Answer:
a. compounding by the day: A = $5967.17
b. compounding by the hour: A = $5967.29
c. compounding by the minute: A = $5967.30
d. compounding by the second: A = $5967.30
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Part (a)If the interest is compounding by the day then n = 365.
Given:
P = $4000r = 4% = 0.04n = 365t = 10 yearsSubstitute the values into the compound interest formula and solve for A:
[tex]\implies A=4000\left(1+\dfrac{0.04}{365}\right)^{365 \times 10}[/tex]
[tex]\implies A=4000\left(1.00010958...\right)^{3650}[/tex]
[tex]\implies A=4000(1.49179200...)[/tex]
[tex]\implies A=5967.16801...[/tex]
[tex]\implies A=\$5967.17[/tex]
Part (b)If the interest is compounding by the hour then:
n = 365 × 24 = 8760Given:
P = $4000r = 4% = 0.04n = 8760t = 10 yearsSubstitute the values into the compound interest formula and solve for A:
[tex]\implies A=4000\left(1+\dfrac{0.04}{8760}\right)^{8760 \times 10}[/tex]
[tex]\implies A=4000\left(1.00000456...\right)^{87600}[/tex]
[tex]\implies A=4000\left(1.49182333...\right)[/tex]
[tex]\implies A=5967.29333...[/tex]
[tex]\implies A=\$5967.29[/tex]
Part (c)If the interest is compounding by the minute then:
n = 365 × 24 × 60 = 525600Given:
P = $4000r = 4% = 0.04n = 525600t = 10 yearsSubstitute the values into the compound interest formula and solve for A:
[tex]\implies A=4000\left(1+\dfrac{0.04}{525600}\right)^{525600 \times 10}[/tex]
[tex]\implies A=4000\left(1.00000007...\right)^{5256000}[/tex]
[tex]\implies A=4000(1.49182466...)[/tex]
[tex]\implies A=5967.29867...[/tex]
[tex]\implies A=\$5967.30[/tex]
Part (d)If the interest is compounding by the second then:
n = 365 × 24 × 60 × 60 = 31536000Given:
P = $4000r = 4% = 0.04n = 31536000t = 10 yearsSubstitute the values into the compound interest formula and solve for A:
[tex]\implies A=4000\left(1+\dfrac{0.04}{31536000}\right)^{31536000 \times 10}[/tex]
[tex]\implies A=4000\left(1.00000000...\right)^{315360000}[/tex]
[tex]\implies A=4000\left(1.49182390...\right)[/tex]
[tex]\implies A=5967.29562...[/tex]
[tex]\implies A=\$5967.30[/tex]
The more compounding periods throughout the year, the higher the future value of the investment. However, the difference between compounding by the day and compounding by the second results in a difference of 13 cents over the year, which is negligible comparatively.
WILL GIVE BRAINLIEST HELP
For questions 1 - 4, which right triangle congruence theorem can be used to show that the two triangles
are congruent?
8
1.
2.
܂
A
B
3.
܂
4.
A
Step-by-step explanation:
1. SAS
2. HL
3. AAS
4 AAS
least common denominator for these two rational expressions, 3/y and
1/7y
Answer:
least common denominator = 7y
Step-by-step explanation:
3/y = 21/7y
1/7y and 21/7y have a least common denominator of 7y.
Emily wants to find out if the carpool line around her school causes too much traffic on neighborhood roads. Which is a valid sample for her survey?
Answer:
25 families living near the school
Step-by-step explanation:
Answer:
25 families living near the school :D
Step-by-step explanation:
Pls Help will give brainliest
2) The angle measures and/or side lengths of a triangle are described. Determine whether the conditions given determine a unique triangle (one triangle), determine more than one triangle, or cannot make a triangle. Explain how you know this.
a) 3 in., 6 in., 10 in.
b) 40°, 65°, 75
A bottle contains 750mL of fruit punch with a concentration of 50% pure fruit juice. Johan
drinks 100mL of the punch and then refills the bottle with an equal amount of a cheaper
brand of punch. If the concentration of juice in the bottle is now reduce to 48%, what was
the concentration in the punch that Johan added?
Answer:
The juice concentration in the punch that Johan added was 35%.
Step-by-step explanation:
Since a bottle contains 750mL of fruit punch with a concentration of 50% pure fruit juice, and Johan drinks 100mL of the punch and then refills the bottle with an equal amount of a cheaper brand of punch, if the concentration of juice in the bottle is now reduced to 48%, to determine what was the concentration in the punch that Johan added, the following calculation must be performed:
750 = 100
650 = X
650 x 100/750 = X
65000/750 = X
86,666 = X
86.666 x 0.5 + 13.333 x 0.4 = 0.486662
86.666 x 0.5 + 13.333 x 0.39 = 0.4853287
86.666 x 0.5 + 13.333 x 0.35 = 0.4799955
Thus, the juice concentration in the punch that Johan added was 35%.
Write the equation of the line in fully simplified slope-intercept form.
Rewrite 2/5 and 4/11 so that they have a common denominator
Answer:
22/55 and 20/55
Step-by-step explanation:
multiply 2 and 5 by 11 to get 22/55, and multiply 4 and 11 by 5 to get 20/55
Approximately how many gallons are in
7 liters? (1 L -0.26 gal.)
A 1.8 gal
C 7.3 gal
B 6.7 gal
D 46 gal
Answer:
A po ang answer kahit icompute pa po.
Step-by-step explanation:
hope it helps you po!
Find the surface area of a triangle prisms
Answer: 544 sq. inch
Step-by-step explanation:
12 x 8 x 0.5 x 2 + 10 x 14 x 2 + 12 x 14 = 544
If a whole pan of brownies is being sold for $16, how much it cost to purchase 3/4
of the pan?
Answer:
$12
Step-by-step explanation:
We have to do this operation:
(16/4) x 3 = 4 x 3 = $12
Answer:
It will cost $12 to purchase 3/4 of the pan of brownies
Step-by-step explanation:
3/4 of 16 is equal to 12.
Hope this helps! Pls mark brainliest
2. Name the numerator and the denominator in each fraction.
a.
11/12
b. 7512
C.
12/0
d. 978
Answer:
a. N=11
D=12
b. N=1
D=7512
c. N=12
D=0
d. N= 1
D=978
Suppose that a random sample of twenty-year-old men is selected from a population and that these men's height and weight are recorded. A regression of weight on height yields , where Weight is measured in pounds and Height is measured in inches. What is the regressions weight prediction for someone who is inches tall
Answer:
Hello your question is incomplete attached below is the complete question
answer : 192.15 pounds
Step-by-step explanation:
Given :
weight = - 99.41 + 3.94*Height
R^2 = 0.81
SER = 10.2
Determine the regression weight prediction
Height of man = 74 inches
Hence : weight = - 99.41 + 3.94 * 74 = 192.15
therefore the regression weight prediction = 192.15 pounds
a triathlon event in which participants run,bike, and swim certain distances is mapped out in a triangle as shown below.
Answer:
A
Step-by-step explanation:
The statement 'the bike distance is greater than the run distance.' must be true.
The correct answer is option D.
What is distance?"It is the length of the line joining the two points."
Angle properties:In any triangle,
the smallest side and smallest angle are opposite one another. the mid-sized side and mid-sized angle are opposite one another.the largest side and largest angle are opposite one another.For given example,
We have given two angles of triangle.
65° and 57°
We know, the sum of all angles of triangle is 180°.
Let 'x' be the remaining angle.
⇒ x + 65° + 57 = 180°
⇒ x +122° = 180°
⇒ x = 58°
We know,
In any triangle,
- the smallest side and smallest angle are opposite one another.
- the mid-sized side and mid-sized angle are opposite one another.
- the largest side and largest angle are opposite one another.
Here,
57° < 58° < 65°
⇒ Run < Bike < Swim
This means, the statement 'the bike distance is greater than the run distance.' is correct.
The correct answer is option D.
Learn more about angle here:
https://brainly.com/question/8729556
#SPJ2
Solve for f(-3)
f(x)=5-x
f(-3)= ?
pls helpppp
HELP PLEASEEEEEE IM BEGGING YOUUU (question): Linda is making a line plot of the data below.
11.25, 12.5, 11.25, 14.125, 10.5, 11.25, 12
Which line plot represents the data correctly?
A.
A line plot shows a number line from 10 to 15 in intervals of 0.25. 10.5 has 1 dot. 11.25 has 3 dots. 12 has 1 dot. 12.5 has 1 dot. 14.125 has 1 dot.
B.
A line plot shows a number line from 10 to 15 in intervals of 0.25. 10.5 has 1 dot. 11.25 has 2 dots. 12 has 1 dot. 12.5 has 1 dot. 14.125 has 1 dot.
C.
A line plot shows a number line from 10 to 15 in intervals of 0.25. 10.5 has 1 dot. 11.25 has 3 dots. 12 has 1 dot. 12.5 has 1 dot. 13.75 has 1 dot.
D.
A line plot shows a number line from 10 to 15 in intervals of 0.25. 10.5 has 1 dot. 11.25 has 3 dots. 12 has 1 dot. 14.125 has 1 dot. ( PLEASE ANSWER ASAP) (i already made this question once pls dont get it wrong again) ill give 60 if correct!!
The answer is D ...........
Answer:
the answer is Actually A believe me i did the test
Step-by-step explanation:
A store sells 12 cans of soup for $21. How much would it cost you to buy 5 cans of soup?
Answer:
8.75$
Step-by-step explanation:
if 12 cans cost $21
1 can cost $21÷12=1.75$
5 cans = 1.75$ ×5
For the number line shown, which statement is not true?
Answer:
The answer is The First One, IaI > b
Step-by-step explanation:
ALGEBRA
tell whether the given value is a solution of the equation. (yes or no)
1. x+16=20;x+4
2. p-4+28;p+32
3. 4w+44;w=10
4. y/6= 6;y=24
Step-by-step explanation:
1. yes 4+16 = 20
2. yes 32 - 4 = 28
3. yes 4(10) = 40
4. no 24/6 = 4
Answer:
I love algebra anyways
the ans is in the picture with the steps
(hope it helps can i plz have brainlist :D hehe)
Step-by-step explanation:
1.yes
2.yes
3.yes
4.no
Given the frequency table what percentage of the students in grade 11-12 like rock music round to the nearest whole percent
Rap rock country row total
Grades 9-10. 40. 30. 55. 125
Grades 11-12. 60. 25. 35. 120
Column totals. 100. 55. 90. 245
A 10%
B. 21%
C. 25%
D 45%
9514 1404 393
Answer:
B. 21%
Step-by-step explanation:
The number of students in grade 11-12 is given in the total column: 120.
The number of those who like rock music is given in the second column: 25.
Then the percentage in 11-12 grade who like rock music is ...
25/120 × 100% ≈ 20.833% ≈ 21%
Mrs. Sleet said he was skinny as a rail and it looked like he hadn’t been ___
right. She gave
him his first pair of _____
please fill in the blank this is from buddy not buddy chapter 11 :)
please help
Answer:
fed, slippers
Step-by-step explanation:
Please help take a look at this photo will give Brainly
Answer:
60 degrees
Step-by-step explanation:
On the diagram, we can see that the two angles have a dash on each of them. This means that they have the same measure.
So, if angle ABD is 60 degrees, then angle DBC would also be 60 degrees.
I hope this helps!
Find the zeros of the function: p(x)=(x−1)(x^2−2x−2).
Answer:
x = 6, x = -4
Step-by-step explanation:
Please help me my head hurt
Answer:
my head hurts also
Step-by-step explanation:
how did snidely spellbinder write a four latter word that begins and ends with e answers
Answer:
He wrote the word "ease"
Please hurry! Timed! What is the scale factor in the dilation?
A. 2/5
B. 1/2
C. 2
D. 2 1/2
Shshshehehehhshehesjhshshahagaga
⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️HELP HELP HELP HELP HELP HELP HELP - A right triangle has a leg length of 21 inches and a hypotenuse length of 29 inches. What is the length of the other leg? *
Answer:
[tex]20[/tex]
Step-by-step-Explanation:
Remember, the Pythagorean Theorem.
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]21^{2} + b^{2}=29^{2}[/tex]
[tex]29^{2} -21^{2} =400[/tex]
sq rt of [tex]400=20[/tex]
Imagine you wish to determine whether the mean number of hours worked per week by men in a sample differs from the national 40-hour average. Use the information below to calculate the t-statisic. Be sure to also specify the degrees of freedom. Weekly Hours Worked by Men Range 60 Minimum value 5 Maximum value 65 Mean 42.31 Standard deviation 10.00 Number of observations 29
Answer:
Step-by-step explanation:
The sample standard deviation (s) divided by the square root of the number of observations in the sample (n).
The U.S. Energy Information Administration claimed that U.S. residential customers used an average of 10,941 kilowatt hours (kWh) of electricity this year. A local power company believes that residents in their area use more electricity on average than EIA's reported average. To test their claim, the company chooses a random sample of 115 of their customers and calculates that these customers used an average of 11,425kWh of electricity last year. Assuming that the population standard deviation is 3217kWh, is there sufficient evidence to support the power company's claim at the 0.02 level of significance
Answer:
The pvalue of the test is 0.0537 > 0.02, which means that there is not sufficient evidence to support the power company's claim at the 0.02 level of significance.
Step-by-step explanation:
The U.S. Energy Information Administration claimed that U.S. residential customers used an average of 10,941 kilowatt hours (kWh) of electricity this year.
This means that the null hypothesis is:
[tex]H_0: \mu = 10941[/tex]
A local power company believes that residents in their area use more electricity on average than EIA's reported average.
This means that the alternate hypothesis is:
[tex]H_a: \mu > 10941[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
10941 is tested at the null hypothesis:
This means that [tex]\mu = 10941[/tex]
To test their claim, the company chooses a random sample of 115 of their customers and calculates that these customers used an average of 11,425kWh of electricity last year. The population standard deviation is of 3217kWh:
This means that [tex]n = 115, X = 11425, \sigma = 3217[/tex]
Value of the z-statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{11425 - 10941}{\frac{3217}{\sqrt{115}}}[/tex]
[tex]z = 1.61[/tex]
Pvalue of the test:
Probability of finding a mean above 11425, which is 1 subtracted by the pvalue of z = 1.61.
Looking at the z-table, z = 1.61 has a pvalue of 0.9463.
1 - 0.9463 = 0.0537
The pvalue of the test is 0.0537 > 0.02, which means that there is not sufficient evidence to support the power company's claim at the 0.02 level of significance.