if 1=2, 3=8, 9=16, 12=57 what is value of 25​

Answer:

Option A is your answer ☺️

Answer:

x = 5

Step-by-step explanation:

Laws of indices states that if the base is same the power can be added or subtracted. Since this is division, the powers are subtracted.

So, 2x - 3 = 7

or, 2x = 7 + 3

or, 2x = 10

or, x = 10/2

or, x = 5

Answer:

0.01  %

Step-by-step explanation:

The given model is;

y = a (0.5)^t/5730

Which is;

y = a(2^-1(t/5730)

Then;

y = a (2^-1/5730)^t

y = a(0.999879)^t

Hence;

Given that the general model is;

y(x)= a(1-r)^x

Where r is the rate percent

Since 1-r =0.999879

r = 0.00012096

y = a(1 - 0.00012096)^t

So;

r= 0.00012096* 100 = 0.01 %

Answer:

\(y=\dfrac{1}{4}x\)

Kelly is correct.

Step-by-step explanation:

One person is able to plant 4 trees

Let x be the number of people

y be the number of trees

The situation is represented by

\(1x=4y\\\Rightarrow y=\dfrac{1}{4}x\)

5 people are able to plant 20 trees

\(5x=5(4y)\\\Rightarrow 5x=20y\\\Rightarrow y=\dfrac{5x}{20}\\\Rightarrow y=\dfrac{1}{4}x\)

So, the situation is represented by \(y=\dfrac{1}{4}x\)

Hence, Kelly is correct.

Answer:

Kelly is correct.

Step-by-step explanation:

One person is able to plant 4 trees

Let x be the number of people

y be the number of trees

The situation is represented by

5 people are able to plant 20 trees

So, the situation is represented by

Hence, Kelly is correct.

To form a triangle, the set of line segments must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we need to check if the given line segments 8 cm, 4 cm, and 3 cm meet this requirement.

We can start by checking if the sum of the two smaller sides (3 cm and 4 cm) is greater than the largest side (8 cm). 3 cm + 4 cm = 7 cm, which is less than 8 cm. Therefore, these three line segments cannot form a triangle.

In general, for a set of line segments to form a triangle, the largest side must be smaller than the sum of the other two sides. In this case, the line segment of 8 cm is too long compared to the other two sides, which makes it impossible to form a triangle.

In conclusion, there are no line segments that meet the requirements to form a triangle with lengths of 8 cm, 4 cm, and 3 cm.

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The solution to the system of simultaneous equations is x = 1, y = -1, and z = -2.

To solve the system of simultaneous equations, we can use the matrix method, specifically the Gaussian elimination technique. Let's represent the given equations in matrix form:

[A] [X] = [B],

where [A] is the coefficient matrix, [X] is the variable matrix containing x, y, and z, and [B] is the constant matrix.

Rewriting the equations in matrix form, we have:

[1 2 -1] [x] [6]

[3 5 -1] [y] = [2]

[-2 -1 -2] [z] [4]

Applying Gaussian elimination, we can perform row operations to transform the matrix [A] into an upper triangular form. After performing the operations, we obtain:

[1 2 -1] [x] [6]

[0 -1 2] [y] = [16]

[0 0 1] [z] [2]

From the last row, we can directly determine the value of z as z = 2. Substituting this value back into the second row, we find -y + 2z = 16, which simplifies to -y + 4 = 16. Solving for y, we get y = -1.

Substituting the values of y and z into the first row, we have x + 2(-1) - 2 = 6, which simplifies to x - 4 = 6. Solving for x, we find x = 1.

Therefore, the solution to the system of simultaneous equations is x = 1, y = -1, and z = -2

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Answer:

x= 22

Step-by-step explanation:

11x - 4 = 238

11x = 242

x= 22

a) The rate of people leaving the health club, L(t), can be calculated as:

L(11) = 0.013(11)^2 - 0.25(11) + 8

b) To find the number of people, we integrate the net rate of change over the time interval:

Number of People at t=20 = Integral of (E(t) - L(t)) dt, from t=0 to t=20

c) This can be done by finding the critical points of the net rate of change and evaluating them to determine whether they correspond to maximum or minimum values.

To determine whether the number of people in the facility is increasing or decreasing at time t=11, we need to compare the rates of people entering and leaving the health club at that time.

a) At time t=11 hours:

The rate of people entering the health club, E(t), can be calculated as:

E(11) = -0.018(11)^2 + 11

Similarly, the rate of people leaving the health club, L(t), can be calculated as:

L(11) = 0.013(11)^2 - 0.25(11) + 8

By comparing the rates of people entering and leaving, we can determine if the number of people in the facility is increasing or decreasing. If E(t) is greater than L(t), the number of people is increasing; otherwise, it is decreasing.

b) To find the number of people in the health club at time t=20, we need to integrate the net rate of change of people over the time interval 0≤t≤20 hours.

The net rate of change of people can be calculated as:

Net Rate = E(t) - L(t)

To find the number of people, we integrate the net rate of change over the time interval:

Number of People at t=20 = Integral of (E(t) - L(t)) dt, from t=0 to t=20

c) To determine the time t at which the number of people in the health club is a maximum, we need to find the maximum value of the number of people over the interval 0≤t≤20.

This can be done by finding the critical points of the net rate of change and evaluating them to determine whether they correspond to maximum or minimum values.

Let's calculate these values and solve the problem.

Note: Since the calculations involve a series of mathematical steps, it would be best to perform them offline or using appropriate computational tools.

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The seat is 99 feet off the ground when it is at the top of the Ferris

wheel.

The height of a seat on a Ferris wheel can be modeled by the function H(t) = 47 sin((π/30)t + (3π/2)) + 52, where t is the time in seconds and H(t) is the height in feet.

To find how far off the ground the seat is when it is at the top of the Ferris wheel, we need to find the maximum value of the function. We know that the sine function has a maximum value of 1, which occurs when the input to the function is (π/2) + kπ, where k is an integer.

Since the input to our function is ((π/30)t + (3π/2)), we need to solve for t when this expression is equal to (π/2) + kπ.

((π/30)t + (3π/2)) = (π/2) + kπ

Multiplying both sides by 30, we get:

πt + 45π = 15π + 30kπ

Subtracting 15π from both sides and simplifying, we get:

t = 30k - 30

This means that the function H(t) will have a maximum value every 30 seconds. To find the maximum height, we can substitute t = 30k - 30 into the function:

H(30k - 30) = 47 sin((π/30)(30k - 30) + (3π/2)) + 52

Simplifying, we get:

H(30k - 30) = 47 sin(kπ - π/2) + 52

Since sin(kπ - π/2) =\((-1)^k\), we can write:

H(30k - 30) =\(52 - 47(-1)^k\)

When k is even, H(30k - 30) is at its maximum height of 99 feet (52 + 47).

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The range of the function f(x) = \(-2^{x}\) + 4 is -∞ < y < 4.

What is range of a function?

All potential values for y are included in a function's range. The equation to determine a function's range is Y = f. (x). If every x value has exactly one y value, then it is merely a function in a relation.

We are given a function which is defined as  f(x) = \(-2^{x}\) + 4.

We know that range is the output we get after substituting the value of x.

So, in this situation, we will get the value for y less than 4 or equal to 4 because when x = 0, we will get 4 and when x = 1, we will get 2 as there is a minus sign before 2 due to which this will be always a negative value.

Thus, the range of the function will be -∞ < y < 4.

Hence, the third option is the correct option.

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Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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Answer:

The inequality is x is less than negative 3.

Answer:

x < -3

Step-by-step explanation:

. subtract 1 from both sides.

. subtract the numbers

. divide both sides by the same factor and flip the relation

because the factor is negative

. cancel the terms that are both in the numerator and the denominator

. divide the numbers

.then you get youre solution

The average deviation of predicted DVD sales from the actual is 12.2279 million dollars. F-critical value is 4.0785>4.0785 we can reject the null hypothesis. The 95% confidence interval is (17.1536, 25.1554). The 95% prediction interval for the given value of x is (-3.8623, 46.1713).

Estimate the level of DVD sales for movies, by using the amount of annual revenue  generated by the box office gross

We randomly selected a sample of 43 movies for the same year.

Excel  α = 0.05,  r^2 = 0.5123

=51.23%

51.23% of the DVD sales variation is explained by annual revenue.

SY.X = 12.2279.

Therefore, the average deviation of predicted DVD sales from the actual is 12.2279 million dollars.

b. The hypothesis being tested is:

Null Hypothesis, H0: β1 = 0

Alternative Hypothesis, H1: β1 ≠ 0

The test statistic, F = (6439.6133/1)/((12570.025 - 6439.6133)/(42 - 1)) = 43.07

The F-critical value is 4.0785.

Since 43.07 > 4.0785, we can reject the null hypothesis.

Therefore, we can conclude that there is a linear relationship between the revenues of DVD sales and the box-office gross.

c. y = bo + b1*x

y = 4.8445 + 0.1631*x

Put x = 100

y = 4.8445 + 0.1631*100 = 21.1545

The 95% confidence interval for the given value of x is:

= y ± t*s*\(\sqrt{0.026249}\)

= 21.1545 ± 2.020*12.2279*\(\sqrt{0.026249}\)

= (17.1536, 25.1554)

d.  The 95% prediction interval for the given value of x is:

= y ± t×s×\(\sqrt{}\)1 + hin [The t-value is calculated using =TINV(0.05,42-1) in Excel]

= 21.1545 ± 2.020*12.2279*\(\sqrt{1 + 0.026249}\)

= (-3.8623, 46.1713)

Therefore, the value is (-3.8623, 46.1713).

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Answer:

4π ft.

Step-by-step explanation:

Area = π r^2 = 4π =  π2^2

- so the radius  is 2 ft,

and the circumfrence = 2 π r

= 2*π*2

= 4π  ft.

The circumference of the circle is 4π feet.

A circle is a two-dimensional figure with a radius and circumference of 2pir.

The area of a circle is πr².

We have,

The formula for the area A of a circle with radius r is given by:

A = πr²

We are given that the area of the circle is 4π ft², so we can set up the following equation:

4π = πr²

Dividing both sides by π, we get:

r² = 4

Taking the square root of both sides, we get:

r = 2

The circumference C of a circle with radius r is given by:

C = 2πr

Substituting r = 2, we get:

C = 2π(2) = 4π

Therefore,

The circumference of the circle is 4π feet.

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Answer:

25.4 degrees

Step-by-step explanation:

Use the inverse sine function to calculate

Answer:

20 Soda Bottles.

Step-by-step explanation:

I have done questions like this before.

Answer:

8

Step-by-step explanation:

19 - 3 = 16

16÷2 = 8

You bought 8 candy bars

Answer:

8

Step-by-step explanation:

You First have spent 3$ on a magazine then $2 for each candy bar in total u had 19$ spent so first u mulitply 8x2 which 16 now 16 + 3=19

The value of the Arrow-Debreu security is calculated as the present value of its expected payoff, discounted at the risk-neutral rate. As a result, the premium of the Arrow-Debreu security can be computed using the following formula: \($P_{t}=\frac{1}{(1+R)^{n-t}}\times \pi$,\)

where π=0.4, R=1.05, n=6, and t=2 (expiry node).

By substituting the values, we obtain:

\($P_{2}=\frac{1}{(1+1.05)^{6-2}}\times 0.4 = \frac{0.4}{(1.05)^4} \approx 0.3058$.\)

Therefore, the premium of the Arrow-Debreu security is approximately $0.3058.

Arrow-Debreu securities are typically utilized in financial modeling to simplify the pricing of complex securities. They are named after Kenneth Arrow and Gerard Debreu, who invented them in the 1950s. An Arrow-Debreu security pays $1 if a particular state of the world is realized and $0 otherwise.

They are generally utilized to price derivatives on numerous assets that can be broken down into a set of Arrow-Debreu securities. The value of an Arrow-Debreu security is calculated as the present value of its expected payoff, discounted at the risk-neutral rate. In other words, the expected value of the security is computed using the risk-neutral probability, which is used to discount the value back to the present value.

The formula is expressed as:

\($P_{t}=\frac{1}{(1+R)^{n-t}}\times \pi$\),

where P_t is the price of the Arrow-Debreu security at time t, π is the risk-neutral probability of the security’s payoff, R is the risk-free rate, and n is the total number of time periods.However, Arrow-Debreu securities are not traded in real life. They are used to determine the prices of complex securities, such as options, futures, and swaps, which are constructed from a set of Arrow-Debreu securities.

This process is known as constructing a complete financial market, which allows for a more straightforward pricing of complex securities.

The premium of the Arrow-Debreu security is calculated by multiplying the risk-neutral probability of the security’s payoff by the present value of its expected payoff, discounted at the risk-neutral rate.

The formula is expressed as

\($P_{t}=\frac{1}{(1+R)^{n-t}}\times \pi$,\)

where P_t is the price of the Arrow-Debreu security at time t, π is the risk-neutral probability of the security’s payoff, R is the risk-free rate, and n is the total number of time periods. Arrow-Debreu securities are not traded in real life but are used to price complex securities, such as options, futures, and swaps, by constructing a complete financial market.

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The 95% confidence interval for the amount of time spent on personal issues is (4.805, 4.95).

Mean time that employees spend on personal issues each week(M) = 4.9 hours

Standard deviation = 0.35 hours

The following formula is used to get the confidence interval for the sample mean and standard deviation given:

μ = M ± t(sM)

where; M = sample mean

t = T-statistic based on confidence interval

Degree of freedom = n - 1

From the question, n = 55

Degree of freedom = 55 - 1

Degree of freedom = 54

(Standard errors)sM = √(s^2/n)

Now putting the value

sM = √(0.352/55)

sM = 0.05

t = 2.005 This is determined using the Excel formula =T.INV.2T at a confidence level of 0.95 and a degree of freedom of 55-1=54. (0.05,54)

Now the confidence interval

μ = M ± t(sM)

μ = 4.9 ± 2.005 × 0.05

μ = 4.9 ± 0.095

μ = (4.9 - 0.095, 4.9 + 0.095)

μ = (4.805, 4.95)

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Answer:

Step-by-step explanation:

Arc length is:

Use the general formula

The solution to the system of inequalities is the region above the line y = -3x – 1 and the region above the line y = 3x – 2.

To solve the system of inequalities, we first graph the lines y = -3x – 1 and y = 3x – 2 on the coordinate plane. The line y = -3x – 1 has a negative slope and y-intercept at -1. It is a straight line that goes downward from left to right. The line y = 3x – 2 has a positive slope and y-intercept at -2. It is a straight line that goes upward from left to right.

The inequality y > -3x – 1 represents all the points above the line y = -3x – 1, and the inequality y > 3x – 2 represents all the points above the line y = 3x – 2. The solution to the system of inequalities is the region that satisfies both conditions, which is the region above both lines.
In summary, the solution to the system of inequalities is the region above the line y = -3x – 1 and the region above the line y = 3x – 2.

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Explanation:

To isolate the Y from y - 3 = 2/5 (x+4), you need to add 3 from both sides to move it to the right side of the equation:

y - 3 = 2/5 (x+4)

+3         +3

y = 2/5 (x+4) + 3

Answer:

add 3 to both sides

or move 3 across the equal sign, which will change its sign from - to +

= y = 2x + 8 / 5 +

The p-value can be found with the F-distribution table or statistical software. If the p-value is less than or equal to α, then answer is option (a),If the p-value is greater than α, then answer is option (b).

To determine the correct statistical decision based on the given F-statistic, F (3, 12) = 2.72, we need additional information such as the significance level (α) of the hypothesis test. The significance level is a predetermined threshold that is used to assess the statistical significance of the results.

The correct decision depends on whether the calculated p-value, which quantifies the strength of evidence against the null hypothesis, is less than or equal to the significance level (α).

To find the p-value, you would need the F-distribution table or statistical software.

Once you have the p-value, you can compare it to the significance level (α) to make a decision:

If the p-value is less than or equal to α, you would reject the null hypothesis, indicating a statistically significant mean difference.

If the p-value is greater than α, you would fail to reject the null hypothesis, suggesting that there is not a statistically significant mean difference.

Therefore, without the significance level or the p-value, it is not possible to determine the correct statistical decision.

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It will take 5 minutes to print a batch of newspapers if 20 printers are used.

What is proportionality?

Proportionality is a mathematical relationship between two variables, where one variable is a constant multiple of the other. In other words, two quantities are proportional if they maintain a constant ratio to each other, meaning that as one quantity increases or decreases, the other quantity changes in the same proportion.

We are given that the time it takes to print a batch of newspapers, m, is inversely proportional to the number of printers used, n, and the equation of proportionality is:

m = k/n

where k is a constant of proportionality. We are also given that when k = 100, the equation is satisfied. So we can substitute k = 100 into the equation to get:

m = 100/n

To find the time it will take to print a batch of newspapers if 20 printers are used, we can substitute n = 20 into the equation:

m = 100/20 = 5

So it will take 5 minutes to print a batch of newspapers if 20 printers are used. Rounded to 1 decimal place, the answer is 5.0 minutes.

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Answer:

4

Step-by-step explanation:

you divide with the 7 with 47.8

Sinus arrest resembles normal sinus rhythm except for one distinguishing characteristic, which is that there is an absence of P waves in the sinus arrest.

Sinus arrest is a condition where the normal functioning of the sinoatrial (SA) node is interrupted. This causes a delay or pause in the heart's electrical impulses, which prevents the heart from beating for a brief period.

The absence of P waves is caused by the interruption of the electrical activity in the sinoatrial node that generates the impulse for the atria to contract.

As a result, the atria and ventricles can stop beating for several seconds, leading to a temporary loss of consciousness, weakness, dizziness, or fainting. Sinus arrest is caused by several factors, including hypoxia, electrolyte imbalance, medication toxicity, vagal stimulation, and cardiac diseases such as heart block or ischemia.

Treatment for sinus arrest depends on the underlying cause, and it may involve lifestyle changes, medication, pacemaker insertion, or other medical interventions.

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yes. yes.

yes, yes,

yes, yes,

Answer:

3

Number 3 has a zero degree

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