Step-by-step explanation:
It is not specified the compounding period, which in general is a month these days. So we will assume money is compounded each month, otherwise there is no point depositing monthly.
1. Yolanda:
APR=5% is equivalent to
Monthly interest = 5%/12 = 5/12% = 5/1200 = 1/240 = i
Monthly deposit = 100 = A
Future value after 14 years = 14*12 months = 168 months = n
FV1 = A((1+i)^n-1)/i
=100*((1+1/240)^168-1)/(1/240)
= $24259.83
2. Zach
He deposits 1200 at the end of the year. The last payment does not benefit from interest.
Since it is a yearly payment, each amount earns interest over a year, giving an annual interest of
(1+i)^12 -1 = 1.051161897881733 -1 =0.051161897881733 = j
Thus for 13 annual payments with annual interest j gives a compounded amount after 14 years, plus the last payment which does not earn interest
FV2 = A((1+j)^n-1)/j
= 1200((1.051161897881733)^13-1)/(0.051161897881733)+1200
= 22613.34
Summary
Total investments:
Yolanda = 12*100*14 = 16800
Zach = 1200 * 14 = 16800
So both investors have invested $16800 over the 14 year period.
Since Yolanda achieves a higher future value after 14 years ($24259.83) over that of Zach ($22613.34), financially Yolanda has a better strategy.
Note:
If zach had invested annually at the beginning of the year, he would have obtained:
A((1+j)^n-1)/j
= 1200((1.051161897881733)^14-1)/(0.051161897881733)
= 24908.88
which is superior over Yolanda's return.
By about how much will f (x comma y comma z )equalsln StartRoot x squared plus y squared plus z squared EndRoot change if the point Upper P (x comma y comma z )moves from Upper P 0 (6 comma 4 comma 12 )a distance of dsequals0.1 unit in the direction of 3 Bold i plus 6 Bold j minus 2 Bold k?
Answer:
pls format
Step-by-step explanation:
Use the place value chart to write 9.807.
Answer:
9 ones, 8 tenths, 0 hundredths, 7 thousandths
Step-by-step explanation:
Answer:
9 thousands
8 hundreds
0 tens
7 ones
Step-by-step explanation:
Hope it helped!
3) BRAINLIEST & 10+ POINTS!!! If a 4 foot blade of a propeller completes 22 revolutions per second, find the angular speed of the blade in radians per second. ~Round your answer to the nearest hundredth. Angular speed = _______________ radians/second
Answer:
44π rads per seconds
Step-by-step explanation:
Already the speed of the 4 foot blade is given as 22 revolutions per sec.
What we have to do is just to convert the 22 revolutions per second to radians.
1 rev = 360°
360° = 2π
So the speed is actually equal to
22 *360 = 7920° per second
Or
22*2π = 44π rad per seconds
What ever way the answers are both same.
According to the New York Stock Exchange, the mean portfolio value for U.S. senior citizens who are shareholders is $183,000. Assume portfolio values are normally distributed. Suppose a simple random sample of 51 senior citizen shareholders in a certain region of the United States is found to have a mean portfolio value of $198,000, with a standard deviation of $65,000.
a. From these sample results, and using the 0.05 level of significance comment on whether the mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation, by using the critical value method. Establish the null and alternative hypotheses.
b. What is your conclusion about the null hypothesis?
Answer:
The test statistic value t = 1.64 < 2.0086 at 0.05 level of significance
Null hypothesis is accepted
The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation
Step-by-step explanation:
Step(i):-
Given mean of the population (μ) = $183,000
Given mean of the sample (x⁻) = $198,000
Given standard deviation of the sample (S) = $65,000.
Mean of the sample size 'n' = 51
level of significance α = 0.05
Step(ii):-
Null hypothesis : H₀ : There is no significance difference between the means
Alternative Hypothesis :H₁: There is significance difference between the means
Test statistic
[tex]t = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]t = \frac{198,000- 183,000 }{\frac{ 65,000}{\sqrt{51} } }[/tex]
t = 1.64
Step(iii)
Degrees of freedom ν = n-1 = 51-1 =50
t₀.₀₅ = 2.0086
The calculated value t = 1.64 < 2.0086 at 0.05 level of significance
Null hypothesis is accepted
Final answer:-
There is no significance difference between the means
The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation
Please answer this correctly
Answer:
1/5
Step-by-step explanation:
The number 5 or greater than 4 is 5.
1 number out of 5 total parts.
= 1/5
P(5 or greater than 4) = 1/5
CAN SOMEONE PLEASE HELP ME THIS IS DUE SOON!!
Answer:
95 ft²
Step-by-step explanation:
Given:
regular pyramid with,
Square base of side length (s) = 5 ft
Slant height (l) = 7 ft
Required:
Surface area
Solution:
Surface area of a regular pyramid = ½*P*l + B
Where,
P = perimeter of the square base = 4(s) = 4(5) = 20 ft
l = slant height = 7 ft
B = area of base = s² = 5² = 25 ft²
Surface area = ½*20*7 + 25
= 10*7 + 25
= 70 + 25
Surface area of regular pyramid = 95 ft²
Select the correct answer. Vector u has its initial point at (-7, 2) and its terminal point at (11, -5). Vector v has a direction opposite that of vector u, and its magnitude is three times the magnitude of u. What is the component form of vector v? A. v = B. v = C. v = D. v =
Answer:
Step-by-step explanation:
vector u=<(11-(-7),(-5-2)>=<18,-7>
as direction is opposite to u
so vector v=-3(18,-7)=(-54,21)
I travelled at 60km/h and took 2 hours for a certain journey. How long would it have taken me if I had travelled at 50km/h?
Answer:
2 hours and 24 minutes
Step-by-step explanation:
2 hours at 60 km/h means you have travelled 2*60=120 km
120 km at 50 km/h takes 120/50 = 2.4 hours
2.4 hours is 2 hours and 0.4*60 = 24 minutes.
Write 0000 using the am/pm clock.
Answer:
12am
Step-by-step explanation:
Answer:
12:00 am or midnight
Step-by-step explanation:
00 00 hrs in 12-hours clock is 12:00 am or 12:00 o'clock midnight.
PLSSSSSSS HELP WILL MARK BRAINLIEST Doug owns a lawn mowing and landscaping business. The income from the business is given by the function f(x) = 2x + 54, where f(x) is the income in dollars and x is the area in square meters of lawn mowed. If he has earned {204, 344, 450, 482} dollars in the last four months, what are the corresponding areas of lawn he mowed?
Answer:
i think this person answered but idrk perseusharrison79
Step-by-step explanation:
For 2 parallelograms, the corresponding side lengths are 1 inch and x inches, and 2 inches and 6 inches.
Not drawn to scale
StartFraction 1 over x EndFraction = StartFraction 2 over 6 EndFraction
StartFraction 1 over x EndFraction = StartFraction 6 over 2 EndFraction
StartFraction 1 over 6 EndFraction = StartFraction 2 over x EndFraction
One-half = StartFraction 6 over x EndFraction
Step-by-step explanation:
Explain the importance of factoring.
Answer:
Factoring is a useful skill in real life. Common applications include: dividing something into equal pieces, exchanging money, comparing prices, understanding time, and making calculations during travel.
Sorry if this is a little wordy, I can get carried away with this sort of thing
anyway, hope this helped and answered your question :)
Jenna worked 13 hours more than Jose last month. If Jenna worked 9 hours for every 4 hours that Jose worked, how many hours did they each work?
For a large sporting event the broadcasters sold 51 ad slots for a total revenue of $136 million. What was the mean price per ad slot?
Answer:
$2.67 million
Step-by-step explanation:
Average price per slot is found by dividing total price by total slots:
($136 million)/(51 slots) ≈ $2.67 million/slot
The mean price per ad slot was $2.67 million.
Suppose you toss a coin 100 times and get 65 heads and 35 tails. Based on these results, what is the probability that the next flip results in a tail?
Answer:
[tex] P(Head) = \frac{65}{100}=0.65[/tex]
[tex] P(Tail) = \frac{35}{100}=0.35[/tex]
And for this case the probability that in the next flip we will get a tail would be:
[tex] P(Tail) = \frac{35}{100}=0.35[/tex]
Step-by-step explanation:
For this case we know that a coin is toss 100 times and we got 65 heads and 35 tails.
We can calculate the empirical probabilities for each outcome and we got:
[tex] P(Head) = \frac{65}{100}=0.65[/tex]
[tex] P(Tail) = \frac{35}{100}=0.35[/tex]
And for this case the probability that in the next flip we will get a tail would be:
[tex] P(Tail) = \frac{35}{100}=0.35[/tex]
Please answer question now in two minutes
Answer:
V lies in the exterior of <STU.
Step-by-step explanation:
V lies in the exterior of <STU.
Please only answer if you are 100% sure about the answer.
Answer:
Choice C.
Step-by-step explanation:
Your choice is correct
2 stands for a starting point which is 2 feet from the home
As the ant moves, over time, the distance increases according to the function
19.25 tons equal Lbs
Answer:
38500lbs
Step-by-step explanation:
2000 lbs is one tone
if we have 19.25 tons, we need to multiply 19.25x2000
The answer is 38500 lb
Answer:
38,500 pounds
Step-by-step explanation:
Every ton is 2,000 pounds.
We want to find out how many pounds are in 19.25 tons.
Set up a proportion.
pounds/tons=pounds/tons
2,000 pounds/ 1 ton= x pounds / 19.25 tons
2,000/1= x /19.25
x is being divided by 19.25. The inverse of division is multiplication. Multiply both sides by 19.25.
19.25*2,000/1= x/19.25 *19.25
19.25*2000=x
38,500=x
There are 38,500 pounds in 19.25 tons.
I paid twice as much by not waiting for a sale and not ordering on line. Which ofthe following statements is also true?
(a) I paid 200% more than I could have online and on sale.
(b) I paid 100% of what I could have online and on sale.
(c) I paid 200% of what I could have online and on sale.
(d) I paid 3 times what I could have online and on sale.
Answer:
Option (c).
Step-by-step explanation:
It is given that, I paid twice as much by not waiting for a sale and not ordering online.
Let the cost of items ordering online be x.
So, now i am paying twice of x = 2x
Now, we have find 2x is what percent of x.
[tex]Percent =\dfrac{2x}{x}\times 100=200\%[/tex]
It means, I paid 200% of what I could have online and on sale.
Therefore, the correct option is (c).
Three girls of a group of eight are to be chosen. In how many ways can this be done?
Answer:
Step-by-step explanation:
8P3=8*7*6=336
The mean arrival rate of flights at Philadelphia International Airport is 195 flights or less per hour with a historical standard deviation of 13 flights. To increase arrivals, a new air traffic control procedure is implemented. In the next 30 days, the arrival rate per day is given in the data vector below called flights. Air traffic control manager wants to test if there is sufficient evidence that arrival rate has increased.
flights <- c(210, 215, 200, 189, 200, 213, 202, 181, 197, 199,
193, 209, 215, 192, 179, 196, 225, 199, 196, 210,
199, 188, 174, 176, 202, 195, 195, 208, 222, 221)
a) Find sample mean and sample standard deviation of arrival rate using R functions mean() and sd().
b) Is this a left-tailed, right-tailed or two-tailed test? Formulate the null and alternative hypothesis.
c) What is the statistical decision at the significance level α = .01?
Answer:
a) The sample mean is M=200.
The sample standard deviation is s=13.19.
b) Right-tailed. The null and alternative hypothesis are:
[tex]H_0: \mu=195\\\\H_a:\mu> 195[/tex]
c) At a significance level of 0.01, there is notenough evidence to support the claim that the arrival rate is significantly higher than 195.
Step-by-step explanation:
We start by calculating the sample and standard deviation.
The sample size is n=30.
The sample mean is M=200.
The sample standard deviation is s=13.19.
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{30}(210+215+200+. . .+221)\\\\\\M=\dfrac{6000}{30}\\\\\\M=200\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{29}((210-200)^2+(215-200)^2+(200-200)^2+. . . +(221-200)^2)}\\\\\\s=\sqrt{\dfrac{5048}{29}}\\\\\\s=\sqrt{174.07}=13.19\\\\\\[/tex]
This is a hypothesis test for the population mean.
The claim is that the arrival rate is significantly higher than 195. As we are interested in only the higher tail for a significant effect, this is a right-tailed test.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=195\\\\H_a:\mu> 195[/tex]
The significance level is 0.01.
The standard deviation of the population is known and has a value of σ=13.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{13}{\sqrt{30}}=2.373[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{200-195}{2.373}=\dfrac{5}{2.373}=2.107[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>2.107)=0.018[/tex]
As the P-value (0.018) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.01, there is notenough evidence to support the claim that the arrival rate is significantly higher than 195.
Find the sum. Please
Answer:
[tex]\dfrac{2y^2 +12y -8}{y^3-3y+2}[/tex]
Step-by-step explanation:
It usually works to factor the denominators, so you can determine the least common denominator.
[tex]\dfrac{2y}{y^2-2y+1}+\dfrac{8}{y^2+y-2}=\dfrac{2y}{(y-1)^2}+\dfrac{8}{(y-1)(y+2)}\\\\=\dfrac{2y(y+2)}{(y-1)^2(y+2)}+\dfrac{8(y-1)}{(y-1)^2(y+2)}=\dfrac{2y^2+4y+8y-8}{(y-1)^2(y+2)}\\\\=\boxed{\dfrac{2y^2 +12y -8}{y^3-3y+2}}[/tex]
Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $43,000 and $61,600. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired.
Required:
a. What is the planning value for the population standard deviation (to the nearest whole number)?
b. How large a sample should be taken if the desired margin of error is as shown below (to the nearest whole number)?
1. $500?
2. $200?
3. $100?
Answer:
a. 4650
b.
1. 332
2. 2076
3. 8306
Step-by-step explanation:
a. The planning value for population standard deviation is,
s = (maximum - minimum) / 4
s = (61600 - 43000) / 4
s = 4650
that is, it would be 4650, the planning value for population standard deviation
b. we have to:
n = (z * s / E) ^ 2
z for confidence level 95% is 1.96, E = 500; 200; 100
replacing:
1.
n = (1.96 * 4650/500) ^ 2
n = 332.2 = 332
2.
n = (1.96 * 4650/200) ^ 2
n = 2076.6 = 2076
3.
n = (1.96 * 4650/100) ^ 2
n = 8306.4 = 8306
The tens digit in a two digit number is 4 greater than one’s digit. If we interchange the digits in the number, we obtain a new number that, when added to the original number, results in the sum of 88. Find this number
Answer:
The original digit is 62
Step-by-step explanation:
Let the Tens be represented with T
Let the Units be represented with U
Given:
Unknown Two digit number
Required:
Determine the number
Since, it's a two digit number, then the number can be represented as;
[tex]T * 10 + U[/tex]
From the first sentence, we have that;
[tex]T = 4 + U[/tex]
[tex]T = 4+U[/tex]
Interchanging the digit, we have the new digit to be [tex]U * 10 + T[/tex]
So;
[tex](U * 10 + T) + (T * 10+ U) = 88[/tex]
[tex]10U + T + 10T + U= 88[/tex]
Collect Like Terms
[tex]10U + U + T + 10T = 88[/tex]
[tex]11U + 11T = 88[/tex]
Divide through by 11
[tex]U + T = 8[/tex]
Recall that [tex]T = 4+U[/tex]
[tex]U + T = 8[/tex] becomes
[tex]U + 4 + U = 8[/tex]
Collect like terms
[tex]U + U = 8 - 4[/tex]
[tex]2U = 4[/tex]
Divide both sides by 2
[tex]U = 2[/tex]
Substitute 2 for U in [tex]T = 4+U[/tex]
[tex]T = 4 + 2[/tex]
[tex]T = 6[/tex]
Recall that the original digit is [tex]T * 10 + U[/tex]
Substitute 6 for T and 2 for U
[tex]T * 10 + U[/tex]
[tex]6 * 10 + 2[/tex]
[tex]60 + 2[/tex]
[tex]62[/tex]
Hence, the original digit is 62
Which could be the side lengths of a triangle? (A) 2,2,4 (B) 3,4,7 (C) 4,5,8 (D) 5,5,10 (E) 7,3,10 PLEASE HELP
Answer:
(C) 4,5,8
Step-by-step explanation:
Since 4+5 = 9 and 9 is bigger than 8, that means that the side 8 can fit into the triangle without there being an open space.
Answer:
Option C { 4,5,8 }
Step-by-step explanation:
By the Triangle Inequality Theorem, the length of two sides together must be greater than the length of the remaining side. Respectively their difference must be less than the length of the another side.
* I like to memorize this concept by thinking about a door. The more you open the door, the greater the distance between the door and the wall - as they are proportional. That is how we concluded this theorem.
______
{ 2, 2, 4 } is our first option. The difference of 4 and 2 is equal to the remaining length, 2. { 3, 4, 7 } is not applicable as well, considering that the addition of 3 and 4 is equivalent to the length of the 3rd side, 7. However, the lengths { 4, 5,8 } have no such " errors. " It could be the side lengths of a possible triangle.
______
Solution = { 4,5,8 }
Find the Prime factors of 1729. Arrange the factors in ascending order. Find a relation between
consecutive prime factors
Answer:
prime factors in ascending order of 1729 is 7 , 13 , 19
relation between consecutive prime factors is 6
Step-by-step explanation:
given data
number = 1729
solution
we get here factors of 1729
1729 = 7 × 13 × 19
so that required prime factors in ascending order of 1729 is 7 , 13 , 19
and
now we get relation between these prime factors is the difference between consecutive prime factors is
13 - 7 = 6
19 - 13 = 6
so relation between consecutive prime factors is 6
Step-by-step explanation:
Prime factors of the number 1729 are 7,13,19
i.e. 1729 =7×13×19
The factors in ascending order are 7,13,19.
Clearly we can see that each consecutive prime factors have difference of 6.
13-7=6
19-13=6
Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two side
bf this triangle?
O 5 cm and 8 cm
O 6 cm and 7 cm
O 7 cm and 2 cm
8 cm and 9 cm
Answer:
It's (D) 8 cm and 9 cm. Hope this helps you!
Step-by-step explanation:
The other 2 sides added have to be greater than 13.
Answer:
8 and 9
Step-by-step explanation:
The triangle inequality states that the sum of the two shortest sides must be greater than the longest side.
Let's check the first one. 5 + 8 > 13 → 13 > 13 which is false.
6 + 7 > 13 → 13 > 13 which is false.
7 + 2 > 13 → 9 > 13 which is false.
8 + 9 > 13 → 17 > 13 which is true.
It is believed that 11% of all Americans are left-handed. In a random sample of 100 students from a particular college with 10123 students, 14 were left-handed. Find a 98% confidence interval for the percentage of all students at this particular college who are left-handed.
Answer:
Step-by-step explanation:
We can calculate this confidence interval using the population proportion calculation. To do this we must find p' and q'
Where p' = 14/100= 0.14 (no of left handed sample promotion)
q' = 1-p' = 1-0.14= 0.86
Since the requested confidence level is CL = 0.98, then α = 1 – CL = 1 – 0.98 = 0.02/2= 0.01, z (0.01) = 2.326
Using p' - z alpha √(p'q'/n) for the lower interval - 0.14-2.326√(0.14*0.86/100)
= -2.186√0.00325
= -2.186*0.057
= 12.46%
Using p' + z alpha √(p'q'/n)
0.14+2.326√(0.14*0.86/100)
= 0.466*0.057
= 26.5%
Thus we estimate with 98% confidence that between 12% and 27% of all Americans are left handed.
Help me with this problem, thank you<3
Answer:
1,050 workers
Step-by-step explanation:
25% = 0.25
0.25 × 1400 = 350
1400 - 350 = 1050
Hope this helps.
Which is NOT supported by this graph?
30
25
20
15
10
Profit
5
(dollars)
0
-10
-15
Cars Washed
Answer:
D -price of car wash keeps getting higher
Answer: The price of a car wash keeps getting higher
Step-by-step explanation:
A tourist can bicycle 28 miles in the same time as he can walk 8 miles. If he can ride 10 mph faster than he can walk, how much time (in hr) should he allow to walk a 25-mile trail? (Hint: How fast can he walk?) ________ hr. (enter a fraction)
Answer:
The answer is [tex]\frac{25}{4}[/tex]
Step-by-step explanation:
Velocity formula:
[tex]v = \frac{d}{t}[/tex]
In which v is the velocity, d is the distance, and t is the time.
A tourist can bicycle 28 miles in the same time as he can walk 8 miles. He can ride 10 mph faster than he can walk:
This means that:
[tex]v = \frac{8}{t}[/tex]
And
[tex]v + 10 = \frac{28}{t}[/tex]
[tex](v + 10)t = 28[/tex]
From the first equation:
[tex]vt = 8[/tex]
So
[tex]vt + 10 = 28[/tex]
[tex]8 + 10t = 28[/tex]
[tex]10t = 20[/tex]
[tex]t = \frac{20}{10}[/tex]
[tex]t = 2[/tex]
He walks 8 miles in two hours, so:
[tex]v = \frac{8}{2} = 4[/tex]
4 miles per hour.
How much time (in hr) should he allow to walk a 25-mile trail?
This is t when [tex]d = 25[/tex]. So
[tex]v = \frac{d}{t}[/tex]
[tex]4 = \frac{25}{t}[/tex]
[tex]4t = 25[/tex]
[tex]t = \frac{25}{4}[/tex]
The answer is [tex]\frac{25}{4}[/tex]