Answer:
The total interest earned at the end of the year was $ 820, and the interest generated by the total deposited was 10.25%.
Step-by-step explanation:
Given that last year, Manuel deposited $ 7000 into an account that paid 11% interest per year and $ 1000 into an account that paid 5% interest per year, and no withdrawals were made from the accounts, to determine what was the total interest earned at the end of year and what was the percent interest for the total deposited, the following calculations must be performed:
7000 x 0.11 + 1000 x 0.05 = X
770 + 50 = X
820 = X
8000 = 100
820 = X
820 x 100/8000 = X
82,000 / 8,000 = X
10.25 = X
Therefore, the total interest earned at the end of the year was $ 820, and the interest generated by the total deposited was 10.25%.
The control department of a light bulb manufacturer randomly picks light bulbs from the production lot every week. The records show that, when there is no malfunction, the defect rate in the manufacturing process (due to imperfections in the material used) is . When or more of the light bulbs in the sample of are defective, the control unit calls repair technicians for service.
Required:
a. Find the mean of p, where p is the proportion of defective light bulbs in a sample of 4400 when there is no malfunction.
b. Find the standard deviation of p.
Answer:
The answer is a
Step-by-step explanation:
Please help it’s a test and I can’t get logged out
Answer:
the anwer is B ( i mean second option)
And you can try it
you will find ;
[tex]y = \frac{x}{3} - 1[/tex]
HAVE A NİCE DAY
Step-by-step explanation:
GREETİNGS FROM TURKEY ツ
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%.
(3a+2b-4c)+(3a+2b-4c)
6
+
4
−
8
Step-by-step explanation:
Please mark me as brain list and please like my answer and rate also
Answer:
hope this will help you more
How many students rank themselves as introverts? Demonstrate your work!!
Answer:
36 (maybe...)
Step-by-step explanation:
Technically there is no way to answer this question, it says that 120 ADULTS were surveyed and then asks how many STUDENTS rank themselves as introverts. But if we a supposed to assume that all adults are students:
The ratio of 3:7 means that for every 3 introverts, there are 7 extroverts.
In other words for every 10 people (total introvert+extrovert) there are 3 introverts.
So to find the number of introverts in the group of 120, just multiply by 3/10 or 0.3
The answer would be 36
Which equation represents a line which is parallel to the line y = -7x - 8?
7x + y = -3
x+ 7y = 7
y - 7x = 6
x- -7y = -28
Answer:
7x+y=-3
Step-by-step explanation:
if m is the slope of a line, then the slope of its parallel line will have the same slope m,
in the given equation, y=-7x-8, the slope is -7
among the options, 1st option has a slope of -7, since,
7x+y=-3
or, y=-7x-3
Answered by GAUTHMATH
The graphs below have the same shape the equation of the bluegrass is f(x)=x^3 what is the equation of the red graph
Answer:
g(x) = x^3 - 2
Step-by-step explanation:
As you can see on the graph, the line has been translated down 2 units.
If the graph of f has the same shape as the graph of g, then the slope remains the same. The y intercept (k) changes by -2 units, so the k value is -2
g(x) = x^3 - 2
Hope this helps!!
A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 50% of this population prefers the color green. If 14 buyers are randomly selected, what is the probability that exactly 12 buyers would prefer green
Answer:
The probability that exactly 12 buyers would prefer green
=0.00555
Step-by-step explanation:
We are given that
p=50%=50/100=0.50
n=14
We have to find the probability that exactly 12 buyers would prefer green.
q=1-p
q=1-0.50=0.50
Using binomial distribution formula
[tex]P(X=x)=nC_r p^r q^{n-r}[/tex]
[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^{14-12}[/tex]
[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^2[/tex]
[tex]P(x=12)=14C_{12}(0.50)^{14}[/tex]
[tex]P(x=12)=\frac{14!}{12!2!}(0.50)^{14}[/tex]
[tex]P(x=12)=\frac{14\times 13\times 12!}{12!2\times 1}(0.50)^{14}[/tex]
[tex]P(x=12)=91\cdot (0.50)^{14}[/tex]
[tex]P(x=12)=0.00555[/tex]
Hence, the probability that exactly 12 buyers would prefer green
=0.00555
express the ratio as a fraction in it's lowest terms.3kg to 800g
Answer:
15 / 4
Step-by-step explanation:
1 kg = 1000 g
3 kg
= 3 x 1000
= 3000 g
3kg to 800g
= 3kg : 800g
= 3000 : 800
= 30 : 8
= 30 / 8
= 15 / 4
15/4 is the fraction representing the ratio of 3 kilograms to 800 grams.
To express the ratio of 3 kilograms to 800 grams as a fraction in its lowest terms.
we need to convert both the quantities to the same units. Since 1 kg is equal to 1000 g, we can convert 3 kg to grams as follows:
3 kg = 3 * 1000 g = 3000 g
Now, we have the quantities in the same unit, and the ratio becomes:
3000 g to 800 g
To express this ratio as a fraction, we place the quantities over each other:
3000 g
-------
800 g
Now, to simplify the fraction to its lowest terms, we find the greatest common divisor (GCD) of the two numbers (3000 and 800) and divide both the numerator and denominator by this GCD.
The GCD of 3000 and 800 is 200, so dividing both by 200 gives us:
3000 ÷ 200 = 15
800 ÷ 200 = 4
Therefore, the ratio 3 kg to 800 g expressed as a fraction in its lowest terms is 15/4.
In summary, we first converted the units to the same (grams) to make the ratio easier to handle. Then, we represented the ratio as a fraction and simplified it to its lowest terms using the GCD method. The final answer, 15/4, is the fraction representing the ratio of 3 kilograms to 800 grams.
To know more about Fraction here
https://brainly.com/question/32865816
#SPJ2
What is the product of
(5^-4)(5^-3)
Answer:
option one is the correct answer
Answer:
1/625
Step-by-step explanation:
The data on the box plot describes the weight of several students in sixth grade. Which of the following statements are true about the data set? Select all that apply.
One-fourth of the students weigh between 90 and 101 pounds.
One-half of the students weigh between 75 and 90 pounds.
The median weight of the sixth graders is 85 pounds.
One-fourth of the students weigh less than 75 pounds.
One-fourth of the students weigh more than 75 pounds.
The total range of weight is 40 pounds.
Answer:
Step-by-step explanation:
B
Help me or ill fail plz
Answer:
1,108 in²
Step-by-step explanation:
SA = (12×20) + (2×20×5 + 2×12×5) + (2×½×12×9)
+ (2×20×11)
= 240+320+108+440
= 1,108 in²
Answer pllllllleeeaaaaasssss
(3.1) … … …
[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{2x-y}{x-2y}[/tex]
Multiply the right side by x/x :
[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{2-\dfrac yx}{1-\dfrac{2y}x}[/tex]
Substitute y(x) = x v(x), so that dy/dx = x dv/dx + v :
[tex]x\dfrac{\mathrm dv}{\mathrm dx} + v = \dfrac{2-v}{1-2v}[/tex]
This DE is now separable. With some simplification, you get
[tex]x\dfrac{\mathrm dv}{\mathrm dx} = \dfrac{2-2v+2v^2}{1-2v}[/tex]
[tex]\dfrac{1-2v}{2-2v+2v^2}\,\mathrm dv = \dfrac{\mathrm dx}x[/tex]
Now you're ready to integrate both sides (on the left, the denominator makes for a smooth substitution), which gives
[tex]-\dfrac12\ln\left|2v^2-2v+2\right| = \ln|x| + C[/tex]
Solve for v, then for y (or leave the solution in implicit form):
[tex]\ln\left|2v^2-2v+2\right| = -2\ln|x| + C[/tex]
[tex]\ln(2) + \ln\left|v^2-v+1\right| = \ln\left(\dfrac1{x^2}\right) + C[/tex]
[tex]\ln\left|v^2-v+1\right| = \ln\left(\dfrac1{x^2}\right) + C[/tex]
[tex]v^2-v+1 = e^{\ln\left(1/x^2\right)+C}[/tex]
[tex]v^2-v+1 = \dfrac C{x^2}[/tex]
[tex]\boxed{\left(\dfrac yx\right)^2 - \dfrac yx+1 = \dfrac C{x^2}}[/tex]
(3.2) … … …
[tex]y' + \dfrac yx = \dfrac{y^{-3/4}}{x^4}[/tex]
It may help to recognize this as a Bernoulli equation. Multiply both sides by [tex]y^{\frac34}[/tex] :
[tex]y^{3/4}y' + \dfrac{y^{7/4}}x = \dfrac1{x^4}[/tex]
Substitute [tex]z(x)=y(x)^{\frac74}[/tex], so that [tex]z' = \frac74 y^{3/4}y'[/tex]. Then you get a linear equation in z, which I write here in standard form:
[tex]\dfrac47 z' + \dfrac zx = \dfrac1{x^4} \implies z' + \dfrac7{4x}z=\dfrac7{4x^4}[/tex]
Multiply both sides by an integrating factor, [tex]x^{\frac74}[/tex], which gives
[tex]x^{7/4}z'+\dfrac74 x^{3/4}z = \dfrac74 x^{-9/4}[/tex]
and lets us condense the left side into the derivative of a product,
[tex]\left(x^{7/4}z\right)' = \dfrac74 x^{-9/4}[/tex]
Integrate both sides:
[tex]x^{7/4}z=\dfrac74\left(-\dfrac45\right) x^{-5/4}+C[/tex]
[tex]z=-\dfrac75 x^{-3} + Cx^{-7/4}[/tex]
Solve in terms of y :
[tex]y^{4/7}=-\dfrac7{5x^3} + \dfrac C{x^{7/4}}[/tex]
[tex]\boxed{y=\left(\dfrac C{x^{7/4}} - \dfrac7{5x^3}\right)^{7/4}}[/tex]
(3.3) … … …
[tex](\cos(x) - 2xy)\,\mathrm dx + \left(e^y-x^2\right)\,\mathrm dy = 0[/tex]
This DE is exact, since
[tex]\dfrac{\partial(-2xy)}{\partial y} = -2x[/tex]
[tex]\dfrac{\partial\left(e^y-x^2\right)}{\partial x} = -2x[/tex]
are the same. Then the general solution is a function f(x, y) = C, such that
[tex]\dfrac{\partial f}{\partial x}=\cos(x)-2xy[/tex]
[tex]\dfrac{\partial f}{\partial y} = e^y-x^2[/tex]
Integrating both sides of the first equation with respect to x gives
[tex]f(x,y) = \sin(x) - x^2y + g(y)[/tex]
Differentiating this result with respect to y then gives
[tex]-x^2 + \dfrac{\mathrm dg}{\mathrm dy} = e^y - x^2[/tex]
[tex]\implies\dfrac{\mathrm dg}{\mathrm dy} = e^y \implies g(y) = e^y + C[/tex]
Then the general solution is
[tex]\sin(x) - x^2y + e^y = C[/tex]
Given that y (1) = 4, we find
[tex]C = \sin(1) - 4 + e^4[/tex]
so that the particular solution is
[tex]\boxed{\sin(x) - x^2y + e^y = \sin(1) - 4 + e^4}[/tex]
A farmer picks pumpkins from a large field. The farmer makes samples of 260 pumpkins and inspects them. If one in fifty pumpkins are not fit to market and will be saved for seeds, what is the standard deviation of the mean of the sampling distribution of sample proportions?
Answer:
[tex]\mu = 5.2[/tex]
[tex]\sigma = 2.257[/tex]
Step-by-step explanation:
Given
[tex]n = 260[/tex] -- samples
[tex]p = \frac{1}{50}[/tex] --- one in 50
Solving (a): The mean
This is calculated as:
[tex]\mu = np[/tex]
[tex]\mu = 260 * \frac{1}{50}[/tex]
[tex]\mu = 5.2[/tex]
Solving (b): The standard deviation
This is calculated as:
[tex]\sigma = \sqrt{\mu * (1-p)}[/tex]
[tex]\sigma = \sqrt{5.2 * (1-1/50)}[/tex]
[tex]\sigma = \sqrt{5.2 * 0.98}[/tex]
[tex]\sigma = \sqrt{5.096}[/tex]
[tex]\sigma = 2.257[/tex]
work out the area of this shape
Answer:
1000
Step-by-step explanation:
the focus of a parabola is (-5,-1) and the directrix is y= -3.
what is an equation of the parabola? (one of the answered above)
Answer:
Step-by-step explanation:
-2
Expand 5(2x-1) please I need it for homework.
10x-5
Answer:
5(2x-1)
5*2x 5*-1
10x-5
Hey there!
5(2x - 1)
= 5(2x) + 5(-1)
= 10x - 5
Therefore, your answer should be: 5x - 5
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
One-ninth of all sales at a local Subway are for cash. If cash sales for the week were $690, what were
Subway's total sales?
Select one:
O a. $22,600
O b. $2,611
O c. $6,210
O d. $2,610
e. None of these
Answer:
c. $6,210Step-by-step explanation:
Total sales = x
x*1/9 = 690x = 690*9x = 6210Correct choice is C
In the diagram below, POR is a diameter, <QPR is a°,<PRS is (4a+12)°. find the value of a
Answer:
22=4
Step-by-step explanation:
0977-=ytb
Which value of n makes the equation true?
-1/2n=-8
Answer:
16?
Step-by-step explanation:
I'm not sure. I hope so.
The formula for centripetal acceleration, a, is given by this formula, where v is the velocity of the object and r is the object’s distance from the center of the circular path:
A= V2/R
Solve the formula for r.
Answer:r=v^2/A
Step-by-step explanation: To solve for r means you have to isolate r on one side and put all the other terms on the other. To get r out from under the fraction, multiply both sides by r. This leaves:
A*r=v^2 so to isolate r, divide by A and get:
r=v^2/A.
FREE
Circle O has a circumference of approximately 250 ft.
What is the approximate length of the diameter, d?
O 40 ft
O 80 ft
O 125 ft
O 250 ft
Save and Exit
Next
Submit
Mark this and return
Answer:
Step-by-step explanation:
circumference = πd ≅ 250 ft
d ≅ 250/π ≅80 ft
Many electronics follow a failure rate described by an exponential probability density function (PDF). Solar panels are advertised to last 20 years or longer, but panels made in China are failing at a higher rate. The time-to-failure of this device is usually exponentially distributed with mean 13 years. What is the probability of failure in the first 5 years
Answer:
The right answer is "0.3193".
Step-by-step explanation:
According to the question,
Mean,
[tex]\frac{1}{\lambda} = 13[/tex]
[tex]\lambda = \frac{1}{13}[/tex]
As we know,
The cumulative distributive function will be:
⇒ [tex]1-e^{-\lambda x}[/tex]
hence,
In the first 5 years, the probability of failure will be:
⇒ [tex]P(X<5)=1-e^{-\lambda\times 5}[/tex]
[tex]=1-e^{-(\frac{1}{13} )\times 5}[/tex]
[tex]=1-e^(-\frac{5}{13})[/tex]
[tex]=1-0.6807[/tex]
[tex]=0.3193[/tex]
Let Y1 and Y2 denote the proportions of time (out of one workday) during which employees I and II, respectively, perform their assigned tasks. The joint relative frequency behavior of Y1 and Y2 is modeled by the density function.
f (y 1,y2)=y 1+y 2 o<=y 1<=1, 0<=y2<=1(0 elsewhere)
a. Find P (Y1< 1/2,y2>1/4)
b. Find P(Y 1+Y2<=1)
Are Y1 and Y2 independent?
(a) The region Y₁ < 1/2 and Y₂ > 1/4 corresponds to the rectangle,
{(y₁, y₂) : 0 ≤ y₁ < 1/2 and 1/4 < y₂ ≤ 1}
Integrate the joint density over this region:
[tex]P\left(Y_1<\dfrac12,Y_2>\dfrac14\right) = \displaystyle\int_0^{\frac12}\int_{\frac14}^1 (y_1+y_2)\,\mathrm dy_2\,\mathrm dy_1 = \boxed{\dfrac{21}{64}}[/tex]
(b) The line Y₁ + Y₂ = 1 cuts the support in half into a triangular region,
{(y₁, y₂) : 0 ≤ y₁ < 1 and 0 < y₂ ≤ 1 - y₁}
Integrate to get the probability:
[tex]P(Y_1+Y_2\le1) = \displaystyle\int_0^1\int_0^{1-y_1}(y_1+y_2)\,\mathrm dy_2\,\mathrm dy_1 = \boxed{\dfrac13}[/tex]
Y₁ and Y₂ are not independent because
P(Y₁ = y₁, Y₂ = y₂) ≠ P(Y₁ = y₁) P(Y₂ = y₂)
To see this, compute the marginal densities of Y₁ and Y₂.
[tex]P(Y_1=y_1) = \displaystyle\int_0^1 f(y_1,y_2)\,\mathrm dy_2 = \begin{cases}\frac{2y_1+1}2&\text{if }0\le y_1\le1\\0&\text{otherwise}\end{cases}[/tex]
[tex]P(Y_2=y_2) = \displaystyle\int_0^1 f(y_1,y_2)\,\mathrm dy_1 = \begin{cases}\frac{2y_2+1}2&\text{if }0\le y_2\le1\\0&\text{otherwise}\end{cases}[/tex]
[tex]\implies P(Y_1=y_1)P(Y_2=y_2) = \begin{cases}\frac{(2y_1+1)(2y_2_1)}4&\text{if }0\le y_1\le1,0\ley_2\le1\\0&\text{otherwise}\end{cases}[/tex]
but this clearly does not match the joint density.
Add. Please show work too.
Answer:
-36m^3-21n^3+85mn^2+36m^2n
Step-by-step explanation:
That's what the calculator says:).
Find the volume of the figure. Express answers in terms of t, then round to the nearest whole number
Please help :)
Answer:
729π ft³
Step-by-step explanation:
Applying,
Volume of a cone
V = πr²h/3.............. Equation 1
Where r = radius of the base, h = height, π = pie
From the question,
Given: r = 9 ft, h = 27 ft
Substitite these values into equation 1
V = π(9²)(27)/3
V = 729π ft³
Hence the volume of the figure in terms of π is 729π ft³
A tree cast a shadow of 30m long and a 2m stick casts one that is 3m long. As show in the below diagram how tall is the tree?
Answer:
20 mStep-by-step explanation:
We have similar triangles here.
BC║DE, AB║AD and AC║AE ⇒ ΔADE ~ ΔABCThe ratio of corresponding sides of similar triangles is same:
BC/DE = AC/AEBC / 2 = 30/3BC / 2 = 10BC = 2*10BC = 20 mTake the similar triangles,
→ ∆ADE ≈ ∆ABC
Now we can find,
The height of the tree in meters,
→ BC/DE = AC/AE
In this equation BC is the height of tree,
→ BC/2 = 30/3
→ BC/2 = 10
→ BC = 10 × 2
→ BC = 20
Hence, the height of the tree is 20 m.
Two competitive brothers, who work in two different industries, were comparing their salaries. Because there is a difference of 4 years in their respective work experience, they decided to compare, not their actual salaries, but to compare their salaries against their company averages to see who is doing better. The following gives the brothers salaries, companies mean, and standard deviation for each company
Brother Salary P sd
Tom 84000 75000 7000
Andy 70578 60000 8200
What is the 2-score of Andy's salary?
a. 1.89
b. 1.89
c. 1.29
d. 0-129
Answer:
c. 1.29
Step-by-step explanation:
Z-score:
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.
Andy 70578 60000 8200
This means that [tex]X = 70578, \mu = 60000, \sigma = 8200[/tex]
What is the z-score of Andy's salary?
This is Z, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70578 - 60000}{8200}[/tex]
[tex]Z = 1.29[/tex]
So the correct answer is given by option c.
For a popular Broadway music the theater box office sold 356 tickets at $80 a piece275 tickets at $60 a piece and 369 tickets at $ 45 a piece. How much money did the box office take in?
Answer:
Step-by-step explanation:
356 * 80 = 28 480
275 * 60 = 16 500
369 * 45 = 16 605
sum = $ 61 585
What does point b represent on the graph ?
Answer:
Step-by-step B represents the $14 John earned in the 2 hours he worked.
explanation:
