8%
Area of a circle
Find the area of a circle with a radius of 8.
Either enter an exact answer in terms of me or use
3.14 for n and enter your answer as a decimal.
units

Answer:

The area of a rectangle is given by the formula A = L x W where A is the area, L is the length, and W is the width.

To find how fast the area of the rectangle is increasing, we need to differentiate the formula for A with respect to time t:

dA/dt = d/dt(L x W)

Using the product rule of differentiation, we get:

dA/dt = dL/dt x W + L x dW/dt

Given that dL/dt = 5 cm/s, dW/dt = 4 cm/s, L = 9 cm, and W = 6 cm, we can substitute these values in the above formula to get the rate at which the area of the rectangle is increasing:

dA/dt = (5 cm/s) x (6 cm) + (9 cm) x (4 cm/s)

dA/dt = 30 cm^2/s + 36 cm^2/s

dA/dt = 66 cm^2/s

Therefore, the area of the rectangle is increasing at a rate of 66 cm^2/s when the length is 9 cm and the width is 6 cm.

Answer:

Each piece is 1/7 m long

Step-by-step explanation:

Wire length = 3/7 m

Pieces = 6

1 piece = 3/7 ÷ 6

= 3/7 ÷ 6/1

= 3/7 × 1/6

= 1/7 m

Answer:

0.8632

0.8696

Step-by-step explanation:

Your answer is accurate, but it's not the most precise option.

f(x) is decreasing and concave up on the interval.  Therefore, trapezoidal rule will give us an area greater than the actual area, but closer than left-hand rule.

If f(x) were a straight line, then midpoint rule would give us the same area as trapezoidal rule.  However, since f(x) is concave up, the midpoint is less than the average of the endpoints.  So midpoint rule will give us an area less than the actual area, but closer than right-hand rule.

You would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

To find the range in which you would expect to find the middle 98% of most pregnancies, you can use the concept of z-scores and the standard normal distribution.

For the given data:

Mean (μ) = 269 days

Standard deviation (σ) = 17 days

To find the range, we need to find the z-scores corresponding to the 1% and 99% percentiles. Since the normal distribution is symmetric, we can find the z-scores by subtracting and adding the respective values from the mean.

To find the z-score for the 1% percentile (lower bound):

z1 = Φ^(-1)(0.01)

Similarly, to find the z-score for the 99% percentile (upper bound):

z2 = Φ^(-1)(0.99)

Now, we can calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

To find the corresponding values in terms of days, we multiply the z-scores by the standard deviation and add/subtract them from the mean:

lower bound = μ + (z1 * σ) = 269 + (-2.33 * 17) ≈ 229.4 days

upper bound = μ + (z2 * σ) = 269 + (2.33 * 17) ≈ 308.6 days

Therefore, you would expect to find the middle 98% of most pregnancies between approximately 229.4 days and 308.6 days.

Now, let's consider drawing samples of size 58 from this population. The mean and standard deviation of the sample means can be calculated as follows:

Mean of sample means (μ') = μ = 269 days

Standard deviation of sample means (σ') = σ / sqrt(n) = 17 / sqrt(58) ≈ 2.229

To find the range in which you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample, we repeat the previous steps using the mean of the sample means (μ') and the standard deviation of the sample means (σ').

Now, calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

Multiply the z-scores by the standard deviation of the sample means and add/subtract them from the mean of the sample means:

lower bound = μ' + (z1 * σ') = 269 + (-2.33 * 2.229) ≈ 264.0 days

upper bound = μ' + (z2 * σ') = 269 + (2.33 * 2.229) ≈ 274.1 days

Therefore, you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

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Answer:

The hourly decay rate is of 1.25%, so the hourly rate of change is of -1.25%.

The function to represent the mass of the sample after t days is \(A(t) = 810(0.74)^t\)

Step-by-step explanation:

Exponential equation of decay:

The exponential equation for the amount of a substance is given by:

\(A(t) = A(0)(1-r)^t\)

In which A(0) is the initial amount and r is the decay rate, as a decimal.

Hourly rate of change:

Decreases 26% by day. A day has 24 hours. This means that \(A(24) = (1-0.26)A(0) = 0.74A(0)\); We use this to find r.

\(A(t) = A(0)(1-r)^t\)

\(0.74A(0) = A(0)(1-r)^{24}\)

\((1-r)^{24} = 0.74\)

\(\sqrt[24]{(1-r)^{24}} = \sqrt[24]{0.74}\)

\(1 - r = (0.74)^{\frac{1}{24}}\)

\(1 - r = 0.9875\)

\(r = 1 - 0.9875 = 0.0125\)

The hourly decay rate is of 1.25%, so the hourly rate of change is of -1.25%.

Starts out with 810 grams of Element X

This means that \(A(0) = 810\)

Element X is a radioactive isotope such that its mass decreases by 26% every day.

This means that we use, for this equation, r = 0.26.

The equation is:

\(A(t) = A(0)(1-r)^t\)

\(A(t) = 810(1 - 0.26)^t\)

\(A(t) = 810(0.74)^t\)

The function to represent the mass of the sample after t days is \(A(t) = 810(0.74)^t\)

Answer:

-12

Step-by-step explanation:

Answer:

8(3+4p)

Step-by-step explanation:

8 goes into 24 and 32, so it can be factored out:

\(24+32p=8(3+4p)\)

Answer:

8(3 + 4p)

Step-by-step explanation:

Factor 24 + 32p

First, factor out the GCF. In this case, the GCF is 8, and we have

8(3 + 4p)

We can't factor anymore so the answer is 8(3 + 4p)

Answer:

142.857

BRAINLIEST, please!

Step-by-step explanation:

2000 / x = 14

x = 2000 / 14

x = 142.857 (about)

To rewrite the expression -2(n-7) using the distributive property, we need to distribute the -2 to both terms inside the parentheses. The distributive property states that for any numbers a, b, and c:

a(b + c) = ab + ac

Applying this property to the given expression:

-2(n-7) = -2 * n + (-2) * (-7)

Simplifying further:

-2(n-7) = -2n + 14

Therefore, the rewritten expression is -2n + 14.

Answer:8

Step-by-step explanation:8x1=8

Answer:

170

Step-by-step explanation:

Answer:

all correct except A.

Step-by-step explanation:

pls mark me brainly if u can

Their exam must have been scheduled on Wednesday, allowing them to start hiking on Thursday after the exams.

To determine the day of the week on which Kai and Finley's exam was scheduled, we need to consider the information provided about the trail being closed on Mondays, Wednesdays, and weekends.

If they had planned to hike to the log cabin for two days after the exams, and the trail is closed on weekends, it means they cannot start hiking on Saturday or Sunday.

Since they cannot start hiking on Saturday or Sunday, the two possible options for the exam day would be Monday or Wednesday, as they have not specified whether the hike starts immediately after the exams or the day after.

However, we can conclude that their exam was not scheduled on Monday, as the trail is closed on Mondays, and they had planned to hike immediately after the exams.

Therefore, their exam must have been scheduled on Wednesday, allowing them to start hiking on Thursday after the exams.

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The unpaid balance after three years is approximately $26971.

The down payment is 25% of $21,000, which is:

Down payment = 0.25 x $21,000 = $5,250

So the amount financed is:

Amount financed = $21,000 - $5,250 = $15,750

We can use the formula for the unpaid balance on a loan to find the unpaid balance after three years. The formula is:

Unpaid balance = P((1 + r)ⁿ - (1 + r)ᵇ)/(1 + r)ⁿ - 1

where:

P = principal (amount financed)

r = monthly interest rate

n = total number of payments

b = number of payments already made

The monthly interest rate is 9%/12 = 0.0075, and the total number of payments is 6 x 12 = 72.

After three years, the number of payments made is 3 x 12 = 36.

Substituting the values into the formula, we get:

Unpaid balance = $15,750((1 + 0.0075)⁷² - (1 + 0.0075)³⁶)/(1 + 0.0075)⁷² - 1

                          = 15750(1.71255270682)-(0.76414896061)-1

Unpaid balance ≈ $26971

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Answer:

ill be figuring this out rn, (theres a caculator thingy online if nobody helps u)

Step-by-step explanation:

44.4 is the Percent and as a fraction its

111/250 (thats what i got)

6.66 as a dec. and as a fraction its 333/50

sorry if these are wrong bur its what i got.

Answer: 214.8

Step-by-step explanation:

First move the decimal to the right, in this case 8.95 = 895., then multiply the 24 by 895. to get 21480., you then move the decimal to the left and you get 214.80 or 214.8.

The values of x for which f(x) = 7 are x = 61 and x = 21.

To find the values of x for which f(x) = 7, we can set up the equation and solve for x.

The given function is f(x) = 0.5|x - 41| - 3.

Setting f(x) equal to 7, we have:

0.5|x - 41| - 3 = 7.

First, let's isolate the absolute value term:

0.5|x - 41| = 7 + 3.

0.5|x - 41| = 10.

To remove the absolute value, we can consider two cases:

Case: (x - 41) is positive or zero:

0.5(x - 41) = 10.

Multiplying both sides by 2 to get rid of the fraction:

x - 41 = 20.

Adding 41 to both sides:

x = 61.

So x = 61 is a solution for this case.

Case: (x - 41) is negative:

0.5(-x + 41) = 10.

Multiplying both sides by 2:

-x + 41 = 20.

Subtracting 41 from both sides:

-x = -21.

Multiplying both sides by -1 to solve for x:

x = 21.

So x = 21 is a solution for this case.

Therefore, the values of x for which f(x) = 7 are x = 61 and x = 21.

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Answer:

14 plates in one stack

Answer:

1/2=10

Step-by-step explanation:

it depends upon the area of the triwngle

Answer:

the slope is 3

Step-by-step explanation:

cause rise over run and its 6/2. the x intercept is 2 if thats helpful?

Answer:

There are totally 280 pages in that book

Step-by-step explanation:

let the total pages be x.

From the question we know that 98 pages are the 35% of total pages...

so,

(98/x)*100 = 35

98/x = 35/100

reciprocal both sides...

x/98 = 100/35

x = 2.857 * 98

x = 280

There are total 280 pages in the textbook.

A percentage is a number or ratio expressed as a fraction of 100.

Given that, in a geography textbook, 35% of the page is coloured and there are 98 coloured pages'

Let the total pages in the textbook be x, then,

35% of x = 98

x = 98*35/100

x = 280

Hence, There are total 280 pages in the textbook.

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The quadrilateral you're describing is a Kite. A kite is a quadrilateral with two pairs of consecutive congruent sides, and its diagonals meet at a right angle.

There are 8 to take Lara and Hayden to volunteer the same number.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Lara already volunteered 50 hours and will volunteer 5 hours more each week.

And, Hayden already volunteered to 10 hours and will volunteer 10 hours each week .

Now, For Lara;

⇒ 50 + 5x

And, For Hayden;

⇒ 10 + 10x

So, For same number of volunteer is,

⇒ 50 + 5x = 10 + 10x

⇒ 50 - 10 = 10x - 5x

⇒ 40 = 5x

⇒ x = 40/5

⇒ x = 8

Thus, There are 8 to take Lara and Hayden to volunteer the same number.

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(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

To solve the exercise using Polya's four-step problem-solving strategy, we will apply the procedures presented in the lesson.

(a) For the series 1+2+3+4+...+392:

Using the arithmetic series formula Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term, we can substitute the values: Sn = (392/2)(1 + 392) = 196(393) = 77,028.

(b) For the series 1+2+3+4...x:

To find the sum of this series, we need to know the number of terms (n) based on the value of x. Since the series follows a consecutive pattern, the number of terms will be equal to x itself. Thus, the sum of the series would be Sn = (x/2)(1 + x).

(c) For the series 546 + 547 + 548 + 549:

Using the arithmetic series formula Sn = (n/2)(a + l), we can determine the number of terms (n) by subtracting 546 from 549 and then adding 1: n = 549 - 546 + 1 = 4. Substituting the values into the formula: Sn = (4/2)(546 + 549) = 2(1095) = 2,190.

The final answer for each part is:

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

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Answer:

3x - 4 = 32

Step-by-step explanation:

We solve for x to find the number (knowing that x is the unknown number).

3x - 4 = 32

3x = 32 + 4

3x = 36

x/3 = 36/3

x = 12

i)50

Steps

30+20=50

ii)7

Steps

75-(30+20)-18

=75-(50)-18

=7

iii)20

Steps

From the available data from the question

iv)30

Steps

From the available data from the questionl

v)From the attcged image file

Answer:

9

Step-by-step explanation:

3 3/4= 3.75.

3.75-2=1.75

1.75+5.5=7.25 or 7 1/4

7.25+1.75=9

The number of minutes spent higher than 38 meters above the ground on the Ferris wheel ride is approximately 1.0918 minutes.

To solve this problem, we need to determine the angular position of the Ferris wheel when it is 38 meters above the ground.

The Ferris wheel has a diameter of 50 meters, which means its radius is half of that, or 25 meters.

When the Ferris wheel is at its highest point, the radius and the height from the ground are aligned, forming a right triangle.

The height of this right triangle is the sum of the radius (25 meters) and the platform height (4 meters), which equals 29 meters.

To find the angle at which the Ferris wheel is 38 meters above the ground, we can use the inverse sine (arcsine) function.

The formula is:

θ = arcsin(h / r)

where θ is the angle in radians, h is the height above the ground (38 meters), and r is the radius of the Ferris wheel (25 meters).

θ = arcsin(38 / 29) ≈ 1.0918 radians

Now, we know the angle at which the Ferris wheel is 38 meters above the ground.

To calculate the time spent higher than 38 meters, we need to find the fraction of the total revolution that corresponds to this angle.

The Ferris wheel completes one full revolution in 2 minutes, which is equivalent to 2π radians.

Therefore, the fraction of the revolution corresponding to an angle of 1.0918 radians is:

Fraction = θ / (2π) ≈ 1.0918 / (2π)

Finally, we can calculate the time spent higher than 38 meters by multiplying the fraction of the revolution by the total time for one revolution:

Time = Fraction \(\times\) Total time per revolution = (1.0918 / (2π)) \(\times\) 2 minutes

Calculating this expression will give us the answer in minutes.

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Answer:

A

Step-by-step explanation:

By completing the square, y = 2x^2 + 2x +1 will be y=2(x+1/2)^2+(1/2) the minimum point is the vertex of the parabola which is (-1/2, 1/2)