Mr. Johnson earns $5.40 an hour. One week, he worked 40 hours and 2 hours overtime, If he is paid time and one-half for overtime, how much did he earn?

Equation that best models the situation is where c = 11

Living plants are used in phytoremediation technologies to purify contaminated soil, air, and water. According to the definition, it involves "the use of green plants, associated microbes, suitable soil amendments, and agronomic techniques to either contain, remove, or render dangerous environmental toxins harmless." The word is a combination of the Greek words phyto (plant) and remedium (remedy) (restoring balance). Despite being appealing due to its low cost, phytoremediation hasn't been shown to significantly address any environmental issues, at least not to the point where contaminated space has been returned. A cost-effective plant-based method of environmental cleanup called phytoremediation is being proposed. It makes use of plants' capacity to concentrate elements and chemicals from the environment and to detoxify different contaminants. The ability of certain plants, known as hyperaccumulators, to bioaccumulate substances is what causes the concentrating effect. The impact of cleanup is very different. Organic contaminants, which can be destroyed, are typically the main targets for phytoremediation while toxic heavy metals cannot. Several field tests supported the viability of employing plants to clean up the environment.

Let the number of crops needed to remove pollution = c

Since one crop can remove 15 mg of pollution per square meter.

Then, "c" number of crops may remove "15 C" mg of pollutant per square meter.

Now, the total amount of pollution per sq. meter Equals 170 mg

Additionally, it is necessary to reduce pollution to 5 mg per square meter.

Consequently, the equation for the scenario is given by,

Pollutants 'c' crops can remove from the total amount of pollution equal the amount of pollution required, or 170-15c=5.

Upon solving the equation, we get, c= 11.

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Answer:

Step-by-step explanation:

Answer:

1. m ∠ 1 = 86°

  m ∠ 2 = 4°

- Problem in the picture

2. m ∠ 1 = 6°

   m ∠ 2 = 84°

Step-by-step explanation:

I'm confused, so I'll just solve both problems (assuming that they are the same type of angle)

1.

m Z1 = (x+84)° and m2 = 2xº.

m ∠ 1 = (x + 84)°

m ∠ 2 = 2x°

Complementary angles are equal to 90°

(x + 84) + 2x = 90

x + 84 + 2x = 90

3x + 84 = 90

      -84    -84

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

3x = 6

÷3  ÷3

-----------

x = 2°

m ∠ 1 = (x + 84)°

m ∠ 1 = (2 + 84)°

m ∠ 1 = 86°

m ∠ 2 = 2x°

m ∠ 2 = 2(2)°

m ∠ 2 = 4°

2. (Problem in the picture)

m ∠ 1 = (x - 6)°

m ∠ 2 = 7x°

Complementary angles are equal to 90°

(x - 6) + 7x = 90

x - 6 + 7x = 90

8x - 6 = 90

     +6    +6

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

8x = 96

÷8    ÷8

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

x = 12

m ∠ 1 = (x - 6)°

m ∠ 1 = (12 - 6)°

m ∠ 1 = 6°

m ∠ 2 = 7x°

m ∠ 2 = 7(12)°

m ∠ 2 = 84°

I hope this helps!

The problem two thirds(6j+9)=3j+7 has one solution.

The given problem is 2/3(6j + 9) = 3j + 7

In order to determine the number of solutions, take the following steps:

Expand the bracket on the left:

(2/3 x 6j) + (2/3 x 9)

4j + 6

4j + 6 = 3j + 7

Combine similar terms :

4j - 3j = 7 - 6

Add similar terms

j = 1

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The absolute value equation for the values of x = -10 and x =-5 will be |( x + 10 )( x + 5 )| =0.

According to the question.

We have solutions of a absolute value equation.

As we knoaw that, the non-negative value of a real number x without regard to its sign is known as its absolute value or modulus equation  in mathematics and is indicated by the symbol |x|.

To find the absolute value equation whose solution are x = -10 and x = -5 we need to add some previous steps, which make the equation an absolute value equation.

|(x+10)(x+5)|=0,

x=-10 and x=-5

Hence, the absolute value equation for the values of x = -10 and x =-5 will be |( x + 10 )( x + 5 )| =0.

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Answer:

67

Step-by-step explanation:

Each time the number goes up by 7. After 9 moretimes 4 will increase by 63.

4+63=67.

The 10th term should be 67

The population of this fast food business is made up of all customers who use the drive-thru window, whereas the sample, or representative group of the population, is made up of every fifth customer as per the concept of statistics.

What are statistics?

A population is a total group from which a statistical sample is taken in statistics. Here, the manager only inquires about the fifth customer's pleasure after becoming interested in his drive-through staff. Therefore, those customers who do not use the drive-thru window at this restaurant are not part of the sample population about whom it is possible to inquire.

As a result, the population of this fast food business is made up of all customers who use the drive-thru window, whereas the sample, or representative group of the population, is made up of every fifth customer.

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The required simplified value of x² +7x +12 divided by x + 2 is x + 5 + [2 / (x + 2)].

To determine the simplified value of  x² +7x +12 divided by x + 2.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
As per the given data,
Division of function,
=  x² +7x +12/ x + 2
= x² + 7x + 10 + 2 / x +2
= (x + 5)(x + 2) + 2 / x + 2
= (x + 5) (x + 2) / x + 2 + 2 / x + 2
= x + 5  + 2 / (x + 2)

Thus, the required simplified value of x² +7x +12 divided by x + 2 is x + 5 + [2 / (x + 2)].

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Answer:

Step-by-step explanation:

Option C uses the multiplication equation to express the figure, 0.27 x 9 = 2.43, by basic algebra.

Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.

Now, firstly refer to the image attached.

Since each large square is one whole, we've been provided with two complete squares, where 4 filled rows and 3 empty rows make up the last entire square row.

According to the third square, the answer is 2.43, i.e., the answer is 2.43 after you multiply to find which of 0.27 and 9 truly equals it, by basic algebra.

The figure is therefore represented by the multiplication equation.

⇒ 0.27 × 9 = 2.43

Hence, Option C uses the multiplication equation to express the figure, 0.27 x 9 = 2.43, by basic algebra.

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The common statistical method of expressing the precision of a series of repetitive measurements is the standard deviation.

It should be noted that the standard deviation is the measure of how dispersed the data is in relation to the mean.

It should be noted low standard deviation implies that data are clustered around the mean, and high standard deviation means data are more spread out.

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Step-by-step explanation:

speed = mph or miles/hour

so, when we are dealing with a distance and compare the time spent on the distance, we have to divide distance by speed

miles / miles/hour = hour

so, we have

m/4 + m/3 = 2

as the sum of the time it took to walk the distance at 4mph and the time it took to walk the distance at 3 mph is 2 hours.

now we multiply by the denominators one after the other to eliminate the fractions.

m + 4m/3 = 8

3m + 4m = 24

7m = 24

m = 24/7 = 3.428571429... miles

The polynomial is:

f(x) = -2*(x + 5)*(x - 4)*(x - 1)*(x - 1)

Let's assume the leading coefficient is A, we know that the degree is 4, the y-intercept is 40, and we have the roots (-5, 4, 1, 1)

Then the polynomial is:

f(x) = A*(x + 5)*(x - 4)*(x - 1)*(x - 1)

Now we use the fact that the y-intercept is 40, so we have:

f(0) = 40 = A*(0 + 5)*(0 - 4)*(0 - 1)*(0 - 1)

        40 = A*-20

        40/-20 = A = -2

Then the polynomial is:

f(x) = -2*(x + 5)*(x - 4)*(x - 1)*(x - 1)

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The length of the ladder to the nearest tenth of a foot as evaluated by trigonometric ratios is; 12.2ft.

Since the base of the ladder as indicated in the task content is 10 feet away from the bottom of a building's wall, it follows that the set-up in discuss is analogues to a right triangle whose adjacent is 10ft;

Therefore, the length of the ladder which is the hypothenuse can be evaluated as follows;

cos 35° = 10/L

L = 10/cos 35

L = 12.2ft.

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1.  The elements of the set are {m, I, s, p}

The elements of the set are the letters in Mississippi. Elements cannot repeat themselves.. So the elements of this set would be {m, I, s, p} since all the other letters are just repetitions.

2. Set of months in a year are

{January,February,March,April,May,June,July,August,September,October,November,December}

3. Verbal Descriptions: It is a verbal description of the set is an English sentence to specify a law that allows us to decide the category of objects to be addressed and to determine whether it is in the set for any particular object.

Since, 3, 6  and 9 are divisible by 3 also less than 10.

4.  Verbal description of the set {a,e,i,o,u} is vowels

In English these five alphabets{a,e,i,o,u} are known as vowels .

since the given set contains only vowels.

5. Yes (1,3,5) is the subset of odd integers.

The set of odd integers is the superset containing elements :-

Let A = { 1 , 3 , 5 , 7 , 9 ,..... ,( 2n + 1 ) }

And,

B = { 1 , 3 , 5 }

B is a subset of A because all elements of B lie in A .

6. Yes (a,b,c) is the subset of letters of the alphabet.

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4=8/3

I hope this helps, I think thin is the right answer

72/8 = 9,

9x5 = 45 boys

Therefore answer is 45 boys

Answer:

-24r⁵ + 4r⁴ + 18r³ - 22r².

Step-by-step explanation:

-2r² (12r³ − 2r² − 9r + 11)

= -24r⁵ + 4r⁴ + 18r³ - 22r²

Answer:

Step-by-step explanation: Refer to attachment.

solution of 1/3x=21 is greater than 21.

A linear equation only has one or two variables. In a linear equation, no variable can be multiplied by a value greater than one or used as the denominator of a fraction. When you find the values that make a linear equation true and plot those values on a coordinate grid, all the points fall on the same line.

Solving the linear equation

x/3 = 21

multiplying  by  3 on  both  sides

x/3 * 3 = 21 * 3

x = 63

→63>21,

that is, solution of the linear equation is greater than 21.

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Answer:

x = 5

Step-by-step explanation:

Mode: The most frequently occurring data value.

Median: The middle value when all data values are placed in order of size.

Mean: The sum of all data values divided by the total number of data values.

As the mode is the most frequently occurring data value, x must be 3, 4, 5 or 8.

If the mode is 3 or 4, then the data set will be {3, 3, 4, 5, 8} or {3, 4, 4, 5, 8}.  Therefore, the median would be 4.

If the mode is 5 or 8, then the data set will be {3, 4, 5, 5, 8} or {3, 4, 5, 8, 8}.  Therefore, the median would be 5.

Therefore, the median is 4 or 5.

[tex]\boxed{\sf mean=\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}}[/tex]

If x = 4, the mean would be:

[tex]\sf \implies mean=\dfrac{3+4+5+8+4}{5}=\dfrac{24}{5}=4.8[/tex]

If x = 5, the mean would be:

[tex]\sf \implies =\dfrac{3+4+5+8+5}{5}=\dfrac{25}{5}=5[/tex]

Therefore, the only value of x that allows the mean, median and mode to all have the same value is x = 5.

The solution of the linear equation:

-x/3 + 4 = 20

Is x = -48

Here we have the linear equation:

-x/3 + 4 = 20

And we want to solve it for x. Which means that we need to isolate x in one of the sides of the linear equation.

Remember that we can perform the same operation in both sides of the equation, so we start by subtracting 4 in both sides, then we get:

-x/3 + 4 - 4 = 20 - 4

-x/3 = 16

Now we can multiply both sides of the equation by -3, then we get:

-3*(-x/3)=  -3*16

x = -48

The solution of the linear equation is x = -48

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Answer:

$167.50

Step-by-step explanation:

Since the state pays 40% of the health insurance, Maggie will have to pay 100 - 40 = 60% of the insurance amount annually

60% = 0.6 decimal

So Maggie pays 0.6 x 6700 = $4,020

Maggie is paid semi-monthly ie 2 paychecks a month

In a year, there are 12 months so Maggie receives 24 paychecks annually

The total insurance amount of 4020 is split over 24 paychecks

So each paycheck deduction will be 4020/24 = $167.50

If a fisherman can row upstream at 2 mph and downstream at 8 mph. He started rowing upstream until he got tired and then started downstream to his start point. How far did the fisherman row if the entire trip took 2 hours is: 6.4 miles.

Let d = the distance to the turn around point

Time = Distance/ Speed

Up time + Down time = 2hrs

d/2 +d/8 =2

Multiply by 8

8×d/2 +8×d/8 =8 (2)

4d + d = 16

5d = 16

Divide both side by 5d

d=16/5

d = 3.2 miles to turn around

Hence,

Round trip = (3.2 miles ×2)

Round trip= 6.4 miles

Therefore If a fisherman can row upstream at 2 mph and downstream at 8 mph. He started rowing upstream until he got tired and then started downstream to his start point. How far did the fisherman row if the entire trip took 2 hours is: 6.4 miles.

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The collection of current NFL players is well defined and is a set

Step-by-step explanation:

For a collection to be termed as a set, it is necessary that it has distinct objects that are defined.

For example, a set of first 10 natural numbers is

A= [1,2,3,4,5,6,7,8,9,10]

It is well defined and therefore called as set which has first 10 natural numbers as its elements.

Same is the case with the collection of current NFL players.

The collection contains defined number of players. Therefore, this collection is called a set.

The members of the collection or team will be known as the elements of the set.

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The order of numbers from Greatest to Least is 5.385, 2.714, 1.538, 0.612.

Arranged in a series that begins with the greatest or largest and ends with the least or smallest.

We can also call it Greatest to Least.

To order the number from greatest to least first we have to find the value of  given square root,

√29 = 5.385

√6/4 = 0.612

19/7 = 2.714

Now, we have the numbers :

5.385, 0.612, 2.714, 1.538

So, we will arrange the above numbers greatest to least

1) 5.385

2) 2.714

3) 1.538

4) 0.612

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Let the height of the cup be h and the extra length be d.

So, when the one cup is placed over another the total height will be h+d.

So, when the one cup is placed over another the total height will be h + d.

When the four cup is placed over each another h + 3d = 11 cm.

So the generalised equation will h +(n-1)d where n is the total number of cups.

When the eight cup is placed over each another = h + 7d = 16.4 cm

h + 3d = 11 cm

h + 7d = 16.4 cm

On solving the above two equation we will get d = 1.35 cm and h = 6.95 cm

So when we put 10 cups on each other  = h +9d

6.95 + (9*1.35) = 19.1

Hence, the height of 10 cup will be 19.1cm.

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The ounces of raisins and peanuts needed for different numbers of serving are :

for 4 serving = 8 raisins and 12 peanuts

for 12 serving = 24 raisins and 36 peanuts

According to the question we have been given that in one number of serving the ratio of number of ounces of raisins to the number of ounces of peanuts is given as :

                               ratio = 2 : 3

We need to find ounces of raisins and peanuts needed for different numbers of serving.

For 4 serving,

              Raisins = 4*2 = 8

              Peanuts = 4*3 = 12

and we see that their ratio = 8/12 = 2/3

For 12 serving,

               Raisins = 12*2 = 24

              Peanuts = 12*3 = 36

and we see that their ratio = 24/36 = 2/3

Hence the ounces of raisins and peanuts needed for different numbers of serving are :

for 4 serving = 8 raisins and 12 peanuts

for 12 serving = 24 raisins and 36 peanuts

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Answer:

5

Step-by-step explanation:

rs + 14s

(6)(1/4) + 14(1/4)

[tex]\frac{6}{4}[/tex] + [tex]\frac{14}{4}[/tex] = [tex]\frac{20}{4}[/tex] = 5

Answer:

5

Step-by-step explanation:

rs + 14s

r = 6

s = 1/4

= 6*1/4 + 14*1/4

= 6/4 + 14/4

= (6+14) / 4

= 20/4

= 5