Cye-Na is starting a juice stand. It takes her 15 minutes to prepare 3 1/4 cups of juice. How many hours would it take her to prepare 32 1/2 cups of juice?​

Answer:

Step-by-step explanation:

(4 + 15.6a) − (7 + 3.7a) =

4 + 15.6a - 7 + 3.7a =

19.3a - 3

Answer:

[tex] \sf \: 11.9a - 3 [/tex]

Step-by-step explanation:

Now we have to,

→ simplify the given expression.

The expression is,

→ (4 + 15.6a) - (7 + 3.7a)

Let's simplify the expression,

→ (4 + 15.6a) - (7 + 3.7a)

→ 4 + 15.6a - 7 - 3.7a

→ (15.6a - 3.7a) + (4 - 7)

→ (11.9a) + (-3)

→ 11.9a - 3

Hence, the answer is 11.9a - 3.

Answer:

LCM of 12 and 42 is 84. it is correct

A recipe says it produces the best summer drink. The recipe calls for 12 cup of lemonade for every 112 cups of iced tea. If 16 cups of the summer drink are made

then 8 cups of lemonade are needed.

What is unitary method?

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Steps to Use Unitary Method

First, let us make a note of the information we have. There are 5 ice-creams.

5 ice-creams cost is $125.

Step 1: Let's find the cost of 1 ice cream.

In order to do that, divide the total cost of ice-creams by the total number of ice-creams.

The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-

creams = 125/5 = 25.

Therefore, the cost of 1 ice cream is $25.

Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams.

The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75.

Finally, we have the cost of 3 ice-creams i.e. $75.

lemonade: tea : total

1                 1    1+1=2

We need a total of 16 and divide it

= 16/2 = 8

Then the composition will be

lemonade:    tea:        total

1*8 = 8      1*8 = 8      2*8 = 16

Hence, 8 cups of lemonade are needed.

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Jada could say to her cousin that we get a negative value which we is needed to make solution complete.

Two or more expressions with an Equal sign is called as Equation.

Given,

Jada was helping her cousin with his math homework.

He was supposed to solve the equation 8 + x = 5.

He said, "If I subtract 8 from both sides, I get x = 5-8.

5 grapes, I can't eat 8 of them!" Jada said.

Actually we can subtract 8 from five but we get a negative value.

5-8=-3

It means we should three more apples to eat.

Hence we can subtract 8 from five which makes sense.

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In a simple linear regression model , if we change the input variable by 1 unit , output variable will change by its slope.

What is linear regression?

According on the value of another variable, a variable's value can be predicted using a linear regression analysis. The dependent variable is the one you're trying to forecast. The term "independent variable" refers to the variable you are using to forecast the value of the other variable.

Main Body:

For linear regression

Y=a + bx + error

If we neglect error

then Y=a + bx.

If x increases by 1

then Y = a +b(x+1) which implies

Y=a + bx + b.

So Y increases by its slope.

Hence their is an increase in the slope in y.

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Answer: Answer: 1m = 60s, what is the equation?

Step-by-step explanation: 1 minute = 60 seconds so 60s = 1m

15 additional kcalories is she likely to burn in the post-exercise period .

What do food calories mean?

jules burns 100 kcalories during her morning walk.

15 additional kcalories is she likely to burn in the post-exercise period .

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Answer:

By counting, we see that the point travels down 3, over 6. This is a slope of -3/6. This then simplifies down to -1/2.

The slope is -1/2

The value are x=1,y=3 and z=-1 when the equation are x+5y-3z=19, 2x-3y+4z=-11 and 4x+y-2z=9.

Given that,

The equation x+5y-3z=19

2x-3y+4z=-11

4x+y-2z=9

We have to find the x,y ad z values. Its is nothing but the zeros of the polynomial.

Take the equations as,

x+5y-3z=19----->equation(1)

2x-3y+4z=-11----->equation(2)

4x+y-2z=9----->equation(3)

Subtracting equation (2) with 2×equation(1)

(x+5y-3z=19)×2⇒ 2x+10y-6z=38

                            2x-3y+4z=-11

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

                            13y-10z=49----->equation(4)

Now,

Subtracting equation (3) with 2×equation(2)

(2x-3y+4z=-11)×2⇒ 4x-6y+8z=-22

                               4x+y-2z=9

                          ---------------------------
                                 -7y+10z=-31-------->equation(5)

Now,

Adding equation (4) and equation(5)

13y-10z=49

-7y+10z=-31

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

6y=18

y=18/6

y=3

Now,

Substitute y=3 in equation(5)

-7(3)+10z=-31

-21+10z=-31

10z=-31+21

10z=-10

z=-10/10

z=-1

Now,

Substitute y=3 and z=-1 in equation(1)

x+5y-3z=19

x+5(3)-3(-1)=19

x+15+3=19

x+18=19

x=19-18

x=1

Therefore, The value are x=1,y=3 and z=-1 when the equation are x+5y-3z=19, 2x-3y+4z=-11 and 4x+y-2z=9.

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a. In 2001, it has been calculated that the number of enrolled students that the school would have is given as 150.

b. In the academic year 2018, 468 thousand students are anticipated to enroll at the institution abroad.

The equation that would be used to get the value of the population has been given to us as follows,

y = 123.1(1.069)^x

We are to find x and use it to solve the equation.

X would be used to tell us the number of years that have passed or what lies as the difference.

in which x is the number of years that have changed.

x = 2001 - 1998 = 3

We have to input the value of x to get the value of y

y = 123.1(1.069)³

This gives us y = 150.4

Hence 150 students  would be enrolled.

b. We have to solve for the year 2018

Similarly, the difference between these years is given as:

x = 2018 - 1998 = 20

Put the value in the equation

y = 123.1 * (1.069)²⁰

Y is therefore  467.5

y ~ 468 thousand

Hence 468 are enrolled in this year.

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Answer:

[tex]\textsf{Solution}: \quad 5 < x < 13[/tex]

[tex]\textsf{Interval Notation}: (5, 13)[/tex]

Step-by-step explanation:

Given inequality:

[tex]|x-9|-3 < 1[/tex]

To solve an inequality containing an absolute value, isolate the absolute value on one side of the inequality:

[tex]\implies |x-9|-3 +3 < 1+3[/tex]

[tex]\implies |x-9| < 4[/tex]

Apply the absolute rule:

[tex]\textsf{If $|u| < a$\; and\; $a > 0$, \;then \; $-a < u < a$}.[/tex]

[tex]\implies -4 < x-9 < 4[/tex]

[tex]\implies -4 < x-9 \;\; \textsf{and}\;\;x-9 < 4[/tex]

Solve case 1:

[tex]\implies -4 < x-9[/tex]

[tex]\implies x-9 > -4[/tex]

[tex]\implies x-9 +9 > -4+9[/tex]

[tex]\implies x > 5[/tex]

Solve case 2:

[tex]\implies x-9 < 4[/tex]

[tex]\implies x-9+9 < 4+9[/tex]

[tex]\implies x < 13[/tex]

Therefore, x is greater than 5 and smaller than 13.

Merge the overlapping intervals to obtain the solution:

[tex]\boxed{5 < x < 13}[/tex]

Answer:

to subtract fractions, find the LCD and then combined

The answer is 1/12.

Answer:

The scale factor is 3

Step-by-step explanation:

Answer:

16:48 or 16 to 48 or 16 / 48

Step-by-step explanation:

Answer:

16:48

Step-by-step explanation:

16 is the total amount of students who want lemonade.
You add 16 with 32 to get 48 students in total.
So the ratio is 16:48.

Answer: y=3x2

Step-by-step explanation:

A parabola that have a focus of (7,3) and a directrix of y = 5 has these attributes

The parabola is a vertical parabola and facing down

the vertex of the parabular is v(7, 4)

p value of the parabola = -1

A parabola refers to  shape that traces equation of the form

ax² + bx + c

The directrix of a parabola refers to a vertical or horizontal line that never touches the parabola and at distance p to the vertex of the parabola., and 2p to the focus of the parabola.

when the directrix is on the y coordinate, the parabola formed is a vertical parabola.

If the value of the directrix is more than the corresponding focus or vertex there will be negative p and the parabola will face downward.

conversely, If the value of the directrix is less than the corresponding focus or vertex there will be positive p and the parabola will face up.

from definition of the directrix we calculate for p

2p = y coordinate of focus - equation of directrix

2p = 3 - 5

2p = -2

p = -1

vertex, v(h, k) compared with f(h, k + p)

h + p = 3

h = 4

therefore vertex is (7, 4)

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245.31 (dollars) is the cost (in dollars) of materials for the least expensive such container.

Calculus maxima and minima are found  using the concept of derivatives. Knowing that the derivative concept gives information about the slope/slope of a function, we find the point where the slope is zero. These points are called inflection points/stationary points. These are the points associated with the maximum or minimum (local) values ​​of the function.

Knowledge of maxima and minima is essential for our everyday problems. In addition, this article also explains how to find the absolute maximum and minimum values.

Solvable maximum and minimum arithmetic problems  are discussed in this article.

Suppose the width is x (m), length of the base is 2x (m), the base area is 2x^2 (m^2).

Since the volume is 10 (m^3), the height has to be 10/2x^2 (m) = 5/x^2.

The cost of making such container is

cost of base: 2x^2*15 = 30x^2

cost of sides: (2*2x*5/x^2 + 2*x*5/x^2)*9 = 270/x

The overall cost is hence the sum of the base and the sides: f(x) = 30x^2 + 270/x

The get the minimum,

df(x)/dx = 30*(2x - 9/x^2) = 0

so x = (9/2)^(1/3) = 1.651 (m)

f(x) = 245.31 (dollars)

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Answer:

Below

Step-by-step explanation:

70 - 69 = 1

   1/1.2 is  .83 S.D. below the mean   for a z-score = -.83

       from a z-score table this corresponds to .2033  or 20.33%

Option a is correct.

$2 more is Addison’s holiday hourly rate than her regular hourly rate

What are Time and Work?

According to fundamental mathematical concepts, time may be described as the amount of time that a specific activity occurs, whereas work can be described as the collection of actions carried out in order to attain a specific activity or outcome. It should go without saying that time is needed to accomplish a task. It implies that time and work have a certain relationship.

The task completed is calculated as the sum of the number of people participating in the work and the number of days it took to finish. The fundamental time and work equation is W = N X D.

W is the amount of work done.

N is the number of people.

D is the number of days or hours needed.

Let r be the regular rate and h the holiday rate.

Then you can write these two equations:

From the first statement:

188.50 = 5h + 16r

From the second statement:

254.00 = 8h + 20r.

There you have a system of two independent equations with two variables, which you can solve by several methods.

If you multiply the first by 8 and the second by 5, you get:

40h + 128r = 1508

40h + 100r = 1270

Subtract the second equation from the first one:

28r = 238

Divide by 28

r = 238/28 = 8.5

You can use now any of the two original statements to find h

254.00 = 8h + 20r

8h = 254 -20(8.5) = 84

h = 84/8 = 10.5

h - r = 10.50 - 8.50 = 2.00

The holiday hourly rate is $2.00 more than the regular hourly rate.

Hence,

$2 more is Addison’s holiday hourly rate than her regular hourly rate

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After evolution of log_6(36)  value obtain is 2..

What is Logarithm?

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 1000 = 103, the logarithm of 1000 in base 10 is 3, or log10 = 3.

Given that;

log6 36

Formula we used to solve this logarithm equation is :

logb(x) = y, if b^y = x

So,

     y = log6 36

     = log6 62

     = 2 log6 6 = 2 x 1

     log6 36 = 2

Hence ,the value log6(36) is  2.

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A storage shed is to be built in the shape of a box with a square base. It is to have a volume of cubic feet.

The dimensions of the most economical shed are height = 10 ft and side 5 ft

Taken data

volume = 250 cubic feet

base costs = $4 per square​ foot

material for the roof costs =  ​$6 per square​ foot

material for the sides costs = ​$2.50 per square foot

to find out the dimensions of the most economical shed solution

let us consider length of side x and height is h

so we can say x²h = 250

and h = 250 / x²

now cost of material  = cost of base + cost top + cost 4 side

cost  = x²(4) + x²(6)  + 4xh (2.5)

cost = 10  x² + 10xh

put here h = 250 / x²

cost = 10  x² + 10x (250/ x² )

cost = 10  x² +  (2500/ x )

if we differentiate and we get

c' = 20 x - 2500 / x²

put c' = 0 solve x

20 x - 2500 / x²  = 0

x = 5

so we say one side is 5 ft  base

and height is  h = 250 / x²

h = 250 / 5²

height = 10 ft

Hence the answer is, the dimensions of the most economical shed are height = 10 ft and side 5 ft

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The volume of a cylinder in terms of r is √V/πh.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

Given that, the volume of a cylinder = πr²h

Solving in terms of r,

r = √V/πh

Hence, The volume of a cylinder in terms of r is √V/πh.

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The number of  blueberry muffins she is left with is 9.

The quantitative relation between two amounts, showing the number of times one value contains or is contained within the other.

Given that, Sarah baked blueberry and chocolate muffins in the ratio of 5:2. she gave 6 blueberry muffins to her brother, and now the ratio of blueberry to chocolate muffins has changed to 3:2.

Let the number of muffins before be 5x and after be 3x, then

5x-6 = 3x

2x = 6

x = 3

Therefore, the number of muffins after = 3*3 = 9

Hence, The number of  blueberry muffins she is left with is 9.

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James is 24 years old.

Let John's age now is J.

Let james's age now is A.

From the question, we have

John is 3/4 the age of  james.

J=3/4*A

J=3A/4

Three years ago, John was 5/7 the age of james.

J-3=5/7*(A-3)

J-3=(5A-15)/7

J=(5A-15)/7+3

3A/4=(5A-15)/7+3

21A=4(5A-15)+84

21A=20A-60+84

A=24

James is 24 years old.

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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The random variable used in this situation is discrete random variable.

What is a random variable?

Suppose there is an event and the outcome of an event has to be represented by a variable. That variable is called random variable.

50 students were randomly sampled and asked questions about their exercise habits. one of the questions they were asked concerned the frequency of exercise, defined to be the number of times they exercised in a week

Since there is a notation about frequency in this question, it cannot be continuous. So it is a discrete random variable.

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Answer:

1.  x = 2

2.  x = 360

3.  x = -41 and x = 49

4.  All real numbers.

5.  x = 1

Step-by-step explanation:

[tex]\begin{aligned}&\textsf{Given}: & \dfrac{x+16}{3}&=3x\\&\textsf{Multiply both sides by 3}: & x+16&=9x\\&\textsf{Subtract $x$ from both sides}: & 16&=8x\\&\textsf{Divide both sides by 8}: & x&=2\end{aligned}[/tex]

Therefore, the solution is x = 2.

[tex]\begin{aligned}&\textsf{Given}: & x &= 0.8x + 72\\&\textsf{Subtract $0.8x$ from both sides}: & 0.2x&=72\\&\textsf{Divide both sides by 0.2}: & x&=360\end{aligned}[/tex]

Therefore, the solution is x = 360.

[tex]\begin{aligned}&\textsf{Given}: & \dfrac{1}{5}|x-4|-3&=6\\&\textsf{Add 3 to both sides}: & \dfrac{1}{5}|x-4|&=9\\&\textsf{Multiply both sides by 5}: &|x-4|&=45 \\\end{aligned}[/tex]

Set the contents of the absolute value equal to both the positive and negative value of the number on the other side of the equation, and solve both equations.

[tex]\begin{aligned}\underline{\sf Equation\; 1}&&\underline{\sf Equation\; 2}\\x-4&=45 & x-4&=-45\\x-4+4&=45+4 & \quad \quad \quad x-4+4&=-45+4\\x&=49 & x&=-41\\\end{aligned}[/tex]

Therefore, the solutions are x = -41 and x = 49.

[tex]\begin{aligned}&\textsf{Given}: & -2(x + 3) &= -2x-6\\&\textsf{Distribute}: &-2x-6&=-2x-6\\&\textsf{Add 6 to both sides}: & -2x&=-2x\\&\textsf{Divide both sides by -2}: & x&=x\end{aligned}[/tex]

Therefore, the solution is all real numbers.

[tex]\begin{aligned}&\textsf{Given}: & \dfrac{3}{2}+\dfrac{1}{2}x & = 2x\\&\textsf{Subtract $\dfrac{1}{2}x$ from both sides}: & \dfrac{3}{2}&=\dfrac{3}{2}x\\&\textsf{Multiply both sides by 2}: & 3&=3x\\&\textsf{Divide both sides by 3}: & 1&=x\end{aligned}[/tex]

Therefore, the solution is x = 1.

Answer: y = -5x+2

Step-by-step explanation:

Slope = [tex]\frac{rise}{run}[/tex] or [tex]\frac{y_{2}-y_{1}}{x_{2}-x{1}}[/tex]

therefore, given those two points,

Slope = [tex]\frac{(-3)-7}{1-(-1)}[/tex]

Slope = [tex]\frac{-10}{2}[/tex]

Slope = -5

Since the m value is the slope, m = -5

In order to find the b value, just substitute the values in the equation with any of the two points given. I'll use (-1,7) but you can use the other one just fine.

let x =1, y = -3

-3=-5(1)+b

-3 = -5+b

-3+5 = b

b = 2

Plug b in the equation:

y=-5x+2

Answer:

∴ x = 32

Step-by-step explanation:

For J to be parallel to K,

(2x)° + (4x-12)° = 180°

   2x + 4x - 12 = 180

                  6x = 192

                 ∴ x = 32

The pair of polygons in the diagram are not similar.

What are polygons?

A closed polygonal chain made up of a finite number of straight-line segments is what defines a polygon in geometry. A polygon can be defined as a region that is circumscribed by a bounding circuit, a plane, or both. The edges or sides of a polygon circuit are its segments.

Solution Explained:

Similar polygons have proportional matching sides and all corresponding angles that are congruent.

Since the polygons' side lengths ensure that they are parallelograms, the congruence of just one pair of related angles is sufficient to guarantee the congruence of all the others.

The ratio of side lengths in the left polygon is 13/8, whereas in the right polygon it is 5.2/2.4, which equals 13/6. The matching sides are NOT proportionate since their ratios are different from one another.

Hence, the pair of polygons are not similar.

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