A catapult is used to launch a boulder. The height of the boulder h can be modeled by the function 60x40 ft², where t is the time in seconds after the boulder is launched. Assuming that the boulder doesn't hit anything, how many seconds after launch will the boulder hit the ground?

If the number of papers is 56, the ratio of the total height in millimeters of 2 mm thick paper to the total height in millimeters of 23 mm thick paper is 2:23.

The ratio is the relative size of two comparable quantities, values, or numbers.

Ratios are computed as the quotients of one value (the numerator) and another (the denominator).

We can depict ratios as decimals, fractions, percentages, or in their standard forms (:).

The total height in millimeters of 2 mm thick paper = 112 mm (56 x 2)

The total height in millimeters of 23 mm thick papers = 1,288 mm (56 x 23)

Ratio = 0.0869 (112 ÷ 1,288) or 2/23 or 8.69%.

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Answer:

Yes, the bottom shelf is parallel to the middle shelf. Angle 6 measures 120°, so angles 6 and 11 are congruent alternate exterior angles.

The expression to represent the given situation is M =30t.

Let's use the variable M to represent Susan's overall piano practice time over the course of t days.

Given that Susan practices the piano for 30 minutes every day, the sum of her practice time over the course of t days is:

M = 30t

As a result, M = 30t is the equation that describes the total amount of time Susan spends practicing the piano over the course of t days.

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The number of miles that he would have saved instead would be = 8.6 miles

The amount of miles he traveled south = 7 miles

The amount of miles he traveled east = 5 miles

To calculate the number of miles he would have saved, the Pythagorean formula is used;

That is :

C² = a²+ b²

a = 7

b =5

c² = 7²+5²

= 49+25

= 74

c = √74

= 8.6 miles

Therefore, he would have travelled 8.6 miles instead of 12 miles.

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The 95% confidence interval of (-0.02, 0.16) mm for the median difference between the methods of soaking the amputated injured newt limbs in a control versus a benjamin solution means that we are 95% confident that the true median difference of healing in mm will exist within the confidence interval of (-0.02, 0.16).

The 95% confidence interval of (-0.02, 0.16) mm means that there is a 95% chance that the true median difference in healing between the methods of soaking the amputated injured newt limbs in a control versus a benjamin solution falls within this range. This means that 95% of all random samples drawn will exist within this confidence interval, and we can be confident that the methods used in this study have at least as much healing as was seen in the sample median difference of new tissue formed in mm. Therefore, with 96% confidence, we can say that the true median difference in healing between the two methods is somewhere within this range. Methods used to generate confidence intervals that bracket the true median difference will form confidence intervals that fit within the confidence interval of (-0.02, 0.16) we have calculated.

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Answer:is this actually a question!

Step-by-step explanation:

The volume of the sports ball is 6286.28 cm³

A sphere is round, has no edges, and is a solid shape. Examples of a sphere include; The playing ball, balloon, and even light bulbs .

A sphere is a 3-dimensional shape ,and it's therefore a solid shape.

The volume of a sphere is expressed as;

V = 4/3 πr³

where r is the radius of the sphere and v is the volume.

the radius of the sphere is half the diameter.

D = 2r

r = 23/2 = 11.5

therefore ;

V = 4/3 × 3.14 × 11.5³

V = 18858.85/3

V = 6286.28 cm³ ( 2 decimal place)

Therefore the volume of the ball is 6286.28 cm³

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Your close relative has to contribute $17,430 in a bond shared finance that yields 3.0% for it to supply $18,000 a year for you.

To calculate the sum that your close relative has to contribute in a bond common finance to supply you with $18,000 per year, you wish to utilize the equation for the display esteem of an annuity.

PV = PMT * (1 - (1 + r)^(-n)) / r

where:

PV = display esteem

PMT = installment sum (in this case, $18,000 per year)

r = intrigued rate (3.0%)

n = number of periods (in this case, 1 year)

Substituting the values into the equation:

PV = $18,000 * (1 - (1 + 0.03)^(-1)) / 0.03

PV = $18,000 * (1 - 0.9709) / 0.03

PV = $18,000 * 0.0291 / 0.03

PV = $17,430

Subsequently, your close relative has to contribute $17,430 in a bond shared finance that yields 3.0% for it to supply $18,000 a year for you.

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Answer: 14 and 14

Step-by-step explanation:

So u would Since 13 and 14 are both consecutive integers and their sum is 27, we have our answer.

Answer:2.7

Step-by-step explanation:

Formula, divide the value in centimeters by 100 so 1 meter equals 100 centimeters

So 270 centimeters = 270/100 = 2.7

To find the percentage of Farmer Gibson's herd that remains after he sold 60 cows, we need to calculate the new total number of cows he has.

Number of cows remaining = Total number of cows - Number of cows sold

Number of cows remaining = 200 - 60

Number of cows remaining = 140

So, Farmer Gibson has 140 cows remaining in his herd.

To find the percentage of cows remaining, we can use the following formula:

Percentage = (Number remaining ÷ Total number) x 100

Plugging in the values we have:

Percentage = (140 ÷ 200) x 100

Percentage = 0.7 x 100

Percentage = 70%

Therefore, Farmer Gibson has 70% of his herd remaining after selling 60 cows.

~~~Harsha~~~

Answer:

B. A cube with side lengths of 2 feet has a volume of 8 cubic feet.

v(s) = s^3, so v(3) = 2^3= 8

The distance between the points G and H is D = 8 units

Given data ,

Let the distance between 2 points be represented as D

Now , let the first point be G ( 0 , 8 )

Let the second point be H ( 8 , 8 )

Now , let the distance between G and H be D , where

D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

D = √ ( 0 - 8 )² + ( 8 - 8 )²

D = √64 units

D = 8 units

Hence , the distance is 8 units

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Answer:

26.5

Step-by-step explanation:

The formula for the area of a trapezoid is:

A = (1/2)h(b₁ + b₂)

where h is the height, b₁ and b₂ are the lengths of the parallel bases.

Substituting the given values:

A = (1/2)(4.3 m)(9.2 m + 3.2 m)

A = (1/2)(4.3 m)(12.4 m)

A = 26.52 m²

Rounding to the nearest tenth:

A ≈ 26.5

Therefore, the area of the trapezoid is approximately 26.5 square meters.

The graph of g(x) = √(x - 16) is given by the image presented at the end of the answer.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in this problem is given as follows:

f(x) =√x

Which has vertex at the origin.

The function g(x) = √(x - 16) is equivalent to g(x) = f(x - 16), which is a translation right 16 units of f(x), according to the graph presented at the end of the answer.

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Answer:I’m not so sure but I’m pretty sure it’s the 4th one?

Step-by-step explanation:

Answer:

Option b

Step-by-step explanation:

For x=1, y=-0.5

For x=0, y=2

For x=1, y=-7/2

Graphing the equation on the coordinate plane we get the second graph.

The best interpretation is  the product of the cube root of 2.07 and the age of the mammal

h = 37.8 (2.07t)³ + 78.6

Now, let's analyze the term (2.07t)³:

Based on this analysis, the best interpretation of (2.07t)³ is:

B. the product of the cube root of 2.07 and the age of the mammal

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Using Pythagorean's theorem we can see that the variables are:

t = 13.86

w = 12.81

Remember that for any right triangle, Pythagorean's theorem says that the sum of the squares of the legs is equal to the square of the hypotenuse, where the hypotenuse is the side opposite to the 90° angle.

Then for the first triangle we can write:

t² + 8² = 16²

Solving for t:

t = √(16² - 8²) = 13.86

For the second triangle we have:

10² + 8² = w²

Solving for w:

w = √(10² + 8²)

w = 12.81

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I'm assuming you mean "How do I find the value of x such that the arc length of the circle defined by (10x-23) is 106?" So, there are two possible values of x that would give a circle with arc length 106: x ≈ 2.71 and x ≈ 1.89.

To find the value of x such that the arc length of the circle defined by (10x-23) is 106, we can use the formula for the arc length of a circle:

Arc Length = θr

where θ is the central angle in radians, and r is the radius of the circle.

In this case, we know the arc length is 106, and we need to find the value of x such that the radius is defined by (10x-23). Let's call this radius r.

We can rearrange the formula to solve for the radius:

r = Arc Length / θ

We also know that the central angle in radians is equal to the arc length divided by the radius.

So we can write:

θ = Arc Length / r

Substituting in the values we have:

θ = 106 / (10x-23)

Now we can solve for x. We know that the central angle for a full circle is 2π radians, so the central angle for a circle with radius (10x-23) is:

θ = (2π)(10x-23)

Setting this equal to our previous expression for θ, we have:

106 / (10x-23) = (2π)(10x-23)

Solving for x:

106 = (2π)(10x-23)(10x-23)

106 = (2π)(100x^2 - 460x + 529)

53 = π(100x^2 - 460x + 529)

53/π = 100x^2 - 460x + 529

100x^2 - 460x + (529 - 53/π) = 0

We can solve this quadratic equation using the quadratic formula:

x = [460 ± sqrt(460^2 - 4(100)(529 - 53/π))] / (2(100))

x ≈ 2.71 or x ≈ 1.89

Therefore, there are two possible values of x that would give a circle with arc length 106: x ≈ 2.71 or x ≈ 1.89.

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The record long jump is 8 inches short of 10 yards.

We know that 1 yard is equal to 3 feet, so 10 yards is equal to 10 x 3 = 30 feet.

To find out how many inches short of 10 yards the record long jump is, we need to first convert 29 feet 4 inches to inches only.

We can do this by multiplying the number of feet by 12 (since there are 12 inches in a foot) and then adding the number of inches:

29 feet 4 inches = (29 x 12) + 4

= 348 + 4

= 352 inches

Now we can find out how many inches short of 10 yards the record long jump is:

30 feet = 30 x 12 = 360 inches

360 - 352 = 8

Therefore, the record long jump is 8 inches short of 10 yards.

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The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

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

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 515, \sigma = 125[/tex]

The proportion of scores less than 675 is the p-value of Z when X = 675, hence:

Z = (675 - 515)/125

Z = 1.28

Z = 1.28 has a p-value of 0.8997.

Hence the percentage is 89.97%.

The proportion of scores greater than 550 is one subtracted by the p-value of Z when X = 550, hence:

Z = (550 - 515)/125

Z = 0.28

Z = 0.28 has a p-value of 0.6103.

1 - 0.6103  = 0.3897, hence the amount is given as follows:

E(X) = 1000 x 0.6103 = 610.

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The radius of the cylindrical cup is 6 centimeters.

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )

Given that the volume of the cylindrical cup is 1356.48 cubic centimeters and the height is 12 cm.

We can substitute these values into the formula and solve for the radius:

V = π × r² × h

r = √( V / (πh) )

r = √( 1356.48 / ( 3.14 × 12) )

r = 6 cm

Therefore, the radius is 6cm.

Option C) 6cm is the correct answer.

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The probability of spinning an even number on the spinner is 40%.

The probability of picking a diamond from a standard deck of playing cards is 25%.

P(even) = number of even sections / total number of sections

= 2/5

= 0.4

= 40%

Therefore, the probability of spinning an even number on the spinner is 40%.

P(diamond) = number of diamonds / total number of cards

= 13/52

= 1/4

= 0.25

= 25%

Therefore, the probability of picking a diamond from a standard deck of playing cards is 25%.

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The minimum sample size required to construct a 95% confidence interval for the population mean is 16.

To determine the minimum sample size required to construct a 95% confidence interval for the population mean circumference of tennis balls within 0.05 inch, we need to use the formula for the margin of error:

Margin of error = Z* (σ/√n)

Where Z* is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.

Since we want a 95% confidence interval, Z* = 1.96 (from a standard normal distribution table).

We are given that σ = 0.10 inch and we want the margin of error to be 0.05 inch. Plugging in the values, we get:

0.05 = 1.96 * (0.10 / √n)

Solving for n, we get:

n = [(1.96 * 0.10) / 0.05]² = 15.36

We can't have a fractional sample size, so we round up to the nearest whole number. Therefore, the minimum sample size required is 16.

This means that the manufacturer needs to randomly select and measure the circumferences of at least 16 tennis balls to estimate the population mean circumference with 95% confidence and a margin of error of 0.05 inch.

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Answer:

B' ( -1,-4)

C' (-6,-5)

Step-by-step explanation:

Take each point and move it one unit left and then 3 units up.

Helping in the name of Jesus.

a) The principal of the account is given as follows: 1238.27 euros.

b) The interest rate of the account is given as follows: 4.3%.

The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are listed and explained as follows:

We can take the ratio between the balances two consecutive years to obtain the interest rate as follows:

r = 1569.4/1504.5 - 1

r = 1.0431 - 1

r = 0.043

r = 4.3%.

After 5 years, the balance was of 1504.50, hence the principal is obtained as follows:

1504.5 = P(1 + 0.043 x 5)

P = 1504.5/(1 + 0.043 x 5)

P = 1238.27 euros.

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The statement that explains the validity of the sampling procedure used by the company is the company applied the same procedure to all three locations and used random sampling to select the times to collect data. The Option A is correct.

The procedure used is valid because they applied the same procedure to all three locations and used random sampling to select the times to collect data.

By using the random sampling, they ensured that they were selecting a representative sample of the entire population of mall visitors.

Also, by applying same procedure to all three locations, they ensured that they were collecting comparable data and this helps to increase the generalizability of their findings and make their decision-making process more reliable.

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