A farmer sells 7.7 kilograms of apples and pears.3/5 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmers market?

Answer:

π³/1296

Step-by-step explanation:

∫ [ (asin x)² dx / √(4 − 4x²) ]

Factoring the denominator:

∫ [ (asin x)² dx / √(4 (1 − x²)) ]

∫ [ (asin x)² dx / (2√(1 − x²)) ]

½ ∫ [ (asin x)² dx / √(1 − x²) ]

If u = asin x, then du = dx / √(1 − x²).

½ ∫ u² du

⅙ u³ + C

Substitute back:

⅙ (asin x)³ + C

Evaluate between x=0 and x=½.

⅙ (asin ½)³ − ⅙ (asin 0)³

⅙ (π/6)³ − ⅙ (0)³

π³/1296

Answer:

[tex]\dfrac{\pi^3}{1296}[/tex]

Step-by-step explanation:

Given integral:

[tex]\displaystyle \int^{1/2}_0 \dfrac{\arcsin^2 (x)}{\sqrt{4-4x^2}}\;dx[/tex]

To evaluate the integral, begin by simplifying the denominator of integrand:

[tex]\begin{aligned}\sqrt{4-4x^2}&=\sqrt{4(1-x^2)} \\ &=\sqrt{4}\sqrt{1-x^2}\\&=2\sqrt{1-x^2}\end{aligned}[/tex]

Therefore:

[tex]\displaystyle \int^{1/2}_0 \dfrac{\arcsin^2 (x)}{2\sqrt{1-x^2}}\;dx[/tex]

Now, evaluate the integral using the method of substitution.

[tex]\textsf{Let $u = \arcsin(x)$}[/tex]

Find du/dx using the common derivative of arcsin(x):

[tex]\boxed{\begin{array}{c}\underline{\textsf{Derivative of $\arcsin(x)$}}\\\\\dfrac{\text{d}}{\text{d}x}\left(\arcsin(x)\right)=\dfrac{1}{\sqrt{1-x^2}}\end{array}}[/tex]

Therefore:

[tex]\dfrac{d}{dx}(u)=\dfrac{d}{dx}\left(\arcsin(x)\right) \\\\\\\dfrac{du}{dx}=\dfrac{1}{\sqrt{1-x^2}}[/tex]

Rearrange to isolate dx:

[tex]dx=\sqrt{1-x^2}\;du[/tex]

Calculate the new limits:

[tex]x=0 \implies u = \arcsin(0)=0[/tex]

[tex]x=\dfrac{1}{2} \implies u = \arcsin\left(\dfrac{1}{2}\right)=\dfrac{\pi}{6}[/tex]

Rewrite the original integral in terms of u and du:

[tex]\displaystyle \int^{\pi / 6}_0 \dfrac{u^2}{2\sqrt{1-x^2}}\;\sqrt{1-x^2}\;du \\\\\\\int^{\pi / 6}_0 \dfrac{u^2}{2}}\;du[/tex]

Evaluate:

[tex]\begin{aligned}\displaystyle \int^{\pi / 6}_0 \dfrac{u^2}{2}}\;du &=\left[\dfrac{u^3}{6}\right]^{\pi / 6}_0\\\\&=\dfrac{\left(\frac{\pi}{6}\right)^3}{6}-\dfrac{(0)^3}{6} \\\\&=\dfrac{\frac{\pi^3}{216}}{6}-0 \\\\ &=\dfrac{\pi^3}{1296}\end{aligned}[/tex]

Therefore, the value of the integral is:

[tex]\Large\boxed{\dfrac{\pi^3}{1296}}[/tex]

Answer:

divide the numbers that are on the paper

Step-by-step explanation:

Answer:

divide

Step-by-step explanation:

hope ur having a good day :)

Answer:

if the side length of a cube = 6, then the surface area of the cube is:

36 + 36 + 36 + 36 + 36 + 36

Step-by-step explanation:

A cube has 6 faces.

so you have to add the faces 6 times to get the total surface area of a cube.

Answer:

Less

Step-by-step explanation:

10 = 10

1/2 < 3/4

1/2 = 50%

3/4 = 75%

Answer:

10 1/2 is less than 10 3/4

Step-by-step explanation:

10 1/2 is 10.5

10 3/4 is 10.75

Answer:

The two‑sample t ‑test is not appropriate because the distributions are not normal and the sample sizes are too small.

Step-by-step explanation:

The complete question is:

The owner of a pita franchise with two locations is interested in the average time that customers spend waiting for service at each store. She believes that the average waiting time at the original location is higher than the average waiting time at the new location.

The pita‑franchise owner has observed in the past that waiting times tend to have a long tail to the right, with most customers served relatively quickly and a few rare customers required to wait a very long time.Is a two‑sample t ‑test appropriate in this setting?The two‑sample t ‑test is appropriate because this is a comparison of the means of two continuous, random variables.The two‑sample t ‑test is not appropriate because the two samples do not have the same size.The two‑sample t ‑test is not appropriate because the sample standard deviations are not equal.The two‑sample t ‑test is not appropriate because the distributions are not normal and the sample sizes are too small.The two‑sample t ‑test is appropriate because the samples are random and contain no outliers, and the populations are normal.

For two sample t-test the distributions must be normal. Here the data, as mentioned in the questions is skewed to the right with long waiting times in the past.

Final answer:

The two-sample t-test is not appropriate for the pita-franchise owner's observations because the waiting times are not normally distributed and the sample sizes are small. A test that does not assume normality, like the Mann-Whitney U test, would be more suitable in this situation.

Explanation:

The two-sample t-test is a statistical method used to determine if the means of two groups are significantly different. One key assumption for a two-sample t-test, however, is that the data should come from populations that are approximately normally distributed, especially if the sample sizes are not large. If the assumption of normality is violated and the sample size is small, as indicated by a distribution with a long tail to the right, the two-sample t-test may not be appropriate. To make an informed decision, it would also be necessary to consider the equality of variances, sample sizes, and independence of the samples.

In the context of a pita-franchise with long-tailed waiting times, the distribution is not normal, indicating that the normality assumption is not met. Consequently, using the two-sample t-test might lead to inaccurate results, especially if the sample sizes are too small to compensate for the lack of normality. In such cases, a different test like the Mann-Whitney U test, which does not assume normality, might be a better choice.

Answer:

See Explanation Below

Step-by-step explanation:

The image of the trianglular prism is missing.

However, I'll answer your question using the attachment below.

The volume of a triangular prism is calculated as follows.

V = ½lbh

Where l = length of the prism

b = base of the prism

h = height of the prism

V = volume of the prism.

From the attachment,

Length, l = 6 cm

Base, b = 3 cm

And Height, h = 4 cm

By substituting each of these values in the formula given above

V = ½lbh becomes

V = ½ * 6 * 3 * 4

V = 3 * 3 * 4

V = 36 cm³

If you follow these steps you'll get the volume of the trianglular prism as it is in your question.

Answer:

its 15

Step-by-step explanation:

ik its 15 because when i put in 24 it was wrong and gave me the awnser which was 15

After a blue marble is drawn and not replaced, the probability of drawing a red marble from the bag containing initially 28 red and 22 blue marbles is 9/16.

The question is asking for the probability of picking a red marble after a blue marble has been picked first and not replaced. The bag originally contains 50 marbles, 28 red ones, and 22 blue ones. After removing one blue marble, there would be 27 red marbles and 21 blue ones left, making a total of 48 marbles.

To find the probability of now drawing a red marble, we divide the number of red marbles by the new total number of marbles:

Probability = Number of Red Marbles / Total Number of Marbles

Probability = 27 / 48

Probability = 9 / 16

Therefore, the probability of drawing a red marble after having already drawn a blue marble and not replacing it is 9/16.

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Answer:

The point estimate is 0.45.

The 95% error margin is 0.042 = 4.2 percentage points.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

Point estimate

We have that [tex]n = 540, x = 243[/tex]

So the point estimate is:

[tex]\pi = \frac{243}{540} = 0.45[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

Error margin:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 1.96\sqrt{\frac{0.45*0.55}{540}}[/tex]

[tex]M = 0.0420[/tex]

The 95% error margin is 0.042 = 4.2 percentage points.

Answer:

Factor the denominators of each expression to find the LCD.

Rename each expression, if needed, by multiplying by a form of one to get the LCD.

Add the numerators, keeping the denominators the same.

If possible, simplify by factoring the numerator and dividing out common factors from both the numerator and denominator.

Step-by-step explanation:

If the assignment your working on is Explaining How to Add Rational Expressions, this is correct according to edg...  Good Luck!!!

Answer:

The critical value that should be used in constructing the interval is T = 5.8408.

The 99% confidence interval for the true mean yield is between 2.943 bushels per acre and 96.268 bushels per acre.

Step-by-step explanation:

We have the standard deviation of the sample, so we use the students t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 4 - 1 = 3

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 3 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 5.8408. This is the critical value.

The margin of error is:

M = T*s = 5.8408*7.99 = 46.668 bushels per acre

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 49.6 - 46.668 = 2.943 bushels per acre.

The upper end of the interval is the sample mean added to M. So it is 49.6 + 46.668 = 96.268 bushels per acre.

The 99% confidence interval for the true mean yield is between 2.943 bushels per acre and 96.268 bushels per acre.

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image for the step by stem explanation to the question

Answer:

[tex]a_{3} = 405[/tex]

Step-by-step explanation:

A geometric sequence is based on the following equation:

[tex]a_{n+1} = ra_{n}[/tex]

In which r is the common ratio.

This can be expanded for the nth term in the following way:

[tex]a_{n} = a_{1}r^{n-1}[/tex]

In which [tex]a_{1}[/tex] is the first term.

In this question:

[tex]a_{1} = 3645, a_{6} = 15[/tex]

Applying the equation:

[tex]a_{6} = a_{1}r^{6-1}[/tex]

[tex]a_{6} = a_{1}r^{5}[/tex]

[tex]3645r^{5} = 15[/tex]

[tex]r^{5} = \frac{15}{3645}[/tex]

[tex]r^{5} = \frac{1}{243}[/tex]

[tex]r = \sqrt[5]{\frac{1}{243}}[/tex]

[tex]r = \frac{1}{3}[/tex]

So

[tex]a_{n} = 3645 \times (\frac{1}{3})^{n-1}[/tex]

[tex]a_{3} = 3645 \times (\frac{1}{3})^{3-1} = 405[/tex]

Answer:

35

Step-by-step explanation:

On subtracting 28 from 63 by adding up we get 35.

To subtract by adding up is special method to find the difference between two numbers. For 63-28, we can do it in the following steps:

We start by using the smaller number, here 28. And add a number to 28 such that it we receive a number that is easy to use further. So, here we can add 2 to it which gives us:

[tex]28 + 2= 30[/tex]

Now we take 30 and we can add another 30 to it. This gives us:

[tex]30+30 = 60[/tex]

Now the goal is to add a number such that the sum of the number and 60 make 63. So, we add 3 to 60 which gives us:

[tex]60+3 = 63[/tex]

Now we need to take the second number we have added in each of the steps (2, 30 and 3) and add them. The sum of these numbers will give us the difference between 63 and 28. Thus we can write it as:

[tex]63-28 = 2+30+3\\\\63-28 = 35[/tex]

Thus on subtracting 28 from 63 by adding up method we get the answer as 35.

Answer:

4 is 133

Step-by-step explanation:

Simple 180-47 is 133

Answer:

They are both acute angles

Step-by-step explanation:

plz mark brainliest

Answer:

20 cm.

Step-by-step explanation:

First, find the perimeter in inches. Since it's a square and all 4 sides are the same, you can multiply 2 x 4 to find the perimeter of 8. Now, convert it to cm by multiplying 8 by 2.5. 8 x 2.5 is 20 cm.

Answer:

-x

Step-by-step explanation:

8x - 9x

Factor out an x

x(8-9)

x (-1)

-x

Answer:

a = 65.37

b = 46.11

B = 35.2

Step-by-step explanation:

sin 54.8 = a / 80

a = 80 sin 54.8 = 65.3715 = 65.4

[tex]b^{2} = c^{2} - a^{2}[/tex]

b=[tex]\sqrt{80^2 - 65.3715^2}[/tex]

b=46.1147 = 46.11

B = 180 - 90 - 54.8 = 35.2

The sides and the angles as follows:

Therefore,

∠A = 54.8°

∠B = 35.2°

∠C = 90°

a ≈ 65.37

b ≈ 46.64

c = 80

The triangle is a right angle triangle. Using trigonometric ratios, let's find a.

sin 54.8 = opposite / hypotenuse

sin 54.8 = a / 80

a = 80 sin 54.8

a = 65.3715918668

a ≈ 65.37

let's use Pythagoras theorem to find b.

c² = a² + b²

b² = c² - a²

b² =  80² - 65²

b² = 6400 - 4225

b² = 2175

b = √2175

b = 46.6368952654

b ≈ 46.64

let's find ∠B

∠A +  ∠B +  ∠C = 180°

∠B = 180 - 54.8 - 90

∠B = 35.2°

Therefore,

∠A = 54.8°

∠B = 35.2°

∠C = 90°

The sides are as follows:

a ≈ 65.37

b ≈ 46.64

c = 80

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Answer:

infinite solutions

Step-by-step explanation:

2 ( n-1 ) + 4n= 2( 3n-1 )

Distribute

2n -2 +4n = 6n -2

Combine like terms

6n -2 = 6n -2

Subtract 6n from each side

6n-2-6n = 6n-2-6n

-2 = -2

This is always true so there are infinite solutions

Answer:

The sum of 10.15 + 31.60 + 34.75 + 40 + 69.25 + 54.75 equals to 185.75

Step-by-step explanation:

10.15 + 31.6 + 34.75 + 40 + 69.25

        = 41.75 + 104 + 40

            = 145.75 + 40

                = 185.75

Alternate forms:

743/4 , 185 3/4

\frac{743}{4} 185\frac{3}{4}

Answer:

240.5

Step-by-step explanation:

Answer:

81+90

Step-by-step explanation:

9^2 + 2[(5+2)^2 -4]

PEMDAS says parentheses first , working inside out

9^2 + 2[(7)^2 -4]

PEMDAS says parentheses first, doe the exponents inside the parentheses

9^2 + 2[49 -4]

Then the subtraction inside the parentheses

9^2 + 2[45]

Then Exponents

81 +2[45]

Then Multiplication

81+90

Finally add

Answer:

A

Step-by-step explanation:

9² + 2[(5+2)² - 4]

81 + 2[(7)² - 4]

81 + 2[49 - 4]

81 + 2(45)

81 + 90

171

124

Answer:

The distribution is uniform and is continuous probability distribution.

The mean of the distribution is μ= 35.5 minutes.

The standard deviation of the distribution is σ= 6.06

P(30<x<40)= 0.476

Step-by-step explanation:

a.The amount of time in minutes until the next bus departs is uniformly distributed between 25 and 46 inclusive.

The distribution is uniform and is continuous probability distribution.

b.Let X be the number of minutes the next bus arrives and a= 25 , b= 46. Hence mean = a+b/2= 25+ 46/ 2= 35.5 minutes.

The mean of the distribution is μ= 35.5 minutes.

c. Standard deviation =   √(b-a)²/12

Standard deviation= √(46-25)²/12= √(21)²/12= √441/12=√36.75= 6.06

The standard deviation of the distribution is σ= 6.06

d. P(30<x<40)

For this we draw a graph . It is also called the rectangular distribution because its total probability is confined to a rectangular region with base equal to (b-a) and height 1/(b-a) .

This can be calculated as

P(30<x<40)= base * height  (in this probability the base is 10)

= (40-30) *(1/ 21)= 10/21= 0.476  

The probability that the time until the next bus departs is between 30 and 40 minutes is 10/21.

The question is asking for the probability that the time until the next bus departs is between 30 and 40 minutes. Since the distribution is uniform, we can find the probability by calculating the fraction of the total range that falls within the desired interval. In this case, the total range is 46-25=21 minutes, and the desired interval is 40-30=10 minutes.

So the probability is 10/21, which can be simplified to 10/21.

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Answer:

7.8《 X《 8.2

Step-by-step explanation:

Let X be the weight of the product

8 - 0.2《 X《 8 + 0.2

7.8《 X《 8.2

Answer:

7.8《 X《 8.2

Step-by-step explanation:

Let X be the weight of the product

8 - 0.2《 X《 8 + 0.2

7.8《 X《 8.2p

EndFraction

StartFraction 24 Over 121 EndFraction

StartFraction 6 Over 11 EndFraction

StartFraction 10 Over 11 EndFraction

Answer:

StartFraction 24 Over 121 EndFraction

Step-by-step explanation:

Answer:

5/24

Step-by-step explanation:

First, we want to get a common denominator, so we multiply them together.

The 2 new fractions are. . .

4/24 (1/6) and 6/24 (1/4)

Now, if you are looking for the number between 4/24 and 6/24, the answer is 5/24.

Answer:

  5

Step-by-step explanation:

Put -6 where x is and do the arithmetic.

  [tex]h(x)=1-\dfrac{2}{3}x\\\\h(-6)=1-\dfrac{2}{3}(-6)=1-\dfrac{-12}{3}=1-(-4)=1+4\\\\\boxed{h(-6)=5}[/tex]

Answer:

Degree 3

Step-by-step explanation:

Highest valued exponent of x variable is 3

Answer:

a) 0.23

b) The 95% confidence interval for the population proportion is (0.1717, 0.2883).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

Point estimate

The point estimate is:

[tex]\pi = \frac{46}{200} = 0.23[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.23 - 1.96\sqrt{\frac{0.23*0.77}{200}} = 0.1717[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.23 + 1.96\sqrt{\frac{0.23*0.77}{200}} = 0.2883[/tex]

The 95% confidence interval for the population proportion is (0.1717, 0.2883).

[tex] \frac{5}{4 {k}^{2} } [/tex]

Answer:5/4k^2

Step-by-step explanation:

5k/6 x 3/2k^3

(5k x 3) ➗ (6 x 2k^3)

15k/12k^3=5/4k^2