The value of y varies directly with x. When y = 75,x= 2. What is the value of y when
xis 2 1/4

Answer:

1 3 and 5

Step-by-step explanation:

Hope this helps

Answer:

1  3

Step-by-step explanation:

The height of the 10th bounce of the ball is 0.6 feet.

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let y represent the height of the ball on the xth bounce.

From the question, a = 5.25 ft. and b = 80% = 0.8, hence:

y = 5.25(0.8)ˣ

For the 10th bounce:

y = 5.25(0.8)¹⁰ = 0.6 feet

The height of the 10th bounce of the ball is 0.6 feet.

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0.7

Step-by-step explanation:

I did the test

The first factor sin(x) equals zero at x = 0, π, and 2π.

The second factor sin(x) + 1 equals zero at sin(x) = -1. In the interval [0, 2π), the only solution is x = 3π/2.

Therefore, the solutions of the equation in the given interval are x = 0, π, 2π, and 3π/2.

1.) The equation 8sin^2(2x) = 4 can be rewritten as 4sin^2(2x) - 2 = 0. Applying the double-angle formula, we have 4(2sin(x)cos(x))^2 - 2 = 0, which simplifies to 16sin^2(x)cos^2(x) - 2 = 0. Dividing by 2 gives 8sin^2(x)cos^2(x) - 1 = 0. Using the identity sin^2(x) = 1 - cos^2(x), we get 8(1 - cos^2(x))cos^2(x) - 1 = 0. Expanding and rearranging, we have 8cos^4(x) - 8cos^2(x) + 1 = 0. This is a quadratic equation in terms of cos^2(x). Letting u = cos^2(x), the equation becomes 8u^2 - 8u + 1 = 0. Solving this quadratic equation, we find u = (8 ± √(8^2 - 4(8)(1)))/(2(8)) = 1/2 ± √(2)/2. Since u = cos^2(x), we have cos(x) = ±√(1/2 ± √(2)/2). Taking the inverse cosine, we find the possible values of x are x = π/4, 3π/4, 5π/4, and 7π/4.

2.) The equation tan^2(4x) = 3 can be rewritten as sin^2(4x)/cos^2(4x) = 3. Using the identity sin^2(x) = 1 - cos^2(x), we have (1 - cos^2(4x))/cos^2(4x) = 3. Multiplying through by cos^2(4x), we get 1 - cos^2(4x) = 3cos^2(4x). Rearranging, we have 4cos^2(4x) = 1. Dividing by 4, we obtain cos^2(4x) = 1/4. Taking the square root, we have cos(4x) = ±1/2. Taking the inverse cosine, we find the possible values of 4x are 2π/3, 4π/3, 8π/3, and 10π/3. Dividing by 4, we get x = π/6, π/3, 2π/3, and 5π/12.

3.) The equation sin(x)(sin(x) + 1) = 0 has two possible solutions: sin(x) = 0 and sin(x) + 1 = 0.

For sin(x) = 0, we have x = 0, π, and 2π.

For sin(x) + 1 = 0, we have sin(x) = -1. The only solution in the interval [0, 2π) is x = 3π/2.

Therefore, the solutions of the equation in the given interval are x = 0, π, 2π, and 3π/2.

1.) In the first equation, we start by using the double-angle formula for sine, which states that sin(2x) = 2sin(x)cos(x). By substituting this into the equation, we get 8sin^2(2x) = 8(2sin(x)cos(x))^2 = 16sin^2(x)cos^2(x).

Next, we apply the identity sin^2(x) = 1 - cos^2(x), which allows us to express the equation solely in terms of cos(x). After substituting this identity, we obtain 16(1 - cos^2(x))cos^2(x) - 2 = 8cos^4(x) - 8cos^2(x) + 1 = 0.

To simplify the equation further, we introduce a substitution u = cos^2(x), which transforms the equation into a quadratic equation in u. Solving this quadratic equation, we find the values of u as u = 1/2 ± √(2)/2.

Finally, we take the inverse cosine of u and solve for x, resulting in the solutions x = π/4, 3π/4, 5π/4, and 7π/4.

2.) In the second equation, we utilize the identity tan^2(x) = sin^2(x)/cos^2(x). By substituting this into the equation, we get sin^2(4x)/cos^2(4x) = 3.

Next, we rearrange the equation by multiplying through by cos^2(4x) to eliminate the denominator. This gives us (1 - cos^2(4x))/cos^2(4x) = 3.

Using the identity sin^2(x) = 1 - cos^2(x), we substitute the expression for sin^2(4x) and obtain 1 - cos^2(4x) = 3cos^2(4x).

Simplifying further, we have 4cos^2(4x) = 1, and dividing by 4 gives cos^2(4x) = 1/4.

Taking the square root of both sides, we get cos(4x) = ±1/2. Then, taking the inverse cosine of the possible values, we find the solutions for 4x as 2π/3, 4π/3, 8π/3, and 10π/3.

Finally, dividing these solutions by 4, we obtain x = π/6, π/3, 2π/3, and 5π/12.

3.) The third equation involves the product of two factors, sin(x) and (sin(x) + 1), equated to zero.

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Answer:

So the volume expands as kinetic energy is gained and the more mass there is the more kinetic energy there will be. Hopefully this helps you and if it doesn't I will add on to it, just lmk.

The predicted fuel efficiency for a speed of 30 miles per hour is given as follows:

26.50 mpg.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function for this problem is defined as follows:

In(Fuel Efficiency) = 1.437 + 0.541 In(Speed).

The speed is of 30 miles per hour, hence the predicted fuel efficiency is given as follows:

In(Fuel Efficiency) = 1.437 + 0.541 x In(30).

In(Fuel Efficiency) = 3.277.

The exponential is the inverse of the ln, hence:

Fuel Efficiency = e^3.277

Fuel Efficiency = 26.50 mpg.

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Answer:

y-1.7 = (-4/5)(x - 0)

Step-by-step explanation:

so m = -4/5 and a point is (0,1.7)

I prefer the slope intercept form of

y=(-4/5)x + 1.7

Answer:

Hopefully this explains o_O, also Merry Christmas!

Step-by-step explanation:

9 x 10^2 = 9 x 100 = 900

3 x 10^-2 = 3 x 1/100 = 0.03

Ratio of 900:0.03

The first one is 30000 bigger than the second

Answer:

  120 customers per hour

Step-by-step explanation:

You want to know the processing rate in customers per hour if there are an average of 6 customers waiting, and the average service time is 3 minutes.

Little's law relates the average queue depth to the response time and the average throughput:

  mean response time = mean number in system / mean throughput

Solving for the throughput, we find ...

  throughput = (number in the system)/(response time)

  throughput = (6 customers)/(3/60 hours) = 120 customers/hour

The average rate of processing is 120 customers per hour.

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Answer:

Step-by-step explanation:

\(y=-2x+8\\\\x=20\)

Substitute ; x =20 in given equation

\(y =-2(20 )+8\\\\y = -40+8\\\\y = -32\)

Thus, the age with the highest birth rate is 58.9, and the highest birth rate is 41.5 births per 1000 women.

Based on the given information, the birth rate in country x is modeled by a function that is dependent on age. In order to determine the age at which the highest birth rate occurs, we need to differentiate the function with respect to age and find its critical points.

d/dx (50sin(0.15x+5)+15) = 0

Using the chain rule, we get:

0.75cos(0.15x+5) = 0

cos(0.15x+5) = 0

Solving for x, we get:

0.15x+5 = (2n+1)π/2

where n is an integer.

x = (2n+1)π/0.3 - 33.33

Since the birth rate function is periodic, we only need to consider the critical points within one period, which is 20π/0.3 or approximately 209.44.

The critical points within this period are:

x = 26.4, 58.9, 91.4, 123.9, 156.4, 188.9

To determine which critical point corresponds to the highest birth rate, we need to plug in each value into the birth rate function and compare the results.

At x = 26.4, the birth rate is 40.4

At x = 58.9, the birth rate is 41.5

At x = 91.4, the birth rate is 41.4

At x = 123.9, the birth rate is 40.0

At x = 156.4, the birth rate is 36.9

At x = 188.9, the birth rate is 32.6

Therefore, the age with the highest birth rate is 58.9, and the highest birth rate is 41.5 births per 1000 women.

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The inverse of the conditional statement "If p then q" is, "p and not q".

What is conditional statement?

"If...then" is how a conditional statement is expressed. If we consider p and q to be the two statements, then p and q can be written under several conditions, such as;

If the "If" component (p) and the "then" part (q) of a conditional statement are both negated, this is known as a conditional statement in reverse. The conditional statement in geometry is known as p → q. Where stands for NOT or negating the statement, the inverse is written as  ~ p → ~  q.

In logic, "p and not q" is identical to the negation of "if p then q."

Therefore, the inverse of the conditional statement "If p then q" is,  

"p and not q".

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Step-by-step explanation:

it's the square equal to the equivalent equation to equal 5 673y

Answer: 55°

Step-by-step explanation:

The angle is in between 50° and 60°

Answer:

55°

Step-by-step explanation:

One ray lies on the 0° mark and the other lies on the 55° mark. To find the measure of the angle, find the difference between the greater angle and the lower angle. 55° - 0° = 55°

Answer:

45

Step-by-step explanation:

sum of angles of triangle is 180:

2k + k + 45 + 180   then 3k = 135

k = 45

Answer:

k = 45

Step-by-step explanation:

all triangles have 180 degrees, so

k = (180 - 45)/3

The total duration of the puberty process can be different for each girl who is about to enter it, as the length of time for the different stages of puberty can vary from person to person.  Hence, if a girl is about to enter puberty, the total process will take a variable length of time for different girls.

The total process of puberty for a girl can take a variable length of time, but typically it takes around 2 to 5 years to complete. The onset of puberty usually occurs between the ages of 8 and 13, with most girls starting around age 11.

The process of puberty includes physical changes such as breast development, the growth of pubic and underarm hair, and the onset of menstruation.

The duration of puberty can also depend on factors such as genetics, nutrition, and overall health. Some girls may experience a shorter or longer duration of puberty than others. However, in general, the process of puberty for a girl usually takes around 2 to 5 years to complete.

Therefore, the correct answer is "a variable length of time for different girls", but typically takes around 2 to 5 years to complete.

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Answer:

PLZ HELP

Step-by-step explanation:

Circle A is located at (6, 5) and has a radius of 4 units. What is the equation of a line that is tangent to circle A from point C (2, 8)?

x = 2

y = −0.75x + 9.5

y = 1.33x + 1.66

x = 8

Notice:

2 is first term

2*4 = 8 is second term

8*4 = 32 is third term

and so on

Each term is multiplied by 4 to get the next term, so it’s geometric. The “common ratio” is whatever you’re multiplying by, which is 4.

The maximum possible number of handshakes that can happen at the party with 23 people with at most 22 other people is 253. This is calculated by combination.

Twenty-three people attend a party. each person shakes hands with at most 22 other people.

To find the maximum possible number of handshakes, assuming that any two people can shake hands at most once, we need to use Combination by finding the number of unique pairs of people in the party.

nCr (combination) to find the number of unique pairs of people.

Therefore,\(^nC_r = \frac{n!}{(n-r)!  r!}\)

where n is the total number of people and r is the number of people in a handshake at a time.

Therefore, the number of unique pairs of people that can shake hands at most once is:

\(^{23}C_2 = \frac{23!}{(23-2)!  (2!)}\) \(=\frac{23 X22}{2} = 253\)

Hence, the maximum possible number of handshakes that can happen at the party is 253.

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Answer:

Step-by-step explanation:

-2(6-4k)-9k=-12+8k-9k=-12-k

False.

The mean of a binomial distribution can be calculated using the formula np, where n is the number of trials and p is the probability of success for each trial. However, knowing the mean is not a requirement to construct a binomial probability distribution.

The distribution can be constructed based solely on the number of trials and the probability of success. The binomial probability formula allows us to calculate the probability of obtaining a specific number of successes in the given trials.

The distribution provides a probability distribution function that describes the likelihood of various outcomes, regardless of whether the mean is known or not.

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36 and 144

Explanation

Two Angles are Supplementary when they add up to 180 degrees

Step 1

Let

x= angle 1

y= angle2

The measure of one angle is four times the measure of the other angle,then

x and y are supplementary angles , then

Step 2

use Equation (1) and (2) to find x and y

replace Equation (1) in Equation (2)

replace the value of y= 36 in equation (1) to find x

Hence, the answer is 36 and 144

The required weight after 43  hours is 72. 96mg

From the information given, we have that;

A Scientist begins with 180 milligrams of a radioactive substance

Let us take Po = 180 milligrams

Using the expression;

\(P(t) = Poe^k^t\)

Substituting the values of t = 33, P = 90mg and Po = 180

90 = 180e^33t

\(e^3^3^t = \frac{1}{2}\)

Take the log of both sides

\(33ln(e^k) = ln (\frac{1}{2} )\)

\(k = -\frac{ln 2}{33}\)

k = - 0. 0210

The equation becomes: P(t) = 150e^-0.0210

Substitute t as 43

\(P(43) = 180e^-^0^.^0^2^1^0 ^*^4^3\)

P(43) = 72. 96 mg

Hence,  72. 96 mg will remain after 43 hours.

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An equivalent function can be written as \(G(t) = 1920 \times 2^t\)

What is equivalent fraction?

Fractions that represent the same amount or portion of a whole, but have different denominators and numerators is called Equivalent fractions.

They are equal in value, but may have different forms.

We can multiply or divide both the numerator and the denominator of a fraction by the same number for find equivalent fractions.

Some examples are 2/4 is equivalent to 1/2 because if you divide both the numerator and the denominator of 2/4 by 2, you get 1/2.

Starting from the given function, we can simplify it as

\(G(t) = 960(2^t + 1) \\ G(t) = 960 \times 2^t \times 2^1 \\ G(t) = 1920 \times 2^t\)

We can see that this function is of the form

\(G(t) = ab^t\)

where a = 1920 and b = 2.

Therefore, an equivalent function can be written as \(G(t) = 1920 \times 2^t\)

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Answer:

(0,-4)

Step-by-step explanation:

Just took the quiz

Answer:

3 1/6

brainliest?

Answer:

The length of the rectangle is 7x + 27

Step-by-step explanation:

Given;

area of the rectangle, A = 21x + 81 units²

width of the rectangle, w = 3 units

let the length of the rectangle, = L

Area of the rectangle = length x width

A = L x w

21x + 81 = 3L

L = ¹/₃(21x + 81)

L = 7x + 27

Therefore, the length of the rectangle is 7x + 27