The figure above shows the probability density function for the random variable x. What is P(3≤x<7)?

The 95​% confidence interval estimate of the mean wake time is equal to (62.61, 88.39).

Given the following data:

Mathematically, a confidence interval of 95% is given by;

α = 1 - 0.95

α = 0.05.

α/2 = 0.05/2 = 0.025.

Also, the degrees of freedom (df) is given by:

Degrees of freedom (df) = n - 1

Degrees of freedom (df) = 16 - 1

Degrees of freedom (df) = 15.

From the Student's t-distribution table, a critical value at t₀.₀₂₅, ₁₅ = 2.131.

Mathematically, the confidence interval for mean is given by:

Mean ± (t-critical × (standard deviation/√(sample size)))

75.5 ± (2.131 × (24.2/√(16))

75.5 ± (2.131 × 6.05)

For the upper end, we have:

75.5 + 12.89 = 88.39

For the lower end, we have:

75.5 - 12.89 = 62.61.

In conclusion, we can deduce that there isn't a significant difference between the mean wake time before and after treatment and as such, this drug isn't effective at the significance level of 0.05.

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The simple interest Trey earns if he makes no additional deposit or withdrawal for a period of 6 years is 600

= 2/100

= 0.02

Simple interest = principal × rate × time

= 5000 × 0.02 × 6

= 600

Therefore, the simple interest Trey earns if he makes no additional deposit or withdrawal for a period of 6 years is 600

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Answer:

Step-by-step explanation:

Equations

7x + 3y = 4z

Second equation

x + y = z                          Multiply the entire equation by 4

4[x + y = z]                      Now distribute the 4 through the equation

4x + 4y = 4z                    Both equations = 4z. Equate the lefts.

Third equation  

7x+3y = 4x + 4y              Subtract 3y from both sides

7x + 3y -3y = 4x + 4y -3y

7x = y + 4x                      Subtract 4x from both sides

7x - 4x = y + 4x - 4x       Combine

3x = y

Answer: 3x = y

Answer:

see the attachment photo!

Probability helps us to know the chances of an event occurring. There are 8 outcomes.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Let's suppose someone flips a fair coin three times.

1. The outcomes of the coins are,

Therefore, there are 8 outcomes.

2. The probability of getting exactly one tail is,

P(X=1) = 2/8 = 1/4

3. The probability of getting at most two tails is,

P(X≤2) = P(X=1) + P(X+2) = 1/4 + 1/2 = 3/4

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Answer:

0 apples

Step-by-step explanation:

Option A

Answer:

C

Step-by-step explanation:

The answer would have to be C cus it can't be A or D

Answer:

Step-by-step explanation:

Remark

The ratio you would use is 7 to 2 to 11

The question is what you you have to multiply these ratios by so the products when added come to 100?

Equation

7*x + 2*x + 11*x = 100        Combine the terms on the left

Solution

20x = 100                           Divide both sides by 20

20x/20  = 100/20              

x = 5

Answer: 55 blue marbles were in the bag.

Answer: 2

Step-by-step explanation:

The value of the expression 5x – 2y + (7x – y)  when x = 7 and y = -2 is 90

The expression is given as:

5x – 2y + (7x – y)

Substitute x = 7 and y = –2 in the above expression

5 * 7 - 2 * -2 + (7 * 7 + 2)

Evaluate the expression

90

Hence, the value of the expression 5x – 2y + (7x – y)  when x = 7 and y = -2 is 90

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Answer:

All equations have like terms

Going by the standard Helium Cylinder/Balloon Chart, the amount of pressure she will require to fill 90 balloons is 300 per squared inch (PSI.)

To get this amount, we simply divide the number of balloons with the total amount of PSI.

Thus:

90/300

= 0.3psi each.

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Answer: 300?

Step-by-step explanation:

tell me if i am wrong

Answer:

83050

Step-by-step explanation:

that's the answer to the question

Answer:

Cylinder

Step-by-step explanation:

Area of rectangular prism = base area * height

                                           = 50 * 5

                                           = 250 square cm

Area of cylinder = base area * height

                          = 50 * 5

                           = 250 square cm

The volume of the fourth doll based on the information given will be 549cm³.

The formula to use will be:

= πr²h

where,

Volume = 8cm³

Diameter = 2.1

Radius = 2.1/2 = 1.05cm

Therefore, 8 = (3.14 × 1.05² × h)

h = 8/(3.14 × 1.05²)

h = 2.31 cm.

The scale factor used is:

= 3.36/2.1

= 1.6

Therefore, the diameter of the fourth doll will be:

= 2.1 × 1.6³

= 8.6

Radius will be:

= 8.6/2 = 4.3.

The height of the fourth doll will be:

= 2.31 × 1.6³

= 9.46

The volume of the fourth doll will be:

= 3.14 × 4.3² × 9.46

= 549cm³

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Answer:

Step-by-step explanation:

'

Answer:

(x+4)(x-5)

Step-by-step explanation:

We can look at it by thinking of two numbers, that add up to -1 and multiply to -20. We can first do this by looking at factors of -20, which are 1, -20, -1, 20, 2, -10, -2, 10, and so on. After looking through it, we can notice that -5 and 4 added equal -1, and when multiplied equal to -20, so they work. So, we factor to (x+4)(x-5)

Answer:

(x +5) (x -4)

Step-by-step explanation:

Factors of 20:

1,20

2,10

4,5

4 and 5 combine to create 1

+5 -4 = 1

(x +5) (x -4)

Answer:

6x^2-3x-2

Step-by-step explanation:

6x^2 + 2x - 20 / 4 x x - 2

6x^2 + 2x - 5x - 2

6x^2 -3x - 2

Answer:

-6

Step-by-step explanation:

we can put the value of x as -2 cause f(-2) we can substitute the value...

f(-2)= 3*-2

-6

Nadia cannot have 18 dimes and 5 quarters.

The equations that represent the question are:

D + Q = 23 equation 1

0.1d + 0.25q = 3.65  equation 2

The number of dimes is 14 and the number of quarters is 9.

The equation that represents the total amount of money she has is: 0.1d + 0.25q = 3.65

0.1(18) + 0.25(5) = 3.05

$3.05 is less than 3.65

D + Q = 23 equation 1

0.1d + 0.25q = 3.65  equation 2

Given the above equations, multiply equation 1 by 0.1

0.1d + 0.1q = 2.3 equation 3

Subtract equation 3 from 2

0.15q = 1.35

Divide both sides by 0.15

q = 1.35 / 0.15

q = 9

To determine the value of d, subtract 9 from 23 : 23 - 9 = 14

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Answer:

Volume of prism 1: 104 cubic inches

Surface area of prism 2: 650 square inches

Step-by-step explanation:

To find the volume of prism 1, set up a proportion using the side lengths and the volume of prism 2.

The ratio of the side lengths will be your scale factor. When finding volume using scale factor, you need to cube the scale factor. The numerator in the proportion are from prism 1 and the denominator is prism 2. Prism 1 is the numerator since it is the new image and we are solving for it's volume.

[tex](\frac {4}{10}) ^{3} =\frac{x}{1625} \\\\\frac{64}{1000} =\frac{x}{1625} \\\\[/tex]

[tex]1000x=104000\\\frac{1000x}{1000} =\frac{104000}{1000} \\x = 104[/tex]

To find the surface area of Prism 2, we are going to setup another proportion, but this time we are going to square the scale factor since we are finding area. Prism 2 will be the numerator and prism 1 will be the denominator.

[tex](\frac{10}{4} )^2 = \frac{x}{104} \\\frac{100}{16} =\frac{x}{104} \\16x=10400\\\frac{16x}{16}=\frac{10400}{16}\\ x= 650[/tex]

Equation of the line CD is equals to [tex]y = \frac{-x}{4} +7[/tex].

" Parallel lines are defined as the lines in the same plane never intersect with each other. They are equidistant to each other in the same plane."

Formula used

[tex]Slope = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

According to the question,

Given,

Coordinates of A [tex](x_{1},y_{1})[/tex] = ( -2 , 5)

Coordinates of B [tex](x_{2},y_{2})[/tex] = ( 6 , 3)

Substitute the value to get the slope of line AB we get,

[tex]Slope of line AB 'm_{1}' =\frac{3-5}{6-(-2)}[/tex]

                    ⇒ [tex]m_{1} = \frac{-2}{8}[/tex]          

                              [tex]= \frac{-1}{4}[/tex]

Coordinates of C [tex](x_{1},y_{1})[/tex] = ( x ,y)

Coordinates of B [tex](x_{2},y_{2})[/tex] = ( 8,5)

Substitute the value to get the slope of line CD we get,

[tex]Slope of line CD 'm_{2}' =\frac{5-y}{8-x}[/tex]

Lines AB and CD are parallel.

Slope of parallel lines are equal.

Therefore,

                     [tex]m_{2} = m_{1}[/tex]          

                 ⇒ [tex]\frac{5-y}{8-x}[/tex] [tex]= \frac{-1}{4}[/tex]

                ⇒[tex]5-y = \frac{-1}{4} (8-x)[/tex]

                ⇒ [tex]y = \frac{-x}{4} +7[/tex]

Hence, equation of the line CD is equals to [tex]y = \frac{-x}{4} +7[/tex].

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Answer:

great question buddy and I wish you the most

Step-by-step explanation:

x-y=b^2/2=2

The answer is 3 I work it out

Based on the calculations, the equation of this parabola is equal to (x - 6)² = 16(y + 4).

Mathematically, the standard equation with the vertex for a parabola is given by:

(y - k)² = 4a(x - h) for horizontal parabola.

(x - h)² = 4a(y - k) for vertical parabola.

where:

By critically observing the points, we can deduce that both the focus and vertex lie on the same vertical line x = 6.

Given the following data:

Focus with points = (6, 2).

Vertex (h, k) = (6, –4).

Note: a = 2 - (-4) = 2 + 4 = 6.

Substituting the given parameters into the formula, we have;

(x - 6)² = 4 × 4(y - (-4))

(x - 6)² = 16(y + 4).

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Answer:

B

Step-by-step explanation:

if it is warm the Megan is swimming

The expression that is equivalent to complex fraction  [tex]\frac{1 - \frac{1}{x}}{2}[/tex] is  [tex]{\frac{x - 1}{2x}}[/tex]

To answer the question, we need to know what fractions are

Fractions are rational numbers written in the form a/b where

where

To find the expression similar to the complex fraction [tex]\frac{1 - \frac{1}{x}}{2}[/tex], we simplify the fraction.

So,  [tex]\frac{1 - \frac{1}{x}}{2}[/tex]

Taking L.C.M of x in the numerator, we have

[tex]\frac{1 - \frac{1}{x}}{2} = \frac{\frac{x - 1}{x}}{2} \\[/tex]

Simplifying, we have

[tex]\frac{1 - \frac{1}{x}}{2} = \frac{\frac{x - 1}{x}}{2} \\= {\frac{x - 1}{2x}}[/tex]

So, the expression that is equivalent to the complex fraction  [tex]\frac{1 - \frac{1}{x}}{2}[/tex] is  [tex]{\frac{x - 1}{2x}}[/tex]

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