A sheet of paper contains a list of 5 double-digit prime numbers.
Their mean is 31, while their median and mode is 29.
The largest number is 41.
Show how you can discover the 5 prime numbers written on the sheet.

The gross pay for this week after working overtime is $471.75.

What is the overtime pay rule?

The civil overtime vittles are contained in the Fair Labor norms Act,  Unless pure, workers covered by the Act must admit overtime pay for hours worked over 40 in a workweek at a rate not lower than time, and That's an illustration of total pay for a hand who worked 42 hours in a workweek Regular pay rate x 40 hours = Regular pay, plus. Regular pay rate x1.5 x 2 hours = Overtime pay, equals.

Usual earning Earning = $8.5 for 30 hours for a week

Overtime = 47 hours-30 =17 hours

Overtime rate = $8.5 + $8.5/2 = $ 12.75 for hour for a week

Gross pay= ($8.5*30)+($12.75*17)

      = 255 + 216.75

       = 471.75.

The gross pay for this week after working overtime is $471.75.

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Answer:

16

Step-by-step explanation:

By factor theorem and limits, it is found that the end behavior of g(x) is that it goes to negative infinity.

The values of x and g(x) are

x    –4 –1  0  1     5 8 12

g(x) 0  –3  –1  –2 0 3 0

We need to find the end behavior of g(x).

The Factor Theorem states that a function with leading coefficient a and zeros x1,x2,x3...xn  is defined by:

g(x)=(x-x1)(x-x2)(x-x3)..(x-xn)

By definition of factor theorem,

g(x)=a(x-(-4))(x-12)

g(x)=a(x+4)(x-12)

g(x)=a(x2-8x-48)

The end behavior is the limit of g(x) as x goes to infinity, thus:

lim[tex]lim \lim_{x \to \infty} g(x)= \lim_{x \to \infty} ax^{2} =a*\infty[/tex]

Since the leading coefficient a is negative:

a*infinity= - infinity

Thus the end behaviour of g(x) it goes to negative infinity.

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Answer:

x = 27

Step-by-step explanation:

All angles in a triangle add up to 180 degrees

180 = (3x - 17) + (x + 40) + (2x - 5)

Combine like terms.

180 = 6x + 18

Subtract 18 from both sides.

162 = 6x

Divide both sides by 6.

x = 27

Answer:

5i is an imaginary number and it's square is - 25.

by definition zero is considered to be both real and imaginary.

Step-by-step explanation:

#studywell #workhard #worksmart

The statement 'Revenue management methodology was originally developed for the banking industry.' is False.

The revenue Management is an analytics technique.

This technique is used to predict consumer behavior at the micro-level, which is ultimately useful in optimizing the product availability and pricing and maximize revenue growth.

This methodology is used by companies in certain industries, particularly those with fixed costs and capacity and products or services that expire.

It is the operational procedures and practices that maximize revenues without creating additional products or services.

Therefore, The statement 'Revenue management methodology was originally developed for the banking industry.' is False.

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122.500$

First hello I hope you are doing. The first step is to multiply 2.500 with 29 and the result is 72.500$ . Then you add the 50.000$ to 72.500$ which is the raise and you have the result which is 122.500$

I hope I helped you

The total distance, in miles, that kara walked at the park this week is 57/20.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that kara walks five days each week. this week she walked 7/8 mile on monday, 3/5 mile on tuesday, 4/10 on wednesday, 1/10 mile on thursday, and 9/10 mile on friday.

Now, in order to find the total distance, in miles, that kara walked at the park this week.

kara walked on Monday = 7/8

kara walked on Tuesday = 3/5

kara walked on wednesday = 4/10

kara walked on thursday=1/10

kara walked on friday= 9/10

Now, to get the total distance in miles by adding both the miles she walked this week:

7/8 + 3/5 +4/10 + 1/10 + 9/10

35/40 + 24 / 40 + 14/10

59/40 + 14/10

114/40

57/20

Therefore, the total distance, in miles, that kara walked at the park this week is 57/20.

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The Second and third car seats are appropriate for a 32-ib child

The first car :

The range  30 ≤x< 32

    So it is not possible for a car seat appropriate for a 32-ib child.

The second car:

The range 15<x <40

     So it is possible for a car seat appropriate for a 32-ib child.

The third car:

The range 30< x< 85

   So it is also possible.

Hence the second and the third ranged car is possible for a 32-ib child.

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Answer:

C. 3x-8

Step-by-step explanation:

To solve this, we put the x values into the functions and calculate the y values.

A

y = (1/2)x - 3

test for (2, -2)

-2 = 1/2 × 2 - 3 = 1 - 3 = -2 correct

test for (6, 10)

10 = 1/2 × 6 - 3 = 3 - 3 = 0 wrong

so, A cannot be right.

B

y = -2x + 2

test for (2, -2)

-2 = -2×2 + 2 = -4 + 2 = -2 correct

test for (6, 10)

10 = -2×6 + 2 = -12 + 2 = -10 wrong

so, B cannot be right.

C

y = 3x - 8

test for (2, -2)

-2 = 3×2 - 8 = 6 - 8 = -2 correct

test for (6, 10)

10 = 3×6 - 8 = 18 - 8 = 10 correct

test for (13, 31)

31 = 3×13 - 8 = 39 - 8 = 31 correct

so, C is a right answer.

D

y = 4x - 10

test for (2, -2)

-2 = 4×2 - 10 = 8 - 10 = -2 correct

test for (6, 10)

10 = 4×6 - 10 = 24 - 10 = 14 wrong

so, D cannot be right.

I hope this helped! Have a good day! :D

Answer:

8x+5=hx-8

collect like terms (values that are alike in one place)

8x-hx = -8-5

8x-hx = -13

8x -hx+13 =0

factorize

x(8-h) + 13 =0

we can't do nothing to it anymore I think

The width and the length of the rectangle are equal to 6√5 units and 3√5 units, respectively.

In this problem we find the area of the rectangle and the ratio of the length to the width of the figure. Mathematically speaking, the area of the rectangle is described by the following formula:

A = (2 · x) · x

A = 2 · x²

If the area of the rectangle is equal to 90 square units, then the width of the rectangle is:

2 · x² = 90

x² = 45

x² = 3² × 5

x = 3√5

The width of the rectangle is equal to 3√5 units. By the given ratio, the length of the rectangle is equal to 6√5 units.

Therefore, the length and width of the rectangle are equal to 6√5 units and 3√5 units, respectively.

The lower part of the picture is not related to the statement.

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The equation of a line in slope-intercept form is  [tex]y = \frac{1}{8} x - \frac{41}{8}[/tex] .

The equation of the line is given below using the slope-intercept method:

y = mx + c

where,

m = the slope of the line

c = y-intercept of the line

(x, y) represent any point on the line

To find the Slope of a line that passes through the points (2, 4) and (3, -4).

m₁ = change in y/change in x

    = y₂ - y₁ / x₂ - x₁

    = Δy/Δx

   = [tex]\frac{-4-4}{3-2}[/tex]

   = [tex]\frac{-8}{1}[/tex]

   = -8

Now, we find the slope of the line perpendicular to the line with the slope -8.

m₂ = -1 / m₁

    = -1 / -8

    = 1/8

So, the slope of the line is 1/8.

Next, we find the equation of a line that passes through the point (1, -5) and has a slope of 1/8.

⇒ y - y₁ = m( x- x₁)

⇒ y + 5 = [tex]\frac{1}{8}[/tex] (x - 1)

Multiplying by 8 on both sides of the equation we get and then solving

⇒ 8y + 40 = x - 1

⇒ 8y = x - 41

 ⇒ [tex]y = \frac{1}{8} x - \frac{41}{8}[/tex]

Therefore, the equation in slope intercept form is  [tex]y = \frac{1}{8} x - \frac{41}{8}[/tex] .

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Lashonda biked for 50,51, and 63 miles on the first three days, to make average 54 miles per she needs to bike 52 miles on the last day.

As given,

Lashonda biked for first three days = 50, 51, 63 miles

Let x miles she bike last day

Average = 54 miles per day

Average = (50 + 51 + 63 + x) /4

⇒ 54 = (164 + x) /4

⇒ x = 216-164

⇒ x= 52 miles

Therefore, Lashonda needs to bike 52miles last day to make average 54miles per day.

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Answer:

Step-by-step explation; c2 + c2 -3c + 5c + 3 - 2

                                        = 2c2 + 2c +1

Answer:

y2 = m*(x2 - x1) + y1

Step-by-step explanation:

m = (y2 - y1) / (x2 - x1)

y2 - y1 = m*(x2 - x1)

y2 = m*(x2 - x1) + y1

Using operations with integers, it is found that the elevation at the end of the trail is of 8,414 feet.

We initially take the initial elevation, and then:

Thus, operations of sum and subtraction with integers are used to find the final elevation.

From the listed points on the problem, the operations are given as follows:

-174, 350, -180, +282.

The trail begins at an elevation of 8136 feet, hence the final point can be found as follows:

8136 - 174 + 350 - 180 + 282 = 8414 feet.

The elevation at the end of the trail is of 8,414 feet.

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[tex]x^2 + 12x=-33 \\ \\ x^2 + 12x+36=3 \\ \\ \boxed{(x+6)^2=3} \\ \\ x+6=\pm \sqrt{3} \\ \\ \boxed{x=-6 \pm \sqrt{3}}[/tex]

Answer: 49x^2=-21x-2 quadratic functions -1/7and -2/7    



Step-by-step explanation:

Quadratic function:

In elementary algebra, the quadratic formula is a formula that provides the solution to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring, completing the square, graphing and others.

Move terms to the left side

49[tex]x^{2}[/tex]  =-21x-2

49[tex]x^{2}[/tex]  -(-21x-2) =0

 Distribute

49[tex]x^{2}[/tex]  -(-21x-2) =0

49[tex]x^{2}[/tex]+21x+2=0

Use the quadratic formula



 x=(-b±√[tex]b^{2}[/tex]  -4ac  ) / 2a

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

 49[tex]x^{2}[/tex]+21x+2=0

let, a=49

b=21

c=2

 Replace with values in this equation

X=(-b±√[tex]b^{2}[/tex]  -4ac  ) / 2a

Simplify

Evaluate the exponent

Multiply the numbers

Subtract the numbers

Evaluate the square root

Multiply the numbers

x=(-21±7) /98

Separate the equations

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.Separate

x=(-21+7) /98

x=(-21-7) /98

Solve

Rearrange and isolate the variable to find each solution

x=-1/7

x=-2/7



                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Learn more about area here https://brainly.in/question/5597925

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Answer:

26

Step-by-step explanation:

I will assume you meant this:    5 ( 7-4)²  ÷ 3 + 11

Using PEDMAS

  Parentheses first

      5 ( -3)² ÷ 3 + 11

  then exponents

     5 ( 9)  ÷ 3 + 11  

   then division

        5 * 3   + 11

    and multiplication

          15 + 11    then addition and or subtraction = 26

Answer:

Step-by-step explanation:

======================================================

Work Shown:

x = amount of sales

0.05x = five percent of sales to represent commission earned

21,000+0.05x = add on the base salary to get total salary

21,000+0.05x = 70,000

0.05x = 70,000-21,000

0.05x = 49,000

x = (49,000)/(0.05)

x = 980,000

----------

Check:

If the real estate agent sold $980,000 worth of property, then s/he earned 5% of 980,000 = 0.05*980,000 = 49,000 dollars in commission.

The total salary for the year is 21,000+49,000 = 70,000 dollars. The answer is confirmed.

Hence , the maximum and minimum relative profit to the appropriate accuracy are 0.33 and 0.31 respectively .

It is given that p=(s-c)/s......(1)  and sales = $340,000 and cost =  $230,000

Putting s = $340,000  , c = $230,000

        p = 340,000 - 230,000 / 340,000

        p = 110000 /340,000

        p =  0.3235

        p = 0.32

The largest variety which will round off to relinquish 0.32 is 0.33 therefore we are saying that 0.33 is that the edge.

The smallest variety which will gather to 0.32 is 0.31 this is often the edge.

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The complete question is given below :

To determine whether a business is making enough profit, the following formula is used p=(s-c)/s where P is relative profit, S is sales and C is costs. If a company has $340 000 worth of sales and $230000 of costs, correct to 2 significant figures, calculate the maximum and minimum relative profit to the appropriate accuracy.

If angle 1 and angle 2 supplementary, angle 2 and angle 3 are supplementary, The measure of  ∠2 = 47° and  ∠3 = 133°.

Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are supplementary  angles as the total of these two angles is 180°. The sum of complimentary angles is 90 degrees.

Given,

the measure of angle 1 = 133°

As, ∠1 + ∠2 are supplementary angles,

⇒  ∠1 + ∠2 = 180°                                        ......(1)

∠2 + ∠3 are supplementary angles,

⇒  ∠2 + ∠3 = 180°                                       .......(2)

From (1),

⇒ 133° + ∠2 = 180°

⇒ ∠2 = 47°

From (2),

47° + ∠3 = 180°

∠3 = 133°

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The result of diving 107 by 10⁻³ is (E) 107,000.

So, we know that 10⁻³ is 0.001.

Therefore, the result of diving 107 by 10⁻³ is (E) 107,000.

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The correct question is given below:

The result of dividing 107 by 10^-3 is?

a. 10-4.

b. 102.5.

c. 1010.

d. 104.

e. 107,000

Numbers of cubes are  224

We have been given that

side length of cubes is = 1 /4 cm

dimension of prism are

2 cm

7/4 cm

1 cm

Each cube with side lengths of 1/4 have a volume of (1/4)3 . To find how many cubes are needed to fill the prism.

Prism: A glass or other transparent object in prism form, especially one that is triangular with refracting surfaces at an acute angle with each other and that separates white light into a spectrum of colors.

To compute the prism volume in the given dimensions (cm³) and the cube volume in the same dimensions, then find the number of cube volumes in the prism volume.

Prism volume = l×w×h

Cube volume = (side)³

than Prism volume =(2×7/4×1)cm

                               = (3.5)cm

and cube volume = (1/4)³cm

                            = (1/64)cm

Then the number of cubes that will fit in the prism is ...

(Prism volume)/(cube volume)

(3.5)/(1/64)cm= 224 cubes

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According to the cross product, The value of x in the expression becomes 16.

According to the statement

We have to find that the value of the expression.

So, For this purpose, we know that the

Cross product is a binary operation on two vectors in three-dimensional space.

From the given information:

The expression is a

StartFraction 4 over 3 EndFraction = StartFraction x over 12 EndFraction

IN simple words, it becomes:

4/3 = x/12

Then we have to find the value of the x then

4/3 = x/12

Now cross multiply each other then

4 =3x/12

3x = 48

Then

x = 48/3

x = 16.

So, According to the cross product, The value of x in the expression becomes 16.

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The number of presales tickets can be obtained as 300. The correct option is (B).

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

Since, total number of people are 400.

Suppose the number of pre-sales tickets be x.

Then, the number of at door tickets is given as 400 - x.

As per the question, the following equation can be written for total money raised as,

⇒ 10x + 20(400 - x) = 5000

⇒ 10x = 3000

⇒ x = 300

Hence, the number of pre-sales tickets is given as 300.

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Answer: The answer would be 100.

Step-by-step explanation:

Answer: It takes 3 hours to drive 135 miles at a speed of 45 miles per hour.

Step-by-step explanation:

Define Time and Distance and Speed:

The length of distance traveled is proportional to the time taken to cover the distance, and we can represent this relationship as

      Distance ∝ Time          (Eq. 1)

The speed of any object is directly proportional to the distance traveled and inversely proportional to the time taken.

Speed ∝ Distance  (Eq.2)

Speed∝1/Time     (Eq.3)

Then, we can represent each parameter through the following equations:

Speed =Distance/Time

Distance=Speed × Time

Time =Distance/Speed

We can write:

Distance covered by driving:  d=135 miles

Driving speed:  s=45 mph

Recall the formula for the relationship of time, distance, and speed.

Time =Distance/Speed

Substitute d=135 and s=45 into the above formula, and simplify.

t=d/s

t=135/45

t=3 hours

Thus, it takes 3 hours to drive 135 miles at a speed of 45 miles per hour.

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The number of mini bottles required is;  68 mini bottles

We are told that a mini bottle of water contains 8 ounces of water.

Now, we are told that you require 4¹/₄ = 4.25gallons of water.

Now from conversions, we know that;

1 gallon = 128 ounces

Thus; 4.25 gallons = 4.25 * 128 = 544 ounces

Since a mini bottle of water contains 8 ounces of water, then we can say that;

Number of mini bottles required is;

544/8 = 68 mini bottles

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