A college student receives an interest-free loan of $9,400 from a relative. The student will repay $200 per month until the loan is paid off.
(a) Express the amount P (in dollars) remaining to be paid in terms of time t (in months). (Give your answer in slope-intercept form.)
(b) After how many months will the student owe $5000?

Answer:

35 trials

Step-by-step explanation:

Probability = Favorable Outcome / Total Outcome

 P = 1/5

Favorable Outcome = 7

Substitute the values,  

1/5 = 7 / Total Outcomes

1/5 =7/x

Cross multiplication:

1x=5*7

x=35

Total Trials = 35

Answer:

2x³ - 2

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

= x(2x² + 2x + 2) - 1(2x² + 2x + 2) ← distribute both parenthesis

= 2x³ + 2x² + 2x - 2x² - 2x - 2 ← collect like terms

= 2x³ - 2

Answer:

6

Step-by-step explanation:

4 divided by 2/3 is 6, because 4 x 2 = 8, and 8/3 is 6.

50 gallons of water leaked out of swimming pool.

Step-by-step explanation:

Total no. of gallons in swimming pool = 1000

Percentage of leaked water = 5%

Gallons of water leaked = 5% of total no. of gallons

[tex]Gallons\ of\ water\ leaked=\frac{5}{100}*1000\\\\Gallons\ of\ water\ leaked=\frac{5000}{100}\\\\Gallons\ of\ water\ leaked= 50\ gallons[/tex]

50 gallons of water leaked out of swimming pool.

Keywords: percentage, division

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Answer:

True

Step-by-step explanation:

This is true because there is no common factor for 7 annd 9

Answer:20592

Step-by-step explanation:

Because you multiply 5 times 2288

Leo has 2574 red marbles.

Let's say that the number of blue marbles Leo has is x. According to the given information, Leo has 9 times as many red marbles as blue marbles. So the number of red marbles Leo has is 9x.

It is also given that he has 2288 more red marbles than blue marbles, which means 9x = x + 2288.

Simplifying the equation, we can subtract x from both sides: 8x = 2288. Dividing both sides by 8, we find that x = 286.

Therefore, Leo has 9 times 286 red marbles, which equals 2574 red marbles.

L=4*W-5

10=W*2+(4*W-5)*2

10=W*2+8*W-10

20=10*W

2=W

L=4*2-5

L=3

Answer:

Infinitely many solutions.

Step-by-step explanation:

10+x=5(1/5x+2)

10+x=x+10

infinitely many solutions

The equation 10+x=5(1/5x+2) has an infinite number of solutions.

To solve the equation 10+x=5(1/5x+2), we need to simplify both sides and then isolate the variable x. Let's start by distributing the 5 to the terms inside the parentheses.

10+x = 5(1/5x+2) becomes:

10+x = 1x+10

Next, we can combine like terms on each side of the equation. Subtracting x from both sides:

10 = x+10-x

The x terms cancel out, leaving us with:

10 = 10

This equation is always true, which means that there are an infinite number of solutions.

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The complete Question is given below

10+x=5(1/5x+2)

Determine whether it has one solution, an infinite number of solution, or no solutions

Answer:

C) Side SW

Step-by-step explanation:

Hello! The included side between <S and <W is side SW. According to the included side rule, this would be the correct answer. I know this is not much of an explanation, but there is not much to it! Hope this helps.

Answer:

Step-by-step explanation:

[tex]\dfrac{1}{3}x<3x+8<-5x\qquad\text{multiply all sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{1}{3\!\!\!\!\diagup_1}x<3\cdot3x+3\cdot8<3\cdot(-5x)\\\\x<9x+24<-15x\\\\\text{Let split it into two inequalities}\\\\(1)\qquad x<9x+24\ \text{and}\qquad (2)\qquad 9x+24<-15x[/tex]

[tex](1)\\x<9x+24\qquad\text{subtract}\ 9x\ \text{from both sides}\\\\-8x<24\qquad\text{change the signs}\\\\8x>-24\qquad\text{divide both sides by 8}\\\\\boxed{x>-3}\\\\(2)\\9x+24<-15x\qquad\text{add}\ 15x\ \text{to both sides}\\\\24x+24<0\qquad\text{subtract 24 from both sides}\\\\24x<-24\qquad\text{divide both sides by 24}\\\\\boxed{x<-1}\\\\\text{From (1) and (2) we have}\\\\-3<x<-1\to\text{There is only one integer in this solution: -2}[/tex]

Answer:

9 = [tex]3^{x}[/tex]

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Given

[tex]log_{3}[/tex] 9 = x ⇔ 9 = [tex]3^{x}[/tex] ← in exponential form

Answer:

its A on edge

Step-by-step explanation:

Answer: In general, a solution of a system in two variables is an ordered pair that makes BOTH equations true. In other words, it is where the two graphs intersect, what they have in common. So if an ordered pair is a solution to one equation, but not the other, then it is NOT a solution to the system

Answer:

[tex]\frac{1}{16}[/tex]

Step-by-step explanation:

[tex]\frac{1}{2} *\frac{1}{2} *\frac{1}{2} *\frac{1}{2} =[/tex][tex]\frac{1}{16}[/tex]

[tex]\frac{1}{2}*\frac{1}{2} =\frac{1}{4}[/tex]

[tex]\frac{1}{4} *\frac{1}{2} =\frac{1}{8}[/tex]

[tex]\frac{1}{8}*\frac{1}{2}=\frac{1}{16}[/tex]

Answer:

a) $13588.08

b) $688.08

Step-by-step explanation:

Melissa had to purchase $12,900 worth of machinery for her business.

She made a down payment of $2100 and after that made monthly payments of $478.67 for the business loan for the rest.

Given that after years of paying monthly payments of $478.67, she finally paid off the loan.

Assume that she took 2 years to repay the loan.

a) Therefore, the total amount Melissa ended up paying for the machinery was $[2100 + (478.67 × 24)] = $13588.08 (Answer)

b) Therefore, the amount of interest that Melissa pay on the loan is $(13588.08 - 12900) =$688.08. (Answer)

According to the 2019 report Canada's Changing Climate Report (CCCR) which was commissioned by Environment and Climate Change Canada, Canada's annual average temperature over land has warmed by 1.7 C since 1948. The rate of warming is even higher in Canada's North, in the Prairies and northern British Columbia

The value of CosA is 0.8191

Step-by-step explanation:

Given SinA= 0.5736

We know that [tex]SinA^{2} + CosA^{2} = 1[/tex]

Replacing value of SinA,

[tex](0.5736)^{2} + CosA^{2} = 1[/tex]

[tex](0.3290) + CosA^{2} = 1[/tex]

[tex] CosA^{2} = 1-0.3290[/tex]

[tex] CosA^{2} = 0.6709 [/tex]

[tex] CosA = 0.8191 [/tex]

The value of CosA is 0.8191

Answer:

5. y-intercept is 8

6. slope is -1/2

7. y=-1/2x+8

Answer:

0.1187

Step-by-step explanation:

A = P (1 + k)^t

where A is the final amount,

P is the initial amount,

k is the monthly growth rate,

and t is the number of months.

70 = 50 (1 + k)^3

1.4 = (1 + k)^3

∛1.4 = 1 + k

k = -1 + ∛1.4

k = 0.1187

Mr Lee drive 31 miles from his house to Brookville and there is an extra information that is parkside is 4 miles south of springfield which is not required.

Given that  

Mr. Lee drove 8 miles from his house to park side .  

Parkside is 4 miles south of springfield.

From Parkside he drove 3 miles to springdale  

Then he drove 20 miles from springdale to brookville.

Need to determine how far Mr Lee drive in all, from his house to Brookville.

Also need to identify Extra or missing information.

Complete drive of Mr Lee from his house to Brookville is equal to 8 miles from his house to park side then 3 miles from Parkside to springdale , then 20 miles from springdale to brookville.

=> Complete drive of Mr Lee from his house to Brookville in miles = 8 + 3 + 20 = 31 miles

Information that is parkside is 4 miles south of springfield is extra information which is not required to determine mr. Lee drive , from his house to Brookville .  

Hence Mr Lee drive 31 miles from his house to Brookville and there is an extra information that is parkside is 4 miles south of springfield which is not required.

The price of less expensive equipment is $1575.

Step-by-step explanation:

Let,

Price of one equipment = x

Price of other equipment = y

According to given statement;

x+y=4000   Eqn 1

x = y+850    Eqn 2

Putting Eqn 2 in Eqn 1

[tex](y+850)+y=4000\\y+850+y=4000\\2y=4000-850\\2y=3150[/tex]

Dividing both sides by 2;

[tex]\frac{2y}{2}=\frac{3150}{2}\\y=1575[/tex]

Putting y=1575 in Eqn 2;

[tex]x=1575+850\\x=2425[/tex]

The price of less expensive equipment is $1575.

Keywords: linear equation, substitution method

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Final answer:

The price of the less expensive piece of equipment is $1575. This was calculated by setting up an equation based on the total cost and the difference in price between the two pieces of equipment and then solving for the unknown price.

Explanation:

To find the price of the less expensive piece of equipment, we will first assign variables to the two pieces of equipment. Let's call the cost of the less expensive piece of equipment x dollars. Since the other piece cost $850 more, the cost of the second piece would then be x + $850. We are given that the total cost of both pieces is $4000, so we can set up the following equation to represent this relationship:

x + (x + $850) = $4000

To solve for x, we combine like terms and get:

2x + $850 = $4000

Subtracting $850 from both sides gives us:

2x = $3150

Dividing both sides by 2, we find the value of x:

x = $1575

Therefore, the price of the less expensive piece of equipment is $1575.

Answer:

13.406

The drawing will help

Answer:

13.406

Step-by-step explanation:

Answer:

12 and 8

Step-by-step explanation:

12 + 8= 20

12 x 8= 96

The two numbers are 12 and 8. They have a sum of 20 and a product of 96, satisfying the given conditions.

To find two numbers whose sum is 20 and whose product is 96, we can set up a system of equations. Let's call the two numbers x and y.

1. The first equation represents their sum:

  x + y = 20

2. The second equation represents their product:

  xy = 96

Now, we need to solve this system of equations. One way to do it is by substitution. From the first equation, we can express y in terms of x: y = 20 - x.

Now, we substitute this expression for y into the second equation:

x(20 - x) = 96

Expanding and simplifying this equation:

20x - x^2 = 96

Rearranging terms:

x^2 - 20x + 96 = 0

Now, we factor the quadratic equation:

(x - 12)(x - 8) = 0

This gives us two possible solutions for x: x = 12 and x = 8.

So, the two pairs of numbers that satisfy the conditions are (12, 8) and (8, 12). In both cases, the sum of the numbers is indeed 20, and their product is 96, as required.

In summary, the two numbers are 12 and 8, and they meet the criteria of having a sum of 20 and a product of 96. These solutions demonstrate how algebraic techniques can be used to solve real-world problems involving unknown values.

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Answer:

B.6 inches

Step-by-step explanation:

Given: Three boards with measurement  24, 36, and 42 inches.

For the longest length of board we have to find out the H.C.F.

And for H.C.F. we will find out the factors,

[tex]24=2\times2\times2\times3\\36=2\times2\times3\times3\\42=2\times3\times7[/tex]

Here 2 and 3 is the common factor of given length of boards.

So the H.C.F. is 6.

Hence the longest length of board that carpenter can cut is 6 inches.

Answer:

The two numbers are -419 and -2095.

Step-by-step explanation:

5x=y

x-y=1676

----------------

x-5x=1676

-4x=1676

x=1676/-4

x=-419

5(-419)=y

y=-2095

The right answer is Option B.

Step-by-step explanation:

Given expression is;

5x√2 - 3√2 + x√2

We can add or subtract square roots only when the values inside the square root are same and the variables are also same.

In the given expression, variable x is same with √2, therefore, adding both the roots

[tex]6x\sqrt{2} -3\sqrt{2}[/tex]

6x√2 - 3√2 is equivalent to 5x√2 - 3√2 + x√2.

The right answer is Option B.

Keywords: square roots, subtraction

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Answer:

Here's the answer. I got it right on my quiz. Hope I could help:)

Answer:

10 square root over 30

Step-by-step explanation:

took the test

Answer:

The exponential function is [tex]C(t)=y(b)^t\ Or\ C(t)=1800(1.15)^1[/tex]

Step-by-step explanation:

Given

[tex]t[/tex] be the number of hours.

[tex]y[/tex] number of bacteria cells.

And we know that an exponential function is [tex]C(t)=y(b)^t[/tex],where [tex]b[/tex] is a positive real number, and in which the argument [tex]t[/tex] occurs as an exponent

The petri dish has [tex]1800[/tex] bacteria cells we can say that [tex]y=1800[/tex]

In the equation as [tex]C[/tex] is function of  time and [tex](t)[/tex] will vary as [tex]1,2,3[/tex] for respective hours.

To find the value of [tex]b[/tex] we have to understand that it is dependent on percent increase if there is increment of [tex]15\%[/tex] then [tex]b=1+15\%=1+\frac{15}{100}=1+0.15=1.15[/tex]

So the exponential function will be [tex]C(t)=y(b)^t[/tex] ,plugging the values it will be equivalent to [tex]C(t)=1800(1+0.15)^1[/tex]

Check:

[tex]15\% of 1800 =0.15\times 1800=270[/tex]

So in first hour the cells will increased by a quantity of [tex]270[/tex] cells.

The number of cells after an hour in the petri dish [tex]=(1800+270)=2070[/tex]

That can also be from the formula.

[tex]C(t)=1800(1.15)^1=2070[/tex]

So the exponential function is [tex]C(t)=y(b)^t\ Or\ C(t)=1800(1.15)^1[/tex]

[tex]y[/tex] will increase exponentially as the value of [tex]t[/tex] increase.

Final answer:

The exponential function to represent the growth of bacteria cells, y, after t hours with an initial amount of 1800 cells and a 15% hourly growth rate is y = 1800(1 + 0.15)^t.

Explanation:

To write an exponential function showing the relationship between the number of bacteria cells, y, and the time in hours, t, we begin by using the initial value of 1800 bacteria cells and apply a 15% increase each hour. The exponential growth formula is given by y = P(1 + r)^t, where P is the initial amount, r is the growth rate (expressed as a decimal), and t is the time.

Since the growth rate is 15%, we convert this to a decimal by dividing by 100, resulting in 0.15. The formula to model this bacterial growth would be y = 1800(1 + 0.15)^t. Therefore, for any given number of hours t, you can calculate the number of bacteria cells y.

Answer:

B, 9.625

Step-by-step explanation:

I know there's a more surefire method of doing this problem but since this is multiple choice, you can use process of elimination to solve it.