Find the value if n in improper fraction.

The preferred gig is the first one since its today's worth is greater than the today's value of the second gig

What is the today's worth of $5000 each year?

The worth of the second gig, which pays $5000 every year for the next 6 years in today's dollar is the present value of all the six annual cash flows discounted using the present value formula of an ordinary annuity as shown below:

PV=PMT*(1-(1+r)^-N/r

PV=present value of annual payments for 6 years=unknown

PMT=annual payment=$5000

r=required return=discount rate=8%

N=number of annual cash flows=6

PV=$5000*(1-(1+8%)^-6/8%

PV=$5000*(1-(1.08)^-6/0.08

PV=$5000*(1-0.630169626883105)/0.08

PV=$5000*0.369830373116895

/0.08

PV=$23,114.40

The fact that the present value of the second option which pays $5000 annually is lesser than the amount receivable immediately, which is $25,000, hence, the first gig is preferred

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In linear equation, - 23,040 is  the value of the expression.

What is linear equation in math?

x = 4, y = 8, a=3, b= 5

= [tex]4x^{1/2} - ax^{-1} ( yx^{1/3} + \sqrt{x} + b )x^{3}[/tex]

value of x = 4, y = 8, a=3, b= 5

=  [tex]4 * 4^{1/2} - 3 * 4x^{-1} ( 8^{1/3} + \sqrt{4} + 5) 4^{3}[/tex]

= 4 * 2 - 3 * 4 * 4 ( 2 + 2 + 5 ) * 64

= 8 - 48 ( 9 ) * 64

= - 40 * 9 * 64

= - 360 * 64

= - 23,040

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C(x) = 0.25x + 45 , Slope is .25 dollars per mile and the y intercept is 45 dollars.

Given,

The cost C(ar), where a is the number of miles driven, of renting a car for a day is $45 + $0.25 per mile.

To find the slope , y - intercept and C(a)

Now, According to the question:

A renting a car for a day is $45 plus  $0.25 per mile.

C(x) = 0.25x + 45

This is in the form y = mx + b where m is the slope and b is the y intercept

The slope is .25 dollars per mile and the y intercept is 45 dollars

Hence, C(x) = 0.25x + 45 , Slope is .25 dollars per mile and the y intercept is 45 dollars.

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Answer:

y = 24x + 80

Where x is the number of weeks of saving and y is the dollar amount in her savings

Explanation:

We need to find the equation of the line. If x is the number of weeks of saving and y is the amount in her savings, the equation has the following form

y = mx + b

Where m is the slope and b is the y-intercept.

The slope can be calculated using two points in the line (x1, y1) and (x2, y2) as follows

Then, replacing (x1, y1) = (0, 80) and (x2, y2) = (5, 200), we get:

Additionally, the y-intercept is the point where the graph crosses the y-axis. In this case, the point is (0, 80), so the value of b is 80.

Therefore, the equation of the line is

y = 24x + 80

Where x is the number of weeks of saving and y is the dollar amount in her savings

An equation that models the number of people employed in some country as medical assistant in the last year x is y = 359 + 14.35x

In this question, we have been given the number of people employed in some country as medical assistant.

We need to write an equation that models the number of people employed in some country as medical assistant in the last year x.

the number of people employed in some country as medical assistant:

in 2004 = 359 thousand

and by 2014 this number is expected to be  560 thousand.

We find the rate of employment.

Consider (x1, y1) = (0, 359) and (x2, y2) = (14, 560)

m = (560 - 359)/(14 - 0)

m = 201/14

m = 14.35

We have been given the line must pass through points (0, 359) and (14, 560)

And, we get the y-intercept c = 359

with slope m = 14.35 and y-intercept c = 359, the equation of the line would be,

y = 14.35x + 359

Therefore, an equation that models the number of people employed in some country as medical assistant in the last year x is y = 359 + 14.35x

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If the endpoint of one diameter of a circle is as follows

Then the centre of the circle can be calculated using the midpoint formula which can be represented below

Therefore, the answer is b. Find the midp

we have the function

In this problem, we have an exponential decay function because the value of the base of the exponential function is less than 1

b=0.75

Part b

Find out the annual percent decrease

b=0.75

b=1-r

0.75=1-r

r=1-0.75

r=0.25

r=25%

therefore

Part c

For y=$50

substitute in the given equation

Solve for t

Apply log on both sides

Given the inequality:

to find which point is a solution to the inequality, there are 2 methods to solve :

by graphing or by substitution by the point in the given inequality

Solving by substitution :

1) point (2 , 2)

so,

So, this point is not a solution

2) Point (-3 , -4)

This point is a solution

3) Point (0 , 2)

So, this point is not a solution

Another sol

The coefficient of z² is 25 and the constant term is 28. The product of 25 and 28 is 700. The factors of 700 which sum to -55 are -20 and -35, so:

The coordinates of the extreme value or the vertex of the parabola is the (h, -c) of the equation form y = (x - h)² - c.

Answer:

6c+11≤67

Step-by-step explanation:

To write this as an inequality, since it says 6 times a number, write:

6c

Now, since it is increased by 11, write:

6c+11

Finally, since it says at most 67, write

6c+11≤67.

Hope that helps!

We are given 42,099

To round off to the nearest thousand, we need to check the hundredth digit

Ten thousandth digit = 4

Thousandth digit = 2

Hundredth = 0

Tenth = 9

Unit = 9

If the hundredth digit is 0, 1, 2, 3 and 4, then you need to round off to the previous thousand

The answe is 42, 000

You have the following equation:

x - 3 = x²

In order to determine if the given equation is linear in x, you consider that a linerar equation is an equation in which the maximum exponet of the variable is 1. In this case you have that the higher exponent of the variable, which is x, is 2. 2 is the higher exponent, Becuase of that, the given equation is not linear, instead of that, the equation is quadratic.

The correct interpretation of the 95% confidence interval is that:

We are 95% sure that the true population mean widget width is between 11.5 and 27.3 units.

The x% confidence interval means that it is x% likely that the population parameter(mean/proportion/standard deviation) is between the bounds of the confidence interval, given by a and b.

The bounds of the confidence interval are given by the estimate of the population parameter plus/minus the margin of error found from the sample size/standard deviation.

In the context of this problem, the bounds of the interval are already given as follows:

11.5 < μ < 27.3

The parameter being estimated is the mean widget width, hence the interpretation is that we are are 95% sure that the true population mean widget width is between 11.5 and 27.3 units.

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Given:

KP = PL

GH = 36 ft

Let's find the measure of arc GM.

Apply the angle arc relationship to find the measure of angle KGL:

GKP + GLP + KGL + KGP = 360 degrees

90 + 90 + 26 + KPL = 360

206 + KPL = 360

Subtract 206 from both sides:

206 - 206 + KPL = 360 - 206

KPL = 154 degrees

To find the measure of arc GM, we have:

Therefore, the length of arc GM is 77 degrees

ANSWER:

77°

Given

(x^4 + 3x^3 y^2 + 4x^2y + 8xy + 12x)*( 11x^2y^3)​

Procedure

The answer is 11x^6y^3+33x^5y^5+44x^4y^4+132x^3y^3

$2352.33

Explanation

the account balance is give by the function

where x represents the time in years

hence, to find how much money Hercules will have after six years, jus replace the x value

so, when x=6

I hope this helps you

The value when 1875 is divided by 41 is 45.73.

What is division?

Division is the opposite of multiplication. If 3 groups of 4 make 12 in multiplication, 12 divided into 3 equal groups give 4 in each group in division.

Given,

1875 ÷ 41

= 45.73

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You know that:

- The total is $212.00 and the sales tax is included.

- The bill without tax was $200.00.

Let be "x" the tax on her groceries (in dollars).

You need to subtract the bill without tax from the total amount of money Sandra paid for the groceries, in order to find the tax in dollars:

To check it, you can multiply the total by 6%:

Hence, the answer is: $12.00 (This is 6% of the total bill)

The solution to the quadratic equation 3x² - 5x + 1 using quadratic formula is; x = (5 + √13)/6 or (5 - √13)/6

The general form of any quadratic equation is written as;

ax² + bx + c = 0

The quadratic formula that is used to solve this is given by;

x = [-b ± √(b² - 4ac)]/(2a)

Now, we are given the quadratic equation as;

3x² - 5x + 1

Thus, using quadratic formula we have;

x = [-(-5) ± √((-5)² - (4 * 3 * 1))]/(2 * 3)

x =  [5 ± √(25 - 12)]/6

x = (5 ± √13)/6

x = (5 + √13)/6 or (5 - √13)/6

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Given:

Admission to a baseball game is $4.00 for general admission and $5.50 for reserved seats.

Let the number of tickets of general admission = x

Let the number of tickets of reserved seats = y

The receipts were $5196.50 ⇒ 4x + 5.5y = 5196.50

The paid admissions 1181 ⇒ x + y = 1181

So, we have the following system of equations:

Substitute with x from (3) into (1) then solve to find y

Substitute with y into equation 3 to find x:

So, the answer will be:

The number of tickets of general admission = 866

The number of tickets of reserved seats = 315

Solution: (a)

Given the equation;

Multiply both sides of the equation by 2;

Divide both sides by the square of the velocity v;

ANSWER:

(b) Given;

We would substitute the value of the energy and the velocity into the formula for mass, we have;

Answer:

3.  72 questions

4.  180 students

5.  120 students

6.  9 puzzles

Step-by-step explanation:

[tex]\begin{aligned}\implies \rm 80\% \;of \; 90 \; questions & =80\% \times 90\\&= \dfrac{80}{100} \times 90\\& = \dfrac{7200}{100}\\& = 72\end{aligned}[/tex]

Therefore, a student must answer 72 questions correctly to pass the test.

[tex]\begin{aligned}\implies \rm 40\%\; of\; 450\; students & = 40\% \times 450\\& = \dfrac{40}{100} \times 450\\& = \dfrac{18000}{100}\\& = 180\end{aligned}[/tex]

Therefore, at least 180 students must plan to attend in order for the school to have the festival.

[tex]\begin{aligned}\implies \rm 40\% \; of \; 300 \; students & = 40\% \times 300\\& = \dfrac{40}{100} \times 300\\& = \dfrac{12000}{100}\\& = 120\end{aligned}[/tex]

Therefore, 120 students chose recycling.

If 55% of 20 puzzles are completed, then 45% of 20 puzzles are left to complete, since 100% - 55% = 45%.

[tex]\begin{aligned}\implies \rm 55\% \; of \; 20 \; puzzles & = 45\% \times 20\\& = \dfrac{45}{100} \times 20\\& = \dfrac{900}{100}\\& = 9\end{aligned}[/tex]

Therefore, Magdalena has 9 puzzles left to complete.

Answer:

The expression becomes;

Explanation:

Given the trigonometric expression;

Simplifying and rewriting the expression;

Recall that;

So, the expression becomes;

Also;

substituting to the above expression;

Therefore, the expression becomes;

The number of groups of 1/9 in 2 are 18.

The value of 2 ÷ (4/9) = 9/2.

We can see a number line with equal intervals of 1/9.

We have to find the number of groups of 1/9 in 2 and the value of 2 ÷ (4/9) .

As we can see in the number line,

2 is two intervals after 16/9 , hence,

2 = 16/9 + 1/9 + 1/9 = 16/9 + 2/9 = 18/9

We can write it as,

(1/9)*18

Hence, there are 18 groups of 1/9 in 2.

The value of  2 ÷ (4/9) = 2*(9/4) = 18/4 = 9/2.

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SOLUTION

We are asked true or false if

Now

So,

So the statement is true.

Note that since the powers or indices are odd numbers, it would be the same

The value of the base number, r is 75 and the corresponding algebraic expression is 0.2r = 15.

What is an algebraic expression and how is it formed?
Variables and constants are used to create algebraic expressions using a variety of techniques. It is a mathematical expression made up of terms and includes variables, constants, and algebraic operations like addition, subtraction, etc. When operations like addition, subtraction, multiplication, division, etc. are performed on any variable, the resulting equations are called algebraic expressions. An algebraic expression (or variable expression) is a grouping of terms that have undergone operations like addition, subtraction, multiplication, division, etc.

Given, the base number is = r
One fifth of the base number will be = (1/5)r = 0.2r
Also, one fifth of r is 15, thus 0.2r = 15 ⇒ r = 15/0.2 = 75
Thus, the value of the base number, r is 75 and the corresponding algebraic expression is 0.2r = 15.

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The algebraic expression "One fifth of r is 15" is represented as r/5 = 15. Solving for r, r = 75.

Let's break this down step-by-step:

1. "One fifth of r" means you are dividing r by 5, which in algebraic terms would be represented as r/5.

2. The phrase "is" in algebra typically signifies the equals sign (=).

3. Finally, "15" is just the number 15.

Putting these together, the algebraic expression for "One fifth of r is 15" is r/5 = 15.

To clarify this further, this equation is saying that if you take the value of r, divide it by 5, the result should be 15. This is an equation you can solve to find the value of r.

If you're curious, solving this equation for r would look like this:

Step 1: Start with the equation r/5 = 15.
Step 2: To isolate r, you need to get rid of the division by 5. You can do this by multiplying both sides of the equation by 5.
Step 3: This gives you r = 15 * 5.
Step 4: Calculate 15 * 5 to get 75. So r = 75.

So, if one fifth of r is 15, then r would be 75.

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This figure indicates that Juanita will run out of ribbon after tying 32 gift bags.

Considering the query;

The quantity of ribbon Juanita has left after tying ribbon on gift bags is represented by the function r = 24 -0.75g.

At r = 0, the function's zero is located.

Therefore;

0 = 24 -0.75g

g = 24/0.75

g = 32.

This figure indicates that Juanita will run out of ribbon after tying 32 gift bags.

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An equivalent equation to show how many kilometers Lamel skated around the rink is x - 5/2.

Linear equations in one variable

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

For example, 2x+3=8 is a linear equation having a single variable in it.

Given that Layla skated x kilometers around the rink, Lamel skated 5/2 less than Layla.

Therefore Lamen skated x - 5/2 kilometers, as Lamen skated 5/2 less than the kilometers skated by Layla

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Given:

Inner radius circle = 10yd

Outer radius circle = 14 yd

One gallon of coating can cover = 4

Find-: How many gallons of coating do we need?

Sol:

The area of a circle is:

The area of the outer circle is:

The area of the inner circle:

So the pool area is:

If one gallon of coating covers 4.

So 75 gallons use for coating.