==>
-240 = X - 500
-240 + 500 = X

260 = X

or

X = 260

Answer: 15,625,000

Step-by-step explanation: x5, 8, 40, 200, 1,000, 5,000, 25,000, 125,000, 625,000, 3,125,000, 15,625,000

Answer: x < 5, see attached

Step-by-step explanation:

     To solve for x, we will isolate the given variable.

Given:

  [tex]\displaystyle 1 > \frac{x}{5}[/tex]

Multiply both sides of the equation by 5:

  [tex]\displaystyle5 > x[/tex]

Flip equation:

  [tex]\displaystyle x < 5[/tex]

     To graph, we will first plot a point on 5 with an open circle. Then, we will shade to the left since x is less than 5. See attached.

The number of photos from Julia dance class = 5/7 or 40/56 photos.

We shall use mathematical operations to calculate the photos that are of Julia dance class

Five sevenths of the images are photos from dance class, meaning that 5/7 x 56 = 40 photos from dance class.

We express the answer as a fraction with a denominator of 56 like this:

Number of photos / Total number of photos = 40/56

Number of photos from dance class / Total number of photos = 5/7

Therefore, the fraction of photos that are of Julia dance class (as a fraction with a denominator of 56) = 5/7 or 40/56.

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The range of the repairs to the cars is 241.

The sample variance is 11, 671.33

The sample standard deviation would be 108.03.

Range = Maximum repair cost - Minimum repair cost

= 456 - 215

= 241

Find mean :

= (422 + 456 + 401 + 215) / 4

= 373. 5

Sample variance :

= Sum of ( each repair cost - mean ) ² / (Number of cars - 1)

= ( 2, 340.25 + 6, 812.25 + 756.25 + 25, 105.25 ) / ( 4 - 1 )

= 11, 671. 33

Sample standard deviation:

= √sample variance

= √11, 671. 33

= 108. 03

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Answer:

Step-by-step explanation:

Answer: 1040

Step-by-step explanation: y=ab

The exponential equation is: y = 1040(1.3^x)

Calculate the value of y, which stands for the albums sold, and x represents the months passed from their release. For an exponential equation structured as y = a(b^x), identify the base b to solve it mathematically.

By analyzing the last month after launch, known as March, 1040 copies were made available for public consumption. One month further down the line, in April, the gross profit jumped up to 1352 units sold.

When we divide the copies traded throughout April by those resold in March, the value identifies the base:

b=1352/1040 ≈ 1.3

Thus, applying the coefficient a for the initial sales registered during March - totaling 1,040 copies - leads us to define the following form for our equations:

y = 1040(1.3^x)

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Sample Response/ Explanation: The data sets could be the same, but not necessarily. It is possible for data sets to differ in their spread but still have the same measures of center. The measures of spread could be different.

The data sets could be the same, but not really. It is possible for the data sets to differ in their spread but still have the same measures of center. The measures of spread could be different though.

The measure of variability that should be used for both sets of data to determine the location with the most consistent temperature is:

Range, because Flower Town is symmetric

A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data points over a range of successive numerical intervals of equal width. The independent variable and dependent variable are plotted along the horizontal axis and the vertical axis, respectively, in the most typical type of histogram.

Now, from the given histograms, we can see that Desert landing is skewed while Flower town is symmetrical entirely.

Thus, The measure of variability that should be used for both sets of data to determine the location with the most consistent temperature is:

Range, because Flower Town is symmetric

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Taxes and transfers are used by the government to more equitably share revenue. A Medicaid participant typically receives $1500 in benefits.

We know that,

Medicare is a health insurance program for seniors, disabled individuals under 65, and dialysis patients. Medicaid is a program that provides financial aid for low-income patients' medical costs.

The federal government and the states share funding for the Medicaid program. The amount that the federal government reimburses states for program costs is known as the Federal Medical Assistance Percentage, or FMAP (FMAP).

Spending on Medicaid is mostly targeted at the elderly and those with disabilities. Despite accounting for over two-thirds of Medicaid spending, seniors and individuals with disabilities make up one in four beneficiaries, which reflects the high per-enrollee expenses for both acute and long-term care.

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The solution set for the given equation is 25.

In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

Next, we would determine the solution set for the given equation by translating the word problem into an equation and then divide both sides of the square root function as follows;

-√x = 5

√x = -5

By taking the square of both both sides of the square root function, we have:

x = (-5)²

x = 25

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Making x as a subject, we get equation as x=(y+2)/5.

The given equation is y=5x-2.

To make x as the subject

y+2=5x

x=(y+2)/5

Therefore, making x as a subject, we get equation as x=(y+2)/5.

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"Your question is incomplete, probably the complete question/missing part is:"

Rearrange the formula to make x the subject y=5x-2.

Answer:

33

Step-by-step explanation:

To solve for the range, simply subtract the largest-value term from the smallest-value term. First, set all numbers from least to greatest:

14 , 23 , 28 , 36 , 40 , 42 , 47

The smallest term is 14.

The largest term is 47.

Subtract 47 with 14:

[tex]47 - 14 = 33[/tex]

The given range value will be 33.

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The numeric ratio of the segment ratio are:

To find the numeric ratios of the given segment ratios, to calculate the distances between the given points.

CD: DB

The distance between C(6,2) and D(4,3) is:

CD = √[(6 - 4)² + (2 - 3)²] = √5

The distance between D(4,3) and B(-4,7) is:

DB = √[(4 + 4)² + (3 - 7)²] = 10

Therefore, the numeric ratio of CD:DB is:

CD:DB = √5:10

CE: CA

The distance between C(6,2) and E(4,2) is:

CE = √[(6 - 4)² + (2 - 2)²] = 2

The distance between A(-4,2) and C(6,2) is:

CA = √[(-4 - 6)² + (2 - 2)²] = 10

Therefore, the numeric ratio of CE:CA is:

CE:CA = 2:10

DE: BA

The distance between D(4,3) and E(4,2) is:

DE = √[(4 - 4)² + (3 - 2)²] = 1

The distance between B(-4,7) and A(-4,2) is:

BA = √[(-4 + 4)² + (7 - 2)²] = 5

Therefore, the numeric ratio of DE:BA is:

DE:BA = 1:5

CD: CB

The distance between C(6,2) and D(4,3) is:

CD = √[(6 - 4)² + (2 - 3)²] = √5

The distance between C(6,2) and B(-4,7) is:

CB = √[(6 + 4)² + (2 - 7)²] = √181

Therefore, the numeric ratio of CD:CB is:

CD:CB = √5:√181

Based on the numeric ratios, determine the type of ratio for each segment ratio:

CD: DB is a part:part ratio

CE: CA is a part:whole ratio

DE: BA is a part:part ratio

CD: CB is a part:whole ratio

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