Answer:
A. Of first 100 multiples of 10
B. 5*10*15*20*25*30*35*40*40*45
C. 100!
I would also like to know whether this kind of question is possible in GMAT and what would be the complexity level.
1. 124
2. 10
3. 24
NO LINKS!!!! Exponential Growth and Decay Part 3
Answer:
6. 14.9 years
7. 4.8 years
8. 28.91 years
Step-by-step explanation:
Exponential growth or decay is described by the function ...
y = a·b^t
where 'a' is the initial value, and 'b' is the growth (or decay) factor. The growth (or decay) factor is one added to the growth rate.
__
This equation can be solved for t to get ...
y/a = b^t . . . . . . . divide by a
log(y/a) = t·log(b) . . . . take logarithms
t = log(y/a)/log(b) . . . . divide by the coefficient of t
Note that the time period is in the same units as the growth rate. (If the growth rate is per quarter, then the value of t will be in quarters.)
__
6.The initial value is a=8000; the final value is y=35000; and the growth rate is 10%/4 = 0.025 per quarter. The above equation will give the time period in quarters.
t = log(35000/8000)/log(1+0.025) ≈ 59.77 . . . quarters
Anisha will have $35,000 after 59.77/4 = 14.9 years.
__
7.No loan payment period is given, so we assume that the $43000 represents the repayment of the entire loan. The growth rate is 6% per year. The time required for the loaned amount to accumulate to a value of $43,000 is ...
t = log(43,000/32,500)/log(1 +0.06) ≈ 4.80 . . . years
If the loan period is 4.80 years, Kevin will have paid 43,000 to pay it off.
__
8.The growth rate is 0.024/12 = 0.002 per month. The number of months to achieve the desired balance is ...
t = log(3200/1600)/log(1 +0.024/12) ≈ 346.92 . . . . months
The balance in the account will be $3200 after 346.92/12 = 28.91 years.
_____
Additional comment
As a crude check on the answers, the "rule of 72" can be used. It says the doubling time is approximately 72 divided by the growth rate in percent. That is, a 10% growth rate will cause the value to double in approximately 72/10 = 7.2 years.
In the first problem, the value grows from 8000 to 35000, which represents a little more than 2 doublings (8000 to 16000 and 16000 to 32000). So, it is reasonable to expect the time period to be near 2 times 7.2 years, or 14.4 years. The value of 14.9 years is not unreasonable.
Answer:
Compound interest formula
[tex]\Large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedQuestion 6Given:
A = $35,000P = $8,000r = 10% = 0.1n = 4t = time (in years)[tex]\begin{aligned}8000\left(1+\frac{0.1}{4}\right)^{4t} & = 35000\\(1.025)^{4t} & = \frac{35000}{8000}\\(1.025)^{4t} & = 4.375}\\\ln (1.025)^{4t} & = \ln 4.375\\4t \ln 1.025 & = \ln 4.375\\4t & = \frac{\ln 4.375}{\ln 1.025}\\t & = 0.25\left(\frac{\ln 4.375}{\ln 1.025}\right)\\t & = 14.9427947\end{aligned}[/tex]
Therefore, she will have $35,000 in 15 years.
Question 7Given:
A = $43,000P = $32,500r = 6% = 0.06n = 1t = time (in years)[tex]\begin{aligned}32500\left(1+\frac{0.06}{1}\right)^{1t} & = 43000\\32500(1.06)^{t} & = 43000\\(1.06)^{t} & = \frac{43000}{32500}\\(1.06)^{t} & = \frac{86}{65}\\\ln (1.06)^{t} & = \ln \left(\frac{86}{65}\right)\\t \ln 1.06 & = \ln \left(\frac{86}{65}\right)\\t & = \dfrac{\ln \left(\frac{86}{65}\right)}{\ln 1.06}\\t & = 4.804621116\end{aligned}[/tex]
Therefore, Kevin will have paid $43,000 on the loan in 4 years and 10 months.
Question 8Given:
A = $3,200P = $1,600r = 2.4% = 0.024n = 12t = time (in years)[tex]\begin{aligned}1600\left(1+\frac{0.024}{12}\right)^{12t} & = 3200\\1600(1.002)^{12t} & = 3200\\(1.002)^{12t} & = \frac{3200}{1600}\\(1.002)^{12t} & = 2\\\ln (1.002)^{12t} & = \ln 2\\12t \ln (1.002) & = \ln 2\\12t & = \dfrac{\ln 2}{\ln 1.002}\\t & = \frac{1}{12}\left(\dfrac{\ln 2}{\ln 1.002}\right)\\t & = 28.91000404\end{aligned}[/tex]
The balance of the account will be $3,200 in 28 years and 11 months.
Find the 97th term of the arithmetic sequence 25, 29, 33, ...25,29,33,...
If the first term is 25 and the common difference is 4. Then the 97th term of the sequence will be 409.
What is a sequence?A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.
The sequence is given below.
25, 29, 33, ...., so on
Then the first term is 25. And the common difference is 4.
Then the 97th term will be given as
[tex]\rm a_n = a + (n - 1)d[/tex]
where
n = 97
a = 25
d = 4
Then we have
a₉₇ = 25 + (97 - 1)4
a₉₇ = 25 + 96 x 4
a₉₇ = 25 + 384
a₉₇ = 409
Then the 97th term of the sequence will be 409.
More about the sequence link is given below.
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A ----------------- transforms some electrical energy into other forms of energy.
Answer:
A solar panel is the best way to transform electrical energy into other forms of energy
Linear math equations pls help will give brainlest
Answer:
Problem 21:
Slope = -3
y-intercept = (0, 7)
Problem 23:
Slope = 1
y-intercept = (0, -2)
Problem 22:
Slope = [tex]\frac{2}{3}[/tex]
y-intercept = (0, 1)
Step-by-step explanation:
In the slope formula, the coefficient of x (the number times x) is the slope. The number added or subtracted from it is the y-intercept.
In problem 21, -3 is the coefficient of x, so thats the slope. 7 is what's being added, so that is the y-intercept.
In problem 23, 1 is the coefficient of x (a singular x is the same as 1, or -1 if the variable is negative), so thats the slope. -2 is what's being subtracted, so that is the y-intercept.
In problem 22, [tex]\frac{2}{3}[/tex] is the coefficient of x, so thats the slope. 1 is what's being added, so that is the y-intercept.
hope this helps!
PLEASE HELP FOR BRAINLIESTTTT!!!!
The graph below shows how much money was given to a charity over five months.
What was the least donation amount in a month?
Answer:
3800
Step-by-step explanation:
Half way between 3700 and 3900
Answer:
3800
Step-by-step explanation:
it's plotted on the line between 3700 and 3900 and 3800 would be in the middle
a box in a shape of a rectangle prism has a length of 3 5/8 inches a width of 2 1/2 inches and a height of 4 inches. what is the volume of the box
Answer:
volume is 36.25inches
145/4
Step-by-step explanation:
L= 3 5/8inches
W= 2 1/2inches
H= 4inches
VOLUME = L×W×H
3 5/8 × 2 1/2 × 4 =
29/8 × 5/2 × 4 = 36.25inches
36.25→145/4
Find the positive solution for c:
8 2 + 15 2 = c 2
Answer:
15
Step-by-step explanation:
8² + 15² = c²
To find : Value of c
8² = 8 x 8 = 64
15² = 15 x 15 = 225
c² = 225
225 = 15 x 15 = 15²
So,
c² = 15²
c = 15
Answer these questions for me please i dont have time to go back and figure this out rn
Answer:
Step-by-step explanation:
in 6 years we know that it will be half, because that's what "half life" means
in 3 years it's only loses 1/2 * 1/2 = 1/4 of it's mass
in 1 year it's only loses 1/6 * 1/2 = 1/12 of it's mass
from that we can make the formula that
current weight of radium = Wr
Mass of radium orginal = Mo
year of time = t ( must be in years, not days, months or weeks )
Wr = (1/12)*t* Mo
draw the graph of y equals (2) x + 1
Answer + Step-by-step explanation:
y = 2x + 1 represents a linear function then the its graph is a line
To draw the line we have to determine two points that lie on that line
If x = 0 → y = 2(0) + 1 = 1 then the point A(0,1) lies on the line
If x = 2 → y = 2(2) + 1 = 5 then the point B(2,5) lies on the line
Now all we have to do is joining the points A and B with a line
The line AB represents our graph
The hanger image below represents a balanced equation.
36
a
a
Find the value of a that makes the equation true.
Answer:
18
Step-by-step explanation:
36 divided by two is 18 therefore 18+18 is 36
Question 5 of 10
Which of the following rational functions is graphed below?
10+
10
10
1 - 10
X1
X- 4
O A. Fx) = x+1
F
OB. FX) = (x-1(x+4)
(x
O C. FX) = x +
1
- x)
X-
O D. F(X) =
1
(x + 1)(x-4)
x
Answer:
A. is the correct answer tnx to the points
The function f(x) = 1/[(x-1)(x+4)] is a rational function with two vertical asymptotes and one horizontal asymptote, which is graphed below.
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
The function f(x) = 1/[(x-1)(x+4)] is a rational function with two vertical asymptotes and one horizontal asymptote.
The vertical asymptotes occur when the denominator, (x-1)(x+4), is equal to zero. This happens when x = 1 or x = -4.
Therefore, the graph will have two vertical asymptotes at x = 1 and x = -4.
The horizontal asymptote can be found by looking at the behavior of the function as x approaches positive or negative infinity. As x gets very large in either direction, the terms (x-1) and (x+4) become insignificant compared to x².
Hence, the correct option is (B) f(x) = 1/[(x-1)(x+4)].
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PLEASE HELP WILL MARL BRAINLIEST
Answer:
3pi/4
Step-by-step explanation:
can't really explain it that well, but I sure hope this helps!! :)
find the area of following quadeilaterals
???????
5. Apply the law of syllogism to form a new statement based on the following:
R S: If the dog jumps in the lake, then it gets wet.
S T: If the dog gets wet, then it can’t come in the house.
The new statement becomes "If the dog jumps in the lake, then it can't come in the house".
What is the law of syllogism?Legal syllogism is a legitimate concept that deals with the law and how it is applied, specifically a type of argument that uses deductive reasoning to determine whether a given act is legal.
We have a statement:
R → S: If the dog jumps in the lake, then it gets wet.
S > T: If the dog gets wet, then it can’t come in the house.
After applying the law of syllogism to form a new statement:
R→T:
If the dog jumps in the lake, then it can't come in the house.
Thus, the new statement becomes "If the dog jumps in the lake, then it can't come in the house".
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Suppose that $16,000 is deposited for five years at 5 % APR. Calculate the interest earned if interest is compounded semiannually. Round your answer to the nearest
cent.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$16000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &5 \end{cases} \\\\\\ A=16000\left(1+\frac{0.05}{2}\right)^{2\cdot 5}\implies A=16000(1.025)^{10}\implies A\approx 20481.35[/tex]
$16000 for five years at 5% APR compounded semiannually gives an interest of 4481 dollars.
What is compound interest?Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.
We know the formula for compound interest compounded semiannually is,
A = P[1 + (r/2)/100]²ⁿ.
Where, A = amount, P = principle, r = rate and n = time in years.
Given, $16,000 is deposited for five years at 5 % compounded semiannually.
A = 16000[1 + (5/2)/100]²ˣ⁵.
A = 16000[1 + 0.025]¹⁰.
A = 16000[1.025]¹⁰.
A = 16000×1.28.
A = 20481.
So, the interest earned is (20481 - 16000) = 4481 dollars.
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tony wants to buy a new radio for his car. It cost $350. He wants to purchase it in four months. How much will he have to save each month?
A person who does not swing from one emotion or another is said to be______.
A. an introvert
B. stable
C. unstable
D. an extrovert
Answer:
Stable. They're solid in they're emotions
Step-by-step explanation:
A bag contains 5 green and 3 white balls (the balls are identical in all respect except colour). A ball is drawn at random from the bag without looking into the bag. What is the probability of getting a green ball? Is it more or less than getting a white ball?
Answer:
Probability of getting a green ball is more than that of getting a white ball.
Step-by-step explanation:
There are in all (5+3= 8) outcomes of the experiment. There are 5 outcomes in favour of the event of getting a green ball as there are 5 identical green balls in the bag.
Therefore, P(a green ball) = 5/8
In the same way,P(a white ball) = 3/8
5/8 > 3/8Thus, clearly the probability of getting a green ball is more than that of getting a white ball.
A particular battery claims to have a mean life of 400 hours with a standard deviation of 30 hours. Approximately what percent of the batteries will last more than 420 hours?
Using the normal distribution, it is found that 25.14% of the batteries will last more than 420 hours.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.In this problem, we have that the mean and the standard deviation are given, respectively, by:
[tex]\mu = 400, \sigma = 30[/tex].
The proportion of the batteries will last more than 420 hours is one subtracted by the p-value of Z when X = 420, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{420 - 400}{30}[/tex]
Z = 0.67
Z = 0.67 has a p-value of 0.7486.
1 - 0.7486 = 0.2514.
0.2514 = 25.14% of the batteries will last more than 420 hours.
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2/3 employees of a company drive to work, 1/3 travel by bus and the rest walk . find the number of who walk.
I need help on these 3 problems cause I’m stuck on them someone pls help
Answer:
Step-by-step explanation:
4. Nicole can make 7 quarts of lemonade with 10 cups of sugar.
If 3/4 cup of sugar is used to make 1 quart of lemonade and 10 cups of sugar are available, then you multiply 3 times 10 (when multiplying fractions, you only multiply with the numerator, not the denominator) which will give you 30.
Now, you can write it as 30/4. Using simple division, you find that 30/4 is 7.5 (or 7 and 1/2), and because we're trying to find how many full quarts we can make using 10 cups of sugar, your answer will be 7.
5. Each person will get 0.83 repeating (or 5/6) boxes of raisins.
In this problem, we have 6 people and we have to share 5 boxes of raisins among all of them. We know that each person can't get 1 because there would have to be 6 boxes (1 for each person), so we have a fraction (or decimal, depending on where you're at).
Dividing 5/6, you'll simply get 5/6 because you can't simply this any further, but if you were to write this as a fraction, you'd get 0.83 repeating (over the 3).
6. Each class will receive 30 boxes of cracker jacks.
We know that there are 153 boxes of cracker jacks available, and this needs to then be split among 5 different classes. So, to find the answer, we have to divide 153 by 5. In doing that, we get 30.6, but because we're trying to find the whole number that the classes will receive, as you can't get a fraction of a box (at least, I assume), then each class will get 30 with 3 boxes remaining.
If v₁ = (3,7) and V₂ = (-2,4), then v₁v₂ is equal to which of the following?
A. (-6,28)
B. 34
C. 22
D. (-21,-8)
equation point-slope form y=4x+17
Answer:
I think it's y - 21 = 4 (x - 1)
Step-by-step explanation:
im sorry if it's wrong
A cyclist covers a distance of 90km in 3 hours, what is the average speed?
Answer: I think it's 30km per hour.
Step-by-step explanation:
So first you have to find what speed the cyclist is going per hour. So first I did 90/3 and that gave me 30.
12. Which equality represents y=3x^2+2 written in function notation?
Answer:
f(x) = 3x^2 + 2
Step-by-step explanation:
Find the exact value of Tan(-420)
Alyssa has a points card for a movie theater. She receives 70 rewards points just for signing up. She earns 12.5 points for each visit to the movie theater. She needs 245 points for a free movie ticket. How many visits must Alyssa make to earn a free movie ticket?
let x be the amount of times she visited the movie theater
[tex]70+12.5x=245\\\\12.5x=175\\\\x=14[/tex]
Alyssa needs to make 14 visits to earn a free movie ticket.
This is our y intercept
Rate of pay=12.5This is our slope.
So our equation is
p=12.5v+70Here v is visits
245=12.5v+7012.5v=175v=14visitsFind the area of the shaded region: 1500 7 cm A = [?] cm² Enter a decimal rounded to the nearest tenth.
The area of the shaded region is [tex]154cm^2[/tex]
Calculations and Parameters:The formula for solving the area of a circle is:
[tex]\pi r^2[/tex]
Where [tex]\pi[/tex]= 3.14
r= 7cm
To find the area, we would input the values together
[tex]3.14 * 7^2[/tex]
= 3.14 * 49
= 153.86cm^2
Rounded to the nearest tenth would be:
154cm^2
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Find the value of y for the given value of x. Round to the nearest hundredth.
y = 0.05 − 10 ln x; x = 0.09
Answer:
[tex]y\approx24.129[/tex]
Step-by-step explanation:
[tex]y=0.05-10\ln x;\: x=0.09\\y=0.05-10\ln(0.09)\\y\approx24.129[/tex]
Answer:
24.129
the answer is that and I need 20 characters
1. Which of the following are statistical questions? Select all that apply.
a. How many 6th grade students like pizza?
b. Did you go to the beach yesterday?
c. What is the favorite food of all FMS students?
d. What was the high temperature of Florida for each day of the week?
e. How does each student get to school in the morning?