Please answer question 5 and 6.
5.Given the functions f(x)=-2x + 4 and g(x) = 2x- 8, find the value of x for which f(x) = g(x).
6.Graph the function

The most appropriate choice for tabular data will be given by-

Specimen B is the longest and its size is 0.011 cm. So Monroe's teacher wants each student to draw the sketch of Specimen B

What is tabular data?

Data given in the form of rows and columns is known as tabular data.

Here,

Size of specimen A = 0.008 cm

Size of specimen B = 0.011 cm

Size of specimen C = 0.0025 cm

Size of specimen D = 0.004 cm

Size of the longest specimen = 0.011 cm

Specimen B is the longest and its size is 0.011 cm. So Monroe's teacher wants each student to draw the sketch of Specimen B

To learn more about tabular data, refer to the link-

https://brainly.com/question/3632175

#SPJ9

Complete Question

The table has been attached

Specimen    Actual length(cm)     Size seen under microscope (cm)

A                          0.008

B                          0.011

C                          0 .0025

D                          0.0040

The Range of the given function graph is gotten as; Option D: (-4, -1, 0, 1, 2)

The range of a function is defined as a set of all possible output values for which a function is said to hold.

Now, when it comes to a function graph, we can easily say that the range of the function of the graph will be the set of possible values along the y-axis. That is all possible y-values.

Now, in the given graph, we are given 5 coordinates and the y values at each of these coordinates would represent the range of the graph. Thus;

Range = (-4, -1, 0, 1, 2)

Read more about Range of function graph at; https://brainly.com/question/12200177

#SPJ1

Answer:

Step-by-step explanation:

32

When earn 2% on $1000 for 2 years if this interest rate is doubled then the interest rate will be 4% and the interest is $80.

From the information, the person earns 2% on $1000 for 2 years and this interest rate is doubled, the interest rate will be: = 2% × 2 = 4%

It should be noted that simple interest is calculated as:

Interest = Principal × Rate × Time / 100

Interest = 1000 × 4 × 2 /100

Interest = 8000 / 100

Interest = $80

Learn more about interest on:

brainly.com/question/25793394

#SPJ1

The measure of each angle are 36° and 144°

What is Supplementary angle?

Two angles are said to be supplementary if their sums total 180 degrees. A linear pair's two angles, like angles 1 and 2 in the illustration below, are always supplementary. But two angles don't have to be close to one another to be supplementary. In the following image, 3 and 4 are supplementary since their sums equal 180 degrees.

Let the provided angle be x, the supplementary angle be y.

y = x + 108 since x has 108° greater than y.

The total of the additional angles is 180°.

x + y = 180,

x + x + 108 = 180,

and x = 180 - 108.

2x = 72

x = 72/2

x = 36

Then,

y = x + 108

y = 36 + 108

y = 144

Consequently, the angles are 36° and 144°.

To learn more about Supplementary angle click on the link

https://brainly.com/question/12919120

#SPJ9

From the graph provided, it can be seen that:

There is a maximum at (6,1)

Therefore, the answer is the following:

The function has a relative maximum of 1 at x = 6

(8x-3)/12

Step-by-step explanation:

Answer:

$82.50

Step-by-step explanation:

82.5 times 0.7 = 57.75

doing 57.75 + 30% wouldn't work, so you have to increase the number (original price) being discounted until you get 57.75

also, the '0.7' is 70% which also means '30% off' because you took 30% away from the original price that was 100%

math calculator saves the day? dont use paper or it would take a long time (unless it was a test or teacher said no)

Answer:

9

Step-by-step explanation:

→ Multiply by every value to see

735 - ( 24.99 × 9 ) = 510.09

∴ He has to add money in the 9th month otherwise he will be charged

Answer:

9

Step-by-step explanation:

24.99 x 9 = 224.91

735 - 224.91 = 510.09

Given the following expression:

Making a comparison statement out of this will be: 27 is 3 times more than 9.

The point of intersection of the system of equations is (3, 4) and this is plotted in the graph shown below.

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect, meet, or cross each other, which is typically represented as an ordered pair containing the point, x-axis and y-axis.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In conclusion, the coordinate (3, 4) is the point of intersection of the given system of equations.

Read more on graphs here: brainly.com/question/4546414

#SPJ1

The linear equation in slope intercept form is y = 200x + 200

where y represents the amount in the savings account of Jacalyn at the end of x months beginning from May.

In the slope intercept form, slope (the numerical coefficient of variable x) is having a numerical value of 200 and vertical intercept is the constant of term of the equation i.e. 200. The positive value of slope indicates that the gradient of straight line representing this linear equation is positive. Positive value of vertical intercept indicates that the linear equation's graph plot shall not pass through the origin but will intercept the y-axis at 200.

To know more about "intercept" click here

https://brainly.com/question/9682526

#SPJ1

This probability of shipment being accepted is 84%.

And most similar deliveries will be allowed since the likelihood of receiving a sample with much more than three damaged batteries is extremely low.

If at least three batteries fail to satisfy standards, the delivery would be approved.

This may be described as a binomial distribution, with n = 54 samples as well as a p = 0.03 probability of not satisfying the parameters of any battery.

If n ≤ 3 the package will be accepted.

The probability of this event is:

P(D ≤ 3) = P(D = 0) + P(D = 1) + P(D = 2) + P(D = 3)

P(D = k) = (n! ÷ (k!(n-k)!)) × [tex]p^{k}[/tex] × [tex](1 - p)^{n - k}[/tex]

P(D = 0) = (54! ÷ (0!(54)!)) × [tex]0.03^{0}[/tex] × [tex](0.97)^{54}[/tex]

P(D = 0) = 1 × 1 × 0.110

P(D = 0) = 0.110

P(D = 1) = (54! ÷ (1!(53)!)) × [tex]0.03^{1}[/tex] × [tex](0.97)^{53}[/tex]

P(D = 1) = 54 × 0.03 × 0.205

P(D = 1) = 0.3321

P(D = 2) = (54! ÷ (2!(52)!)) × [tex]0.03^{2}[/tex] × [tex](0.97)^{52}[/tex]

P(D = 2) = 1431 × 0.0009 × 0.205

P(D = 2) = 0.264

P(D = 3) = (54! ÷ (3!(51)!)) × [tex]0.03^{3}[/tex] × [tex](0.97)^{51}[/tex]

P(D = 3) = 24804 × 0.000027 × 0.211

P(D = 3) = 0.141

Then,

P(D ≤ 3) = P(D = 0) + P(D = 1) + P(D = 2) + P(D = 3)

P(D ≤ 3) = 0.110 + 0.3321 + 0.264 + 0.141

P(D ≤ 3) = 0.8471

Learn more about the binomial distribution at

https://brainly.com/question/13044555?referrer=searchResults

#SPJ9

The number of breakfast Greg can eat from a box of cereal if he eats 1 1/2 servings for breakfast everyday is 8 breakfast.

Number of breakfast Greg can eat in a regular-sized box = A regular-sized box of cereal / servings of breakfast eaten everyday

= 12 ÷ 1 1/2

= 12 ÷ 3/2

= 12 × 2/3

= 24/3

= 8 breakfast

Cost of regular-sized box of cereal = $4.29.

Cost of one breakfast from a regular-sized box of cereal = Cost of regular-sized box of cereal ÷ Number of breakfast Greg can eat in a box

= $4.29 / 8

= 0.53625

Approximately,

$0.54 per breakfast

Number of breakfast Greg can eat in a family-sized box = A family-sized box of cereal / servings of breakfast eaten everyday

= 18 servings / 1 1/2

= 18 ÷ 3/2

= 18 × 2/3

= 36/3

= 12 servings

Therefore, the number of more servings of breakfasts Greg could eat from 1 family-sized box

= Number of breakfast Greg can eat in a family-sized box - Number of breakfast Greg can eat in a regular-sized box

= 12 servings - 8 servings

= 4 servings

Read more on unit rate:

https://brainly.com/question/620388

#SPJ1

Answer:

= 4 servings

Step-by-step explanation:

3⁴-21÷7

According to PEMDAS ( order of operations):

First, Do exponents before multiplying or dividing: 3^4

81-21÷7

Then, divide before subtracting (27÷7 )

81- 3

Finally, subtract

78

The most appropriate choice for probability will be given by:

Probability that the number of households in these 4 who own homes is exactly 4 = [tex]\frac{42}{455}[/tex]

What is Probability?

Probability of an event is the chance of occurance of that event.

Probability can be obtained by Number of favourable outcomes divided by the total number of outcomes

Probability varies from 0 to 1.

Here,

Total number of households = 15

No of households to be selected = 4

4 households can be selected from 15 households in [tex]15 \choose 4[/tex] ways

                                                                                      = [tex]\frac{15!}{(15-4)! \times 4!}\\[/tex]

                                                                                      = [tex]\frac{15!}{11! \times 4!}[/tex]

                                                                                       [tex]=\frac{15 \times 14 \times 13 \times 12}{1 \times 2 \times 3 \times 4}[/tex]

                                                                                       = [tex]1365[/tex] ways

Now,

Number of households who own homes = 9

4 households can be chosen from 9 households in [tex]9 \choose 4[/tex] ways

                                                                                  [tex]\frac{9!}{(9-4)! \times 4!}\\[/tex]

                                                                                = [tex]\frac{9!}{5! \times 4!}[/tex]

                                                                                [tex]=\frac{9 \times 8 \times 7 \times 6}{1 \times 2 \times 3 \times 4}[/tex]

                                                                                = [tex]126[/tex]

Probability that the number of households in these 4 who own homes is exactly 4 = [tex]\frac{126}{1365}[/tex]

               = [tex]\frac{42}{455}[/tex]

To learn more about probability, refer to the link:

brainly.com/question/251701

#SPJ9                  

Answer:

[tex]n_{i+1} = -5n_i - 1[/tex]

Step-by-step explanation:

-5*2 - 1 = -11

-5*-11 - 1 = 54

Because the prisms are stacked onto one another, they have a total volume of 320 cubic units

The possible question is added at the end of the solution and as an attachment

From the attached figure, we have the following parameters

The volume of a prism is the prodict of its dimensions

This means that

Cube = Length^2

Cuboid = Base area * Height

So, we have the following equations

Shape 1 = a^3

Shape 2 =a^2b

Shape 3 =a^2c

Substitute the known values in the above equation

So, we have

Shape 1 = a^3 = 4^3 = 64

Shape 2 =a^2b = 4^2 * 6 = 96

Shape 3 =a^2c = 4^2 * 10 = 160

Add the above values

Prism volume =64 + 96 + 160

Evaluate the sum

So, we have

Prism volume = 320

Hence, the volume of the three prisms is 320 cubic units

Read more about volumes at

https://brainly.com/question/463363

#SPJ1

Answer:

Tom is currently 5 and Bill is currently 11

Step-by-step explanation:

Let b = Bill's current age

Let t = Tom's current age

We have 2 unknowns so we need to equations to solve for this.

b = t + 6  

(b-3) = 4(t-3)  We have to subtract 3 from both Tom and Bill's current age

b- 3 = 4t - 12  Distribute the 4 and then substitute in t + 6 for b.

t + 6 -3 = 4t -12  Combine like terms

t + 3 = 4t -12  Subtract t from both sides of the equation

3 = 3t - 12  Add 12 to both sides of the equation

15 = 3t  Divide both sides by 3

5 = t  Tom is 5.  Since Bill is 6 years old, her is 11.

Check:

11 = 5+ 6

Three years ago, Tom would have been 2 and Bill would have been 8.  Bill is four times older than Tom.  2x4 = 8.

The factored expression of the expression given as 12b - 30 is 6(2b - 5)

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

12b - 30

Factor out the common factor from the expression

So, we have

12b - 30 = 3 * 4b - 3 * 10

Factor out 3 from the expression

So, we have

12b - 30 = 3(4b - 10)

Factor out 3 from the expression

So, we have

12b - 30 = 6(2b - 5)

The expression above cannot be further simplified

This means that the expression has been completely factored and cannot be further factored

Hence, the equivalent expression of the expression given as 12b - 30 when it is factored by grouping is 6(2b - 5)

Read more about expression at:

https://brainly.com/question/723406

#SPJ1

The net cost equivalent is the price the customer pays after deducting all the discounts. To find the net cost equivalent given an amount n of discounts, we use the following formula

Where d is the discount written as a decimal.

In our problem, we have a series discount of 20/10/10/20, therefore, the net cost equivalent is

Answer:

it would be 29 five

Step-by-step explanation:

I can't do the small number so it's just typed big

The slope of line of best fit is 6.47887 which is approximately 6.5.

A line of best fit is a straight line that minimizes the distance between it and some data. The line of best fit is used to express a relationship in a scatter plot of different data points. It is an output of regression analysis and can be used as a prediction tool for indicators and price movements.

To calculate the slope of the equation, we need to solve for some parameters.

The equation of regression is given as

[tex]y = bX + a[/tex]

let's solve for the unknown parameters b and a.

[tex]b = \frac{SP}{SS_x}=\frac{3176.2}{490.24} = 6.47887 = 6.5[/tex]

The slope of the line of best fit is given as 6.5.

Learn more on line of best fit here;

https://brainly.com/question/1441182

#SPJ1

Answer: 6.5

Step-by-step explanation: i took the test

Answer:

In ten year you will be 10 years older than you are now and so will your brother. The 6 years difference will remain if no one dies.

Step-by-step explanation:

You are z years old

Your brother is 6 years younger than z years; z - 6 years

In 10 years time, you will be z + 10 years

Your brother will be z - 6 years + 10 years = z + 4 years

OR

In 10 years time, you will be z + 10 years

You brother is still 6 years younger than you, so is z + 10 years - 6 years = z + 4 years

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

y < 6x + 9 eq. 1

Step 02:

systems of inequalities

y > 6x + 7 eq. 1

<9

Graph

y = 6x + 9 eq. 2

Unlimited/Infinite solutions

The answer is:

(-4 , 32)

(3 , 25)

We are given two box plots of a variable, for two different towns. Recall that the structure of a box plot is

where Q1 is the 25th percentile (or quartile 1), Q2 is the median and Q3 is the 75th percentile (or Quartile 3). This type of graphs tells us how the data is distributed, and more specially it can tell us how the data is spread across the different values the variable could take. So the way to analyze the spread from the graph is by considering the inter quartile range (IQR). This amount can be calculated by simply finding the difference between Q3 and Q1. If this range is really small, this would mean that the data is less spread and if this range is big, then this would mean that the data is more spread.

Using the given box plots, we can determine the following:

Town A: Q3 = 40, Q1 = 20, IQR = 40-20=20

Town B: Q3 = 45, Q1=35, IQR = 45-35 = 10

So, this would lead to option D.

The number of mosquitoes will be increased by 5 inches of rain.

Maximum mosquito population = 25000

We are given the following in the question:

M(x) = 10x - x²

where M(x) denotes the number of mosquitos in millions and x denotes the amount of rainfall in inches.

To begin, we differentiate M(x) with respect to x, yielding

d(M(x)) /dx = d(10x - x²) /dx = 10 -2x

When we set the first derivative to zero, we get

d(M(x)) /dx = 0

10 - 2x = 0

x = 5

We get the same result when we differentiate M(x) with respect to x:

d²(M(x)) / dx² = -2

d²(M(x)) / dx² < 0

As a result of the double differentiation test, the maxima for M(x) occur at x = 5.

when the rainfall is 5 inches, the most mosquitoes are present.

Maximum mosquito population:

M(5) = 10(5) - (5)² = 25

As a result, the maximum number of mosquitos is 25000.

To learn more about derivatives refer to :

https://brainly.com/question/12047216

#SPJ13

The choice that can be used to find the expression (three times the number increased by six is twenty-four) is (C) 3m + 6 = 24.

So,  three times the number increased by six is twenty-four:

Therefore, the choice that can be used to find the expression (three times the number increased by six is twenty-four) is (C) 3m + 6 = 24.

Know more about expressions here:

https://brainly.com/question/723406

#SPJ13

The correct question is given below:

Grace is thinking of a number. She states that three times the number increased by six is twenty-four. Which choice can be used to find

(A) 3(2-6) = 24

(B)3-6=24

(C) 3m + 6 = 24

(D) 9x2=18+6=2

The cost of a t-shirt is $25, the cap costs $20 and the stuffed animal costs $15

Let t-shirts be represented by x, the cap is represented by y and stuffed animals are represented by z

Items purchased by family:

4 t-shirts + 1 cap + 1 stuffed animal

The total cost of the items was = $135

Equation: 4x+y+z=135--------(1)

Items purchased by couple 1:

2 t-shirts + 1 cap + 3 stuffed animals

The total cost of the items was = $115

Equation: 2x+y+3z=115------(2)

Items purchased by couple 2:

2 t-shirts + 1 cap + 1 stuffed animals = $85

Equation: 2x+y+z=85------(3)

Subtracting equation (3) from (2) we get:

2z = 30

z = 15

Substituting the value of z=15 in equations (1) and (3) we get the following equations:

4x+y+15=135

4x+y=120------(4)

And, 2x+y+15=85

2x+y=70-------(5)

Multiplying equation (5) with 2 and subtracting equation (4) we get:

4x+2y=140

4x+y=120

y = 20

So, x = 25

Learn more about linear equations:

https://brainly.com/question/13738061

#SPJ1