1. Arturo earns n dollars per hour. Next month
he will receive a 2% raise in pay per hour. The
expression n +0.02n is one way to represent
Arturo's pay per hour after the raise. Write
an equivalent simplified expression that will
represent his pay per hour after the raise.

a. Two out of every 3 seniors at Lewis High apply for college, so the number of seniors who apply for college is 2/3 (or approximately 0.67) times the total number of seniors at Lewis High.

b. The number of seniors who apply for college is one-third (or approximately 0.33) less than the number of seniors who don't apply.

c. One-third (or approximately 0.33) of the graduating seniors at Lewis High do not apply to college.

d. Three out of every 5 seniors who apply for college are female students, so two out of every 5 seniors who apply for college are male students. Therefore, the fraction of seniors who are males who apply for college is 2/5 (or approximately 0.4).

The number of males who apply for college is 2/3 of the total number of seniors who apply for college, which is (2/3) * (2/5) = 4/15 (or approximately 0.27) times the total number of graduating seniors at Lewis High.

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Answer:

114

Step-by-step explanation:

5 : 6

5 + 6 =11

5/6 x y = 95

y = 95 / 5/6

= 95 x 6/5

= 114

Therefore total number of employees is 114 :)

Answer:

[tex]\textsf{a)} \quad \overrightarrow{CA} =2\textbf{a}[/tex]

[tex]\textsf{b)} \quad \overrightarrow{AB} =\textbf{b}-\textbf{a}[/tex]

[tex]\textsf{c)} \quad \overrightarrow{BC} =-\textbf{a}-\textbf{b}[/tex]

Step-by-step explanation:

A parallelogram is a quadrilateral where opposite sides are equal in length and parallel to each other.  

The diagonals of a parallelogram are not equal in length, but they bisect each other (divide into two equal parts).

Therefore, if OA = a then CO = a.

Similarly, if OB = b then DO = b.

Part (a)

Express the vector CA in terms of a:

[tex]\begin{aligned}\overrightarrow{CA} &= \overrightarrow{CO} + \overrightarrow{OA}\\&=\textbf{a}+\textbf{a}\\&=2\textbf{a}\end{aligned}[/tex]

Part (b)

Express the vector AB in terms of a and b:

[tex]\begin{aligned}\overrightarrow{AB} &= \overrightarrow{AO} + \overrightarrow{OB}\\&= -\overrightarrow{OA} + \overrightarrow{OB}\\&= \overrightarrow{OB}-\overrightarrow{OA}\\&=\textbf{b}-\textbf{a}\end{aligned}[/tex]

Part (c)

Express the vector BC in terms of a and b:

[tex]\begin{aligned}\overrightarrow{BC} &= \overrightarrow{BO} + \overrightarrow{OC}\\&= -\overrightarrow{OB} - \overrightarrow{CO}\\&= -\overrightarrow{CO}-\overrightarrow{OB}\\&=-\textbf{a}-\textbf{b}\end{aligned}[/tex]

Variance analysis is the quantitative investigation of the difference between actual and planned behavior. This analysis is used to maintain control over a business through the investigation of areas in which performance was unexpectedly poor.

Variance analysis is the study of deviations of actual behaviour versus forecasted or planned behaviour in budgeting or management accounting. This is essentially concerned with how the difference of actual and planned behaviors indicates how business performance is being impacted.

Comparing Budget with Actual: Variance analysis helps in managing the annual budgets by monitoring the budgeted figures and comparing it with the actual revenue/cost. In case of companies which are project or program driven, the financial data are evaluated at key intervals such as month close, quarter end, etc.

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Answer:

Let the weight of Train A be x tons. Then the weight of Train B is 537 - x tons. We know that the difference between their weights is 421 tons, so we can set up an equation to solve for x:

x - (537 - x) = 421

Expanding the right side:

x - 537 + x = 421

Combining like terms:

2x = 958

Dividing both sides by 2:

x = 479

So Train A weighs 479 tons and Train B weighs 537 - 479 = 58 tons.

Step-by-step explanation:

Answer:

The amount of time Jill trained this month is 125% of the amount of time she trained last month, which was 80 hours. To find the number of hours she trained this month, we can multiply 80 hours by 125%:

80 hours * 125% = 80 hours * 1.25 = 100 hours

So Jill trained for 100 hours this month.

Answer:

100hours

100 hours / 80 hours * 100% = 125%

Step-by-step explanation:

The amount of time Jill trained this month is 125% of the amount of time she trained last month, which was 80 hours. So, she trained for 125% of 80 hours = 100 hours.

To find this answer as a percentage, we can calculate what percentage of 80 hours 100 hours is:

100 hours / 80 hours * 100% = 125%

So Jill trained for 125% of the amount of time she trained last month.

Answer:

Step-by-step explanation:

His salary after 7 years would be $57000 per year

Answer:

Step-by-step explanation:

the answer for this question would be $57,000.

The correct statement regarding the solution to the system of equations is given as follows:

b. (1,2) is a solution to both the lines A and B.

We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.

This point of intersection is a solution to both of the equations, hence it is the solution to the system of equations.

The coordinates of the point of intersection in this problem are given as follows:

(1,2).

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Answer: 16*(1/8)

Step-by-step explanation:

Answer:

46.4

Step-by-step explanation:

lets use a multiplier instead

100-39=61

so 76 x 0.61 = 61% of 76

76 x 0.61 = 46.36

rounded to the nearest tenth would be rounded up

46.4

The required speed of the object increase only one time.

We can see how far an object has moved over time by looking at a distance-time graph. The motion is faster when the graph is steeper. A horizontal line indicates that an object is at rest and not altering position. A downward sloping line indicates that the thing is going back to the beginning.

As we can see that upwards and downwards in the graph, which says about the increase and decrease in speed of the object.

First speed of object increase, then constant for some time.After that it decreases and then constant, at last it was decrease.

So, the speed of car is increase only one time.

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The measurement units along with  the measured quantities are given as -

Measurement units are used to measure the total amount of any specific quantity.

Given are the units to measure the various quantities as given.

{a} -

Height of building is measured in meters.

The height of a building : meters

{b} -

Small quantities of mass is measured in grams.

The mass of a pen : grams

{c} -

The capacity of a paddling pool : liters

Therefore, the measurement units along with  the measured quantities are given as -

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In the given diagram, the measure of angle B, m ∠B, is 22°

From the question, we ae to calculate the measure of angle B

From the law of cosines, we can write that

cos B = (a² + c² - b²)/2ac

From the given diagram,

a = 6

b = 5

c = 10

Thus,

cos B = (6² + 10² - 5²)/2(6)(10)

cos B = (36 + 100 - 25)/120

cos B = 111/120

B = cos⁻¹(111/120)

B = 22.3316°

B ≈ 22°

Hence, m ∠B = 22°

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Answer: 1440x or 1440

Step-by-step explanation:

Answer:

a=x-89|4|-3<69

Step-by-step explanation:

Answer:All the oceans in the world

Only the ocean in which the Great Barrier Reef is found

Coral in all the oceans of the world

Only coral found in the Great Barrier Reef

Step-by-step explanation:

Answer: all oceans

Step-by-step explanation:

on solving the provided question we can say that  the selling price of the fiction novel series is $61.56.

Cost: The cost price is the amount paid for an item at the time of purchase or the cost for producing it. Costs are identified by the notation C.P. Selling price: The selling price is the price at which a thing is sold. The amount that the seller really receives when the sale is complete is known as the selling price. The price a seller pays for a good or service is really called the cost. A profit percentage is then added.

markup rate is 62%,

t the seller is adding 62% of the cost to the price to make a profit.

Markup = 62% of Cost = [tex]0.62 * $38 = $23.56[/tex]

Selling price = [tex]Cost + Markup = $38 + $23.56 = $61.56[/tex]

the selling price of the fiction novel series is $61.56.

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The value of the greatest integer such that the smaller integer  subtracted from 6 times the greater integer, difference is 41 is 8.

An equation is a mathematical statement containing two expressions on either sides which are connected with an equal to sign.

Either sides of an equation is called as left hand side and right hand side.

Given that,

When an integer is subtracted from 6 times the next consecutive integer, the difference is 41.

Let the integer be x.

Then the next consecutive integer will be x + 1

6 times the next consecutive integer means 6 (x + 1).

an integer is subtracted from this means 6 (x + 1) - x.

The difference of this is 41.

6 (x + 1) - x = 41

By distributive property,

6x + 6 - x = 41

5x + 6 = 41

5x = 41 - 6

5x = 35

x = 7

Hence the value of the integer is 7 and the value of next consecutive integer is 8.

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The date that is 75 days from now, if today is February 22, 2023, is May 8, 2023.

To find the date that is 75 days from now, we can start with the current date and add 75 days to it. This can be done by adding the number of days to the day of the month, and if necessary, advancing to the next month or year.

For example, if today is February 22, 2023, we can count forward 75 days on a calendar to find the date that is 75 days from now. This would take us to May 8, 2023.

Here is the mathematical calculation:

Current date + 75 days = (February 22, 2023) + 75 days

= February 22, 2023 + 75 days

= (February 22, 2023 + 31 days) + (44 days)

= March 25, 2023 + 44 days

= (March 25, 2023 + 30 days) + (14 days)

= April 24, 2023 + 14 days

= (April 24, 2023 + 14 days)

= May 8, 2023

Therefore, the date that is 75 days from now, if today is February 22, 2023, is May 8, 2023.

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Applying one of the properties of a parallelogram, the value of x is 10°, then 6x=60° and 12x=120°.

There are different quadrilaterals, for example square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, a parallelogram presents some properties that are presented below.

The figure of the exercise shows two adjacent angles. From the property: the adjacent angles are supplementary, you have:

6x+12x=180

18x=180

x=10°

Therefore, 6x= 6*10=60° and 12x=12*10=120°.

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The amount of the worker monthly tax will equals to K4,850.

An income tax refers to the tax imposed on individuals or entities in respect of the income earned by them. It is computed as the product of a tax rate times the taxable income. They may vary by type or characteristics of the taxpayer and the type of income

To calculate the worker's monthly tax, we need to determine the amount of salary that falls into each tax bracket and then calculate the tax owed for each bracket:

The worker's monthly tax is then computed as:

=  K1,500 + K3,000 + K350

= K4,850.

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The length of the right triangle x is 2√5 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the sides of the right triangle can be found using Pythagoras's theorem,

Hence,

c² = a² + b²

where

Therefore,

x² = 6² - 4²

x² = 36 - 16

x² = 20

square root both sides

x = √20

x = 2√5

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The measure of each interior angle is 120 degrees.

In conclusion, the measure of each interior angle of a regular polygon with central angles measuring 60 degrees is 120 degrees.

The measure of each interior angle of a regular polygon with central angles measuring 60 degrees can be found using the formula (n-2)180/n, where n is the number of sides of the polygon.

First, we need to find the number of sides of the polygon. Since the measure of each central angle is 60 degrees, we can use the formula 360/n = 60 to find the number of sides.

Solving for n, we get: 360/n = 60 360 = 60n n = 360/60 n = 6 So the polygon has 6 sides.

Now we can use the formula (n-2)180/n to find the measure of each interior angle:

(6-2)180/6 = (4)180/6 = 720/6 = 120 degrees

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Answer: [tex]8x^{3}-22x^{2} +19x-6[/tex]

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

Answer:

Step-by-step explanation:

= 1/4 + 2/5

= 5/20 + 8/20

= 13/20

Answer:

Step-by-step explanation:

The formula for the volume of a cone is given by:

V = (1/3)πr^2h

where V is the volume of the cone, r is the radius of the base, h is the height of the cone, and π is the mathematical constant pi (approximately equal to 3.14159).

Substituting the given values, we get:

471 = (1/3) x 13.4 x 5^2 x h

Multiplying both sides by 3 and dividing by 13.4 x 25, we get:

h = 471 x 3 / (13.4 x 25)

h ≈ 6.98 yards (rounded to two decimal places)

Therefore, the height of the cone is approximately 6.98 yards.

To find the angle of elevation, we need to determine the height of the plane relative to the trees, and then use the tangent function to find the angle. Let's call the height of the plane "h".

We can set up a right triangle with the height of the plane, the distance from the runway to the trees, and the height of the trees.

We have:

h / (150 + 75) = 100 / h

Solving for h, we find that:

h = 125

So the height of the plane relative to the trees is 125 feet.

Now we can use the tangent function to find the angle:

tan(angle) = 100 / 125

angle = tan^-1(100 / 125)

angle = approximately 53.13 degrees

Rounding to the nearest hundredths, the angle of elevation that the pilot must take to avoid crashing into the trees is 53.13 degrees.

After considering all the combinations of three pieces of wood, we can conclude that Ennis can make 2 different triangular borders for his vegetable garden.

A triangle is a shape with three sides, and each side can be considered as a side length. In order to form a triangle, the sum of the lengths of the two shorter sides must be greater than the length of the longest side.

To find the number of different triangular borders that Ennis can make, we need to consider all the combinations of three pieces of wood as the sides of the triangle. There are four pieces of wood, so the number of combinations of three pieces is 4 choose 3, which is 4.

Now, we need to determine if each combination of three pieces of wood forms a triangle. If the sum of the lengths of the two shorter sides is greater than the length of the longest side, it forms a triangle. If not, it does not form a triangle.

If Ennis uses the 8-inch and 10-inch pieces as two sides, he can use the 12-inch or 18-inch piece as the third side, and it forms a triangle.

If he uses the 8-inch and 12-inch pieces as two sides, he can only use the 10-inch piece as the third side, and it forms a triangle. If he uses the 8-inch and 18-inch pieces as two sides, it does not form a triangle.

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