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Answer:

16.67% probability of getting 2 blues

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the marbles are selected is not important. So we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

What is the probability of getting 2 blues?

Desired outcomes:

Two blue marbles, from a set of 4.

[tex]D = C_{4,2} = \frac{4!}{2!(4-2)!} = 6[/tex]

Total outcomes:

Two marbles, from a set of 9.

[tex]T = C_{9,2} = \frac{9!}{2!(9-2)!} = 36[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{6}{36} = 0.1667[/tex]

16.67% probability of getting 2 blues

Answer:

(4,1)

Step-by-step explanation:

(1+7)/2 = 4

(9+(-7))/2 = 1

Answer:

  25 m, 27 m

Step-by-step explanation:

The perimeter is twice the sum of length and width, so that sum is 52 m. Half that is the average of length and width, so will be the even integer between the two consecutive odd integers.

  52/2 = 26

The length and width are 25 m and 27 m.

Answer:

A-8

Step-by-step explanation:

Any other higher number plugged in makes the equation false

Answer:

3

Step-by-step explanation:

Solving the inequality

2x-1>=5

2x>=6

x>=3

The graph should have a shaded circle on 3 and a line pointing to values increasing.

Answer:

-8.5

Step-by-step explanation:

-4x+8=42

-4x=42-8

-4x=34

x=34/-4

x=-8.5

Answer:C

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

Source: Dude trust me

Answer:

514 square meters

Step-by-step explanation:

Consider the length of p;

[tex]11 * p * 3 = 528,\\33 * p = 528,\\p = 528 / 33 = 16 meters[/tex]

11, 3, and p act as the length, width, and height of this rectangular prism. We can apply the volume formula length * width * height, and thus made 11 * p * 3 equivalent to the volume 528. Now let us determine the surface area;

[tex]Area of Side 1 = 16 * 11 = 176 square meters,\\Area of Side 2 = 3 * 16 = 48 square meters,\\Area of Side 3 = 11 * 3 = 33 square meters,\\\\Surface Area = 2 * ( 176 ) + 2 * ( 48 ) + 2 * ( 33 ) = 352 + 96 + 66 = 514 square meters[/tex]

Hope that helps!

Answer:

514 square meters

Step-by-step explanation:

Since the volume of a rectangular prism is the product of the width, length, and height, 11*3*p=528. Therefore, p=528/(11*3)=16. Now, you can find the surface area. The surface of a rectangular prism is made up of 3 pairs of rectangles. One pair has dimensions of 11 by 3, one pair has dimensions of 16 by 3, and the last pair has dimensions of 16 by 11. The surface area of this figure is therefore:

[tex]2(11\cdot 3)+2(16\cdot 3) + 2(16\cdot 11)=66+96+352=514 m^2[/tex]

Hope this helps!

Answer:

x = 5

Step-by-step explanation:

3x - 7 + 4x = 28

Combine like terms

7x -7 = 28

Add 7 to each side

7x - 7 +7  = 28+7

7x = 35

Divide each side by 7

7x/7 = 35/7

x = 5

Answer:

[tex]\frac{\pi x^3}{3}[/tex]

Step-by-step explanation:

[tex]V=\pi r^2h\frac{1}{3}[/tex]

[tex]V=\pi x^2x\frac{1}{3}[/tex]

[tex]V=\pi x^3\frac{1}{3}[/tex]

[tex]V=\frac{\pi x^3}{3}[/tex]

[tex]V=1.047198x^3[/tex]

Answer:

Step-by-step explanation:

1/12 pi x ^3

Answer:

2.54 seconds

Step-by-step explanation:

We can use the following equation to model the vertical position of the ball:

S = So + Vo*t + a*t^2/2

Where S is the final position, So is the inicial position, Vo is the inicial speed, a is the acceleration and t is the time.

Then, using S = 2.5, So = 0.4, Vo = 14 and a = -9.8 m/s2, we have that:

2.5 = 0.4 + 14*t - 4.9t^2

4.9t^2 - 14t + 2.1 = 0

Solving this quadratic equation, we have that t1 = 2.6983  s and t2 = 0.1588 s.

Between these times, the ball will be higher than 2.5 m, so the amount of time the ball will be higher than 2.5 m is:

t1 - t2 = 2.6983  - 0.1588 = 2.54 seconds

The complete question is;

An eight-sided die, which may or may not be a fair die, has four colors on it; you have been tossing the die for an hour and have recorded the color rolled for each toss. What is the probability you will roll a green on your next toss of the die? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

orange brown green yellow

46 23 32 19

Answer:

probability of rolling green on the next toss of the die = 4/15

Step-by-step explanation:

We are given how many times each of the colours appeared for each toss and they are;

Orange - 46

Brown - 23

Green - 32

Yellow - 19

Thus,

Total number of tosses = 46 + 23 + 32 + 19 = 120 rolls

Thus, probability of rolling green on the next toss of die will be = number of times green appeared/total number of rolls = 32/120 = 4/15

Answer:

The domain of the function H(t), is [-5, 30].

The range of the function H(t), is [(10% + average), (average - 20%)]

Step-by-step explanation:

The domain of a function is the complete set of possible values of the independent variable.

For this question, the function is H(t), with the temperature, t, serving as the independent variables and H(t) the evidently dependent variable.

The domain of a function refers to all the possible independent variable values that will give corresponding real dependent variable values.

For this question, Alice's model has the probability for the occurrence of heart disease (in percents relative to the global average) at an area, H(t) varying with the temperature of that area in degree Celsius.

At a temperature of -5°C (the lowest temperature in the model), the probability is 10% above the average.

Then, the probability decreases with increase in temperature, taking a value 20% lower than the average when the temperature is at its highest of 30°C in the model.

So, temperature ranges from -5°C to 30°C and the probability for the occurrence of heart disease ranges from 10% above the average to 20% below the average.

The domain of the function H(t), from the definition given above would therefore be [-5, 30]

And the range of the function H(t), is [(10% + average), (average - 20%)]

Hope this Helps!!!

The Real Number type is more appropriate fro the domain of H(t).

The domain of H(t) is given as  [tex]-5 \leq t \leq 30[/tex]

Given that:

The lowest temperature included in the model is -5° C

The highest temperature included in the model is 30° C

The domain of H includes the values of the temperature. Since the temperature can be non integer too, sometimes rational too, thus we use Real Number type for the domain of H(t).

The domain of H(t) will be given by the following interval on real number line:

[tex]\begin{aligned} Domain(H(t)) = [-5, 30]\\\end{aligned}[/tex]

or [tex]-5 \leq t \leq 30[/tex].

Hence, the Real Number type is more appropriate fro the domain of H(t).

The domain of H(t) is given as  [tex]-5 \leq t \leq 30[/tex].

Learn more here:

https://brainly.com/question/9463453

Answer:

  M(h) = 73.18025h

Step-by-step explanation:

The composite function is ...

  M(B(L(h))) = M(B(28.75h)) = M(1.78(28.75h)) = M(51.175h)

  = 1.43(51.175h) = 73.18025h

The composite function is ...

  M(h) = M(B(L(h))) = 73.18025h

Answer:

a

Step-by-step explanation:

Answer:

Lucas groups the polynomial (12x^3 + 8x) + (–6x^2 – 4) to factor → 2 (2 x - 1) (3 x^2 + 2)

Step-by-step explanation:

Factor the following:

12 x^3 - 6 x^2 + 8 x - 4

Hint: | Factor out the greatest common divisor of the coefficients of 12 x^3 - 6 x^2 + 8 x - 4.

Factor 2 out of 12 x^3 - 6 x^2 + 8 x - 4:

2 (6 x^3 - 3 x^2 + 4 x - 2)

Hint: | Factor pairs of terms in 6 x^3 - 3 x^2 + 4 x - 2 by grouping.

Factor terms by grouping. 6 x^3 - 3 x^2 + 4 x - 2 = (6 x^3 - 3 x^2) + (4 x - 2) = 3 x^2 (2 x - 1) + 2 (2 x - 1):

2 3 x^2 (2 x - 1) + 2 (2 x - 1)

Hint: | Factor common terms from 3 x^2 (2 x - 1) + 2 (2 x - 1).

Factor 2 x - 1 from 3 x^2 (2 x - 1) + 2 (2 x - 1):

Answer: 2 (2 x - 1) (3 x^2 + 2)

Answer:

Both students are correct because polynomials can be grouped in different ways to factor. Both ways result in a common binomial factor between the groups. Using the distributive property , this common binomial term can be factored out. Each grouping results in the same two binomial factors.

Step-by-step explanation:

this is the sample response provided by edge

Answer:-8

Step-by-step explanation:

8 - 2 × 8

8 - 16

-8

Answer:

after three years

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

A cone with a radius of 1-unit will be obtained by rotating the 3-D figure.

Answer:

x = 22

x = 4,6

Step-by-step explanation:

3x - 22 = 44

3x = 44 + 22

3x = 66

x = 66/3

x = 22

5/6 = 10/2x - 3

5/6 + 3 = 10/2x

5/6 + 18/6 = 10/2x

23/6 = 10/2x

23/6 * 2 = 10x

46 = 10x

x = 46/10

x = 4,6

Answer:

\sqrt(12) hope this helped.

Answer: 368 ways

Step-by-step explanation: To find the total number of probabilities, you multiply all the factors together to get total outcome. 16 * 23 = 368

Answer:

C.

Step-by-step explanation:

[tex]\frac{1}{5} +\frac{5}{6}[/tex] ≈ 1

5 + 8 + 1 = 14

[tex]answer \\ 2\\ solution \\ 10x - 3(x - 6) = x + 30 \\ or \: 10x - 3x + 18 = x + 30 \\ or \: 10x - 3x - x = 30 - 18 \\ or \: 7x - x = 12 \\ or \: 6x = 12 \\ or \: x = \frac{12}{6} \\ x = 2 \\ hope \: it \: helps[/tex]

Answer:

x=2

Step-by-step explanation:

10x - 3(x- 6) = x + 30

Distribute

10x -3x+18 = x+30

Combine like terms

7x + 18 = x+30

Subtract x from each side

6x+18 = 30

Subtract 18 from each side

6x = 30-18

6x = 12

Divide by 6

6x/6 = 12/6

x =2

Answer:

A

Step-by-step explanation:

The combinations of decisions and true states of nature for a test of​ hypothesis is given below:

Note that when [tex]H_o[/tex] is False, then the Alternate Hypothesis, [tex]H_a[/tex] is True.

Therefore Option A gives the possible combinations.

The possible choices in Option A are ordered below to correspond to the results above.

Answer:

Volume of the machine part = 114π inches³

Step-by-step explanation:

Volume of the machine part = Volume of cylinder + Volume of hemisphere

Volume of cylinder = [tex]\pi r^{2}h[/tex]

Where r = radius of the cylinder

h = height of the cylinder

Volume of the cylinder = [tex]\pi(\frac{6}{2})^{2}(12)[/tex]

                                      = 108π inches³

Volume of the hemisphere = [tex]\frac{2}{3}\pi r^{3}[/tex]

                                             = [tex]\frac{2}{3}\pi (3)^{3}[/tex]

                                             = 6π inches³

Total area of the machine part = 108π + 6π

                                                   = 114π inches³

Answer:

m > 82.28

Step-by-step explanation:

Price to Pay (P)

distance (m)

Company A

Pa = 0.80m

Company B

Pb = 65 + 0.01m

Company A charge more than B is written like this

0.8m > 65 + 0.01m

then we can solve this inequality

(0.8 - 0.01)m > 65

0.79m > 65

m > 65/0.79

m > 82.28 miles

so if Maya will go more than 82.28 miles, I suggest Company B is cheaper

Answer:

Step-by-step explanation:

Hello!

An ANOVA was conducted to analyze the variable

Y: sales of "People" magazine over a 5-week period

This was studied in 4 Borders outlets in Chicago.

So this test has one factor: "Borders outlets" and four treatments: "Store 1, store 2, store 3 and store 4"

For each store you have the data for the weekly sales over a 5-week period so the sample sizes are:

n₁=n₂=n₃=n₄= 5 weeks

Store 1

∑X₁= 540; ∑X₁²= 58434

X[bar]₁= 108

S₁²= 28.50

S₁= 5.34

Store 2

∑X₂= 437; ∑X₂²= 38663

X[bar]₂= 87.40

S₂²= 117.30

S₂= 10.83

Store 3

∑X₃= 455; ∑X₃²= 41899

X[bar]₃= 91

S₃²= 123.50

S₃= 11.11

Store 4

∑X₄=505; ∑X₄²= 51429

X[bar]₄= 101

S₄²= 106

S₄= 10.30

Totals

N= n₁ + n₂ + n₃ + n₄= 4*5= 20

∑Mean= 108+87.40+91+101= 387.4

∑Variance= 28.50+117.30+123.50+106= 375.30

∑Standard deviation= 5.34+10.83+11.11+10.30= 37.58

Hypothesis test:

H₀: μ₁= μ₂= μ₃= μ₄

H₁: At least one population mean is different.

α: 0.05

The statistic for this test is

[tex]F= \frac{MS_{Treatments}}{MS_{Error}} ~~F_{k-1;N-k}[/tex]

k-1= 3 Df of the treatments, k=4 number of treatments

N-k= 16 Df of errors, N=20 total number of observations in all treatments

[tex]F_{H_0}= \frac{441.78}{93.83}= 4.71[/tex]

The critical region and p-value for this test are one-tailed to the right.

Using the critical value approach:

[tex]F_{k-1;N-k;1-\alpha }= F_{3;16;0.95}= 3.25[/tex]

The decision rule is:

If [tex]F_{H_0}[/tex] ≥ 3.25, reject the null hypothesis.

If [tex]F_{H_0}[/tex] < 3.25, do not reject the null hypothesis.

Using the p-value approach:

Little reminder: The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).

So under the distribution F₃,₁₆ you have to calculate the probability of the calculated  [tex]F_{H_0}[/tex]:

P(F₃,₁₆≥4.71)= 1 - P(F₃,₁₆<4.71)= 1 - 0.9847 = 0.0153

p-value= 0.0153

The decision rule for this approach is

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

The p-value is less than the level of significance, so the decision is to reject the null hypothesis.

I hope this helps!

Answer:

10% probability that both the bus and train will be more than 5 minutes late

Step-by-step explanation:

Independent events:

If two events, A and B, are independent, we have that:

[tex]P(A \cap B) = P(A)*P(B)[/tex]

What is the probability that both the bus and train will be more than 5 minutes late?

The bus being more than 5 minutes late is independent of the train, and vice versa. So

Event A: Bus more than 5 minutes late

Event B: Train more than 5 minutes late

The train is more than 5 minutes late 1/6 of the times they use it

This means that [tex]P(B) = \frac{1}{6}[/tex]

The bus is more than 5 minutes late 3/5 of the times they use it.

This means that [tex]P(A) = \frac{3}{5}[/tex]

Then

[tex]P(A \cap B) = \frac{3}{5}*\frac{1}{6} = \frac{3}{30} = 0.1[/tex]

10% probability that both the bus and train will be more than 5 minutes late