there are 40 students in ms. vitales wednesday night aerobics class of the 40 students 30% are african american 45% are caucasian and the rest are hispanic how many of the students in the aerobics class are hispanic

Answer:

Step-by-step explanation: X=1

The calculated measure of t from the given equation is 15 degrees

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

10

to

25°

When expressed properly, we have

10° + t° = 25°

Evaluate the like terms

So, we have

t° = 15°

Hence, the value of t° is 25°

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Answer:

Step-by-step explanation:

4:1 and 6:1

Answer:

To expand (x-y)³ using Pascal’s triangle, we can write:

    1

 1     1

1 2 1

1 3 3 1

Each row of the triangle represents the coefficients of the binomial expansion of (a+b)ⁿ, with the top row being n=0.

So for (x-y)³, we take the fourth row of the triangle (starting with n=0), and substitute x and y into the formula, alternating the signs of y:

1x³ + 3x²(-y) + 3x(-y)² + 1(-y)³

= x³ - 3x²y + 3xy² - y³

Thus, (x-y)³ = x³ - 3x²y + 3xy² - y³.

Answer:

36°

Step-by-step explanation:

angle a= 180-117

angle a=63°. because angles on straight line add to 180°

angle b= 180-81-63

angle b=36°. because angles in triangle add to 180°

The equation of the line is

To find the equation of the line passing through the points (2,2) and (-2,0), we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where

m is the slope of the line, and

(x1, y1) are the coordinates of one of the points on the line.

First, we need to find the slope of the line. The slope is given by:

m = (0 - 2) / (-2 - 2) = -1/2

substituting the points

y - 2 = (-1/2)(x - 2)

Expanding the right side and simplifying, we get:

y - 2 = (-1/2)x + 1

y = (-1/2)x + 3

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Step-by-step explanation:

Area of a kite = D1 × D2/2

D1 = 6.9 + 13.8 = 20.7m

D2 = 9.2 + 9.2 = 18.4m

Area =. 20.7 × 18.4

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

2

= 190.44m²

Answer: C

Step-by-step explanation:

your typical equation for varies inversely is y=k/x

here E = k/d² from the wording of problem.  plug in numbers to solve for k.

120=k/20²

k=48000

plug k back in to get generic E equation.  

E=48000/d²

Answer:  the ball reaches a maximum height of 76 ft, and it takes 2 seconds to reach the highest point.

Step-by-step explanation: The acceleration induced by gravity is estimated to be approximately -32 ft/s^2, with the negative value indicating its downward direction.

At the apogee of the ball's trajectory, its vertical velocity experiences a momentary cessation.

The duration required for the ball to attain its maximum height can be determined through employment of the equation t = Vf / a, in which Vf denotes the attained final velocity (which is zero in the present scenario) and a denotes the gravitational acceleration. Upon substitution of the given numerical values, the resulting value of t is determined to be equal to 2 seconds, achieved through the utilization of the equation t = 64 / 32.

The determination of the maximum height achieved by the ball can be achieved through utilization of the formula h = hi + Vit + 1/2at^2, with hi denoting the initial height (12 ft), Vi representing the initial velocity (64 ft/s), a signifying the acceleration due to gravity (-32 ft/s^2), and t representing the time it takes for the ball to reach the apex of its trajectory (2 seconds). Upon entering the provided numerical values into the formula, the resulting value for the height of the object can be determined as h = 12 + 64(2) + 1/2(-32)(2)^2, which equates to 76 feet.

The answer of the given question based on the quadrilateral is , the line segment corresponding to EH⎯ is AD⎯.

A line segment is a part of a line that consists of two endpoints and all the points between those endpoints that are collinear (lying on the same straight line). In other words, a line segment is a straight line that is bounded by two distinct points. A line segment is usually denoted by drawing a line over the two endpoints and labeling it with a single letter representing the segment name or by labeling the endpoints with capital letters and drawing a bar over them to indicate the segment between them.

A line segment has a finite length and can be measured using a ruler or a measuring tape. The length of line segment is distance between its two endpoints.

In the pre-image, the line segment corresponding to EH⎯ is AD⎯.

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In the given problem, the ramp weighs 10,125 pounds.

To calculate the weight of the ramp, first, determine its volume and then multiply it by the weight of concrete per cubic foot.

The ramp is shaped like a right triangle prism, with a triangular base and three rectangular faces. The ramp's measurements are as follows:1.5 feet in height15 feet is the length of the base (b).6 feet in length (l).

The area of the triangular base can be determined using the triangle area formula: A = 0.5 * b * h A = 0.5 * 15 * 1.5A = 11.25 ft^2

The volume of the ramp can be estimated by multiplying the base area by the ramp length: V = A * l V = 11.25 feet 2 feet 6 feet

V = 67.5 ft^3

Finally, the weight of the ramp can be calculated by multiplying the volume by the weight of concrete per cubic foot:W = V * 150 lbs/ft3 W = 67.5 feet * 150 lbs/ft3 W = 10,125 pounds

As a result, the ramp weighs 10,125 pounds.

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The correct options are- B. x = –4 – √2 and D. x = –4 + √2 are the roots of the given quadratic equation.

When a square is complete, a quadratic is written in the shape of a squared bracket, and if necessary, a constant is added. Finding the function's highest or minimum value and the time it happens is one use for the square-root method.

Given quadratic equation:

x² – 8x + 16 = 2

This can be written as:

x² – 2*4x + 4² = 2

(x + 4)² = 2

Taking square root both sides:

√(x + 4)² = √2

(x + 4) = ±√2

x = ±√2  - 4

Or x = -4 + √2 and x = -4 - √2

Thus, the roots of the quadratic equation found by using the method of completing the square are - x = -4 + √2 and x = -4 - √2

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Complete question:

Use completing the square to solve this quadratic equation. Check all that apply. x² – 8x + 16 = 2

A. x = 4 –√2

B. x = –4 – √2

C. x = 4 + √2

D. x = –4 + √2

Therefore, the magnitude of the acceleration is instantaneously zero at t = 5/3 and t = 1. Therefore, the displacement of P from the origin when t = 2 is -8/3 meters.

A function is a mathematical concept that describes a relationship between two sets of values, called the domain and the range. It is a rule or a set of rules that assigns a unique output value for every input value in the domain. In other words, it is a process that takes one or more inputs and produces a corresponding output. Functions are commonly represented using equations, graphs, or tables. They are used in various branches of mathematics, science, engineering, and technology to model real-world phenomena, make predictions, and solve problems.

Here,

(a) To find the acceleration, we need to take the derivative of the velocity function with respect to time:

a = dv/dt

= d/dt (t³ - 4t² + 5t + 1)

= 3t² - 8t + 5

(b) To find the values of t for which the magnitude of the acceleration is instantaneously zero, we need to solve the equation:

|a| = |3t² - 8t + 5|

= 0

This occurs when 3t² - 8t + 5 = 0, which factors as (3t - 5)(t - 1) = 0. Therefore, the magnitude of the acceleration is instantaneously zero at t = 5/3 and t = 1.

(c) To find the displacement of P from the origin when t = 2, we need to integrate the velocity function from t = 0 to t = 2:

s = ∫(v dt)

= ∫(t³ - 4t² + 5t + 1 dt)

= (1/4)t⁴ - (4/3)t³ + (5/2)t² + t + C

We know that s(0) = 3, so we can solve for C:

3 = (1/4)(0)⁴ - (4/3)(0)³ + (5/2)(0)² + 0 + C

C = 3

Therefore, the displacement of P from the origin when t = 2 is:

s(2) = (1/4)(2)⁴ - (4/3)(2)³ + (5/2)(2)² + 2 + 3

= -8/3 meters

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Therefore, the freight train traveled for 16.67 + 10 = 26.67 hours before the passenger train caught up with it.

let's call the time it took for the passenger train to catch up with the freight train "t" (in hours).

During this time, the freight train traveled at its average speed of 45 km/h for t + 10 hours, while the passenger train traveled at its average speed of 72 km/h for t hours.

We know that the distance both trains traveled is the same, since the passenger train caught up with the freight train. So, we can set up the following equation:

distance traveled by freight train = distance traveled by passenger train

[tex](45 km/h) x (t + 10 h) = (72 km/h) x t[/tex]

Simplifying this equation, we get:

[tex]45t + 450 = 72t[/tex]

[tex]27t = 450[/tex]

t = 16.67 hours

Therefore, the freight train traveled for 16.67 + 10 = 26.67 hours before the passenger train caught up with it.

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Answer:

-23

Step-by-step explanation:

15(-3)/9 + 4(-3)-6

-45/9 + (-12)-6

-5 + (-18)

-23

(missed the -6 sorry)

Answer:

-23

Step-by-step explanation:

15(-3)/9 +4(-3) -6 = -5 -12 -6 = -23

The base of the triangle is 3/2 feet or 1 1/2 feet

Triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

The area of triangle is expressed as ;

A = 1/2 bh

The area of the of the triangle is 2/15 and the height is 2/5.

2/15 = 1/2 b × 2/5

2/15 = 2b/10

20 = 30b

divide both sides by 30

b = 30/20

b = 3/2

there the base of the triangle is 3/2.

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As a result, 1.554 g of sugar are included in the low-sugar yoghurt as if the low-sugar yoghurt has 26% less sugar.

A proportion is put up using a single unit when using a unitary method. For instance, the price of 1 apple is $2/3 if 3 bananas cost $2. The cost among one unit of something like the quantity "apples" is represented by this value of $2/3. In a similar vein, if a car can drive 300 km on 20 litres of gas, how far can it go on one litre of gas? The answer is 15 km (300/20). Finance, science, and engineering are just a few of the fields where the unitary technique can be applied to solve issues.

given

Regular yoghurt contains: If only 7% of the daily required amount of sugar is present in it:

7% of 30 g = [tex](7/100) * 30 g = 2.1 g[/tex]

This indicates that 2.1 g of sugar are present in ordinary yoghurt.

Hence, if the low-sugar yoghurt has 26% less sugar than the standard yoghurt, it contains:

[tex]1.554 g = 2.1 g - (26/100) x 2.1 g = 2.1 g - 0.546 g[/tex]

As a result, 1.554 g of sugar are included in the low-sugar yoghurt as if the low-sugar yoghurt has 26% less sugar.

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Hence, the quotient is [tex]2x^2[/tex] in its simplest form as the numerator by the denominator to simplify the quotient.

In addition, ratios can be used to compare components of an ensemble, such as the ration of a circle's surface area to its circumference. As it is a linear correlation that cannot be reduced, the ratio in this instance is not simplified. In mathematics, science, economics, and many other disciplines, ratios are frequently employed to explain and study the quantitative relationships between various values.

given

The ratio is:

[tex]4x^5 / (2x^3)[/tex]

We can divide the numerator by the denominator to simplify the quotient.

By dividing 4x5 by 2x3, we obtain:

[tex](4x^5) / (2x^3) = 2x^(5-3) = 2x^2[/tex]

Hence, the quotient is [tex]2x^2[/tex] in its simplest form as the numerator by the denominator to simplify the quotient.

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Answer:

p = 1 or p = 7

So first number line is the answer we are looking for.

Step-by-step explanation:

|8-2p| = 6

To do that, we need to get rid of the brakes and rewrite equation in two forms:

8 - 2p = 6

or

8 - 2p = -6

For the first state:

8 - 2p = 6

- 2p = -2

2p = 2

p = 1

Now, the second state:

8 - 2p = -6

- 2p = -14

2p = 14

p= 7

Answer:

10/3

Step-by-step explanation:

u = 2

v = 5

7 + 3(v - 2u)

= 7 + 3(5 - 2*2)

= 7 + 3(5 - 4)

= 7 + 3(1)

= 7 + 3

= 10

u + 1

= 2 + 1

= 3

7 + 3(v - 2u)/u + 1

= 10/3

The volume of the modelled Saturn is 2176.40 cm³.

Eliza made sphere-shaped models of the Earth and Saturn out of playdough for a science project. The model of Earth has a diameter of 4.8 cm and the model of Saturn has a diameter of 45.6 cm.

Therefore, the volume of the spherical Saturn can be found as follows:

volume of the Saturn = 4 / 3 πr³

where

r = radius

Therefore,

r = 45.6 / 2 = 22.8 cm

volume of the Saturn = 4 / 3 × 3.14 × 22.8²

volume of the Saturn = 4 / 3 × 3.14 × 519.84

volume of the Saturn = 6529.1904 / 3

volume of the Saturn = 2176.3968

volume of the Saturn = 2176.40 cm³

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Answer:

addition and subtraction

The choice of auto insurance plan depends on the value of the vehicle and financial situation. Plan 2 with higher coverage and deductibles is better for expensive vehicles and those with higher financial stability.

Insurance is a contract between an individual or an entity and an insurance company. The individual or entity pays a premium, and in return, the insurance company agrees to pay for losses or damages that occur, as per the terms of the policy.

Financial stability refers to a situation where an individual, household, company, or economy can manage their financial resources and obligations in a sustainable manner, without facing significant risks or uncertainty.

According to the given information:

Based on my vehicle's value and my financial situation, I have decided to choose Plan 1.

Bodily injury liability coverage provides protection if I were to injure someone while driving, and the amount of coverage in Plan 1 ($25,000 per person up to $50,000 per accident) is adequate for my needs. Property damage liability coverage provides protection for any damage I might cause to someone else's property while driving, and the $25,000 coverage in Plan 1 is also sufficient.

Collision insurance provides coverage for any damage to my own vehicle in the event of an accident, regardless of who is at fault. The $100 deductible in Plan 1 means that I would have to pay the first $100 of any repair costs, but the lower annual premium makes this plan more affordable for me.

Comprehensive insurance provides coverage for non-collision events, such as theft, fire, and natural disasters. Again, the lower annual premium of Plan 1 with a $50 deductible makes it more cost-effective for me.

Uninsured/underinsured motorist coverage is not included in either plan, so I would need to decide if I want to add this coverage as an additional policy or not.

Overall, based on the value of my vehicle and my financial situation, Plan 1 provides adequate coverage at a more affordable price. However, it is important to note that everyone's situation is unique and insurance needs may vary. It is always a good idea to shop around and compare different policies before making a final decision.

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a) The only outcome that satisfies both events X and Y is the letter C.

b) The outcomes that satisfy either event X or event Y are {A, B, C, E, G}.

c) The complement of event X is {D, E, F, G}.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

The outcomes for each of the following events are:

(a) Event "X and Y": {C}

To satisfy both events X and Y, the letter selected must come before "D" (which includes the letters A, B, and C) and must be one of the letters in the word "CAGE" (which includes only the letter C). Therefore, the only outcome that satisfies both events X and Y is the letter C.

(b) Event "X or Y": {A, B, C, E, G}

The outcomes that satisfy event X are A, B, and C (since they come before "D"), and the outcomes that satisfy event Y are C, A, G, and E (since they are letters found in the word "CAGE"). Therefore, the outcomes that satisfy either event X or event Y are {A, B, C, E, G}.

(c) The complement of event X: {D, E, F, G}

The complement of event X is the set of outcomes that do not satisfy event X. The outcomes that do not satisfy event X are D, E, F, and G (since they come after or are equal to "D"). Therefore, the complement of event X is {D, E, F, G}.

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The standard deviation of the random variable X is 2.73861279.

Standard deviations is a measure of the spread of a data set around the mean. It is calculated by taking the square root of the variance of the data set and is used to measure the variability of a data set from the mean. Standard deviations are used to measure the probability of a certain outcome occurring and can be used to compare different data sets to see how much variability there is in the data.

Standard deviation is a measure of dispersion of data points around the mean of the data set. It is a measure of the variability of the data set. It is calculated by taking the square root of the variance of the data set.

Variance is the average of the squared differences of each data point from the mean. It is calculated by taking the sum of the squares of the differences of each data point from the mean and dividing by the number of data points minus one.

In this case, the mean of the data set is 3, because the probabilities of -2 and 5 are equal.

The variance of the data set is calculated as follows:

Variance = (0.3*(3-(-2))2 + 0.2*(3-3)2 + 0.5*(3-5)2) / (3-1)

Variance = (0.3*25 + 0 + 0.5*4) / 2

Variance = 7.5

The standard deviation of the data set is calculated by taking the square root of the variance, which is equal to 2.73861279.

Therefore, the standard deviation of the random variable X is 2.73861279.

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Note that the value of C that satisfies the mean value theorem is -11/6

The mean value theorem in mathematics says that for each given planar arc between two end points, there exists at least 1   point where the tangent to the arc   is parallel to the secant between its ends. It is one of the most significant findings in real -  world analysis.

To apply the mean value theorem, we need to check 2 conditions

f(x) is continuous on [-3, -1]

f(x) is differentiable on (-3, -1)

f(x) = (x^2-1/3x) satisfies both conditions.

Now, let's find the value of c that satisfies the mean value theorem:

f(-1) - f(-3) = f'(c)(-1 - (-3))

(2/3) - (-26/3) = f'(c)(2)

f'(c) = -4

To find the value of c, we need to solve for c in f'(c) = -4 ...  

f '(x) = d/d x(x²  -1/3x)

= 2x - 1/3

2c - 1/3 = -4

2c = -4 + 1/3

c = -11/6

So we can state that  the value of c that satisfies the mean value theorem is -11/6

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.

A’(-12,18), B’(-6,6), C’(12,-6), D’(12,12)

Answer:

Hey

So my brother posted this on Yahoo

Draw a line from the center of the circle to one of the ends of the chord (water surface) and another to the point at greatest depth. A right-angled triangle is formed. Length of side to the water-surface is 5 cm, the hypot is 7 cm.

What you do now is the following:

Calculate the angle θ in the corner of the right-angled triangle by: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7)

So θ is approx 44.4°, so the angle subtended at the center of the circle by the water surface is roughly 88.8°

The area shaded will then be the area of the sector minus the area of the triangle above the water in your diagram.

Shaded area ≃ 88.8/360*area of circle - ½*7*7*sin88.8°

= 88.8/360*π*7² - 24.5*sin 88.8°

≃ 13.5 cm²

(using area of ∆ = ½.a.b.sin C for the triangle)

b)

volume of water = cross-sectional area * length

≃ 13.5 * 30 cm³

≃ 404 cm³

Hoped it Helped

Step-by-step explanation:

Hey

So my brother posted this on Yahoo

Draw a line from the center of the circle to one of the ends of the chord (water surface) and another to the point at greatest depth. A right-angled triangle is formed. Length of side to the water-surface is 5 cm, the hypot is 7 cm.

What you do now is the following:

Calculate the angle θ in the corner of the right-angled triangle by: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7)

So θ is approx 44.4°, so the angle subtended at the center of the circle by the water surface is roughly 88.8°

The area shaded will then be the area of the sector minus the area of the triangle above the water in your diagram.

Shaded area ≃ 88.8/360*area of circle - ½*7*7*sin88.8°

= 88.8/360*π*7² - 24.5*sin 88.8°

≃ 13.5 cm²

(using area of ∆ = ½.a.b.sin C for the triangle)

b)

volume of water = cross-sectional area * length

≃ 13.5 * 30 cm³

≃ 404 cm³

Hoped it Helped