6 friends share 3 apples. How much each friend receive?

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).

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:

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

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:

  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:

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:

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:

Degree 3

Step-by-step explanation:

Highest valued exponent of x variable is 3

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

Answer:

Check the explanation

Step-by-step explanation:

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

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:

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:

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:

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:

[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:

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:

4 [tex]\frac{1}{2}[/tex]

OR

[tex]\frac{9}{2}[/tex]

Step-by-step explanation:

I'm not exactly sure which type of fraction you're asking for, so I'll put both.

This would be the fraction for 4.5 because the 0.5 is half of 1, while we already have a whole number, being 4.

OR

9 divided by 2 is 4.5, making the fraction for 4.5, [tex]\frac{9}{2}[/tex]

Answer:

9/2

Step-by-step explanation:

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:

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

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:

P(N = n) = [tex](1-P)^{n-1} \times P[/tex]  

Step-by-step explanation:

to find out

Find the PMF PN (n)

solution

PN (n)

here N is random variable

and n is the number of times

so here N random variable is denote by the same package that is N (P)

so here

probability of N is

P(N ) = Ф ( N = n)          ..................  1

here n is = 1, 2,3, 4,...................... and so on

so that here P(N = n) will be

P(N = n) = [tex](1-P)^{n-1} \times P[/tex]  

[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

Answer:

45π or 141.4 [tex]cm^{3}[/tex]

Step-by-step explanation:

The volume of a cone is [tex]V=\frac{1}{3} \pi r^{2} h[/tex]

Here we have a diameter of 6 cm which means we have a radius of 3 (dividing by 2)

Our height here is 15 cm

Plugging in all our values we get [tex]\frac{1}{3}\pi[/tex][tex](3)^{2} (15)[/tex] which gives us 45π or 141.4 [tex]cm^{3}[/tex]

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:

The y intercept is (0,-22)

Step-by-step explanation:

To find the y intercept, set x =0 and solve for y

f(0)=-0^2+10*0-22

    = -22

Final answer:

To find the y-intercept of a quadratic function, substitute x = 0 into the function and calculate the value. In this case, the y-intercept of the function [tex]f(x) = -x^2 + 10x - 22[/tex] is at y = -22.

Explanation:

The y-intercept of a quadratic function is the point where the graph intersects the y-axis, and it occurs when x = 0. To find the y-intercept of the quadratic function [tex]f(x) = -x^2 + 10x - 22[/tex], substitute x = 0 into the function.

Replace x with 0: f(0) =[tex]-(0)^2 + 10(0) - 22[/tex]

Calculate the value: f(0) = 0 + 0 - 22 = -22

Therefore, the y-intercept of the quadratic function is at y = -22.

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:

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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