Find the area of the following triangle. Show each of the math steps that you use to find the area. Then explain how to go about finding the area of this particular triangle (explain each one of the steps that you showed with your math).
100 POINTS IF YOU ANSWER CORRECTLY AND ILL GIVE BRAINLIEST

Length of Wire = 176 cm

It's bent into a square.

Side of square = 176/4 = 44 cm

Area of square = Side × Side = 44 × 44 = 1,936 sq.cm

Then it's bent into a circle.

Circumference of the circle = 2πr = 176 cm

Circumference = r = 176/2 × 7/22 = 28 cm

Area of circle = πr^2

Area = 22/7 × 28 × 28

Area = 2,464 sq.cm

The Circle will have more area than the square.

one real eigenvalue. find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace.

What is eigenvalue?

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that, when the linear transformation is applied to it, changes at most by a scalar factor. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by lambda.

a) -4

b) 1

c) 1

Step-by-step explanation:

a) The matrix A is given by:

\(A=\left[\begin{array}{ccc}-3 & 0 & 1 \\2 & -4 & 2 \\-3 & -2 & 1\end{array}\right]\\\)

where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:

\(A-\lambda I=\left[\begin{array}{ccc}-3-\lambda & 0 & 1 \\2 & -4-\lambda & 2 \\-3 & -2 & 1-\lambda\end{array}\right]\)

and by taking the determinant:\(\begin{aligned}& {[(-3-\lambda)(-4-\lambda)(1-\lambda)+(0)(2)(-3)+(2)(-2)(1)]-[(1)(-4-\lambda)(-3)+(0)(2)(1-} \\& \lambda)+(2)(-2)(-3-\lambda)]=0 \\& -\lambda^3-6 \lambda^2-12 \lambda-16=0\end{aligned}\)

and the roots of this polynomial is:

\(\begin{aligned}& \lambda_1=-4 \\& \lambda_2=-1+i \sqrt{3} \\& \lambda_3=-1-i \sqrt{3}\end{aligned}\)

hence, the real eigenvalue of the matrix A is -4.

b) The multiplicity of the eigenvalue is 1.

c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)

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Complete Quetion

The matrix A= (−3 0 1, 2 −4 2, −3 −2 1) has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace. The eigen value = has multiplicity = and the dimension of the corresponding eigenspace is:_______.

The present value of this annuity is $1,516 (rounded to the nearest whole dollar).

The formula for determining an annuity's present value is as follows:

PV = PMT [(1 - (1 + r)(-n)) / r] in which:

PV is the present value PMT is the payment per period, r is the interest rate per period, and n is the number of periods. In this example, Marie will receive $300 per year for the next six years, with an annual interest rate of 5%.

PMT = $300, r = 5%, 0.05, n = 6, and we can use this formula  fto figure out the present value:

PV = $300 [(1 - (1 + 0.05)(-6)) / 0.05] PV = $300 [(1 - (1.05)(-6)) / 0.05] Let's figure out the value now:

The present value of this annuity is therefore $1,516 (rounded to the nearest whole dollar): PV = $300  [(1 - 0.74726) / 0.05] PV = $300  [0.25274 / 0.05] PV = $300  5.0548 PV = $1,516.44

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We can use the unit circle or reference angles. For the range O≤θ<2π, let's find the solutions: The solutions for θ in the given equation are θ = π/3, 2π/3, 4π/3, and 5π/3.

To write the equation in terms of a single angle, we can use the double-angle identity for cosine:

cos(2θ) = 2cos^2(θ) - 1

Given the equation cos(2θ) = -2cos^2(θ), we can substitute the right side of the equation with the double-angle identity:

2cos^2(θ) - 1 = -2cos^2(θ)

Now, let's simplify the equation:

2cos^2(θ) - 1 + 2cos^2(θ) = 0

Combining like terms:

4cos^2(θ) - 1 = 0

Now, let's isolate cos^2(θ) by moving -1 to the other side:

4cos^2(θ) = 1

Dividing both sides by 4:

cos^2(θ) = 1/4

Taking the square root of both sides:

cos(θ) = ±√(1/4)

cos(θ) = ±1/2

Now, we have two equations:

1) cos(θ) = 1/2

2) cos(θ) = -1/2

To solve for θ, we can use the unit circle or reference angles. For the range O≤θ<2π, let's find the solutions:

1) cos(θ) = 1/2:

θ = π/3 and θ = 5π/3

2) cos(θ) = -1/2:

θ = 2π/3 and θ = 4π/3

Therefore, the solutions for θ in the given equation are:

θ = π/3, 2π/3, 4π/3, and 5π/3.

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0.38 is 7/18 (filling space)

Answer:

0.388888889

Step-by-step explanation:

Signal a) is not absolutely band-limited and so, its Nyquist sampling rate cannot be determined. Signal b) is absolutely band-limited with an absolute bandwidth of B Hz, and its Nyquist sampling rate is 2B.

Let x(l) be a band-limited signal with absolute bandwidth B Hz. For each of the signals below, we need to determine whether the signal is absolutely band-limited, and if so, express the Nyquist sampling rate for the signal in terms of B.

a) x(0) + x(t - 1)dx(t)dt:For this signal, let us apply the Fourier transform. The Fourier transform of the first term is 2πX(ω)δ(ω), and that of the second term is e^(-jω)X(ω).

Thus, X(ω) = 2πX(ω)δ(ω) + e^(-jω)X(ω)On rearranging this expression, we get: X(ω) = [1 / (1 - 2πδ(ω))]e^(-jω)Therefore, the signal is not absolutely band-limited because it has components at all frequencies.

Hence, the Nyquist sampling rate cannot be determined.b) x:For this signal, let us consider its Fourier transform. Its Fourier transform will be a scaled version of the Dirac comb function, centered at ω = 0, with a spacing of 2π. Hence, X(ω) = 2πBδ(ω).

The signal is absolutely band-limited with absolute bandwidth B Hz, and hence, the Nyquist sampling rate will be 2B. The Nyquist sampling rate is twice the absolute bandwidth, and so, the sampling rate for this signal will be 2B Hz.

Thus, the answer to the question is as follows:Signal a) is not absolutely band-limited and so, its Nyquist sampling rate cannot be determined. Signal b) is absolutely band-limited with an absolute bandwidth of B Hz, and its Nyquist sampling rate is 2B.

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Answer:

21

Step-by-step explanation:

You have to distribute the 7 in this case:

f(x) = 7(-x + 3)

f(x) = -7x + 21

The y-intercept is the number without the x with it. So, with this function it is 21.

I hope this helps!!

- Kay :)

Answer:

It is B!!!

Step-by-step explanation:

Molecules at the surface are strongly attracted to the molecules below. Then the correct option is B.

The tendency to reduce space produced by the tension of a convective surface film as a result of the topmost layer's particulate being drawn to the liquid's mass.

The molecules underneath are strongly drawn to the species on the surface.

Then the correct option is B.

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The correct answer is D. No, the result from part (a) could not be the actual number of survey subjects who said that their companies conduct criminal background checks on all job applicants.

b. No, the result from part (a) could not be the actual number of survey subjects who said that their companies conduct criminal background checks on all job applicants.

This is because a count of people must result in a whole number, and in this case, the number of survey subjects is 163, which is a whole number. The result from part (a), which is 115.73, is not a whole number and therefore cannot represent the actual count of survey subjects. It is likely that the percentage was calculated based on a rounded value of the actual count.

In part (a), the question asks for the exact value that is 71% of 163 survey subjects. To find this value, we multiply 163 by 0.71, which gives us 115.73. However, since the count of survey subjects must be a whole number, 115.73 cannot represent the actual number of individuals who said that their companies conduct criminal background checks on all job applicants.

It is important to note that in survey research, percentages are often calculated based on rounded numbers or estimated values. The result is then presented as a whole number or a percentage for ease of understanding and interpretation. In this case, the percentage of 71% was likely rounded from a more precise calculation, and the result of 115.73 is the exact value obtained from that calculation. However, when dealing with counts of people, it is necessary to have whole numbers, as you cannot have a fraction of a person.

#In a study conducted by a human resource management organization, 163 human resource professionals were surveyed. Of those surveyed, 71% said that their companies conduct criminal background checks on all job applicants.  a. What is the exact value that is 71% of 163 survey subjects? The exact value is 115.73. (Type an integer or a decimal. Do not round.) b. Could the result from part (a) be the actual number of survey subjects who said that their companies conduct criminal background checks on all job applicants? Why or why not? A. Yes, the result from part (a) could be the actual number of survey subjects who said this because the result is statistically significant. B. Yes, the result from part (a) could be the actual number of survey subjects who said this because the polling numbers are accurate. C. No, the result from part (a) could not be the actual number of survey subjects who said this because that is a very rare outcome. D. No, the result from part (a) could not be the actual number of survey subjects who said this because a count of people must result in a whole number.

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The value of X from the similar triangles above would be = 4. That is option B.

To determine the value of X from the missing part of the similar triangles, the formula that should be used is given below as follows:

VR/VU = VQ/VT

Where;

VR = 33

VU = 44

VQ = 8x-2

VT = 40

That is;

33/44 = 8x-2/40

33×40 = 44(8x-2);

1320 = 352x-88

1320+88 = 352x

1408 = 352x

X = 1408/352

= 4.

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The average score of 301, for a simple random sample of 1,000 students, is approximately 0.95.

a) To determine the likely size of the chance error in the average score of 301 for a cluster sample of 1,000 students, we need additional information about the cluster sampling design.

The cluster sampling method involves dividing the population into clusters, selecting a subset of clusters, and then sampling all individuals within the selected clusters.

The likely size of the chance error depends on the within-cluster variability and the between-cluster variability.

Without information about the variability at each level, we cannot accurately estimate the size of the chance error in this specific scenario.

Therefore, we cannot fill in the blank without more details regarding the cluster sampling design and the variability present in the clusters.

b) If a simple random sample of 1,000 students was tested, we can estimate the likely size of the chance error in the average score of 301. Since a simple random sample implies that each student has an equal chance of being selected, we can use the standard error of the mean formula to estimate the size of the chance error.

The standard error of the mean (SE) is calculated as the standard deviation (SD) divided by the square root of the sample size (n):

SE = SD / √n

Given that the SD is 30 and the sample size (n) is 1,000, we can calculate the standard error:

SE = 30 / √1000 = 30 / 31.62 ≈ 0.95

Therefore, the likely size of the chance error in the average score of 301, for a simple random sample of 1,000 students, is approximately 0.95.

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Answer:

A) 3.996 inches

B) 0.01

C) option B

Step-by-step explanation:

Note: The diameter of the lid is between : 3.95 and  4.05

A) calculate the supplier set mean diameter

std = 0.02 inch

P( x < 3.95 ) = 1% = 0.01

= P ( Z < \((\frac{3.95 - u }{0.02})\) ) = P ( Z < -2.3263 ) = 0.01

therefore :

\((\frac{3.95 - u }{0.02})\)  = -2.3263

hence : u = 3.996 inches ( mean diameter )

B) At mean diameter = 3.98 calculate the value of std

P ( X < 3.95 ) = 0.01

= P ( Z < \(( \frac{3.95-3.98 }{std } )\) )  = P ( Z < -2.3263 ) = 0.01

therefore

\(( \frac{3.95-3.98 }{std } )\) = -2.3263

hence std = 0.01 inch

C) option B is preferable because its mean diameter is smaller and  the percent of lids too large to fit is considered more carefully using option B

Mario has 3,628,800 different ways to arrange the 10 science fiction novels on his shelf.

When we want to arrange a set of n distinct objects in a row, the number of possible arrangements is given by n factorial, or n!, which is the product of all positive integers from 1 to n. In other words, n! = n x (n-1) x (n-2) x ... x 3 x 2 x 1.

In this case, Mario has 10 science fiction novels that he wants to arrange on a shelf, and each of these novels is distinct. Therefore, there are 10 possible choices for the first book he places on the shelf. Once he has placed the first book, there are only 9 remaining books to choose from for the second position. For the third position, there are 8 remaining books to choose from, and so on. Therefore, the total number of possible arrangements of the 10 books is:

10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800.

Therefore, Mario has 3,628,800 different ways to arrange the 10 science fiction novels on his shelf.

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Answer:

40

Step-by-step explanation:

2% of 400 is 8

400 x 0.02 = 8

10% of 400 is 40

10% of the asked number is 40.

A percentage is a number or ratio that can be expressed as a fraction of 100.

Given that, 2% of a number equals 8

Let the number be x,

2% of x = 8

x = 8x100/2

x = 400

10% of 400 = 10/100x400 = 40

Hence, 10% of the asked number is 40.

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Answer:

10 4-seated cars

Step-by-step explanation:

To write an equivalent series with the index of summation beginning at n = 1, you'll need to shift the index of the original series. The original series is:

Σ (−1)^n * 1/(n+1) * x^n, with n starting from 0.

To shift the index to start from n = 1, let m = n - 1. Then, n = m + 1. Substitute this into the series:

Σ (−1)^(m+1) * 1/((m+1)+1) * x^(m+1), with m starting from 0.

Now, replace m with n:

Σ (−1)^(n+1) * 1/(n+2) * x^(n+1), with n starting from 0.

This is the equivalent series with the index of summation beginning at n = 1.

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Answer:

(x+1)²= 49, the answer is B

Step-by-step explanation:

x² + 2x = 48

x² + 2x + (2/2)² -  (2/2)²= 48 --[what we are trying to do is to complete a square by adding (2/2)² -  (2/2)²]

(x+1)²= 49, the answer is B

Answer:

hey I'm pretty sure it's B. (x+2)²=49

Step-by-step explanation:

x²+2x+(2\2)²=48 + (2\2)²

(x+1)²=49

2 over 2 by the power of 2 = 1

To find the length of the curve r(t) = sqrt(2)ti, we need to use the arc length formula:L = ∫[a,b] ||r'(t)|| dt,where ||r'(t)|| is the magnitude of the derivative of the curve.

First, we need to find r'(t):

r'(t) = (d/dt) [sqrt(2)ti] = sqrt(2)i

The magnitude of r'(t) is ||r'(t)|| = sqrt(2).

So, the length of the curve is:

L = ∫[0,1] sqrt(2) dt = sqrt(2) * [t] [0,1] = sqrt(2)

Therefore, the length of the curve r(t) = sqrt(2)ti is sqrt(2).

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The geometric transformation shown in the line of music notation is a reflection. The Option B is correct.

In music notation, a line with notes on one side and rests on the other side is a reflection of the original line. This is because the line appears to be flipped horizontally with the notes and rests switching sides while maintaining the same distance from the line.

A glide reflection or translation would involve shifting the line horizontally or vertically without flipping it while the true reflection involves flipping the line across a mirror axis. Therefore, the transformation shown in the line of music notation is a reflection.

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Answer:

9:30am

Step-by-step explanation:

To find what time simply add all of the minutes together and subtract. All of the steps take 100 minutes to do. 11.10 am is 670 minutes. So 670 - 100 = 570 then divide by 60 to get the time ie 9:30 am

The value of the expression 1+1+1+1+11+1+1+1+11+1x0+1 is 30.

To evaluate the given expression, we follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

First, we perform the multiplication: 1x0 = 0. The expression now becomes 1+1+1+1+11+1+1+1+11+0+1.

Next, we perform the addition and subtraction operations from left to right: 1+1 = 2, 2+1 = 3, 3+1 = 4, 4+11 = 15, 15+1 = 16, 16+1 = 17, 17+1 = 18, 18+11 = 29, 29+0 = 29, and finally 29+1 = 30

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PLEASE GIVE BRAINLIEST <33

Answer:

The answer is 30

Step-by-step explanation:

First we'll start with PEMDAS

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

We'll start with multiplication: 1x0=0

Now the equation is: 1 + 1 + 1 + 1 + 11 + 1 + 1 + 1 + 11 + 1

Since we have two sets of 11, it would equal 22

Now the equation is: 22 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1

We have eight sets of 1. Adding them all together would equal 8.

Now the equation is: 22 + 8 which would equal 30

Answer:

Step-by-step explanation:

1) Number of white chocolate bars = x

Number of dark chocolate bars = y

Total bars = 15

x + y = 15 --------------(I)

Total cost = Php. 340

20x + 25y = 340 ----------------(II)

2)  We can use elimination method to solve this equations.

Multiply equation (I) by (-20) and then add the equations.

(I)* (-20)          -20x  -20y = - 300

(II)                    20x + 25y = 340     {Now add and x will be eliminated}

                                  5y = 40

                                    y = 40/5

y = 8

Substitute y = 8 in equation (I)

x + 8 = 15

      x = 15 - 8

x = 7

3) Number of dark chocolate bars = 8

Answer:

A. B. D. C.

Step-by-step explanation:

We are given v = ds/dt, v = 9.8t + 9, s(0) = 17. We need to find the position of a body moving along a coordinate line at time t.

Using the formula of velocity, we can integrate it with respect to t to find the position of the body at any time t. The formula for velocity is:v = ds/dt... (1) Integrating equation (1) with respect to t, we get's = ∫vdt + C ...(2)

Here, C is the constant of integration, and it is found using the given initial position. Given, s(0) = 17Substitute s = 17 and t = 0 in equation (2).17 = ∫(9.8t + 9)dt + C [∵ s(0) = 17]17 = 4.9t² + 9t + C

Therefore, C = 17 - 4.9t² - 9tOn substituting the value of C in equation (2), we get:s = ∫vdt + 17 - 4.9t² - 9t ...(3)Now, we can substitute the given velocity, v = 9.8t + 9, in equation (3).s = ∫(9.8t + 9)dt + 17 - 4.9t² - 9ts = 4.9t² + 9t + 17 - 4.9t² - 9ts = 9t + 17

Hence, the position of the body at time t is 9t + 17 units.

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4 is the value of w which makes the equation true.

What is an equation?

It is given that,

3(−4w−5)=−7(5+w)

by solving the equation,

-12w-15=-35-7w

12w-7w=35-15

5w=20

w=20/5

∴w=4

Hence, 4 is the value of w which makes the equation true.

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The correct probabilities are P(at least two tails) = 0. 5 and P(at least one heads) = 0. 875.

Let's calculate the probabilities based on the given sample space:

Total number of outcomes (sample space) = \(2^{3}\) = 8

P(one tails):

From the sample space, there are four outcomes that have exactly one tails: HTT, THT, TTH, TTT.

So, P(one tails) = 4/8 = 0.5

P(three heads):

From the sample space, there is only one outcome that has three heads: HHH.

So, P(three heads) = 1/8 = 0.125

P(one heads and two tails):

From the sample space, there are three outcomes that have one heads and two tails: HHT, HTH, THH.

So, P(one heads and two tails) = 3/8 = 0.375

P(at least two tails):

From the sample space, there are four outcomes that have at least two tails: TTH, THT, HTT, TTT.

So, P(at least two tails) = 4/8 = 0.5

P(at least one heads):

From the sample space, there are seven outcomes that have at least one heads: HHH, HHT, HTH, THH, THT, TTH, TTT.

So, P(at least one heads) = 7/8 = 0.875

Therefore, the correct probabilities are:

P(one tails) = 0.5

P(three heads) = 0.125

P(one heads and two tails) = 0.375

P(at least two tails) = 0.5

P(at least one heads) = 0.875

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A) Let the side length of the square base be x, and the height of the box be h. Then, the volume of the box is given by:

V = \(x^2\) * h = 8500

Solving for h, we get:

h = 8500 / \(x^2\)

The surface area of the box can be expressed as:

S = 2x^2 + 4xh

Substituting the value of h obtained above, we get:

S = \(2x^2\) + 4x(8500 / \(x^2\)) = 2\(x^2\)+ 34000 / x

Thus, the surface area of the box can be expressed as a function of x.

B) To graph the function, plot the surface area (S) on the y-axis and the side length of the square base (x) on the x-axis. Since x cannot be negative, the domain of the function is (0, infinity). As x gets very large or very small, the surface area approaches infinity, so we should only graph the function for values of x that make sense in the context of the problem.

C) The minimum amount of cardboard required to construct the box is equal to the surface area of the box. To find the minimum surface area, we need to find the minimum of the function S(x) obtained in part A.

D) To find the dimensions of the box that minimize the surface area, we need to find the value of x that minimizes the function S(x). We can do this by taking the derivative of S(x) with respect to x, setting it equal to zero, and solving for x. This gives us:

dS/dx = 4x - 34000/\(x^2\) = 0

Multiplying both sides by \(x^2\) and solving for x, we get:

x = (8500/2\()^(1/3)\) ≈ 18.3

Therefore, the dimensions of the box that minimize the surface area are a square base with side length of approximately 18.3 inches, and a height of:

h = 8500 / \(x^2\) ≈ 26.2 inches

E) UPS might be interested in designing a box that minimizes the surface area because it can reduce the amount of cardboard used in each box, resulting in cost savings and a reduced environmental impact. Additionally, minimizing the surface area of a box can make it more efficient to stack and transport, reducing shipping costs and making the overall process more sustainable.

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A) The Surface Area = \(X^2 + 34000/X\)

B) The y-axis and the side length X on the x-axis.

C) The minimum amount of cardboard required to construct the box is approximately 1649.39 square inches.

D) The dimensions of the box that minimize the surface area are X = 20.5 inches and Y = 16.87 inches.

E)  Smaller boxes take up less space in delivery trucks and planes, allowing more packages to be shipped at once and reducing transportation costs.

A) Express the surface area of the box as a function of X:

Let the side length of the square base be X and the height of the box be Y. Then, we know that the volume of the box is 8500 cubic inches, so:

\(X^{2Y} = 8500\)

To find the surface area of the box, we need to add up the area of each face. There are 5 faces in total (the bottom square and 4 identical rectangular sides), so:

Surface Area = \(X^2 + 4XY\)

We can substitute the value of Y from the equation for volume, giving:

Surface Area = \(X^2 + 4X(8500/X^2)\)

Surface Area = \(X^2 + 34000/X\)

B) Graph the function found in part a:

To graph this function, we can plot the surface area on the y-axis and the side length X on the x-axis. The graph will have a minimum value, which we can find using calculus or by using a graphing calculator.

C) What is the minimum amount of cardboard that can be used to construct the box:

The minimum amount of cardboard required to construct the box is the surface area of the box. To find this minimum value, we need to find the minimum point on the graph in part b. From the graph or by using calculus, we can see that the minimum occurs at X = sqrt(8500/5) = 20.5 inches. Substituting this value into the equation for surface area, we get:

Surface Area = \(20.5^2 + 4(20.5)(8500/20.5^2)\)= 1649.39 square inches

D) What are the dimensions of the box that minimize the surface area:

From part c, we know that the minimum occurs at X = sqrt(8500/5) = 20.5 inches. To find the height of the box, we can substitute this value of X into the equation for volume:

\(X^2Y = 8500\)

\((20.5)^2 Y = 8500\)

\(Y = 8500/(20.5)^2 = 16.87\) inches

E) Why might UPS be interested in designing a box that minimizes the surface area:

UPS and other parcel delivery services are always looking for ways to reduce their costs and increase efficiency. By designing a box that minimizes the surface area while still containing the same volume of goods, they can reduce the amount of cardboard used for each shipment. This would save them money on materials and shipping costs, while also reducing their environmental impact. Additionally, smaller boxes take up less space in delivery trucks and planes, allowing more packages to be shipped at once and reducing transportation costs.

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Inequality can be used to determine x, the greatest number of 120-kilogram crates that can be loaded onto the shipping container is  8000 + 120C <= 27500

An inequality is a relationship that allows us to contrast two or more mathematical expressions.

Knowing that;

Each carton weighs 120 kg.

The container's maximum weight when loaded is 27500 kg.

Weight of the container as it is currently loaded: 8000 kg

Now that we have merged, we have;

Solution

because 8000 grams have already been loaded kilograms

into the container

each crate weighs 120 kilograms.

so 8000 + 120C <= 27500

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Answer:

\(x\leq -2\)

Step-by-step explanation:

Solve for x:

\(-4x+20\geq 28\)

Subtract 20 on both sides

\(-4x\geq 8\)

Flip the sign and multiply both sides by -4

\(16x\leq -32\)

Divide by 16

\(x\leq -2\)

The probability that the student receives a grade above C is 0.75

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability that the student receives a grade above C be P ( C )

And , the equation will be

Let the probability you will get an A in this class is P ( A ) = 0.25

Let the probability you will get a B in this class is P ( B ) = 0.50

Now , the events P ( A ) and P ( B ) are mutually exclusive events

So , P ( A ∩ B ) = 0

And , P ( A ∪ B ) = P ( A ) + P ( B ) - P ( A ∩ B )

On simplifying the equation , we get

P ( A ∪ B ) = P ( C )

And , probability that the student receives a grade above C = P ( A ) + P ( B )

The probability that the student receives a grade above C = 0.25 + 0.50

The probability that the student receives a grade above C = 0.75

Hence , the probability is 0.75

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