Micah wants to know how much principal, P, he should invest at interest rate, r, to have an amount, A, of money at the end of t years. He knows that the formula for the final amount earned using simple interest can be found using the formula, A - P(1 + rt). Which equation is rewritten correctly to isolate principal, P
Answers
The correct equation to isolate principal, P, is:
What is simple interest?Simple interest refers to the interest that is earned on an initial amount of money, known as the principal, over a fixed period of time. It is called "simple" because it is calculated based only on the initial principal amount and does not take into account any interest earned on the interest itself, which is known as compound interest.
To isolate principal, P, we need to rearrange the given formula as follows:
\(A - P(1 + rt) =\) Interest earned on principal (I)
The interest earned on the principal (I) is given by:
\(I = Prt\)
Now, we can rewrite the above formula as:
\(A = P + I\)
Substituting the value of I, we get:
\(A = P + Prt\)
Now, we can isolate P by subtracting Prt from both sides:
\(A - Prt = P\)
Therefore, the correct equation to isolate principal, P, is:
\(P = (A - Prt)\)
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The correct equation to isolate P is c. P = A/(1 + rt)
What is simple interest?Simple interest is the term used to describe the interest that is accrued over a predetermined amount of time on an initial sum of money, known as the principal. It is known as "simple" interest because it is computed just using the initial principal sum and ignores any interest that has been earned on top of the interest itself, a concept known as compound interest.
The formula for the final amount earned using simple interest is A = P(1 + rt), where A is the total amount at the end of t years, P is the principal amount, r is the interest rate, and t is the time in years.
To isolate P, we can rearrange the formula as:
A = P(1 + rt)
Divide both sides by (1 + rt):
A/(1 + rt) = P
Therefore, the correct equation to isolate P is:
c. P = A/(1 + rt)
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Related Questions
The width of a rectangle is 5 feet less than the length. The perimeter is 62. Find the length and width of the rectangle.
Variables: ___________________________
Model equation: ______________________________
Length of the rectangle: ______________________________
Width of the rectangle: ______________________________
Answers
Perimeter formula: p = 2(w + l)
The perimeter is 62.
p = 62
The width of a rectangle is 5 feet less than the length.
w = l - 5
Substitute and solve.
62 = 2[(l - 5) + l)]
62 = 2l + 2l - 10
62 = 4l - 10
72 = 4l
18 = l
Substitute and solve for the width
w = 18 - 5
w = 13
Therefore, the length is 18 and the width is 13.
Best of Luck!
Answer:
see below and attached.
Step-by-step explanation:
Perimeter (P) = 2 L (Length) + 2 W (Width)
where P = 62
W = L - 5
P = 2L + 2W
62 = 2L + 2(L -5)
62 = 2L + 2L - 10
72 = 4L
L = 72/4
L = 18
W = L - 5
W = 18 - 5
W = 15
Variables : P, L, W
Model equation: P = 2L + 2W
Length of the rectangle: 18
Width of the rectangle: 13
You are studying the relationship between playing video games and how much children enjoy reading books. Which research method would be most effective at helping you identify whether there is a causal relationship between these two variables?
Answers
Research methods involve qualitative research, experiments, and questionnaires
The research method would be most effective to identify the causal relationship is experiment
How to determine the research methodFrom the question, we understand that:
The study involves two variablesThe variables are video games and reading booksTo determine the relationship between any set of variables, the variables must be put to test.
This test is referred to as experiment
Hence. the best research method is to carry out an experiment
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Help Help Help Help please
Brainliest if correct
Answers
Answer:
least to greatest
|y-z|
|x-y|
|x-z|
z
Step-by-step explanation:
Which of the following statements about correlation and causation is true?
Group of answer choices
Correlation cannot occur without causation.
Correlation and causation are always unrelated.
Causation implies correlation.
Correlation implies causation.
Answers
The true statement is "Causation implies correlation.."
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
The list of options
As a general rule, causation means that there is a cause-and-effect relationship between variables.
A correlation doesn't imply causation, but causation always implies correlation
Correlation can occur without causation, meaning that two variables can be statistically related without one causing the other.
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A rectangle has a length of 64 cm. The rectangle is reduced by a scale factor of 3/4. What is the length of the reduced rectangle?
Answers
Answer:
48 cm
Step-by-step explanation:
64 divided by 4 is 16. multiply 16 by 3 and the answer is 48.
find f (25/29) if f (x)=-5x+5
Answers
Answer:
f(25/29) = \(\frac{20}{29}\)
Step-by-step explanation:
In order to do this problem, we need to plug in \(\frac{25}{29}\) for x. When we plug it in we get \(f(x) = -5(\frac{25}{29}) + 5\). After this we can start by multiplying. When we multiply \(-5(\frac{25}{29} )\) we get \((\frac{-125}{29}) + 5\). Since the fraction cannot be simplified any further, we can now add 5. In order to add 5 we need to find a common denominator, which in this case will be 29. Changing the denominator to 29 gives us \((\frac{-125}{29}) + \frac{145}{29}\) because when changing the denominator we have to multiply the numerator by the same number. After adding these fractions we get our answer of \(\frac{20}{29}\).
Marneashia has a total of 14 chickens . If she has 2 times as many chickens as dogs write and solve an equation to determine the number of dogs she has.
Answers
The correct answer is 2x = 14; x = 7
How did we figure this out?For this equation we are going to divide the numbers to find are answer.Divide by 2 on both sides of the equal sign, 14 divided by 2 is 7.Therefore, The correct answer is 2x = 14; x = 7
Find the x-intercepts of the graph
Answers
Answer:
(1,0) and (3,0)
Step-by-step explanation:
y=x^2-4x+3
To factor we need to know what numbers add up to -4 and multiply will equal to 3.
y=(x-3)(x-1)
The zeroes would be 3 and 1.
x=3 so y=0 for (x-3)
x=1 so y=0 for (x-1)
If right pls give me brainliest thank you.
Answer:
(1, 0) and (3, 0)
Step-by-step explanation:
\(y=x^2-4x+3\)
Plug y as 0 to find the x-intercepts.
\(0=x^2-4x+3\)
Factor right side.
\(0=x^2-1x-3x+3\)
\(0=x(x-1)-3(x-1)\)
\(0=(x-1)(x-3)\)
Set factors equal to 0.
\(x-1=0\\x=1\\x-3=0\\x=3\)
x=1 or x=3 when y=0
3x - 9 + 4x
Please Help
Answers
Answer:
Add like terms 7x - 9
Step-by-step explanation:
7x-9
which method would you use to round 2.6 to the closest whole number?
Answers
Answer:
Step 1: Locate and underline the whole numbers place (2) then look at the digit to the right (6):
2.6
Step 2: In this case, the digit to the right (6) is 5 or above. So, we add 1 to the whole numbers place (2). The digit(s) after the (2) are replaced by zeros (or dropped). Thus, we get 3 as the answer.
In short: 2.6 rounded to the nearest whole number is 3.
A ride at a carnival has two types of cars for children to ride. One type has 2 seats and one has 4 seats. There are 25 cars, and they can seat a total of 70 children, how many 4-seated cars are there?
Answers
Answer:
There are 10 and 4 seated cars
Step-by-step explanation:
I hope this helps you
Participants in a survey were asked the number of hours of television they
watch each week. The dot plot shows the distribution of their responses.
·
H
0 2
4 6 8 10 12 14 16
Number of Hours
After the data was recorded in the dot plot, another response was found for a
participant who watches 30 hours of television each week. How will this
additional data point affect the mean number of hours of television watched
each week?
A. The effect on the mean number of hours cannot be determined.
B. The mean number of hours will decrease.
C. The mean number of hours will increase.
D. The mean number of hours will remain the same.
Answers
Explanation: since the graph in increasing and so is the number of minutes tv watched the graph should increase as well
7.20 which is higher? determine if i or ii is higher or if they are equal. explain your reasoning. for a regression line, the uncertainty associated with the slope estimate, b1, is higher when i. there is a lot of scatter around the regression line or ii. ii. there is very little scatter around the regression line
Answers
II is higher. When there is very little scatter around the regression line, it means that the data points are tightly clustered and the relationship between the variables is strong.
In this scenario, the slope estimate, b1, is likely to be more precise and have less uncertainty. The regression line will have a small standard error of estimate, indicating that the predicted values are close to the actual values.
On the other hand, when there is a lot of scatter around the regression line, it means that the data points are more spread out and the relationship between the variables is weaker. In this scenario, the slope estimate, b1, is likely to be less precise and have more uncertainty. The regression line will have a larger standard error of estimate, indicating that the predicted values are further from the actual values.
In summary, the amount of scatter around the regression line affects the precision of the slope estimate. When there is very little scatter, the slope estimate is likely to be more precise and have less uncertainty. Conversely, when there is a lot of scatter, the slope estimate is likely to be less precise and have more uncertainty.
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An assembly line has 10 stations with times of 1, 2, 3, 4, …, 10, respectively. What is the bottleneck time?
Answers
The bottleneck time is 10, as this is the longest time for any station in the assembly line.
What is the bottleneck time?In this assembly line, the bottleneck time is 10. This is the amount of time it takes for a product to pass through the longest station, station 10, and is the limiting factor in the line's overall efficiency.This is referred to as the bottleneck time because it is the maximum time that can be achieved, regardless of how efficient the other nine stations are.The bottleneck time is an important concept in assembly line and production management, as it helps to determine the optimal speed of the line and the maximum output that can be achieved.If the bottleneck time is longer than necessary, it can lead to higher costs and slower production.To improve the bottleneck time, managers can look for ways to reduce the time it takes to complete each task, or reduce the number of tasks required.Additionally, managers may need to invest in additional resources, such as robots, to increase the speed of the bottleneck station.To learn more about The bottleneck time refer to:
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Jeff is using 11 green tiles and seven yellow tiles to design a section of an outdoor patio which ratio compares the number of green tiles to total number of tiles in one section
Answers
Answer:
11:18
Step-by-step explanation:
We know
Jeff is using 11 green and seven yellow tiles to design an outdoor patio section.
11 + 7 = 18 tiles
So, we know the total number of tiles is 18.
Which ratio compares the number of green tiles to the total number of tiles in one section
We know he uses 11 green tiles, so the ratio is
11:18
For positive acute angles A and B, it is known that cos A = 8/17 and sin B = 3/5. Find the value of sin(A - B) in simplest form.
Answers
The expansion of Cos(A-B) is:
\(\text{Cos(A}-B)=CosACosB+SinASinB\)We are provided with the following:
\(\text{Cos A=}\frac{8}{17},Sin\text{ B=}\frac{3}{5}\)We will have to obtain the values of Cos B and Sin A. Thus, we have:
To be obtain Sin A, we have to get the value of the third side, which is the opposite side, by applying the pythagoras theorem. Thus, we have:
\(\begin{gathered} (\text{Hypotenuse)}^2=(\text{Opposite)}^2+(\text{Adjacent)}^2 \\ 17^2=O^2+8^2 \\ 289=O^2+64 \\ 289-64=O^2 \\ O^2=225 \\ O=\sqrt[]{225} \\ O=15 \\ \text{Thus, Sin A=}\frac{Opposite}{\text{Hypotenuse}} \\ Sin\text{ A=}\frac{15}{17} \end{gathered}\)To be obtain Cos B, we have to get the value of the third side, which is the adjacent side, by applying the pythagoras theorem. Thus, we have:
\(\begin{gathered} \text{Hyp}^2=\text{Opp}^2+\text{Adj}^2 \\ 5^2=3^2+A^2 \\ 25=9+A^2 \\ 25-9=A^2 \\ A^2=16 \\ A=\sqrt[]{16} \\ A=4 \\ \text{Thus Cos B=}\frac{Adjacent\text{ }}{\text{Hypotensue}} \\ \text{Cos B=}\frac{4}{5} \end{gathered}\)Now that we have obtained the values of Cos B and Sin A, we can then go on to solve the original problem.
\(\begin{gathered} \text{Cos(A}-B)=\text{CosACosB}+\text{SinASinB} \\ Cos(A-B)=\mleft\lbrace\frac{8}{17}\times\frac{4}{5}\mright\rbrace+\mleft\lbrace\frac{15}{17}\times\frac{3}{5}\mright\rbrace \\ \text{Cos(A-B)=}\frac{32}{85}+\frac{45}{85}_{} \\ \text{Cos(A}-B)=\frac{77}{85} \end{gathered}\)
15,23,31,39, find the 60th term
Answers
Answer:
487
Step-by-step explanation:
We can use this formula to find the 60th term:
8n+7
What is 100% as a fraction
Answers
Answer:
1/1
100% as a fraction can be written as 1/1, which can be "simplified" to 1. In other words, 100% is the whole.
Hope this helps ^-^
The U.S. Senate consists of 100 senators, with 2 from each of the 50 states. There are 50 Democrats in the Senate. A committee of size 10 is formed, by picking a random set of senators such that all sets of size 10 are equally likely. a) Find the expected number of Democrats on the committee. b) Find the expected number of states represented on the committee (by at least one senator) c) Find the expected number of states such that both of the state's senators are on the committee.
Answers
Note that based on probabilities,
The expected number of Democrats on the committee is 5.
The expected number of states represented on the committee is 26.
The expected number of states such that both of the state's senators are on the committee is 9.09.
How is this so ?a) The probability that a randomly chosen senator is a Democrat is 50/100 = 1/2.
So, the expected number of Democrats on a committee of size 10 is
1/2 * 10 = 5.
b) The minimum number of states that can be represented on a committee of size 10 is 2, and the maximum numberis 50.
The expected number of states representedon the committee is the average of these two values, which is (2 + 50)/ 2 = 26.
c) There are 50 states, and each state has 2 senators. So, there are a total of 100 pairs of senators.
The probability that a randomly chosen pair of senators both belong to the same state is 50/100 * 49/99
= 1/11.
The expected number of states such that both of the state's senators are on the committee is 100 * 1/11 = 9.09.
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We call a natural number "nice" if there are only even digits in its recording. How many "nice" four-digit numbers are there?
Answers
Answer:
I suppose that this refers to numbers like:
N = abcd
Where a, b, c and d are single digits.
We want to find the number of 4-digit numbers such that:
a, b, c and d are even numbers.
So let's count the number of options for each digit, where we impose that the possible digits must be even.
a: Here we have the options {2, 4, 6, 8} ( 0 is an even digit, but if we take a = 0, then this would be a 3 digit number) Then we have 4 options for a.
b: Here we have the options {0, 2, 4, 6, 8}. 5 options in total.
c: Here we have the options {0, 2, 4, 6, 8}. 5 options in total.
d: Here we have the options {0, 2, 4, 6, 8}. 5 options in total.
The total number of possible combinations will be equal to the product of the number of options for each selection.
C = 4*5*5*5 = 500
There are 500 "nice" numbers of 4-digits.
Blair's new computer cost $5 less than twice the cost of her old
computer. Her new computer cost $709. How much did Blair's old
computer cost?l
Answers
Therefore , the solution of the given problem of expressions comes out to be cost $357.
What does an expression mean?It is preferable to use moving integer variables, which can be rising, decreasing, or blocking, rather than estimates that are generated at random. They could only assist one another by exchanging resources, knowledge, or answers to problems. A declaration of truth equation may include the justifications, components, and mathematical comments for strategies like extra disapproval, production, and mixture.
Here,
Let's say Blair's previous PC cost "x" dollars.
Her new computer cost $5 less than twice as much as her previous one, according to the information provided, which can be written as:
=> Cost of Blair's new computer = 2x - 5
She also purchased a new PC, which cost her $709. In light of these two bits of knowledge, we can construct the following equation:
=> 2x - 5 = 709
In order to find "x," add 5 to both parts, divide by 2, and we get:
=> 2x = 714
=> x = 357
Blair's previous PC therefore cost $357.
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Which of these health care plans do federal and state governments offer?
Answers
Answer:
For Plato, the answer is A: Medicaid and Medicare
What's the value? (yelping for help)
Answers
cos(20°) is the correct answer.
Congratulations! This is the unit circle. Literally everyone hates this. Everyone takes this in Trigonometry though, and it's required. I literally failed Trigonometry because of this and had to retake it when getting my degree in Mathematics.
So, what is the x-coordinate of this? Well, for any angle or (angle in triangle) \(\alpha\), the coordinates are always (\(cos(\alpha), sin(\alpha)\)).
In this case, angle \(\alpha\) is 20°, and so the x-coordinate will be cos(20°) while the y-coordinate will be sin(20°).
Hope this helped!
Answer: cos 20
Step-by-step explanation:
can someone simplify these please?
1. (-5) - (-6) +(-1)
2. (-3.1) - (-7.5) + (+1.8)
3. (-9) + (-2) - (-6) + (-5)
Answers
1. 0
2. 12.4
3. -10
Which of the following is not a piece of required information in order to determine sample size? a. estimated population standard deviation b. estimated population median c. acceptable level of sampling error d. desired level of confidence e. All are necessarv to determine sample size.
Answers
E. All are necessary to determine sample size is not a piece of required information in order to determine sample size.
Determining an appropriate sample size is an important step in the research process as it helps to ensure that the results from the sample will be representative of the population as a whole. In order to accurately determine the appropriate sample size, you need to have an estimated population standard deviation, an estimated population median, an acceptable level of sampling error, and a desired level of confidence. The population standard deviation and median will help you determine the central tendency and variability of the population, while the acceptable level of sampling error and desired level of confidence will help you determine the margin of error you are willing to accept in your results. All four of these pieces of information must be taken into consideration in order to accurately determine the appropriate sample size.
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solve the following equation show your work 3{-x + (2x + 1)} = x - 1
Answers
Answer:
x = -2
Step-by-step explanation:
For this problem, we must simply solve for x. To do this, we will need equation operations, and the use of the distributive property.
Let's work this line by line until we have the value for x:
3{-x + (2x + 1)} = x - 1
3*-x + 3*(2x + 1) = x - 1
-3x + 6x + 3 = x - 1
3x + 3 = x - 1
2x = -4
x = -2
Now we can check our answer for x by plugging back into the original equation and see if the left hand side is equal to the right hand side:
3{-x + (2x + 1)} = x - 1
3{-(-2) + (2(-2) + 1)} ?= (-2) - 1
3{2 + (-4 + 1)} ?= -3
3{2 + (-3)} ?= -3
3{-1} ?= -3
-3 == -3
Thus, we have found the solution for x to be equivalent to negative 2.
Cheers.
Answer:
x = - 2Step-by-step explanation:
3{-x + (2x + 1)} = x - 1
First solve the terms in the bracket first
That's
3 (- x + 2x + 1 ) = x - 1
3( x + 1) = x - 1
Expand the terms in the bracket
We have
3x + 3 = x - 1
Simplify
3x - x = - 1 - 3
2x = - 4
Divide both sides by 2
We have the final answer as
x = - 2Hope this helps you
which is the solution set for ?
- 4 (-x+a)+5<8
Answers
The solution of the given function is x < 3 + 4a.
What is a function?
A function is uniquely represented by the set of all pairings (x, f (x)), known as the function graph, which is a popular way of visualizing the function. When the domain and codomain are real number sets, each pair may be thought of as the Cartesian coordinates of a point in the plane. Functions are frequently employed in science, engineering, and the majority of mathematical areas. Most disciplines of mathematics say that functions are "the major subjects of investigation." If the domain and codomain set of two functions f and g are the same and their output values agree over the whole domain, they are equivalent.
The solution of the given function is
-4(-x+a)+5<8
or, 4x - 4a + 5 < 8
or, x < 8 - 5 + 4a
or, x < 3 + 4a
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z = 2 is what percentile? percentile state your answer to the nearest tenth of a percent.
Answers
The value of 2 is at the 0.1 percentile is the answer.
The percentile rank refers to the percentage of the distribution that falls at or below a given score. In statistics, percentiles are used to compare measurements, ranking, and scoring between different entities.
In this scenario, z=2 is what percentile is the question to be answered.
To solve the problem, the Z-score formula is used, which is given by; $$Z = (x - μ) / σ$$ where; Z is the standard score, x is the value of interest, μ is the mean, and σ is the standard deviation of the population.
For instance, assume a normal distribution with a mean of 10 and a standard deviation of 2.5.
Using the z-score formula, we get: Z = (2 - 10) / 2.5 = -3.2
Therefore, Z = -3.2 corresponds to the .1 percentile.
This implies that the value of 2 is greater than 0.1% of the population, meaning that it is close to the lowest score of the distribution.
The value of 2 is at the 0.1 percentile.
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Help me with with this please
Answers
Answer: (4.5 , 6.5)
-11 + 20 / 2 = 4.5
14 + (-1) / 2 = 6.5
Your friend says that 1 liter is equal
to 1 cup because 1 = 1. Do you
agree?
Answers
Answer:
No
Step-by-step explanation:
A liter and a cup are totally different units; therefore, unless a liter and a cup are equal, it can't be possible.