A certificate of deposit offers a nominal interest rate of 2.5 percent annually.
If inflation is 1 percent, what is the real rate of return?
To solve this question, the real rate of return formula is used, and we apply the data given in the exercise into the formula to find the real rate of return.
Formula for the real rate of return:
[tex]R = \frac{1 + N}{1 + i} - 1[/tex]
In which N is the nomial rate and i is the inflation rate, as decimals.
A certificate of deposit offers a nominal interest rate of 2.5 percent annually.
This means that [tex]N = 0.025[/tex]
Inflation is 1 percent
This means that [tex]i = 0.01[/tex]
What is the real rate of return:
Now we apply the formula:
[tex]R = \frac{1 + 0.025}{1 + 0.01} - 1[/tex]
[tex]R = 1.0149 - 1[/tex]
[tex]R = 0.0149[/tex]
0.0149*100% = 1.49%
Thus, the real rate of return is of 1.49%.
For another example of a similar problem, you can check https://brainly.com/question/20164190
n a history class there are 88 history majors and 88 non-history majors. 44 students are randomly selected to present a topic. What is the probability that at least 22 of the 44 students selected are non-history majors
Answer:
0.5675 = 56.75% probability that at least 22 of the 44 students selected are non-history majors.
Step-by-step explanation:
The students are chosen without replacement from the sample, which means that the hypergeometric distribution is used to solve this question. We are working also with a sample with more than 10 history majors and 10 non-history majors, which mean that the normal approximation can be used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
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.
Approximation:
We have to use the mean and the standard deviation of the hypergeometric distribution, that is:
[tex]\mu = \frac{nk}{N}[/tex]
[tex]\sigma = \sqrt{\frac{nk(N-k)(N-n)}{N^2(N-1)}}[/tex]
In this question:
88 + 88 = 176 students, which means that [tex]N = 176[/tex]
88 non-history majors, which means that [tex]k = 88[/tex]
44 students are selected, which means that [tex]n = 44[/tex]
Mean and standard deviation:
[tex]\mu = \frac{44*88}{176} = 22[/tex]
[tex]\sigma = \sqrt{\frac{44*88*(176-88)*(176-44)}{176^2(175-1)}} = 2.88[/tex]
What is the probability that at least 22 of the 44 students selected are non-history majors?
Using continuity correction, as the hypergeometric distribution is discrete and the normal is continuous, this is [tex]P(X \geq 22 - 0.5) = P(X \geq 21.5)[/tex], which is 1 subtracted by the p-value of Z when X = 21.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{21.5 - 22}{2.88}[/tex]
[tex]Z = -0.17[/tex]
[tex]Z = -0.17[/tex] has a p-value of 0.4325
1 - 0.4325 = 0.5675
0.5675 = 56.75% probability that at least 22 of the 44 students selected are non-history majors.
Which graph best represents the equation -4x + 5y = 8
Answer:
a or b
Step-by-step explanation:
the pictures are a little hard to tell apart but im my opinion go for a because its the closest
Answer:
A.)
Step-by-step explanation:
I took the test.
the recipe for pumpking pie instructs you to bake the pie at 425∘F, for 15 minutes and then reduce the oven temperature to 350∘F. What is the change in temperature in degrees Celsius?
Answer:
ΔT = -75°F
Step-by-step explanation:
ΔT = T₁ - T₀ = 350 - 425 = -75°F
Write this ratio as a fraction in simplest form without any units.
7 gallons to 40 quarts
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Answer:
7/10
Step-by-step explanation:
In order to make the units cancel, they must be the same. There are 4 quarts in 1 gallon, so 40 quarts = 10×4 quarts = 10×(1 gal) = 10 gal.
Then the ratio is ...
(7 gal)/(10 gal) = 7/10
find the LCM of 210, 280, 360 by prime factorisation
Answer:
Step-by-step explanation:
210=2x3x5x7
280=2x2x2x5x7
360=2x2x2x3x3x5
Answer:
210= 2×3×5×7
280=2×2×2×5×7
360=2×2×2×3×3×5
common factors=2×2×2×3×5×7=840
uncommon factors=3
L.C.M=Common factors× uncommon factors
L.C.M=840×3
L.C.M=2520
Step-by-step explanation:
i hope it will be helpful
plzz mark as brainliest
Anna earned $9 an hour babysitting. She wants
to buy a 16 GB iPod that is $120. Anna has
saved $45 so far. How many more hours of
babysitting does she need to do to earn the rest
to purchase the iPod
Answer:
8.33 hours
Step-by-step explanation:
120-45 = 75
75 ÷ 9 = 8.33
A forest has 800 pine trees, but a disease is introduced that kills a fourth of the pine trees in the forest
every year.
Which graph shows the number y of pine trees remaining in the forest 2 years after the disease is
introduced?
In a graph
The exponential function that models the number of trees after t years is given by:
[tex]A(t) = 800\left(\frac{3}{4}\right)^t[/tex]
Hence, after 2 years, 450 trees will be remaining, as the graph at the end of this answer shows.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem:
The forest has 800 pine trees, hence A(0) = 800.Each year, a disease is introduced that kills a fourth of the pine trees in the forest every year, hence [tex]r = \frac{1}{4}[/tex].Then, the equation is:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 800(1 - \frac{1}{4})^t[/tex]
[tex]A(t) = 800\left(\frac{3}{4}\right)^t[/tex]
After 2 years:
[tex]A(2) = 800\left(\frac{3}{4}\right)^2 = 450[/tex]
450 trees will be remaining.
You can learn more about exponential functions at https://brainly.com/question/25537936
Which expression is equivalent to:
15x + 20y
5(4x+3y)
5(3x+4y)
5y(3x + 4)
Answer:
5(3x+4y)
Step-by-step explanation:
f(x) = 3x3
3.3 – 2.02 + 4x - 5
g(x) = 6x - 7
Find (f + g)(x).
Answer:
C) (f+g)(x)= 3x^3-2x^2+10x-12
The number formed by subtracted 1 from smallest 7-digit number is
Step-by-step explanation:
the number formed by subtracting 1 from the smallest 7 digit number is largest 6 digit number.
Find the missing side length. Leave your answers radical in simplest form. PLEASE HURRY
Answer:
y=8 and x=8 ✔3. the check is meant to be square root symbol lol
What is the slope-intercept equation of the line below?
10 minutes left
Answer:
y=-3x+4
Step-by-step explanation:
The y intercept is 4 because the line crosses the y axis at the 4 tic mark
The slope will be -3 because the y decreases by 3 every time the x incerases by 1
y=mx+b
y=-3x+4
What are the factors of 60 ???
Answer:
Factors are 1,2,3,4,5,6,10,12,15,20,30,60
Step-by-step explanation:
Hope this helps
Factors refers to those numbers which muntiplied that no.here, numbers that muntiply 60 are 1,2,3,4,5,6,10,12,15,20,30,60.
thus these numbers are factors of 60.
In how many ways can a committee of 3 men and 2 women can be formed from 7 men and 5 women?
Answer:
in five (5) ways a committee can be formed from 7 men and 5 women
Devaughn is 6 years older than Sydney. The sum of their ages is 56 . What is Sydney's age?
Answer:
Devaughn = 31, Sydney = 25
Step-by-step explanation:
(56-6)÷2= 25
So they would both be 25 if they were the same age but Devaughn is 6 years older so 25+6=31
ATQ
[tex]\\ \sf\longmapsto x+x+6=56[/tex]
[tex]\\ \sf\longmapsto 2x+6=56[/tex]
[tex]\\ \sf\longmapsto 2x=56-6[/tex]
[tex]\\ \sf\longmapsto 2x=50[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{50}{2}[/tex]
[tex]\\ \sf\longmapsto x=25[/tex]
interest on 600 2 years at rate of paise per rupee per month
a game is played with a fishpond containing 100 fish; 90 white, 9 red, and 1 blue. a contestant randomly catches a fish and receives payments as follows: $0.30 for white, $1.00 for red, and $10.00 for blue. If it cists $0.60 to play this game, how much (on average) does a contestant win on each play
Answer:
loses 14 cents
- $0.14
Step-by-step explanation:
90% $0.30 $(0.30) $(0.27)
9% $1.00 $0.40 $0.04
1% $10.00 $9.40 $0.09
$(0.14)
what equation shows a slope of 2/3 and a white intercept of 0, -2
y = 2/3 x - 2
Or
y + 2 = 2/3 ( x )
Answer:
y= 2/3x - 2
hope this helps :)
what is the main protein of a scientific investigation A. To form an opinion B. to test a hypothesis C. To persuade a bias D. To teach a lesson
Answer:
D.To teach a lesson
Step-by-step explanation:
Hope it helps you
The correlation coefficient, r, between the ages of employees, x, and the number of sick days taken per year, y, equals 0.81.
Complete the statement based on the information provided.
The value of r is
✔ positive
and is relatively close to
✔ 1
, so the variables are
✔ closely
associated. It appears that, as the age of an employee increases, the number of sick days taken
✔ increases
.
Answer:
✔ positive
✔ 1
✔ closely
✔ increases
ED2021
13 is subtracted from the product of 4 and a certain number. The result is equal to the sum of 5 and the original number. Find the number.
Answer:
The number is 6.
Step-by-step explanation:
[tex]4x-13=x+5\\3x-13=5\\3x=18\\x=6[/tex]
Can someone do #2?❤️
Answer:
b
Step-by-step explanation:
A proportional relationship is a straight line. Is must also go through the point (0,0)
b
Answer:
Step-by-step explanation:
A proportional relationship is a straight line. Is must also go through the point (0,0)
how many 50 cents coins are there in $10:50
Answer:
21
Step-by-step explanation:
you divide 10.50 by 50
Rewrite the expression as the algebraic expression in x
Sin
(tan^-1(x))
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Answer:
sin(tan^-1(x)) = x/√(x² +1)
Step-by-step explanation:
We know that for an angle in a right triangle...
Tan = Opposite/Adjacent
and
Sin = Opposite/Hypotenuse
so we can let Opposite = x and Adjacent = 1. The Pythagorean theorem tells us that ...
Hypotenuse² = Opposite² + Adjacent² = x² +1
Then the sine of the angle is ...
sin(tan^-1(x)) = x/√(x² +1)
Graphs of the following equations are straight lines except :
A. 3x+2y=8
B. y=x/2-5
C. x=4y
D. y=x^2+3
Answer:
D.
Step-by-step explanation:
D. This contains an x^2 and is called a parabola ( curved line like a U).
Answer:D
Step-by-step explanation: d is the correct answer
Please answer! These r my last questions
Answer:
8. -2a+14
9. w=3/2
Step-by-step explanation:
8.
The distributive property states that we can multiply each component in the parenthesis separately by the number on the outside, and then add that up to get our final answer.
For -2(a-7), this means that we can multiply -2 by a and then -2 by -7 (as 2 is the number on the outside, and a and -7 are the components in the parenthesis), add them up, and get our answer. This can be expressed as
-2 * a + (-2) * (-7) = final answer
= -2 * a + 14
We know that -2 * -7 = 14 because 2 * 7 = 14, and the two negatives in multiplication cancel each other out
9.
Using the subtraction property of equality, we can isolate the variable (w) and its coefficient (-2/3) by subtracting 5, resulting in
(-2/3)w = 4-5 = -1
Next, we can use the multiplication property of equality to isolate the w. To isolate the w, we can multiply its coefficient by its reciprocal. The reciprocal is the fraction flipped over. For (-2/3), its reciprocal is (-3/2), flipping the 2 and 3. We can multiply both sides by (-3/2) to get
w = (-3/2)
To check this, we can plug (-3/2) for w in our original equation, so
(-2/3) * (-3/2) + 5 = 4
-1 + 5 = 4
4 = 4
This works!
This figure shows △ABC. BD¯¯¯¯¯ is the angle bisector of ∠ABC.
What is AD?
Answer:
AD = 8/3 units
Step-by-step explanation:
Based on the angle bisector theorem, angle bisector BD divides AC into AD and CD such that they are proportional to AB and CB.
This implies:
AB/AD = CB/CD
AB = 8
CB = 10
Set AD equal to x
AD = x
CD = 6 - x
Substitute the values
8/x = 10/(6 - x)
8(6 - x) = 10(x)
48 - 8x = 10x
48 - 8x + 8x = 10x + 8x
48 = 18x
48/18 = 18x/18
8/3 = x
x = 8/3
AD = 8/3 units
Answer:8/3
Step-by-step explanation:
I just took the quiz
You can run at a speed of 4 mph and swim at a speed of 2 mph and are located on the shore, 6 miles east of an island that is 1 mile north of the shoreline. How far (in mi) should you run west to minimize the time needed to reach the island
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Answer:
5.423 miles
Step-by-step explanation:
Let x represent the distance to run. Then the remaining distance to the point that is closest to the island is (6-x) miles. The straight-line distance (d) to the point x from the island is given by the Pythagorean theorem:
d² = 1² +(6 -x)² = x² -12x +37
d = √(x² -12x +37)
The total travel time is the sum of times running and swimming. Each time is found from ...
time = distance/speed
total time = x/4 + d/2 = x/4 +(1/2)√(x² -12x +37)
__
The total time will be minimized when its derivative with respect to x is zero.
t' = 1/4 +(1/4)(2x -12)/√(x² -12x +37) = 0
Multiplying by 4 and combining fractions, we can see the numerator will be ...
√(x² -12x +37) +2x -12 = 0
Subtracting the radical term and squaring both sides, we get ...
4x² -48x +144 = x² -12x +37
3x² -36x +107 = 0
The quadratic formula tells us the smaller of the two roots is ...
x = (36 -√(36² -4(3)(107)))/(2(3)) = (36 -√12)/6 ≈ 5.423 . . . mi
You should run 5.423 miles west to minimize the time needed to reach the island.
__
A graphing calculator solves this nicely. The attached graph shows the time is a minimum when you run 5.423 miles.
(1 point) There were 23.7 million licensed drivers in California in 2009 and 22.76 million in 2004. Find a formula for the number, N, of licensed drivers in the US as a function of t, the number of years since 2004, assuming growth is (a) Linear N(t)
Answer:
N(t) = 0.188t + 22.76
Step-by-step explanation:
Number of licensed drivers in 2004 = 22.76 million
Number of licensed drivers in 2009 = 23.7 million
Number of licensed drivers, N as a function of t since year 2004 ;
General form of a linear function :
y = mx + c
c = intercept ; m = slope
Intercept c = value of y ; when x = 0
Here, population after uerssmmx,
Hence,
In 2004 ;
22.76 = mx + c
x = 0
22.76 = c
Number in 2009
x = number of yesrs after 2004 ; x = 2000 - 2004 = 5years
We can find the slope :
y = m*5 + 22.76
y = 23.7 in 2009
23.7 = 5m + 22.76
23.7 - 22.76 = 5m
m = 0.94 / 5
m = 0.188
Hence, the linear function can be written as :
N(t) = 0.188t + 22.76
