Find the range of values which satisfy the following:

8x-11>5 and 15(6x+2)>-150
x>

Answer: ______

Answers

Answer 1

The range of values that satisfy the given inequalities, 8x - 11 > 5 and 15(6x+2) > -150, is x > -2 OR x > 2

Solving Linear Inequalities: Determining range of values

From the question, we are to determine the range of values which satisfy the given inequalities.

The given inequalities are

8x - 11 > 5 and 15(6x+2) > -150

To determine the range of values that satisfy the inequalities, we will solve each of the inequalities separately

Solving 8x - 11 > 5

Add 11 to both sides

8x - 11 + 11 > 5 + 11

8x > 16

Divide both sides by 8

8x/8 > 16/8

x > 2

Solving 15(6x+2) > -150

Divide both sides by 15

15(6x+2)/15 > -150/15

6x + 2 > -10

Subtract 2 from both sides

6x + 2 - 2 > -10 - 2

6x > -12

Divide both sides by 6

6x/6 > -12/6

x > -2

Putting the two solutions together,

x > -2 OR x > 2

Hence, the solution is x > -2 OR x > 2

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Related Questions

Select all ordered pairs that are a solution to -5x + 3y > 12

options:
(3, 9)
(-5, 5)
(3, -6)
(-2, -5)
(2, 8)
(-6, 0)

Answers

The ordered pairs that are a solution to the given linear equation -5x + 3y > 12 are:

(-5, 5)(2, 8)(-6, 0)

How to determine the solution?

In order to determine which ordered pairs are true solutions based on the given linear equation, we would have to test each of the ordered pairs by substituting their values into the linear equation as follows;

For ordered pair (3, 9), we have:

-5x + 3y > 12

-5(3) + 3(9) > 12

-15 + 27 > 12

12 > 12 (False).

For ordered pair (-5, 5), we have:

-5x + 3y > 12

-5(-5) + 3(5) > 12

25 + 15 > 12

40 > 12 (True).

For ordered pair (3, -6), we have:

-5x + 3y > 12

-5(3) + 3(-6) > 12

-15 - 18 > 12

-33 > 12 (False).

For ordered pair (-2, -5), we have:

-5x + 3y > 12

-5(-2) + 3(-5) > 12

10 - 15 > 12

-5 > 12 (False).

For ordered pair (2, 8), we have:

-5x + 3y > 12

-5(2) + 3(8) > 12

-10 + 24 > 12

14 > 12 (True).

For ordered pair (-6, 0), we have:

-5x + 3y > 12

-5(-6) + 3(0) > 12

30 + 0 > 12

30-5 > 12 (True).

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The equation of line k is y+2=-6(x-7).line l includes the point (-6,8) and is perpendicular to line k. What is the equation of line l?

Answers

The equation of line [L] would be y = (1/6)x + 9.

What is the general equation of a Straight line?

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have a equation of line [k] is y + 2 = -6(x - 7). Line [L] includes the point (-6,8) and is perpendicular to line k.

We have the equation of line [K] as -

y + 2 = - 6(x - 7)

y = - 6(x - 7) - 2

y = - 6x + 42 - 2

y = - 6x + 40

Slope of line [L] will be -

m[L] = 1/6

Assume the equation to be -

y = (1/6)x + c

Line [L] includes the point (-6, 8), so we can write -

8 = (1/6) x (- 6) + c

8 + 1 = c

c = 9

So, the equation will be -

y = (1/6)x + 9

Therefore, the equation of line [L] would be y = (1/6)x + 9.

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Find the value of x in the triangle below:

Answers

The value of x in the given triangle is x = 12  .

Angle Sum Property of the Triangle states that the sum of measure of all three sides of the triangle is 180° .

In the question ,

a triangular figure is given

in which , the measure of angle A is (6x - 19)°

the measure of angle B is [tex]=[/tex] 84°

the measure of angle C is [tex]=[/tex] (3x + 7)°

So , By Angle sum property ,

we get

∠A + ∠B + ∠C [tex]=[/tex] 180°

substituting the values of angle A, B and C ,

we get

(6x - 19)° [tex]+[/tex] 84° + (3x + 7)° [tex]=[/tex] 180°

6x - 19 [tex]+[/tex] 84 [tex]+[/tex] 3x + 7 [tex]=[/tex] 180

9x + 72 = 180

9x = 180 - 72

9x = 108

x = 108/9

x = 12

Therefore , the value of x is [tex]=[/tex] 12

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x represents the number
of comic books Priya buys
at the store, all at the same
price, and y represents the
amount of money (in
dollars) Priya has after
buying the comic books.

Answers

By using the concept of equation of line in slope intercept form, it can be obtained that

a)  x- intercept is 5

  This means, Priya has exhausted all her money by buying 5 comics

   y- intercept is 20

   This means, Priya had $20 before buying any comics

b) Slope = -4

   This means Priya's money has been decreasing by $4 after buying        one comics    

c)  Equation of line

     y = -4x + 20

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan \theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

x represents the number of comic books Priya buys at the store

y represents the amount of money (in dollars) Priya has after buying the comic books.

a)From the figure, it is clear that x- intercept is 5

  This means, Priya has exhausted all her money by buying 5 comics

   From the figure, it is clear that y- intercept is 20

   This means, Priya had $20 before buying any comics

b) The line passes through (5, 0) and (0, 20)

    Slope = [tex]\frac{20 - 0}{0 -5}[/tex] = -4

     This means Priya's money has been decreasing by $4 after buying

    one comics

c) Equation of line

   y - 0 = -4(x - 5)

   y = -4x + 20

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Complete Question

The figure has been attached-

The ____ of 12 is -12.

Answers

Answer; the  Negative of 12 is -12

Step-by-step explanation: first of all the reciprocal of 12 is 1 over 12. so that's not it. The absolute value of 12 is still 12 so that's not it. So the only thing that it can be is the Negative of 12 is -12  

The area of a rectangle is 110 square units. It’s length measures 11 units. Find the length of diagonal

Answers

The diagonal of the rectangle is 14.87 units.

What is a rectangle?

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Area of rectangle = 110 square units

Length = 11 units

Area of a rectangle = Length x Wide.

110 square units = Length x Wide

110 = 11 x Wide

Wide = 110/11

Wide = 10

Now,

The diagonal of a rectangle.

Using the Pythagorean theorem we get,

Diagonal² = Wide² + Length²

Diagonal² = 10² + 11²

Diagonal² = 100 + 121

Diagonal² = 221

Diagonal = √221

Diagonal = 14.87 units.

Thus,

The diagonal of the rectangle is 14.87 units.

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Graph f(z)=-0.25z +4.

Answers

The graph of the function f(z) = - 0.25z + 4 is drawn.

What is a Graph?

Drawing the graph (curve) of the appropriate function is the process of graphing a function. Although graphing simple functions like linear, quadratic, cubic, etc. is very straightforward, complicated functions like rational, logarithmic, etc. need some expertise and an understanding of certain mathematical principles.

Drawing a function's representation as a curve on a coordinate plane is known as graphing. Every point on a curve (or graph) that represents a function satisfies the function equation.

A collection of edges that are ordered pairings of vertices (also known as directed edges, directed links, directed lines, arrows, or arcs) is displayed

The graph of the function is drawn. On the x-axis, the z-variable variables and on the y-axis the f(z) values are shown.

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which equations are true when k = - 50? Select two correct answers.
1.5 - k/5 = 11.5
-2k + 78 = -22
-4k + 80 = -120
6k - 150 = -150
K/10 -3 = -8

30 POINTS IF YOU ANSWER!!

Answers

There are two equations which are true. They are 1.5 - k/5 = 11.5 and K/10 -3 = -8.

Given,

The equations;

1.5 - k/5 = 11.5-2k + 78 = -22-4k + 80 = -1206k - 150 = -150K/10 -3 = -8

The value of k = -50

We have to solve the given equations using k as -50 and find the true ones;

Lets check;

1.5 - k/5 = 11.5

1.5 - (-50/5) = 11.5

1.5 - (-10) = 11.5

1.5 + 10 = 11.5

11.5 = 11.5

This equation is true.

-2k + 78 = -22

(-2 x -50) + 78 = -22

100 + 78 = -22

178 ≠ -22

This equation is false

-4k + 80 = -120

(-4 x -50) + 80 = -120

200 + 80 = -120

280 ≠ -120

This equation is false

6k - 150 = -150

(6 x -50) - 150 = -150

-300 - 150 = -150

-450 ≠ -150

This equation is false

k/10 -3 = -8

(-50/10) - 3 = -8

-5 - 3 = -8

-8 = -8

This equation is true.

That is,

There are two equations which are true. They are 1.5 - k/5 = 11.5 and K/10 -3 = -8.

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find the unit rate of $36 : 1/2 hour

Answers

Answer:

$72 / hr

Step-by-step explanation:

$36 / (1/2 hr ) =  $72 per hour

assume the average number of times that a typical american says a word that is considered to be profane is 4 times per day with a standard deviation of 5.6. a sample of 15 students from your university is found to vocalize 3.4 profane words per day. assume that we expect the students at your university to vocalize fewer profane words. conduct directional (left-tailed) hypothesis test to determine if there is a difference between you university's population and the general population. what is the z-observed value for the test?

Answers

The z-observed value for the test of average number of times that a typical american says a word that is considered to be profane is -0.41.

Define the term z-score?A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from mean are used to measure Z-score.

The formula for calculating the z-score is-

z = (x - μ)/s

in which,

n = sample size (= 15)

μ = mean (= 4)

σ = standard deviation (= 5.6)

s = σ/√n

s = 5.6/√15

s = 1.44

Put the value in z score;

z = (3.4 - 4)/1.44

z = -0.41

Because of how near to zero this test statistic is, we will not be able to rule out the null hypothesis. Seven.

There isn't enough proof to claim that there is a mean difference or that it exists in your circumstance.

Thus, they're basically arguing that we can't rule out the null hypothesis.

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The first side of a triangle is 2 feet longer than
the second. The third side is 5 feet shorter than
twice the second. The perimeter is 49 feet. Find
the length of each side.

Answers

The length of the first side of the triangle is 15 feet, the length of the second side of the triangle is 13 feet and the third side is 21 feet.

According to the question,

We have the following information:

The first side of a triangle is 2 feet longer than the second. The third side is 5 feet shorter than twice the second. The perimeter is 49 feet.

Let's take the second side to be x feet.

So, we have the following sides:

First side = (x+2) feet

Third side = (2x-5) feet

Perimeter = 49

x+x+2+2x-5 = 49

4x-3 = 49

Adding 3 on both the sides:

4x = 49+3

4x = 52

Dividing by 4 on both the sides:

x = 52/4

x = 13 feet

First side = 2+13

First side = 15 feet

Third side = 2*13-5

Third side = 26-5

Third side = 21 feet

Hence, the length of the first side of the triangle is 15 feet, the length of the second side of the triangle is 13 feet and the third side is 21 feet.

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room attendants at your hotel typically clean one room every 20 minutes. one-fifth of the rooms take 40% longer to clean due to various issues. how much time will it take to clean 175 rooms?

Answers

Method 1 - treat all rooms the same and add the extra time for difficult rooms
Time = 175 x 20 + 175/5 x 20 x 0.4 = 3500 + 280 = 3780 min = 63 hours

Method 2 - calculate standard rooms and difficult rooms separately
Time = 175 x 4/5 x 20 + 175/5 x 20 x 1.4 = 2800 + 980 = 3780 min = 63 hours

Ben bowled 151 and 183 in his first two games. What must he bowl in his third game to have an average of at least 1702​

Answers

Answer:

1368

Step-by-step explanation:

let 3rd game be x

151+183+x=1702

334+x=1702

x=1702-334

x=1368

Given a point (5,-6) and slope m = -2

Write the Point-Slope Equation of the line.

Please give me a great explanation and explain like your talking to a baby please. Thanks :)

Answers

Answer:

y+6 =-2(x-5)

Step-by-step explanation:

The question is asking for the equation of the line

The equation for point-slope form is always written as y-y₁=m(x-x₁)

y₁ and x₁ are the points given to you in this order (x₁, y₁)

so x₁=5 and y₁=-6

Now you plug in all the numbers you have into the point slope form

y- (-6)= -2(x-5)

When you subtract a negative (a double negative you get a positive)

y+6=-2(x-5)

Point-Slope form is usually the easiest form of a line to write since you do not need to solve for any intercepts or other points. You have y on one side of the equation, usually the left to make it easier to read, and x on the other, usually the right.You subtract the point that you are given from the y and the x. Multiply everything that is on the same side of the equation of the x by the slope (m).

Notes:

For y₁ and x₁, they could be any point on the line. For example, (1,2) is also on this line. So the equation would be

y-2=-2(x-1)

Alexi like her drink to have a ratio of liquid yo ice of 1 to 3. A fat food retaurant put 16 oz of ice in her 32 oz cup

Answers

Alexi will not like the drink because the ratio of liquid to ice is 1/1.

Alexi likes her drink to have a liquid-to-ice ratio of about 1/3. A fast food restaurant put 16 ounces of ice in her 32-ounce cup. We need to find out if Alexi will like her drink or not, and if not, why not.

Let the ratio of the liquid to the ice in the drink be represented by the variable "R". The total volume of the cup is 32 ounces. The amount of ice in the cup is 16 ounces. So the amount of liquid in the drink is the difference between these two amounts. Hence, the amount of liquid in the cup is 32 - 16 = 16 ounces.

The ratio of the amount of liquid to the amount of ice in the drink is calculated below.

R = 16/16

R = 1/1

Hence, the ratio of the amount of liquid to the ice in the drink is 1/1. So, Alexi will not like her drink.

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At the beginning of the game, April had a core of −150 point. April played for another 20 minute, and her final core wa −35

Answers

The expression that represents the change in April's score from the start to the end of the game is 355 - 150 = 205.

April played a game. The score at the beginning of the game was 150 points. After twenty minutes, her score was 355 points. We have to determine the change in her score from the beginning of the game to the end of the game.

Let the change in the score be represented by the variable "C". The change in her score is calculated below. The change in the score is the difference between the final and the initial score of April.

C = 355 - 150

C = 205

Hence, the change in her score from the beginning of the game to the end of the game is 205 points.

The complete question is given below.

At the beginning of the game, April had a score of 150 points. April played for another 20 minutes, and her final score was 355. Write and then evaluate a subtraction expression to determine the change of her score from the beginning of the game to the end of the game.

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Use the following sequence to complete the parts: 8, 5, 2, -1,...
Is this arithmetic or geometric? (Type A or G)
What are the NEXT 3 terms?
What is the equation? t(n) =
What would be the 100th term?
n+
Is-345 a part of the sequence? (Type Y or N)

Answers

The given sequence is arithmetic sequence. The next three terms of the sequence are -4,-7,-10. the equation can be given as 11-3n. the 100th term of the sequence is -289.

What is a sequence?

A sequence is a function from natural numbers to the set of real numbers. it maps the set of number numbers on the set of real numbers.

We are given a sequence 8, 5,2, -1,.....

Now the first term of the sequence is 8 and common difference is -3.

As the difference between 2 consecutive terms is same, the given sequence is arithmetic.

now substituting this in the standard equation

we get,

t(n) = a+ (n-1)d

t(n)= 8+(n-1)(-3)

t(n) = 8-3n+3

t(n) = 11-3n                           (1)

Now we have to find the 5th, 6th, 7th term of the sequence

We substitute n=5, n=6, n=6 in equation 1

We get

t(5) = 11-3(5)

t(5) = 11-15

t(5) = -4

And,

t(6) = 11-3(6)

t(6) = 11-18

t(6) = -7

And,

t(7) = 11-3(7)

t(7) = 11-21

t(7) = -10

Hence the next three terms are -4, -7, -10.

The equation is t(n) = 11-3n

The 100th term would be given as

t(100)  = 11-3(100)

t(100)  = 11-300

t(100) = -289

Hence, The given sequence is arithmetic sequence. The next three terms of the sequence are -4,-7,-10. the equation can be given as 11-3n. the 100th term of the sequence is -289

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What is the radical form of each of the given expressions? Drag the answer into the box to correctly match each expression.
2 2/3 -
3 1/3 -
3 3/2 -
2 1/2 -

Answers

The radical form of each of the given expressions are;

1) 2^(2/3) =  ∛(2²)

2) 3^(1/3) = ∛3

3) 3^(3/2) = √3³

4) 2^(1/2) = √2

What is the radical form of the exponent form?

The radical form of the expression [tex]a^{\frac{x}{y} }[/tex] is; [tex]\sqrt[y]{a^{x} }[/tex]

Thus, we can solve each of the given expressions;

1) We are given the expression as 2^(2/3).

Thus;

x = 2 and y = 3 and we have; ∛(2²)

2) We are given the expression as 3^(1/3).

Thus, x = 1 and y = 3 and so we have;

∛3

3) We are given the expression as 3^(3/2). Thus;

x = 3 and y = 2 and so we now have; √3³

4) We are given the expression as 2^(1/2). Thus;

x = 1 and y = 2 and so we now have; √2

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a researcher measures anxiety levels among participants in the presence and absence of a fearful stimulus. she wants to know if anxiety levels were higher in the fearful stimulus condition. if the same participants are observed in each group, then what type of statistical design is appropriate for this study? group of answer choices a one-way between-subjects anova a one-way within-subjects anova an independent t-test a dependent t-test

Answers

Using the theories of statistical design, we got that both related sample t test and one-way within-subjects ANOVA is the appropriate statistical design for the study in which a researcher measures anxiety levels among participants in the presence and absence of a fearful stimulus.

Statistical design of experiments and the  response surface methodology has become a standard tool for the medium development. There are several applications reported in literature, such as the production of antibiotics, secondary metabolites, and enzymes.

Applications of statistical design of experiment shown in the Table 1 and several other studies use exclusively of the response surface method with quadratic polynomial models and the central composite design with on average 20–30 experiments. In most cases, the important components were identified by fractional factorial design or by the Plackett–Burman design with 10–15 experiments. Methods for narrowing  optimal variable range are only infrequently applied.

Hence, when a researcher measures anxiety levels among participants in the presence and absence of a fearful stimulus and wants to know if anxiety levels were higher in the fearful stimulus condition and if the same participants are observed in each group, then the appropriate statistical design is  that both related sample t test and one-way within-subjects ANOVA .

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please help, I will really appricaite it :)

Answers

Step-by-step explanation:

uploading the picture is an excellent way to make sure we get the original problem definition.

but I just answered this (even without the picture). so, you need it again ?

verify by drawing a diagram if the median and altitude of an isosceles triangle can be the same

Answers

The statement "The median and altitude of an isosceles triangle can be same", is verified by drawing diagram

The statement is  

"The median and altitude of an isosceles triangle can be same"

Draw an isosceles triangle ABC with BD = CD,

Draw a line segment AD perpendicular to the side BD

Here AD is the height of the triangle which is the altitude of the triangle

From the figure we can see that the length of BD = length of CD

Where D is the mid point of the line BD.

Therefore the line AD is the median of the triangle

Hence, The statement "The median and altitude of an isosceles triangle can be same", is verified by drawing diagram

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If you add a prime number to itself, is the sum composite or prime?

Answers

Answer: The sum of two prime numbers is always even (which is composite).

Hope this helped :)

estion 11 of 42
What is the equation of a line with a slope of 6 and a y-intercept of -2
O A. y = -2x + 6
OB. y = 6x + 2
OC. y = 6x-2
OD. y = 2x+6

Answers

The answer is C y = 6x-2

Select the correct answer. Which expression is equivalent to , if x ≠ 0 and y ≠ 0? A. B. C. D.
see image below:

Answers

The expression similar to  [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex] obtained by using the laws of indices is option A.

A. [tex]2\cdot x^2 \cdot y\sqrt[3]{7\cdot x \cdot y^2}[/tex]

What are the laws of indices?

According to some of the laws of indices, we have;

[tex]\dfrac{1}{x^n} =x^{-n}[/tex]

[tex]x^m \cdot x^n = x^{m+n}[/tex]

[tex]\sqrt[m]{x^n} =x^{\frac{n}{m} }[/tex]

The expression can be presented as follows; [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex]

Simplifying the above expression gives;

[tex]\sqrt[3]{56\cdot x^7\cdot y^5 } = \sqrt[3]{8 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 }[/tex]

[tex]\sqrt[3]{8 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 } = \sqrt[3]{2^3 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 }[/tex]

Collecting terms with an index of a multiple of 3 gives;

[tex]\sqrt[3]{2^3 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 } = \sqrt[3]{2^3\cdot x^6 \cdot y^3 \times 7\cdot x \times y^2 }[/tex]

[tex]\sqrt[3]{2^3\cdot x^6 \cdot y^3 \times 7\cdot x \times y^2 } = 2\cdot x^2 \cdot y \times \sqrt[3]{ 7\cdot x \cdot y^2 }[/tex]

The expression that is equivalent to  [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex]is option A.

A. [tex]2\cdot x^2 \cdot y \times \sqrt[3]{ 7\cdot x \cdot y^2 }[/tex]

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y y< 2x-3

How would I graph this ?

Answers

The graph of the inequality is attached below.

We are given an inequality. The inequality is linear in nature. An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. The inequality is given below.

y < 2x - 3

We need to graph the inequality. The first step is to find out the corresponding equation of the straight line. The equation is found by replacing the greater-than or less-than sign with the equal-to sign. The equation is given below.

y = 2x - 3

We plot this equation on the graph with a dotted line. Now we shade the area that satisfies the given inequality. The graph is given below.

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If the average daily sales in a store for the past 5 days was (2.3q + 1.4) dollars, express the total sales amount for the past 5 days as an algebraic expression.

Answers

The algebraic expression is C(5) =2.5 * 5 + 1.4 and the total cost is $13.9

How to determine the total sales amount?

From the question, the equation of the total sales amount is given as

Equation = 2.3q + 1.4

Where q represents the number of days

Rewrite as

Cost = 2.3q + 1.4

Express the equation as a cost function

So, we have the following representations

C(q) = 2.3q + 1.4

When the number of days is 5, we have

q = 5

Substitute the known values in the above equation So, we have the following equation

C(5) =2.5 * 5 + 1.4

Evaluate the products

C(5) = 12.5+ 1.4

Evaluate the sum

C(5) = 13.9

Hence, the total cost for the 5 days is $13.9

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sophie's favorite number is a two-digit number. if she reverses the digits, the result is $45$ less than her favorite number. the sum of the digits in her favorite number is $11$. what is sophie's favorite number?

Answers

Sophie's favorite number is 83

We have that;

A two-digit number is Sophie's preferred number. Her favorite number is 45 less when the digits are in reverse. Her favorite number has digits that add out to 11 in total.

To get Sophie's favorite number, we need to assume the case as;

Let,

⇒10x + y = 10y + x + 45

   x + y = 11

   y = 11-x

⇒10x + 11 - x = 10(11 - x) + x + 45

  10x + 11 - x = 110 - 10x + x + 45

  9x + 11 = 155 - 9x

  18x + 11 = 155

  18x = 144

  x = 8

Therefore, y = 11 - 8

                  y = 3

Sum = x + y = 8 + 3 = 11

Hence, the given condition is satisfied.

Sophie's favorite number is 83.

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Draw the straight line y=2x-3

Answers

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The table is

x   0     1     2

y  -3    -1     1

The graph of the line is given below.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Equation of a line:

y = 2x  - 3

y = 2 x 0 - 3 = -3

y = 2 - 3 = -1

y = 2 x 2 - 3 = 4 - 3 = 1

Table

x   0     1     2

y  -3    -1     1

The graph of the straight line is given below.

Thus,

The table is

x   0     1     2

y  -3    -1     1

The graph of the line is given below.

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from a group of 12 students, we want to select a random sample of 5 students to serve on a university committee. how many combinations of random samples of 5 students can be selected?

Answers

The number of combinations of random samples of 5 students can be 792.

Given, 12 groups of students

We have to select random samples of 5 students,

Here we will use the combination formula,

Cₙ,ₓ = n! / x! (n - x)!

Here n=12 and x=5

Cₙ,ₓ = 12! / 5! (7!)

Cₙ,ₓ = 479,001,600 / (120) × (5040)

Cₙ,ₓ = 792

Therefore the possible ways of selecting the random samples of 5 students are 792.

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Write the equation for the absolute value function graphed
Thank you!

Answers

The equation using the absolute value function is x+2y-8=0.

What is an Absolute Value Function?The graph opens up or down depending on the value of variable a, which also indicates how far it stretches vertically.We can determine the graph's horizontal and vertical shifts using the variables h and k.The general form of the Absolute value function is f(x) = a|x-h| + k.

In the given graph, we have:

(h, k) ∈ (4, 2) and a = -1/2

In the general absolute value function, substitute these values:

Let's f(x) be y:

y = a | x - h | + k= (-1/2) |x-4| + 2 = (-x/2) + (4/2) +2 = -x/2 + 4   (Multiply with 2)2y = -x + 8x + 2y - 8 = 0

Therefore, the equation using the absolute value function is x+2y-8=0.

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