6.1.3
What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?

Answer:

Step-by-step explanation:

hello,

I assume that you mean

[tex]h(x)=\dfrac{12}{x-1}[/tex]

so first of all let's take x real different from 1 , as this is not allowed to divide by 0

[tex](hoh^{-1})(x)=x=h(h^{-1}(x))=\dfrac{12}{h^{-1}(x)-1} \ \ \ so\\h^{-1}(x)-1=\dfrac{12}{x} \\\\h^{-1}(x)=1+\dfrac{12}{x}[/tex]

and this is defined for x real different from 0

hope this helps

Answer:

1/2

Step-by-step explanation:

The numbers that are 6 or even on the cards are 2, 4, and 6.

3 cards out of a total of 6 cards.

3/6 = 1/2

Answer:

1/2 chance

Step-by-step explanation:

There are 3 numbers that fit the rule, 2, 4, and 6. 3/6 chance of picking one or 1/2, simplified.

Answer:

  (3.6, 0), (0, -2)

Step-by-step explanation:

To find the y-intercept, set x=0:

  -5·0 +9y = -18

  y = -18/9 = -2

To find the x-intercept, set y=0:

  -5x +9·0 = -18

  x = -18/-5 = 3.6

The intercepts are ...

  x-intercept: 3.6

  y-intercept: -2

please see the attached picture for full solution..

Hope it helps..

Good luck on your assignment...

Given:

An equilateral triangle JKL inscribed in circle M.

Solution:

To draw an equilateral triangle inscribed in circle follow the steps:

1: Draw a circle with any radius.

2. Take any point A, anywhere on the circumference of the circle.

3.  Place the compass on point A, and swing a small arc crossing the circumference of the circle.

Remember the span of the compass should be the same as the radius of the circle.

4. Place the compass at the intersection of the previous arc and the circumference and draw another arc but don't change the span of the compass.

5. Repeat this process until you return to point A.

6. Join the intersecting points on the circle to form the equilateral triangle.

So the correct option is A. The width must be equal to the radius of circle M.

Answer:

The 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night is (0.133, 0.161).

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].

For this problem, we have that:

[tex]n = 2305, \pi = \frac{339}{2305} = 0.147[/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}} = 0.147 - 1.96\sqrt{\frac{0.147*0.853}{2305}} = 0.133[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.147 + 1.96\sqrt{\frac{0.147*0.853}{2305}} = 0.161[/tex]

The 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night is (0.133, 0.161).

Answer:

Explained below.

Step-by-step explanation:

The question is:

Compare the distributions using either the means and standard deviations or the five-number summaries. Justify your choice.

Set A: {36, 51, 37, 42, 54, 39, 53, 42, 46, 38, 50, 47}

Set B: {22, 57, 46, 24, 31, 41, 64, 50, 28, 59, 65, 38}

The five-number summary is:

The five-number summary for set A is:

Variable   Minimum       Q₁         Median        Q₃         Maximum

  Set A       36.00       38.25        44.00       50.75        54.00

The five-number summary for set B is:

Variable   Minimum       Q₁         Median        Q₃         Maximum

 Set B         22.00      28.75        48.00       58.50         65.00

Compute the mean for both the data as follows:

[tex]Mean_{A}=\frac{1}{12}\times [36+51+37+...+47]=44.58\approx 44.6\\\\Mean_{B}=\frac{1}{12}\times [22+57+46+...+38]=44.58\approx 44.6[/tex]

Compare mean and median for the two data:

[tex]Mean_{A}>Median_{A}\\\\Mean_{B}>Median_{B}[/tex]

Compute the standard deviation for both the set as follows:

[tex]SD_{A}=\sqrt{\frac{1}{12-1}\times [(36-44.6)^{2}+...+(47-44.6)^{2}]}=6.44\approx 6.4\\\\SD_{B}=\sqrt{\frac{1}{12-1}\times [(22-44.6)^{2}+...+(38-44.6)^{2}]}=15.56\approx 15.6[/tex]

Answer:

(f o g) = x, then, g(x) is the inverse of f(x).

Step-by-step explanation:

You have the following functions:

[tex]f(x)=-\frac{2}{x}-1\\\\g(x)=-\frac{2}{x+1}[/tex]

In order to know if f and g are inverse functions you calculate (f o g) and (g o f):

[tex]f\ o\ g=f(g(x))=-\frac{2}{-\frac{2}{x+1}}-1=x+1-1=x[/tex]

[tex]g\ o\ f=g(f(x))=-\frac{2}{-\frac{2}{x}+1}=-\frac{2}{\frac{-2+x}{x}}=\frac{2x}{2-x}[/tex]

(f o g) = x, then, g(x) is the inverse of f(x).

Answer:

If the correlation coefficient is 1, then the slope must be 1 as well.

Step-by-step explanation:

Coefficient of correlation is used in statistics to determine the relationship between two variables. Correlation coefficient and slope always have same sign. It measures the strength of linear relation between two variables. The values of correlation coefficient ranges between 0 to 1. where 0 determines that there is no relationship between two variables.

If the correlation coefficient is 1, then the slope must be 1 as well.

The correlation coefficient (ρ) is a measure that determines the degree to which the movement of two different variables is associated.

So, the false statement is:

If the correlation coefficient is 1, then the slope must be 1 as well.

Learn more:https://brainly.com/question/16557696

Answer: 151

Step-by-step explanation:

if prior population proportion is unknown , then the formula is used to find the sample size :

[tex]n=0.25(\frac{z_{\alpha/2}}{E})^2[/tex]

, where [tex]z_{\alpha/2}[/tex] = Two tailed critical value for significance level of [tex]\alpha.[/tex]

E = Margin of error.

Given : margin of error = 8%= .08

For 95% confidence level , two tailed critical value = 1.96

Now, the required sample size :

[tex]n=0.25(\frac{1.96}{0.08})^2\\\\=0.25(24.5)^2\\\\=150.0625\approx151[/tex]

Hence, the size of the sample needed = 151.

Answer:

x = 15

y = 90

Step-by-step explanation:

Step 1: Find x

We use Definition of Supplementary Angles

9x + 3x = 180

12x = 180

x = 15

Step 2: Find y

All angles in a triangle add up to 180°

3(15) + 3(15) + y = 180

45 + 45 + y = 180

90 + y = 180

y = 90°

Answer:

a. The volume of Pyramid A is double that of Pyramid B.

b. The new volume of B is equal to the volume of A.

Step-by-step explanation:

The base of pyramid A is a rectangle with length 10 meters and width 20 meters.

The base of pyramid B is a square of side length 10 meter.

Both pyramids have the same height, h.

The volume of a pyramid is given as:

V = lwh / 3

where l = length

w = width

h = height

The volume of Pyramid A is:

V = (10 * 20 * h) / 3 = 66.7h cubic metres

The volume of Pyramid B is:

V = (10 * 10 * h) / 3 = 33.3h cubic metres

By comparing their values, the volume of Pyramid A is double that of Pyramid B.

If the height of B increases to 2h, its new volume is:

V = (10 * 10 * 2h) / 3 = 66.7h cubic metres

The new volume of B is equal to the volume of A.

Answer:

x = 7

Step-by-step explanation:

This problem can be solved using angular bisector theorem.

It states that if any angle of triangle is bisected by a line , then that line

divides the opposite side of that angle in same proportion as that of two other sides which contain the angle.

__________________________________

Here one angle is is divided into parts theta

Thus,

using angular bisector theorem

14/21 = 6/3x-12

=> 14(3x-12) = 21*6

=> 3x-12 = 21*6/14 = 9

=> 3x = 12+9 = 21

=> x = 21/3 = 7

Thus, x = 7

Answer:

multiply 0.85x40

Step-by-step explanation:

Answer:

Step-by-step explanation:

1l ........8.5 miles

x l .......6 miles

-----------------------

x=6*1/8.5

x=0.70 l

2*0.7=1.4 l petrol/day ( to work and come back home)

5*1.4=7 l/week ( 5 days works in a week)

7*1.26=8.82 L /week

8.82>8.5

The petrol costs more

So the answer is NO

Answer:

The first first five terms of this sequence are

Step-by-step explanation:

[tex]a(n) = 27(0.1)^{n - 1} [/tex]

where n is the number of term

For the first term

n = 1

[tex]a(1) = 27(0.1)^{1 - 1} = 27(0.1) ^{0} [/tex]

= 27(1)

Second term

n = 2

[tex]a(2) = 27(0.1)^{2 - 1} = 27(0.1)^{1} [/tex]

= 27(0.1)

Third term

n = 3

[tex]a(3) = 27(0.1)^{3 - 1} = 27(0.1)^{2} [/tex]

Fourth term

n = 4

[tex]a(4) = 27(0.1)^{4 - 1} = 27(0.1)^{3} [/tex]

Fifth term

n = 5

[tex]a(5) = 27(0.1)^{5 - 1} = 27(0.1)^{4} [/tex]

Hope this helps you

yes

Step-by-step explanation:

parallelogram are quadrilaterals with two sets of parallel sides. since square must be quadrilaterals with two sets of parallel sides ,then all squares are parallelogram ,a trapezoid is quadrilateral.

Answer:

  the height of the cylinder is 7 units greater than the radius

Step-by-step explanation:

When you match the forms of the equations ...

  [tex]V=\pi r^2(r+7)\\V=\pi r^2h[/tex]

you see that the factor (r+7) corresponds to the height (h) of the cylinder. That is ...

  the height of the cylinder is 7 units greater than the radius.

Answer:

y-int = C/B

Step-by-step explanation:

Ax + By = C

y-int = C/B

Answer:

I hope this helps.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

1, 3, 4, 6, 2, 4, 5, 6, 2, 3, 1, 4, 0, 4, 4, 4, 8, 9, 7, 4

Arrange the numbers from smallest to largest

0,1, 1,2,2, 3,3, 4, 4,4,4,4,4 , 4, 5, 6, 6,   7, 8, 9,

There are 20 numbers

The middle number is between 10 and 11

0,1, 1,2,2, 3,3, 4, 4,4   ,4,4,4 , 4, 5, 6, 6,   7, 8, 9,

The median is 4

Solution,

Arranging the data in ascending order:

0,1,1,2,2,3,3,4,4,4,4,4,4,4,5,6,6,7,8,9

N(total number of items)= 20

Now,

Median:

[tex] (\frac{n + 1}{2)} ) ^{th \: item} \\ = (\frac{20 + 1}{2} ) ^{th \: item} \\ = \frac{21}{2} \\ = 10.5 \: th \: \: item[/tex]

Again,

Median:

[tex] \frac{10 \: th \: item + 11 \: th \: item}{2} \\ = \frac{4 + 4}{2} \\ = \frac{8}{2} \\ = 4[/tex]

Answer:

B

Step-by-step explanation:

The answer is B because in order for the square root of a number to be equal to another number, the answer squared should be the number under the square root.

B. [tex](-4)^2\neq -16[/tex].

Hope this helps.

Answer:

The difference of the functions is (f-g)(x) = 3x - 3

Step-by-step explanation:

In the problem, we are asked to find the difference of the two functions, f(x) and g(x). When we see (f-g)(x), this means that we are going to subtract g(x) from f(x).

f(x) = 5x - 2

g(x) = 2x + 1

(f-g)(x) = (5x - 2) - (2x + 1)

Distribute the negative to (2x + 1)

(f-g)(x) = 5x - 2 - 2x - 1

Combine like terms. Make sure your answer is in standard form.

(f-g)(x) = 3x - 3

So, the answer to the equation is (f-g)(x) = 3x - 3

Answer:

data bar

Step-by-step explanation:

Answer:

chart

Step-by-step explanation:

Answer:

I think so you meant to write 62 as 6^2

If this is the question , then the answer is 6 x 6

HOPE THIS HELPS AND PLS MARK AS BRAINLIEST

THNXX :)

Answer:

B. 6 × 6

Step-by-step explanation:

6²

The square of a number means that the number is multiplied by itself.

6 × 6 (expanded form)

Answer:

[tex]\huge\boxed{x=\sqrt{66}}[/tex]

Step-by-step explanation:

ΔADC and ΔABD are similar (AAA)

Therefore the cooresponging sides are in proportion:

[tex]\dfrac{AD}{AC}=\dfrac{AB}{AD}[/tex]

Substitute

[tex]AD=x;\ AC=6+5=11;\ AB=6[/tex]

[tex]\dfrac{x}{11}=\dfrac{6}{x}[/tex]          cross multiply

[tex](x)(x)=(11)(6)\\\\x^2=66\to x=\sqrt{66}[/tex]

Answer:

2.99

Step-by-step explanation:

Take the total cost and divide by the number of cards

71.76/24 = 2.99

The cost per car is 2.99

Answer:

b. $2.99.

Step-by-step explanation:

To get the price per car, you get the total price divided by the total number of cars.

That would be 71.26 / 24 = 2.969166667, which is most close to b. $2.99. Those are some cheap cars!

Hope this helps!

Answer:

A velocity of 120km/h is needed to cover the distance in one hour

Step-by-step explanation:

The velocity formula is:

[tex]v = \frac{d}{t}[/tex]

In which v is the velocity, d is the distance and t is the time.

A car travelling from Ibadan to Lagos at 90 km/hr takes 1 hour 20 min.

This means that [tex]v = 90, t = 1 + \frac{20}{60} = 1.3333[/tex]

We use this to find d.

[tex]v = \frac{d}{t}[/tex]

[tex]90 = \frac{d}{1.3333}[/tex]

[tex]d = 90*1.3333[/tex]

[tex]d = 120[/tex]

The distance is 120 km.

How fast must one travel to cover the distance in one hour?

Velocity for a distance of 120 km(d = 120) in 1 hour(t = 1). So

[tex]v = \frac{d}{t}[/tex]

[tex]v = \frac{120}{1}[/tex]

[tex]v = 120[/tex]

A velocity of 120km/h is needed to cover the distance in one hour

Answer:

a) [g ° h](x)  = 3x² +6

b) [h ° g](x) =3 x²+36x+108

Step-by-step explanation:

Explanation:-

a)

Given g(x) = x+6 and h(x) = 3x²

Given [g ° h](x) = g(h(x))

                          = g(3x²)       (∵ h(x) =3x²)

                         = (3x²)+6      (∵ g(x) =x+6)

∴ [g ° h](x)  = 3x² +6

b)

Given [h ° g](x) = h (g(x))

                          = h(x+6)     (∵ g(x) =x+6)

                         = 3 (x+6)²    (∵ h(x) =3x²)

                         = 3 (x²+2(6)x+36)    (∵ (a + b)² = a²+2ab+b²)

                         = 3 (x²+12x+36)

                        = 3 x²+36x+108)

     ∴ [h ° g](x) =3 x²+36x+108

Answer:

-978

Step-by-step explanation:

1.) Use Distributive property (by multiplying 15 by the values in parentheses): -735=15m + 13935

2.) Subtract 13,935 on both sides, to move that value to the left side, to further  isolate the variable m.

-735-13935=15m + 13935 - 13935

3.)-Simplify/Combine Like Terms

-14,670=15m

4.) Divide both sides by 15 to isolate and solve for m

-14,670/15=15m/15

5.) Simplify

-978=m    

6.) Rearrange so m is on left side and value is on right side

m=-978