The distance a freely falling body covers in the nth second is given by s(n)=d(n)-d(n-1). Show s(n) in terms of g, in simplified form

Answer:

42/56 = 3/4

Step-by-step explanation:

Answer:

The simplified fraction is [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Simplifying Fractions

A given fraction [tex]\frac{a}{b}[/tex] can be simplified if a and b have common factors, i.e. if they can be evenly divided by at least one equal number.

The fraction is:

[tex]\frac{42}{56}[/tex]

We'll simplify it by 2 since both numbers are even:

[tex]\frac{42}{56}=\frac{21}{28}[/tex]

The next prime common factor is 7. Dividing by 7:

[tex]\frac{42}{56}=\frac{21}{28}=\frac{3}{4}[/tex]

Thus, the simplified fraction is [tex]\frac{3}{4}[/tex]

Answer:

A lot

Step-by-step explanation:

Why am I baking cakes. I SUCK.

There are 12 ounces of sugar will he need in his smaller cake.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The normal recipe calls for 8 ounces of butter and 16 ounces of sugar.

Let the amount of sugar will he need in his smaller cake = x

So, By definition of proportion, we get;

⇒ Amount of Butter / Amount of Sugar

⇒ 8 / 16 = 6 / x

⇒ x = 6 × 16 / 8

⇒ x = 12 ounces

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Answer:

1/6y^3

Step-by-step explanation:

Answer:

1/6y^3

Step-by-step explanation:

cancel the common factor of y^2 and y^5

Answer:

0.1587 = 15.87% probability that the weight of a randomly selected candy bar is less than 8 ounces.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The distribution of actual weights of 8-ounce chocolate bars produced by a certain machine is Normal with mean 8.1 ounces and standard deviation 0.1 ounces.

This means that [tex]\mu = 8.1, \sigma = 0.1[/tex].

(a) Find the probability that the weight of a randomly selected candy bar is less than 8 ounces

This is the pvalue of Z when X = 8. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{8 - 8.1}{0.1}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587

0.1587 = 15.87% probability that the weight of a randomly selected candy bar is less than 8 ounces.

Answer:

the zeros of the function are those that result, when plugged into the equation, in zero; the zeros are -3, 1, and 1/2

Step-by-step explanation:

all possible factors:

±3/2,  ±1/2,  ±3,  ±1

2x³ + 3x² - 8x + 3

let '2' = p and let '3' = q

factors of 'p' are 1 and 2

let '3' = q

factors of 'q' are 1 and 3

possible factors are q/p

Answer:

None

Step-by-step explanation:

Answer:

Across

Evapotranspiration is the sum of evaporation from plants.

Earth is surrounded by invisible gases that form a thin protective blanket that we call the atmosphere.

Water flows downhill because gravity is a form of potential energy – and the water, or anything that falls or rolls downward – flows in response to differences in potential energy (from high to low). ... Therefore, the potential energy that drives groundwater movement includes both pressure and gravity.

Precipitation: hail, rain, freezing rain, sleet and snow.

Condensation is the opposite of vaporization. Condensation occurs when a gas loses energy, slows in motion so that its cohesive force pulls the molecules close, but the molecules still have enough energy to break away from one connection only to connect with another molecule.

Down

Alternatively evaporation of the liquid should leave a solid residue. ... Dissolving is a reversible process and the solute can be recovered from a solution by evaporation though it will not always be in the exactly the same form as at the start.

Boiling. If a liquid is heated the particles are given more energy and move faster and faster expanding the liquid.

Answer: No entiendo la historia y no vengas por mí, solo quería los puntos jajaja

Step-by-step explanation:

Answer:

The speed of the plane in still air and the speed of the jet stream are 525 miles per hour and 75 miles per hour.

Step-by-step explanation:

From Mechanical Physics, we know that absolute velocity of the airplane ([tex]v_{A}[/tex]) is equal to sum of the absolute velocity of the jet steam [tex](v_{J})[/tex] and the relative velocity of the airplane with respect to jet stream (velocity of the airplane in still air) ([tex]v_{A/J}[/tex]). Al velocities are measured in miles per hour. Let suppose that both jet stream and airplanes travels at constant velocity. Now, we construct the following system of linear equations:

Flight with the jet stream

[tex]v_{J}+v_{A/J} = \frac{2700\,mi}{4.5\,h}[/tex]

[tex]v_{J}+v_{A/J} = 600\,\frac{mi}{h}[/tex] (1)

Flight against the jet stream

[tex]v_{J} -v_{A/J} = -\frac{2700\,mi}{6\,h}[/tex]

[tex]v_{J}-v_{A/J} = -450\,\frac{mi}{h}[/tex] (2)

The solution of this system of linear equations is:

[tex]v_{J} = 75\,\frac{mi}{h}[/tex], [tex]v_{A/J} = 525\,\frac{mi}{h}[/tex]

The speed of the plane in still air and the speed of the jet stream are 525 miles per hour and 75 miles per hour.

it describes the relationship between the three sides of a triangle. any triangle the sum of length of two sides is always great er then the third side.

Answer:

I think the answer is 900

Step-by-step explanation:

Use the formula to find the area of a trapeziod (search it up the find it)

Then fill in the numbers where they belong.

Answer:

27

Step-by-step explanation:

3/4*36=27

therefore the answer is

27

Answer:

6x−9x−5+8+7x

=6x+−9x+−5+8+7x

Combine Like Terms:

=6x+−9x+−5+8+7x

=(6x+−9x+7x)+(−5+8)

=4x+3

Answer:

=4x+3

Step-by-step explanation:

I hope this helps

Answer:

=4x + 3

Step-by-step explanation:

Add the numbers

6

Answer:

Step-by-step explanation:

Find the image attached

Since ABCD is a square, <ACB = 45 degrees

Given <ACB = 11x-32

Equate both

11x-32 = 45

11x = 45+32

11x = 77

x = 77/11

x = 7

Hence the value of x is 7

From the Moore's Law, the predicted number of transistors per IC in 1992 would be approximately 4,096,000.

Given data:

Based on this exponential growth pattern, use the estimate of 4,000 transistors per IC in 1972 to predict the number of transistors per IC in 1992.

To predict the number of transistors per IC in 1992, determine how many doublings occurred during the 20-year period from 1972 to 1992.

Since each doubling represents a multiplication by 2, calculate the number of doublings as follows:

Number of doublings = (1992 - 1972) / 2

Number of doublings = 20 / 2

Number of doublings = 10

Now, use this number of doublings to predict the number of transistors per IC in 1992:

Predicted number of transistors per IC in 1992 = 4,000 * (2^10)

Predicted number of transistors per IC in 1992 = 4,000 * 1,024

Predicted number of transistors per IC in 1992 ≈ 4,096,000

Hence, based on Moore's Law and the estimate of 4,000 transistors per IC in 1972, the predicted number of transistors per IC in 1992 would be approximately 4,096,000.

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Answer:

0.49

Step-by-step explanation:

49/100 = 0.49

I uh apparently need to explain more

Answer: 37.5%

Step-by-step explanation:

200-125=75

75 divided by 200 is 0.357

since we need percent so were gonna move the decimal point 2 places so the final answer is 37.5% remain unsold

Answer:

The new jar is smaller.

Step-by-step explanation:

Like what the statements says, the normal size of coffee is reduced by 1/5 and it become as the new jar which is smaller than the original.

Answer:

C

Step-by-step explanation:

Answer:

C. x = 8 is a solution, but x = 6 is not

Step-by-step explanation:

12 + 6 = 18

12 + 8 = 20

20 - 12 = 8

Answer:

x=13.5

Step-by-step explanation:

You are on the right track with sin34/x=sin27/11 (remember you don't need all three angles/sides)

[tex]\frac{sin34}{x}[/tex] = [tex]\frac{sin27}{11}[/tex]

(sin27)(x)=6.15112193818

x=6.15112193818/0.45399049974

x=13.5490102584

Answer:

They are the same

Step-by-step explanation:

When you convert 0.578 into a percentage you get 57.8%

When you convert 57.8% into a decimal you get 0.578

Hello!

[tex]\large\boxed{x = 8}[/tex]

The two angles pictured are corresponding angles, so they are congruent.

Therefore:

17x - 4 = 12 + 15x

Isolate for x by subtracting 15x from both sides:

2x - 4 = 12

Add 4 to both sides:

2x = 16

Divide both sides by 2:

x = 8.

Answer:

x=8

Step-by-step explanation:

These angles are what we call corresponding angles. This simply means that they are the same. Therefore, we set 17x-4 equal to 12+15x. To isolate x, add 4 to both sides, and subtract 15x from both sides. 2x=16. x=8. To check, both angles = 132 degrees.

Answer:

The volume is: [tex]V = \frac{\pi}{3}[/tex] cubic units

Step-by-step explanation:

Volume of a solid:

The volume of a solid, given by the function f(x), over an interval between a and b, is given by:

[tex]V = \pi \int_{a}^{b} (f(x))^2 dx[/tex]

y = x, y =1, x = 0

This means that the upper function is y = 1, and the lower function is y = x. So

[tex]f(x) = (1 - x)[/tex]

The lower limit of integration is x = 0.

The upper limit is y = x when y = 1, so x = 1.

Then

[tex]V = \pi \int_{a}^{b} (f(x))^2 dx[/tex]

[tex]V = \pi \int_{0}^{1} (1-x)^2 dx[/tex]

[tex]V = \pi \int_{0}^{1} (1-2x+x^2) dx[/tex]

[tex]V = \pi (x-x^2+\frac{x^3}{3})|_{0}^{1} dx[/tex]

[tex]V = \pi(1 - (1^2) + \frac{1^3}{3})[/tex]

[tex]V = \frac{\pi}{3}[/tex]

Answer:

8

Step-by-step explanation:

ratios of legs = 3x and 4x

Pythagorean theorum:

A^2+B^2=C^2

3x^2+4x^2=10^2

9x^2+16x^2=100

25x^2=100  --> divide by 25

x^2=4 --> x=2

length of longer leg is 4x = 4 x 2 = 8

The length of the longer leg of the triangle is 8.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

Given that, the legs of the right triangle are in the ratio of 3:4.

Therefore, let the legs of the triangles be 3x and 4x.

Since the hypotenuse of the triangle is 10, using the Pythagorean theorem it follows:

10² = (3x)² + (4x)²

100 = 9x² + 16x²

100 = 25x²

x² = 4

x = 2

Therefore, the lengths of the legs are:

3(2) = 6, and

4(2) = 8

Hence, the length of the longer leg of the triangle is 8.

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Answer:

97% of her laps are completed in less than 134 seconds.

The fastest 5% of her laps are under 125.96 seconds.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 129.71, \sigma = 2.28[/tex]

Find the percent of her laps that are completed in less than 134 seconds.

We have to find the pvalue of Z when X = 134. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{134 - 129.71}{2.28}[/tex]

[tex]Z = 1.88[/tex]

[tex]Z = 1.88[/tex] has a pvalue of 0.9699, so 97% of her laps are completed in less than 134 seconds.

The fastest 5% of her laps are under how many seconds?

This is the 5th percentile of times, which is X when Z has a pvalue of 0.05, that is, X when Z = -1.645. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.645 = \frac{X - 129.71}{2.28}[/tex]

[tex]X - 129.71 = -1.645*2.28[/tex]

[tex]X = 125.96[/tex]

The fastest 5% of her laps are under 125.96 seconds.

Answer:

gg

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

2 x 2 =4

Answer:0.125

Step-by-step explanation:

There is only 1/8 that is whistle so convert into percent and get 0.125. Hope this helps

Answer:

0.125

Step-by-step explanation:

There are 8 possibilities.

Only 1 whistle.

1/8 = 0.125