In a test run, a certain car accelerates uniformly from zero to 22.4 m/s in 2.10 s. (a) what is the magnitude of the car's acceleration?

Answer:

Option C, the second one. (B and C are switched)

Step-by-step explanation:

a * a = a2

a * b = +ab

⬇️

2ab

⬆️

b * a = +ba or +ab

Two b's make b2 and don't worry, even with the negative sign it is a b2.

Answer:

40

Step-by-step explanation:

i would say 40? because it will be a constant for how many times you do X. for example if it's Y = 40 (2) it would equal 80 because no matter what number you put in X 40 will have to be multiplied

If the three sides of the triangle is (x + 5), (2x - 3), (21 - x), then the perimeter of the triangle is 23 + 2x

The perimeter of the triangle is the summation of all three sides of the triangle

Perimeter = a + b + c

= (x + 5) + (2x - 3) + (21 - x)

= 2x + 23

= 23 + 2x

Therefore, if the three sides of the triangle is (x + 5), (2x - 3), (21 - x) then the perimeter of the triangle  23 + 2x.

Any two-dimensional figure's perimeter is determined by the space surrounding it. By adding the lengths of the sides, we can determine the perimeter of any closed shape.

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The annual percentage yield (APY) to the nearest thousandth of a percent is approximately 4.642%.

To solve the given problem, we can use the compound interest formula:

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

Where:

A is the final amount

P is the principal amount (initial investment)

r is the annual interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the number of years

a. To find the amount after 4 years, we can substitute the values into the formula:

A = 28000(1 + 0.045/4)^(4*4)

Calculating inside the parentheses first:

A = 28000(1 + 0.01125)^(16)

Evaluate (1 + 0.01125)^(16):

A ≈ 28000(1.19235)

A ≈ $33,389.80

Therefore, the amount after 4 years is approximately $33,389.80.

b. To calculate the interest earned, we subtract the principal amount from the final amount:

Interest earned = A - P

Interest earned = $33,389.80 - $28,000

Interest earned = $5,389.80

The interest earned after 4 years is $5,389.80.

c. To find the amount after 1 year, we substitute the values into the formula:

A = 28000(1 + 0.045/4)^(4*1)

Calculating inside the parentheses first:

A = 28000(1 + 0.01125)^(4)

Evaluate (1 + 0.01125)^(4):

A ≈ 28000(1.045)

A ≈ $29,260

Therefore, the amount after 1 year is $29,260.

d. To calculate the interest earned after 1 year, we subtract the principal amount from the final amount:

Interest earned = A - P

Interest earned = $29,260 - $28,000

Interest earned = $1,260

The interest earned after 1 year is $1,260.

e. The annual percentage yield (APY) is a measure of the effective annual rate of return, taking into account the compounding of interest. To calculate the APY, we can use the formula:

APY = (1 + r/n)^n - 1

Where r is the annual interest rate and n is the number of times the interest is compounded per year.

In this case, the annual interest rate is 4.50% (or 0.045) and the interest is compounded quarterly (n = 4).

Plugging in the values:

APY = (1 + 0.045/4)^4 - 1

Using a calculator or software to evaluate (1 + 0.045/4)^4:

APY ≈ (1.01125)^4 - 1

APY ≈ 0.046416 - 1

APY ≈ 0.046416

To convert to a percentage, we multiply by 100:

APY ≈ 4.6416%

The annual percentage yield (APY) to the nearest thousandth of a percent is approximately 4.642%.

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The system of equations that would be used to find the number of boxes of printer paper, represented by p, and the number of printer ribbons, represented by R, that Denny plans to purchase is 11.99p+5.95R = 65.72 and 12.25p+5.80R = 65.75.

According to the question,

We have the following information:

At ACE computers ,a box of paper cost $11. 99 each while printer ribbons cost $5. 95 each. This would result in a total cost of $65. 72. At better computer, a box of paper cost $12. 25 each while printer ribbons cost $5.80 each. This will result in total cost of $65. 75.

Now, the number of boxes of print paper is p and the number of printer ribbons is R.

So, we have the following equations for each case respectively:

11.99p+5.95R = 65.72

12.25p+5.80R = 65.75

Hence, the system of equations that would be used to find the number of boxes of printer paper, represented by p, and the number of printer ribbons, represented by R, that Denny plans to purchase is 11.99p+5.95R = 65.72 and 12.25p+5.80R = 65.75.

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The probability of finding 0 contaminated pieces in  225 g of chocolate is 5.57 X 10⁻⁷.

Here the number of contaminated fragments follows a Poisson process. Hence, let the distribution for the same be X.

Hence we get X ~ Poi(λt)

where λ is the mean no. of contaminated pieces and t is the no. of bars consumed.

For P(X = x) we get [(λt)ˣ  e^(-λt)]/x!

Here λ = 14.4 and t = 1 Hence we will get

P(X = x) = [(14.4)ˣ e⁻¹⁴°⁴]/x!

Here we need to find the probability of the no. of contaminated pieces = 0

Therefore

P(X = 0) = [(14.4)⁰ e⁻¹⁴°⁴]/0!

Hence the probability of finding 0 contaminated pieces in a bar of chocolate is

P(X = 0) =  e⁻¹⁴°⁴

= 5.57 X 10⁻⁷

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Answer:

is it trigonometry...?

Answer:

Step-by-step explanation:

The value of 10x + 3, when x satisfies the equation 5x + 6 = 10, is 11.

To find the value of 10x + 3, we first need to solve the equation 5x + 6 = 10 for x. Then, we can substitute the obtained value of x into 10x + 3 to find its value.

Let's solve the equation 5x + 6 = 10:

5x = 10 - 6

5x = 4

x = 4/5

Now, substitute the value of x into 10x + 3:

10(4/5) + 3

(40/5) + 3

8 + 3 = 11

Therefore, the value of 10x + 3, when x satisfies the equation 5x + 6 = 10, is 11.

Complete Question:

If 5x+6=10, what is the value of 10x+3?

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Jon deposits $1,000 at the end of each year for 5 years into a savings account that earns 5% annually. After 10 years, he uses the accumulated amount to purchase a perpetuity that pays P at the end of each year.

The value of P can be calculated using the formula for the future value of an ordinary annuity. The future value of an ordinary annuity formula can be used to determine the accumulated value of a series of equal payments made at regular intervals. In this case, Jon makes deposits of $1,000 at the end of each year for 5 years, earning an annual interest rate of 5%. The future value of this annuity after 5 years can be calculated as follows:

\(FV = P * [(1 + r)^{n - 1}] / r\)

Where FV is the future value, P is the payment amount, r is the interest rate per period, and n is the number of periods. Plugging in the values, we have:

FV = 1000 * \([(1 + 0.05)^{5 - 1}]\) / 0.05

  ≈ 1000 * [1.276281 - 1] / 0.05

  ≈ 1000 * 0.276281 / 0.05

  ≈ 552.562

After 10 years, the accumulated amount will be twice this value, as no further deposits are made. Therefore, the value of the perpetuity, P, is approximately $1,105.12 (twice the calculated value).

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Answer: D

Step-by-step explanation:

The increase in temperature is positive, and the absolute value is always positive. So |-8 - 23| is your answer.

The estimated median price of a single-family home in Charleston/No. Charleston in the 1st Quarter of 2008 is $201,048. If the median price continues to decrease at the same rate for the next two years, the estimated median price of a single-family home in the 1st Quarter of 2011 would be $144,458.

(a) To estimate the median price of a single-family home in the 1st Quarter of 2008, we need to calculate the original price before the 8.15% decrease. Let's assume the original price was P. The price after the decrease can be calculated as P - 8.15% of P, which translates to P - (0.0815 * P) = P(1 - 0.0815). Given that the end of 1st Quarter of 2009 median price was $184,990, we can set up the equation as $184,990 = P(1 - 0.0815) and solve for P. This gives us P ≈ $201,048 as the estimated median price of a single-family home in the 1st Quarter of 2008.

(b) If the median price of a single-family home falls at the same rate for the next two years, we can calculate the price for the 1st Quarter of 2011 using the estimated median price from the 1st Quarter of 2009. Starting with the median price of $184,990, we need to apply an 8.15% decrease for two consecutive years. After the first year, the price would be $184,990 - (0.0815 * $184,990) = $169,805.95. Applying the same percentage decrease for the second year, the price would be $169,805.95 - (0.0815 * $169,805.95) = $156,012.32. Therefore, the estimated median price of a single-family home in the 1st Quarter of 2011 would be approximately $144,458.

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From the given information provided, the cube root of 12,167 by prime factorization method is approximately 23.

You can find the cube root of 12,167 using a calculator or by using the prime factorization method.

Using the prime factorization method, we can express 12,167 as the product of its prime factors:

12,167 = 19 × 641

Since the cube root of a product is equal to the product of the cube roots of the factors, we can find the cube root of 12,167 as follows:

∛12,167 = ∛(19 × 641)

∛12,167 = ∛19 × ∛641

∛12,167 = 2.7144 × 8.0186

∛12,167 = 23.1649 (rounded to four decimal places)

Therefore, the cube root of 12,167 is approximately 23.

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If you save $2,015.82 every year at an interest rate of 8%, you can retire in 30 years and live another 25 years while still having enough money to spend $80,000 per year.

To calculate the amount you need to save per year for the next 30 years, we can use the future value of an ordinary annuity formula.

The future value of an ordinary annuity formula is:

\(FV = P \cdot \left(\frac{(1 + r)^n - 1}{r}\right)\)

Where:

FV = Future value of the annuity

P = Payment amount per period

r = Interest rate per period

n = Number of periods

In this case:

P = Amount you need to save per year

r = 8% = 0.08 (annual interest rate)

n = 30 (number of years)

We want the future value (FV) to be equal to the amount needed to spend per year during retirement, which is $80,000.

Using the formula, we can calculate the amount you need to save per year:

\(\$80,000 = P \cdot \left[\left(1 + 0.08\right)^{30} - 1\right] / 0.08\$\)

Simplifying the equation:

\($80000 = P \cdot [1.08^{30} - 1] / 0.08$\)

$80,000 * 0.08 = P * [1.08³⁰ - 1]

$6,400 = P * [1.08³⁰ - 1]

Dividing both sides by [1.08³⁰ - 1]:

\($P = \dfrac{\$6400}{1.08^{30} - 1}$\)

Calculating [1.08³⁰ - 1]:

[1.08³⁰ - 1] ≈ 3.172024

Dividing $6,400 by 3.172024:

P ≈ \($\frac{6,400}{3.172024} \approx$ $2,015.82\) (rounded to the nearest cent)

Therefore, you need to save approximately $2,015.82 per year into your investment account at the end of each year for the next 30 years.

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There are 69300 possible ways of selecting six bottles randomly with two bottles of each variety.

Probability is a branch of mathematics concerned with numerical descriptions of how likely an event is to occur or how likely a statement is to be true. In the given question, we have to select 6 bottles randomly with two bottles of each variety,

= ¹⁰C₂× ⁸C₂ × ¹¹C₂

¹⁰C₂= [1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10] / [(1 × 2)(1 × 2 × 3 × 4 × 5 × 6 × 7 × 8)]

= 90/2

= 45

Similarly,  ⁸C₂  = 28

In the same way ¹¹C₂= 55

= ¹⁰C₂× ⁸C₂× ¹¹C₂

= 45 × 28 × 55

= 69300

Therefore, there are 69300 possible ways of selecting 6 bottles with two bottles of each variety.

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After 15 more years of contributions of $4,000 at the end of each quarter, the retirement account will be worth approximately $760,514.47.

To calculate this, we need to use the formula for the future value of a lump sum. A lump sum is a one-time payment made at the beginning or end of a specific period. In this case, we're looking at the future value of the retirement account after 15 more years of contributions.

Using the given information, we can plug in the values and solve for FV:

PV = $150,000

Pmt = $4,000

r = 10%

n = 4 (since interest is compounded quarterly)

t = 15 years

First, we need to calculate the future value of the current investment of $150,000:

FV1 = $150,000 x (1 + 0.1/4)⁴ ˣ ¹⁵ = $548,534.24

Then, we can calculate the future value of the quarterly contributions of $4,000 over 15 years:

FV2 = $4,000 x [(1 + 0.1/4)⁶⁰ - 1] / (0.1/4) = $211,980.23

Finally, we can add FV1 and FV2 to get the total future value of the retirement account after 15 more years:

Total FV = FV1 + FV2 = $548,534.24 + $211,980.23 = $760,514.47

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Answer:

8

Step-by-step explanation:

∡AB + ∡BC + ∡CD = 180°

∡CD = ∡AE

∡AB + ∡BC + ∡AE = 180°

(8x + 6)° + (6x + 2)° + (7x + 4)° = 180°

8x + 6 + 6x + 2 + 7x + 4 = 180

21x + 12 = 180

21x = 180 - 12

21x = 168

x = 8

The limiting velocity is 17.89 ft/s.

This problem involves solving a differential equation that models the motion of the skydiver under the influence of air resistance and gravity. The differential equation is:

m dv/dt = mg - kv^2

where m is the mass of the skydiver (including equipment), g is the acceleration due to gravity, k is a constant that represents the strength of the air resistance, and v is the velocity of the skydiver.

To solve this differential equation, we need to use separation of variables:

m dv/(mg - kv^2) = dt

Integrating both sides, we get:

(1/k) ln|(mg - kv^2)/mg| = t + C

where C is an arbitrary constant of integration that we will determine later. Solving for v, we get:

v(t) = sqrt((mg/k)) * tanh(sqrt(k/m) * (t + C))

Now we can use the initial conditions to determine the value of C. At t = 0, the skydiver has not yet fallen, so v(0) = 0. Therefore:

C = -tanh^-1(0) = 0

Now we have:

v(t) = sqrt((mg/k)) * tanh(sqrt(k/m) * t)

We are given that the skydiver falls for 14 seconds before opening the parachute. During this time, the air resistance is 0.76 |v|, so k = 0.76. Also, the mass of the skydiver is given as 172 lbf, which is equivalent to 172/32 slugs. Therefore:

m = 172/32 = 5.375 slugs

(a) To find the speed of the skydiver when the parachute opens, we need to evaluate v(14). Using the formula above, with k = 0.76 and m = 5.375, we get:

v(14) = sqrt((mg/k)) * tanh(sqrt(k/m) * 14)

= sqrt((32*5.375/0.76)) * tanh(sqrt(0.76/5.375) * 14)

= 103.51 ft/s

So the speed of the skydiver when the parachute opens is 103.51 ft/s.

(b) To find the distance fallen before the parachute opens, we need to compute the integral of v(t) from t=0 to t=14:

x(14) = integral of v(t) dt from 0 to 14

= (sqrt(mg/k)/sqrt(k/m)) * ln|cosh(sqrt(k/m) * 14)|

= (sqrt(32*5.375/0.76)/sqrt(0.76/5.375)) * ln|cosh(sqrt(0.76/5.375) * 14)|

= 1047.01 ft

So the distance fallen before the parachute opens is 1047.01 ft.

(c) Finally, we need to find the limiting velocity v, which is the value that v(t) approaches as t goes to infinity. When the parachute is open, the air resistance is 151 |v|, so k = 151. Using the formula for v(t) above, with k = 151 and m = 5.375, we have:

v(t) = sqrt((mg/k)) * tanh(sqrt(k/m) * t)

= sqrt((32*5.375/151)) * tanh(sqrt(151/5.375) * t)

As t goes to infinity, tanh(sqrt(151/5.375) * t) approaches 1, so v(t) approaches:

v = sqrt((mg/k)) = sqrt((32*5.375/151)) = 17.89 ft/s

So the limiting velocity is 17.89 ft/s.

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Answer:

Your answer is 21

Hope that this is helpful. Vote and like it

x=3 and y=2 because 6+6 = 12 and 2 times 3 is 6 :)

We have to determine whether the given series converges or diverges. The given series is as follows: `(n+4)! / 4!(n!)` Let's use the ratio test to find out if this series converges or diverges.

The Ratio Test: It is one of the tests that can be used to determine whether a series is convergent or divergent. It compares each term in the series to the term before it. We can use the ratio test to determine the convergence or divergence of series that have positive terms only. Here, a series `Σan` is convergent if and only if the limit of the ratio test is less than one, and it is divergent if and only if the limit of the ratio test is greater than one or infinity. The ratio test is inconclusive if the limit is equal to one. The limit of the ratio test is `lim n→∞ |(an+1)/(an)|` Let's apply the Ratio test to the given series.

`lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `lim n→∞ [(n+5)/4] * [1/(n+1)]` `lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `lim n→∞ (n^2 + 9n + 20) / (4n^2 + 20n + 16)`

As we can see, the limit exists and is equal to 1/4. We can say that the given series converges. The series converges. To determine the convergence of the given series, we use the ratio test. The ratio test is a convergence test for infinite series. It works by computing the limit of the ratio of consecutive terms of a series. A series converges if the limit of this ratio is less than one, and it diverges if the limit is greater than one or does not exist. In the given series `(n+4)! / 4!(n!)`, the ratio test can be applied. Using the ratio test, we get: `

lim n→∞ |(an+1)/(an)| = lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `= lim n→∞ [(n+5)/4] * [1/(n+1)]` `= lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `= 1/4`

Since the limit of the ratio test is less than one, the given series converges.

The series converges to some finite value, which means that it has a sum that can be calculated. Therefore, the answer is a).

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Jina still has to jog a distance of 3(3)/(10) miles to reach her school.

To calculate the remaining distance, we subtract the distance Jina has already covered from the total distance between her house and school.

Given that the total distance from her house to school is 4(1)/(2) miles and Jina has already jogged 1(2)/(5) miles, we can subtract the distance covered from the total distance:

4(1)/(2) - 1(2)/(5) = 4(5)/(10) - 1(4)/(10) = 4(1)/(10) = 3(3)/(10) miles.

Therefore, Jina still has to jog a distance of 3(3)/(10) miles to reach her school.

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Answer:

-2/3 + 0

= 2

– — + 0

3 2

Add — 2/3 and 0 to get – —

3

2

= – —

3

= (–1).2/3 = –0.666666667

the answer is = –0.666666667

Step-by-step explanation:

#Carry on learning

The graph of the exponential function y = 2(9/5)ˣ is attached below

The graph of an exponential function has the general form of y = a^x, where "a" is the base of the exponential function and "x" is the exponent. The graph of an exponential function has some distinctive features:

1. The domain of the function is all real numbers.

2. The range of the function is positive real numbers.

3. The graph of an exponential function always passes through the point (0, 1), because any number raised to the power of zero is one.

As x approaches negative infinity, the graph of the function approaches the x-axis, but never touches it.

As x approaches positive infinity, the graph of the function approaches the y-axis, but never touches it.

4. The graph of an exponential function is always increasing or always decreasing, depending on whether the base "a" is greater than one or less than one, respectively.

5.The graph of an exponential function becomes steeper and steeper as it moves away from the y-axis, indicating that the function is growing or decaying at an increasing rate.

The graph of y = 2(9/5)ˣ is attached below using the table of values given;

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The single-precision floating point representation of 0.5625 in hexadecimal is: 0x3E100000.

Identify the sign bit. In this case, the number is positive, so the sign bit is 0.

Convert the decimal number to binary. The decimal number 0.5625 (or 9/16) can be converted to binary as follows: 0.1001.

Convert the 32-bit binary number to hexadecimal. To do this, group the binary number into blocks of 4, from right to left, and convert each block into its hexadecimal equivalent:

0000 -> 0

0000 -> 0

0000 -> 0

0000 -> 0

0000 -> 0

0001 -> 1

0000 -> 0

0111 -> 7

1110 -> E

0 -> 0

So, the single-precision floating point representation of 0.5625 in hexadecimal is: 0x3E100000.

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Answer:

A

Step-by-step explanation:

go by the equation: a n= a n 1 + (n-1)

so fill that in & you get a n = 112+50(n-1)