Answer:
1. A = 3/12
B= 4/12
C = 5/12
2......
3. Randy
Step-by-step explanation:
3+4+5 = 12
therefore there are 12 letters in the box
we can say that there are 3/12 A's in the box and do the same for the remaining letters
question two does not make sense
3. the person who has the lowest fraction in value which is A
Suppose that the consensus forecast of security analysts of your favorite company is that earnings next year will be $5.00 per share. The company plows back 50% of its earnings and if the Chief Financial Officer (CFO) estimates that the company's return on equity (ROE) is 16%. Assuming the plowback ratio and the ROE are expected to remain constant forever:
If you believe that the company's required rate of return is 10%, what is your estimate of the price of the company's stock?
Answer:
$250
Step-by-step explanation:
according to the constant dividend growth model
price = d1 / (r - g)
d1 = next dividend to be paid
r = cost of equity
g = growth rate
Sustainable growth rate is the rate of growth a company can afford in the long term
sustainable growth rate = plowback rate x ROE
b = plowback rate. It is the portion of earnings that is not paid out as dividends
g = 0.50 x 0.16 = 0.08 = 8%
5 / (10% - 8%)
5 / 2%
5 / 0.02 = $250
A point is selected at random from a line segment of length l, dividing it into two line segments. What is the probability that the longer line segment is at least three times as long as the shorter segment
Answer:
3/4
Step-by-step explanation:
Let a be the length of the shorter line segment and b be the length of the longer line segment.
Since the length of the line segment is l, we have that the length of the line segment equals length of shorter line segment + length of longer line segment.
So, l = a + b
Since we require that the longer line segment be at least three times longer than the shorter line segment, we have that b = 3a
So, l = a + b
l = a + 3a
l = 4a
The probability that the shorter line segment will be a(or 3 times shorter than b) is P(a) = length of shorter line segment/length of line segment = a/l
Since l = 4a.
a/l = 1/4
So, P(a) = 1/4
The probability that a will be less than 3 times shorter that b is P(a ≤ 1) = P(0) + P(a) = 0 + 1/4 = 1/4
The probability that b will be 3 times or more greater than a is thus P(b ≥ 3) = 1 - P(a ≤ 1) = 1 - 1/4 = 3/4
3. Express the strength of a solution both as a ratio and as a percentage if
2 L of the solution contain 400 mg of solute.
Answer:
1 : 5000
0.02%
Step-by-step explanation:
A solution = solute + solvent
A 2 Litre solution = (2 * 1000) = 2000 mg
Having, 400 mg of solute ;
Recall ;
1 mg = 0.001 ml
400 mg = (0.001 * 400) = 0.4 ml
The strength of the solution :
Amount of solute / Amount of solution
0.4 / 2000
As a ratio :
0.4 / 2000 = (0.4 * 10) / (2000*10) = 4 / 20000 = 1 / 5000 = 1 : 5000 (as a ratio)
0.4 / 2000
= 0.0002
(0.0002 * 100%) = 0.02% (As a percentage)
True or False? The total surface area of a cube can be calculated using its volume.
Answer: false
Step-by-step explanation:
Surface Area Formula Surface Area Meaning
SA=2B+Ph Find the area of each face. Add up all areas.
SA=B+12sP Find the area of each face. Add up all areas.
SA=2B+2πrh Find the area of the base, times 2, then add the areas to the areas of the rectangle, which is the circumference times the height.
for a science fair project javier is recording the amount of water that evaporate from a bucket in a month he creates a table like this i will give point for the best answer
week 1 2/16 inch
week 2 1/16 inch
week 3 3/16 inch
week 4 2/16 inch
how much water had evaported from the bucket at the end of week 2
what was the total amount of water that evaported in the four weeks
if javier orignally put 4 inches of water in the bucket how many inches of water were left after the experment was completed
Answer: [tex]\dfrac{3}{16},\ \dfrac{1}{2}, \dfrac{7}{2}\ \text{inch}[/tex]
Step-by-step explanation:
Given
Javier created a table for the amount of water evaporated in each week
After two weeks, the amount of water evaporated is
[tex]\Rightarrow \dfrac{2}{16}+\dfrac{1}{16}\\\\\Rightarrow \dfrac{2+1}{16}=\dfrac{3}{16}\ \text{inch}[/tex]
Total amount of water evaporated in four weeks is
[tex]\Rightarrow \dfrac{2}{16}+\dfrac{1}{16}+\dfrac{3}{16}+\dfrac{2}{16}\\\\\Rightarrow \dfrac{2+1+3+2}{16}=\dfrac{8}{16}\\\Rightarrow \dfrac{1}{2}\ \text{inch}[/tex]
If Javier originally puts 4 inches of water, amount of water left in the bucket
[tex]\Rightarrow 4-\dfrac{1}{2}\\\\\Rightarrow \dfrac{4\times 2}{2}-\dfrac{1}{2}\\\\\Rightarrow \dfrac{8-1}{2}=\dfrac{7}{2}\ \text{inch}[/tex]
It has been determined that 60% of the people in a certain midwest city who are responsible for preparing the evening meal have no idea what they are going to prepare as late as 4PM in the afternoon. A recent survey was conducted from 1000 of these individuals. For the sampling distribution of the sample proportion to be reasonably Normal, the sample must have been obtained in the right way (ideally, a simple random sample) and the sample size must be large (so that at least 10 or more successes and failures). Are these conditions met
Answer:
Random sample, [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], so yes, both conditions were satisfied.
Step-by-step explanation:
60% of the people in a certain midwest city who are responsible for preparing the evening meal have no idea what they are going to prepare as late as 4PM in the afternoon.
This means that [tex]p = 0.6[/tex]
A recent survey was conducted from 1000 of these individuals.
This means that [tex]n = 1000[/tex]
Also, a random sample, so the first condition was satisfied.
The sample size must be large (so that at least 10 or more successes and failures).
[tex]np = 1000*0.6 = 600 \geq 10[/tex]
[tex]n(1-p) = 1000*0.4 = 400 \geq 10[/tex]
So yes, both conditions were met.
I need a fast help please
Answer:
(5) c
(6) c
(7) b
(8) a
Step-by-step explanation:
(5) The multiplicative inverse of a number n, is the number which when multiplied by n will give a result of 1 which is a multiplicative identity. The multiplicative inverse of a number is actually the reciprocal of that number. For example, the multiplicative inverse of n is 1/n. The multiplicative inverse of 5 is 1/5. The multiplicative inverse of 5/6 is 6/5.
Therefore, the multiplicative inverse of [tex]\frac{-11}{15}[/tex] is [tex]\frac{-15}{11}[/tex]
(6) To solve 7m + 12 = -4m + 78, follow these steps;
i. Collect like terms by putting terms with m on the left hand side and the terms without m on the right hand side as follows;
7m + 4m = 78 - 12
ii. Now solve both sides;
11m = 66
iii. Divide both sides by 11;
[tex]\frac{11m}{11} = \frac{66}{11}[/tex]
m = 6
(7) Let the number be x;
10 more than twice number is 22 implies that
10 + 2x = 22
Now solve the equation;
2x = 22 - 10
2x = 12
x = 6
(8) The interior angles of a given polygon are the angles of its vertices that are within or inside of the polygon.
The sum of the interior angles of a polygon is given by;
(n-2) x 180°
where;
n = number of sides of the polygon.
For example;
For a triangle, which has n = 3 sides, the sum of these interior angles is (3 - 2) x 180° = 180°
For a rectangle/square, which has n = 4 sides, the sum of these interior angles is (4 - 2) x 180° = 360°.
For a pentagon, which has n = 5 sides, the sum of these interior angles is (5 - 2) x 180° = 540°
Therefore, depending on the number of sides n, the sum of the interior angles of a given polygon is given by;
(n-2) x 180°
B
13 ft.
5 ft.
A
C
12 ft.
Find the value of Cos (B) =
Answer: the answer is 12/13
Think about tossing two coins.
What is
P (H on first coin)? ………………………….
P (H on second coin)? ……………………..
List the paired outcomes for tossing two coins: ………………………………
How many ways are there for two coins to land? ………………………
What is P (HH)? …………………………
Given:
Two coins are tossed.
To find:
1. P(H on first coin)?
2. P(H on second coin)?
3. List the paired outcomes for tossing two coins.
4. How many ways are there for two coins to land?
5. What is P(HH)?
Solution:
If a a coin is tossed, then we have to possible outcomes, i.e., heads (H) and tails (T).
It is given that two coins are tossed.
1. The probability of getting a heads on first coin is:
[tex]P(H \text{ on first coin})=\dfrac{1}{2}[/tex]
2. The probability of getting a heads on second coin is:
[tex]P(H \text{ on second coin})=\dfrac{1}{2}[/tex]
3. If two coins are tossed, then the total possible outcomes are:
[tex]\{HH,HT,TH,TT\}[/tex]
4. The number of ways for two coins to land is 4.
5. The probability of the heads on both tosses is:
[tex]P(HH)=\dfrac{1}{4}[/tex]
Therefore, the required solution are:
1. [tex]P(H \text{ on first coin})=\dfrac{1}{2}[/tex]
2. [tex]P(H \text{ on second coin})=\dfrac{1}{2}[/tex]
3. List of possible outcomes is [tex]\{HH,HT,TH,TT\}[/tex].
4. Number of possible outcomes is 4.
5. [tex]P(HH)=\dfrac{1}{4}[/tex]
The number 55 is attached to a two-digit number to its left and the formed 4-digit number is divisible by 24. What could be the 2-digit number? List all options.
Given:
The number 55 is attached to a two-digit number to its left and the formed 4-digit number is divisible by 24.
To find:
The 2-digit numbers.
Solution:
Let the two digit number be [tex]ab[/tex]. Then the 4 digit number will be [tex]55ab[/tex].
We know that the number [tex]55ab[/tex] lies in the range 5500 to 5599.
Now,
[tex]5500=229\times 24+4[/tex]
It means, [tex]5500-4=5496[/tex] is divisible by 24. So, the numbers lie in the range 5500 to 5599 and divisible by 24 are:
[tex]5496+24=5520[/tex]
[tex]5520+24=5544[/tex]
[tex]5544+24=5568[/tex]
[tex]5568+24=5592[/tex]
Therefore, the possible 2-digit numbers are 20, 44, 68, 92.
evaluate:(0.0001)-¾
Answer:
0.001
Step-by-step explanation:
(0.0001)^-3/4=((0.1)⁴)^-3/4
(0.1)^4×-3/4
0.1^‐3
0.001
Find the perimeter of a football field which measures 90m by 60m
Hello!
[tex]\large\boxed{P = 300m}[/tex]
Use the following formula for the perimeter:
P = 2l + 2w, where:
l = length
w = width
Therefore:
P = 2(90) + 2(60)
Simplify:
P = 180 + 120 = 300 m
Answer:
well how about you use common sense 100 yards long on each side 200 yards then add 5o yards since the the that is how wide it is then add another 50 and you get 300 yards then convert that to meters
2.What is the value of x if x/4 + 12 = 4 ?
Answer:
Step-by-step explanation:
Answer:
hope it will help u
You can afford a $950 per month mortgage payment. You've found a 30 year loan at 8% interest. a) How big of a loan can you afford? b) How much total money will you pay the loan company? c) How much of that money is interest?
Answer:
129469.3194
342000
212530.6806
Step-by-step explanation:
Going to assume that the 8% is a nominal, montly rate
which means the effective monthly rate is .08/12= .006667
using the annuity immediate formula...
a.)
[tex]950(\frac{1-(1+.006667)^{-30*12}}{.006667})=129469.3194[/tex]
b.) we would pay 950*30*12= 342000
c.) the amount in interest would be 342000-129469.3194=212530.6806
a) The loan one can afford is $1,29,460.2
b) The total amount of money paid to the loan company over the life of the loan is $342,000.
c) $212539.8 of the total amount paid is interest.
To determine the answers to these questions, we'll need to use the formula for calculating a fixed monthly mortgage payment:
[tex]M = \frac{P \times r \times (1 + r)^n}{((1 + r)^n - 1)}[/tex]
where:
M is the monthly payment,
P is the principal loan amount,
r is the monthly interest rate (annual interest rate divided by 12),
and n is the total number of payments (number of years multiplied by 12).
Given:
Monthly payment (M) = $950
Loan term = 30 years
Interest rate = 8% per year
a) How big of a loan can you afford?
Let's calculate the principal loan amount (P):
First, we need to convert the annual interest rate to a monthly interest rate:
r = 0.08 / 12
= 0.00667
n = 30 years × 12 months
n= 360
Using the formula and plugging in the values we have:
[tex]950 = \frac{P \times 0.00667 \times (1 + 0.00667)^{360}}{((1 + 0.00667)^{360} - 1)}[/tex]
[tex]950 = \frac{P \times 0.00667 \times 10.948}{10.948 - 1}[/tex]
[tex]950=\frac{P \times 0.07302316}{9.948}[/tex]
[tex]950\times9.948 = 0.0730P[/tex]
Divide by 0.073:
Now we can solve for P:
[tex]P=\frac{9450.6}{0.0730}[/tex]
[tex]P = 1,29,460.2[/tex]
Therefore, you can afford a loan amount of $1,29,460.2
b) The total amount paid to the loan company can be calculated by multiplying the monthly payment by the total number of payments:
Total amount = Monthly payment × Total number of payments
Total amount =[tex]$950 \times 360[/tex]
Total amount = [tex]342,000[/tex]
Therefore, the total amount of money paid to the loan company over the life of the loan is $342,000.
c) To find out how much of the total amount paid is interest, we can subtract the principal loan amount from the total amount:
Interest = Total amount - Principal loan amount
Interest = [tex]342,000 - 129460.2[/tex]
=$212539.8
Therefore, $212539.8 of the total amount paid is interest.
To learn more on Simple Interest click:
https://brainly.com/question/30964674
#SPJ4
Tom's graduation picnic costs $4 for every attendee. At most how many attendees can there be if Tom budgets a total of $36 for his graduation picnic?
Instructions: Drag and drop the correct name for each angle. Each angle has more than one name so be sure to identity all the correct names
Answer/Step-by-step explanation:
Recall: an angle can be named in three different ways:
i. Using one letter which is the vertex of the angle. i.e. if the vertex of the angle is A we can name the angle as <A.
ii. Using the number of the labelled angle. i.e. is the angle is labelled 2, we can name it <2
iii. Using the three letters of the angles with the vertex angle in the middle. i.e. if the three points that form an angle are A, B, C and the vertex is B, we can name the angle as <ABC.
✔️Let's name the each angle given according:
1. <G, <3, and <FGH
2. <D, <4, and <CDE
3. <S and <TSR (the number seems blur and difficult to read. Whatever number is used to label the angle is what you'd use in naming the angle)
Parallel lines
What is the segment
Answer:
Step-by-step explanation:
The asymptote of the function f(x) = 3x + 1 – 2 is . Its y-intercept is
Answer:
-1
Step-by-step explanation:
1-2=-1
y=mx+b
b= y intercept
Answer:
-1
Step-by-step explanation:
A right rectangular prism has a length of 2 1/4 cm, width of 8 cm, and height of 20 1/2 cm.
What is the volume of the prism?
Enter the answer in the box.
cm³
Answer:
369 cm^3
Step-by-step explanation:
you just multiply all the numbers together
Answer:
369 cm³.
Step-by-step explanation:
Volume of a rectangular prism is just length × width × height. So:
2.25 × 8 = 18
18 × 20.5 = 369
So, the volume is 369 cm³.
Solve the given system by the substitution method.
3x + y = 14
7x - 4y = 20
Answer:
(4, 2 )
Step-by-step explanation:
Given the 2 equations
3x + y = 14 → (1)
7x - 4y = 20 → (2)
Rearrange (1) making y the subject by subtracting 3x from both sides
y = 14 - 3x → (3)
Substitute y = 14 - 3x into (2)
7x - 4(14 - 3x) = 20 ← distribute parenthesis and simplify left side
7x - 56 + 12x = 20
19x - 56 = 20 ( add 56 to both sides )
19x = 76 ( divide both sides by 19 )
x = 4
Substitute x = 4 into (3) for corresponding value of y
y = 14 - 3(4) = 14 - 12 = 2
solution is (4, 2 )
Answer:
[tex]3x + y = 14 \\ y = 14 - 3x \\ substitute \: y \: into \: equation \: 2\\ 7x - 4(14 - 3x) = 20 \\ 7x - 56 + 12x = 20 \\ 19x = 76 \\ x = \frac{76}{19} =4 \\ y = 14 - 3( 4 ) = 2 \\ [/tex]
A, B and C are collinear points. B is between A and C. AB=12 BC=18 AC=3x Find X.
Answer:
[tex]x =10[/tex]
Step-by-step explanation:
Given
[tex]AB = 12[/tex]
[tex]BC = 18[/tex]
[tex]AC = 3x[/tex]
Required
Solve for x
Since B is in between both points, then:
[tex]AC = AB + BC[/tex]
This gives
[tex]3x = 12 + 18[/tex]
[tex]3x = 30[/tex]
Divide by 3
[tex]x =10[/tex]
A committee raised 7/9 of their target goal last year and another 1/9 of the goal this year. What fraction of their goal has been raised
First, find 40% of 3,000:
0.40 * 3000 = 1200
So they raised 1200 so far.
Now subtract 1200 from the total they want to raise:
3000 - 1200 = 1800
So they need $1,800 more to meet their goal.
Answer:
8iriiruruj
Step-by-step explanation:
u4u the UK. We have a good idea to advertise the UK. I have been a
Ellen, Nick, and Ryan went shopping together. One of them bought a hat, another bought sunglasses, and another bought a belt. One paid $6, another paid $8, and another paid $10.
1) Nick bought the hat.
2) Ellen spent $8.
3) The belt did not cost $10.
4) Ryan spent the most. Which of the following is true?
(a) Nick bought the hat for $10.
(b) Ellen bought the belt for $8.
(c) Ryan bought the sunglasses for $8.
(d) Ryan bought the belt for $10
(e) Ryan bought the hat for 56.
Answer:
see down
Step-by-step explanation:
d is correct answer
me to
ICS A
V
t
V
30
A vehicle accelerates from 0 to 30 m/s in 10 seconds on a
straight road, then travels 15 seconds at a constant velocity.
Next it slows down, coming to a stop in 5 seconds. The car
waits 10 seconds, and then backs up for 5 seconds
accelerating from 0 to -10 m/s. Draw a graph showing the
vehicle's velocity vs time by following these steps.
20
What is the velocity of the vehicle at 0 seconds?
v m/s
Velocity (m/s)
es
10
40
20 30
Time (s)
Elementary
-10
S
Secondary
< Previous Activity
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US 1:09
The function c(r)=2r+12.5 represents the cost c, in dollars, of riding r rides
at a carnival. How much does it cost to get into the carnival? *
1 point
A.$2
B. $12.50
C. $14.50
D.r
what is the slope of the function, represented by the table of values below?
A. -2
B. -3
C. -4
D. -6
Answer:
B. -3
Step-by-step explanation:
A venture capital company feels that the rate of return (X) on a proposed investment is approximately normally distributed with mean 30% and standard deviation 10%.
(a) Find the probability that the return will exceed 55%.
(b) Find the probability that the return will be less than 25%
(c) What is the expected value of the return?
(d) Find the 75th percentile of returns.
Answer:
a) 0.0062 = 0.62% probability that the return will exceed 55%.
b) 0.3085 = 30.85% probability that the return will be less than 25%
c) 30%.
d) The 75th percentile of returns is 36.75%.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean 30% and standard deviation 10%.
This means that [tex]\mu = 30, \sigma = 10[/tex]
(a) Find the probability that the return will exceed 55%.
This is 1 subtracted by the p-value of Z when X = 55. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55 - 30}{10}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a p-value of 0.9938
1 - 0.9938 = 0.0062
0.0062 = 0.62% probability that the return will exceed 55%.
(b) Find the probability that the return will be less than 25%
p-value of Z when X = 25. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{25 - 30}{10}[/tex]
[tex]Z = -0.5[/tex]
[tex]Z = -0.5[/tex] has a p-value of 0.3085
0.3085 = 30.85% probability that the return will be less than 25%.
(c) What is the expected value of the return?
The mean, that is, 30%.
(d) Find the 75th percentile of returns.
X when Z has a p-value of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 30}{10}[/tex]
[tex]X - 30 = 0.675*10[/tex]
[tex]X = 36.75[/tex]
The 75th percentile of returns is 36.75%.
help pls I need it badly
9514 1404 393
Answer:
22
Step-by-step explanation:
For calculators without a cube root key, you can use the 1/3 power. The attached shows the quotient to be about 22.
Is a linear model or a quadratic model a better fit? Quadratic model graph quadratic model linear model
X S2.0.2
A rocket is fired upward with an initial velocity v of 80 meters per second. The quadratic function S(t) = -52 + 80t can be used to find
the heights of the rocket, in meters, at any time t in seconds. Find the height of the rocket 8 seconds after it takes off. During the
course of its flight, after how many seconds will the rocket be at a height of 290 meters?
9514 1404 393
Answer:
320 m after 8 seconds5.6 seconds, 10.4 seconds to height of 290 mStep-by-step explanation:
To find the height at 8 seconds, evaluate the formula for t=8.
S(t) = -5t^2 +80t
S(8) = -5(8^2) +80(8) = -320 +640 = 320
The height of the rocket is 320 meters 8 seconds after takeoff.
__
To find the time to 290 meters height, solve ...
S(t) = 290
290 = -5t^2 +80t
-58 = t^2 -16t . . . . . . . divide by -5
6 = t^2 -16t +64 . . . . . complete the square by adding 64
±√6 = t -8 . . . . . . . . . take the square root
t = 8 ±√6 ≈ {5.551, 10.449}
The rocket is at 290 meters height after 5.6 seconds and again after 10.4 seconds.
