A professor expects the education and health service industries to increase total employees by 14.8% from 2009 to 2016. Based on the employment graph below, approximately how many new jobs will the education and health service industries gain between 1/2009 and 1/2016?

Answer:

The new yearly salary is $16,800

Step-by-step explanation:

Amount of raise.

5% = 0.05

Multiply the original salary times the percentage of the raise.

$16000 * 0.05 = $800

New salary .

$16000 + $800 = $16,800

One-step Solution

$16000+($16000 * 0.05) =$16,800

Answer:

n = 41/10 OR 4.1

Step-by-step explanation:

10n + 2 =43

10 + 2 - 2 = 43 - 2

10n = 43 - 2

10n = 41

10n/10 = 41/10

n = 41/10

Answer:

Step-by-step explanation:

10n + 2 = 43 what is the value of n

10n + 2 = 43

10n = 43 - 2

10n = 41

n = 41/10

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

check

10 * 41/10 + 2 = 43

41 + 2 = 43

43 = 43

the answer is good

The following are the results:

[container 1] = aₙ = aₙ₋₁  ₊  4.5 ; a₁ = 0

[container 2] = aₙ = ₋4.5 ₊ 4.5n

[container 3] = 68 , 57 , 46 , 35 , 24, ..

[container 4] = aₙ = 79 ₋ 11n

[container 5] = 12 , 19 , 33 , 40

[container 6] = aₙ = aₙ₋₁ ₊ 7; a₁ = 12

Given the sequence is : 0,4.5,9,13.5,18,..

recursive formula = aₙ=a₍ₙ₋₁₎+4.5 where a₁ = 0

Explicit formula = aₙ = a₁ ₊ (n ₋ 1)4.5

= 0 ₊ (n ₋ 1)4.5

aₙ = ₋4.5 ₊ 4.5n

b. given, we have recursive formula: aₙ = aₙ₋₁  ₋ 11 ; a₁ = 68

here we have the common difference as 11, and the initial term is 68.

hence the sequence will be 68 , 57 , 46 , 35 , 24, ..

Explicit formula = a₁ ₊ (n ₋ 1)11

aₙ = 68 ₊ 11n ₋ 11

aₙ = 79 ₋ 11n

c. the explicit formula is given, aₙ = 5 ₊ 7n

here we have the common difference as 7.

so the sequence is 12,19,33,40

and the recursive formula is aₙ = aₙ₋₁ ₊ 7; a₁ = 12

Hence we get the acquired results.

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Given the value of the circumference, the radius of the circle to the nearest tenth is 7.0m.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The circumference of a circle is expressed mathematically as;

C = 2πr

Where r is radius and π is constant pi ( π = 3.14 ).

Given the data in the question;

Plug the given values into the circumference formula above and solve for r.

C = 2πr

44m = 2 × 3.14 × r

44m = 6.28 × r

Reorder the equation and divide both sides by 6.28

6.28 × r = 44m

( 6.28 × r )/6.28 = 44m/6.28

r = 44m/6.28

r = 7.0m

Given the value of the circumference, the radius of the circle to the nearest tenth is 7.0m.

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Answer: 9.6 meters

Step-by-step explanation:

See attached image

The missing value in the table below assuming a linear relationship is 18

The table of values represents the given parameters

From the question, we understand that the relationship is a linear relationship.

This means that the x and y values change at constant rate

From the table, we have

As x increases by 1, y increases by 2

So, the missing value is

Missing value = 16 + 2

Evaluate

Missing value = 18

Hence, the missing value in the table below assuming a linear relationship is 18

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The actual volume of the cylinder is 61.73 cm³

Percentage error is the error introduced in a measurement. The formula for the error is given as :

           Error = Percentage error * measured volume

According to the question we have been given that

                        determined volume of cylinder =  58.8 cm³

                         Percentage error  = 4.98%

thus, error = 4.98% * 58.8

                 = 0.0498 * 58.8

                 = ±2.93 cm³

The formula for the actual volume is given as

 Actual volume = measured volume ± error

                          = 58.8 ± 2.93 cm³

As the error is high we will do addition we get

                         = 58.8 + 2.93 cm³

                         = 61.73 cm³

hence the actual volume is 61.73 cm³

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The list that shows all the possibilities for the number of toy soldiers Jamal could place in each line is 1, 2, 17 and 34.

From the information, Jamal has 34 toy soldiers. He wants to arrange the soldiers into one or more equal-sized lines.

It should be noted that the factors of 34 are 1, 2, 17, and 34.

Therefore, the list that shows all the possibilities for the number of toy soldiers Jamal could place in each line is 1, 2, 17 and 34.

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700 is a reasonable estimate for the pieces of paper the business office uses in 7 days

The office uses 307 pieces of paper every 3 days

The first is to calculate the number of paper used per day

= 307/3

= 102.3

The number of paper used in 7 days can be calculated as follows

= 7 × 102.3

= 716

Hence 700 is a reasonable estimate for the pieces of paper the business office uses in 7 days

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15x+180 is the required expression. Let the number be 'x'. For more than we would use addition.

A mathematical expression is the collection of mathematical symbols that results from the valid combination of numbers and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.

2x + 3 is an illustration of a mathematical expression with a variable. Each and every variable needs to have a coefficient, or a value multiplied by the variable. The number 2 is the coefficient of x in the expression 2x + 3, which translates to 2x times plus 3.

Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing.

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Answer: $127

Step-by-step explanation: $81.75+$45.25=$127

The range of data set 1 is 4

The range of data set 2 is 4.

A line plot is a graph that is made up of a number line and check marks above the number line. The check mark above the number represents the frequency of the number in the data set. For example, if the number 3 on the number line has 2 checkmarks above it, it means 3 has a frequency of 2.

The range is the difference between the highest number in a dataset and the smallest number in the dataset. Range is a measure of variation.

Range = highest number - lowest number

The range of data set 1 = 7 - 3 =  4

The range of data set 2 : 7 - 3 =  4

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Answer:

Step-by-step explanation:

The exponent is -3, making it 10 to the power of negative 3. When an exponent is negative, the solution is a number less than the origin or base number. To find our answer, we move the decimal to the left 3 times:

9.2 -> 0.0092

The answer is D.

Answer:

0.0092.

Step-by-step explanation:

I have an explanation on this same question. Apparently, you have a duplicate of this.

Answer:

No they do not because it does not qualify for a triangle due to the extreme differences in messurments

Step-by-step explanation:

Answer: the bus's speed on the level road was 65 milles per hour

Step-by-step explanation:

Let the bus's speed on the level road is x mph

Hence, the bus's speed on the winding road is (x-20) mph

Thus,

3(x)+5(x-20)=420

3x+5x-100=420

8x-100=420

8x-100+100=420+100

8x=520

Divide both parts of the equation by 8:

x=65 mph

Yes, area of the triangle also get doubled when the height of the triangle is doubled.

As given in the question,

Let 'b' be the base of the triangle

'h' be the height of the triangle

Area of the triangle = (1/2) × b × h

Base of the new triangle = b

Height of the new triangle doubled =2h

Area of new triangle = (1/ 2) × b × 2h

                                   = 2 {(1/2) × b × h}

                                   = 2 Area of original triangle

Therefore, area of the triangle also get doubled when the height of the triangle is doubled.

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The value of cos 67.4° is 5/13.

According to trigonometric identities used in mathematics, sin of an angle is equal to cos of 90 - the given angle. Mathematically, this means that, suppose we have an angle x, then-

sin(90 - x) = cos x

Here, we are given that sin 22.6° = 5/13. As we can observe that (90 - 67.4) is equal to 22.6, and we need to find the value of cos  67.4° only. Thus we can write the given equation as follows-

sin22.6° = sin(90 - 67.4°)

= cos 67.4°

Thus, sin 22.6° = cos 67.4°

Hence, cos 67.4° = 5/13

Thus, the value of cos 67.4° comes out to be 5/13.

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Correct answer is B. In A, there is no number from which to regroup (all the numbers may be added together), so you must regroup. In B, the number 6 cannot be added to the number 2, therefore you must regroup.

Making groups of ten while doing math operations like addition or subtraction is known as regrouping. This frequently occurs while dealing with double digits. Technically speaking, it also happens whenever you get a response that is more than 10.

Additionally, if the numbers you are adding result in a two-digit number and they are not in the farthest left column, you must regroup. When the numbers you are subtracting from are more than the ones you are subtracting from, you regroup.

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Answer:

[tex]f\left(x\right)=\begin{cases}2x\:+\:10&-6\:\le x\: < \:-3\\ -x\:+\:1&-3\: < \:x\: < \:2\end{cases}[/tex]

Step-by-step explanation:

Looking at the graph we can see that it is a linear graph of the form

y = mx + b where m is the slope and b is the y intercept.

In one region the slope is positive and the other region it is negative

Interval 1 is -6 ≤ x < -3
How do I know that one uses a ≤ and the other uses a <?
A filled circle means that the point is included in the domain(range of x values) and therefore (≤, ≥) and an unfilled circle means it is not(<, >)

Find the slope of line in this interval
Take two points, say (-5, 0) and (-3, 4)

Slope = rise/run = (4 - 0)/(-3 - (-5) = 4/2 = 2

So slope of line is 2 and its equation in slope-intercept form is

y = 2x + b

Choose any point, plug in values, solve for b

Point (5, 0) is chosen
0 = 2(-5) + b

0 = -1 + b

or

b = 10

So equation of line in the interval (-6 ≤ x < -3) is
y = f(x) = 2x + 10

Interval 2: -3 < x < 2

We see this line intersects the y axis at y = 1

So b = 1

Equation is y = mx + 1

Choose point x = 0, y = 1 to find slope m

At x  = 0, y = m(1) + 1 = m + 1

So m + 1 = 0

m = -1

So equation of this line is

y = f(x) = -1x + 1 in the interval -3 < x < 2

Putting all these together we get the piecewise function as:
[tex]f\left(x\right)=\begin{cases}2x\:+\:10&-6\:\le x\: < \:-3\\ -x\:+\:1&-3\: < \:x\: < \:2\end{cases}[/tex]

The percentage of students who spend less than 4 hours a week on screens which reported a grade average below 80 is 50%

Given, we have the report representing children spending time online, on social media or watching T.V, which has there effect on there grades as above or below 80.

By the question we know that the number of students who spends less than 4 hours a week on screen is:

9 + 9

= 18

And among the 18 students there are 9 students whose grade average is below 80.

So the percentage of the students who spends 4 hours a week on screen is:

= 9 ÷ 18 × 100%

= 100/2

= 50%

hence 50% students spend less than 4 hours a week on screens.

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Answer:

24

Step-by-step explanation:

Because 300 cookies / 38 cookies = 7.89,..

Then 7.89,... x 3 = 23.68,...

round to the nearest tenths= 24

In order to meet the demand for the bake sale, a total of 300 cookies will be prepared, requiring the use of precisely 24 fresh eggs.

To calculate how many eggs you need to make 300 cookies, set up a proportion based on the information given in the cookie recipe:

Number of eggs / Number of cookies = Constant ratio

Let the number of eggs needed for 300 cookies as "x."

So,  x eggs / 300 cookies = 3 eggs / 38 cookies

Now, cross-multiply and solve for "x":

x * 38 = 3 * 300

38x = 900

x = 900 / 38

x = 23.6842

x ≈ 24

Therefore, you need 24 eggs to make 300 cookies for the bake sale.

Thus, option (b) is correct.

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The most reasonable conjecture for the number of triangles in the eighth figure in the pattern is that there are 8 triangles in the eighth figure in the pattern

The given figure represents the given parameter

From the figure, we have the following parameters

When represented as a sequence, we have the following terms

4, 6, 8.....

The above sequence represents an arithmetic sequence with the following properties

First term, a = 4

Common difference, d = 2 i.e. 6 - 4

The most reasonable conjecture for the number of triangles in the eighth figure in the pattern is calculated by the following arithmetic sequence formula

Tn = a + (n - 1) * d

So, we have

T8 = 4 + (8 - 1) * 2

Evaluate

T8 = 18

Hence, the most reasonable conjecture for the number of triangles in the eighth figure in the pattern is that there are 8 triangles in the eighth figure in the pattern

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Answer:

13

Step-by-step explanation:

u multiply 4.50 x 3 it makes it 13.5 so they basically need to pay more .

Answer:

C intercept is 800, n intercept is -3.3333...

Step-by-step explanation:

C = 240n + 800 is a linear equation (the graph is a line)

C-intercept is the point with the coordinates ( 0, C-intercept ) where the line C = 240n + 800 is intersecting the vertical C-axis and

n-intercept is the point with the coordinates (n-intercept, 0) where the line C = 240n + 800 is intersecting the horizontal n-axis.

Find the C-intercept:

n has to be 0 for our line to intercept the C-axis, so substitute n = 0 in our given equation

C = 240n + 800

C = 240·0 + 800

C = 800

Find the n-intercept:

C has to be 0 for our line to intercept the n-axis, so substitute C = 0 in our given equation

C = 240·n + 800

0 = 240·n + 800, subtract 800 from both sides

-800 = 240 ·n, divide both sides by 240

-800/240 = n

-3.(3) = n

Step-by-step explanation:

I guess the result is needed again in slope-intercept form.

this is in general

y = ax + b

"a" being the slope, "b" being the y-intercept (y value when x = 0).

when a line is parallel to another line, this means they both have the same slope.

so, we can use the same "a" from the original line : -1

to get "b" we use the given point coordinates :

5 = -1×-3 + b = 3 + b

2 = b

so, the full equation is

y = -x + 2

The correct answer is 3.5.

Let t be the amount of time each steamer takes.

Two steamers that are headed in opposite directions depart a port on a river at the same time, according to the information provided.

Given that both steamers move at the same speed, they would cover the same distance in t hours.

Given that both steamers covered 140 miles, we can write the following equation to reflect this data:

                              rate             time                distance

First stream            20               t                       20t

Second stream      20               t                       20t

                                                                           140

setting the equation ,

20t + 20t = 140

40t = 140

t = 140/40

t = 3.5

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Step-by-step explanation:

1 pound is equivalent to 3500 calories.

if you burn 450 more calories per day, it will take as many days as the times 450 fits into 3500 :

3500 / 450 = 7.77777777... days

for 10 pounds we need to burn 10×3500 = 35000 calories.

35000 / 450 = 77.77777777... days (10 times more logically than for 1 pound).

Answer:

Sue Black: 40 hours, $270

Jerry Atrix: 30 hours, $154.50

Sam Ting: 38.75 hours, $339.06

Step-by-step explanation:

Firstly, 40 hours is a workweek of 8-hour shifts. It's good to remember. Otherwise, we can multiply 8 by 5 and get 40 anyway. That's the hours of Sue Black, and she earns:

40*$6.75 = $270

Jerry worked for (note you can easily add in memory if you do the fractions first):

7.25+3+6.75+8+5 = 7.25+6.75 + 3+8+5 = 14 + 16 = 30

Earnings:

30*$5.15 = $154.50

Sam worked a quarter of an hour less than Sue each day. That means that his total time was:

40 - 5 * 0.25 = 40 - 1.25 = 38.75

Earnings:

38.75*$8.75 = $339.0625 ≈$339.06

Answer:

9.3333333

Step-by-step explanation:

14÷1.50=9.333333