A population has a mean of 128 and a standard deviation of 32. Suppose a sample of 64 is selected. What is the probability that the sample mean will be within +- 5 of the population mean?

We need to know the simple mathematical operations to solve this problem. The final answer on multiplying the sum of 4 and 5 by the difference of 14 and 8 is 54.

We have to use addition, subtraction and multiplication to solve the question. First we need to find the sum which means add 4 and 5. Next we need to find the difference between 14 and 8 which means we need to subtract 8 from 14. Finally we have to multiply both the values to get the final answer.

4+5=9

14-8=6

(4+5) x (14-8)=9 x 6=54

Therefore the final value that we get on multiplying the sum of 4 and 5 by the difference of 14 and 8 is 54.

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The solutions to the equations are :

1.  x= 8 ; y = -2

2.infinitely many solutions.

3. x= - 2 ; y = 0

4.  x= -1 ; y = 5

How are the equations solved?

1.  x+4y=0  --(1)

  3x+2y= 20  ---(2)

(1)*3

3x+ 12y =0   ---(3)

(3) - (2)

(3x+ 12y) -(3x+2y -20)

10y +20= 0

10 y = -20

y = - 2

Substituting y in equation(1)

x+ 4 (-2) = 0

x = 8

The solutions to the equations are x= 8 and y = -2

2.  6x+3y=54  --(1)

2x+y=18   ----(2)

(2)*3

6x+3y=54 --(3)

(3) = (1)

0 = 0

The equations have infinitely many solutions.

3.  x -3y= -2  --(1)

10x+8y=-20  ---(2)

(1)*10

10x - 30y +20 = 0--(3)

(3) - (2)

(10x - 30y +20 )- (10x+8y +20)

-38y = 0

 y = 0

Substituting y in equation(1)

x - 0 = -2

x = -2

The solutions to the equations are x= - 2 and y = 0

4.

3x-y=-8  ---(1)

5x+2y=5  ---(2)

(1)*2

6x -2y+16 =0---(3)

(3) +(2)

(6x -2y+16) +(5x+2y-5)

11x +11 = 0

11x = -11

x = -1

Substituting x in equation(1)

3(-1) -y = -8

-3- y = - 8

- y = -8+3

-y = -5

y = 5

The solutions to the equations are x= -1 and y = 5

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Explanation:

Taking into account the law of cosines, we can write the following equation:

Then, replacing the values for a, b, and c, we get:

Solving for cos A, we get:

Therefore, the value of angle A is:

Now, we can use the law of sines, we can write the following equation:

So, replacing the values and solving for B, we get:

In the same way, Angle C is equal to:

So, the answers are:

A = 51.3°

B = 18.2°

C = 69.5°

As given by the question

There are given that the agent received $5880 commission on a sale of $84000.

Now,

The rate of commission is:

Hence, the rate of commission is 7%.

0.262144 = 26.2% of getting all the 6 questions correctly.

What is Binomial probability ?

The binomial probability is the probability of exactly x successes on n repeated trials, and each trial can only have two outcomes.

This is a binomial distribution problem

Binomial distribution function is represented by :

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 6 multiple choice questions

x = Number of successes required = 6 (we want to get it all right.

p = probability of success = 0.8 (80% chance of getting any individual question right; 0.8 probability of getting each question correctly)

q = probability of failure = 1 - 0.8 = 0.2

P(X = 6) = ⁶C₆ (0.8)⁶ (0.2)⁶⁻⁶

             = 1(0.262144)(1)

             = 0.262

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Answer:

2(4t - 1)

Step-by-step explanation:

8t - 2

The common multiple is 2 because 2 will go into both 8 and 2. Move the multiple of 2 outside, and add ():

2(4t - 1)

1) Let's find out how many times there are more visitors by dividing the number of visitors from A by B's visitors:

Dividing firstly 8 by 4, and then using the exponents pro

In linear equation, Joshua should buy is 255 + 6s ≥ 333.

What is linear equation in math?

Let the sets of spoons be represented by s

The restaurant needs at least 333 spoons.

Each set on sale contains 8 spoons

There are currently 333 spoons.

At least as an inequality is ≥

Hence:

255 + 6 × s ≥ 333

255 + 6s ≥ 333

Therefore, inequality tha can be used to determine s the minimum number of sets of spoons Joshua should buy is

255 + 6s ≥ 333

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Given:

In 2000, the profit of Company A was $9,875,000.

Each year after 2000, the profits fell by $29,532 on average.

So, the losses of the profit per year = $29,532

We will construct a linear model for this scenario

Let the number of years after 2000 = x

And the profit after the year 2000 = y

the linear model will be: y = mx + b

Where m is the slope which represents the losses per year and the b is the initial profit of the year 2000

So, the linear model will be:

now, we will use the equation to find the profit in the year 2030

so, x = 2030 - 2000 = 30

substitute x = 30 into the equation:

So, the answer will be:

The equation of the model: y = -29532x + 9875000

The profit in the year 2030 = 8989040

Given:

A positive number shows a deposit

A negative number shows withdrawals.

Find-: What could $6+

-60 represent

Sol:

+6 represent is:

-60 represent is:

So the answer is:

$6 deposit followed by a $60 withdrawal

We have to solve the following equation for the variable x:

For doing so, we assume that the variables a, b, c and d behave as normal numbers, and we will move the terms with x to the left side, and those who doesn't have it, to the right.

Now, we will factor the variable x, as we want to have just one expression with x, thus:

And lastly, we will divide both sides by 2a-c, and we obtain:

Which is the asked expression for x.

c) (1,0)

1) In order to perform this translation firstly, locate point A in the graph. A is at (-4, 1).

2) Secondly, apply the given rule for this translation for this point.

Pre-image rule Image

(-4,1) (x+5, y-1) (-4+5, 1-1)= (1, 0)

Since the question just asks us A' then We can stop it here and say A' will be at (1,0)

3) So A', is going to be located at point ( 1,0)

171 is 0.9% of 19000

let the unknown number be = y

0.9% * y = 171

0.9% = 0.009

0.009 × y = 171

0.009y = 171

DIvide both sides by 0.009:

0.009y/0.009 = 171/0.009

y = 19,000

Hence, 171 is 0.9% of 19000

We would expect the answer to be a lot greater than 171 because the percentage is quite small (less than 1%). Divindg a number by a very small decimal makes the result large.

Hence, the number would be large.

The most appropriate choice for unitary method will be given by-

Length of driveway  in the drawing is 3 inch

What is unitary method?

Unitary method is the method in which value of a single unit can be calculated from the value of a multiple unit and value of a multiple unit can be calculated from the value of a single unit.

Sometimes value of single unit is less than value of multiple unit

For example - cost of food and quantity of food

Sometimes value of single unit is more than value of multiple unit

For example- Number of men and time taken by those men to do a work

Here,

Scale used by Maureen is 1 inch = 8ft

Actual length of house's driveway = 24 feet

8 ft of room is equal to 1 inch on scale

1 ft of room is equal to [tex]\frac{1}{8}[/tex] inch on scale

24 feet of room is equal to [tex]\frac{1}{8} \times 24[/tex] inch on scale

24 feet of room is equal to 3 inch on scale

Length of driveway  in the drawing is 3 inch

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Answer:

Exactly three times.

Step-by-step explanation:

(6/7) / (2/7) = (6/7) * (7/2) = 3/1 * 1/1 = 3

The graph of a function is given.

When the function of x is -3, that is

That means the input value which is x, gives us negative 3.

Looking at negative 3 from the graph, the value of x where the graph equals negative 3 (on the vertical axis, or y-axis) is either negative 2 or 1. That is

Also, when the input of the function is zero, then you'll have the output as

This means when the value of x is zero, then the output as shown on the graph is 1 (that is the graph touches the y-axis at 1)

Therefore;

(a) One value of x for which f(x) = -3 is -2 (OR 1)

(b) f(0) = 1

ANSWER

$51

EXPLANATION

Let the cost of one cookie be c.

Let the cost of one brownie be b.

3 cookies and 5 brownies cost $19. This means that:

3 * c + 5 * b = 19

3c + 5b = 19 ___(1)

2 cookies and 10 brownies cost $26. This means that

2 * c + 10 * b = 26

2c + 10b = 26 ____(2)

We have two simultaneous equations:

3c + 5b = 19 ___(1)

2c + 10b = 26 ____(2)

From (2):

2c = 26 - 10b

Divide through by 2:

c = 13 - 5b

Put this in (1):

3(13 - 5b) + 5b = 19

=> 39 - 15b + 5b = 19

Collect like terms:

-15b + 5b = 19 - 39

-10b = -20

Divide through by -10:

b = -20 / -10

b = $2

Remember that:

c = 13 - 5b

=> c = 13 - 5(2)

c = 13 - 10

c = $3

Therefore, one cookie costs $3 and one brownie costs $2.

Therefore, the cost of 13 cookies and 6 brownies is:

13 * 3 + 6 * 2

=> 39 + 12

=> $51

13 cookies and 6 brownies cost $51

Answer:

Step-by-step explanation:

46656

Richard’s net pay for the week if he earns $2,200 is equal to $1,797.65.

Mathematically, net pay can be calculated by using this formula:

Net pay = Gross pay - Deductions.

First of all, we would determine Richard's Medicare tax and Social Security tax on $1,000 as follows:

Medicare tax = $2,200 × 1.45/100

Medicare tax = $31.9

Social Security tax = $1,000 × 6.2/100

Social Security tax = $62

Since Richard claims 2 exemptions and paid weekly, we would calculate the withholdings from his weekly pay by using the information provided in Table 1 (see attachment):

Two (2) exemptions = $76.9 × 2 = $153.8

Withholdings = $2,200 - $153.8

Withholdings = $2046.2

Since Richard claims to be married, we would calculate his federal tax withholdings by using the information provided in Table 1 (see attachment):

Over $1,606 = $198.40 plus 25%

= $2046.2 - $1,606 = $440.2

Federal tax withholdings = $198.40 + (25/100 × $440.2)

Federal tax withholdings = $198.40 + $110.05

Federal tax withholdings = $308.45

Now, we can calculate Richard's net pay as follows:

Richard's net pay = Gross pay - Medicare tax - Social Security tax - Federal tax withholdings

Richard's net pay = $2,200 - $31.9 - $62 - $308.45

Richard's net pay = $1,797.65

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There can be two methods that we can use to solve this problem. As per composition of the function, we substitute the function g(x) on the x's of f(x) o get fog. We have

We then substitute 7.5 on the resulting function above to evaluate (f o g) (7.5). We get

The other way around is to start evaluating g(x) for x = 7.5 and then the value that we got in g(x) will be substituted on f(x). We got

The answers to both subparts are with the help of trigonometric functions:

So, (A) The side of the house to the ladder reach:

(B) The horizontal distance between the bottom of the ladder and the house:

Therefore, the answers to both subparts are with the help of trigonometric functions:

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no solution (2nd option)

Explanation:

8x - 6y = 6 .....equation 1

-12x + 9y = 18 .....equation 2

Using elimination method:

we will eliminate y by making both coefficient of y to be the same.

This is done by multiplying equation 1 by 3 and equation 2 by 2

24x - 18y = 18 .....equation 1

-24x + 18y = 36 ....equation 2

Adding both equation:

24x - 24x -18y + 18y = 18 + 36

0 + 0 = 54

Since 0 is not equal to 54, there is no solution (2nd option)

________________________________

x= red titles

two times = 2x

50

2x= 0.5x + 75

2x - 0.5x = 75

(2- 0.5) x = 75

1.5 x = 75

x= 75/ 1.5

x= 50

_______________________

Can you see the updates?

_________________________

Answer

Option D = 50

____________________

Do you have any questions regarding the solution?

Since it is given that trapezoids are similar so,

So value of y is 20.

we have

y/a - 16 = h

solve for y

that means -----> isolate the variable y

so

Adds 16 both sides

y/a=(h+16)

Multiply by a both sides

The next three terms of the following sequences are:

7. The next three terms are 2, 2, and 3.

8. The next three terms of the sequence are 4, 8, and 16.

9. The next three terms of the sequence are 3, 6, and 9.

10. The next three terms of the sequence are 1, 2, and 3.

7.

Consider the recursive formula,

f( 0 ) = 3, f( n ) = f( n - 1 ) + ( n - 2 )

The next three terms of the sequence will be n = 1, 2, and 3.

Then,

f( 1 ) = f( 1 - 1 ) + ( 1 - 2 )

f( 1 ) = f(0) - 1 = 3 - 1 = 2

The second term of the sequence,

f( 2 ) = f( 2 - 1 ) + ( 2 - 2 )

f( 2 ) = f( 1 ) + 0

f( 2 ) = 2

The third term,

f( 3 ) = f( 3 - 1 ) + ( 3 - 2 )

f( 3 ) = f( 2 ) + 1

f( 3 ) = 2 + 1 = 3

8.

Consider the recursive formula,

f( 1 ) = 2, f(n ) = 2f( n - 1 )

The next three terms of the sequence will be n = 2, 3, 4.

Therefore,

f( 2 ) = 2f( 2 - 1 )

f( 2 ) = 2( f (1) )

f( 2 ) = 4

f( 3 ) = 2f( 3 - 1 )

f( 3 ) = 2f( 2 )

f( 3 ) = 8

f( 4 ) = 2f( 4 - 1 )

f( 4 ) = 2f( 3 )

f( 4 ) = 16

Hence, the next three-term are 4, 8, and 16.

9.

Consider the recursive formula,

f( 0 ) = 0, f( n ) = f( n - 1 ) + 3

The next three terms of the sequence will be n = 1, 2, 3.

Then,

f( 1 ) = f( 1 - 1 ) + 3

f( 1 ) = 0 + 3 = 3

f( 2 ) = f( 2 - 1 ) + 3

f( 2 ) = 3 + 3 = 6

f( 3 ) = f( 3 - 1 ) + 3

f( 3 ) = f( 2 ) + 3

f( 3 ) = 6 + 3 = 9

10.

Consider the recursive formula,

f( 0 ) = 1, f( 1 ) = 1, f( n ) = f( n - 1) + f( n - 2 ), for n > 1

Then, the next three terms will be n = 2, 3, 4

f( 2 ) = f( 2 - 1 ) + f( 2 - 2 )

f( 2 ) = f( 1 ) + f( 0 )

f( 2 ) = 1 + 0 = 1

f( 3 ) = f( 3 - 1 ) + f( 3 - 2 )

f( 3 ) = f( 2 ) + f( 1 )

f( 3 ) = 1 + 1 = 2

f( 4 ) = f( 4 - 1 ) + f( 4 - 2)

f( 4 ) = f( 3 ) + f( 2 )

f( 4 ) = 2 + 1

f( 4 ) = 3

The next three terms of the sequence are 1, 2, and 3.

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Answer:Here I hope this helps

1/10=irrational

1/16=rational

1/4=rational

1/2=irrational

1/8=irrational

Step-by-step explanation: you can go into desmos graphing calculator and plug in each number into the square root and it will tell you if its irrational or not.

The value of the given expression is -64.

what is value?

Given expression:

y^2-x^4y

=y^2-x^4y

=y(y-x^4)

Putting value x=2, y=8

8(8-2^4)

=-64

The value of the given expression is -64.

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The constant of variation is 1.6, and then the direct variation equation is:

y = 1.6*x

A direct variation between two variables can be written as:

y = k*x

Where k is called the constant of variation.

Here we know that when x = 20, the value of y is 32, replacing that in the above equation we get:

32 = k*20

Solving this for k we get:

32/20 = k = 1.6

Then the equation is:

y = 1.6*x

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