Mr. Wilson invested money in two accounts. His total investment was $20,000. If one account pays 5% in interest and the other pays 2% in interest, how much does he have in each account if he earned a total of $550 in interest in 1 year?
Answers
a = amount invested at 5%
b = amount invested at 2%
now, we know the total invested by Mr Wilson was 20000, so whatever "a" and "b" might be, we know that a + b = 20000.
\(a + b = 20000\implies b = 20000-a \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{5\% of a}}{\left( \cfrac{5}{100} \right)a}\implies 0.05a~\hfill \stackrel{\textit{2\% of b}}{\left( \cfrac{2}{100} \right)a}\implies \begin{array}{llll} 0.02b\\\\ \stackrel{substituting}{0.02(20000-a)} \end{array}\)
now, we know the total of earned interest is 550 bucks, so then
\(0.05a~~ + ~~0.02(20000-a)~~ = ~~550\implies 0.05a+400-0.02a=550 \\\\\\ 0.03a+400=550\implies 0.03a=150\implies a=\cfrac{150}{0.03}\implies a=5000 \\\\\\ ~\hspace{24em}\stackrel{20000~~ - ~~5000}{b=15000}\)
Related Questions
A national grocery store chain designed a study to determine whether its customers would be interested in home delivery. The
chain randomly surveyed 1,000 customers from around the country. It concluded from the study that 80% of all customers who
hopped in the chain's stores were interested in the service. What is the sample in the study?
Answers
The group of people who participated in the study's sample survey was chosen at random to participate in it by the national grocery store chain. In this instance, the sample comprises the 1,000 customers from throughout the nation that participated in the survey. They are a segment of the total consumer base that frequents the chain's retail outlets.
The chain randomly surveyed 1,000 customers from around the country. It concluded from the study that 80% of all customers who hopped into the chain's stores were interested in the service. The nationwide grocery store chain randomly selected the participants in the study's sample survey from the general public.
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b. An investment worth i costs $10 to withdraw, then the remaining amount is shared
between four people. Suppose each person gets $40. How much was the
investment worth?
Equation:
Solve it:
Answers
Answer:
the equation 10 = x - y
Step-by-step explanation:
Let x represent the initial value of the investment, and let y represent the amount of money that each person receives after the investment is withdrawn.
We know that the cost of withdrawing the investment is $10, so we can write the equation 10 = x - y. We also know that each person receives $40, so we can write the equation y = 40.
We can now solve for x by substituting the value of y into the first equation. Since y = 40, we can substitute 40 for y in the equation 10 = x - y to get 10 = x - 40. Solving this equation for x, we find that x = 50.
Therefore, the initial value of the investment was $50.
Cliff takes out a $5,000 personal loan with 7
fixed annual interest compounded monthly to pay for his wedding. He repays the loan in 2 year.s
How much total interest does Cliff pay on his loan?
Answers
Cliff pays a total interest of approximately $679.90 on his $5,000 loan.
To calculate the total interest paid on the loan, we need to use the formula for compound interest:
\(A = P(1 + r/n)^{(nt)}\)
Where:
A is the final amount (loan amount + interest)
P is the principal (loan amount)
r is the annual interest rate (in decimal form)
n is the number of times interest is compounded per year
t is the number of years
Given that Cliff takes out a $5,000 loan with a fixed annual interest rate of 7% compounded monthly, we can substitute the values into the formula:
P = $5,000
r = 7% = 0.07
n = 12 (monthly compounding)
t = 2 years
\(A = 5000(1 + 0.07/12)^{(12 \times 2)\)
Calculating this expression:
A ≈ 5000\((1.00583)^{(24)\)
A ≈ 5000(1.13598)
A ≈ 5679.90
The final amount (A) is the loan amount plus the total interest paid. Therefore, to find the total interest paid, we subtract the principal (P) from the final amount (A):
Total Interest = A - P
Total Interest = 5679.90 - 5000
Total Interest ≈ $679.90
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Pls I don't understand
Answers
The unit rate of the relationship will be 10/3. The correct option is C.
The given equation is,
y = 10/3x + 8
The general form of an equation of the line is,
y = mx + c
here, the slope will be 10/3
Slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for a given change in the independent variable.
The slope of a line is represented by the ratio of the change in the y-axis (vertical) to the change in the x-axis (horizontal) between any two points on the line. It can also be interpreted as the rate of change of the dependent variable with respect to the independent variable.
A positive slope indicates an upward trend, while a negative slope indicates a downward trend. The slope of a line is often denoted by the letter m.
The unit relationship will be 10/3.
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It was cloudy 12 out of 30 days in April. Which value is equivalent to the fraction of days it was cloudy in April? (Not college its middle school btw)
Answers
Answer:
You included no options so I will list some of the various fractions and decimal that are equivalent to the fraction of days it was cloudy in April.
In fraction form, the value can be simplified to;
⁶/₁₅⁴/₁₀²/₅In decimal form, the value would be;
= 12 ÷ 30
= 0.4
17/3x+17-2/3x-15 what is the solution
Answers
Answer:
Step-by-step explanation:
\(\sf \dfrac{17}{3}x+17-\dfrac{2}{3}x-15 = \dfrac{17}{3}x-\dfrac{2}{3}x+17-15\)
\(=\dfrac{17-2}{3}x + 2\\\\\\=\dfrac{15}{3}x+2\)
How do I find the value
Answers
Answer:
A= 180-41=
A= 139 degrees
B= 180-41
B = 139 degrees
Step-by-step explanation:
On a straight line its 180 degrees
A is separating a straight line with a 41-degree angle so.
A= 180-41
A= 139 degrees
B is also separating a straight line with a 41-degree angle so.
B= 180-41
B = 139 degrees
Answer:
Hi
Please mark brainliest
What is the volume of the cone with height of 6 m and diameter of 8 m rounded to the nearest cubic meter
Answers
Answer:
101 m^3
Step-by-step explanation:
v = π * r^2 * h/3
= π * 4^2 * 6/3
v= 100.53 m^3
v= 101 m^3 to the nearest cubic meter
Please look at the pic and help!!
Answers
Answer:
4x² + 22x - 12
Step-by-step explanation:
A = bh/2
A = (4x - 2)(2x + 12)/2
A = (8x² + 48x - 4x - 24)/2
A = (8x² + 44x - 24)/2
A = 4x² + 22x - 12
Bob goes on a hike and walks at a pace of 2 1/2 miles per hour. Which rates are equivalent to 2 1/2 miles per hour? Select ALL that apply.
Answers
Answer:
Step-by-step explanation: !!DISCLAIMER IM NOT ALWAYS THE SMARTEST BUT IM PRETTY SURE THIS IS RIGHT!
!well what I did. You know that 60 minutes=one hour. So I put 2 & 1/2 over 60.
Make 2 & 1/2 a improper fraction=5/2.
So 5/2 over 60
Then divide. 5/2 divided by 60 ( which is 60/1)
Then leave change flip, meaning leave the 5/2 change the division sign to multiplication, and flip, which you would flip 60/1 to 1/60
So we have 5/2 times 1/60. Multiply across. 5 times 1= 5. 2 times 60=120
So we have 5/120
Now we simplify 120 divided by 5 = 24. And 5 divided by 5 = 1
So 1/24
That’s all I know.. I know it didn’t have the answers but I hoped it help a bit
Find f(2), f(1), f(0), and f(-1) for f(x) = 3x + 8.
Answers
Answer:
Step-by-step explanation:
Solution
When, x=2
f(2)=3×2+8
=14
Again,
When, x=1
f(1)=3×1+8
=11
When, x=0
f(0)=3×0+8
=8
When, x=-1
f(-1)= 3×(-1)+8
=5
If you found my answer useful then please mark me brainliest.
A plane flew at a constant speed between Denver and Chicago.
It took the plane 1.5 hours to fly 915 miles.
How far would the plane fly in t hours at this speed?
Answers
Answer:
\(406.66t\)
Step-by-step explanation:
1.5 : 915 = 610
610 ÷ 2 = 305
305 ÷ 3 = 101.66
101.66 × 4 = 406.66 mph
Thus, the answer is 406.66 × t
Mark Brainliest if it's correct!
Write an exponential function in the form y=ab^xy=ab
x
that goes through points (0, 13)(0,13) and (3, 832)(3,832).
Answers
Answer: Down Below
Step-by-step explanation: y=ab%5Ex
that goes through points (0, 10) and (2, 490)
y=ab%5Ex.......plug in (0, 10)
10=ab%5E0
10=a%2A1
a=10
so far
y=10b%5Ex......plug in (2, 490)
490=10b%5E2
b%5E2=490%2F10
b%5E2=49
b=sqrt%2849%29
b=7
your function is:+y=10%2A7%5Ex
A function assigns the values. The exponential function that goes through (0, 13) and (3, 832) is y=13(4)ˣ.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the exponential eqation is y=abˣ, substitute any one of the point in equation we will get,
13 = ab⁰
13 = a ₓ 1
a = 13
Therefore, the function can be written as y=13bˣ.
Substitute other point in the equation,
832 = 13 (b³)
b³ = 832/13
b³ = 64
b = 4
Hence, the exponential function that goes through (0, 13) and (3, 832) is y=13(4)ˣ.
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`H_0: p = 0.63`
`H_1: p > 0.63`
Your sample consists of 150 subjects, with 96 successes. Calculate the test statistic, rounded to 2 decimal places
`z=`
Answers
The test statistic, rounded to 2 decimal places is equal to
How to calculate value of the test statistic?For this sample, the hypothesis is given by:
H₀: μ₁ ≤ μ₂
H₁: μ₁ > μ₂
Assuming this sample has a normal distribution, we would use a pooled z-test to determine the value of the test statistic:
Substituting the given parameters into the formula, we have;
\(z = \frac{\frac{96}{150} \;-\;0.63}{\sqrt{0.63\; +\; \frac{1\;-\;0.63}{150}} }\\\\z = \frac{0.64 \;-\;0.63}{\sqrt{0.63\; +\; \frac{0.37}{150}}}\\\\z = \frac{0.01}{\sqrt{0.63\; +\; 0.0025}}\\\\z = \frac{0.01}{\sqrt{0.6325}}\\\\\)
z = 0.01/0.7953
z = 0.013.
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At a dinner, the meal cost $22 and a sales tax of $1.87 was added to the bill.
How much would the sales tax be, in dollars and cents, on a $66 meal?
Answers
What is (123
) ÷ (18
)?
Answers
Answer:
6.8333333333 or 41/6
Step-by-step explanation:
Mr. Jackson needed to sell his camper. He priced it at $75,000 the first day. The second day he reduced the price by 15%. What was the price of the car after this reduction?
A.$11,250
B.$63,750
C.$60,000
D.$86,325
Answers
Answer: the answer is b
Step-by-step explanation:
\( \frac{a(3 + a)}{3} \leqslant \frac{z(a - 1) {}^{2} }{15} - \frac{(a - 1)(4 - a)}{5} + \frac{1}{5} \)
can anyone help me?
Answers
z=2a^2/(a-1)^2 + 30a/(a-1)^2 - 15/(a-1)^2
an even number. each card is worth a different number of points (this point value is written on the card). alice and bob then take turns removing either the leftmost or rightmost card from the row, until all the cards are gone. at that point, the player who has collected the most points is declared the winner.
Answers
The best strategy for Alice is to take the card with the highest point value. This will maximize her chances of winning, since she can then choose the last card from the remaining cards. Bob should take the card with the lowest point value, as this will minimize Alice's chances of winning.
Alice always takes the first turn. Bob can either take the leftmost card or the rightmost card. If Alice takes the leftmost card and Bob takes the rightmost card, then Alice will have the advantage of being able to make the last move. If Bob takes the leftmost card and Alice takes the rightmost card, then Bob will have the advantage of being able to make the last move.
The best strategy for Alice is to take the card with the highest point value. This will maximize her chances of winning, since she can then choose the last card from the remaining cards. Bob should take the card with the lowest point value, as this will minimize Alice's chances of winning.
Alice should also be aware of Bob's strategy and try to anticipate what card he will take. If Alice can guess correctly, she can adjust her strategy to ensure she takes the card with the highest point value. If she guesses incorrectly, she should still attempt to take the card with the highest point value.
Alice should take the card with the highest point value and Bob should take the card with the lowest point value. Alice should also anticipate Bob's strategy and adjust accordingly to ensure she takes the card with the highest point value.
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One interior angle of a triangle is 43°, and the other two angles are congruent. Choose the equation that could be used to determine the degree measure of one of the congruent angles. 2x + 43 = 180 2x − 43 = 90 x + 43 = 180 x − 43 = 90
Answers
Answer:
x − 43 = 90
Step-by-step explanation:
2x + 43 = 180
2x − 43 = 90
x + 43 = 180
x − 43 = 90
A number is multiplied by 6, and that product is added to 3. The sun is equal to the product of 3 and 11
Answers
Answer:
x = 5
Step-by-step explanation:
3 + x * 6 = 3 * 11
3 + 6x = 33
6x = 30
x = 5
For addition, drag tiles onto the board.
To form a group, place one tile on top of another.
VX
Use the interactive tool to find the difference.
(-4)-6
Board sum: 0
Help lol
Answers
Step-by-step explanation:
Hint:Respiration is the metabolic reactions occurring in the cells to convert chemical energy from oxygen or nutrients into ATP (adenosine triphosphate). Catabolic reactions involved in respiration which break the large molecules into small molecules. This reaction occurs in a series of biochemical processes and some are redox reactions.
Please help. Miguel had 2 bags containing number tiles as shown below. Without looking, Miguel selected one tile from each bag. What is the probability that Miguel selected two numbers less than 3?
Answers
The probability of Miguel selecting a tile number less than 3 from each bag -1 is 1/5 and bag-2 is 2/5.
The given tiles in bag-1 = {2, 4, 5, 8, 9}
Total number of tiles in bag-1 = 5
The number of tiles less than number 3 in the bag - 1 = 1
The probability of Miguel selecting a tile number less than 3 =
number of tiles less than 3 / total number of tiles = 1/3
The given tiles in bag-2 = {0, 1, 3, 6, 7}
Total number of tiles in bag-2 = 5
The number of tiles less than number 3 in the bag-2 = 2
The probability of Miguel selecting a tile number less than 3 =
number of tiles less than 3 / total number of tiles = 2/3
From the above analysis, we solved the problem.
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Divide 1/4÷2/3 and express the answer in the simplest terms. If necessary, use / for the fraction bar.
1/4 ÷ 2/3 =
Answers
Answer:
3/8
Step-by-step explanation:
find the Least Common Denominator, change the numerators as needed, divide, then simplify.
Answer:
the answer is 3/8
Step-by-step explanation:
brainiest rate 5 stars and thank mee : )
You want to walk from home to a clothing store that is 3/4 miles away. You stop for a rest after 1/2 miles. How much farther do you have to walk?
Write your answer as a fraction in simplest form.
Answers
Answer:
1/4 miles.
Step-by-step explanation:
If I want to walk from my house to a clothing store 3/4 of a mile away, this implies that the location is 0.75 miles from my home.
Now, if after walking 1/2 mile I decide to stop, I will have traveled 0.5 miles in total. In this way, when I get back on my way, I will have to travel 0.25 miles to reach my destination (0.75 - 0.50).
Therefore, since 1 divided by 4 equals 0.25, I have to walk 1/4 mile to reach my destination.
X +3
2x²
2x2 - 4x -4
2x]
Squash
| 4x-7
Beans
N
W
E
Corn
Š
4x - 21
Pumpkins
2x + 5
Potatoes
X + 8
x² - 13
3x - 4x + 6
1. Write and simplify the polynomial expression that represents the length of the south side
of the field. (10 points)
Answers
Answer:
the heck is all that I can’t solve this fix it then I will
Step-by-step explanation:
Victor knows who killed his brother, but remains silent in chapters 5-8 of Frankenstein. Why?
A. He doesn't want to be executed.
B. He fears people will think he's insane if he tells the truth.
C. He is afraid Elizabeth will hate him.
D. He is afraid of being expelled from school.
Answers
Answer: b
Step-by-step explanation:
i took the quiz duhh
Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of μ = 1.1 kg and a standard deviation of o= 4.6 kg.
Complete parts (a) through (c) below.
b. If 25 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg.
The probability is
(Round to four decimal places as needed.)
Answers
The probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given,
Amounts of weight that male college students gain during their freshman year are normally distributed
mean of μ = 1.1 kg and
Standard deviation of o= 4.6 kg.
Z score=x-μ/o
=25-1.1/4.6
=23.9/4.6
=5.196
Z score=x-μ/o
=25-1.1/0
=0
Z score=25-1.1/3
=23.9/3
=7.966
By observing the z table the probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%
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Corners of equal size are cut from a square with sides of length 8 meters (see figure).
Determine the domain of the function. (Enter your answer using interval notation.)
(b) Use a graphing utility to graph the area function over its domain. Use the graph to find the range of the function. (Enter your answer using interval notation.)
What would be the length of each side s of the figure?
Answers
The domain of the function is given as -4√2 and 4√2
the length of the sides is 8cm
How to solve for the shapeThe area of this square is given as 8 x 8 = 64
each shaded triangle is a right angled triangle
1/2 *x*x = x²/2
Since we have 4 triangles we would have
4x²/2
When the triangles are cut the area would be
A = 64 - 2x²
such that 64 = 2x²
x² = 32
domain would be x = ± √32
-4√2 , 4√2
b. The solution to the graph is contained in the image that i have attached.
c. The length of each of the sides would be √64. Remember that this is a square.
Hence the length is = 8
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!! HELP IM IN 7TH GRADE AND M LEARNING 9TH AND 8TH GRADE MATH!!
QUESTION~
If f(x) = 2|x| is graphed on a regular
coordinate grid, does the graph
form an acute, right, or obtuse
angle at its vertex?
Answers
Answer:
The vertex forms an acute angle.
