Choose the figure that models 4 divided by 4/3

lynn got the better deal than Roger.

percentage, a relative value indicating hundredth parts of any quantity.

Given,

lynn bought a new crash cymbal for her drum set. it costs 120$ but she received a 15% student discount.

Convert 15% to decimal form

15%=15/100=0.15

0.15×120=18

So 15% of 120 is 18.

Iynn bought crash cymbal for her drum set is 120-18=102

Roger bought the same crash cymbal from another store for$130

Roger applied coupon of $25.

So 130-25=$105

When we compare both Iynn and Roger, Iynn got the crash cymbal for a better deal.

Hence lynn got the better deal than Roger.

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The percentage increase for each of the given figures are;

a) 6%

b) 6%

c) 12%

Percentage increase is simply defined as the percentage by which a figure increases. The formula to calculate percentage increase is;

Percentage increase = (Final value - Initial Value)/initial value) * 100%

a) We are given;

Original quantity = 100

New quantity = 106

Thus;

Percentage increase = (106 - 100)/100 * 100%

Percentage increase = (6/100) * 100%

Percentage increase = 6%

b) We are given;

Original quantity = 10

New quantity = 16

Thus;

Percentage increase = (16 - 10)/10 * 100%

Percentage increase = (6/10) * 100%

Percentage increase = 60%

c) We are given;

Original quantity = 50

New quantity = 56

Thus;

Percentage increase = (56 - 50)/50 * 100%

Percentage increase = (6/50) * 100%

Percentage increase = 12%

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Complete question is;

Find the percent increase for the given original and new quantities in parts a through c.

a) Original quantity:100 New quantity:106

b) Original quantity:10 New quantity:16

c) Original quantity:50 New quantity:56

The calculation of the ratios, resulting from the square feet occupied by Departments A and B, and the amounts of allocated overhead costs to the two departments are as follows:

                           Ratio      Amount

Department A       1/5        $10,000

Department B      4/5       $40,000

The ratio is the relative value relationship shared by two or more numbers.

Ratios are fractional values depicted in fractions, decimals, and percentages.

Like proportions, ratios show how much a value or variable is contained in another.

Total overhead = $60,000

Department   Square Feet  Ratio    Amount of Overhead Allocated

Dept. A            10,000         A = 1      B = $15,000 ($60,000 x 1/4)

Dept. B            30,000         = 3     D = $45,000 ($60,000 x 3/4)

Ratios = 10,000:30,000

= 1:3

Sum of Ratios = 4

Thus, based on the ratios, Department A is allocated $15,000, while Department B will be allocated $45,000 of the distributable overhead costs.

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Answer:

1.342

Step-by-step explanation:

4^x+64^x=272

4^x+(4^3)^x=272

4^3x+4^x=272

(4^x)^3+4^x=272

(4^x)^3+4^x-272=0

u^3+u-272=0 ==> substitute 4^x with u

Now, use synthetic division to find roots:

[tex]\sqrt[3]{272}[/tex]31   |    1    0              1             -272

                       [tex]\sqrt[3]{272}[/tex]1     [tex]\sqrt[3]{272^2}[/tex]      272

                 1    [tex]\sqrt[3]{272}[/tex]1      [tex]\sqrt[3]{272^2}[/tex]       0

4^x=[tex]\sqrt[3]{272}[/tex]

log 4 (4^x)=log 4 ([tex]\sqrt[3]{272}[/tex])=1.342

Answer:

v = 99

Step-by-step explanation:

given v varies directly as g then the equation relating them is

v = kg ← k is the constant of variation

to find k use the condition v = 36 when g = 4 , then

36 = 4k ( divide both sides by 4 )

9 = k

v = 9g ← equation of variation

when g = 11 , then

v = 9 × 11 = 99

Answer:  x = 8   y = 21

Step-by-step explanation:

7x + 12 = 12x - 28

40 = 5x

x = 8

180 = 12(8-28) + 9y - 77

180 = 96 - 28 - 77 + 9y

180 = -9 + 9y

189 = 9y

y = 21

Answer:

x=8

y=21

Step-by-step explanation:

9y-77+12x-28=180

9y+12x=285

7x+12=12x-28

5x=40

x=8

9y+96=285

9y=189

y=21

Answer:  12/0

Step-by-step explanation:  (5−3)(2)+8

(2)(3)−7+1

=

(2)(2)+8

(2)(3)−7+1

=

4+8

(2)(3)−7+1

=

12

(2)(3)−7+1

=

12

6−7+1

=

12

−1+1

=

12

0

=

1

0

;)

The value of P=2 and Q=8 as in AP, The difference in two terms is equal between all the terms.

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. Sn = n/2[2a + (n 1) d] is the formula to determine the sum of an arithmetic progression. where an is the first term in the arithmetic progression, n is the total number of terms, and d is the common difference. If there is always the same difference between any two consecutive terms in a series of numbers, that progression is known as an arithmetic progression. Simply put, it means that the previous number in the series is added to determine the next number in the series.

Here,

18--12=30/3=10

P=-12+10

=-2

Q=-2+10

=8

P=2 and Q=8 as in AP, the difference between the two terms is equal for all terms.

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Answer:

1/2a (4a+7)

Step-by-step explanation:

First You Divide:7/2a+ 2a^2

Rearrange Terms: 2a^2+ 7/2a

Find the Common Factor: 1/2(4a^2+7a)

Rewrite in the Fraction Form: 1/2a (4a+7)

I know this is the right answer because I learned this in 5th grade.

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The value of the x is 60 km and the value of the y is 70 km.

Given that a man travels x km at 60 km/h and y km at 40 km/h and the total time traveled is 11/4 i.e 2.75 h.

Let's suppose that the time traveled for the x km is t1, time traveled for the y km is t2 and total time is T ,so by using the speed distance formula t1 & t2 will be :

t1 = x/60 and t2 = y/40 ;

T = t1 + t2;

i.e 2.75 = x/60 + y/40 ;

Multiply both sides with 120,

330 = 2x + 3y ............i

Now given that man traveled 5x km at 40 km/h and 3y km at 50 km/h in total time of 11. 7 hours. Similarly the equation for this situation will be :

T = t1 + t2;

x/8 + 3y/50 = 11.7 ;

Multiply both sides with 200, we will get

25x + 12y = 2340 .........ii

Now by simplifying the equation i and ii we will get the value of x and y which are 60 and 70 respectively.

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Answer:

36,288

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solutionx% of 199 is 761 is  382.41206…% Answer 

Convert x% into a decimal and multiply by 199

In order to convert a percent to a ratio, divide it by 100:     

a%=a100 

a=x

x% =x100 

Convert to decimal form=0.01x

Multiply 0.01x by 199

=0.01x· 199=1.99x

Solve 1.99x=761  

1.99x=761  

x=761/1.99

x=382.41206%

If Jolyn scores 48 points, and the z-score of this value is 3, then her mean points in this normally distributed game is equal to 27.

In a normal distribution, the relative score or z-score can be calculated by using this formula:

[tex]z=\frac{x\;-\;u}{\sigma}[/tex]

Where:

Making mean (μ) the subject of formula, we have:

μ = x - zσ  x

Substituting the given parameters into the formula, we have;

Mean point, μ = 48 - (3 × 7)

Mean point, μ = 48 - 21

Mean point, μ = 27.

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Based on the mathematical statements, Zoe is 56 years old and Luke is 66 years old, now

From the question, we have the following statements that can be used in our computation:

30 years ago

Zoe was 2/3 as old as Luke

18 years ago

Zoe was 5/6 as old as Luke

Let their present ages be represented as

Zoe = x

Luke = y

So, we have the following representations

30 years ago

Zoe was 2/3 as old as Luke

x - 36 = 2/3(y - 36)

18 years ago

Zoe was 5/6 as old as Luke

x - 18 = 5/6(y - 18)

So, we have the following system of equations

x - 36 = 2/3(y - 36)

x - 18 = 5/6(y - 18)

Make x the subject in x - 18 = 5/6(y - 18)

x = 5/6(y - 18) + 16

Substitute x = 5/6(y - 18) + 16 in x - 36 = 2/3(y - 36)

5/6(y - 18) + 16 - 36 = 2/3(y - 36)

Open the brackets

5/6y - 15 + 16 - 36 = 2/3y - 24

Evaluate the like terms

5/6y - 35 = 2/3y - 24

Multiply through by 6

5y - 210 = 4y - 144

Evaluate the like terms

y = 66

Substitute y = 66 in x = 5/6(y - 18) + 16

x = 5/6(66 - 18) + 16

Evaluate

x = 56

Recall that

Zoe = x

Luke = y

So, we have

Zoe = x = 56

Luke = y = 66

Hence, they are 56 and 66 years, now

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The required expression is 3h(150) + h(270) which is the correct answer would be an option (D).

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

Since each house will have 3 smaller bedrooms that required 150 square feet of carpet

⇒ 3 × 150

Each house will have 1 larger bedroom that requires 270 square feet of carpet.

⇒ 270

So, (3 × 150 + 270) × h

⇒ 3h(150) + h(270)

Thus, The required expression is 3h(150) + h(270).

Hence, the correct answer would be an option (D).

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The question seems to be incomplete the completed part has been attached below

The average hourly pay of person making 4500 per year is 21.63 per hour.

Given that,

we have to find what does a person making $45,000 a year make per hour on average, Assume a 52-week year and a 40-hour workweek.

To calculate this

The ratio of the sum of the values in a given set to all the values in the set is the mean value, which is the definition of the average.

We have to multiply 52-week year and a 40-hour work week.

40×52

2080

Now, divide 45000 by 2080

45000/2080

21.63

Therefore, The average hourly pay of person making 4500 per year is 21.63 per hour.

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Answer:

y = -338

Step-by-step explanation:

[tex]-26 = \dfrac{y}{13}[/tex]

Multiply by 13 on both sides.

[tex]-26 \cdot 13 = y[/tex]

[tex]-338 = y[/tex]

y = -338

Answer:

-338

Step-by-step explanation:

-26=y/13

cross multiplying

y=-26×13

y=-338

The operating income of Division B will increase by $640,000

Given that: Division B incurs variable costs of $10 per unit and  a transfer price of $18 per unit is established between the two divisions and 80,000 units of materials are transferred to Division A

This cost of production by division B is:

cost = $10 × 80,000 = $800,000

Division B uses a transfer price of $18 per unit. That is:

Selling price = $18  × 80,000 = $1,440,000

Operating income increase = Selling price - cost

Operating income increase = $1,440,000 - $800,000 = $640,000

Therefore, Division B's operating income increase will be $640,000

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By the concept of polynomial, first second and third option are correct.\

What is polynomial?

At first it is important to know about algebraic expression

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

An algebraic expression of the form [tex]a_0+a_1x+a_2x^2 + ....+a_nx^n[/tex] is called a polynomial of degree n

For the First Option

5 - 2a is in the form of [tex]b_0 + a_1a[/tex]

So the first option is a polynomial

For the second option

[tex]4 - 8^2 -16\\4 -64 -16\\-76[/tex]

which is a constant

And all constants are polynomial

So the second option is a polynomial

For the third option

[tex]5x^3 +4x^13x +1\\5x^3 + 12x^2 +1[/tex]

which is of the form [tex]a_0+a_1x + a_2x^2 + a_3x^3, a_1 = 0[/tex]

So the third option is a polynomial

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Answer:

1.2

Step-by-step explanation:

3/2 ÷ 1 1/4

Answer:

1.2

Step-by-step explanation:

Just did it on khan academy.

120 ounces of 35% salt and 90 ounces of water is needed to obtain 210 ounces of a mixture that is 20% salt.

An equation shows the relationship between two or more numbers and variables.

Let x represent the amount of water and y represent the amount of 35% solution.

She wants to obtain 210 ounces of a mixture that is 20% salt. Hence:

x + y = 210   (1)

Also:

0% of x + 35% of y = 20% of 210

0.35y = 42

y = 120

x + y = 210

x + 120 = 210

x = 90

120 ounces of 35% salt and 90 ounces of water

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Required values are to be put in blank space,

a. 99

b. 10

c. 5

after using logarithmic properties.

The other technique to write exponents in mathematics is using logarithms. A numbers  base based logarithms is equal to other number. A logarithm performs exponentiation's exact opposite function

For example:

If 10² = 100 then log₁₀¹⁰⁰ = 2.

Some logarithmic properties used are:

All of the questions are based on simple logarithmic properties:

a. In this properties used are,

   logₐˣ + logₐⁿ = logₐˣⁿ

   log₅⁹ + log₅¹¹ = ?

   comparing with general form, we get

   log₅⁹ + log₅¹¹ = log₅⁹⁹

b. In this properties used are,

   logₐˣ - logₐⁿ = logₐ[tex]^{x/n}[/tex]

   ? - log₉⁷ = log₉[tex]^{10/7}[/tex]

   comparing with general form, we get

   log₉¹⁰ - log₉⁷ = log₉[tex]^{10/7}[/tex]

c. In this properties used are,

   logₐ⁽ˣ⁾ⁿ = n logₐˣ

   log₂[tex]^{1/25}[/tex] = log₂⁽[tex]^{1/5}[/tex]⁾² = -2 log₂⁽⁵⁾

   Comparing with general form, we get

   log₂[tex]^{1/25}[/tex] = -2log₂⁵

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Answer:

D, 2/3

Step-by-step explanation:

Using the Slope formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] we can find the slope of the line.

Input values:

[tex]m=\frac{6-4}{5-2}=\frac{2}{3}[/tex]

[tex]m=\frac{2}{3}[/tex]

Basically,  Least Common Multiple(LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers. GCF/HCF ( Greatest/Highest Common Factor) is the highest number that divides exactly into two or more numbers.

Answers:

9) LCM of 36, 3, 12 = 36

   GCF of 36, 3, 12 = 3

10) LCM of 6, 54, 12 = 108

     GCF of 6, 54, 12 = 6

11) LCM of 16, 8, 12 = 48

   GCF of 16, 8, 12 = 4

Answer:

[tex]\frac{4}{7}[/tex]

Step-by-step explanation:

Slope = m

m = [tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}}[/tex]

m = [tex]\frac{7-3}{9-2}[/tex] = [tex]\frac{4}{7}[/tex]

The mean value is 7.6. Option (D) is the correct answer.

The number of successes in a sample of size n drawn with replacement from a population of size N is frequently modeled using the binomial distribution.

The mean value of a binomial distribution is,

[tex]\mu =np\\=38*0.2\\=7.6[/tex]

Multiplication:

In mathematics, multiplying two or more numbers yields the product of the numbers. It is one of the basic mathematical operations that we carry out on a regular basis. The most obvious application is using multiplication tables. The multiplication of two numbers in mathematics represents the repeated addition of one number in respect to another. These numbers can be natural numbers, whole numbers, fractions, integers, or other types of numbers. When m is multiplied by n, m is either multiplied by n times or added to itself n times.

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Answer:

162.4$

Step-by-step explanation:

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A Linear equation in standard form is

2x + y = -4

slope of the function = -2

the perpendicular line equation in standard form -x + 2y = -6

A standard equation is of the form Ax + By = C

A = 2

B = 1

C = -4

Rearranging the equation to the slope intercept form of the form as

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

Ax + By = C

By = -Ax + C

y = -Ax/B + C

calculation of slope

m = -A/B

substituting the values of A and B

m = - 2/1

m = -2

a new perpendicular slope, m' is given by

m' = -1/m

plug in the value of m

m' = -(1/-2)

m' = 1/2

new equation passing through point (8, 1)

(y - y₁) = m'  (x - x₁)

y - 1 = 1/2(x -8)

y - 1 = x/2 - 4

y = x/2 - 3

writing in standard form

y = x/2 - 3

2y = x - 6

-x + 2y = -6

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The simplified value of (2x - 4)² is 4x² - 16x + 16.

First, let us understand the algebraic identities;

Algebraic identities are equations in which the left hand side of the equation is identically equal to the right hand side of the equation.

Some of the identities are:

We are given (2x - 4)².

Use the identity (a - b)² = a² - 2ab + b² to expand to the given expression.

So, a = 2x and b = 4.

Put it into the identity, we will get;

Therefore,

(2x - 4)² = (2x)² - 2 * 2x * 4 + (4)² = 4x² - 16x + 16

Thus, the simplified value of (2x - 4)² is 4x² - 16x + 16.

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