Find the prime factorization of
the number 68.
Order the factors from least to greatest.
Remember, 1 is not a prime number.
[?] × [×]
Enter the number that belongs in the green box.

Answer:

[tex]l=\frac{A}{W}\\[/tex]

Step-by-step explanation:

Sometimes we have to manipulate a variable this is often easier to do when we solve for the variable we want and input numbers into the rest of the equation

Let's say A=16 and w=8

Solving for l would me using the A=lw and inputing those values

A=lw

16=l(8)

[tex]\frac{16}{8}=\frac{8l}{8}[/tex]

[tex]l=\frac{16}{8} \\[/tex]  or [tex]l=2[/tex]

If A = 16 and w = 8, we could substitute those values into the original equation(A=lw) and say that

[tex]l=\frac{A}{W}[/tex]

Sometimes we have to manipulate a variable.

This is often easier to do when we solve for the variable we want and input numbers into the rest of the equation.

I hope this explanation is helpful :)

The value x is 1 and y is 3.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

x+ y = 4

y= 3x

Now solving above equations

x+ 3x = 4

4x = 4

x= 1

and, y = 3x = 3

Hence, the value x is 1 and y is 3.

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Answer:

$1.50

Step-by-step explanation:

first, find the unit rate which is 0.3 (7.2/24)

then multiply that by 5

Answer:

7.2 weeks

Step-by-step explanation:

12 + [tex]\frac{7}{3}[/tex] x = 42 - [tex]\frac{11}{6}[/tex]x  Multiply all the way through by 6 to clear the fractions

72 + 14x = 252 -11x  Add 11x to both sides

72 + 25x = 252  Subtract 72 from both sides

25x = 180  Divide both sides by 25

x = 7.2

Answer:

h(3)=4

Step-by-step explanation:

Answer:

Step-by-step explanation:

The value of x= 110 degrees as it is corresponding to the angle equal to 110 degrees.

To boost the level of trust in the forecasted values, a balancing point must be attained.

The two phrases confidence interval and precision are intended to provide an accurate estimate of an object's measurability. We can compromise on the confidence level if the precision rises, but if the confidence level rises, the precision of the anticipated value likewise deteriorates.

Therefore, a balance point between these two variables must be reached in order to improve our confidence in the numbers being forecasted without compromising an accurate evaluation of accuracy. ensuring that accuracy and confidence are both upheld.

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The unit rate of the Coca-Cola is $ 1.032 and the unit rate of the Pepsi is $ 1.245.

Given, cost of Coca-Cola is

$1.29 for 1.25L

and cost of Pepsi is

$2.49 for 2L

we have to find the unit rate of each of the following,

As, the cost of Coca-Cola is

$1.29 for 1.25L

$1.29 = 1.25L

1 L = 1.29/1.25

1 L = $ 1.032

Now, the cost of Pepsi is

$2.49 for 2L

$2.49 = 2L

1 L = 2.49/2

1 L = $ 1.245

Hence, the unit rate of the Coca-Cola is $ 1.032 and the unit rate of the Pepsi is $ 1.245.

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The cost of a box of pasta is $2. 64, then what will you be charged for pasta this week is $1,125.

The average cost, or how much it generally costs to produce a unit, can be discovered using the cost function. The average cost function is defined as A(x)=C(x)x, where x > 0. The average cost per unit is calculated by dividing the total cost by the number of units produced.

Given,

Your ending inventories this week for pasta were 35, 41, 32, 19, and 47 boxes. You par value is 120 and a supplier comes each night.

Par level = [(120 - 35) + (120 - 41) + (120 - 32) + (120 - 19) + (120 - 47)]

Par level = [85 + 79 + 88 + 101 + 73]

Par level = 426 units.

Charges = par level × cost

Charges = 426 × 2.64

Charges = 1,124.64

Charges ≈ $1,125

The cost of a box of pasta is $2. 64, then what will you be charged for pasta this week is $1,125.

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Answer:

oh no

Step-by-step explanation:

Answer:

y = -6x - 50

Step-by-step explanation:

y = mx + b

Since it is perpendicular to y=1/6, the slope is -6. (Opposite reciprocal)

y = -6x + b.

Substitute to get: -2 = 48 + b

b = -50

y = -6x - 50

Answer:

2

Step-by-step explanation:

first turn the fractions improper to get 16/3 divided by 8/3

then keep the first fraction the same but flip the second fraction and change divide to multiply to get 16/3 times 3/8

last multiply across to get 48/24 then simplify to get 2

2

Step-by-step explanation:

[tex] \frac{ 5\frac{1}{3} }{2 \frac{2}{3} } [/tex]

[tex] = \frac{ \frac{15 + 1}{3} }{ \frac{6 + 2}{3} } [/tex]

[tex] = \frac{ \frac{16}{3} }{ \frac{8}{3} } [/tex]

Shift denominator term i.e. 8/3 to numerator. Then, the fraction will be get reciprocal i.e. 8/3 to 3/8.

[tex] \frac{16}{3} \times \frac{3}{8} [/tex]

[tex] = { \red{ \tt{ \frac{ \cancel{48^{2}}}{ \cancel {24}_{1}}}}}[/tex]

= 2

Answer:

I don't know I just got the app

Step-by-step explanation:

; /

Answer:

I think 24

Step-by-step explanation:

-6 + 24 =18

The mean will be increased by 2, and the standard deviation will remain the same (option D).

The first step is to determine the initial mean and standard deviation of the data.

Mean is the average of a set of numbers.

Mean = sum of numbers / total number in the data

(2 + 3 +3 + 5 + 5 + 6) / 6

24 / 6 = 4

Standard deviation is used to determine how the values in a group differs from the mean of the values in the group. It is a measure of variation.

Standard deviation of the initial data = √[{(2 - 4)² + (3 -4)² + (3 - 4)² + (5 - 4)² + (5 - 4)² + (6 - 4)²} / 6] = 1.414

Now, determine the mean and the standard deviation of the new data

New data : (2 + 2 =4)

3 + 2 = 5

3 + 2 = 5

5 + 2 = 7

5 + 2 = 7

6 + 2 = 8

Mean = (4 + 5 + 5 + 7 + 7 + 8) / 6 = 6

Standard deviation = √[{(4 - 6)² + (5 - 6)²+ (5 - 6)² + (7 - 6)² + (7 - 6)² + (8 - 6)²} / 6] = 1.41

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Answer:

Step-by-step explanation:

1. Area for triangle. Base* Height/2

Here the base it 13 units and height is 11 units. Apply to the formula:

13*11/2=

71.5 sq units

2. Answer: 71.5 sq units

Answer:

4 × v = 60

= 15

Step-by-step explanation:

v represents Victor's savings

4 × v = 60

4v = 60

Divide both sides by 4v

v = 60/4

v = 15

The number of pages Giovanni can read in 2 hours is approximately 103.

Giovanni can read 300 words per minute. There are approximately 350 words on a page.  

The number of pages he can read in 2 hours can be calculated as follows:

Therefore,

1 hour = 60 minutes

2 hours = 120 minutes.

Therefore,

1 minute = 300 words

120 minutes = ?

cross multiply

number of words he can read in 2 hours = 120 × 300 = 36000

350 words = 1 page

36000 words = ?

cross multiply

number of pages he read in 2 hours = 36000 / 350

number of pages he read in 2 hours = 102.857142857

Therefore, he read about 103 pages in 2 hours.

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The number of small boxes sent is 7 and the number of large boxes sent is 8  .

In the question ,

it is given that ,

the number of books that a small box can hold = 25 books

the number of books that a large box can hold = 35 books .

let the number of small boxes be "s" ,

So , the total number of books in s boxes will be 25s .

since the total number of boxes given is 15 ,

So , the number of large boxes = 15 - s

So , the number of books in the (15-s) large boxes  = 35(15-s),

also given that total books altogether = 455 ,

According to the question ,

the equation becomes

25s + 35(15-s) = 455

25s + 35*15 - 35s = 455

525 - 10s = 455

10s = 525 - 455

10s = 70

s = 70/10

s = 7 boxes

and large boxes = 15 - 7 = 8 boxes .

Therefore , The number of small boxes sent is 7 and the number of large boxes sent is 8  .

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Answer:

Mikhail is 42 years old

Step-by-step explanation:

Answer: ? = 50, same side interior angles

? = 84, alternate interior angles

Step-by-step explanation:

130 + x = 180

-130   =    -130

x = 50

alternate interior angles are congruent

50° is the value of the missing angle.

Since u and v lines are parallel so the angle asked and the angle with the value of 130° are alternate interior angle.

Alternate interior angles have the following characteristics:

Therefore,

x+130 = 180

x =180-130

x =50°

therefore, the missing angle is 50°.

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As per the given tax percent deduction from Marquis gross pay of $816 , the gross pay is reduced by $174.66.

As given in the question,

Gross pay taken by Marquis is equal to $816

Items withheld from Marquis gross pay are as follow:

1. Federal tax = $92

2. Social security tax = 6.2% of gross pay

6.2% of 816

= (6.2/100) × 816

= $50.592

3. Medicare tax = 1.45% of gross pay

= 1.45% of 816

= (1.45/100) × 816

= $11.832

4. State tax = 22% of federal tax

= 22% of 92

= ( 22 /100) × 92

= $20.24

Total reduced tax amount from Marquis gross pay

= $ ( 92 + 50.592 + 11.832 +20.24 )

= $ 174.664

≈ $174.66

Therefore,  for the given tax percent deduction from Marquis gross pay of $816 , the gross pay is reduced by $174.66.

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The number of standard deviations a score has from the population mean is measured by the z-score, also known as the standard score.

The range of the z-scores is from 3 to 3 on the normal distribution curve, and values outside of this range are called outliers. The z-score's formula is as follows:

Z=X-μ/σ

First, convert the given X value into a Z-score. Keep in mind that equals 50 and equals 360.As a result,

Z = 400-360/50 = 0.80

A measure of how dispersed the data are in relation to the mean is called the standard deviation (or ).Data with a low standard deviation are grouped around the mean, while data with a high standard deviation are more dispersed.

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Required inequalities are 0.20x=1.20, 0.10y = 1.20 and 0.20x + 0.10y = 1.20. Combination of fruits open to Kojo are (6,0), (1,10), (2,8), (3,6), (4,4), (5,2), (0,12)

Given,

Kojo is given $1.20 to buy some peaches and apples. Peaches cost 20c each, apples 10c each.

He is told to buy at least 6 individual fruits, but he must not buy more apples than peaches.

Let x be the number of peaches Kojo buys.

Let y be the number of apples Kojo buys.

(a)Since Kojo has $1.20 to buy peaches and apples; and each peach and apple costs 20c and 10c respectively.

We have the following inequalitites:

0.20x = 1.20

0.10y = 1.20

0.20x + 0.10y = 1.20

(b)Possible combinations of fruits are as follows:

x = 1.20/0.20 = 6

y = 1.20/0.10 = 12

x = 1,2,3,4,5 ; y = 10,8,6,4,2

Thus, Required inequalities are 0.20x=1.20, 0.10y = 1.20 and 0.20x + 0.10y = 1.20. Combination of fruits open to Kojo are (6,0), (1,10), (2,8), (3,6), (4,4), (5,2), (0,12)

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The solution of the system of the equations are; x =  -2/3, y = -1/2 and z = 1.

An equation is an expression that shows the relationship between two or more numbers and variables.

The system of equation is given by;

3x − 4y + z = 2 ---- (1)

−9x + 12y − 3z = − 6 -------(2)

4x − 2y − z = -16  -----(3)

Now we add equations 1 from equation 3;

(3x − 4y + z ) + (4x − 2y − z ) =  2 -16

7x - 6y = -14 -----(4)

Further we multiply equation 3 by 3 and subtract from equation 2;

3(4x − 2y − z) - (−9x + 12y − 3z ) = -48 + 6

12x - 6y - 3z + 9x - 12y + 3z = 42

21x  - 18y = 42-----(5)

Now we multiply equation 4 by 3 and add it to equation 4

3(-3x + 3z) + (9x + 4z) = 5×3 - 2

-9x + 9z + 9x + 4z = 15 -2

13z = 13

z = 1

Now we put z = 1 in equation number 5

-3x + 3×1 = 5

-3x + 3 = 5

-3x = 5 - 3

-3x = 2

x = -2/3

y = -1/2

Therefore, the solution of the system of the equations are; x =  -2/3, y = -1/2 and z = 1.

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Answer:

y=-4x+5;

Step-by-step explanation:

the linear functions are represented by the power of x as 1

Answer:

y=-4x+5

Step-by-step explanation:

the degree of the variable(x) in the function is 1.

After solving the value of x is 14.048.

Given:

KM represents an angle bisector.

Let y be the length of KM.

From the figure:

[tex]12.3^{2} = 5.4^{2} +y^{2}[/tex]

151.29 - 29.16 = [tex]y^{2}[/tex]

130.13 = [tex]y^{2}[/tex]

y = 11.407

[tex]x^{2} =8.2^{2} +11.407^{2}[/tex]

= 67.24 + 130.13

= [tex]\sqrt{197.37}[/tex]

x = 14.048.

Therefore After solving the value of x is 14.048.

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The probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is ;

Pr(C & fewer than 3) = 0.1985

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Here, we are required to find the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years.

Let Pr(C) be the number of consumers who believe that cash will be obsolete in the next 20 years.

Therefore, since 39.7% believe so,

Pr(C) = 39.7/100 = 0.397

If 6 consumers are selected randomly, the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years will be;

Probability of 2 out 6 to believe so or Probability of 1 out of 6 to believe so.

Pr(2/6) + Pr (1/6)

Therefore the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is;

Pr (fewer than 3) = (2/6) + (1/6)

Pr (fewer than 3) = 3/6

Therefore, the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is ;

Pr(C) × Pr (fewer than 3)

i.e 0.397 × (3/6) = 0.1985

Therefore, the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is ;

Pr(C & fewer than 3) = 0.1985

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The slope intercept form of equation of required line is

[tex]y = \frac{3}{2}x + \frac{1}{2}[/tex]

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.

Here,

Slope of the line = 1.5

The line passes through (21, 32)

Equation of required line =

[tex]y - 32 = 1.5(x - 21)\\y - 32 = \frac{3}{2}(x - 21)\\2y - 64 = 3x - 63\\2y = 3x - 63 + 64\\2y = 3x + 1\\y = \frac{3}{2}x + \frac{1}{2}[/tex]

Putting x = 1 on the line,

[tex]\frac{3}{2} \times 1 + \frac{1}{2}\\[/tex]

[tex]\frac{3 + 1}{2}\\\\\frac{4}{2}\\\\2[/tex]

(1, 2) is coordinate of another point on the line

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The X and Y angles created by lines intersection in the pictures are 18° and 54°.

Based on the picture, angle ∠MON is a right angle hence it has an 90° angle. We then know that the ∠MOA is 72°. Because angle ∠MOA lies within the angle ∠MON, hence we can write the following formula:

∠MON = ∠MOA +∠AON = 90°

∠MON = 72° + ∠AON = 90°

∠AON = 18° ... (i)

If we focus on the line CD being intersected by the line AB, hence we can conclude that the angles form by this intersection will follow these rules:

∠AOD = ∠BOC

∠AOC = ∠BOD

∠AOD + AOC = 180°

∠BOC + ∠BOD = 180°

Based on the picture, we know that:

∠BOC = x

∠AOC = ∠MOA + ∠MOC

∠AOC = 72° + y ...(ii)

∠AOD = ∠AON + ∠NOD

∠AOD = 18° +2x

∠BOC = 3x ... (iii)

Because we already know that ∠BOC = AOD, hence we could rewrite the formula into:

∠BOC = ∠AOD

3x = 18° + 2x

x = 18° ... (iv)

To find the value of y, we need to focus on angle ∠AOC. Based on the previous calculations and formulas, we  know that:

∠AOC + ∠BOC = 180° ... (v)

Input equations (ii) and (iv) into (v)

∠AOC + ∠BOC = 180°

(72° + y) + 3x = 180°

72° + y + 3(18°) = 180°

126° + y = 180°

y = 54° ... (vi)

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