4. Juan has 28 paperback books that measure
re 1 1/4 inches each, how many books will fit on one
shelf if each shelf measures 30 inches?

Answer:

a. A = 647

   P = 120

b. A = 192

   P = 70

Step-by-step explanation:

a. A = (16 x 12) + (13 x 35) = 192 + 455 = 647

   P = 16 + 12 + 19 + 13 + 35 + 25 = 120

b. A = (12 x 8) + (8 x 12) = 96 + 96 = 192

   P = 12 + 8 + 7 + 8 + 12 + 8 + 7 + 8 = 70

The value of x that makes the lines m and n to be parallel lines is 45 degrees

The figure that completes the question is added as an attachment

From the figure, we have the following angles

Angle = x and 3x

The angles are interior of parallel lines

This means that they add up to 180 degrees

So, we have the following equation

Angle 1 + Angle 2 = 180 degrees

Substitute the known values in the above equation

So, we have

x + 3x = 180

Evaluate the like terms in the above equation

So, we have:

4x = 180

Divide both sides of the above equation by 4

So, we have

x = 45

Hence, the value of x that makes the lines m and n to be parallel lines is 45 degrees

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probability of picking a yellow ball: 10/20 (1/2)

probability of picking a red ball: 6/20 (3/10)

1/2 times 3/10 =

3/20

x=x

Step-by-step explanation:

finding by mathematical operation and distribution law over multiplication added with subtraction is the formula now it might be easy for you

The shape 1 and shape 2 are congruent pentagons becuase shape 2 is a reflection of shape 1.

Given that shape 1 and shape 2 are congruent pentagons.

We are required to choose the option which is correct according to the given statemment that shape 1 and shape 2 are congruent pentagons.

Pentagons are the shape which have 5 sides and 5 angles.

Two shapes are congruent if they are copy of each other means all the corresponding sides are equal to each other.

The shape 1 and shape 2 are congruent pentagons becuase shape 2 is a reflection of shape 1.

Hence the shape 1 and shape 2 are congruent pentagons becuase shape 2 is a reflection of shape 1.

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Answer: D $30

Step-by-step explanation:

$12.79 rounds to $13

$2.33 round to $2

$14.65 rounds to $15

Add the estimates: 13+2+15= $30

The required function is P(t)=50000 + 5000t.

In this problem we need to form the function of the population in a town.

Here it is given that the initial population of the town is 50000.

the rate at which the population increases is 5000 per year.

So, the increase for the first year will be 5000. And the population will be 55000.

Then again for the next year the growth will be 5000 and the population will be 50000 + (5000×2)

        = 60000

So we can see clearly that the population is varying with time and we can write the function as P(t)=50000 + 5000t where t is the time in years.

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Answer:

7: #3. 8: #2

Step-by-step explanation:

in the first question the format is simply (x, y) and because it is a translation, we are basically just moving the point by these numbers, with this information, it is simply moving x to the left(negative) 8 times, and y(up/positive) 4 times. The next question is simply moving the point across the x axis by the same amount that it is above the x axis, so it would be one down from the x-axis' bold line, or in this case moved 2 y-units down. Hope this helps mate :)

Answer: I think ok not sure but yet positive but i think it is  y= -7

Step-by-step explanation:

the exponential form of the complex number \[ e^{17\pi i/60} e^{27\pi i/60} e^{37\pi i /60} e^{47 \pi i /60} e^{57 \pi i/60}\]

= (2+[tex]\sqrt{3}[/tex]) [tex]e^3^7^\pi^ i^/^6^0.[/tex]

[tex]e^1^7^\pi ^i/^6^0[/tex] + [tex]e^2^7^\pi^ i^/^6^0[/tex]+⋯+[tex]e^5^7^\pi ^i^/^6^0[/tex]

=[tex]e^1^7^\pi ^i^/^6^0[/tex](1+[tex]e^\pi^ i^/^6[/tex]+....+[tex]e^4^\pi ^i^/^6[/tex])

=[tex]e^1^7^\pi ^i^/^6^0[/tex] (1−[tex]e^5^\pi ^i^/^6[/tex]) ÷ (1−[tex]e^\pi ^i^/^6[/tex])

=[tex]e^1^7^\pi ^i/^6^0[/tex] ([tex]\frac{1}{2}[/tex](2+[tex]\sqrt{3}[/tex]) + [tex]\frac{1}{2}[/tex](3+2[tex]\sqrt{3}[/tex])i)

=(2+[tex]\sqrt{3}[/tex])e17πi/60(12+([tex]\sqrt{3}[/tex]/ [tex]2[/tex]) i )

=(2+[tex]\sqrt{3}[/tex])[tex]e^1^7^\pi ^i^/^6^0[/tex] [tex]e^\pi ^i^/^3[/tex]

=(2+[tex]\sqrt{3}[/tex]) [tex]e^3^7^\pi^ i^/^6^0.[/tex]

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x(x – 5) = 176 is the correct equation to find the greater integer.

As the question mentions, the greater integer is x. So, the smaller integer will be (x - 5). Also, we are informed that their product is 176.

Now, representing the given information as mathematical expression -

x(x – 5) = 176

On further multiplication on Left Hand Side, we get the equation -

x² - 5x = 176

Rewriting the equation -

x² - 5x - 176 = 0

Further solving the equation to validate it.

x² - 16x + 11x - 176 = 0

x (x - 16) + 11 (x - 16) = 0

(x - 16) (x + 11) = 0

x = 16, -11

As stated, the integers are positive. So, the value of x and hence greater integer is 16.

Value of small integer = 16 - 5

Value of small integer = 11

So, the two integers are 16 and 11. Their product is 176 hence, our formed equation is correct.

Therefore, the equation that can be used to find x is : x(x – 5) = 176.

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The complete question is -

Two positive integers have a product of 176. One integer is 5 less than the other integer. Which equation can be used to find the value of x, the greater integer?

x² + 5 = 176

x(x + 5) = 176

x(x – 5) = 176

x² – 5 = 176

Answer:

41

Step-by-step explanation:

5y+x

Evaluate the expression

Let x=6 and y=7

5*7 +6

Multiply first

35 +6

Then add

41

Answer:

it 41

Step-by-step explanation:5(7)+6=41

The algebraic equation of the verbal statement is (x + 2) / 5 = 8 and the value of x is 38.

Algebraic Equation

An algebraic equation means the statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations, namely, addition, subtraction, multiplication, division, raising to a power, and extraction of a root.

Given,

The quotient of two more than a number and five is eight.

Here we  need to translate the given verbal statement into an algebraic expression and solve it.

The quotient of two more than a number and five is eight.

Let, the number be x.

According to the question, the equation is

=> (x + 2) / 5 =8

=> x + 2 = 8 x 5

=> x + 2 = 40

=> x = 40 - 2

=> x = 38

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The solution of the simultaneous equations are x = 2, 3 and y = 3,9.

In mathematics; a set of simultaneous equations, also known as a system of equations or an equation system, it is a finite set of equations for which common solutions are sought.

WE have given simultaneous equations as;

y = x^2    ...(i)

y = x + 6  .....(ii)

Now Equating (i) and (ii) we get,

x^2 = x + 6

or, x^2 - x - 6 = 0

Then Solving we get;

x^2 - 3x - 2x - 6 = 0

x(x - 3) -2(x - 3) = 0

(x - 2)(x - 3) = 0

So, x = 2, 3

Now Putting x = 2, 3 in equation (i) we get;

y = 2^2

y = 4

and,

y = 3^2

y = 9

Thus, y = 3,9

Hence the solution of the simultaneous equations are x = 2, 3 and y = 3,9.

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The  proportion of initial sales were spent on marketing by small businesses  is between 5 and 10%.

The correct option is A.

The U.S. Small Business Administration estimates that small businesses typically want to spend between 7-8% of one‘s revenue on marketing, provided that their companies have profit margins of 10-12%.

In order for sales to know exactly where the buyers are and assist them in progressing toward a purchase, marketing can give sales representatives the opportunity to be as knowledgeable as the buyers themselves. In summary, marketing can actually improve sales representatives' performance, which can have an effect on revenue generation.

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I understand that the question you are looking for is:

In one study, small businesses starting out spent what percentage of sales on marketing?

A) 5 to 10%

B) 8 to 15%

C) 15 to 19%

D) 25 to 32%

Answer:

31.5

Because if you Subtract 21 from 84 you get 63
then if you divide 63 by 2 you get 31.5 so your Answer would be 31.5.

$26.8 is the total cost and Chicken Fajita Taco is the most

expensive meal .

What in mathematics is a linear equation?

Hamburger + Bacon Cheeseburger  + Chicken Fajita Taco + French Fries, Small + French Fries, Large + Onion Rings + Cole Slaw + Soft Drink, Small + Soft Drink, Large + Milkshake + Juice

=  $3.25 + $4.75 +  $3.50 +  $1.55 + $1.90 + $2.40 + $1.45 +  $1.30 + $1.65 +  $3.25 + $1.80

= $26.8

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Answer:

x⅔

Step-by-step explanation:

1. we understand the concept that x÷x is a subtraction as an instance, x³/x² = x¹ so we can apply this knowledge in this question

2. x⅚ / x⅙ --> x⅚-⅙

--> x^4/6 [simplify this]

--> x^4/6 [ divide 2 at the numerator and also the denominator]

--> x⅔

Last but not least, you got your 2 points

The answer is -28

We're asked to multiply 4 by -7

The multiplication is straight forward, the first number is a positive integer and the second number is a negative integer

4 × (-7)

= -28

Hence the multiplication of both numbers will give -28

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It take 8.205 minutes to fill a queen sized mattress.

'Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

Given dimensions:

Twin sized air mattress (39 by 8.75 by 75 inches).

Queen sized mattress (60 by 8.75 by 80 inches)

Now, Volume of twin sized mattress

=39* 8.75* 75

= 25593.35 cubic inch

Volume of queen sized mattress,

=60* 8.75* 80

= 42000 cubic inch

as, To fill 25593.35 cubic inch it takes 5  minutes

so, to fill 1 cubic inch = 5/25593.35

and, So to fill 42000 cubic inch it will take = 42000* 5/25593.35

=8.205 minutes

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Answer:

6 miles per hour!

Step-by-step explanation:

The slope of the line as shown in the diagram attached below = rise/run = 3/5.

The rise of a line over the run of a line would give us the slope of a line on a coordinate plane.

With the given line in the diagram, the image attached below shows the rise as represented by a red line while the run is represented by the blue line.

Therefore, we have:

Run = 10 units

Rise = 6 units

Slope (m) of the line = rise/run = 6/10

Simplify

Slope (m) of the line =  3/5

Therefore, the slope of the line as shown in the diagram attached below = rise/run = 3/5.

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Answer:

Step-by-step explanation:

If she made 60$ she only needs 140$ more to get to 200$

Equation are defined by equating two or more expressions. The solution to the system of equation is (k, (1+5k)/2)

System of equations are equations are equations that contains several variables and expression.

Given the system of equations

5x - 2y = -1

-15x + 6y = 3

Divide equation 2 through by -3 to have:

-15x/-3 + 6y/-3 = 3/-3

5x  - 2y = -1

You can see that both equations are equal. Let x = k so that;

5k - 2y = -1

-2y = -1 - 5k

2y = 1 + 5k

y = (1+5k)/2

Hence the solution to the system of equation is (k, (1+5k)/2)

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The value of csc x=-13/5.

Given that the sin x=-5/13 and x∈[3π/2 , 2π).

A trigonometric function is a real function that relates the angle of a right triangle to the ratio of the lengths of the two sides. The basic functions are sin, cos, tan, cot, sec, csc.

The given function is sin x=-5/13.

As we all know that sin x=1/csc x or csc x=1/sin x.

As it is given that x∈[3π/2 , 2π) that means x lies in fourth quadrant and in fourth quadrant sin and csc is negative in it.

So, we will apply this identity csc x=1/sin x, we get

csc x=1/(-5/13)

csc x=-13/5

And it also lies in x∈[3π/2 , 2π).

Hence, the value of csc x when sin x=-5/13 and x∈[3π/2 , 2π) is csc x=-13/5.

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(b) We have 13 possibilities that a five-card hand will contain four of a kind.

(c) We have 12 possibilities that a five-card hand will contain a full house.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

The probability of an occurrence is a number between 0 and 1, with 1 representing certainty and 0 representing impossibility.

Since there are no other conceivable outcomes and the coin is fair, the odds of both the possibilities, "heads" and "tails," are equally likely to occur. As a result, the probability of either occurrence is half (which could also be written as 0.5)

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Probability that no zebras collide is 0.25

The zebras are represented as z1, z2 and z3.

Z1 to B, Z2 to C, and Z3 to A come first [tex]= (\frac{1}{2})^3[/tex]

Following that, z1 to C, z2 to A, and z3 to B = [tex](\frac{1}{2})^3[/tex]

Consequently, the likelihood of no collision is 2×1/8 = 0.25.

Discrete and continuous probability distributions are the two main categories in which probability distributions fall. There are numerous varieties of probability distributions within each category.

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Answer: $9.30

Step-by-step explanation:

7.44/4 = 1.86

1.89 x 5 = $9.30