The area of a rectangle is (x4 + 4x3 + 3x2 – 4x – 4), and the length of the rectangle is (x3 + 5x2 + 8x + 4). If area = length × width, what is the width of the rectangle? x + 1 x – 9 x + 4 x – 1.

x-value that corresponds to the z-score of 2.33 is 81.65.

Mean = 70

Standard deviation = 5

z score = 2.33

Using the z-score formula:

z = (x - mean) / SD

Plug the values:

2.33 = (x-70)/5

    x = 5(2.33) +70

    x = 81.5

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Answer:

A ≈ 314.2 units

Step-by-step explanation:

       To find the area of the circle, we will use the given formula. We are given the diameter (d), 20, and the radius (r) is half of the diameter. 20 units / 2 = 10 units for our radius (r).

               A = πr²

               A = π(10)²

               A ≈ 314.15927

       Now, we are asked to round to the nearest tenth.

               A ≈ 314.2 units

For the given line of best fit, equation which represents the prediction of values between the actual data points is representing an example of interpolation.

As given in the question,

Given line of best fit equation,

Here prediction is to be done for the values which are between the actual data points.

The predicted values are within the range.

Predicted values represents either extrapolation or interpolation

If predicted values are outside the actual points it is extrapolation.

Here it is between the actual data points.

So, it is interpolation.

Therefore, for the given line of best fit, equation which represents the prediction of values between the actual data points is representing an example of interpolation.

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Yes, the cost y in dollars and the amount of yogurt x are proportional the equation is y = 0.08x.

Given:

At the local dairy farm, kareem buys a 32-oz container of yogurt for $2. 56. Jonah buys a 6-oz container of yogurt for $0. 48.

y varies directly as x :

y = kx

k = constant of proportionality

y = 2.56 and x = 32

y = kx

k = y/x

= 2.56/32

k = 0.08

substitute k we get

y = 0.08x.

so x and y are directly proportional.

Therefore Yes, the cost y in dollars and the amount of yogurt x are proportional the equation is y = 0.08x.

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Answer: 45x + 75y < 2000

Step-by-step explanation:

x = # of desks

45 = cost/desk

y = # of tables

75 = cost/table

2000 = maximum dollar amount that can be spent

inequality:

45x + 75y < 2000

Answer:

0.00825814344701024621501758678697

Step-by-step explanation:

Use a calculator please<3

If the Wilson family drove 472 miles in 8 hours. The family that traveled at the higher rate of speed  and  rate is: D: Wilson; 59 mi/h

Using this formula to find the speed

Speed = Distance /Time

Let plug in the formula

Rate of speed for Gonzalez family

Rate of speed  = 342 ÷ 6

Rate of speed = 57 mph

Rate of speed  for Wilson family

Rate of speed = 472 ÷ 8

Rate of speed = 59 mph

Therefore the correct option is D.

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The solution set of the inequalities can be identified by investigating the coefficient of x^2

The graph of a parabola is represented by a curve as used in the graphs attached in the equation

Parabolic graphs are also called graph of quadratic equation

The equation is usually in this form

y = ax^2 + bx + c

when it is "y =" it is a vertical parabola the graph will either opens up or down

The coefficient  of "x^2" which is "a" says if the curve opens upwards or downwards. when a is:

y > x^2 - 1 "a" is positive hence opens upwards

y ≤ -x^2 + 4  "a" is negative hence opens downwards

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Answer:

B

Step-by-step explanation:

You Basically need to find halfway between 5a and -3 which has a difference of 8 so halfway is 4 so 3a +4=a

and as it is on the same line it would be (a,-2b)

Amount of money in the account after 19 years when no deposits or withdrawals are done for the invested amount $3,500 with 3.5% interest rate compounded quarterly is equal to $6,800(nearest hundred dollars).

As given in the question,

Amount  invested by Nathan is principal 'P' = $3,500

Interest rate 'r' = 3.5% compounded quarterly

Number of compounding periods per year for given quarterly 'n'  = 4

Time period 't'= 19 years

Amount of money in the account after 19 years when no deposits or withdrawals are done.

Let 'A' be the amount.

Formula used:

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

Substitute the value in the formula we get,

A = 3500 × [ 1 + (0.035/4) ]⁽⁴⁾⁽¹⁹⁾

   =  3500 × [ 1 + 0.00875]⁽⁴⁾⁽¹⁹⁾

   =  3500 × [ 1.00875]⁷⁶

   = 6,786.06 (approximately)

   = $6800 (nearest hundred dollars)

Therefore, amount of money in the account after 19 years when no deposits or withdrawals are done for the invested amount $3,500 with 3.5% interest rate compounded quarterly is equal to $6,800(nearest hundred dollars).

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Answer:

y=9

x=3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Bring one of the equations into the other one:

3x = x + 6

3x - x = 6

2x = 6

x= 3

Then, bring the found value to find the value other variable:

y = 3x = 3(3) = 9

The interest when the classmate is calculating the amount in a savings account after 10 years is $2600.

From the information, the classmate is calculating the amount in a savings account after 10 years and the deposit is $13,000 and the annual simple interest rate is 2%.

It should be noted that interest is calculated as:

= (Principal × Rate × Time) / 100

= ($13000 × 2 × 10) / 100

= $2600

The simple interest is $2600.

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Answer:

34a^3

Step-by-step explanation:

Since every term is alike we can add and subtract freely

(I wont be writing a^3 on every term to make this less confusing)

17 + 19 - 25 - (-17 + 19 - 25)

first the parenthesis do what is inside the parenthesis

17 + 19 - 25 - (-23)

now add everything

11 - (-23)

simplify

11 + 23

34

everything of course has a^3 at the end so

34a^3 is the answer

Answer:

23) $248,943.75

24) $384

Step-by-step explanation:

23) 266,250/100= 2662.5 which is 1%

     2662.5×6.5=17,306.25 which is 6.5%

     Since it is a mark up we subtract 17,306.25 from 266,250 to find the

     original price.

24) 320÷10=32 which is 10%

     32×2= 64 which is 20%

     Since it is a discount we add 64 to 320 to find the original price.

;)

Answer:

1. 8.9x10^5

2. 5.05x10^1

3. 7x10^26

4. 1.8x10^11

5. 4x10^4

6. 7x10^-18

7.  7.1x10^4

8. 6.6x10^-3

9.  9x10^19

10. 1.8x10^7

11. 2x10^10

12. 5x10^10

Answer:

70 students and 130 adults

Step-by-step explanation:

The value of the expression w-8 is 6 when w=8

An expression is combination of variables, numbers and operators.

The given expression is w minus 8

w-2

The w is the variable and 2 is the number and minus is the operator

Now given variable w is 8

So substitute the value 8 in the expression w-2

8-2=6

Hence 6 is the value of the expression w-2 when w=8

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Answer:

it would already be in it the y is alone

Answer:

View explanation.

Step-by-step explanation:

y =  -2x+10

M is the slope or how much the y value increases every time the x value increases by one. b is the y-intercept or when x=0.

It is already in y=mx+b form.

A painter can paint 60 square feet every 1 hour.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A painter can paint 15 square feet every 1/4 hour.

Now,

Since, A painter can paint 15 square feet every 1/4 hour.

Let painter can paint in every 1 hour = x square feet

So, By definition of proportional as;

⇒ 15 / (1/4) = x / 1

Solve for x as;

⇒ 15 × 4 = x

⇒ x = 60 square feet

Thus, A painter can paint 60 square feet every 1 hour.

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The time spent by Khadijah to work on her history project is 2 hrs.

Addition and subtraction are the two basic arithmetic operations in Mathematics. In Addition, we sum up two or more numbers to get another number and it is denoted by the symbol (+).

In subtraction, we take away a number from another number and it is denoted by (-).

Here we have      

Khadijah has at most 3 hrs to work on a math assignment and a history project.

The time taken by Math assignment = 1 hrs

Here we need to find the time that can be spent working on her history project.

[ Here we will use subtraction to get the answer ]

From given data  

The time can be spent on History = Total time - Time taken by Math  

= 3 hrs - 1 hr = 2hrs

Therefore,

The time spent by Khadijah to work on her history project is 2 hrs.

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Answer:

B) [tex]8(2)^{x}[/tex]

Step-by-step explanation:

Using the Product Property of Exponents, we know that two exponents with the same base can have their exponents added together.

Step 1 - Convert 8 to an exponent with a base of 2:

[tex]8 = 2^{3}[/tex]

Step 2 - Use the Product Property of Exponents:

[tex]2^{3} *2^{x}[/tex]

[tex]2^{x+3}[/tex]

Hope this helps and have a great day! :)

The graph of the given table of data is attached below. And the best scale for this one is x axis 1 cm = 20 units and y axis 1 cm = 1 units. The value of A is 60 and the value of B is 140.

Graph:

Graph can be used to view the table of data in a visual manner for the easy understanding of the given range of data.

Given,

Here we have the table of data that contains the details about the length and their corresponding mass in kg.

Now, we have to plot this data on the graph and then we have to find the best scale suitable for this graph.

Finally, we have to find the value of A and B in the plotted graph.

In order to plot the graph for the given table, we have to input the values on the graphing calculator,

Then we get the graph like the following.

While we lookin into the graph we have identified then the best scale suitable for this graph is

x axis

1 cm = 20 units and

y axis

1 cm = 1 units.

Now, the value of A is 60 and the value of B is 140.

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Answer:

see screenshot

Step-by-step explanation:

the equation is always f(x) = m * x + b
with b being where the graph hits the y axis and m being how much the graph rises or drops (then m is negative) when you go 1 to the right on the x axis

Answer:

18m + 30

Step-by-step explanation:

times everything in the bracket by 6

Answer:

1/4 is a equivalent ratio

Step-by-step explanation:

hope it helped :)

Answer:

-240

Step-by-step explanation:

−16√3⋅5√3

-16(5)√(3*3)

When you multiply numbers with the same radical (in this case square root) the numbers inside the radical can be multipled with each other. The numbers outside (in this case -16 and 5) should also be multiplied with each other.

-16(5)√9

-80√9

-80*3

-240

The equation in slope intercept form is y = -4x + 24.

From the graph:

yellow points are (6,0) and (4,8).

slope intercept form is y = mx + c.

slope m = 8 - 0 / 4 - 6

= 8/-2

= -8/2

= -4

Substitute  m and (6,0)

y = mx + c

0 = -4*6 + c

c = 24

y = mx + c

y = -4x + 24.

Therefore The equation in slope intercept form is y = -4x + 24.

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