Step-by-step explanation:
You deposit some money into a bank account paying 4% simple interest per year. You received $72 in interest after 3 years. How much the deposit (principal) was?
Question 3
The distribution of random variable R has mean 10 and standard deviation 4. The distribution of random variable S
has mean 7 and standard deviation 3. If Rand S are independent, what are the mean and standard deviation of the
distribution of R-S?
Mean 3 and standard deviation 1
B
Mean 3 and standard deviation 5
Mean 3 and standard deviation 7
mong
D
Mean 17 and standard deviation 1
E
Mean 17 and standard deviation 5
Answer:
(B) Mean 3 and standard deviation 5
Step-by-step explanation:
Property of mean
The mean of the sum or difference of two random variable R and S is the sum of their means.
μ (R-S) = μ(R) - μ(S)
μ(R-S) = 10 - 7 = 3
Property of standard deviation
The variance of Independent variable R and S is is the sum of their variances. Even when we subtract two random variables, we still add their variances; subtracting two variables increases the overall variability in the outcomes.
σ^2(R-S) = σ^2 (R) + σ^2(S)
= 16 + 9 ( variance = (standard deviation)^2 )
= 25
σ(R-S) = 5
The mean of the distribution of R-S is 3 and the standard deviation of the distribution of R-S is 5 and this can be determined by using the given data.
Given :
The distribution of random variable R has a mean of 10 and a standard deviation of 4. The distribution of random variable S has mean 7 and standard deviation 3.The following steps can be used in order to determine the mean and standard deviation of the distribution of R-S:
Step 1 - The mean can be determined by using the below formula.
[tex]\rm \mu(R-S) = \mu(R)-\mu(S)[/tex]
Step 2 - Substitute the values of [tex]\rm \mu(R)[/tex] and [tex]\rm \mu(S)[/tex] in the above expression.
[tex]\rm \mu(R-S) = 10-7[/tex]
[tex]\rm \mu(R-S) = 3[/tex]
Step 3 - The standard deviation can be determined by using the below formula.
[tex]\rm \sigma^2(R-S) = \sigma^2(R)+\sigma^2(S)[/tex]
Step 4 - Substitute the values of [tex]\rm \sigma(R)[/tex] and [tex]\rm \sigma(S)[/tex] in the above expression.
[tex]\rm \sigma^2(R-S) = 16+9[/tex]
[tex]\rm \sigma(R-S) = 5[/tex]
Therefore, the correct option is B).
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Hermina cut a 10 by 15 piece of cardboard down the diagonal
What is the c of the cut, in inches??
Answer:
[tex]\sqrt{325}[/tex]
Step-by-step explanation:
This is because you use Pythagorean theorem. a^2 + b^2 = c^2.
Identify the type of slope each line has. Place your answer under each graph.
-3, 0, 1/2, undefined
if it is going down its negative if it goes up its positive
first one you can tell because each one to the right it goes 3 down
2nd is 0 because there is no slope to it, last one is undefined because it cant be all the numbers when x is -4
Are the ratios 20:16 and 10:8 equivalent?
Matthew is competing in a race. He runs 20 kilometers in 2 hours. At the rate given how many kilometers can Matthew run in 1 hour?
Answer:
Mattew would run 10 kilometers in 1 hour
Step-by-step explanation:
20/2 = 10 Kilometers
2/2 = 1 hour
Write an equation for the graph below which represents a logarithmic function f with base 2 or 3 translated and/or reflected. X=3 (7,1) (5,0) (4,-1)
Answer:
The answer is "[tex]\log(x-3)- \log(2)[/tex]"
Step-by-step explanation:
The asymptote is that when the group is 0 within. Let's all assume that log base 2 is: Log(ax-b); a position mostly online also they know. Let's use this (5,0) and log(5a-b)=0; they get out of it 5a-b=1; now that the results for a and b must be known. So we can say unless the asymptote is x=3, 3a-b=0; then we have the equations system, and with a and b we can solve
[tex]\to b=5a-1 \\\\ \therefore\\\\\to 3a-(5a-1)=0\\\\\to 3a-5a+1=0\\\\\to -2a+1=0\\\\\to -2a=-1\\\\\to a=\frac{1}{2} \ and\ b= \frac{3}{2}[/tex]
[tex]\to \log(\frac{x}{2}-\frac{3}{2})\\\\\to \log(\frac{(x-3)}{2})\\\\\to \log(x-3)- \log(2)[/tex]
Anyone wanna help me with this
Question 1 Answer: both of them equal 20
Step-by-step explanation: when you add 9+3 it equals 12 then you add 8 and that makes 20. 9+8 also equals 17 then you add 3 which equals 20
The sum of three non-negative numbers is 36, and one of the numbers is twice one of the other numbers. What is the maximum value of the product of these three numbers?
Answer: 726.
Step-by-step explanation:
we have:
a, b and c non-negative numbers.
we know that:
a + b + c = 36.
(i also assume that the numbers are whole numbers)
and "one of the numbers is twice one of the others"
Then we can write:
a = 2*b
replacing that in the above equation, we get:
2*b + b + c = 36
3*b + c = 36.
Then the product between the 3 numbers will be:
P = a*b*c = (2*b)*b*c = 2*b^2*c.
Because we have b squared in the product, we want to find the maximum possible value of b, such that:
3*b + c = 36.
3*b = 36 - c
We know that 36 is a multiple of 3, and also is 3*b.
Then 36 - c must also be a multiple of 3, this means that c must be a multiple of 3 (and the smallest possible), which is 3.
Then if we have:
3*b = 36 - 3 = 33
3*b = 33
b = 33/3 = 11.
The prodct will be:
P = 2*(11^2)*3 = 726.
The maximum value of the product of the three given numbers is;
P_max = 726
Let the three non-negative numbers be x, y and z
We are told that they sum up to 36.
Thus;
x + y + z = 36.
Now, one of the numbers is twice one of the other numbers.
Thus;
x = 2y
Then, we now have;
2y + y + z = 36
⇒ 3y + z = 36.
We want to find the maximum value of the product between the 3 numbers. Let's say their product is P, then we have;
P = xyz
P = 2y²z
Since y is squared here, then let's make 3y the subject in 3y + z = 36.
3y + z = 36.
3y = 36 - z
since 3 is multiplied by y, it means that 36 - z be a multiple of 3 and we can infer that z must also be a multiple of 3. If we take z = 3, we have;
Then if we have:
3y = 36 - 3
3y = 33
y = 33/3
y = 11.
Since Product is P = 2y²z, then we have;
P = 2 × 11² × 3
P_max = 726
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Is d=2t portional or non portional?
Hii, can someone please help? I'm giving BRAINLIEST
Answer:
It would Be C I hoped this helped
I need it fasttttttt
5. Rex deposited $900 into an
account that earns 4% simple
interest. How many years will it
take for the value of the
account to reach $1,800?
Answer:
well, there is already $900 so 1800-900=900 now we need 4% of 900 which is $36 900 divided by 36 is 25
it will take 25 years
Step-by-step explanation:
plz mark brainliest i answered first
The number of years that will it take for the value of the account to reach $1,800 should be 25 years.
Calculation of the number of years:Since the deposited amount is $900
The rate of interest is 4%
The future value is $1,800
So here the balance amount should be
= $1,800 - $900
= $900
Now 4% of $900 = 36
So the number of year should be
= [tex]900\div 36[/tex]
= 25 years
hence, The number of years that will it take for the value of the account to reach $1,800 should be 25 years.
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Solve for r. r + 62 ÷ 2 =1
Hey there!
“r + 62 ÷ 2 = 1”
Combine your like terms
(62 ÷ 2)
62 ÷ 2 = 31
New equation
r + 31 = 1
SUBTRACT by 31
Like: r + 31 - 31 = 1 - 31
Cancel out: 31 - 31 because that gives you 0
Keep: 1 - 31 because that gives you the value of “r”
1 - 31 = -30
Therefore, your answer is: r = -30 ☑️
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
The revenue function is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x) is the unit price. If p(x)=34(3)−x6, find the revenue if 6 units are sold. Round to two decimal places.
Craig likes to collect vinyl records. Last year he had 10 records in his collection. Now he has 12 records. What is the percent increase of his collection.
Please answer with explanation.
Answer:
Craig's collection increased by 20%.
Step-by-step explanation:
Original amount: 10
New amount: 12
To find the percent increase, we first need to find how much Craig's record collection increased by. To do this, subtract the old amount from the new amount:
12 - 10 = 2
The amount his collection increased by is 2. To find the per cent increase, divide 2 by the original amount of records:
[tex]\frac{2}{10}=\frac{1}{5}= 0.20[/tex]
Convert the decimal into a percentage:
0.20 * 100 = 20%
The percent increase of Craig's record collection is 20%.
I need help answering the second one. please i really need to pass my final and this is extra credit.
Karl is a basketball player whose height is 76in. His team’s mean height is 79.5 in.
a) What is Karl’s z-score?
b) What percent of players in the team are shorter than Karl?
Helpppp ! Will give brainlist!
Answer:
5 parks
7 parks
9 parks
10 months
Step-by-step explanation:
1 month: 5 state parks
2 months:5+2=7 state parks
3 months:7+2=9 state parks
x months : 23 state parks
23-9 state parks = 14 state parks
14/2=7 it means 7 months more
3+7=10 months
10 months : 23 state parks
A car travels 180 miles in 3 hours, which is a rate of miles per hour.
Answer:
540
Step-by-step explanation:
multiply 180 by 3
Help plz:))) I’ll mark u brainliest
10 ez POINTS
the smallest three digit whole number ending with 9
Answer:
769
Step-by-step explanation:
Answer:
109
Step-by-step explanation:
Mellssa will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $44 and costs an additional S0.14 per mile driven.
The second plan has an initial fee of $51 and costs an additional $0.09 per mile driven
For what amount of driving do the two plans cost the
Same?
mile
17
What is the cost when the two plans cost the same?
X
5
?
Answer:
Step-by-step explanation:
44+.14x = 51+.09x
.05x=7
140=x, or the amount of driving the two needs to do for the plans to be the same
44+14(.14)
plug it back in to find the cost
$63.60
Please help me help me!! PLS
Answer:
m
Step-by-step explanation:
An urn contains 17 white balls and 18 red balls. A sample of four balls is selected at random from the urn. What is the probability that the sample contains two white balls and two red ones?
a. 0.0286
b. 0.2286
c. 0.3974
d. 0.0944
e. 0.0442
f. None of the above.
Answer:
c. 0.3974
Step-by-step explanation:
Given;
number of white balls, W = 17
number of red balls, R = 18
Total number of balls, T = 35
The number of ways the event will occur is given by
= P(2 whites) and P(2 reds)
= P(2whites) x P(2 reds)
= 17C2 x 18C2
= 136 x 153
= 20,808
The total number of possible outcome
= 35C4
= 52,360
The probability = 20,808 / 52,360
= 0.3974
The correct option is "C"
Probability that the sample contains two white balls and two red ones is equal to 0.3974.
So, option c. is correct.
Permutations and combinationsProbability is a discipline of mathematics concerned with numerical explanations of the likelihood of an event occurring or the truth of a claim.
Number of white balls [tex]=\boldsymbol{17}[/tex]
Number of red balls [tex]=\boldsymbol{18}[/tex]
Total number of balls [tex]=\boldsymbol{35}[/tex]
Probability that the sample contains two white balls and two red ones
[tex]=\frac{\binom{17}{2}\binom{18}{2}}{\binom{35}{4}}[/tex]
[tex]=\frac{\frac{17!}{15!2!}\frac{18!}{16!2!}}{\binom{35!}{31!4!}}[/tex]
[tex]=\boldsymbol{0.3974}[/tex]
So, option c. is correct.
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The different kinds of beads that Casey is
using to make purses come in packages of
3 and 9. What is the least number of each
kind of bead that Casey can buy to have an
equal number of each of the different kinds
of beads?
Answer:
Casey can buy 3 packages with 3 beads and one package with 9 beads to have the same number of beads of each kind.
Step-by-step explanation:
Given that:
The beads come in packages of 3 and 9.
To calculate the least number of beads that Casey can have, we will find the least common multiple of both packages.
Package of three = 3, 6, 9, 12, 15
Package of nine = 9, 18, 27, 36
The least common multiple of 3 and 9 is 9.
Hence,
Casey can buy 3 packages with 3 beads and one package with 9 beads to have the same number of beads of each kind.
Every 100 pounds on Earth are equivalent to 38 pounds on Mars.A boy weighs 60 pounds on Earth how much would he weigh on Mars
Answer:
22.8 pounds
Step-by-step explanation:
The answer is 22.8 because when you divide 100 by 38 you get 2.63157894737 and if you divide 60 by 2.63157894737 you get 22.8
I’m so confused, please help
I think is D
PLEASE MARK ME AS BRAINLIEST
If you want to buy an item in a store that costs $9 and is on sale for 20% off, then how much would the item actually cost you after the discount? Round to the nearest cent.
Answer:
Step-by-step explanation:
20% off is $1.80
9-1.8
the cost would be $7.20
Find two postive numbers such that the ratio of the two numbers is 5 to 3 and the product of the two numbers is 540.
Answer:
337.5 and also 202.5
Step-by-step explanation:
do 8x = 540 since 5 and 3 are in a ratio... so you get 5x plus 3x. Then you solve for x and get 67.5..67.5 times 3 is 202.5 and 67.5 times 5 is 337.5.
Answer:
[tex]lets \: number \: to \: be \: 5x \: and \: 3x \\ a.c \: \: \: \: \: (5x) \times (3x) = 540 \\ 15 {x}^{2} = 540 \\ {x}^{2} = \frac{540}{15} \\ {x}^{2} = 36 \\ x = \sqrt{36} \\ x = 6 \\ so \: number \: will \: be \\ 5x = 5 \times 6 = 30 \\ 3x = 3 \times 6 = 18 \\ [/tex]mark it as a Breallent answer and like❤PLEASE HELP!!! The half life of carbon-11 is 20 minutes. A sample of carbon-11 has
25mCi. How much is left after 1 hour?*
A)12.5mci
B)10.2mCi
C)2.25mci
D)3.125mci
Answer:
3.125 (D)
Step-by-step explanation:
1 is 1/2
25-1 4
20x3 = 60mins
3.125 would be took away results end with what you have took for this equation
What does the point (0, 0) mean in this situation?
Answer:
at 0 hours, 0 miles were traveled
what is 656x106 rounded
Answer:
69536
LOLLLLLLLLLL
Answer:
69536
Step-by-step explanation: and rounded to the nearest what