The height (in feet) of a rocket from ground level is given by the function f(t) = -16t² + 220t. What is the instantaneous velocity of the rocket 12 seconds after its launch?

Answer:

70%

Step-by-step explanation:

you do it

Answer:

Let x = smaller number and

y = larger number.

x + y = 42

x + 4y = 147

----------------

3y = 105

y = 35, so x = 7

The numbers are 7 and 35.

7 + 4(35) = 7 + 140 = 147

Margo will pay $22 in interest after 6 months.

Margo borrows $1,100 and agrees to pay it back with a 4% annual interest rate after 6 months. To calculate the interest she will pay, follow these steps:

1. Convert the annual interest rate to a decimal: 4% = 0.04.
2. Calculate the interest for one year: Principal x Annual Interest Rate = Interest for One Year. In this case: $1,100 x 0.04 = $44.
3. Since Margo is paying the loan back after only 6 months, we need to find the interest for half a year. To do this, simply divide the interest for one year by 2: $44 ÷ 2 = $22.

So, Margo will pay $22 in interest after 6 months.

In summary, Margo borrows $1,100 at a 4% annual interest rate. We first convert the interest rate to a decimal (0.04) and find the interest for one year by multiplying the principal by the annual interest rate ($1,100 x 0.04 = $44). Finally, we calculate the interest for 6 months by dividing the one-year interest by 2 ($44 ÷ 2 = $22). Therefore, Margo will pay $22 in interest after 6 months.

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The box that replaces the question mark is Box D.

Option D is the correct answer.

We have,

In a figure pattern, the concept used involves identifying and recognizing the underlying rules or principles that govern the sequence of figures.

By observing the given figures and understanding the patterns or relationships between them, we can predict or generate the next figure in the sequence.

From the pattern,

We see that,

The figure is rotating clockwise.

Now,

The box that replaces the question mark would be:

Box D

Thus,

The box that replaces the question mark would be Box D

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The proportion to determine the pay increase of Jan is 25/x = 27.50/y , where x is the current year and y is the next year

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the value of A is

Let the amount Jan makes this year ( x ) be = $ 25

And , Next year, she will make an additional $2.50 per hour

Let the amount Jan makes next year ( y ) be = $ 27.50

On simplifying the proportion , we get

25/x = 27.50/y

Hence , the proportion is 25/x = 27.50/y

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Answer:

180

Step-by-step explanation:

180

Got it correct

The value of the angle in the given interval is; θ = 180°

We are given the trigonometric problem as:

5 sec θ + 5 = 0

Now, the values must be on the interval:

0° ≤ θ < 360°

We know that sec θ = 1/cos θ

Thus:

5/cos θ + 5 = 0

5/cos θ = -5

cos θ = -5/5

cos θ = -1

θ = cos⁻¹-1

θ = 180°

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Answer:

The answer is 13 to the nearest gallon

Step-by-step explanation:

1litre =0.264gallon

50litre=x

x×1=50×0.264

x=13.2gallon

x=13 to the nearest gallon

Answer:

-1/4

Step-by-step explanation:

you can use equation

-5/4 - x = -1

on solving

value of x is -1/4

The minimum sample size required to construct a 95% confidence interval for the population mean of tennis ball circumferences with a maximum error of estimate of 0.05 inch, assuming a population standard deviation of 0.10 inch, is 62.

To find the minimum sample size required to construct a 95% confidence interval for the population mean, we can use the formula:

n = (z*σ / E)^2

where:

n = sample size

z = z-score for the desired confidence level (95% confidence level corresponds to a z-score of 1.96)

σ = population standard deviation

E = maximum error of estimate, which is half the width of the confidence interval (in this case, 0.05/2 = 0.025)

Substituting the given values, we get:

n = (1.96 * 0.10 / 0.025)²

n = 61.44

Rounding up to the nearest whole number, we get a minimum sample size of 62.

Therefore, the minimum sample size required to construct a 95% confidence interval for the population mean of tennis ball circumferences with a maximum error of estimate of 0.05 inch, assuming a population standard deviation of 0.10 inch, is 62.

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Casey will earn $595.42 more interest with annual compound interest compared to annual simple interest over 10 years.

Simple interest is paid just on the initial amount deposited or borrowed and is computed as a percentage of the principal amount. In other words, interest earned or charged is calculated purely on the principal amount, without taking into consideration interest from prior periods. On the other hand, compound interest adds the principal amount to the interest earned or charged in prior periods to determine the interest earned or charged in the current period. In comparison to simple interest, compound interest results in higher overall interest payments or earnings since the interest generated or charged climbs exponentially over time. Compound interest is more prevalent and beneficial for long-term investments in general.

The compound interest is given as:

[tex]A = P(1 + r/n)^{(nt)}[/tex]

Substituting the values of P = 500, n = 1, r = 0.06 and t = 10 we have:

[tex]A = P(1 + r/n)^{(nt)} = 500 * (1 + 0.06/1)^{(1*10)} = $895.42[/tex]

Now, simple interest is given as:

SI = Prt = 500 * 0.06 * 10 = $300

Now, the difference is:

895.42 - 300 = $595.42

Hence, Casey will earn $595.42 more interest with annual compound interest compared to annual simple interest over 10 years.

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The probability that all men will be interview first is 0.05.

Probability helps with finding out the likelihood of the occurrence of an event and measures chance of an event happening.

Given data:

Men = 3

Women = 3

Total people:

= 3 + 3

= 6

Probabilities of men:

P(first man) = 3/6 = 1/2

P(second man) = 2/5

P(third man) = 1/4

Required probability is:

P(first 3 men) = 1/2 * 2/5 * 1/4

P(first 3 men) = 0.05

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The equivalent expressions of the expression  (3/4)x-1 are (3x/4) - 1, 3x/4 - 4/4 and 0.75x - 1

The given expression is (3/4)x-1

Three divided by four times of x minus one

We have to find three equivalent expressions of given expression

Equivalent expressions are expressions that work the same even though they look different.

(3x/4) - 1

3x/4 - 4/4

and 0.75x - 1 are equivalent expressions

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The exponential decay can be written as:

y = 550mg*(1 - 0.066)^t

A general exponential decay can be written as:

y = A*(1- r)^x

Where A is the initial amount, r is the rate of decay, and x is the variable.

Here we know that we start with a sample of 550 mg, and this sample decays at a rate of 6.6% per year.

Then the amount of sample that we have after t years is given by the exponential decay:

y = 550mg*(1 - 0.066)^t

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Step-by-step explanation:

3^2x = 11

we take the logarithm (to the base of 3) of both sides.

log3(3^2x) = log3(11)

2x = log3(11) = log(11)/log(3)

x = log(11)/log(3) / 2 = log(11)/(2×log(3)) =

= 1.091329169... ≈ 1.09

Answer:

3^2x = 11

we take the logarithm (to the base of 3) of both sides.

log3(3^2x) = log3(11)

2x = log3(11) = log(11)/log(3)

x = log(11)/log(3) / 2 = log(11)/(2×log(3)) =

= 1.091329169... ≈ 1.09

Step-by-step explanation:

The figure that satisfies the condition of the net  for the rectangular prism is the figure in the option at the bottom right of the screen.

A rectangular prism is a three dimensional figure consisting of six rectangular shaped faces, with the pair of opposite faces parallel to each other.

The net for the rectangular prism is one that can be folded to produce the rectangular prism.

The net of the rectangular prism will have the faces with the longest sides penultimate to each other.

The figure that satisfies the condition of the faces with the longest sides being separated by another side in between is the figure on the bottom right of the the screen. Please find attached

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y² = 2x - 2 is not a function since the one value of x related to more than one values of y via this given relation.

A relation is called a function only if it is well defined that is each input value that is each value of x is related to only one output value that is the value of y.

Here given the relation is y² = 2x - 2

So, either y = + √(2x - 2) or y = - √(2x - 2)

For suppose one value of x is, x = 3.

y = + √(2*3 - 2) = + √(6 - 2) = + √4 = + 2

y = - √(2*3 - 2) = - √(6 - 2) = - √4 = - 2

So here one input value x = 3 is related to two values of y that are y = -2, +2 via the relation y² = 2x - 2.

Hence, y² = 2x - 2 is not a function.

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Answer:

1.1 is the square root number

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the answer you find the sqrt of 1.21 then add the number i to the end.

[tex]\sqrt{-1.21} =\\\sqrt{-1.21} = 1.1 * i\\\sqrt{-1.21} = 1.1 i\\[/tex]

The real number root is 1.1 or the number without the i

1) 9 × 1 × 4

2) 1 × 4 × 0 = 1 × 4 × 0

3) 8 + 9 = 3 + 11

4) 8 + 7 + 2 = 20 ÷ 2 + 7

A reasonable estimate of the number of books he will read in the next six weeks is between 13.8 - 1.4 = 12.4 and 13.8 + 1.4 = 15.2 books.

Normal usually refers to the word "normal" in a normal distribution with mean μ and standard deviation σ, the z-score of a measure X is;

Z = (X - μ)/ σ

We are given that;

Books= 6.9

Number of weeks= 3

Error= + 0.7

Now,

The margin of error is the range of values that are likely to contain the true value of a measurement. In this case, the margin of error is + 0.7, which means that the true average number of books Noel read in the first 3 weeks could be anywhere from 6.9 - 0.7 = 6.2 to 6.9 + 0.7 = 7.6.

To estimate the number of books he will read in the next six weeks, we can assume that he will read at the same rate as in the first three weeks. This means that we can use a proportion to find the estimated number of books:

3/6 = (6.9 +/- 0.7)/x

where x is the estimated number of books in the next six weeks. Solving for x, we get:

x = (6.9 +/- 0.7) * (6/3) x = (6.9 +/- 0.7) * 2 x = 13.8 +/- 1.4

Therefore, by Statistics the answer will be 13.8 - 1.4 = 12.4 and 13.8 + 1.4 = 15.2 books.

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By creating and solving various equation-:(A) x + y + z = 24, x(8000) + y(16000) + z(24000) = 520000. (B) x = 8, y = 8, z = 8. (C) Solution with 8 tank cars of each capacity minimizes the monthly leasing cost at $15,800.

Cost refers to the monetary value of goods, services or resources that are used or consumed to achieve a particular goal or objective.

An equation is a mathematical statement that asserts that two expressions are equal. It contains variables, coefficients, and mathematical operators.

According to the given information:

(A) Let x be the number of 8,000 gallon tank cars, y be the number of 16,000 gallon tank cars, and z be the number of 24,000 gallon tank cars. The total carrying capacity can be expressed as:

8000x + 16000y + 24000z = 520000 ... (1)

Since we have a total of 24 tank cars, the total number of tank cars can be expressed as:

x + y + z = 24 ... (2)

(B) To solve this system of equations, we can use substitution. Solving equation (2) for x, we get:

x = 24 - y - z

Substituting this expression for x into equation (1), we get:

8000(24 - y - z) + 16000y + 24000z = 520000

Simplifying this equation, we get:

8000y + 16000z = 200000

Dividing both sides by 8000, we get:

y + 2z = 25 ... (3)

We can use equations (2) and (3) to solve for y and z:

y = 25 - 2z, x = 24 - y - z

Substituting these expressions into equation (1), we get:

8000(24 - (25 - 2z) - z) + 16000(25 - 2z) + 24000z = 520000

Simplifying this equation, we get:

16000z = 160000

z = 10

Substituting z = 10 into y = 25 - 2z and x = 24 - y - z, we get:

y = 5, x = 9

Therefore, the solution is x = 9, y = 5, and z = 10.

(C) To minimize the monthly leasing cost, we need to calculate the total cost for each solution and choose the one with the lowest cost. The monthly leasing cost can be expressed as:

450x + 650y + 1150z

Substituting x = 9, y = 5, and z = 10, we get:

450(9) + 650(5) + 1150(10) = $28,350

Therefore, the solution that minimizes the monthly leasing cost is x = 9, y = 5, and z = 10, with a monthly leasing cost of $28,350.

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Answer:

To solve for FD, we can use the property of similar triangles, which states that corresponding sides of similar triangles are in proportion. Specifically, we can use the ratios of corresponding sides of triangle ABC and triangle DEF:

AB/DE = BC/EF = CA/FD

Plugging in the given values, we get:

11/2.2 = 7.9/EF = 7.6/FD

Simplifying the middle ratio, we get:

EF = (2.2 x 7.9)/11 = 1.58

Now we can solve for FD by rearranging the third ratio:

7.6/FD = 11/2.2

FD = (2.2 x 7.6)/11 = 1.52

Therefore, FD = 1.52 (to two decimal places).

Step-by-step explanation:

The length of side FD is 1.58 .

Given,

Triangle ABC ~ Triangle DEF

So,

Property of similar triangles, which states that corresponding sides of similar triangles are in proportion.

Specifically, we can use the ratios of corresponding sides of triangle ABC and triangle DEF:

AB/DE = BC/EF = CA/FD

Substitute the given values, we get:

11/2.2 = 7.9/EF = 7.6/FD

Simplifying the middle ratio, we get:

EF = (2.2 x 7.9)/11 = 1.58

Now we can solve for FD by rearranging the third ratio:

7.6/FD = 11/2.2

FD = (2.2 x 7.6)/11 = 1.52

Therefore, FD = 1.52

Hence option 2 is correct .

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Answer:

Step-by-step explanation:

17

The formula for compound interest is given by:

A = P(1 + r/n)^(nt)

Where:

A = final amount

P = principal (initial amount)

r = annual interest rate (as a decimal)

n = number of times the interest is compounded per year

t = time (in years)

Using this formula, we can calculate the final amount of the CD as follows:

A = 2250(1 + 0.03/4)^(4*2)

A = 2250(1 + 0.0075)^8

A = 2250(1.0075)^8

A = 2250(1.063853)

A = $2398.12 (rounded to the nearest cent)

Therefore, the CD will be worth approximately $2398.12 at maturity.

Answer:

[tex]P = 20.4 in[/tex], [tex]A = 22.4 in^2[/tex]

Step-by-step explanation:

P = 2l + 2w

A = lw

For this figure l = 7in and w = 3.2 in

P = 2l + 2w

P = 2(7) + 2(3.2)

P = 14 + 6.4

P = 20.4 in

A = lw

A = 7 x 3.2

A = 22.4 in^2

Note that the UCLr the correct upper control limit is 29.210 (Option B) See the attached excel calculation and the related graph.

When samples are taken at regular intervals from an industrial or commercial process, the "bar x and R chart," also known as a control chart, is a form of scheme used in statistical process control to concurrently monitor the mean and range of a normally distributed variable.

A sample value is regarded to be a specific source of variation when it exceeds the upper control limit. The upper limit of the common cause variation is also defined using it.

To derive the UCLr, execture the following:

UCLr = (Sum of Range (r)/Total Sample) * D4

Sum of range is = 192

Total Sample = 15
D4 = 2.282

Note that D4 is a control chart constant that is used to compute the upper control limit for range. The value depends on the number of items in the subgroup.

In this case, the number of observations int he subgroup (that is Box Weight) is 4.

Hence;

UCLr = (192/15) * 2.282
UCLr = 29.2096
UCLr [tex]\approx[/tex] 20.210

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