Colton works at an electronics store as a salesperson. Colton earns a 7% commission on the total dollar amount of all phone sales he makes, and earns a 3% commission on all computer sales. Colton had twice as much in phone sales as he had in computer sales and earned a total of $85 in commission. Write a system of equations that could be used to determine the dollar amount of phone sales Colton made and the dollar amount of computer sales he made. Define the variables that you use to write the system.

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Explanation:

"bisect" means to "divide in half"

So segment WY is split into two smaller equal pieces.

Segments WX and XY are the same length

WX = XY

6k+8 = 11k-12

6k-11k = -12-8

-5k = -20

k = -20/(-5)

k = 4

We get the speed of the object as 5365 miles / day after rounding off.

We are given that an object is moving at a speed of 360 kilometers per hour.

We know that:

1 km = 0.621 miles.

So, 360 km will be:

360 km = 223.56 miles.

Also, we know that:

we have 24 hours in 1 day.

1 day = 24 hours.

1 hour = 1 / 24 day.

Re-writing the speed of the object, we get that:

223.56 miles in 1 / 24 day

That is:

5365.44 miles / day.

Rounding off:

= 5365 miles / day.

Therefore, we get the speed of the object as 5365 miles / day after rounding off.

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Answer:

$235

Step-by-step explanation:

‎‎‎‎‎‎‎‎‎‎.....................

You require the score of 78 to do equally well in exam 2.

To compare both the scores, we need to compute the z scores of both exams and then compare the values. The formula for z-score is:

Z = (X - μ)/σ

Where X = score obtained

           μ = mean score

          σ = standard deviation

For Exam 1:

Z = (91 - 79)/8

  = 12/8

Z = 3/2

To perform similarly well on the second exam, let x equal z 3/2.

For Exam 2:

Z = (x - 60)/12

3/2 = (x - 60)/12

By cross multiplying we get

2(x - 60) = 12 * 3

x - 60 = 36 /2

x - 60 = 18

x = 18 + 60

x = 78

Therefore, Consequently, you must achieve a score of 78 to perform equally well in Exam 2.

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The amount Logan should charge for each cupcake is $1.60 based on the markup of 35%

What is equivalent inputs for 60 cupcakes?

The equivalent inputs for 60 cupcakes, means the number of cupcakes that the materials used would have yielded in cupcakes if there was no wastage, hence, the cost per unit needs to be expressed to include 20% wastage

equivalent cost per unit=$0.95/(1-20%)=$1.1875

The 35% markup needs to be added to the equivalent cost per unit since markup is the profit as a percentage of cost

selling price=$1.1875*(1+35%)

selling price=$1.60

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Answer:

equation : 3x + 5y + 2 = 0

Step-by-step explanation:

y - y1 = m (x - x1)

y - (-1) = -3/5 ( x - 1 )

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

5y + 5 = -3x + 3

3x + 5y + 2 = 0

Answer:

Step-by-step explanation:

7(4x-5) - 4(6x+5) = -91

28x - 35 - 24x -20 = -91

28x - 24x = -91 + 35 + 20

4x = -36

x = -36 : 4

x = -9

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a) The total distance covered is 56 feet

b) The total displacement is 14 feet

c) The average speed  in the first, second, and third parts of the car’s motion are; 5 feet/sec,  0 feet/sec and  4.2 feet/sec

d) The average speed of the car is 3.5 feet/sec

e) The average velocity of the car is 0.875 feet/sec

We must understand that the distance is the difference between two points but the displacement is the distance between two points in a definite direction. This implies that the distance is a scalar quantity while the distance is a vector quantity. Being a vector quantity means that when we are computing the displacement that we must take into account the direction of the motion and this also applies to the calculation of the velocity of the car.

Let us now carry pout the calculations;

a) Total distance = 35 feet +  21 feet = 56 feet

b) Total displacement =  35 feet -   21 feet = 14 feet

c) Average speed of the first, second, and third parts of the car’s motion;

i)  35 feet / 7 seconds = 5 feet/sec

ii) 0 feet/sec ( it sat still)

iii) 21 feet/5 seconds = 4.2 feet/sec

d) The cars average speed = 56 feet/16 seconds = 3.5 feet/sec

e) Average velocity = 14 feet/ 16 seconds = 0.875 feet/sec

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Answer: Tablet costs $225

Laptop costs $135

Step-by-step explanation:

Laptop is = x

Tablet = T

x + 3t = 810

x + t = 360

x = 360 - t

360 - t + 3t =810

2t = 450

t = 225

x + 225 = 360

x = 135

The range measures the difference between the minimum value and the maximum value in a dataset. The interquartile range measures the difference between the first quartile (25th percentile) and third quartile (75th percentile) in a dataset. This represents the spread of the middle 50% of values

Answer:

y = 4x + 7

or y - 4x = 7

Step-by-step explanation:

x + 4y = 2

4y = -x + 2

y = -1/4x + 2

The slopes of two perpendicular lines are negative reciprocals of each other. So the slope of the perpendicular line should be negative reciprocal of -1/4, then it is 4

Given m = 4, y = 3, x = -1

y = mx + b

3 = 4(-1) + b

3 = -4 + b

b = 7

y = 4x + 7

Answer:

x = 5.94

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

We note that 2, 4 is the least common multiple of 6,8 and 12

We have to find the smallest 3 -digit multiple of 24.

Also 24 × 4 = 96 and 24 ×5 = 120.

The smallest 3-digit number which is exactly divisible by 6,8 and 12 is 120.

Answer:

120

Step-by-step explanation:

Answer: m=2

Step-by-step explanation:

Highlighted points: (0, 4) and (-4, -4)

m=(y2-y1)/(x2-x1)

m=(-4-4))/(-4-0)

m=(-8)/(-4)

m=2

Answer:

Step-by-step explanation:

E - 4,-2

F - 6, -3

G - 1, -4

The speed of plane in still air is 715 MPH and the speed of the wind is 65 MPH

Distance travelled by airplane = 3900 miles

Time taken by the plane to travel the distance with the wind = 5 hours

Time taken by the plane to travel the distance against the wind = 6 hours

Let the speed of the plane in still air be x

Let the speed of the wind be y

Finding the speed of the air and airplane when distance is covered with the wind using the formula:

Speed of airplane + Speed of wind = Distance/Time

x + y= 3900/5

x + y = 780------(1)

Finding the speed of the air and airplane when distance is covered against the wind using the formula:

Speed of airplane - Speed of wind = Distance/Time

x - y = 3900/6

x - y = 650------(2)

Equating (1) and (2) we get:

2x = 1430

x = 715

Putting x = 715 in (1) we get:

y = 65

So, Speed of airplane in still air is 715 MPH and Speed of wind is 65 MPH  

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Answer: 31 sides

Step-by-step explanation: 4 sides per quadrilateral so 16 sides and 5 sides per pentagon so 15 sides. 16 + 15 = 31.

Answer: l=32/3 meters

w=16/3 meters

Step-by-step explanation:

P=perimeter, l=length, w=width

P=2l+2w

32=2(2w)+2w

32=4w+2w

6w=32

w=32/6

w=16/3 meters

32=2l+2(16/3)

32=2l+32/3

(32=2l+32/3)*3

96=6l+32

6l=64

l=64/6

l=32/3 meters

The organization’s employees are a part of the finance team, if the size of the finance team makes up two-fifths of the remainder is 13%

What is the number of employees who are regarded as remainder?

The number of employees out of the total workforce left after having deducted the number of employees making up the sales team, the customer support team the software development and HR departments is computed as shown below:

remainder of workforce=80,000-16,000-24,000-14,000

remainder of workforce=26,000

finance team=2/5*26000

finance team=10,400

finance team as % of total workforce=10,400/80,000

finance team as % of total workforce=13.00%

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The translation of the phrase The sum of -15y and 16y is −4 is

-15y + 16y = -4 and the value of y is -4.

An algebraic equation is written in the form of variables and constants and we combine these variables and constants with arithmetic operations.

In the given question there is a statement The sum of -15y and 16y is −4 and we have to express it in form of numerical and solve for y or find the value of y.

∴ The sum of -15y and 16y is −4 can be expressed numerically as,

-15y + 16y = -4.

y = -4.

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There are two ways to say 1900 in word form.

1900 = nineteen hundred

1900 = one thousand, nine hundred

Both are equally valid.

Answer: one thousand nine hundred

Step-by-step explanation:

Answer:

Step-by-step explanation:

If a GP has a positive common ratio and negative first term, it means all its terms are negative since formed by a product of positive and negative numbers.

We can only see one sequence with all negative terms and common ratio of 5, this is REID's.

For the given distributions, we have that:

a) The traditional course has a range of 29.8, while the flipped course has a range of 28.2. Thus the traditional course is more dispersed using the range.

b) The traditional course has a standard deviation of 8.67, while the flipped course has a standard deviation of 7.63. Thus the traditional course is also more dispersed using the standard deviation.

The range of a distribution is given by the difference between the greatest value and the smallest value.

Hence, for the Traditional classroom, the range is given by:

86.4 - 56.6 = 29.8.

For the Flipped classroom, the range is given by:

92.6 - 64.4 = 28.2.

Hence:

The traditional course has a range of 29.8, while the flipped course has a range of 28.2. Thus the traditional course is more dispersed using the range.

Using a calculator, following the described procedure, the standard deviations are given as follows:

Hence:

The traditional course has a standard deviation of 8.67, while the flipped course has a standard deviation of 7.63. Thus the traditional course is also more dispersed using the standard deviation.

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The answer for the given question is 59/90

A fraction is said to be in lowest terms when the greatest common factor (GCF) of the numerator and denominator is 1. Now that this is in mind, let's continue to solve.

Given, 5/9+1/10 and we have to convert or reduce it into the lowest terms.

So, let's proceed to solve this question

First add 5/9 and 1/10 i.e.,

= 5/9+1/10

Taken LCM of 9 and 10 which comes out to be 90.

Then, adding, we get

= 50+9/90

= 59/90

59/90 is already in its lowest form because the numerator and denominator have no common factor other than 1. So it's already at its most basic level.

Therefore, 59/90 is the required answer.

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Answer:

84 minutes

Step-by-step explanation:

360 per hour = 6 per min

140 per hour = 2 1/3 per min

Both together do 8 1/3 per min.

In 3 minutes, both machines together do 25 packages.

700/25 = 28.

In 3*28 minutes, which is 84 minutes, both machines together seal 700 packages.

Thanks!

When the subject is changed for x, the equation is x = 1 - 1/(1 - (1/(1 - y)^2)))

The equation is given as

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

The question implies that we change the subject and make x the subject

However, in the equation;

The subject of the equation is x

This means that when the subject is changed for x, the equation is x = 1 - 1/(1 - (1/(1 - y)^2)))

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Answer:

128 feet

Step-by-step explanation:

8*16 is 128 feet

Answer: 14 1/7

Step-by-step explanation: