how to write the justification for a function if its exponential

The height to which the hollow sphere rolls up the incline is the same as the height to which the hollow cylinder rolls up, which is 1.0 m in this case.

To determine the height to which the hollow sphere rolls up the incline, we can use the principle of conservation of energy. The initial kinetic energy of both the hollow cylinder and hollow sphere is the same since they have the same mass and initial velocity. This kinetic energy is converted into potential energy as they roll up the incline. The potential energy gained by an object of mass m and height h is given by the formula:

PE = mgh

Since both the hollow cylinder and hollow sphere have the same mass, we can compare their potential energies. Let's assume the potential energy gained by the hollow cylinder is PE_cylinder and the potential energy gained by the hollow sphere is PE_sphere.

PE_cylinder = mgh_cylinder  ... (1)

PE_sphere = mgh_sphere  ... (2)

Since the initial velocity and mass are the same for both objects, we can equate their potential energies:

PE_cylinder = PE_sphere

mgh_cylinder = mgh_sphere

h_cylinder = h_sphere

Therefore, the height to which the hollow sphere rolls up the incline is the same as the height to which the hollow cylinder rolls up, which is 1.0 m in this case.

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See my explanation in the pic

The weight of the green sea whale is approximately 123 kilograms. The data set that could be represented by the box plot is iii. 54, 60, 65, 66, 67, 69, 70, 72, 73, 75, 76.

To calculate the weight of the green sea whale with a given z-score and determine which data set could be represented by a given box plot, we can follow these steps:

Calculating the weight of the green sea whale:

Mean (μ) = 139.9

Standard Deviation (σ) = √variance

= √49.0

= 7

Using the formula for z-score: z = (x - μ) / σ

We can rearrange the formula to solve for x (weight of the green sea whale):

x = z * σ + μ

Plugging in the values:

x = (-2.3) * 7 + 139.9

x ≈ 123

Therefore, the weight of the green sea whale is approximately 123 kilograms.

Determining the data set represented by the box plot:

By comparing the values in each data set to the values shown in the box plot, we can identify which data set matches the given box plot.

Looking at the data sets i, ii, and iii, we observe that the data set that matches the values on the box plot is iii. 54, 60, 65, 66, 67, 69, 70, 72, 73, 75, 76.

The weight of the green sea whale is approximately 123 kilograms. The data set that could be represented by the given box plot is iii. 54, 60, 65, 66, 67, 69, 70, 72, 73, 75, 76.

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Based on the given information, the conclusion of the t-test with a p-value of 0.03 and a significance level (α) of 0.05 is that we reject the null hypothesis. If the significance level is changed to α = 0.01, the decision remains the same.

In hypothesis testing, the p-value represents the probability of obtaining results as extreme as the observed data, assuming that the null hypothesis is true. The significance level (α) is the predetermined threshold used to make a decision about the null hypothesis.

When α = 0.05, it means that we are willing to accept a 5% chance of making a Type I error, which is rejecting the null hypothesis when it is actually true. In this case, since the p-value (0.03) is less than the significance level (0.05), we have sufficient evidence to reject the null hypothesis. Thus, we conclude that there is a statistically significant difference between the groups being compared.

If the significance level is changed to α = 0.01, it means we are now requiring stronger evidence to reject the null hypothesis. However, since the p-value (0.03) is still less than α, the decision remains the same. We would still reject the null hypothesis and conclude that there is a statistically significant difference between the groups.

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Answer:

9000

4-digit numbers..

Answer:

Olivia's puppy, it weighed 5 pounds.

Step-by-step explanation:

By dividing the output power (work completed) by the input power ratio, the motor's efficiency may be determined. In this instance, the input power is 300 W, and the output power is 2400 joules (400 N * 6.0 m). As a result, the motor has an efficiency of 2400 J/300 W, or 8.0.

The input power is 300 W.

Time (t) = 20 s

Height is 6.0 metres.

(F) = 400 N Load

Output power (Pout) is calculated as follows: F x h = 400 N x 6.0 m = 2400 J

Efficiency (e) is calculated as Pout / P = 2400 J / 300 W = 8.0.

A motor's efficiency can be determined by dividing its output power by its input power. Assuming that the input power is 300 W and the output power equals the amount of work completed, the load (F) and height can be multiplied to determine the output power (h). The output power in this example is 2400 joules (400 N * 6.0 m) since the load is 400 N and the height is 6.0 m. The motor's efficiency is 2400 J/300 W, or 8.0, as a result. Knowing the input power, output power, and length of time it took the motor to lift the load will help you determine the efficiency. In this illustration, the time is 20 s, and the input power is 300 W.

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False. The expression \((3ab - 6a)^2\) is not the same as 2(3ab - 6a).

The expression\((3ab - 6a)^2\) is not the same as 2(3ab - 6a).

To simplify \((3ab - 6a)^2\), we need to apply the exponent of 2 to the entire expression. This means we have to multiply the expression by itself.

\((3ab - 6a)^2 = (3ab - 6a)(3ab - 6a)\)

Using the distributive property, we can expand this expression:

\((3ab - 6a)(3ab - 6a) = 9a^2b^2 - 18ab^2a + 18a^2b - 36a^2\)

Simplifying further, we can combine like terms:

\(9a^2b^2 - 18ab^2a + 18a^2b - 36a^2 = 9a^2b^2 - 18ab(a - 2b) + 18a^2b - 36a^2\)

The correct simplified form of \((3ab - 6a)^2 is 9a^2b^2 - 18ab(a - 2b) + 18a^2b - 36a^2\).

The statement that\((3ab - 6a)^2\) is the same as 2(3ab - 6a) is false.

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Answer:

Step-by-step explanation:

The loop will run an infinite number of times

Answer:

I need to know how many gallons you have.

Step-by-step explanation:

You should multiply the amount by how many gallons.

Answer:

whats the question

Step-by-step explanation:

Answer:

X=3+1/8

Step-by-step explanation:

X * 40/6 = 125/6

(Multiply each side by 6 to get rid of the denominator)
X *40=125
Divide each side by 40
X = 125/40
X= 25/8
X=3+1/8

Answer:

Step-by-step explanation:

Imagine the numbers are plotted on the number line.

Order on the number line which is from least to greatest:

Answer:

\(d=\sqrt{58}\approx7.6\)

Step-by-step explanation:

To find the distance between any two points, we can use the distance formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2\)

Our first point, A, is at (1, 1) and our second point, B, is at (-2, 8).

Let's let A(1, 1) be (x₁, y₁) and B(-2, 8) be (x₂, y₂). Substitute this into the distance formula:

\(d=\sqrt{(-2-1)^2+(8-1)^2\)

Subtract:

\(d=\sqrt{(-3)^2+(7)^2\)

Square:

\(d=\sqrt{9+49}\)

Add:

\(d=\sqrt{58}\)

This cannot be simplified.

So, the distance between the two points is √58 or about 7.6 units.

And we're done!

So... where's my cookie :)?

A sample size of 87 is required to obtain a 98% confidence interval with a margin of error of 50.

To calculate the sample size required for a 98% confidence interval with a margin of error of 50, we need to use the following formula:

n = [Z*(σ/ME)]^2

where:

n = the sample size needed

Z = the Z-score for the desired confidence level (98% or 2.33)

σ = the standard deviation of apartments for rent in the area ($200)

ME = the margin of error ($50)

Plugging in the given values, we get:

n = [2.33*(200/50)]^2

n = [9.32]^2

n ≈ 86.7

Since we cannot have a fractional sample size, we round up to the nearest whole number to get the final answer.

Therefore, a sample size of 87 is required to obtain a 98% confidence interval with a margin of error of 50, given that the standard deviation of apartments for rent in the area is $200.

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Answer:

\( 18 \%\: of \: x = 63 \\ \frac{18}{100} x = 63 \\ x = \frac{63 \times 100}{18} \\ x = 350\)

Answer:

350

Step-by-step explanation:

To figure out the number, divide 63 by 18%

63/0.18 = 350

You can check by doing the opposite operation with your answer:

350 · 0.18 = 63

Answer:

V = 75\(\pi\) or 235.619449... cm / 235.62 cm

Hope this helps!

Step-by-step explanation:

The formula for the volume of a cone is  \(V=\frac{1}{3} *h*\pi r^{2}\).

\(V = \frac{1}{3} *9*\pi 5^{2}\)  ( Simplify 1/3 and 9 )

\(V=3*25\pi\)

\(V=75\pi\)

V = 235.619449019 or 235.62

======================================

Work Shown:

A = 1110 = final amount

r = 0.037 = decimal form of the interest rate

n = 1 = compounding frequency (annual)

t = 13 = time in years

----------

A = P(1+r/n)^(n*t)

1110 = P(1+0.037/1)^(1*13)

1110 = P(1.60370259909214)

1.60370259909214P = 1110

P = 1110/1.60370259909214

P = 692.14828274792

P = 692.15 ....... rounding to the nearest cent

P = 700 .... rounding to the nearest hundred dollars

Answer:

P≈ 700

Step-by-step explanation:

Answer:

m∠QRS = 30°

m∠SRT = 75°

Step-by-step explanation:

Now,

The sum of m∠QRS and m∠SRT is equal to m∠QRT which is 105°

So,

m∠QRS + m∠SRT = m∠QRT

(6x)° + (14x + 5)° = (105)°

6x + 14x + 5 = 105

20x + 105 - 5

20x = 100

x = 100/20

x = 5

Thus, The value of x is 5°

Now,

m∠QRS = (6x)° = 6 × 5 = 30°

m∠SRT = (14x + 5)° = 14(5) + 5 = 70 + 5 = 75°

Answer:The answer 60.7371385562.

Step-by-step explanation:

The square root of 3,689 is approximately 60.74.

\(\sqrt{3689} = 60.74\) (approx)

a. To calculate velocity, we need to take the derivative of the position function, r(t). So, the formula for velocity is v(t) = r'(t) = [sqrt(2)(e^t - e^-t) + sqrt(2)t(e^t + e^-t)]a.

b. To calculate acceleration, we need to take the second derivative of the position function, r(t). So, the formula for acceleration is a(t) = r''(t) = [sqrt(2)(e^t + e^-t) + sqrt(2)t(e^t - e^-t) + 2sqrt(2)t(e^t + e^-t)]a.

c. To calculate distance, we need to integrate the velocity function, v(t), over a certain time interval. So, the formula for distance is d(t1, t2) = ∫[t1, t2] v(t) dt = ∫[t1, t2] [sqrt(2)(e^t - e^-t) + sqrt(2)t(e^t + e^-t)]a dt.

d. To calculate position, we need to integrate the acceleration function, a(t), twice over a certain time interval. So, the formula for position is r(t1, t2) = ∫[t1, t2] ∫[t1, t] a(s) ds dt + r(t1), where r(t1) is the initial position at time t1.


a. Velocity (v) can be calculated using the derivative of the position function r(t). In this case, v(t) = dr(t)/dt.

b. Acceleration (a) can be calculated using the derivative of the velocity function v(t). So, a(t) = dv(t)/dt.

c. Distance (d) can be calculated by finding the definite integral of the velocity function v(t) with respect to time over a specific interval. In other words, d = ∫|v(t)|dt, where the integration limits correspond to the interval of time you're interested in.

d. Position (r) is given by the function r(t) = sqrt(2)t * e^t * e^(-t), which represents the position of the object at any given time t.

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Step-by-step explanation:

\(\tt{} \frac{ \sqrt[3]{60} }{ \sqrt[3]{36} } \)

\(\tt{} \frac{ \sqrt[3]{5} }{ \sqrt[3]{3} } \)

\(\tt{} \frac{ \sqrt[3]{5} }{ \sqrt[3]{3} } \times \frac{ \sqrt[3]{ {3}^{2} } }{ \sqrt[3]{ {3}^{2} } } \)

\(\tt{} \frac{ \sqrt[3]{5} \sqrt[3]{ {3}^{2} } }{ \sqrt[3]{3} \sqrt[3]{ {3}^{2} } } \)

\(\tt{} \frac{ \sqrt[3]{5 \times {3}^{2} } }{ \sqrt[3]{3 \times {3}^{2} } } \)

\(\tt{} \frac{ \sqrt[3]{5 \times 9} }{ \sqrt[3]{ {3}^{3} } } \)

\(\tt{} \frac{ \sqrt[3]{45} }{3}\)

\(\tt{}1.18563\)

The sample mean of the weights at the birth of the randomly chosen infants is 7.6 pounds.

Given: The sample of seven infants was selected randomly and the weights are: {9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6} (in pounds)

What is a sample?

A sample can be defined as a part of something big or a whole. It can be some of the elements from a given set of elements.

For example: Let us consider the set of natural numbers. The set of natural numbers has an infinite number of elements in it. We choose some numbers from the set, say {2, 7, 9, 10, 99, 200, 234}. These chosen numbers are known as samples from the set of natural numbers.

What is the sample mean?

The sample mean is the average value of the samples or it is the mean of all the elements which exist in the given sample.

The sample mean is denoted by x⁻ which is pronounced as x bar.

The formula to calculate sample mean (x⁻) is:

Sample Mean (x⁻) = Summation of all the elements in the sample / Total number of elements in the sample.

x⁻ = ∑xₙ / n

where,

∑xₙ = Summation of all the elements in the sample

n = Total number of elements in the sample

x⁻ = Sample mean

Now let's solve the given question:

The given sample is {9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6}

The summation of the elements in the sample is:

∑xₙ = 9.0 + 7.3 + 6.0 + 8.8 + 6.8 + 8.4 + 6.6

∑xₙ = 52.9

The total number of elements in the sample is:

n = 7

Therefore, the sample mean (x⁻) is:

x⁻ = ∑xₙ / n

x⁻ = 52.9 / 7

x⁻ = 7.5571 ≈ 7.6

Hence the sample mean of the weights at the birth of the randomly chosen infants is 7.6 pounds.

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Disclaimer: The question is incomplete. The complete question is mentioned below:
Question: A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the sample mean?

61 matchsticks need to make 20 squares.

Given,

From the figure,

Matchsticks are used to make the pattern.

To make these 4 squares, you need 13 matchsticks.

To find the how many matchsticks do you need to make 20 squares?

Now, According to the question:

Let the need matchsticks be 'n'

The number of the squares to make 1 square , you need 4 matchsticks,

and when you need to add one square, you need three more matchsticks .

So , we have to make  n no. of squares you need

4 + 3(n - 1) matchsticks     (n \(\geq\) )

= 4 + 3n - 3

= 1 + 3n

When, n = 20

1 + 3 x 20

= 61

Hence, 61 matchsticks need to make 20 squares.

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A quadrilateral shape called a trapezoid that has exactly one set of parallel sides. Isosceles Trapezoid: A trapezoid with congruent non-parallel sides.

A quadrilateral is a polygon with four vertices, four sides, and four angles, all of which add up to 360 degrees. The quadrilateral is formed by two triangles when the diagonals are drawn. The angle total for these two triangles is 180°. As a result, the quadrilateral has a 360° total angle.

With four sides, four vertices, and four angles, a quadrilateral is a closed shape and a specific kind of polygon. A quadrilateral's internal angles add up to 360 degrees in all cases. The four angles found at each vertex of a four-sided form are referred to as the interior angles of a quadrilateral and are the only angles in a quadrilateral. Every quadrilateral's internal angles add up to 360 degrees.

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The point (7, -π/2) in polar coordinates corresponds to the rectangular coordinates (0, -7), representing a point on the negative y-axis.

In polar coordinates, a point is represented by its distance from the origin (r) and its angle from the positive x-axis (θ). For the given point (7, -π/2), the distance from the origin is 7 units (r = 7), and the angle is -π/2 radians.

To convert this point to rectangular coordinates, we can use the following formulas:

x = r * cos(θ)

y = r * sin(θ)

Applying these formulas to the given values, we get:

x = 7 * cos(-π/2)

y = 7 * sin(-π/2)

The cosine of -π/2 is 0, and the sine of -π/2 is -1, so we can substitute these values into the formulas:

x = 7 * 0 = 0

y = 7 * (-1) = -7

Therefore, the rectangular coordinates for the point (7, -π/2) are (0, -7). This represents a point on the negative y-axis, where the x-coordinate is 0 and the y-coordinate is -7.

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The true statements about the graph y = 4x2 + 28x + 49 are as follows;

(b) The equation 2x + 7 = 0 can be used to find a zero of the function.

(d) The graph has a double root at x = -7/2.

(e) The graph intersects the y-axis at y = 49.

The graph of a function f is the graph of the equation y = f (x).

The function is given as:

\(\rm y = 4x^2 + 28x + 49\)

Express 28x and 14x + 14x; so, we have:

\(\rm y = 4x^2 + 14x+14x + 49\)

Factorize

\(\rm y = 4x^2 + 14x+14x + 49\\\\y = 2x(2x+7)+7(2x+7)\\\\y=(2x+7)(2x+7)\)

Express as a perfect square

\(\rm y = (2x+7)^2\)

This means that the graph of the equation has a double root.

It also means that 2x + 7 = 0 can be used to determine the root/zero of the function.

Substitute 0 for x in to determine the y-intercept

\(\rm y = (2x+7)^2\\\\\rm y = (2(0)+7)^2\\\\\rm y = (0+7)^2\\\\y=49\)

This means that the graph intersects with the y-axis at y = 49

Hence, the true statements are (b), (d), and (e)

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Answer:

b,d, and ,e

Step-by-step explanation:

trust i just did it

Answer:

B: X less than or equal to 12

x≤12

Step-by-step explanation:

Corey owns a 50acre vineyard

Corey wants rainfall amounts to be at most 12 inches per year

Let rainfall=x

Corey wants amount of rainfall (x) to be at most 12 inches per year

x is at most 12 inches per year

In inequality, the appropriate symbol representing “at most” is the “less than or equal to”

(≤) symbol

So, substituting the symbol

We have,

x≤12

B: X less than or equal to 12

Answer:

  (a) $14,912 saved

  (b) $58,000 aid needed

Step-by-step explanation:

Nola is saving $200 each month. That means she will have saved 60 times that amount after 60 months:

  60 × $200 = $12,000

When she adds that to her current savings she will have saved a total of ...

  $12,000 +2,912 = $14,912 . . . by the time she starts college

__

The figure is telling you Nola will need $72,912 for 4 years of college. If she funds $14,912 from her own savings, then she will need an additional amount of ...

  $72,912 -14,912 = $58,000 . . . . amount of financial aid needed

Answer:

x = 19

Step-by-step explanation:

1 = x - 18

1 + 18 = x

x = 19