The Central Limit Theorem says that when sample size n is taken from any population with mean μ and standard deviation σ when n is large, which of the following statements are true? The distribution of the sample mean is approximately Normal. The standard deviation is equal to that of the population. The distribution of the population is exactly Normal. The distribution is biased. A I and II B I only C II and III D I, III, and IV E II only

Answer:

n = 5

Step-by-step explanation:

To start off, we know that whenever the bases are the same, their exponents are equal to each other. Therefore, since both of the numbers bases are the same (both are z), we know that they will be equal.

The n can be distributed to the [tex]z^2[/tex] so that it now reads to be:

[tex]z^2^n = z^{10}[/tex]

Exponents are equal, so:

2n=10

Divide the 2 on both sides:

n=5

Answer:

n =5

Step-by-step explanation:

z^2^n

We know that a^b^c = a^ (b*c)

z^(2n)

This is equal to z^10

Since the bases are the same, the exponents are the same

2n = 10

Divide by 2

2n/2 = 10/2

n = 5

Answer:

4√(7^5) and (4√7)^5

Step-by-step explanation:

7^5/4

The above can be expressed as follow: Method 1:

7^5/4

(7^5)^1/4

Recall:

(a^m)^1/n = n√(a^m)

Therefore,

(7^5)^1/4 = 4√(7^5)

Method 2:

7^5/4

(7^1/4)^5

Recall:

(a^1/m)^n = (m√a)^n

Therefore,

(7^1/4)^5 = (4√7)^5

From the illustration above, we can see that 7^5/4 can be expressed as 4√(7^5) and (4√7)^5

Answer:

1/2 a minute (30 seconds)

Step-by-step explanation:

475/50=9.5

450/50=9

9-9.5=.5

Answer:

C

Step-by-step explanation:

Calculate the ratio of corresponding sides, image to preimage, that is

scale factor = [tex]\frac{DE}{AB}[/tex] = [tex]\frac{14}{35}[/tex] = [tex]\frac{2}{5}[/tex] → C

Answer:

The probability that 100 or fewer will have 3 ​girls is 0.00734.

Step-by-step explanation:

The complete question is:

In a family with ​3 children, the probability that all the children are girls is approximately 0.125. In a random sample of 1000 families with ​3 children, what is the approximate probability that 100 or fewer will have 3 ​girls? Approximate a binomial distribution with a normal distribution.

Solution:

Let X represent the number of families who has 3 girls.

The random variable X follows a Binomial distribution with parameters n = 1000 and p = 0.125.

But the sample selected is too large.

So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

1. np ≥ 10

2. n(1 - p) ≥ 10

Check the conditions as follows:

 [tex]np=1000\times 0.125=125>10\\\\n(1-p)=1000\times (1-0.125)=875>10[/tex]

Thus, a Normal approximation to binomial can be applied.

So,  [tex]X\sim N(\mu=np,\sigma^{2}=np(1-p))[/tex]

The mean and standard deviation are:

[tex]\mu=np=1000\times 0.125=125\\\\\sigma=\sqrt{np(1-p)}=\sqrt{1000\times 0.125\times (1-0.125)}=10.46[/tex]

Compute the probability that 100 or fewer will have 3 ​girls as follows:

Apply Continuity correction:

[tex]P(X\leq 100)=P(X<100-0.50)[/tex]

                  [tex]=P(X<99.50)\\\\=P(\frac{X-\mu}{\sigma}<\frac{99.5-125}{10.46})\\\\=P(Z<-2.44)\\\\=0.00734[/tex]

*Use a z-table.

Thus, the probability that 100 or fewer will have 3 ​girls is 0.00734.

Answer:

14 hours 20 minutes

Step-by-step explanation:

→ Convert 2 hours and 40 minutes into minutes

2 hours + 40 minutes ⇒ 2 hours = 120 minutes + 40 minutes ⇒ 120 + 40 ⇒ 160 minutes

→ Convert 11 hours and 40 minutes into minutes

11 hours + 40 minutes ⇒ 11 hours = 660 minutes + 40 minutes ⇒ 660 + 40 ⇒ 700 minutes

→ Add the total minutes together

700 minutes + 160 minutes = 860 minutes

→ Convert 860 minutes into hours

860 minutes = 14 hours + 20 minutes

Explanation:

Assuming you meant to say

P(A) = 11/20

P(B|A) = 13/20

then,

P(A∩B) = P(A)*P(B|A)

P(A∩B) = (11/20)*(13/20)

P(A∩B) = (11*13)/(20*20)

P(A∩B) = 143/400

Answer:

C. 35

Step-by-step explanation:

x^2 + 12^2 = (x + 2)^2

x^2 + 144 = x^2 + 4x + 4

144 = 4x + 4

4x = 140

x = 35

Answer:

C

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean Theorem (a² + b² = c², in this case a = x, b = 12 and c = x + 2) to solve for x.

x² + 12² = (x + 2)²

x² + 144 = x² + 4x + 4

144 = 4x + 4

140 = 4x

x = 35

Answer:

f(x)= x-6

g(x)= x^1/2 (x+3) =√x(x+3) = x √x + 3√x

g(x) × f(x)

=(x√x + 3√x) (x-6)

= x²√x -6x√x + 3x√x - 18√x

= x²√x -3x√x - 18 √x

= x^5/2 - 3x^3/2 - 18^1/2

= √x^5 - 3√x^3 - √18 (B)

Note:

√x = x^1/2

x √x = x^1 × √x= x^1+1/2= x^3/2

x²√x= x^2 × x^1/2 = x^2+1/2 = x^ 5/2

I hope this helps

if u have question let me know in comments ^_^

Answer:

[tex]\sqrt{13}[/tex]

Step-by-step explanation:

Use the distance formula:

[tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]

Insert the values:

[tex](2_{x1},5_{y1})\\\\(-1_{x1},3_{y2})\\\\\\sqrt{(-1-2)^2+(3-5)^2}[/tex]

Simplify:

[tex]\sqrt{(-1-2)^2+(3-5)^2}\\\\ \sqrt{(-3)^2+(-2)^2}\\\\ \sqrt{9+4}\\\\\sqrt{13}[/tex]

The distance between the two points is the square root of 13.

:Done

Answer: [tex]\sqrt{13}[/tex] or 3.61

Step-by-step explanation:

[tex]\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

[tex]\sqrt{\left(-1-2\right)^2+\left(3-5\right)^2}[/tex]

[tex]\sqrt{9+4}[/tex]

[tex]=\sqrt{13}[/tex]

Answer:

The simplified answer of the given equation is -57.

Step-by-step explanation:

For this problem, we are given values for our variables.

k = -1

n = -4

So, let's plug these numbers into our expression so we can easily solve it.

-(-1)² - (4(-1) - 6(-4)) + 9(-4)

Simplify your parentheses.

-(-1)² - (-4 + 24) - 36

-(-1)² - 20 - 36

Now, simplify your exponents.

-1 - 20 - 36

Combine -1 and -20.

-21 - 36

Now, subtract -21 from 36.

-57

Answer:

-18

)())()()()()()()( ;)

Answer:

6 pepper fruits

Step-by-step explanation:

Given the following :

Fraction of pepper in terms of tomato = 2/3

Number of fruits on pepper plant = 9

Therefore number of pepper fruits on pepper plant:

2/3 * number of tomato fruits

2/3 * 9

(2 * 3) = 6

6 pepper fruits.

Answer:

you need to add 11 red circles

Step-by-step explanation:

1:3     one red and three blues

r=12   b=3

r:b  =12:3

12:3 is the same as 4:1

you have to add 11 red circles

Answer:

Step-by-step explanation:

Hey there!!!,

in this problem we are expected to present an equation for the given scenario, and a way out is to model it after the equation of line

i.e y= mx+c

From the problem statement we can see that the constant amount Myles have is $635, and also earnings of $120 weekly.

Comparing the statement withe equation of line we have

  y= 120x+ 635

as "x" is the number of weeks worked and $635 is the constant amount at hand.

Should you need further clarification on this, let me know

[tex]\dfrac{DI}{DR}=\dfrac{DE}{DZ}\\\\\dfrac{DI}{6+2.8}=\dfrac{3}{6}\\\\6DI=26,4\\DI=4,4[/tex]

Answer:

The age of Noi is 13.333 Years and the age of Noy is 12.67 years

Step-by-step explanation:

The given  information are;

The sum of the ages of Noi and Noy = 26 years

Four times Noi's age - Two times Noy's age = 28

Let the age of Noi = X and let the age of Noy = Y

We have;

X + Y = 26 years.................(1)

4X - 2Y = 28 years.............(2)

Divide equation (2) by 2 to get;

(4X - 2Y)/2 = (28 years)/2 which gives;

2X - Y = 14 years.................(3)

Add equation (3) to equation (1), to get;

X + Y +  2X - Y = 26 years + 14  years

3X = 40 years

X = 40/3 = 13.333 Years

From equation (1), X + Y = 26 years, therefore;

Y = 26 - X = 26 - 13.33 = 12.67 years

Therefore, the age of Noi = 13.333 Years and the age of Noy = 12.67 years.

Answer:

Assuming x is the number, then [tex]x=1.6[/tex]

Step-by-step explanation:

If the product of a number and 5 is 8, the equation becomes:

[tex]5x=8[/tex] (assuming x is the unknown number).

We can isolate the variable x by dividing both sides by 5.

[tex]5x\div5 = 8\div5\\x = 1.6[/tex]

Hope this helped!

Answer:

a = 0, i, -i, 1, -1

Step-by-step explanation:

What we're basically looking for here is a number, that when multiplied by itself any amount of times, will get us with the same number.

We know that 0 times and number will be 0, so 0 works.

1 times any number will be 1, and -1 would also work as -1² = 1.

i would also work as it represents the square root of a negative, and -i would also work.

Hope this helped!

Answer:

1. C = 10π, A = 25π

2. 9 cm³

Step-by-step explanation:

Formula for circumference = πd

Formula for area of a circle = πr²

1. Set up the equation for circumference

10π

2. Set up the equation for area (radius = 1/2diameter) and solve

π(5²) = 25π

Formula for volume of a square pyramid = 1/3s² · h

The volume of a square pyramid is equal to 1/3 of the volume of a cube. The formula for a volume of a cube is s³ which is equal to s² · h because a cube has the same side length for all sides. Therefore, the volume of a square pyramid that perfectly fits within a given cube would equal 1/3 the volume of the cube.

1. Set up the equation and solve

27 ÷ 3 = 9

Answer:

Step-by-step explanation:

3.

diameter is equal two radiuses

D = 10 = 2R   ⇒  R = 5

circumference:  C = 2πR = 2R•π = 10π

area:                    A = πR² = π•5² = 25π

4.

If square pyramid fit perfectly inside cube then its base is the same as a face of cube, and the height (H) of pyramid is equal to the edge (S) of its base.

[tex]A_p=\frac13S^2\cdot H =\frac13S^2\cdot S=\frac13S^3=\frac13A_c=\frac13\cdot27\,cm^3=9\,cm^3[/tex]

Answer:

Step-by-step explanation:

[tex]-8\left(-10\right)-7 \times \frac{1}{-1}=87\\\\\mathrm{Apply\:rule}\:-\left(-a\right)=a\\\\=8\times \:10-7\times \frac{1}{-1}\\\\8\times \:10=80\\\\7\times \frac{1}{-1}=-7\\\\=80-\left(-7\right)\\\\\mathrm{Apply\:rule}\:-\left(-a\right)=a\\\\=80+7\\\\=87[/tex]

Answer:

3.66

Step-by-step explanation:

calculate their shares and then add the amount they gave to Jack

Answer:

Let the distance from home to the park be x

Going to the park

Distance=vt

x=14t¹ ——(1)

Going back home

x=10t² ——(2)

Total time=t¹+t²

2.5=t¹+t²

Solving equ. 1 and 2 simultaneously

10x=140t¹

14x=140t²

Adding

4x=140(t¹+t²)

24x=140(2.5)

x=14.58 miles

Total distance= 2x

= 29.16miles

Step-by-step explanation:

Answer:

either 2 or 2 1/2

Step-by-step explanation:

Since the pre-image gets bigger, the scale factor is larger than 1.

Answer:

c as in neither.

Step-by-step explanation:

the question does not give enough info because there are not two variables to be dependant on

Answer:

The Answer would be ∠W ≅ ∠C

Step-by-step explanation:

Only one that is congruent

The measure of the angle ∠TWM is congruent to the measure of the angle ∠ADC. Therefore, the correct option is B.

Two triangles are said to be congruent if their corresponding sides and angles are equal.

A triangle is a three-sided polygon with three edges and three vertices in geometry.

Given that the triangle ∆MTW is congruent to the triangle ∆CAD.

So, we have

∠MTW ≅ ∠CAD

∠WMT ≅ ∠DCA

∠TWM ≅ ∠ADC

If two triangles are equivalent, the ratio of matching sides will stay constant.

The proportion of the point ∠TWM is harmonious with the proportion of the point ∠ADC.

Therefore, at that point, the right choice is B.

Learn more about congruent triangles here:

brainly.com/question/4364353

#SPJ3

Answer:

22 and 23

Step-by-step explanation:

Step 1: Solve the square root

[tex] \sqrt{100 \times 5} [/tex]

[tex] \sqrt{ {10}^{2} \times 5 } [/tex]

We can move the 10² out because it matches the index of the root

[tex]10 \sqrt{5} [/tex]

Step 2: Input into calculator to find decimals

[tex]10 \sqrt{5} = 22.36[/tex]

Therefore the square root of 500 lies between 22 and 23

22 and 23

Because 5000 is between 222

(484) and 232 (529), the square root of 500 is in between 22 and 23..

Answer:

29 divided by 5

quotient is 5 4/5

Step-by-step explanation:

I just took that test from school

Answer: 29 divided by 5. 5 4/5

Step-by-step explanation:

I have proof plz mark me brainliest

Answer:

9 - n^2

Step-by-step explanation:

Answer: 9-x^2

Step-by-step explanation:

no work needed

Answer:

See explanation

Step-by-step explanation:

When we have a positive number and a negative number, let's imagine it with a number line.

<-----------0----------->

If we have the positive number 1:

<-----------0--1-------->

And we want to subtract 1 from it, the number would move to the left

1 - 1 = 0

<-----------0----------->

However, if we were to subtract a negative number, they are opposites. It can't move to the left because that's what a positive number does. The only other way to go: right.

1 + -1 = 2

<-----------0--1--2----->

Hope this helped!