She made sales of =$61,200.00
WHAT is compound intrest?Compound interest is, to put it simply, interest that is earned on interest. Compound interest is interest that is earned on both the initial principal and interest that builds up over time in a savings account.Over time, you will earn more interest if an account has a greater interest rate and compounding occurs more frequently. Compound interest is calculated as follows:Initial balance = 1 + (interest rate / period's worth of compoundings).acc to our question-
Step-by-step explanation:
1.5% = 0.015 , 4% = 0.04 , 5% = 0.05
16,000 × 0.015 = $240.00
$25,000 × 0.04 = $1,000.00
$2,250.00 - ($240.00 + $1,000.00) = $1,010.00
$1,010.00 ÷ 0.05 = $20,200.00
$20,200.00 + $25,000.00 + $16,000.00 = $61,200.00
hence,She made sales of =$61,200.00
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A tutor has 21 students in their tutor group. Within this group,
15 students have attended at least one tutorial. Calculate the
percentage of students in this tutor group who have attended at least
one tutorial.
Give your answer correct to the nearest whole number.
The percentage of students in the tutor group that have attended at least one tutorial is 71%
How to find the percentage?The percentage of students who have attended at least a single tutorial in the tutor group can be found by the formula:
= Number of students who attended at least one tutorial / Total number of students in tutor group x 100%
Number of students who attended at least one tutorial = 21 students
Total number of students in tutor group = 15 students
The percentage is therefore:
= 15 / 21 x 100%
= 0.7142857 x 100%
= 71.42%
= 71%
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The volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P. Suppose that V= 70 cm^3 when T = 420 kelvin and P = 18 kg/cm^2 . Find the pressure when T = 140 kelvin and V = 60 cm^3.
In a case where the expression is give as volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P, then the pressure will be 7kg/cm^2.
How can the pressure be calculated?V = k T/ P
and V= 70 cm^3
T = 420 kelvin
P = 18 kg/cm^2
where K is constant of proportionality,
70 =( k * 420) / 18
k = (70 * 18) / 420
k= 3
Then we were given that the pressure=?
T = 140 kelvin
V = 60 cm^3
then V = k T/ P
P= kT/V
P= (3*140)/60
=7
Then the pressure is 7kg/cm^2
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hellp foo You are considering different investment strategies to save for your retirement.
Option 1: You invest $25/ month at a rate of 3.25% APR compounded monthly for 30 years.
Option 2: You invest $75/ quarter at a rate of 4.00% APR compounded monthly for 30 years.
Option 3: You invest $1,000 at a rate of 6.25% APR compounded monthly for 30 years.
1) Which option was the least amount invested and what was the investment plan?
2) Which option yielded the highest amount at the end of the 30 years and what was the basis of the plan?
3) What is the difference in the principal invested for the highest and lowest final balances? What is the difference in the interest earned?
4) Is it better to invest more money in the beginning or the end of the 30 years?
1) Option 3 had the least amount invested. The investment plan was to invest a certain amount in the beginning and let it grow at an interest of 6.25% APR compounded monthly for 30 years.
2) Option 2 yielded the highest amount at the end of 30 years. The plan was to invest $75/quarterly i.e, $25/monthly at an interest of 4.00% APR compounded monthly for 30 years.
3) Difference in principle is $8000 and the difference is interest is $2976.83
4) It is better to invest more at the end of 30 years.
Define interest.
When you borrow money, you must pay interest, and when you lend money, you must charge interest. The most common way to represent interest is as a percentage of a loan's total amount per year. The loan's interest rate is denoted by this proportion.
Solution Explained:
First, let's calculate the amount after adding the compound interest using
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex], where P is principal, r = interest rate, n = number of times interest is compounded monthly, and t = time
After calculation (For Op 1 and 2, the principal is $9000 and 3 is $1000)
Option 1 has $15275.50
Option 2 has $17467
Option 3 has $6489.17
Interest for Option 1 = $6275.50
Interest for Option 2 = $8466
Interest for Option 3 = $5489.17
After this solving the questions will be easy to understand.
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Answer:
contributions:
1 $25/ month at a rate of 3.25% APR
2 $75/ quarter at a rate of 4.00%
3 $1,000 at a rate of 6.25% APR
total interest rate:
1 $6275.50
2 $8466
3 $5489.17
final balances:
1 $15275.50
2 $17467
3 $6489.17
questions 1-4
1: Option 3 had the least amount invested
2: option 2
3: Difference is $8000 – and interest difference in $2976.83
4: it’s better to invest more at the end of 30 years
Step-by-step explanation:
i did the assignment
What is the y-intercept of the graph shown?
Responses
b=2b
b=−2b
b=−3b
b=3b
The y-intercept of the graph as shown is 2.
How to find the y-intercept of a line?The equation of a line can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptThe y-intercept is the point where the graph intersects the y-axis. In other words, it is the value of y when x = 0 .
Therefore, let's trace the value of y when x = 0 on the graph.
Hence, when x = 0, y = 2
Therefore,
b = y-intercept = 2
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Answer:b=2b
b=−2b
b=−3b
b=3b
Step-by-step explanation: because I tought myself i know
Question 2 (1 point) Find the area of a triangle with two sides measuring 6 meters and 8 meters with an included angle of 137 degrees. D. 15.8 m² OB. 12. 7m² Oc 16.4m² A. 14.3 m²
Answer:
1). True
2). x = 16.4 m^2
3). A = 24, h = 4
4). A = 18.39
5). 162
Step-by-step explanation:
I took this quiz on K12 and got everything correct! Brainliest welcome! :)
After raining for 3/4 of an hour, a rain gauge 2/5 of the way full if it continued to rain at the same rate for 15 more minutes what fraction of the rain gauge will be filled
When it rains at the same rate for 15 more minutes, the fraction of the rain gauge that will be filled is 2/15.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.
From the information, after raining for 3/4 of an hour, a rain gauge 2/5 of the way full. It's important to note that 3/4 is (3 × 1/4).
Therefore, we will divide 2/5 by 3 and this will be:
= 2/5 ÷ 3
= 2/5 × 1/3
= 2/15
This is the value of the rain gauge.
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4x (x + 10) + 55 = 180
x = 5/2 and x = -25/2 are the solutions to the equation 4x (x + 10) + 55 = 180.
What is the solution to the quadratic equation?Given the equation in the question;
4x (x + 10) + 55 = 180
To solve for x, apply distributive property to eliminate the parenthesis.
4x (x + 10) + 55 = 180
4x(x) + 4x(10) + 55 = 180
4x² + 40x + 55 = 180
4x² + 40x + 55 - 180 = 0
4x² + 40x - 125 = 0
Now, we use the quadratic formula to solve the quadratic equation.
x = (-b±√(b² - 4ac)) / (2a)
From 4x² + 40x - 125 = 0
a = 4b = 40 c = -125Plug these into the formula and solve for x.
x = (-b±√(b² - 4ac)) / (2a)
x = ( -40 ± √( (40)² - ( 4 × 4 × -125))) / ( 2 × 4 )
x = ( -40 ± √( 1600 - ( -2000) )) / ( 8 )
x = ( -40 ± √( 1600 + 2000 )) / ( 8 )
x = ( -40 ± √( 3600 )) / ( 8 )
x = ( -40 ± 60) / ( 8 )
x = ( -40 - 60) / ( 8 ), ( -40 + 60) / ( 8 )
x = ( -100 )/( 8 ), ( 20 )/( 8 )
x = -25/2, 5/2
Therefore, the solution to the quadratic equation is x = -25/2, 5/2.
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mathhhhhhhhhhhhhhhhhhhh
Answer: x = 4. This solution relates to the original equation because when you substitute x for 4, the equation will simplify correctly as 0 = 0.
Step-by-step explanation:
To solve, we will isolate the variable with inverse operations.
Given:
3x - 12 = 0
Add 12 to both sides of the equation:
(3x - 12) + 12 = (0) + 12
3x = 12
Divide both sides of the equation by 3.
(3x) / 3 = (12) / 3
x = 4
This solution, x = 4, relates to the original equation because when you substitute x for 4, the equation will simplify correctly as 0 = 0.
Answer:
x=4
Step-by-step explanation:
3x-12 = 0
Solve the equation
Add 12 to each side using the addition property of equality
3x-12+12 = 0+12
3x= 12
Divide each side by 3 using the division property of equality
3x/3 = 12/3
x = 4
The solution is what satisfies the original equation
Given that f(x) = x² 13x + 30 and
g(x)= x-3, find f(x) · g(x) and
express the result as a polynomial in simplest form.
The simplest polynomial form of f(x)×g(x) is x³ - 16x² + 69x - 90.
What is a polynomial?An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).Sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer, makeup polynomials. For instance, the polynomial 3x+2x-5: A description of polynomials.So, f(x) × g(x):
Calculate as follows:
Therefore, the simplest polynomial form of f(x)×g(x) is x³ - 16x² + 69x - 90.
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Question 13(Multiple Choice Worth 2 points)
(Multi-Step Percent Problems MC)
A gaming system costs $600 and is on sale for 35% off. After the discount, there is a 5% tax. What is the final price of the gaming system?
$409.50
$390.00
$220.50
$210.00
I need help I’ve been stuck on this problem for like 40 minutes already!!!
Given that 150 students were interviewed, 85 signed for mathematics, 70 signed for English, and 50 signed for both. Draw a venn diagram to show.
How many signed for only mathematics
How many signed for English only
English or Mathematics
Neither English nor Mathematics
English and Mathematics
1. 35 signed up for only mathematics
2. 20 signed up for only English
3. 85 or 70 is English or mathematics
4. Neither math or English is 45
5. English and Math is 50
How to solve the Venn diagram1. How many signed for only mathematics
We have to define only mathematics as x
while we have math = m
English as E
Math and English as ME
only math
X = M - ME
= 85 - 50
= 35
2. Only English
E - ME
= 70 - 50
= 20
3. English or mathematics =
85 or 75
4. Neither English nor Mathematics
150 - (85 + 70 - 50)
= 45
5. The number for math and English is what is the intersection = 50
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A sea otter is underwater. Its position below sea level changes by -73.5 ft in 3 minutes. What is the
average change in the otter's position each minute? Is the otter going deeper or toward the surface of
the water? Explain your reasoning. Show your work!!! (4 pts)
Change in Otter's position per minute:
The otter is swimming..
The average change in the otter's position each minute is -24.5 ft per minute and the otter goes deeper.
What is average change?
The ratio of "change in the function values" to "change in the interval endpoints" is referred to as the average rate of change of a function f(x) over an interval [a, b].
Here, we have
Sea level changes by -73.5 ft in 3 minutes
So, we apply the average change formula, and we get
= -73.5/3
= - 24.5 ft per minute
And the otter goes deeper because - 24.5 < 0
Hence, the average change in the otter's position each minute is -24.5 ft per minute and the otter goes deeper.
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2. When a large truckload of mangoes arrives at a packing plant, a random sample of 150 is selected and examined for
bruises, discoloration, and other defects. Suppose 15 mangoes do not meet the required standards.
(a) Estimate with 90% confidence the percent of all mangoes on the truck that fail to meet the standards.
(b) What was the margin of error associated with your estimate. Explain its meaning.
(c) Explain the meaning of “90% confidence” in the context of this application.
(d) What would be the most conservative sample size necessary to estimate the true percent of mangoes that fail to
meet standards within 3% at 90% confidence?
a) The 90% confidence interval of the percentage of all mangoes on the truck that fail to meet the standards is: (7.55%, 12.45%).
b) The margin of error is: 2.45%.
c) The 90% confidence is the level of confidence that the true population percentage is in the interval.
d) The needed sample size is: 271.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The variables are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.90}{2} = 0.95[/tex], so the critical value is z = 1.645.
The sample size and the estimate are given as follows:
[tex]n = 150, \pi = \frac{15}{150} = 0.1[/tex]
The margin of error is of:
[tex]M = z\sqrt{\frac{0.1(0.9)}{150}} = 0.0245 = 2.45\%[/tex]
The interval is given by the estimate plus/minus the margin of error, hence:
The lower bound is: 10 - 2.45 = 7.55%.The upper bound is: 10 + 2.45 = 12.45%.For a margin of error of 3% = 0.03, the needed sample size is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.1(0.9)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.1(0.9)}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.1(0.9)}}{0.03}[/tex]
[tex](\sqrt{n}})^2 = \left(\frac{1.645\sqrt{0.1(0.9)}}{0.03}\right)^2[/tex]
n = 271 (rounded up).
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The depth of a local river averages 20 ft, which is represented as |−20|. In January, it measured 6 ft deep, or |−6|, and in July, it was 22 ft, or |−22|. What is the difference between depths in January and July?
Answer: 2 ft.
Step-by-step explanation:
|-20| = 20, |-22| = 22
22 - 20 = 2
IQ is normally distributed with a mean of 100 and a standard deviation of 15. a) Suppose one individual is randomly chosen. Find the probability that this person has an IQ greater than 95. Write your answer in percent form. Round to the nearest tenth of a percent. P (IQ greater than 95) = % b) Suppose one individual is randomly chosen. Find the probability that this person has an IQ less than 125. Write your answer in percent form. Round to the nearest tenth of a percent. P (IQ less than 125) = % c) In a sample of 600 people, how many people would have an IQ less than 110? people d) In a sample of 600 people, how many people would have an IQ greater than 140? people
Am I correct? Did I do this right?
Answer:
Step-by-step explanation:
Yes, you did it right.
What is 10,483,190 in word form?
Answer:
Ten million, Four hundred eighty-three thousand, one hundred ninety
Step-by-step explanation:
Break it down! into the tens digit, hundreds digit, etc.
Use the equation below to find p, if m = 5 and v = 23.
p = mv
The numerical value of p in the equation p = mv, when m = 5 and v = 23 is 115.
What is the value of p in the given equation?Given the equation in the question;
p = mvm = 5v = 23To determine the value of p, plug in the values of m and v and simplify.
p = mv
Plug in m = 5 and v = 23
p = 5 × 23
Multiply 5 and 23
p = 115
Therefore, the value of p is 115.
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Answer:
115
Step-by-step explanation:
m = 5
v = 23
p = mv
p = (5)(23)
p = 115
Pls help would really mean a lot
Answer:
Use AAA congurency rule
Step-by-step explanation:
1 angle=52
2 angle=58
3 angle=78
Peter and Parker work for a cleaning crew. Peter can clean a room in 15 minutes less time than it takes Parker to do the same job. Working together,
they can clean two rooms in 110 minutes. Approximately how long does it take Peter to clean a room by himself?
Peter will take 47.5 minutes to clean the room.
In the question ,
it is given that ,
Peter and Parker are working for a cleaning crew ,
let the time taken by Parker to clean the room is = x minutes .
So ,according to the question ,
time taken by Peter to clean the room is = (x - 15) minutes .
Working together, they clean two rooms in 110 minutes
which is represented , by the equation ,
x + x - 15 = 110
2x = 110 + 15
2x = 125
x = 125/2
x = 62.5
Parker takes 62.5 minutes and Peter takes 47.5 minutes .
Therefore , Peter will take 47.5 minutes to clean the room .
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Write an equation in standard form of the line that passes through
(–9, 4) and has a slope of –2/3.
(Add explanation please )
Also, Write the standard form of the equation y + 4 = – ⅗ (x – 8).
Answer:
2x + 3y = - 63x + 5y = 4-------------------------------
Standard form of a lineax + by = cGivenPoint on the line (-9, 4) and a slope m = - 2/3Use point- slope form and convert to standardy - y₁ = m(x - x₁), where (x₁, y₁) is the point on the liney - 4 = - 2/3(x - (-9))y - 4 = - 2/3(x + 9)3(y - 4) = - 2(x + 9)3y - 12 = - 2x - 182x + 3y = 12 - 182x + 3y = - 6Standard of the line y + 4 = - 3/5(x - 8)y + 4 = - 3/5(x - 8)5(y + 4) = - 3(x - 8)5y + 20 = - 3x + 243x + 5y = 24 - 203x + 5y = 4A self-employed person who completes work on a project-by-project basis is
known as:
A. an independent contractor.
B. a wage-earning employee.
C. an exempt employee.
OD. a salaried employee.
SUBMIT
Answer:
A: Independent contractor
Step-by-step explanation:
There are 12 red balls and 7 green balls in a
non-transparent black bag. What is the
least number of balls we need to take out to be certain we have taken out the
following?
two green or two red balls
The least number of balls we require to take out to be sure that we have two green or two red balls is 14.
What is the combination of balls?In the bag, there are a total number of balls of;
Total number of balls = 12 + 7 = 19 balls
Inside the bag, we have 12 red balls and 7 green balls.
The balls are selected without replacement, and this means that they are removed from the bag, and replaced back.
In theory, we could pick 12 balls, and all 12 being red, while also 13, with 12 red and 1 green e.t.c
Therefore, at least 14 balls are needed to guarantee that there are at least 2 green or two red balls
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For Zendaya's lemonade recipe, 3 lemons are required to make 18 cups of lemonade. At what rate are lemons being used in cups of lemonade per lemon?
The unit rate of cups of lemonade per lemon is in the ratio of 6:1.
What is the unit rate?The unit rate is the ratio of two or more quantities or values that are compared to one another.
Unit rates are also known as the constants of proportionality, constant rate, rate of change, or slope.
Zendaya's Lemonade Recipe:The number of lemons required to make 18 cups of lemonade = 3 lemons
Rate of lemonade per lemon = 18/3 = 6/1
Ratio = 6:1 or 1:6
Conversely, the rate of lemon per cup of lemonade = 1/6
Thus, we can conclude that for Zendaya to make 6 cups of lemonade, she requires 1 lemon, or alternatively, the ratio of lemon to a cup of lemonade is 1:6.
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Find the square root that is a real number
The square root of √-36 is 0.
What is square root?A number can be obtained by multiplying the square root of that integer by itself. The word "square root" is represented by the symbol "sqrt"—square root of, end square root. The opposite of squaring an integer is finding its square root. In mathematics, a square root is a factor that, when multiplied by itself, equals the original integer. For instance, the square roots of 9 are both 3 and -3.So, √-36:
Calculate the square root as follows:
Therefore, the square root of √-36 is 0.
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A person deposits $8,000 into a savings account at an interest rate of 6.5%. The interest is compounded quarterly. If no other money is deposited into the account, what will the balance be after 12 years? Round to the nearest cent.
If a person deposits $8,000 into a savings account at 6.5% interest compounded quarterly for 12 years, the balance (future value) will be $17,342.70.
What is the future value?The future value is the compounded present value of an investment for a future period.
The future value can be computed using the FV formula, table, or an online finance calculator as below.
N (# of periods) = 48 quarters (12 years x 4)
I/Y (Interest per year) = 6.5%
PV (Present Value) = $8,000
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $17,342.70
Total Interest = $9,342.70
Thus, the future value of a present investment of $8,000 at 6.5% interest compounded quarterly for 12 years is $17,342.70.
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What number when multiplied by 1 1/4 has a product of 1
Answer: 4/5 or 0.8
Step-by-step explanation:
[tex]1\frac{1}{4}[/tex] * [tex]\frac{4}{5}[/tex] = [tex]\frac{1}{1}[/tex] = 1
[tex]1\frac{1}{4}[/tex] is also equal to 1.25.
1.25 * 0.8 = 1
Answer:
4/5
Step-by-step explanation:
because 4 is half of a half two fourths are a half and 4/4 are 1 whole
f(x)=x² +6
Find an equation for the tangent line to the graph of f(x) = x² +6 at (5,31).
y=
Answer:
y = x^2 + 6 given equation
y = m x + b equation of straight line required
dy/dx = 2 x tangent to given curve
dy/dx = slope = 2 * 5 = 10
Thus our line must be of the form
y = 10 x + b
31 = 10 * 5 + b at the point required
b = 31 - 50 = -19
Then our final equation becomes
y = 10 x - 19
Write a quadratic function h whose only zero is −13.
The quadratic function whose only zero is -13 is h(x) = x² + 26x + 169
Quadratic functionFrom the question, we are to write a quadratic function whole only zero is -13.
Since -13 is the only zero of the function,
Then,
x = -13 twice
This means that (x + 13) is a factor of the function
Since x = -13 twice,
Then,
The quadratic function h is
h(x) = (x + 13)(x + 13)
Expand the quadratic function by distributing
h(x) = x(x + 13) + 13(x + 13)
h(x) = x² + 13x + 13x + 169
h(x) = x² + 26x + 169
Hence, the function is h(x) = x² + 26x + 169
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