A large population has skewed data with a mean of 70 and a standard deviation of 6. Samples of size 100 are taken, and the distribution of the means of these samples is analyzed. a) Will the distribution of the means be closer to a normal distribution than the distribution of the population?
b) Will the mean of the means of the samples remain close to 70?
c) Will the distribution of the means have a smaller standard deviation?
d) What is that standard deviation?
a. Yes.
b. Yes.
c. Yes.
d. 0.6.

Answer:

x≤8

Step-by-step explanation:

let the number be x

¾x+14≤20

LCM=4

3x+56≤80

3x≤80-56

3x≤24

x≤8

I am unable to add number line here

Answer:

0.5

Step-by-step explanation:

you just need see at one point. i see at point (1, 0.5)

Answer:

36

Step-by-step explanation:

The tangents from the same point are equal. Each point of the triangle extend 2 tangents to the circle.

Tangents from the uppest point: 8+8=16

Tangents from the lowest point: 4+4=8

Tangents from the third point:

10-4=6

6+6=12

Perimeter: 16+8+12=36units

Brainliest please~~

Answer:

Treatment variable = Teaching methods

Confounding variable = Teacher's teaching prowess

Step-by-step explanation:

The treatment variable here is that variable which is applied on the student in other to ovtujba measure of the dependent or response variable, the response variable here is the test score, while the treatment variable is the independent variable, which are the teaching methods.

The confounding variable is that variable which is capable of causing a spurious association in our measurement and also has an effect on the test score. However, this variable isn't taken into account during our experiment. One possible confounding variable could be the Teacher's individual teaching prowess regardless of the teaching method. This could cause the student to get a better grasp of what is being taught by one teacher than the other.

Answer:Treatment variable = Teaching methods

Confounding variable = Teacher's teaching prowess

Step-by-step explanation:

Answer: i think

the corrcect answer is 0.5*10^-1

Step-by-step explanation:

hope this helps

9514 1404 393

Answer:

  g(x) = 3|x|

Step-by-step explanation:

Each value of g is 3 times the corresponding value of f:

  g(x) = 3·f(x)

  g(x) = 3|x|

Answer:

5x+50

Step-by-step explanation:

you have one x. An x plus fifty. And 3 mire x's. So 5 x's and a 50.

Answer:

15=225

20= 400

Step-by-step explanation:

the small 2 means multiply that number two times :)

Answer:

[tex]15^2\\[/tex] = 225

[tex]20^{2}[/tex] = 400

Step-by-step explanation:

[tex]x^{2}[/tex] = [tex]x[/tex] × [tex]x[/tex]

basically it's the number times itself

15 × 15 = 225

20 × 20 = 400

Answer:

Whe we have two functions, f(x) and g(x), the composite function:

(f°g)(x)

is just the first function evaluated in the second one, or:

f( g(x))

And the domain of a function is the set of inputs that we can use as the variable x, we usually start by thinking that the domain is the set of all real numbers, unless there is a given value of x that causes problems, like a zero in the denominator, for example:

f(x) = 1/(x + 1)

where for x = -1 we have a zero in the denominator, then the domain is the set of all real numbers except x = -1.

Now, we have:

f(x) = x^2

g(x) = x + 9

then:

(f ∘ g)(x) = (x + 9)^2

And there is no value of x that causes problems here, so the domain is the set of all real numbers, that, in interval notation, is written as:

x ∈ (-∞, ∞)

(g ∘ f)(x)

this is g(f(x)) = (x^2) + 9 = x^2 + 9

And again, here we do not have any problem with a given value of x, so the domain is again the set of all real numbers:

x ∈ (-∞, ∞)

(f ∘ f)(x) = f(f(x)) = (f(x))^2 = (x^2)^2 = x^4

And for the domain, again, there is no value of x that causes a given problem, then the domain is the same as in the previous cases:

x ∈ (-∞, ∞)

(g ∘ g)(x) = g( g(x) ) = (g(x) + 9) = (x + 9) +9 = x + 18

And again, there are no values of x that cause a problem here, so the domain is:

x ∈ (-∞, ∞)

Given:

[tex]YA[/tex] is the angle bisector of [tex]\angle XYZ[/tex].

[tex]m\angle XYZ=52^\circ[/tex]

To find:

The measure of [tex]m\angle ZYA[/tex].

Solution:

It is given that [tex]YA[/tex] is the angle bisector of [tex]\angle XYZ[/tex]. It means

[tex]m\angle XYA=m\angle ZYA[/tex]            ...(i)

Now,

[tex]m\angle XYA+m\angle ZYA=m\angle XYZ[/tex]

[tex]m\angle ZYA+m\angle ZYA=52^\circ[/tex]            [Using (i)]

[tex]2m\angle ZYA=52^\circ[/tex]

Divide both sides by 2.

[tex]m\angle ZYA=\dfrac{52^\circ}{2}[/tex]

[tex]m\angle ZYA=26^\circ[/tex]

Therefore, the required value is [tex]m\angle ZYA=26^\circ[/tex].

Answer:

$6.40 per movie

Step-by-step explanation:

Since the fifth movie is free, find the total cost by multiplying 8 by 4:

8(4)

= 32

Find how much you actually pay per movie by dividing this by 5:

32/5

= 6.4

So, you are actually paying $6.40 per movie

Answer:

$6.40

Step-by-step explanation:

If you buy five movies, but only pay for the first four, then that is the first amount we need to find. Paying $8 for four movies means you are paying $32. If you are paying $32 for five movies, then you are paying $6.40 per movie.

Math:

8 + 8 + 8 + 8 + 0 = 32

32/5 = 6.4

tan²(θ) - sin²(θ) = sin²(θ)/cos²(θ) - sin²(θ)

-- because tan(θ) = sin(θ)/cos(θ) by definition of tangent --

… = sin²(θ) (1/cos²(θ) - 1)

-- we pull out the common factor of sin²(θ) from both terms --

… = sin²(θ) (1/cos²(θ) - cos²(θ)/cos²(θ))

-- because x/x = 1 (so long as x ≠ 0) --

… = sin²(θ) ((1 - cos²(θ))/cos²(θ))

-- we simply combine the fractions, which we can do because of the common denominator of cos²(θ) --

… = sin²(θ) (sin²(θ)/cos²(θ))

-- due to the Pythagorean identity, sin²(θ) + cos²(θ) = 1 --

… = sin²(θ) tan²(θ)

-- again, by definition of tan(θ) --

Answer:

x =56 (corresponding angles are equal)

Answer:

56°

Step-by-step explanation:

Since these two lines are parallel, and these two angles are at the corresponding position, the required angle measure is 56

Answer:

15

Step-by-step explanation:

Because 3/4 of 20 or 75% of 20 is 15

Answer:

25 liters of 20%

50 liters of 50%

Step-by-step explanation:

x = liters of 50%

75 - x = liters of 20%

50x + 20(75 - x) = 40(75)

50x + 1500 - 20x = 3000

30x = 1500

x = 50

75 - x = 25

Answer:

1

Step-by-step explanation:

Slope = change in y over change in x

If you look at the graph as y goes up 1 x goes up 1

So slope = 1/1 or just 1

Answer:

m=1

Step-by-step explanation:

Hi there!

We're given the graph of a line and we need to find the slope of the line

There are many ways to do this, but the easiest is to calculate it from two points

The formula for the slope (m) calculated from 2 points is [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex], where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) are points

So we can take 2 points from the graph of the line to find the slope

For example, let's take (-1,0) and (0,1)

Let's label their values to avoid any confusion before we substitute their values into the formula

[tex]x_{1}[/tex]=-1

[tex]y_{1}[/tex]=0

[tex]x_{2}[/tex]=0

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

now substitute into the formula *remember: we have SUBTRACTION in the slope formula

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

substitute

m=[tex]\frac{1-0}{0--1}[/tex]

simplify

m[tex]\frac{1}{0+1}[/tex]

simplify again

m=[tex]\frac{1}{1}[/tex]

divide

m=1

Therefore the slope of the line is 1

Hope this helps! :)

Answer:

The radius of the circle is 3 units

The center of the circle lies on the x-axis.

The radius of this circle is the same as the radius of the circle whose equation is x^2 + y^2 = 9

Step-by-step explanation:

Answer:

The price of the house is $ 853,735.05.

Step-by-step explanation:

Since Mr. Arju wishes to purchase a house, and to buy the house he needs to make a down payment of $ 300,000 and also pay $ 15,000 every quarter for the next 8 years, if the interest charge is 9% per year compounded quarterly, to determine what is the price of the house, the following calculation must be performed:

300,000 + (15,000 x 12 x 8) = X

300,000 + (180,000 x 8) = X

300,000 + 1,440,000 = X

1,740,000 = X

X x (1 + 0.09 / 4) ^ 8x4 = 1,740,000

X x (1 + 0.0225) ^ 32 = 1,740,000

X x 1.0225 ^ 32 = 1,740,000

X x 2.0381030257737 = 1,740,000

X = 1,740,000 / 2.03810

X = 853,735.05

Therefore, the price of the house is $ 853,735.05.

Answer:

-666

Step-by-step explanation:

a1 = 6

an = -5 an-1  +4

a2 = -5 a1 +4 = -5*6 +4 = -30 +4 = -26

a3 = -5 a2 +4 = -5 (-26) +4 = 130+4 = 134

a4 =  -5 a3 +4 = -5 (134) +4 = -670+4 =-666

Answer:

-65

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Given f(x) then f(x + a) is a horizontal translation of f(x)

• If a > 0 then shift left by a units

• If a < 0 then shift right by a units

Here the shift is 2 units to the right

Then

f(x) = x² and g(x) = (x - 2)² → D

Explanation:

We replace x with x-1 to shift 1 unit to the right. This is because we're making each new input 1 smaller than the old input, which means we're moving the xy axis 1 unit to the left while keeping the f(x) curve fixed in place. That gives the illusion f(x) is moving 1 unit to the right.

The -1 at the end will subtract 1 from the y coordinate and shift everything down by 1 unit.

Answer:

D

Step-by-step explanation:

1 unit Right ³√x-1

unit down (³√x-1)-1

Answer:

D

C

Step-by-step explanation:

One equation must have a slope that is the negative reciprocal of the other equation's slope.

The the sentence I've given you is correct, it is probably a little difficult to understand. Let's use an example

y = 1/2 x + 4

The slope of this line = 1/2

Therefore if you want a negative reciprocal, it would - 2 so y=-2x would be perpendicular to y = 1/2x + 4.

Just to be sure you understand, I'll put the graph of these two equations below.

===================================

So to answer your question

8)

is D. All the others have signs that are the same. They are reciprocals but with signs the same.

9) This is a little harder. You have reciprocals in all of them. But the slope must be positive. So that means that only a and c can be true. A does not go through (4,-1). C does.

y = 1/4 * 4 - 2

y = 1 - 2

y = - 1

So the answer is C

Answer:

4.69

Step-by-step explanation:

4+9/100+6/10​

4 is a whole number

9/100 = .09

6/10 = .6

Adding together

4+.09+.6

4.69

Answer:

4.69

Step-by-step explanation:

[tex] \small \: 4 + \frac{9}{100} + \frac{6}{10} \\ [/tex]

[tex] \small4 + \frac{9}{100} + \frac{3}{5} \\ [/tex]

[tex] \small \frac{100 \times 4}{100 \times 1} + \frac{9}{100} + \frac{ 3 \times 20}{5 \times 20} \\ [/tex]

[tex] \small \frac{400}{100 \times 1} + \frac{9}{100} + \frac{ 60}{100} \\ [/tex]

[tex] \small \frac{400 + 9 + 60}{100 \times1} \\ [/tex]

[tex] \small \frac{469}{100 \times 1} \\ [/tex]

Divide we get

4.69

Answer:

The value of this investment at the end of the 5 years is of $662.5.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Dina invests $600 for 5 years at a rate of 2% per year compound interest.

This means that [tex]P = 600, t = 5, r = 0.02, n = 1[/tex]. Thus

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]A(t) = 600(1 + \frac{0.02}{1})^{t}[/tex]

[tex]A(t) = 600(1.02)^t[/tex]

Calculate the value of this investment at the end of the 5 years.

This is A(5). So

[tex]A(5) = 600(1.02)^5 = 662.5[/tex]

The value of this investment at the end of the 5 years is of $662.5.

Answer:

the answer is B because y depends on x