14b. State the domain of the function below. Use interval notationf(x) = 3Vx + 1 - 5

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

Answer:

not ennough information to answer the question

Step-by-step explanation:

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)

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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Explanation

The formula for the Amount based on compound interest is given as:

Since the principal is compounded annually, therefore n =1. Also, P = principal = $7000, ratte = r = 8%, t= time

Hence when t = 1 year

Answer A: $7560

When t = 2 years

Answer B: $8164.8

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: c.800 that's the answer

The correct estimate of the number of plates on the plate rack is 800.

The number of racks of plates in the City Restaurant is 19.

The number of plates in each rack is 37.

We need to find the estimated number of the total plates on the plate rack in the City Restaurant.

To find the estimate, we will round off the numbers to the nearest ten.

Rounding a number implies simplifying it while retaining its value close to what it was. The end output is less precise but more usable.

The number of racks of plates is rounded off and becomes 20.

The number of plates in each rack is rounded off and becomes 40.

The total number of plates in the rack is given by the multiplication of the two numbers obtained.

The total number of plates on the plate rack is 20x40 = 800.

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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

Answer:

Step-by-step explanation:

46656

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)

In this problem we have that

the solution is the shaded area above the dashed line

so

Find the equation of the dashed line

x -----> outside temperature

y ----> inside temperature

Find the slope

take the points (0,20) and (10,30)

m=(30-20)/(10-0)

m=10/10

m=1

the equation is

y=x+20

therefore

the inside temperature is always 20 degrees warmer than the outside temperature

Let be "a" the number of medals that Country A won, "b" the number of medals that Country B won, and "c" the number of medals that Country C won.

You can set up the following System of equations using the information given in the exercise:

In order to solve the System of equations, you can follow these steps:

1. Substitute the second equation into the third equation:

2. Substitute this new equation and the second original equation, into the first original equation:

3. Solve for "c":

4. Knowing the value of "c", you can substitute it into the second original equation and then evaluate, in order to find the value of "b":

5. Knowing the value of "b" and "c", you can substitute them into the third original equation and then evaluate, in order to find the value of "a":

Therefore, the answer is:

- Country A won 76 medals.

- Country B won 25 medals.

- Country C won 18 medals.

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.

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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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)

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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For the linear regression the dependent and independent variables are:

y: "weight of a woman" (measured in pounds)

x: "height of a woman" (measured in inches)

You have to calculate the estimated linear regression equation:

Where

b₀ is the estimate of the y-intercept

b₁ is the estimate of the slope

To calculate both by hand you have to use the following formulas:

y bar and x bar are the sample means for the weight and height

n is the number of women observed, in this case the sample size is

n=5 women

Next calculate the needed summatories, i.e. add each obervation from the corresponding variables

∑xi= 335

∑xi²= 22455

∑yi=670

∑xiyi=44962

ybar=∑yi/n= 670/5=134 pounds

xbar=∑xi/n= 335/5=67 inches

Replace the values in the formulas:

Slope:

y-intercept

The estimated linear equation is:

y=-348.4+7.20x

b)

The y-intercept of the linear regression indicates the value of the estimated mean of the variable y when x equals zero.

The slope of the linear regresion insicates the change of the estimated mean of the variable y when the variable x increases one unit.

So in terms of this exercise you can interpret the y-intercept as:

-348.4pounds is the estimated average weight of women when their height is zero inches.

→ Note that this interpretation has no logical meaning, at least not one applicable in real life, but for the regression is a valid mathematical result and interpretation.

And the slope can be interpreted as:

7.2pounds/inches is the modification of the estimated average weight of weomen when their height increases 1 inch.

Explanation

Area:

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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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%.

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

$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

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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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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________________________________

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?

Given:

a = 4

b = 5

c = unknown

Let's find the length of c.

Here, we are given a right triangle, where c is the longest side.

The longest side of a right triangle is called the hypotenuse.

To find the hypotenuse, apply Pythagorean Theorem:

Input values into the equation above:

Take the square root of both sides:

Therefore, the length of the missing side, c =

Answer:

See below

Step-by-step explanation:

The MONTHLY payment for each loan is just the interest and principal paid for each month

I just used the first line of each amortization:

First one  26 + 196 = $ 222 per month

Second one 26 + 127 = $ 153 per month

     Sorry if the numbers are incorrect....the image is very fuzzy....

           but this is the method for the answer .

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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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