Sarah invested $800 in an account paying an interest rate of 3.5% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 8 years?
Answers
Answer:
$ 1,057.22
Step-by-step explanation:
A = $ 1,057.22
A = P + I where
P (principal) = $ 800.00
I (interest) = $ 257.22
After 8 years, total amount will be $1057.
Given that,
Principal amount that invested is (P) $800.Annual interest rate is (r) 3.5% or 0.035.We need to find total amount after (t) 8 years when, interest is compounding quarterly n (4).According to the given data, calculation are as follows,
Compound interest formula,
A = [tex]P (1 + \frac{r}{n} )^{nt}[/tex]
A = [tex]800 (1 + \frac{0.035}{4} )^{4\times 8}[/tex]
A = [tex]800 (1 + 0.00875 )^{32}[/tex]
A = $800 [tex]\times[/tex] 1.3215
A = $1057.2 or $1057.
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Related Questions
In ΔMNO, the measure of ∠O=90°, the measure of ∠M=39°, and MN = 5.3 feet. Find the length of NO to the nearest tenth of a foot.
Answers
Answer:
3.3 ft
Step-by-step explanation:
Side NO is opposite the angle M, so the applicable trig relation is ...
Sin = Opposite/Hypotenuse
Opposite = Hypotenuse×Sin
NO = MN×sin(39°) = (5.3 ft)sin(39°)
NO ≈ 3.3 ft
g Suppose a factory production line uses 3 machines, A, B, and C for making bolts. The total output from the line is distributed as follows: A produces 25%, B produces 35%, and C produces 40%. The defect rate for A is 5%, B is 4%, and C is 2%. If a bolt chosen at random is found to be defective, what is the probability that it came from machine A
Answers
Answer:
The probability that it came from A, given that is defective is 0.362.
Step-by-step explanation:
Define the events:
A: The element comes from A.
B: The element comes from B.
C: The element comes from C.
D: The elemens is defective.
We are given that P(A) = 0.25, P(B) = 0.35, P(C) = 0.4. Recall that since the element comes from only one of the machines, if an element is defective, it comes either from A, B or C. Using the probability axioms, we can calculate that
[tex]P(D) = P(A\cap D) + P(B\cap D) + P(C\cap D)[/tex]
Recall that given events E,F the conditional probability of E given F is defined as
[tex]P(E|F) = \frac{P(E\cap F)}{P(F)}[/tex], from where we deduce that
[tex]P(E\cap F) = P(E|F)P(F)[/tex].
We are given that given that the element is from A, the probability of being defective is 5%. That is P(D|A) =0.05. Using the previous analysis we get that
[tex] P(D) = P(A)P(D|A)+P(B) P(D|B) + P(C)P(D|C) = 0.05\cdot 0.25+0.04\cdot 0.35+0.02\cdot 0.4 = 0.0345[/tex]
We are told to calculate P(A|D), then using the formulas we have
[tex] P(A|D) = \frac{P(A\cap D)}{P(D)}= \frac{P(D|A)P(A)}{P(D)}= \frac{0.05\cdot 0.25}{0.0345}= 0.36231884[/tex]
WILL MARK BRAINLIEST!
I thought of a three-digit number. If I add all the possible two-digit numbers made by using only the digits of this number, then one third of this sum is equal to the number I thought of. What is the number I thought of?
Answers
Answer:
198
Step-by-step explanation:
If you add 11,18, 19, 81, 88, 89, 91, 98, 99 then the sum would be 594 then dividing by 3 would be 198.
PLZ MARK BRAINLIEST!!!
5 Points
Multiply (x2 + 3x + 4)(3x2 - 2x + 1).
O A. 4x2 + x + 5
O B. 3x4 + 11x + 19x2 + 11x + 4
O C. 3x4 - 6x2 + 4
O D. 344 + 7 x° +7x2 - 5x+ 4
Answers
Answer: 3x^4+7x^3+7x^2+11x+4
Step-by-step explanation:
(x^2+3x+4)(3x^2-2x+1)
3x^4-2x^3+x^2+9x^3-6x^2+3x+12x^2-8x+4
Collect like terms
3x^4-2x^3+9x^3+x^2-6x^2+12x^2+3x+8x+4
3x^4+7x^3+7x^2+11x+4
Answer:
To multiply (x^2 + 3x + 4) and (3x^2 - 2x + 1), we need to distribute each term of the first polynomial to every term in the second polynomial:
(x^2 + 3x + 4)(3x^2 - 2x + 1)
= x^2 * (3x^2 - 2x + 1) + 3x * (3x^2 - 2x + 1) + 4 * (3x^2 - 2x + 1)
Now, let's simplify each term:
= 3x^4 - 2x^3 + x^2 + 9x^3 - 6x^2 + 3x + 12x^2 - 8x + 4
Combining like terms:
= 3x^4 + (-2x^3 + 9x^3) + (x^2 - 6x^2 + 12x^2) + (3x - 8x) + 4
= 3x^4 + 7x^3 + 7x^2 - 5x + 4
So, the product of (x^2 + 3x + 4) and (3x^2 - 2x + 1) is 3x^4 + 7x^3 + 7x^2 - 5x + 4.
Therefore, the correct answer is option C: 3x^4 + 7x^3 + 7x^2 - 5x + 4.
Drew is driving out of state to go to a theme park. The total distance he is driving is 500.34 miles. He has driven 0.45 of the
distance so far, Drew calculated that he has driven 250.17 miles.
Is Drew's calculation reasonable or not? Explain your answer. If his calculation is not reasonable, determine the number of miles
Drew has actually driven.
Answers
The calculation is not reasonable, because 0.45 is less tha 1/2 ( 0.50) and what he has for an answer is half the distance ( 250.17 is 1/2 of 500.34).
To find actual mileage, multiply by 0.45:
500.34 x 0.45 = 225.153 miles.
Round the answer as needed.
The Elster family drove 9.25 hours on the first day of their road trip. How many minutes is this equivalent to?
Answers
Answer:
555 minutes
Step-by-step explanation:
A survey of 1,562 randomly selected adults showed that 522 of them have heard of a new electronic reader. The accompanying technology display results from a test of the claim that 35% of adults have heard of the new electronic reader. Use the normal distribution as an approximation to the binomial distribution, and assume a 0.05 significance level to complete parts (a) through (e). Is the test two-tailed, left-tailed, or right-tailed? Left-tailed test Two-tailed test Right tailed test What is the test statistic? (Round to two décimal places as needed.) What is the P-vahie?
Answers
Answer:
a) We want to test the claim that 35% of adults have heard of the new electronic reader, then the system of hypothesis are.:
Null hypothesis:[tex]p=0.35[/tex]
Alternative hypothesis:[tex]p \neq 0.35[/tex]
And is a two tailed test
b) [tex]z=\frac{0.334 -0.35}{\sqrt{\frac{0.35(1-0.35)}{1562}}}=-1.326[/tex]
c) [tex]p_v =2*P(z<-1.326)=0.184[/tex]
d) Null hypothesis:[tex]p=0.35[/tex]
e) Fail to reject the null hypothesis because the P-value is greater than the significance level, alpha.
Step-by-step explanation:
Information provided
n=1562 represent the random sample selected
X=522 represent the people who have heard of a new electronic reader
[tex]\hat p=\frac{522}{1562}=0.334[/tex] estimated proportion of people who have heard of a new electronic reader
[tex]p_o=0.35[/tex] is the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Part a
We want to test the claim that 35% of adults have heard of the new electronic reader, then the system of hypothesis are.:
Null hypothesis:[tex]p=0.35[/tex]
Alternative hypothesis:[tex]p \neq 0.35[/tex]
And is a two tailed test
Part b
The statistic for this case is given :
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.334 -0.35}{\sqrt{\frac{0.35(1-0.35)}{1562}}}=-1.326[/tex]
Part c
We can calculate the p value using the laternative hypothesis with the following probability:
[tex]p_v =2*P(z<-1.326)=0.184[/tex]
Part d
The null hypothesis for this case would be:
Null hypothesis:[tex]p=0.35[/tex]
Part e
The best conclusion for this case would be:
Fail to reject the null hypothesis because the P-value is greater than the significance level, alpha.
What is a description of an undefined term?
Answers
Answer:
In Geometry, we have several undefined terms: point, line and plane. From these three undefined terms, all other terms in Geometry can be defined. In Geometry, we define a point as a location and no size. ... And the third undefined term is the line.
Step-by-step explanation:
The box plots show the weights, in pounds, of the dogs in two different animal shelters.
Weights of Dogs in Shelter A
2 box plots. The number line goes from 6 to 30. For the weights of dogs in shelter A, the whiskers range from 8 to 30, and the box ranges from 17 to 28. A line divides the box at 21. For shelter B, the whiskers range from 10 to 18, and the box ranges from 16 to 20. A line divides the box at 18.
Weights of Dogs in Shelter B
One-half of the dogs in each shelter are between which weights?
between 8 and 30 pounds in shelter A; between 10 and 28 pounds in shelter B
between 8 and 17 pounds in shelter A; between 10 and 16 pounds in shelter B
between 21 and 30 pounds in shelter A; between 18 and 28 pounds in shelter B
between 28 and 30 pounds in shelter A; between 20 and 28 pounds in shelter B
Answers
Hope this helps
Answer:
the 2nd one
i am pretty sure
Step-by-step explanation:
You walk in a room and on the bed there are 2 dogs, 4 cats, one giraffe, 5 cows and a duck, 3 chickens flying above; how many legs are on the floor?
Answers
Answer:
0
Step-by-step explanation:
they are on the bed
The total legs on the floor excluding chicken is 50 legs
Word problemsFrom the given question, the following animals have 4 legs
dogs, cats, girraffe and cows
Duck and chickens both have 2 legs
The total number of legs on the floor = 4(2) + 4(4) + 1(4) + 5(4) + 1(2)
Total number. = 8 + 20 + 22
Total number = 50legs
Hence the total legs on the floor excluding chicken is 50 legs
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HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answers
Answer:
D. x+10
Step-by-step explanation:
-2x² - 16x +40 = -2(x²+8x -20) = -2(x+10)(x-2)
If your born on 1900 how old would have you been on 2009?
Answers
Answer: 109 years old
Step-by-step explanation:
2009-1900=109
Answer:
109years old
Step-by-step explanation:
1900
1900 to 2000 is 100 years old
2000 to 2009 is 9 years old
100+9=109
The scores on one portion of a standardized test are approximately Normally distributed, N(572, 51). a. Use the 68-95-99.7 rule to estimate the range of scores that includes the middle 95% of these test scores. b. Use technology to estimate the range of scores that includes the middle 90% of these test scores.
Answers
Answer:
a) The range of scores that includes the middle 95% of these test scores is between 470 and 674.
b) The range of scores that includes the middle 90% of these test scores is between 488.1 and 655.9.
Step-by-step explanation:
68-95-99.7 rule:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Z-score:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
Mean [tex]\mu = 572[/tex], standard deviation [tex]\sigma = 51[/tex]
a. Use the 68-95-99.7 rule to estimate the range of scores that includes the middle 95% of these test scores.
By the 68-95-99.7 rule, within 2 standard deviations of the mean.
572 - 2*51 = 470
572 + 2*51 = 674
The range of scores that includes the middle 95% of these test scores is between 470 and 674.
b. Use technology to estimate the range of scores that includes the middle 90% of these test scores.
Using the z-score formula.
Between these following percentiles:
50 - (90/2) = 5th percentile
50 + (90/2) = 95th percentile.
5th percentile.
X when Z has a pvalue of 0.05. So when X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 572}{51}[/tex]
[tex]X - 572 = -1.645*51[/tex]
[tex]X = 488.1[/tex]
95th percentile.
X when Z has a pvalue of 0.95. So when X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 572}{51}[/tex]
[tex]X - 572 = 1.645*51[/tex]
[tex]X = 655.9[/tex]
The range of scores that includes the middle 90% of these test scores is between 488.1 and 655.9.
Using the numbers 4.3, -1.07, and -2.971, write an expression containing both addition and subtraction that simplified to a positive number.
Answers
Answer:
4.3 + (-1.07)+(-2.971)
Step-by-step explanation:
4.3 + (-1.07)+(-2.971)
4.3 -1.07-2.971
4.3 - 4.041= 0.259
Which would neatly fill the gap in the prism shown below? Check all that apply.
3
2
21 / 2
6 blocks each measuring 5x1x1
12 blocks each measuring 3 x1x1
6 blocks each measuring 5x1x1
Answers
Answer:
b, d
Step-by-step explanation:
(12 blocks each measuring One-fourth times 1 times 1)(6 blocks each measuring One-half times 1 times 1)finished the exam review and was correct (sorry for the late response)
The gap would be filled in the prism shown below as 12 blocks each measuring One-fourth times 1 x 1. 6 blocks each measuring One-half times 1 x 1.
How to find the volume of a prism?If the prism is such that if we slice it horizontally at any height smaller or equal to its original height, the cross-section is the same as its base, then its volume is:
[tex]V = B \times h[/tex]
where h is the height of that prism and B is the area of the base of that prism.
The block has a volume of 2 x 5/2.
The remaining part of the block is filled by
12 blocks each measuring One-fourth times 1 x 1.
6 blocks each measuring One-half times 1 x 1.
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Which weigh more 8,112ounces or 505 pounds
Answers
Answer
8,112 ounces
Step-by-step explanation:
505 pounds converted into ounces= 8080 ounces which is not more than 8,112
Step-by-step explanation:
1 pound = 16 ounces
505 pound = 505 x 16 = 8080 ounces
So 8112 ounces weighs more
The difference of two supplementary angles is 70 degrees. Find the measures of the angles.
Answers
Answer:
DUEDY A. 32 degrees
Step-by-step explanation:
PATROLLING WEE WOOO
Xd
Answer:
55 125
Step-by-step explanation:
Let the smaller angle = x
Let the larger angle = x + 70
They are supplementary so the total of the two angles, by definition must be 180 degrees. Note that you should understand that any number of angles can but supplementary as long as they all add up to 180 degrees.
x + x + 70 = 180
2x + 70 = 180
2x + 70 - 70 = 180 - 70
2x = 110
2x/2 = 110/2
x = 55
the smaller angle = 55 degrees
The larger angle = 55 + 70 = 125
Can somebody please solve this? I'm confused
Answers
Answer:
9
Step-by-step explanation:
Not sure if it is right, don't at me :)
The object below is a cubical lunch box having each edge as 10 cm.
Find its surface area.
A
600 cm2
B
360 cm2
C
300 cm2
D
36 cm2
Answers
Answer:
B
Step-by-step explanation:
The total surface area of a cubical lunch box having each edge as 10 cm is 600 square centimeter. Therefore, option A is the correct answer.
What is surface area of a cube?The surface area of the cube all six faces of the cube are made up of squares of the same dimensions then the total surface area of the cube will be the surface area of one face added six times to itself. The formula to find the surface area of a cube is 6a², where a is edge.
Given that, the cubical lunch box having each edge as 10 cm.
Here, surface area = 6×10²
= 600 square centimeter
Therefore, option A is the correct answer.
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The mean of this set of data (23,13,17,11,11)
Answers
Answer:
The mean is 15
Step-by-step explanation:
To find the mean, add up all the numbers and divide by the number of numbers
(23+13+17+11+11)/ 5
75 /5
15
What is W in this equation, -12u+13=8w-3
Answers
Answer:
w = (-3/2)u + 2
Step-by-step explanation:
Since we don't know the value of u, we can only solve -12u+13=8w-3 for w in terms of u.
Adding 3 to both sides, we get -12u+13=8w-3 => -12u+16=8w, or
8w = -12u + 16
Reduce this by dividing all three terms by 8:
w = (-12/8)u + 2
... and then reduce the fraction: w = (-3/2)u + 2
Find an equation for the nth term of the arithmetic sequence.
a16 = 21, a17 = -1
Answers
Answer:nth term=a1 - 27n + 27
Step-by-step explanation:
first term =a1
common difference=d=-1-21
d=-27
Using the formula
Tn=a1 + d x (n-1)
nth term=a1 + (-27)(n-1)
nth term=a1 - 27n + 27
What is the perimeter?
30 km
22 km
33 km
36 km
Answers
Answer:
121 km
Step-by-step explanation:
i added all the number together
................................................
Answers
Answer:
V =108 ft^3
Step-by-step explanation:
The volume is found by
V = Bh where B is the area of the base
B = the area of the trapezoid
B = 1/2 (b1+b2)*h of the trapezoid
B = 1/2(4+6)*4 = 1/2(10)*4 = 20
Now we can find the volume
V = 20* 9
V =108 ft^3
Select the correct answer.
The surface areas of two cubes are in a ratio of 1 : 9. What is the ratio of their volumes?
A 1:3
B. 1:9
C. 1:27
D. 1:81
Answers
Answer:
C. 1:27
Step-by-step explanation:
a²/b²=1/9 => a=1 and b=3
a³/b³=1³/3³=1/27
C. 1:27
I agree with the other answer. Here's another way to see why the answer is 1:27
The surface areas are in ratio 1:9. This means we could have one square that has area 1 and the larger square is area 9.
The smaller square has sides of 1 and the larger square has sides of 3 (square root both area values).
Now if we had a cube that has dimensions of 1 unit, then the volume is 1*1*1 = 1 cubic unit. If we had a larger cube with dimensions of 3 units, then the volume is 3^3 = 3*3*3 = 27 cubic units. We can fit 27 smaller 1x1x1 cubes into the larger 3x3x3 cube.
Brian is ordering books online. He has $100 to spend on the books. Each book costs $7. The shipping charge for the entire order is $8. The
number of books, b, that Brian can buy is represented by the inequality 7b+8 < 100. How many books can Brian buy without overspending?
Answers
Answer:
13 books.
Step-by-step explanation:
If 100-8 equals 92 divided by 7 equals 13 rounded. That is the # of books.
PLZ MARK BRAINLIEST!!!
Answer:
13 books
Step-by-step explanation:
7b+8 < 100
Subtract 8 from each side
7b+8-8 < 100-8
7b< 92
Divide each side by 7
7b/7 < 92/7
b< 13 1/7
Since we cannot buy part of a book, Brian can buy 13 books without overspending
estamate 1/4 x 19= plz i neeed awnser
Answers
Answer:
1/4 x 19=4.75 rounded to 4.8 or 5
Step-by-step explanation:
please mark brainliest if this helped
Answer:
4.75
Step-by-step explanation:
simple math you would find a number that both 4 and 19 have in common make that tha dominator and mutiple the number that equaled the dominator by the numerator to make them like fractions. mutiply across and make a simple fraction
I go threw so much I'm only 19 years old
it's been months since I felt at home
But is okay cause I'm rich sike I'm still sad as a bih right
Answers
Answer:
juice wrld
Step-by-step explanation:
fast
Answer:
yuh
Step-by-step explanation:
What is (7p + 6) - (9p - 7)?
Answers
Answer:
-2p +13
Step-by-step explanation:
(7p + 6) - (9p - 7)
Distribute the minus sign
(7p + 6) - 9p + 7
Combine like terms
7p -9p +6 +7
-2p +13
Answer:
-2p + 13
Step-by-step explanation:
Distribute the -1 to (9p - 7):
7p + 6 - 9p + 7
Add like terms (7p and -9p, 6 and 7):
-2p + 13
How many ways can 12 swimmers finish in first, second, and third place
Answers
This can be solved using something called permutation. There are 12 possible swimmers that can be in first place. After that, 11 swimmers left to be in second place. Finally there are 10 swimmers left for third place. Multiply these together you get 12•11•10=1320. Hope this helps!!
