In a certain distribution, the mean is 70 with a standard
deviation of 3. At least what fraction of the numbers are
between the following pair of numbers?
61 and 79

Answer:

N = 20

Step-by-step explanation:

5/3 = 1 2/3

20/12 = 1 8/20

They are equivalent

The probability with replacement is = 1/16

The probability without replacement is= 5/16

What do you mean by probability with replacement?

When the results must be put back into the sample space, the probability with replacement is utilized. This means that once an item is selected, it is replaced in the sample space, keeping the sample space's total number of elements constant.

Since cards should be replaced, 5 lions or 5 birds

so, the probability is

= 5/20 ÷ 5/20

=1/16

without replacement,

since cards should not be put back, for the second draw only 19 cards are left

so, the probability is

=5÷20 × 5÷19

=5/16

Hence ,

The probability with replacement is = 1/16

The probability without replacement is= 5/16

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Answer:

Domain: (neg infinity, pos infinity)

Range: (pos infinity, 3]

Step-by-step explanation:

For the given equation (x/4)+3= 1/5, the value of x which will make the given equation valid is lies between the numbers of ( -10 and -15).

As given in the question,

Given equation is equal to :

(x/4)+3= 1/5

Simplify the given equation (x/4)+3= 1/5 to get the value of x we have,

(x/4)+3= 1/5

Take least common multiple of 4 and 1 we get,

( x + 12) / 4 = 1/5

⇒5( x +12 )  =  4

⇒ 5x + 60 = 4

⇒ 5x = -56

⇒ x= -11.2

-11.2 lies between (-10 and -15).

Therefore, for the given equation (x/4)+3=1/5, the value of x which will make the given equation valid is lies between the numbers of

(-10 and -15).

The complete question is:

Consider the following equation:

(x/4)+3= 1/5

The value of x that will make the equation above valid lies between

which of the following numbers?

A) 10 and 15

B) -1 and -5

C) 1 and 5

D) -10 and -15

E) -5 and -10

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Answer

Infinite solutions

Step-by-step explanation:

try any example you want it keeps going on and on.

Answer:

4/9

Step-by-step explanation:

Based on the given conditions, formulate: 12 division symbol(12 +15)

Calculate the sum or difference: 12/27

Cross out the common factor: 4/9

get the result:

Answer: 4/9

Answer:

3,4,5

Step-by-step explanation:

x+x+1+x+2

therefore ,

4(x+2)=17+3

4x+8=20

4x=20-8

4x=12

x=3

∵∵∵∵∵∵∵∵∵∵∵∵.........................ω

The percent of the decrease in the size of the sugar order is 40%.

According to the question,

We have the following information:

Sweet Treats Bakery ordered 1,090 kilograms of sugar. This time, the bakery is ordering 654 kilograms.

We know that following formula is used to find the percent decrease:

100*(original amount-final amount)/original amount

(More to know: the same formula is used to find the percent increase. It can used to find any percent increase or decrease given that the final and initial amount or price is given.)

100(1090-654)/1090

100*436/1090

40%

Hence, the percent of the decrease in the size of the sugar order is 40%.

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The amount of money that Lena needs to put each quarter for the annuity to have a total value of $96,000 is $953.45.

An annuity is when a series of payment is made either at the beginning of a period or at the end of a period over a period of time.

An ordinary annuity is when the payment is made at the end of the period. When the interest is compounded quarterly, it means that four times in a year, the amount that is invested and the interest that has already being earned increase in value.

The formula that can be used to determine the quarterly payments is:

Payment = future value / annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

Payment = $96,000 / [{(1.009^72) - 1} / 0.009]  = $953.45

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The value of x in given triangle is 6.403

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given triangle is a right angled triangle whose one angle is 90 degrees.

We find the value of x by using pythagoras theorem.

the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse

4²+5²=x²

16+25=x²

41=x²

Take square root on both sides

x=√41=6.403

Hence the value of x in given triangle is 6.403

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The correct system of equations is 5x-y=2,x-5y=10

In order to find the system of equations of the graph, we have to check the solution in the graph and then check for the system of equations that gives the same value.

Looking at the graph, the values of x and y at the point of intersection is the solution. Thus:

x =  0 and y = -2

Let's check the equations now:

5x+3y=-6, 3x+5y=-10

Solve for x and y using elimination

3 (5x+3y=-6)

5 (3x+5y=-10)

15x + 9y = -18

15x + 25y = -50

-6y = 32

y = -32/6 = -16/3 (This cannot be the system)

3x-5y=10, x-5y=-10

3x-5y = 10

x-5y = -10

2x = 20

x = 20/2 = 10  (This cannot be the system)

5x-y=2,x-5y=10

1(5x-y=2)

5(x-5y=10)

5x -y =2

5x-25y = 50

24y = -48

y = -48/24 = -2

put y = -2 into 5x -y =2:

5x -(-2) =2

5x + 2 = 2

5x = 0

x = 0

Therefore, 5x-y=2,x-5y=10 is the system of equations. The 3rd option is the answer. Move it to the box

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Answer:

282 inches

Step-by-step explanation:



24*8+

The mean of the probability distribution of X is 0.9375.

Given that,

From the given

We have to find the probability distribution of X and mean of X.

Now, We know,

X --                               0         1          2        3        4

Probability of X--        1/2     1/4       1/8      1/16     1/16

The mean is average of the distribution

Statistics refers to deviation as the difference between the observed value of a data point and the expected value. The average deviation of a data point from the mean, median, or mode of the data collection is known as the mean deviation, sometimes known as the mean absolute deviation. 

μₓ=0×1/2+1×1/4+2×1/8+3×1/16+4×1/16

μₓ=1/4+1/4+3/16+1/4

μₓ=15/16

μₓ=0.9375

Therefore, The mean distribution of X is 0.9375.

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Answer:

The Board of Governors of the Federal Reserve System is responsible for the discount rate and reserve requirements, and the Federal Open Market Committee is responsible for open market operations.

Step-by-step explanation:

The error in this answer is that : The sum of angle of triangle is 180°

What is Triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Since, we know that Angle sum property of triangle is

∠A + ∠B + ∠C = 180°

Now, let ∠A = 115, ∠B = 39 and ∠C = m∠1

Substituting the value, we get

115° + 39° + m∠1 = 180°

154° + m∠1 = 180°

m∠1 = 180 - 154

m∠1 = 26°

Thus, m∠1 = 26°

Hence, The error for finding m∠1 is that angle sum of the triangle is equal to 180° and not 360°

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Answer:

The answer is 35 children and 105 adults

Step-by-step explanation:

we don't know the number of kids or adults in the theater , so they are unknown.

x: adults

y: kids

we know that y=3x (1)

we also know that all the people in the theater are 140.

so we also know that x+y= 140 (2)

And now you need to take (1) and put it in (2):

y=3x

x+y= 140 x+3x=140 =} 4x=140=} x=140/4=} x=35 kids. so if we put on (1) the number of the kids we have the number of adults: y=3*35=}y=105 adults

I hope I helped !

The functions f(x) = (2x - 3) / 2 and g(x) = (2x + 3) / 2 are the inverse functions because the composite of the given functions equal to x that is fog = x and gof = x.

The conditions for two functions f and g to be inverses: f(g(x)) = x or g(f(x)) = x.

where, f(g(x)) and g(f(x)) is the composite function.

We are given:

f(x) = (2x - 3) / 2

g(x) = (2x + 3) / 2

Let us find the value of f(g(x)) and g(f(x)):

Substitute the value of x with g(x) in f(x), we will get:

f(g(x)) = (2 * g(x) - 3) /2 = (2 * ((2x + 3) / 2) - 3) /2 = (2x + 3 - 3) / 2 = 2x / 2 = x

So, f(g(x)) = x.

Substitute the value of x with f(x) in g(x), we will get:

g(f(x)) = (2 * f(x) + 3) /2 = (2 * ((2x - 3) / 2) + 3) /2 = (2x - 3 + 3) / 2 = 2x / 2 = x

So, g(f(x)) = x.

Thus, the functions f(x) = (2x - 3) / 2 and g(x) = (2x + 3) / 2 are the inverse functions because the composite of the given functions equal to x that is fog = x and gof = x.

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Answer:

x = 4.5

Step-by-step explanation:

5(2x + 1) = 50  Distribute the 5

5(2x) + (5) (1) = 50

10x +5 = 50  Subtract 5 from both sides

10x = 45  Divide both sdies by 10

x = 4.5

Answer:

w<-28

Step-by-step explanation:

multiply both sides by 2 : -6 > w +22

subtract 22 : w < -28

Answer:

Step-by-step explanation:

What is the value of 3 + 5x when x=3?

3 + 5x =

3 + 5 × 3 =

3 + 15 =

18

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

Answer:

F-1(x) = 4x2 - 3 x<0

The ordered pair that is not a solution to the inequality y ≥ 2x² - 4x + 2 is:

(-1,6).

The inequality is given as follows:

y ≥ 2x² - 4x + 2.

Each ordered pair has the following format:

(x-coordinate, y-coordinate).

Then the numeric value of the inequality is going to be calculated for each ordered pair, as follows:

Then the numeric values of the inequality for each ordered pair are presented as follows:

The contradiction, that is, the statement which is false, is given at the following ordered pair:

(-1,6).

Hence it is not a solution to the given inequality.

The ordered pairs are given by the image shown at the end of the answer.

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Answer:10,000

Step-by-step explanation:

Answer: 260 calories

Step-by-step explanation:

    If one serving has 80 calories, we will multiply 80 by 3 1/4 to find the total number of calories in 3 1/4 servings.

80 calories * (3 1/4) servings = 260 calories

Answer:

Step-by-step explanation:

there are 6 numbers, but 3 and 6 take up double the space, so the probabilities are not 6 but 8

1/8 is your answer

Answer:

31

Step-by-step explanation:

2⋅5+5⋅3+2⋅3

10+15+6

31

The area of the garden with a base of [tex]6\frac{1}{2}[/tex] feet and a height [tex]2\frac{5}{8}[/tex] feet is equal to 17.06 square feet.

What is a Parallelogram?

In the given question, it is said that the garden decided to be created by the Johnson family is in the shape of a parallelogram.

The base and height of the parallelogram are given as  [tex]6\frac{1}{2}[/tex] feet and [tex]2\frac{5}{8}[/tex] feet respectively.

[tex]\implies b=6\frac{1}{2} =\frac{13}{2}[/tex], and

[tex]h=2\frac{5}{8} =\frac{21}{8}[/tex]

The area of a parallelogram is calculated using the formula,

[tex]A=b \times h[/tex]

Substituting the values in the given formula, we get

[tex]A=\frac{13}{2} \times \frac{21}{8} \\\implies A=\frac{273}{16}\\ \implies A=17.06 ft^{2}[/tex]

Therefore, the required area of the garden is equal to 17.06 square feet.

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