Mathematics College

The formula A=P(1+r)t is used to show the total amount owed for a loan with a simple annual interest rate.

Solve for r.

Answers

Answer 1
We are asked to express r in terms of A, P, and t.

We first divide both sides of the equation by t, which gives us

                                         
                     [tex]\displaystyle{ \frac{A}{t}=P(1+r) [/tex], 


then, dividing both sides by P, we have

                     [tex]\displaystyle{ \frac{A}{Pt}=1+r [/tex].

Swap the sides:

                    [tex]\displaystyle{ 1+r= \frac{A}{Pt}[/tex] 
      
Finally subtracting 1 from both sides gives us

                     [tex]\displaystyle{ r=\frac{A}{Pt}-1[/tex].


Answer 2

Answer:  [tex]r=(\frac{A}{P})^{\frac{1}{t}}-1[/tex]


Step-by-step explanation

Compound interest is the addition of interest to the principal sum of a deposit or a loan.

Let P = principal amount which was taken as a loan then the accumulated amount A is given by

[tex]A=P(1+r)^t[/tex].......(1)

where, r is the rate of simple annual interest in decimal.

t is the time applied for interest.

For solving r divide both sides of equation by P in (1),we get

[tex]\frac{A}{P}=(1+r)^t\\\Rightarrow(\frac{A}{P})^{\frac{1}{t}}=1+r\\\Rightarrow\ r=(\frac{A}{P})^{\frac{1}{t}}-1[/tex].

Related Questions

5y-x=10 (solve for y).

Answers

To solve 5y - x = 10 for y, add x to both sides and then divide by 5, resulting in the solution y = (x + 10) / 5.

To solve the equation 5y - x = 10 for y, follow these steps:

Add x to both sides of the equation to isolate terms with y on one side: 5y = x + 10.  

Now, divide both sides of the equation by 5 to solve for y:

y = (x + 10) / 5.

The solution for y when given an equation of the form 5y - x = 10 is y = (x + 10) / 5.

by which conversion factor can 800 meters be multiplied to change in to miles?

Answers

there are 1000 meters in 1 kilometer.

and there are 1.609 kilometers in 1 mile.

if there are 1.609 kilometers in 1 mile, then there are 1.609 * 1000 meters in 1 mile, or 1609 meters

[tex]\bf \cfrac{800~\underline{m}}{1}\cdot \cfrac{mile}{1609~\underline{m}}\implies \cfrac{800}{1609}~mile\implies 800\cdot \cfrac{1}{1609}~mile[/tex]

Show that for the same shear angle, there are two rake angles that give the same cutting ratio.

Answers

the answer to this question is a equilater triangule

Leo has 421 prize tickets. He can get 1 prize for every 100 tickets. How many prizes can Leo get? How many tickets will he have left over?

Answers

He can get 4 prizes and he will have 21 tickets left over.

421 / 100 = 4.21

 so he will win 4 prizes and have 21 tickets left over.

ANYONE????
Use infinite geometric summation to write 0.18 as a fraction whose numerator and denominator have no common factors. Recall that 0.18 means 0.18181818 . . . .

Answers

Your denominator is going to be 4 digits. "18,18,18,18".

The soccer team voted on what they wanted to eat. There are 20 members on the team. Six members voted for pizza, 10 voted for chicken, and the rest voted for hot dogs. Which ratio represents the number of votes for hot dogs to chicken? 1/5 2/5 3/5 5/2

Answers

3/5 i believe :D (hope this helps)

The answer is 2/5 because hot dogs to chicken is 2/5


At one university, the students are given z-scores at the end of the each semester, rather than the traditional gpas. the mean and standard deviation of all students' cumulative gpas, on which the z-scores are based, are 2.7 and 0.5, respectively

Answers

The students with z-scores below -1.6 would be put on probation, and the corresponding probationary GPA is 1.9.

Given data:

To translate z-scores to corresponding GPAs, you can use the formula:

GPA = (z * standard deviation) + mean

Given:

Mean (μ) = 2.7

Standard Deviation (σ) = 0.5

Let's calculate the corresponding GPAs for the given z-scores:

For z = 2.0:

GPA = (2.0 * 0.5) + 2.7

= 1.0 + 2.7

= 3.7

For z = -1.0:

GPA = (-1.0 * 0.5) + 2.7

= -0.5 + 2.7

= 2.2

For z = 0.5:

GPA = (0.5 * 0.5) + 2.7

= 0.25 + 2.7

= 2.95

For z = -2.5:

GPA = (-2.5 * 0.5) + 2.7

= -1.25 + 2.7

= 1.45

Now, to determine the corresponding probationary GPA for z = -1.6:

GPA = (-1.6 * 0.5) + 2.7

= -0.8 + 2.7

= 1.9

Hence, students with z-scores below -1.6 would be put on probation, and the corresponding probationary GPA is approximately 1.9.

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The complete question is attached below:

At one university, the students are given z-scores at the end of each semester rather than the traditional GPAs. The mean and standard deviation of all students’ cumulative GPAs, on which the z-scores are based, are 2.7 and .5, respectively.

- translate each of the following z-scores to corresponding GPA: z=2.0, z=-1.0, z=.5, z =-2.5.

- Students with z-scores below -1.6 are put on probation. What is the corresponding probationary GPA?

There are 5 slots, each containing the letters w, r, l, d or o. one letter is picked at random from each slot. what are the odds that the letters stored in these slots read the word world?

Answers

In the first slot lets calculate the chance of getting a w: 1/5

In the second slot calculate the chance of getting a o: 1/4 (notice how it's 4 not 5 because you already have one letter in the first slot so you have 4 left to choose from.)

In third slot, chance of getting a r: 1/3

In fourth slot, chance of getting a l: 1/2

In the fifth slot, if you got all the first four letters right, than you would be left with one letter, so your chances are 1/1 (100%) for the fifth slot



To calculate probability multiply all the fractions we got above: 1/5 x 1/4 x 1/3 x 1/2 x 1/1

We will then get: 1/(5x4x3x2x1) = 1/120

1/120 is the probability of the 5 slots showing the word "world"
Final answer:

The probability of the 5 letter slots randomly making the word 'world' is calculated by finding the product of the probability of choosing each letter correctly, which for this problem, is (1/3125).

Explanation:

To calculate the probability of picking the letters 'w', 'o', 'r', 'l', 'd' in that order, we understand that we are dealing with a probability problem regarding independent events. This scenario means that the outcome of each selection does not affect the others.

Here, each slot contains 5 distinct letters. The probability of picking a specific letter correctly is 1/5 (1 way to pick a correct letter divided by 5 total letters). So, the probability of picking each letter correctly and in the order of 'world' is the product of the probabilities of choosing each letter correctly i.e P(choosing all five correct letters) = P(choosing 1st correctly) X P(choosing 2nd correctly) X P(choosing 3rd correctly) X P(choosing 4th correctly) X P(choosing 5th correctly) = (1/5) X (1/5) X (1/5) X (1/5) X (1/5) = (1/3125).

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Charlie's father is 41 years old. His age is two years more than three times Charlie's age. What is Charlie's age?

Answers

41 - 2 is 39
39 divided by 3 is 13
Charlie is 13 years old

Final answer:

By setting up a linear equation, it is determined that Charlie is 13 years old based on the given information that his father is two years more than three times Charlie's age and is 41 years old.

Explanation:

The problem presented is a classic example of a linear equation in the subject of mathematics. We are given that Charlie's father is 41 years old, and his age is two years more than three times Charlie's age.

To determine Charlie's age, we can set up the equation as follows: Let x represent Charlie's age. The father's age is then described by the expression 3x + 2.

Since we know the father is 41 years old, we have:

3x + 2 = 41

Subtract 2 from both sides of the equation to isolate the terms with x:

3x = 39

Now, divide both sides by 3 to solve for x:

x = 39 / 3

x = 13

Therefore, Charlie is 13 years old.

Determine the unit rate. Use mental math when you can. 6 golf balls for $15. 2 dozen tennis balls for $36. 4lb meat for $18. 24 tickets for $480.

Answers

Final answer:

To determine the unit rate for each item, divide the total cost by the number of units. This gives us $2.50 per golf ball, $1.50 per tennis ball, $4.50 per pound of meat, and $20 per ticket.

Explanation:

The question involves determining the unit rate of different items. A unit rate is the cost per one unit of an item. To calculate each unit rate, we divide the total cost by the number of units.

For 6 golf balls for $15, the unit rate is $15 ÷ 6 = $2.50 per golf ball.For 2 dozen (24) tennis balls for $36, the unit rate is $36 ÷ 24 = $1.50 per tennis ball.For 4lb of meat for $18, the unit rate is $18 ÷ 4 = $4.50 per pound of meat.For 24 tickets for $480, the unit rate is $480 ÷ 24 = $20 per ticket.

These calculations can often be made using mental math, especially when dealing with simple numbers or common multiples.

What is the slope of y=1/5x - 4?

Answers

1/5 because y=mx+b where m=the slope so in y=1/5x+-b, 1/5 is the slope. 
Given that the equation is  [tex]y= \frac{1}{5}x-4 [/tex]
the slope is [tex] \frac{1}{5}[/tex] and the -4 is the intercept or where the line crosses the y- axis

suppose someone tells you that she has a triangle with sides having lengths 2.6,8.1 and 8.6. Is this a right triangle? why or why not? Is there an angle in the triangle larger than 90 degree?

Answers

If you're only provided with the lengths of a triangle, and you're asked to determine whether or not the triangle is right or not, you'll need to rely on the Pythagorean Theorem to help you out. In case you're rusty on it, the Pythagorean Theorem defines a relationship between the legs of a right triangle and its hypotenuse, the side opposite its right angle. That relationship is a² + b² = c², where a and b are the legs of the triangle, and c is its hypotenuse. To see if our triangle fits that requirement, we'll have to substitute its lengths into the equation.

How do we determine which length is the hypotenuse, though? Knowledge that the hypotenuse is always the longest length of a right triangle helps here, as we can clearly observe that 8.6 is the longest we've been given for this problem. The order we pick the legs in doesn't matter, since addition is commutative, and we'll get the same result regardless of the order we're adding a and b.

So, substituting our values in, we have:

(2.6)² + (8.1)² = (8.6)²

Performing the necessary calculations, we have:

6.76 + 65.61 = 73.96
72.37 ≠ 73.96

Failing this, we know that our triangle cannot be right, but we do know that 72.37 < 73.96, which tells us something about what kind of triangle it is. Imagine taking a regular right triangle and stretching its hypotenuse, keeping the legs a and b the same length. This has the fact of increasing the angle between a and b. Since the angle was already 90°, and it's only increased since then, we know that the triangle has to be obtuse, which is to say: yes, there's an angle in it larger than 90°.

Find the dimensions of the rectangle with area 120 square inches and smallest possible perimeter

Answers

Here, A = L*W and P=2L+2W.  Maximize P.  Subst. L = A/W for L in the 2nd equation:

P=2(A/W) + 2W.  This is to be minimized.

dP/dW = 2[-A/(W^2)) + 2W.  But A = 120 sq in:

dP/dW = 2[-120/(W^2)) + 2W   set this equal to 0 and solve for W.
Once you have W, find L:  L=120/W

Let 2[-120/(W^2)) + W] = 0.  Then   [-120/(W^2)) + W] = 0

Multiplying all terms by W^2 gives us -120 + W^3 = 0.

w^3 = 120 cubic inches.  Find the cube root to find W.  

W = cube root of 120 = 4.93 inches.  L = 120/W, or L = 120/4.93 inches

Summary:  W = 4.93 inches and L = 24.33 inches   (answer)

A carpenter has a 6-foot long board. He wants to cut the board into pieces that are 4/5 foot long. How many pieces of length 4/5 foot can the carpenter cut from the board? What length of the original board will be left after the carpenter has cut all the pieces that are 4/5 foot long?

Answers

Ok so take 6 divided by 4/5 or 6 x 5/4 = 7.5 but you don't want .5 of a board so you will have 7 boards and 0.4 feet of board left over because half of 4/5 is 0.4

Answer:

Number of pieces=7

Length of board remaining=[tex]\frac{2}{5}[/tex]

Step-by-step explanation:

We are given that a carpenter has board of length=6 foot

Length of each piece of board=[tex]\frac{4}{5}[/tex] foot

We have to find the number pieces of given length of piece can be made from given board.

In order to find the number of pieces we will divide the total length of board by the length of each piece.

Therefore, number of pieces =[tex]\frac{6}{\frac{4}{5}}[/tex]

Number of pieces=[tex]7\frac{1}{2}[/tex]

Length of each piece =[tex]\frac{4}{5}[/tex]

Therefore, number of pieces=7

Length used in 7 pieces =[tex]7\times\frac{4}{5}=\frac{28}{5}[/tex]

Length of board remaining=[tex]6-\frac{28}{5}=\frac{2}{5}[/tex]

At a​ school, 126 students play at least one sport. This is 40​% of the students at the school. How many students are at the​ school?

Answers

126 + 60% (76) = 202 students
There are 315 students at the school. You can solve this multiple ways, but I made a proportion.   40%              100%
                                 ----      x         ------
                                126                  x

You are building a new house on a cartesian plane whose units are measured in miles. Your house is to be located at the point (2,0) . Unfortunately, the existing gas line follows the curve y= √(16 x^2 +5x+16). It costs 400 dollars per mile to install new pipe connecting your house to the existing line. What is the least amount of money you could pay to get hooked up to the system?

Answers

find the derivative of the equation to find its critical points. And the compute the distance from the house to the critical point (local minimum).However, I'm unable to compute the derivative. Kindly help with explanation.

A bird leaves its nest and travels 12 miles per hour downwind for x hours. On the return trip, the bird travels 2 miles per hour slower and has 3 miles left after x hours. What is the distance of the entire trip? How long does the entire trip take?

Answers

3 hours

On the way there, 1.5x12 = 18
On the way back, 1.5x10 = 15

12x = 10x + 3

Subtract 10x from both sides

2x = 3

Divide by two on each side

x = 3/2 or 1 1/2 hours

Distance of the trip:

12 * 2 * 3/2 = 36 miles

How long does the trip take:

3/2 + 3/2 + 3/10 = 3 3/10 hours

3 hours

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The expression 1/3b−1/3 factored is

Answers

(1/3)(b-1) is the simplest set of factors.

Answer:

[tex]\frac{1}{3}[b-1][/tex]

Step-by-step explanation:

we have

[tex]\frac{1}{3}b-\frac{1}{3}[/tex]

Factor the coefficient [tex]\frac{1}{3}[/tex] of both terms

[tex]\frac{1}{3}b-\frac{1}{3}=\frac{1}{3}[b-1][/tex]

If bethany earned $51,740 last year, how much did she earn per week?

Answers

52.14 dollars per week.

The fracture toughness (in ) of a particular steel alloy is known to be normally distributed with a mean of 28.3 and a standard deviation of 0.77. We select one sample of this alloy at random and measure its fracture toughness. Given that the fracture toughness is at least 27, what is the probability that the fracture toughness will be between 29 and 40.3? is it just P(X <= 40.3) - P(X <= 29)? How do I use the 27?

Answers

This is a conditional probability question.

The conditional probability is given as follows: The probability of an event A given B is given by

[tex]P(A|B)= \frac{P(A\cap B)}{P(B)} [/tex]

Thus, given that the fracture toughness of a particular steel alloy is known to be normally distributed with a mean of 28.3 and a standard deviation of 0.77.

The probability that the fracture toughness will be between 29 and 40.3 given that the fracture toughness is at least 27 is given by

[tex]P(29 \leq X \leq 40.3 \, | \, X \geq 27)= \frac{P(29 \leq X \leq 40.3)\cap P(X \geq 27)}{P(X \geq 27)} \\ \\ =\frac{P(29 \leq X \leq 40.3)}{P(X \geq 27)}[/tex]

[tex]P(29 \leq X \leq 40.3)=P\left(z \ \textless \ \frac{40.3-28.3}{0.77}\right)- P\left(z \ \textless \ \frac{29-28.3}{0.77}\right) \\ \\ =P(z\ \textless \ 15.58)-P(z\ \textless \ 0.91)=1-0.81835=0.18165[/tex]

[tex]P(X \geq 27)=1-P(x\ \textless \ 27) \\ \\ =1-P\left(z\ \textless \ \frac{27-28.3}{0.77}\right)=1-P(z\ \textless \ -1.688) \\ \\ =1-0.04568=0.95432[/tex]

Thus, the probability that the fracture toughness will be between 29 and 40.3 given that the fracture toughness is at least 27 is given by

[tex]\frac{P(29 \leq X \leq 40.3)}{P(X \geq 27)}= \frac{0.18165}{0.95432} =\bold{0.1903}[/tex]

9x-5y=-32 in slope intercept form

Answers

The slope intercept form of a linear equation has the following form where the equation is solved for y in terms of x:

y = a + bxb  is the slopea  is a constant term. It is the y intercept, the place where the line crosses the y axis.

 

Example 1

y = -13 + 7x

This equation is in slope intercept form. The y intercept is (0,-13) and the slope is 7.

Example 2

4x + 3y = 12

Rewrite this equation in slope intercept form.

3y = 12 - 4x

The equation is now in slope intercept form. The y intercept is (0,4) and the slope is
-4/3.

 

Example 3

5x - 3y - 15 = 0

Rewrite this equation in slope intercept form.

3y = -15 + 5x

The equation is now in slope intercept form. The y intercept is (0,-5) and the slope is 
5/3.

Example 4

The equation is now in slope intercept form. The y intercept is (0,-7.5) and the slope is 
1.5.

The width of a rectangle is equal to m cm, but its length is five times greater than the width. Find the area of the rectangle.

Answers

width= m
length= 5m

Area= l×w
Area= 5m×m
Area=5m^2
(^=exponent)

The area will be 5m^2

All real numbers at least 3 units from -2

Answers

yes the are real 3 -2
Such numbers are divided into two sets.
The first set is (-infinity, -5].  All numbers in this set are 3 or more units from -2.
The second set is [1, infinity).  Same reasoning.
Drawing a diagram might help you understand this problem better.

Emily bought a video game console and some games for $350. The video game console cost $200. Each game cost $25. How many games did Emily purchase?

Answers

300-200=150
25x6=150
so the answer is she bought 6 games

what is absolute value of these set of numbers?

Answers

= (6×-2) - (-3×-4)
= -12 - 12 = -24
that's the determinant tho, not absolute value

A bag contains 90 marbles some red and some transparent the ratio of red marbles to transparent ones is 1:4. how many red marbles are there? andwer

Answers

18 red marbles because add the ratio togather which is 5 and divide 90 by 5=18 for 1

a girl scout has (5x-12) boxes of cookies and sells (3x+18) of them. Write an expression to represent the amount of boxes she has left. Also can you show me the work that gets this answer not just the answer

Answers

You have to subtract 3x + 18 from 5x - 12:

=> 5x - 12 - ( 3x + 18) = 5x - 12 - 3x - 18 = 5x - 3x - 12 - 18 = 2x - 30

The first step was to apply distributive property to supress the parenthesis, after that the terms were arranged and the like terms combined.

Answer: 2x - 30

Jessica is measuring two line segments. The first line segment is 30 cm long. The second line segment is 500 mm long. How long are the two line segments together? (answer in cm)

Answers

convert mm to cm

1mm = 0.1 cm

500 * 0.1 = 50cm

50 +30 = 80cm total length

How do you write .625 as a fraction

Answers

Since there are 3 digits in this problem it means that the number for the denominator will be 1000. the answer to this is 625/1000

To turn a decimal into a fraction, first notice that the number to the right of the decimal point is 625. The 6 represents the tens, the 2 represents the hundreds, and the 5 represents the thousands. So, we can put 625 over 1000 or 625/1000.

Notice that the fraction [tex]\frac{625}{1000}[/tex] is not in lowest terms. To turn the fraction into lowest terms, we can divide both the numerator and the denominator by 125.

[tex]\frac{625}{1000}[/tex] ÷ [tex]\frac{125}{125}[/tex] = [tex]\frac{5}{8}[/tex]

Therefore, .625 can be written as the fraction 5/8, which is in lowest terms.

What is the quotient?
-5 1/4 ÷ 2 3/4
Enter your answer as a mixed number, in simplified form, in the box.

Answers

- 5 1/4 ÷ 2 3/4 =

= - 21/4 ÷ 11/4

= - 21/4 * 4/11

= - 21/11

= - 1 10/11
Final answer:

To divide -5 1/4 by 2 3/4, convert both numbers to improper fractions, multiply the first fraction by the reciprocal of the second fraction, and simplify the result. The quotient is -1 10/11.

Explanation:

To divide -5 1/4 by 2 3/4, first convert both mixed numbers to improper fractions. -5 1/4 can be written as -21/4, and 2 3/4 can be written as 11/4. Next, divide -21/4 by 11/4. To divide fractions, multiply the first fraction by the reciprocal of the second fraction. So, (-21/4) * (4/11) = -21/11. This quotient can be written in mixed number form as -1 10/11, which is the simplified answer.

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