ACTIVITY 1: Complete the table below by computing the unknown component of simple interest.

The probability that a student is a graduate student given they are a history major is approximately 0.16.

The likelihood or chance that an event will occur is quantified by probability. A number between 0 and 1, where 0 denotes that the occurrence is impossible and 1, denotes that the event is certain, is generally used to express it.

We are given the following information:

Total number of students who are history major: 463

Total number of graduate students: 261

Number of graduate students who are history major: 73

We can use the formula for conditional probability to find the probability that a student is a graduate student given that they are a history major:

P(graduate | history) = P(graduate and history)/P(history)

P(graduate | history) = 73/463

P(graduate | history) ≈ 0.1575 (rounded to the nearest hundredth)

Therefore, the probability that a student is a graduate student given they are a history major is approximately 0.16.

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Answer: C

Step-by-step explanation:

We need to turn 50% into a fraction first to make it easier,

50% is equal to 1/2 because 50/100 is simplified to 1/2.

Now let's multiply!

24 x 1/2 = 24/2 = 12/1 = 12

The number of cups of frozen strawberries that are needed to make 3 gallons of punch is equal to 48 cups.

In this exercise, you're required to determine the number of cups of frozen strawberries that are needed to make 3 gallons of punch.

Thus, we would apply direct proportion.

Note: There are 16 cups of frozen strawberries in a gallon.

By direct proportion:

16 cups = 1 gallon

X cups = 3 gallons

Cross-multiplying, we have:

X = 16 × 3

X = 48 cups of frozen strawberries.

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Answer:

how many points will you give?

Step-by-step explanation:

Answer:

Step-by-step explanation:

I'm sorry, but there isn't enough information to solve for the missing side of a triangle with just the perimeter given as 8x-6. We would need at least one more piece of information, such as the lengths of the other sides or angles of the triangle.

Answer:

Step-by-step explanation:

To calculate the monthly payment on a loan, you can use the formula for the monthly payment on an annuity: P = (r * PV) / (1 - (1 + r)^(-n)), where P is the monthly payment, r is the monthly interest rate, PV is the present value of the loan (i.e., the amount borrowed), and n is the total number of monthly payments.

In this case, the amount borrowed is $56,937 and the interest rate is 6.3% per year. To convert this to a monthly interest rate, we divide by 12: r = 0.063 / 12 = 0.00525. The loan term is 5 years, so the total number of monthly payments is n = 5 * 12 = 60.

Substituting these values into our formula for the monthly payment, we get: P = (0.00525 * 56937) / (1 - (1 + 0.00525)^(-60)) ≈ $1102.53. So, the monthly payment on this loan would be approximately $1102.53.

The average speed of the ferry is 54.54 miles per hour.

The expression for the average speed is given [tex]\frac{2d}{\frac{d}{50}+\frac{d}{60} }[/tex].

Now, the given expression can be solved as follows

2d÷ (6d/300 + 5d/300)

= 2d÷(11d/300)

= 2d×300/11d

= 600/11

= 54.54 miles per hour

Therefore, the average speed of the ferry is 54.54 miles per hour.

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The resulting arrow should end at -6 1/2. This is because -4 - 2 1/2 is equal to -6 1/2.

In mathematics, an expression is a combination of numbers, variables, and operators that can be evaluated to produce a value. Expressions can be simple or complex and are used to represent mathematical relationships and operations.

To find -4 - 2 1/2 expression on the number line by drawing an arrow, we need to start at -4 and then move left by 2 1/2 units.

To do this, we can draw an arrow starting at -4 and then mark off 2 1/2 units to the left. One way to represent 2 1/2 units is to divide the space between -4 and -5 into two equal parts, and then mark off one of those parts.

The resulting arrow should end at -6 1/2. This is because -4 - 2 1/2 is equal to -6 1/2.

Here's an example of what the arrow would look like:

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The surface area of the triangular pyramid is 147.6 cm².

The surface area of a three-dimensional object is the total area of all its faces.

To calculate the surface area of the triangular pyramid, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Answer:

2(1/2)(11)(7) + 11(14) + 14(8) + 14(9) = 469 in.^2

The correct answer is A.

Answer:

The answer is going to 5

Step-by-step explanation:

I hope this helps you

Θ(x) = tan⁻¹(5x / (4(x - 13))), and Θ is maximized when the distance the cow must stand from the billboard x₀ = 26.

To find Θ, use similar triangles. Let the distance from the cow to the top of the billboard be h. Then, using similar triangles:

h / x = 5 / (x - 13)

Solving for h:

h = 5x / (x - 13)

The vertical angle subtended by the billboard at the cow's eye is equal to the angle whose tangent is given by:

tan(Θ) = h / 4

Substituting for h:

tan(Θ) = 5x / (4(x - 13))

To maximize Θ, find the value of x that maximizes tan(Θ). Taking the derivative of tan(Θ) with respect to x and setting it equal to zero:

d/dx (tan(Θ)) = 5(52 - 26x) / (4(x - 13))² = 0

Solving for x:

x₀ = 26

Substituting x₀ into the expression for Θ:

Θ(x₀) = tan⁻¹(5(26) / 4(13)) = tan⁻¹(5/2)

Therefore, Θ(x) = tan⁻¹(5x / (4(x - 13))), and Θ is maximized when x₀ = 26.

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Answer:

Elin concluded that car B travels a distance of 265.8 km during the same time based on her interpretation of the given information.

Step-by-step explanation:

My apologies for the confusion. Let's analyze how Elin arrived at her answer.

According to the given information, car A travels 221.5 km at a given time. Elin interpreted the statement "car B travels 1.2 times the distance car A travels at the same time" to mean that the distance traveled by car B is 1.2 times the distance traveled by car A.

To calculate the distance traveled by car B, Elin multiplied the distance of car A (221.5 km) by 1.2:

Distance of Car B = 1.2 * Distance of Car A

Distance of Car B = 1.2 * 221.5 km

Distance of Car B = 265.8 km

Therefore, Elin concluded that car B travels a distance of 265.8 km during the same time based on her interpretation of the given information.

Answer:

cos 2x

f(x)=4•sin(x)•cos(x)

Step-by-step explanation:

Applying the intersecting secants and chords theorem, the indicated measures in the circle is: HW = 35 units;   MN = 49.5 units.

To find the measures indicated, we will apply the intersecting secants and chords theorem to form an equation, then solve.

a. HZ * HW = HX * HY [based on the intersecting secants theorem]

Plug in the values:

16.8 * HW = 14 * 42

HW = 588/16.8

HW = 35 units

b. VK * VJ = VM * VN [based on the intersecting chords theorem]

Plug in the values:

27 * 18 = 36 * VN

VN = 486/36

VN = 13.5 units

MN = VM + VN = 36 + 13.5

MN = 49.5 units

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Answer:

last choice:  2b²/a³

Step-by-step explanation:

2a⁻³/b⁻² = 2·(1/a³) / (1/b²) = 2·(1/a³)(b²) = 2b²/a³

The value of f(2020) is 39/100.

Given function is,

f(25) = 80

And f(xy) = f(x)/y²   .....(i)

Since

f(25) = 80

Then we define function as

f(x) = x + 55   .....(ii)

Now we can write 2020 = 101 x 20

So f(2020) = f(101x20) = f(101)/20²                from (i)

                                    =  (101 + 55)/400       from(ii)

                                    = 156/400

                                    = 39/100

Hence, f(2020) = 39/100

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The terminal point of 13π/6 is (-√3/2, 1/2) by using unit circle.

The quadrants of a graph are the four sections that divide the coordinate plane. The quadrants are numbered in a counterclockwise direction starting from the positive x-axis.

1. Quadrant I is located in the upper-right section and contains points with positive x and y-coordinates.

2. Quadrant II is located in the upper-left section and contains points with negative x-coordinates and positive y-coordinates.

3. Quadrant III is located in the lower-left section and contains points with negative x and y-coordinates.

4. Quadrant IV is located in the lower-right section and contains points with positive x-coordinates and negative y-coordinates.

The quadrants are useful for determining the signs of coordinates, angles, and for plotting points on a graph.

To find the terminal point of 13π/6, we can start by recognizing that this angle is greater than 2π, which is one complete revolution around the unit circle.

To bring the angle back within one revolution, we can subtract 2π, which gives us 13π/6 - 2π/1 = 13π/6 - 12π/6 = 1π/6.

The angle 1π/6 is in the standard position between the positive x-axis and the first quadrant. The reference angle is π/6, which is the angle between the terminal side and the x-axis.

Since the angle is in the 2nd quadrant, the x-coordinate will be negative and the y-coordinate will be positive. Using the unit circle, we can find the values of sine and cosine at π/6 and then negate the value of cosine since the angle is in the second quadrant.

cos(π/6) = √3/2

sin(π/6) = 1/2

Therefore, the terminal point of 13π/6 is (-√3/2, 1/2).

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Answer:

To write 1/4 (x - 12) in words, you would say "one-fourth of the quantity obtained by subtracting 12 from x."

Answer:

period :  π ; amplitude : 2

Step-by-step explanation:

Correct me if I'm wrong!!

Answer:

The y-intercept of the graph of the equation is -9. This means that the graph crosses the y-axis at the point (0, -9).

Step-by-step explanation:

To solve this question, we need to plug in x = 0 into the given equation and simplify. We get:

y = 6(0 - 1/2)(0 + 3) y = 6(-1/2)(3) y = -9

Therefore, the y-intercept of the graph of the equation is -9. This means that the graph crosses the y-axis at the point (0, -9).

Answer: 27.33

Step-by-step explanation: If you use a calculator to do the hard stuff the rest is a breeze

1. The probability that P(X > 979) = 0.567

2. The probability that P(M > 979) = 0.956

To calculate the probability that  a single randomly selected value is more than 979 dollars.

 979-1016

= -37/209

= -0.177

P(X > -0.177) = 0.5675

Therefore P(X > 979) = 0.568

To calculate that a sample of size is randomly selected with a mean that is more than 979 dollars.

209 / √94 = 21.557

-37/ 21.557 = -1.7164

P(Z > -1.714) = 0.9564

therefore P(M > 979) = 0.956

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Answer:

let the children be x

let the dog be y

for the heads

x+y = 14 --- eqn 1

for the legs

2x + 4y = 40 ----- eqn2

since the children have 2 legs each and the dogs have 4 legs each

x + y = 14

2x+4y=40

through elimination method

multiply eqn1 by 2 and multiply eqn2 by 1

2x + 2y = 28

2x + 4y = 40 , then subtract

-2y = -12

to get y divide both sides by -2

y = 6

since in eqn 1

x+y=14

x = 14-y = 14-6 = 8

x = 8, y = 6

the children are 8 while the dogs are 6

Answer:

Step-by-step explanation:

so the entire angle sum is 180 degrees then subtract 61 from 180 and divide by 2. hope it helps :)

The general formula for f'(x) would be f' (x) = - 8 sin (x) + C.

The most general formula based on the first would be f(x) = 8 cos ( x ) + Cx + D.

To find the most general formula for f ' ( x ), we need to integrate f'' ( x ) with respect to x:

f'' ( x ) = - 8 cos (x)

f' (x) = ∫ ( -8cos(x)) dx

f ' (x) = - 8 sin(x) + C, where C is an arbitrary constant.

We need to integrate f'( x ) with respect to x to find the most general formula for f ( x ):

f'(x) = - 8 sin(x) + C

f(x) = ∫ ( - 8sin ( x ) + C) dx

f(x) = 8 cos ( x ) + Cx + D, where D is another arbitrary constant.

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Answer:

123 feet/41 yards

Step-by-step explanation:

When solving problems like this, we need to understand and note down what we already know to make our lives easier.

- He walks 13 different dogs

- the park is a perfect square

- he takes each dog for one full lap

- That day, he walked 6396ft

- He takes each dog the same distance

Now, let's find the unit value (how much ft does he walk if he takes JUST ONE dog around Greenpoint Park?)

Just divide: 6396 / 13 = 492 ft

Meaning, that when Harrold takes JUST ONE dog around the park, which is a perfect square, he walks 492 feet.

One full lap around the square shaped park is just 4 sides of the square.

So, he walks 492 ft every 4 sides.

However, the question specifically asked for one side.

Just divide again to get your answer:

492 / 4 = 123 ft

Therfore, the length of one side of the park is 123 feet, which is 41 yards.