Change 61.5 km into metres.

Answer:

8.2

Step-by-step explanation:

The absolute value of a number is just how far away the number is from 0 (zero) on a number line. For example, -5 is 5 units away from 0 on a number line, meaning that the absolute value of -5 is 5.

In this case, -8.2 is 8.2 units away from 0 on a number line, meaning that the absolute value of -8.2 is 8.2.

Answer: 1875

Step-by-step explanation:

The nth term of a geometric progression is given as:

= ar^n-1

Given a = 3 ; r = 5, the nth term will be:

= ar^n-1

= 3 × 5^n-1

The fifth term will be:

= 3 × 5^n-1

= 3 × 5^5-1

= 3 × 5⁴

= 3 × 625

= 1875

The fifth term is 1875

The given statement is true. If f '(x) < 0 for 7 < x < 10, then f is decreasing on (7, 10).

If f '(x) < 0 for 7 < x < 10, then f is decreasing on (7, 10).

Declining Function: A function f is said to be decreasing on an interval I if for any two values x₁ and x₂ in I, with x₁ < x₂, then f (x₁) > f (x₂).

Since f '(x) < 0 for 7 < x < 10, it implies that the slope of the tangent line to the curve at every point in the interval (7,10) is negative. That means the graph of f is declining in that interval.

Therefore, the given statement is true. If f '(x) < 0 for 7 < x < 10, then f is decreasing on (7, 10).
This is because a negative first derivative, f'(x), indicates that the function is decreasing. The fact that f'(x) < 0 for all values of x in the given interval (7, 10) implies that the function is continuously decreasing throughout that interval.

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Answer:

168 cubic inches

Step-by-step explanation:

The parameters given are:

four 2 in. platys, seven 1 in. guppies, and a 3 in. loach, 

Four 2 inches platys = 4 × 2 = 8 inches

Seven 1 inches guppies = 7 × 1 = 7 inches

A 3 inches leach = 3 inches

The smallest capacity tank you can buy will be

V = 8 × 7 × 3

V = 168 cubic inches

Therefore, the smallest capacity of tank you can buy is 168 cubic inches

Answer: 22 Gallons

Step-by-step explanation:

i. The Fourier transform of (t - 2) - 38(t - 3) is [(jw)^2 + 38jw]e^(-2jw). ii. The Fourier transform of e^(-2t)u(t) is 1/(jw + 2). iii. The Fourier transform of e^(-3t+12)u(t-4) can be obtained using the result of ii. as e^(-2t)u(t-4)e^(12jw). iv. The Fourier transform of e^(-2|t|)cos(t) is [(2jw)/(w^2+4)].

i. To find the Fourier transform of (t - 2) - 38(t - 3), we can use the linearity property of the Fourier transform. The Fourier transform of (t - 2) can be found using the time-shifting property, and the Fourier transform of -38(t - 3) can be found by scaling and using the frequency-shifting property. Adding the two transforms together gives [(jw)^2 + 38jw]e^(-2jw).

ii. The function e^(-2t)u(t) is the product of the exponential function e^(-2t) and the unit step function u(t). The Fourier transform of e^(-2t) can be found using the time-shifting property as 1/(jw + 2). The Fourier transform of u(t) is 1/(jw), resulting in the Fourier transform of e^(-2t)u(t) as 1/(jw + 2).

iii. The function e^(-3t+12)u(t-4) can be rewritten as e^(-2t)u(t-4)e^(12jw) using the time-shifting property. From the result of ii., we know the Fourier transform of e^(-2t)u(t-4) is 1/(jw + 2). Multiplying this by e^(12jw) gives the Fourier transform of e^(-3t+12)u(t-4) as e^(-2t)u(t-4)e^(12jw).

iv. To find the Fourier transform of e^(-2|t|)cos(t), we can use the definition of the Fourier transform and apply the properties of the Fourier transform. By splitting the function into even and odd parts, we find that the Fourier transform is [(2jw)/(w^2+4)].

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Answer:

<D = 130°

Step-by-step explanation:

Supplementary = 180°

<C = 50°

<D = ?

<C + <D = 180°

180° - 50° = 130°

<D = 130°

Answer:

64

Step-by-step explanation:

Answer:

-0.28571428571

Step-by-step explanation:

Answer:

-0.28571428571

Step-by-step explanation:

Answer:

9/4

Step-by-step explanation:

for the line y = 9/4x + 2, its slope is 9/4

The slopes of parallel lines are equal so the slope of the parallel line is also 9/4

Answer:

x = 36 , 2x = 72 , 3x = 108 , 4x = 144

Step-by-step explanation:

2x = P+Q      (ΔABC, exterior angle property)

4x = R+S       (ΔDBC, exterior angle property)

4x + 2x = P+Q+R+S = (P+R) + (Q+S) = (180 - 3x) + (180 -x)  (supplementary)

6x = 360 - 4x

10x = 360

x = 36

2x = 72

3x = 108

4x = 144

check: sum of interior angles = (180 x 4) - (36+72+108+144) = 360

Answer: True

Step-by-step explanation:    

The perm pattern that includes a central rectangle and two sections at each side is the contour pattern.

The contour pattern in a perm involves dividing the hair into three sections, with a rectangular section in the center and two additional sections on each side. The hair is then wrapped around perm rods in a pattern that follows the contour of the head. This pattern is often used to create natural-looking waves or curls.

The other patterns listed - rectangle pattern, spiral bricklay pattern, and alternating oblong pattern - are not typically used in perming hair.

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The power of the hypothesis test is approximately 0.296, or 29.6%. This means that there is a 29.6% chance of correctly rejecting the null hypothesis when the true mean lifetime is 50,000 miles.

The power of a statistical test is the probability of rejecting the null hypothesis when the alternative hypothesis is true. In this case, the null hypothesis is that the mean tire lifetime is at least 50500 miles, and the alternative hypothesis is that it is less than 50500 miles.

To calculate the power of the test, we need to know the true mean lifetime of the tires, which is given as 50000 miles. We also need to know the significance level of the test, which is 5%. This means that if we were to repeat the test many times, we would expect to make a Type I error (rejecting the null hypothesis when it is true) in 5% of cases.

Using a normal distribution with a mean of 50500 miles and a standard deviation of 5500 miles, we can calculate the test statistic for a sample size of 150 tires. The test statistic is:

t = (x - μ) / (s / √n)

where x is the sample mean, μ is the hypothesized mean (50500 miles), s is the standard deviation of the sample, and n is the sample size.

Since we are testing the hypothesis that the mean tire lifetime is less than 50500 miles, we are interested in the left-tailed test. The critical value of t for a one-tailed test with 149 degrees of freedom and a significance level of 5% is -1.655.

If the true mean lifetime is 50000 miles, then the distribution of sample means is centered at 50000 miles. The probability of getting a sample mean less than 50500 miles (the null hypothesis) when the true mean is 50000 miles is the probability of getting a sample mean that is more than 1.655 standard errors below the mean. This probability can be calculated using a standard normal distribution table or a calculator, and is approximately 0.04.

Therefore, the power of the test is 1 - 0.04 = 0.96, or 96%. This means that if the true mean tire lifetime is 50000 miles, we have a 96% chance of correctly rejecting the null hypothesis that the mean is at least 50500 miles, and concluding that it is less than 50500 miles.
To calculate the power of the hypothesis test, follow these steps:

1. State the null hypothesis (H0) and the alternative hypothesis (H1).
H0: μ ≥ 50,500 miles
H1: μ < 50,500 miles

2. Determine the significance level (α).
α = 0.05

3. Calculate the standard error of the sample mean.
Standard error (SE) = σ / √n = 5,500 / √150 = 449.44

4. Find the critical value (z-score) that corresponds to the 5% significance level.
Since it's a one-tailed test and α = 0.05, the critical z-score is -1.645.

5. Calculate the test statistic at the true mean (50,000 miles).
Test statistic (z) = (sample mean - true mean) / SE = (50,500 - 50,000) / 449.44 ≈ 1.11

6. Calculate the power by finding the probability of rejecting H0 when H1 is true.
Since the test statistic is 1.11 and the critical value is -1.645, we need to find the area to the left of -1.645 + 1.11 = -0.535. Using a standard normal table or calculator, the probability (power) is approximately 0.296.

The power of the hypothesis test is approximately 0.296, or 29.6%. This means that there is a 29.6% chance of correctly rejecting the null hypothesis when the true mean lifetime is 50,000 miles.

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Answer:

it should be -8 and -65 you would use parentheses first then you would have the negative integers in it's place

i) The mean of x is 68.33 grams.

ii) The standard deviation of x is 2.23 grams.

A standard deviation or (σ ) is a measurement of the data's dispersion from the mean. A low standard deviation indicates that data are concentrated around the mean, whereas a high standard deviation shows that data are more dispersed.

If the standard deviation is close to zero, the data points are close to the mean; otherwise, if the standard deviation is high or low, the data points are, respectively, above or below the mean.

i) Properties of expected values establish that

\($\mathrm{E}(W)=\mathrm{E}(P)+\mathrm{E}\left(X_1\right)+\ldots+\mathrm{E}\left(X_{12}\right)$\)

Because all 12 eggs have the same mean weight, this becomes

\($\mathrm{E}(W)=\mathrm{E}(P)+12 \times \mathrm{E}\left(X_i\right)$\)

We were told that

\($\mathrm{E}(W)=840$ and $\mathrm{E}(P)=20$, so we can solve\)

\($840=20+12 \times \mathrm{E}\left(X_i\right)$ to find $\mathrm{E}\left(X_i\right)=\frac{840-20}{12} \approx 68.33$ grams.\)

ii) Because of independence, properties of variance establish that

\($${Var}(W)={Var}(P)+{Var}\left(X_1\right)+{Var}\left(X_2\right)+\ldots+{Var}\left(X_{12}\right)$$\)

Because all 12 eggs have the same variance of their weights, this becomes

\(${Var}(W)={Var}(P)+12 \times {Var}\left(X_i\right)$\)

We were told that

\(${SD}(W)=7.9\ \text {and}\ {SD}(P)=1.7$ Therefore, ${Var}(W)=(7.9)^2=62.41$ and ${Var}(P)=(1.7)^2=2.89$\)

We can solve

\($ 62.41=2.89+12 \times {Var}\left(X_i\right)$\)

To find

\(${Var}\left(X_i\right)=\frac{62.41-2.89}{12}=4.96$\)

Thus, SD\((X_i\right))=\sqrt{(4.96)} \approx\) 2.23 grams.

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Answer:

3 + 3 = 6

8 + 8 + 8 = 24

24 + 6 = 30

31 - 30 = 1

1 inch of the board is left

Answer: 19/20000000

Step-by-step explanation:

To find the 4th order Newton's divided-difference interpolating polynomial for f(x)=ln(x) with x=1,4,5,6,8, we first need to calculate the divided differences:

A. (a) The 4th order Newton's divided-difference interpolating polynomial for the function f(x) = ln(x) using the given data points is:

P(x) = ln(1) + (x - 1)[(ln(4) - ln(1))/(4 - 1)] + (x - 1)(x - 4)[(ln(5) - ln(4))/(5 - 4)(5 - 1)] + (x - 1)(x - 4)(x - 5)[(ln(6) - ln(5))/(6 - 5)(6 - 1)] + (x - 1)(x - 4)(x - 5)(x - 6)[(ln(8) - ln(6))/(8 - 6)(8 - 1)]

B. (a) To find f(x) at x = 7 and x = 9 using the interpolating polynomial, substitute the respective values into the polynomial expression P(x) obtained in the previous part.

Explanation:

A. (a) The 4th order Newton's divided-difference interpolating polynomial can be constructed using the divided-difference formula and the given data points. In this case, we have five data points: (1, ln(1)), (4, ln(4)), (5, ln(5)), (6, ln(6)), and (8, ln(8)). We apply the formula to calculate the polynomial.

B. (a) To find the value of f(x) at x = 7 and x = 9, we substitute these values into the polynomial P(x) obtained in the previous part. For x = 7, substitute 7 into P(x) and evaluate the expression. Similarly, for x = 9, substitute 9 into P(x) and evaluate the expression.

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Answer: 6 & 10 (Just to backup the other person. ^)

Step-by-step explanation:

Right on Edge. 2022

The concept of consecutive integers is explained as follows:

Consecutive numbers, or consecutive integers, are integers that follow each other in order. The difference between any two consecutive numbers is always 1. For example, the consecutive numbers starting from 1 would be 1, 2, 3, 4, 5, and so on. Similarly, the consecutive numbers starting from -3 would be -3, -2, -1, 0, 1, 2, and so on.

It is important to note that if we have a consecutive sequence of integers, one number will be even, and the next number will be odd. This is because the parity (evenness or oddness) alternates as we move through consecutive integers.

Furthermore, the sum of two consecutive numbers (and, in fact, the sum of any number of consecutive numbers) is always an odd number. This is because when we add an even number to an odd number, the result is always an odd number.

To generate a sequence of consecutive integers, we can start with any integer n and then use n, n+1, n+2, and so on to obtain consecutive integers. For example, if n is an integer, then n, n+1, and n+2 will be consecutive integers.

Here are some examples of consecutive integers:

- Starting from 1: 1, 2, 3, 4, 5, ...

- Starting from -3: -3, -2, -1, 0, 1, 2, ...

- Starting from 1004: 1004, 1005, 1006, 1007, ...

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Answer:

400

Step-by-step explanation:

10 packs makes 1 bracelet and there's 10 beads in each pocket.

400 beads in total

Answer: This is neither a permutation or a combination. It is a trick question.

Step-by-step explanation: To solve this question, you would just multiply the two numbers by each other. So in this case it would be 8*3 because of the fundamental counting principle.

Total number of outcomes (n) = 2

Let E be the event of getting a yellow colored side of the coin.

Therefore, n(E) = 1

Therefore, P(E) = n(E)/n = 1/2

Answer:

1/2

Hope it helps.

If you have any query, feel free to ask.

The y-intercept of a function happens when the function "cuts" the y-axis.

This can be calculated as the value of the function f(x) when x=0.

Then, if we replace x by 0, we get the y-intercept:

The y-intercept for this function is f(0)=18.

Answer:

need points srry

Step-by-step explanation:

Answer:3/4

Step-by-step explanation:

18/24=6/8=3/4

Answer:

18/24

Step-by-step explanation:

There are 24 hours in a day.
The cat sleeps 18 hours of the 24 hour day.
Therefore, the fraction is 18/24.

Answer:

slope = -2

Step-by-step explanation:

(-5,2) (-8,8)

equation to find slope: \(\frac{y1 - y2}{x1 - x2}\)

\(\frac{2-8}{-5+8}\) = \(\frac{-6}{3}\) = \(\frac{-2}{1}\) = -2

The volume of the rectangular block is 128 cm³ and the volume of each of the block after reduced to half is 64 cm³, half of the original volume.

Volume of a three dimensional shape is the space occupied by the shape.

Given that, for a wood block,

Length = 4 cm

Width = 4 cm

Height = 8 cm

Volume of a rectangular block = Length × Width × Height

                                                   = 4 cm × 4 cm × 8 cm

                                                   = 128 cm³

Then, imagine that you are cutting the block into 2 exactly equal halves.

Height of each of the block reduced to half.

Height of one block = 8 cm / 2 = 4 cm

Volume of each block = Length × Width × Height

                                     = 4 cm × 4 cm × 4 cm

                                     = 64 cm³

Volume of each block = 64 cm³ = 128 cm³ / 2 = Original volume / 2

Hence when the height is reduced to half, volume of each of the block is half the volume of whole block.

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Answer:

6/250, 9/375, etc...

Step-by-step explanation:

multiply(GIANT ONE)

3/125 x 2/2 = 6/250

3/125 x 3/3 = 9/375