A box contains 3 red and 7 green marbles. If 9 marbles are drawn without replacement, what is the expected number of red marbles?

for points sorry Answer:

Step-by-step explanation:

The false statement among the following statements is: |ez| = |e³|. Here, e is the Euler number, and z is a complex number. Therefore, the correct answer is option (i) |ez| = |e³|.

We know that e^(ix) = cos(x) + i sin(x)

It is also known as Euler's formula, where e is the Euler number, i is the imaginary unit, x is the angle in radians. This formula connects the trigonometric functions with the exponential function. In this question, e is the Euler number, and z is a complex number. So, ez = |ez| × e^(iθ), where θ is the angle of the complex number z from the positive real axis. In the same way, e³ = |e³| × e^(i3θ)Here, the modulus of ez is |ez|, and the modulus of e³ is |e³|. It is not necessary that both will be equal because the value of θ may differ. Hence, the false statement is |ez| = |e³|.

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The integrating factor for the given differential equation is |x^2 - 1|.

To find the integrating factor for the given differential equation, we start by rearranging the equation in the form:

dy/dx + (2y)/(x^2 - 1) = (4(x + 1))/(x^2 - 1)

The integrating factor (IF) is given by the exponential of the integral of the coefficient of y, which in this case is (2/(x^2 - 1)). Therefore, the integrating factor IF is:

IF = exp ∫ (2/(x^2 - 1)) dx

To evaluate this integral, we can use a substitution. Let u = x^2 - 1, then du = 2x dx. Substituting this back into the integral, we get:

IF = exp ∫ (1/u) du = exp(ln|u|) = |u|

Since u = x^2 - 1, we have:

IF = |x^2 - 1|

Therefore, the integrating factor for the given differential equation is |x^2 - 1|.

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Answer:(2,36)and (3,54)

Step-by-step explanation:

Answer:

(2, 36) and (3, 54)

Step-by-step explanation:

I just answer the question from iready and I got it correct.

Answer: B

The surface area of the right cylinder is 140π cubic units or 439.60 cubic units.

Step-by-step explanation:

We have formula to find the surface area of a right cylinder.

Surface area = 2πr(h + r)

Given: r = 5 and h = 9,

Now plug in the value of r and h in the above formula, we get

Surface area = 2π.5 (9 + 5)

= 10π(14)

Surface area = 140π

The value of π = 3.14, when we plug in the value of π, we get

The surface area = 140 × 3.14

= 439.60 cubic units.

Therefore, the surface area of the right cylinder is 140π cubic units or 439.60 cubic units.

Hope this helped!!!

The measure of each angle in the triangle is 24 degrees, 36 degrees, and 120 degrees.

Let's denote the three angles of the triangle as A, B, and C. According to the given ratio of 2:3:10, we can assign the values 2x, 3x, and 10x to angles A, B, and C, respectively, where x is a common factor.

The sum of the angle measures in a triangle is always 180 degrees. Therefore, we can set up the following equation:

2x + 3x + 10x = 180

Simplifying the equation, we get:

15x = 180

Dividing both sides by 15, we find:

x = 12

Now we can substitute x back into the expressions for each angle:

Angle A = 2x = 2(12) = 24 degrees

Angle B = 3x = 3(12) = 36 degrees

Angle C = 10x = 10(12) = 120 degrees

Therefore, the measure of each angle in the triangle is 24 degrees, 36 degrees, and 120 degrees.

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The 95% confidence interval for the population proportion is approximately (0.7465, 0.7935).

(a) To calculate a 90% confidence interval for the population proportion, we can use the formula:

Confidence Interval = sample proportion ± z * sqrt((sample proportion * (1 - sample proportion)) / sample size)

Given that the sample proportion is p = 0.77 and the sample size is n = 800, we need to find the critical value, z, corresponding to a 90% confidence level.

Using a standard normal distribution table or a statistical software, the critical value for a 90% confidence level is approximately 1.645.

Substituting these values into the formula, we have:

Confidence Interval = 0.77 ± 1.645 * sqrt((0.77 * (1 - 0.77)) / 800)

Calculating the confidence interval, we get:

Confidence Interval = 0.77 ± 0.0191

Therefore, the 90% confidence interval for the population proportion is approximately (0.7509, 0.7891).

(b) Similarly, to calculate a 95% confidence interval, we need to find the critical value corresponding to a 95% confidence level. The critical value is approximately 1.96 for a 95% confidence level.

Using the same formula and substituting the values, we have:

Confidence Interval = 0.77 ± 1.96 * sqrt((0.77 * (1 - 0.77)) / 800)

Calculating the confidence interval, we get:

Confidence Interval = 0.77 ± 0.0235

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This tutorial provides step-by-step instructions on how to perform an independent samples t-test in SPSS and interpret the results.

The tutorial outlines the following steps to conduct an independent samples t-test in SPSS:

Access the Analyze menu.

Select "Compare Means" and then "Independent-Samples T Test."

Drag and drop the dependent variable into the "Test Variable(s)" box and the grouping variable into the "Grouping Variable" box.

Define the groups by clicking on "Define Groups" and inputting the coded values that represent each group.

Click "Continue" and then "OK" to run the test.

The results will be displayed in the SPSS data viewer.

By following these steps, users can conduct an independent samples t-test to compare means between two groups and assess whether there is a statistically significant difference. The result provides information such as the t-value, degrees of freedom, and p-value, which is used to interpret the significance of the difference between the means of the two groups. Researchers can then make conclusions based on the statistical findings from the independent samples t-test.

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The correct interpretation of `f(6) = 44,500` is that in the year 2011, a company that opened in 2005 will produce 44,500 units of products is the answer.

Given, `f(t)` be the number of units produced by a company `t` years after opening in 2005.

According to the question, `f(6) = 44,500`. It means six years after the company opened, which is in the year 2011, the company will produce 44,500 units of products.

The statement "six years from now, 44,500 units will be produced" (option a) is not correct because the year is not specified. The company will produce 44,500 units of products in the year 2011, not six years from the present.

The statement "in 2009, 44,500 units are produced" (option b) is not correct because in the year 2009, the company will only have been open for four years, and not enough information is provided to calculate the number of units produced.

The statement "in 2006, 44,500 units are produced" (option c) is not correct because in the year 2006, the company will have only been open for one year, and not enough information is provided to calculate the number of units produced.

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Answer:

1875

Step-by-step explanation:

750 x 2.5 = 1,875

Answer:

£139

Step-by-step explanation:

£12.50 * 11 = 137.50

137.50 + 1.50 = £139

Answer:

137.5 + 1.50 = £139

Step-by-step explanation:

Please Give brainliest

Answer:

[tex]14/50\\[/tex]

Step-by-step explanation:

The equation for sine is sine = opposite/ hypotenuse

The opposite of W is 14 and the hypotenuse the the side across the 90° angle, which is 50.

So, when you set up the equation it should be [tex]14/50[/tex].

Answer:

red = 28 apples

green = 13 apples

equations:

r + g = 41

r = g + 15

Step-by-step explanation:

r = number of red

g = number of green

r = g + 15 (the number of red apples is 15 more than the number of green apples)

r + g = 41

Substitute the first equation into the second and solve for a numerical value of g

(g + 15) + g = 41

2g + 15 = 41

2g = 26

g = 13

Now solve for a numerical value of r

r = g + 15

r = 13 + 15

r = 28

checking the math:

r + g = 41

28 + 13 = 41

Please lmk if you have any questions.

Answer:

72 cm

Step-by-step explanation:

It would be multiplied by 8 so the length would become 72 cm

Step-by-step explanation:

12x^2 + 8x

4x ( 3x + 2)

2x^2 - 16x

2x ( x - 8)

Answer:

a=25

b=7

Step-by-step explanation:

Answer:

lateral surface area =perimeter of base×height=

={4+7+7+11)×6=174 km²

Step-by-step explanation:

Answer:

answer I have no clue sorry dude

Answer:

972 cubic feet

Step-by-step explanation:

12 by 9 by 7.5

+

1.5 by 9  by 12

Answer:

891 ft³

Step-by-step explanation:

First I'll find the volume of the rectangular prism. (l * w * h)

12 * 9 * 7.5

Multiply 12 by 9 to get 108.

108 * 7.5

Now, multiply 108 by 7.5 to get 810. (756 + 54 = 810)

810

Now for the triangular prism. (1/2(l * w * h))

1/2(12 * 9 * 1.5) (I figured the height was 1.5 since the height of the rectangular prism was 7.5; the entire figure's height was 9)

Multiply 12 by 9 to get 108.

1/2(108 * 1.5)

Multiply 108 by 1.5 to get 162. (108 + 54 = 162)

1/2(162)

Multiply 162 by 1/2 to get 81. (162/2)

81

Now add that to 810 to get 891.

810 + 81

891 ft³

The volume of the garage is 891 ft³.

Answer:

40 units

Step-by-step explanation:

For a square, all the sides are equal and the interior angles are equal and all equal to 90. Hence;

m<BOJ = 90 degrees

m<BOJ = 4x - 6

Equating both to get x;

4x - 6 = 90

4x = 90+6

4x = 96

x = 96/4

x = 24

Since all the sides are equal, hence BO = JO = 2x-8

JO = 2x - 8

Substitute x = 24 into JO

JO = 2(24) - 8

JO = 48 - 8

JO = 40

Hence the measure of JO is 40 units

The set of vectors (b) (-3,0,4), (5,-1,2), (1,1,3) are linearly dependent. The other given sets of vectors in R3 are linearly independent.

Let's review the given sets of vectors in R₃ to determine which ones are linearly dependent.

(a) (4.-1,2), (-4, 10, 2).

To check if the given set is linearly dependent or not, we need to check whether there are non-zero scalars such that their linear combination is equal to

0.a(4,-1,2) + b(-4,10,2) = (0,0,0).

The system of equations can be written as;

4a - 4b = 0-1a + 10b = 00a + 2b = 0.

Clearly, a = b = 0 is the only solution.

So, the set is linearly independent.

(b) (-3,0,4), (5,-1,2), (1, 1,3)

To check if the given set is linearly dependent or not, we need to check whether there are non-zero scalars such that their linear combination is equal to

0.a(-3,0,4) + b(5,-1,2) + c(1,1,3) = (0,0,0).

The system of equations can be written as;

-3a + 5b + c = 00a - b + c = 00a + 2b + 3c = 0

Clearly, a = 2, b = 1, and c = -2 is a solution.

So, the set is linearly dependent.

(c) (8.-1.3). (4,0,1).

To check if the given set is linearly dependent or not, we need to check whether there are non-zero scalars such that their linear combination is equal to

0.a(8,-1,3) + b(4,0,1) = (0,0,0).

The system of equations can be written as;

8a + 4b = 01a + 0b = 0-3a + b = 0.

Clearly, a = b = 0 is the only solution.

So, the set is linearly independent.

(d) (-2.0, 1), (3, 2, 5), (6,-1, 1), (7,0.-2).

To check if the given set is linearly dependent or not, we need to check whether there are non-zero scalars such that their linear combination is equal to

0.a(-2,0,1) + b(3,2,5) + c(6,-1,1) + d(7,0,-2) = (0,0,0)

The system of equations can be written as;

-2a + 3b + 6c + 7d = 00a + 2b - c = 00a + 5b + c - 2d = 0

Clearly, a = b = c = d = 0 is the only solution.

So, the set is linearly independent.

Therefore, The set of vectors (b) (-3,0,4), (5,-1,2), (1,1,3) are linearly dependent. The other given sets of vectors in R₃ are linearly independent.

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a. Using the z-score, the probability of a randomly chosen mouse having a mass of less than 20.7 grams is approximately 0.2794.

b. The probability that a randomly chosen mouse has a mass more than 21.02g is 0.0985

c.  The probability of a mouse having a mass between 20.65 and 20.95 grams is approximately 0.6474.

d. About 10% of all mice have a mass of less than 20.5649 grams.

a) To find the probability that a randomly chosen mouse has a mass of less than 20.7 grams, we can use the normal distribution.

First, we need to standardize the value of 20.7 grams using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

The z-score for the data is;

z = (20.7 - 20.8) / 0.17 = -0.5882

P = 0.2794

b) To find the probability that a randomly chosen mouse has a mass of more than 21.02 grams, we also need to standardize the value:

z = (21.02 - 20.8) / 0.17 = 1.2941

P = 0.0985

Using the standard normal distribution table or a calculator, we find that the probability corresponding to this z-value is approximately 0.0985.

c) To find the proportion of mice that have a mass between 20.65 and 20.95 grams, we can standardize both values:

For 20.65 grams:

z₁ = (20.65 - 20.8) / 0.17 = -0.8824

For 20.95 grams:

z₂ = (20.95 - 20.8) / 0.17 = 0.8824

Using the standard normal distribution table or a calculator, we can find the probabilities corresponding to these z-values. The probability of a mouse having a mass between 20.65 and 20.95 grams is approximately 0.6474.

d) To find the mass of mice that corresponds to the 10th percentile, we need to find the z-score associated with the 10th percentile. We can use the standard normal distribution table or a calculator to find this value.

The z-score associated with the 10th percentile is approximately -1.2816.

Next, we can use the z-score formula to find the corresponding mass value:

z = (x - μ) / σ

-1.2816 = (x - 20.8) / 0.17

Solving for x, we get:

x = -1.2816 * 0.17 + 20.8 ≈ 20.5649 grams

Therefore, 10% of all mice have a mass of less than 20.5649 grams.

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Answer:

[tex]\frac{75}{4\pi }[/tex] inches or approximately 5.97 inches  

Step-by-step explanation:

Use the cone volume formula: V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]

The diameter is 8 inches, so the radius will be 4 inches.

Plug in the radius and volume, and solve for h

V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]

100 = [tex]\pi[/tex](4²)([tex]\frac{h}{3}[/tex])

100 = 16[tex]\pi[/tex][tex]\frac{h}{3}[/tex]

Divide each side by 16[tex]\pi[/tex]

[tex]\frac{25}{4\pi }[/tex] = [tex]\frac{h}{3}[/tex]

Cross multiply and solve for h:

4[tex]\pi[/tex]h = 75

h = [tex]\frac{75}{4\pi }[/tex]

So, the cone's height is [tex]\frac{75}{4\pi }[/tex] or approximately 5.97 inches  

Answer:

e) yes, symmetric around the y-axis

f) minimum at (0,0)

g) x-intercept at 0

Step-by-step explanation:

Answer:

85 wpm

Step-by-step explanation:

From the scatter plot, we can see the following;

At 20 hours, average typing speed = 34 wpm

At 30 hours, the average typing speed = 40 wpm

At 40 hours, the average typing speed = 51 wpm

At 50 hours, the average typing speed = 65 wpm

Average differences = ((40 - 34) + (51 - 40) + (65 - 51))/3 = 10.3

Approximating to a whole number = 10

Now, we can approximate that at 60 hours, average typing speed = 65 + 10 = 75 wpm

At 70 hours, the average typing speed = 75 + 10 = 85 wpm

Answer:

85 wpm

Step-by-step explanation:

I took this test!

Step-by-step explanation:

x - 3 > -4

= x > -4+3

= x > -1 _ Answer

The standard deviation for the given test scores is 20, and the variance is 400

We have,

To find the standard deviation and variance for the given test scores, we can follow these steps:

Calculate the mean (average) of the test scores:

Mean (μ) = (92 + 92 + 92 + 52 + 52) / 5 = 80

Calculate the deviation of each test score from the mean:

Deviation = Test score - Mean

For the given test scores:

Deviations = (92 - 80), (92 - 80), (92 - 80), (52 - 80), (52 - 80)

= 12, 12, 12, -28, -28

Square each deviation:

Squared Deviations = Deviation²

Squared Deviations = 12², 12², 12², (-28)², (-28)²

= 144, 144, 144, 784, 784

Calculate the variance:

Variance = (Sum of Squared Deviations) / (Number of Scores)

Variance = (144 + 144 + 144 + 784 + 784) / 5

= 2000 / 5

= 400

Calculate the standard deviation:

Standard Deviation = √Variance

Standard Deviation = √400

= 20

Therefore,

The standard deviation for the given test scores is 20, and the variance is 400.

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Answer:

Selling price of the laptop is $600.

Step-by-step explanation:

Let the sale price of the laptop = $x

Regular price of the laptop = $750

Discount on each computer = 20%

Selling price of the laptop 'x' = 750 - (20% of 750)

                                                = 750 - [tex](\frac{20}{100}\times 750)[/tex]

                                                = 750 - 150

                                                = $600

Therefore, selling price of the laptop is $600.