Deepak stacked 14 copies of the same book. each book is 1 3/8 inches thick. How high is the stack?

The orbital increased by factor [tex]2^3^/^2[/tex] .Hence, correctander is option D by equation  T²=A³

The relationship between a planet’s orbital period(T) and the planet’s mean distance from the sun(A)  is given by equation T²=A³

Given equation is T²=A³

The distance between the planet X and sun is represented by d

Time-period of the planet X:

T²=d³

Distance between planet Y and the sun is represented by d'

d'= 2d

T'²=d'² = (2d)³ = 8d³

On dividing  (1)and (2).

T'/T = 8d³/d³

=8

=2√2

=[tex]2^3^/^2[/tex]

Hence, the orbital increased by factor [tex]2^3^/^2[/tex] .

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The equation T^2=A^3 shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU. If planet Y is twice the mean distance from the sun as planet X, by what factor is the orbital period increased? A. 2^1/3. B. 2^1/2. C. 2^2/3. D. 2^3/2

Answer:

The list of rational numbers below are ordered from greatest to least.

15, 6.7, , 100%, -55%,

To determine which of the following numbers could NOT be the missing value in the list above, we need to determine the correct order of the numbers in the list.

First, we can convert the percentages to decimals:

100% = 1

-55% = -0.55

Now we can order the numbers from greatest to least:

15, 6.7, 1, -0.55, x

We know that x is a rational number, so it can be expressed as a fraction. We can eliminate answer choices C and D because they are not rational numbers.

Next, we can compare x to the other numbers in the list. We know that x must be less than 6.7, so we can eliminate answer choice A.

That leaves us with answer choice B, -2.5. This number could be the missing value in the list, so the answer is B.

After 4 years of saving $315 per month at 7% annual interest rate, Bernard will have saved approximately $10,864.11.

To calculate the amount that Bernard will have saved after 4 years, we can use the formula for compound interest:

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

Where:

A = the amount of money Bernard will have saved after 4 years

P = the amount of money Bernard is putting into savings each month = $315

r = the annual interest rate = 7% = 0.07

n = the number of times interest is compounded per year (monthly compounding in this case) = 12

t = the number of years = 4

Substituting the given values into the formula, we get:

A = 315(1 + 0.07/12[tex])^{(12\times 4)[/tex]

A = 315(1.00583333[tex])^{48[/tex]

A = 315(1.31564)

A = $10,864.11

Therefore, after 4 years of saving $315 per month at 7% annual interest rate, Bernard will have saved approximately $10,864.11.

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The solution is, the nth term of the sequence is: an = 250 * 0.4(n-1)

To find a formula for the nth term of the sequence 250, 100, 40, we need to first determine the pattern or rule that generates the sequence. If we divide each term by the previous term, we get the following ratios:

100/250 = 0.4

40/100 = 0.4

We can see that each term is obtained by multiplying the previous term by the common ratio of 0.4.

So, the formula for the nth term of the sequence is:

an = a1* r(n-1)

where a1= 250 is the first term, r = 0.4 is the common ratio, and n is the term number.

The solution is, the nth term of the sequence is: an = 250 * 0.4(n-1)

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compplete question:

What is a formula for the nth term of the given sequence 250,100,40

Answer:

6)  $35,198.32

7)  $43,492.33

Step-by-step explanation:

To solve both these problems, we can use the formula for compound interest:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given values:

Substitute the given values into the formula and solve for A:

[tex]A=8000\left(1+\dfrac{0.1}{4}\right)^{4\cdot 15}[/tex]

[tex]A=8000\left(1+0.025\right)^{60}[/tex]

[tex]A=8000\left(1.025\right)^{60}[/tex]

[tex]A=35198.3179905[/tex]

[tex]A=35198.32[/tex]

Therefore, the balance of Anisha's account after 15 years will be $35,198.32.

[tex]\hrulefill[/tex]

Given values:

Substitute the given values into the formula and solve for A:

[tex]A=32500\left(1+\dfrac{0.06}{1}\right)^{1\cdot 5}[/tex]

[tex]A=32500\left(1+0.06\right)^{5}[/tex]

[tex]A=32500\left(1.06\right)^{5}[/tex]

[tex]A=43492.331272[/tex]

[tex]A=43492.33[/tex]

Therefore, Kevin will pay a total of $43,492.33 over the course of the 5 year loan (assuming he doesn't pay any of the loan back over those 5 years).

A circle with Centre [tex](a,b)[/tex]  has the general equation:

[tex](x-a)^2 + (y-b)^2 = r^2[/tex]

where [tex]r[/tex] is the radius and [tex](a,b)[/tex] is the Centre.

Given that the Centre is at [tex](0,9)[/tex], the equation is as follows:

[tex](x-0)^2 + (y-9)^2 = r^2[/tex]

If we simplify, we get:

[tex]x^2 + (y-9)^2 = r^2[/tex]

The fact that the circle comprises the coordinates  [tex](65,12)[/tex]  is also provided. Therefore, we may change these values into the equation and find [tex]r[/tex]:

[tex]65^2 + (12-9)^2 = r^2[/tex]

[tex]4225 + 9 = r^2[/tex]

[tex]r^2 = 4234[/tex]

When we square the two sides, we obtain:

[tex]r = \sqrt{4234}[/tex]

The circle's equation is as follows:

[tex]x^2 + (y-9)^2 = 4234[/tex]

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Answer:

L'' = (6, - 5 )

Step-by-step explanation:

the translation rule (x, y ) → (x + 3, y - 3 ) means

add 3 to the original x- coordinate and

subtract 3 from the original y- coordinate

then

L (3, - 2 ) → L'' (3 + 3, - 2 - 3 ) → L'' (6, - 5 )

The tax deduction is explained below.

We need to take into account a few things in order to establish how much, if any, of the $1,000,000 loss Ethan may deduct in the current year.

We need to know Ethan's basis in his ELS shares, or shareholder basis. Shareholder basis, which is changed yearly based on numerous criteria such as income, losses, donations, and payouts, symbolizes the investment a shareholder has in the S corporation.

Ethan might be entitled to deduct the loss up to the amount of his basis if his basis is positive.

We must assess if Ethan is covered by the at-risk regulations. The shareholder's amount at risk in the S corporation is the only amount that can be deducted for losses under the at-risk regulations.

If Ethan is subject to these rules, his loss deduction could be limited based on his at-risk amount.

A few tax provisions were temporarily changed as a result of the CARES Act. The CARES Act specifically altered the exclusions for business losses for non-corporate taxpayers, including individual S company shareholders. Ethan might not be able to deduct the $1,000,000 loss because of restrictions on company losses that existed prior to the CARES Act.

The excess business loss limitation for non-corporate taxpayers was temporarily suspended under the CARES Act.

This meant that Ethan and other individual shareholders could write off business losses without being constrained by the prior cap of $250,000 ($500,000 for married taxpayers filing jointly).

Therefore, regardless of any restrictions that could have existed before to the passage of the CARES Act, Ethan would be permitted to deduct the entire $1,000,000 loss in the current year if the CARES Act is applicable.

Taxpayers were temporarily helped by being able to deduct losses from other income. It's crucial to remember that the CARES Act was passed in reaction to the COVID-19 outbreak and that some of its requirements could not be in force at the moment.

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Answer:

Hard bop energetic and emotional style of music developed in response to cool jazz and featured fast tempos, loud dynamics, and blues and gospel influences.

Step-by-step explanation:

The nearest tenth of a percent an interest rate of 4.5% would be required for Luke to end up with $8,900 after 5 years with daily compounding.

The formula for compound interest to solve the problem:

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

A is the final amount, P is the initial principal, r is the interest rate, n is the number of times the interest is compounded per year and t is the time in years.

P = $7,600

A = $8,900

t = 5 years

n = 365 (compounded daily)

The interest rate r.

Rearrange the formula and solve for r:

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

Substituting the values we know:

r = [tex]365[(8,900/7,600)^{(1/(5 \times 365))} - 1][/tex]

≈ 4.5%

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The number of pounds of 40% alloy and 61% alloy required to make the third alloy containing 46% aluminum is 16.29 pounds and 40.71 pounds respectively.

Let

[tex]\sf x + y = 57[/tex]

[tex]\sf 40x + 61y = 46\times57[/tex]

[tex]\sf x + y = 57[/tex]

[tex]\sf 40x + 61y = 2622[/tex]

Solve simultaneously

From (1)

[tex]\sf x = 57 - y[/tex]

Substitute into (2)

[tex]\sf 40x + 61y = 2622[/tex]

[tex]\sf 40(57-y) + 61y = 2622[/tex]

[tex]\sf 2280 -40y+61y = 2622[/tex]

[tex]\sf -40y+61y = 2622-2280[/tex]

[tex]\sf 21y = 342[/tex]

[tex]\sf y = \dfrac{342}{21}[/tex]

[tex]\sf y = 16.29 \ pounds[/tex]

Substitute y = 16.29 pounds into (1)

[tex]\sf x + y = 57[/tex]

[tex]\sf x + 16.29 = 57[/tex]

[tex]\sf x = 57 - 16.29[/tex]

[tex]\sf x = 40.71 \ pounds[/tex]

So therefore, the number of pounds of 40% alloy and 61% alloy is 16.29 pounds and 40.71 pounds respectively.

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Answer:

To simplify the expression |2(11-3)/2|^2, we follow the order of operations (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right).

First, simplify the expression inside the absolute value:

2(11-3)/2 = 2(8)/2 = 16/2 = 8

Now, simplify the absolute value of 8, which is simply the magnitude of 8:

|8| = 8

Finally, square the result:

8^2 = 8 * 8 = 64

Therefore, the simplified value of |2(11-3)/2|^2 is 64.

Step-by-step explanation:

The measure of angle a is 35°

The chord of a circle is the line segment joining any two points on the circumference of the circle.

The diameter is the longest chord of a circle which passes through the center of the circle.

For chords that meet inside of a circle, the measure of the angle formed is one-half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Using the above concept (That is the given hint in the question), we can say:

∠a = (29 + 41)/2

∠a = 70/2

∠a = 35°

Therefore, the measure of angle a is 35°

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Complete Question

Check attached image

Answer: line a is parallel to line b

Step-by-step explanation:

the only 2 lines they're talking abt are line a and line b

The factorization of p(x) is p(x) = (x + 5)^2 (x - 3).

There are different methods to find the zeros of a polynomial, but one common approach is to use the Rational Root Theorem to test possible rational roots and then use polynomial division to factor out the roots found.

The Rational Root Theorem states that if a polynomial with integer coefficients has a rational root p/q (where p and q are integers with no common factors other than 1), then p must divide the constant term and q must divide the leading coefficient.

In the case of p(x) = x³ + x² + 8x - 60, the constant term is -60 and the leading coefficient is 1, so the possible rational roots are of the form p/q, where p is a factor of -60 and q is a factor of 1. Therefore, the possible rational roots are ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20, ±30, ±60.

Since the remainder is not zero, x = 1 is not a root of p(x). We can repeat this process with each possible root until we find all the actual roots.

Using this method, we find that the zeros of p(x) are:

x = -5 (with multiplicity 2) and x = 3.

Therefore, the factorization of p(x) is:

p(x) = (x + 5)² (x - 3)

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The profit as a percentage of the cost price​ is 20%

From the question, we have the following parameters that can be used in our computation:

The profit is the difference beyween the selling price and the coste price

So, we have

Profit = 540000 - 450000

Evaluate

Profit = 90000

Next, we have

Percentage = Profit/Cost price * 100

This gives

Percentage = 90000/450000* 100

Evaluate

Percentage = 20%

Hence, teh percentage is 20%

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Answer:

Step-by-step explanation:

To find the profit as a percentage of the cost price, we need to calculate the profit first.

Profit = Selling price - Cost price

Profit = #540,000 - #450,000

Profit = #90,000

Now we can calculate the profit percentage as follows:

Profit percentage = (Profit / Cost price) x 100

Profit percentage = (#90,000 / #450,000) x 100

Profit percentage = 20%

Therefore, the profit as a percentage of the cost price is 20%.

Answer:

a] 24.5; b] 2.8; c] 39.59.

Step-by-step explanation:

a. after t=1sec:

h(1)=-4.9*1²+27*1+2.4; ⇔h(1)=24.5 [m];

b. more than 30 [m] heigh:

-4.9t²+27t+2.4≥30; ⇔ 4.9t²-27t+27.6≤0; ⇔(t-1.35)(t-4.15)≤0;

Δt≈4.15-1.35=2.8 [sec];

c. maximum height:

h'(t)=-9.7t+27; ⇒ h'(t)=0, ⇒ -9.7(t-2.78)=0; ⇒ t=2.78 [sec], then

[tex]h_{max}=h(2.78)=-4.9*2.78^2+27*2.78+2.4=39.59[m].[/tex]

Compare the linear relationships shows that

Equation B has the greater slope. It has a slope of 106, and Equation A has a slope of 58, which is smaller.

Equation A is given as y = 58x

The slope is 58

For Equation B  

Slope of Equation B = (change in y) / (change in x)

= (729 - 623) / (13 - 12)

= 106 / 1

= 106

Comparing the slopes, we can see that the slope of Equation B (106) is greater than the slope of Equation A (58)

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the unit rate is 4 meters per second, meaning that for every second that passes, the distance increases by 4 meters.

The table shows the relationship between time and distance time is measured in seconds and distance is measured in meters.

The table provides us with the data points of time and distance allows us to examine the relationship between these two variables.

The table as time increases the distance also increases.

This suggests that there is a positive relationship between time and distance.

The unit rate of the relationship tells us how much distance changes for every unit of time.

The unit rate is 4 meters per second meaning that for every second that passes, the distance increases by 4 meters.

The relationship shown in the table is not necessarily a linear relationship.

A linear relationship would mean that the distance changes by the same amount for each unit of time.

The increase in distance is not constant over time.

From 5 seconds to 10 seconds the distance increases by 20 meters but from 10 seconds to 15 seconds the distance increases by 20 meters again and from 15 seconds to 20 seconds the distance increases by 20 meters yet again.

The table provides us with a snapshot of the relationship between time and distance and by examining the data we can identify patterns and relationships that can help us understand the behavior of these variables.

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The probability that at least one barrel develops a leak over a 20-year period is approximately 0.1813 or 18.13%.

Since leaks in different barrels are independent, the probability that none of the 10,000 barrels develops a leak in a given year is:

0.99999¹⁰⁰⁰⁰ = 0.9048

Therefore, the probability that at least one barrel develops a leak in a given year is:

1 - 0.9048 = 0.0952

Now we can use the same approach to find the probability that no barrel develops a leak in 20 years:

0.99999²⁰⁰⁰⁰⁰ = 0.8187

Therefore, the probability that at least one barrel develops a leak over a 20-year period is:

1 - 0.8187 = 0.1813

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Answer:

The option that the margin of error accounts for in the given interval is sampling variation.

Step-by-step explanation:

Answer:

5 burgers and 7 milkshakes

Step-by-step explanation:

1.5x5=7.5

2x7=14

7.5+14=21.5

The box plot contains a median of 9, Q1 as 7, and Q3 as 12.

The Smallest: value is 5 and the largest value is 15.

Option B is the correct answer.

We have,

To find the median, we need to arrange the numbers in order:

5, 6, 8, 9, 9, 11, 11, 13, 15

The median is the middle number, which is 9.

To find the quartiles, we first need to find the median of the lower half and upper half of the data.

Lower half: 5, 6, 8, 9, 9

Upper half: 11, 11, 13, 15

To find Q1, we find the median of the lower half:

(6 + 8)/2 = 7

To find Q3, we find the median of the upper half:

(11 + 13)/2 = 12

The smallest number is 5 and the largest number is 15.

Therefore,

Median: 9

Q1: 7

Q3: 12

Smallest: 5

Largest: 15

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Answer:

To calculate the distance around the outside of the circular fire pit (circumference), we can use the formula:

Circumference = π × diameter

Given that the diameter of the pit is 3 feet, we can substitute this value into the formula:

Circumference = π × 3 feet

For the exact distance, we can use the value of π (pi) as 3.14159 (approximately):

Circumference ≈ 3.14159 × 3 feet

Circumference ≈ 9.42477 feet

For the approximate distance, we can round π to 3:

Circumference ≈ 3 × 3 feet

Circumference ≈ 9 feet

To calculate the area inside the circular fire pit, we can use the formula:

Area = π × (radius)^2

The radius is half of the diameter, so in this case, the radius is 1.5 feet.

For the exact area, using π as 3.14159:

Area ≈ 3.14159 × (1.5 feet)^2

Area ≈ 7.06858 square feet

For the approximate area, rounding π to 3:

Area ≈ 3 × (1.5 feet)^2

Area ≈ 6.75 square feet

Therefore, the homeowner would need to buy approximately 9 bricks to outline the pit, and approximately 7.07 square feet of sand to cover the space inside the pit (or approximately 6.75 square feet if rounding to a whole number).

Step-by-step explanation:

Pythagorean theorem is represented by triangle B.

In this question we find four cases of triangle, of which we must determine what triangle can be explained by Pythagorean theorem. This theorem offers a relationship between the three sides of the triangle:

r² = x² + y²

Where:

Please notice that hypotenuse is the longest side of the triangle. Graphically speaking, there is a right triangle, that is, a triangle with one right angle. Then, triangle B express the relationship according to Pythagorean theorem.

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Answer:

$690

Step-by-step explanation:

To find the interest earned in three years, we can use the interest formula

Interest = Principal x Rate x Time

- Principal = $600 (the amount John deposited)

- Rate = 5% per year (as a decimal, this is 0.05)

- Time = 3 years

Interest = $600 x 0.05 x 3 = $90

Therefore, John will earn $90 in interest over 3 years.

To find his account balance, including interest, after 3 years, we can simply add the interest earned to the original principal:

Account balance = Principal + Interest

Account balance = $600 + $90 = $690

Therefore, John's account balance, including interest, after 3 years will be $690.

Answer:

Simple interest: 690, compound interest: 694.5

Step-by-step explanation:

Simple interest  = PRT/100 = 600*5*3/100 = 90 = 600+90 = 690

compound interest = P(1+r/100)^n = 600(1+5/100)^3 = 694.5

Your answer depends on if its simple or compound interest if not said so either of the answers I have given to you is right :)

Answer:

The correct answer is (D) 4/5.

Step-by-step explanation:

First, we need to find the number of cars that are neither red nor have a backup camera.

Number of cars that are not red = 50 - 12 = 38

Number of cars that do not have a backup camera = 50 - 10 = 40

Number of cars that are neither red nor have a backup camera = 38 + 10 - 50 = 8

Therefore, the probability of selecting a car that is not red and does not have a backup camera is:

P(not red and no backup camera) = 8/50

Simplifying:

P(not red and no backup camera) = 4/25

So the correct answer is (D) 4/5.

The profit function is given as follows:

P(x) = -0.5x² + 53x - 300.

The profit if 53 mowers are sold is given as follows:

P(53) = -$1,598.5. (loss).

The profit function is obtained as the subtraction of the revenue function by the cost function, as follows:

P(x) = R(x) - C(x).

The functions for this problem are given as follows:

Hence the profit function is given as follows:

P(x) = -0.5x² + 91x - (38x + 300)

P(x) = -0.5x² + 53x - 300.

The profit if 53 mowers are sold is given as follows:

P(53) = -0.5(53)² + 53(2) - 300

P(53) = -$1,598.5.

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Answer: x= 3

Step-by-step explanation:

We solve the given equation to obtain value of x

Step 1: We open the bracket:

8x-6-8=4+2x

Step 2: We transform terms with x to left hand side and constants to the right hand side and change their signs

8x-2x=4+6+8

6x=18

x=18/6

Thus, x=3

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A reason that completes the proof for step 6 include the following: A. Definition of midsegment.

In Mathematics and Geometry, a midsegment can be defined as a type of line segment that is typically used for connecting the midpoints of two (2) sides of a triangle.

In order to prove that a midsegment is parallel to the median, it is imperative that the definition of the midsegment must be applied.

According to the definition of the midsegment, which states that a line segment connects the midpoints of the two (2) sides of a given triangle (ΔMNO), we can logically deduce the following:

P' = (r, s)

Q' = (r + t, s)

R' = (t, 0)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.