Answer:
35.2% probability that the sample mean will be 246 pages or more
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 245 \sigma = 15, n = 33, s = \frac{15}{\sqrt{33}} = 2.61[/tex]
What the probability that the sample mean will be 246 pages or more?
This is 1 subtracted by the pvalue of Z when X = 246. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{246 - 245}{2.61}[/tex]
[tex]Z = 0.38[/tex]
[tex]Z = 0.38[/tex] has a pvalue of 0.6480.
1 - 0.6480 = 0.3520
35.2% probability that the sample mean will be 246 pages or more
Point D' is the image of D(-2, 1) under a reflection across the x-axis.
Answer:
-2, -1
Step-by-step explanation:
the x same cause if you reflect across the x-axis so you move on the y-axis. and reflect means the same distance from the point you reflect (that it was 1 cause it was 1 point above the x-axis) just negative so -1 now. if the original point was -2,-1 so the answer was -2,1.
A researcher finds that of 1000 people who said that they attend a religious service at least once a week, A stopped to help a person with car trouble. Of 1200 people interviewed who had not attended a religious service at least once a month, B stopped to help a person with car trouble. At the 0.05 significance level, test the claim that the two proportions are equal.
Answer:
There is enough evidence to support the claim that the proportions are not equal. (P-value: 0.048).
Step-by-step explanation:
The question is incomplete:
"A researcher finds that of 1000 people who said that they attend a religious service at least once a week, 31 stopped to help a person with car trouble. Of 1200 people interviewed who had not attended a religious service at least once a month, 22 stopped to help a person with car trouble. At the 0.05 significance level, test the claim that the two proportions are different."
This is a hypothesis test for the difference between proportions.
The claim is that the proportions are not equal.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
The significance level is 0.05.
The sample 1, of size n1=1000 has a proportion of p1=0.031.
[tex]p_1=X_1/n_1=31/1000=0.031[/tex]
The sample 2, of size n2=1200 has a proportion of p2=0.018.
[tex]p_2=X_2/n_2=22/1200=0.018[/tex]
The difference between proportions is (p1-p2)=0.013.
[tex]p_d=p_1-p_2=0.031-0.018=0.013[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{31+22}{1000+1200}=\dfrac{53}{2200}=0.024[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.024*0.976}{1000}+\dfrac{0.024*0.976}{1200}}\\\\\\s_{p1-p2}=\sqrt{0+0}=\sqrt{0}=0.007[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.013-0}{0.007}=\dfrac{0.013}{0.007}=1.98[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]P-value=2\cdot P(z>1.98)=0.048[/tex]
As the P-value (0.048) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportions are not equal.
How many lbs to a kg?
Answer:
The answer would be, 0.454
Step-by-step explanation:
1 pound= 0.454 kilogram
Answer:
1kg = 2.20462262 rounded 2.20
Solve the two-step equation. -9x + 0.4 = 4 Which operation must be performed to move all the constants to the right side of the equation? Then, which operation must be performed to isolate the variable? The solution to the equation is x = .
Answer:
x = -0.4
Step-by-step explanation:
We have the equation:
-9x + 0.4 = 4
First, the operation to move all the constants to the right side is subtraction since we would have to subtract 0.4 from each side, let's see this:
[tex]-9x+0.4=4\\-9x+0.4-0.4=4-0.4\\-9x=3.6[/tex]
Now, we have all the constants on the right side of the equation.
Now, the operation we need to perform to isolate the variable is division (since the x has a -9 that is being multiplied by x) we need to do the opposite operation:
[tex]-9x=3.6\\\frac{-9x}{-9} =\frac{3.6}{-9} \\x=-0.4[/tex]
Thus, the answer to this equation is x= -0.4
Answer:
1.) Which operation must be performed to move all the constants to the right side of the equation?
✔ Subtract 0.4 (C)
2.) Then, which operation must be performed to isolate the variable?
✔ Divide by -9 on both sides. (D)
3.) The solution to the equation is x =
✔ -0.4 (B)
Step-by-step explanation:
I hope this helps!! Have a wonderful day!! :))
help, surface area. will mark brainliest!
Answer:
3024
Step-by-step explanation:
Find the area of the isosceles triangles, and add then with the three rectangles to get surface area.
14*24/2 * 2 = 336, and you have 25*42 * 2 = 2100, and finally you have 14*42 = 588. so the sum should be 3024
Solve the formula for c
m=h/c-w
Answer:
c = h/(m+w)
Step-by-step explanation:
m=(h/c)-w
Add w to each side
m+w=h/c-w+w
m+w = h/c
Multiply each side by c
c(m+w) = h/c*c
c(m+w) = h
Divide each side by (m+w)
c(m+w)/(m+w) = h/(m+w)
c = h/(m+w)
Conduct the following test at the alpha = 0.10 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume that the samples were obtained independently using simple random sampling.
Test whether p1 not equals p2. Sample data are x1 = 28, n1 = 254, x2 = 38, and n2 = 301.
Answer:
a) H0: p1 - p2 = 0
H1: p1 - p2 ≠ 0
b) z=-0.58
c) p-value = 0.562
Step-by-step explanation:
We need to determine whether p1 is not equals p2, so the null and alternative hypothesis are:
H0: p1 - p2 = 0
H1: p1 - p2 ≠ 0
Where p1 and p2 are the proportions of the population. Additionally, the proportions of the sample p1' and p2' are calculated as:
[tex]p1'=\frac{x1}{n1}=\frac{28}{254}=0.1102\\p2'=\frac{x2}{n2}=\frac{38}{301}=0.1262[/tex]
Then, the test statistic is calculated using the following equation:
[tex]z=\frac{(p1'-p2')-(p1-p2)}{\sqrt{p'(1-p')(\frac{1}{n1}+\frac{1}{n2})} }[/tex]
Where p' is calculated as:
[tex]p'=\frac{x1+x2}{n1+n2}=\frac{28+38}{254+301}=0.1189[/tex]
So, replacing the values, we get that the test statistic is:
[tex]z=\frac{(0.1102-0.1262)-(0)}{\sqrt{0.1189(1-0.1189)(\frac{1}{254}+\frac{1}{301})}}=-0.58[/tex]
Finally, using the standard normal table, the p-value is equal to:
[tex]p-value=2*P(z<-0.58)=2*0.281=0.562[/tex]
The p-value is greater that the value of alpha 0.1, so we can't reject the null hypothesis and there is evidence to said that p1 and p2 are equals.
an employee of a grocery store is placing an order for soda. there are 8 varieties of soda and they are sold in cases. each case contains all the same variety of soda. the store will order 50 cases total. how many ways are there to place the order
Answer:
There are 536,878,650 ways to place the order.
Step-by-step explanation:
The order in which the cases are put is not important. So we use the combinations formula to solve this question.
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]
In this question:
8 varieties from a set of 50. So
[tex]C_{50,8} = \frac{50!}{8!(50-8)!} = 536878650[/tex]
There are 536,878,650 ways to place the order.
60 POINTS Explain the process and solve a logarithmic equation. log x + log 8 – 2log 4 = 7.
Answer:
[tex]x = 20000000[/tex]
Step-by-step explanation:
Recall the power property of logarithms which states:
[tex]log(a^n)=n\,\,log(a)[/tex]
to re-write [tex]2\,log(4)=log(4^2)=log(16)[/tex]
and then use the product and quotient rules of logarithms:
[tex]log (A*B)=log(A)+log(B)[/tex]
and
[tex]log (\frac{A}{B} )=log(A)-log(B)[/tex]
to rewrite the combination of logarithms on the left of the equal sign as a single logarithm:
[tex]log(x)+log(8)-2\,\,log(4)=7\\log(x)+log(8)-log(16)=7\\log(\frac{8\,x}{16}) =7\\log(\frac{x}{2}) =7[/tex]
and now re-write this equation in exponent form to get rid of the logarithm:
[tex]10^7=\frac{x}{2} \\2\,\,\,10^7 = x\\x = 20000000[/tex]
Express this decimal as a fraction.
0.8 repeating decimal
According to R.L. Polk & Co., the average age of cars and light trucks in the U.S. is 10.8 years. Assume that the standard deviation for this population is 3.7 years. A sample of 35 randomly selected vehicles was selected. What is the probability that the sample mean will be greater than 10 years?
Answer:
10.03% probability that the sample mean will be greater than 10 years
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 10.8, \sigma = 3.7, n = 35, s = \frac{3.7}{\sqrt{35}} = 0.6254[/tex]
What is the probability that the sample mean will be greater than 10 years?
This is 1 subtracted by the pvalue of Z when X = 10. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{10 - 10.8}{0.6254}[/tex]
[tex]Z = -1.28[/tex]
[tex]Z = -1.28[/tex] has a pvalue of 0.1003
10.03% probability that the sample mean will be greater than 10 years
Find 3 points that solve the equation -x + 2y= 2
Answer:
(0,1)
(-2,0)
(2,2)
Step-by-step explanation:
HELP.
The number of reports of a certain virus has increased exponentially since 1960. The current number of cases can be approximated using the function r(t) = 207 e ^ 0.005t, where t is the number of years since 1960. Estimate the number of cases in the year 2010.
Answer:
The number of cases in the year 2010 is 266.
Step-by-step explanation:
An exponential function is one that the independent variable x appears in the exponent and has a constant a as its base. Its expression is:
f(x)=aˣ
being a positive real, a> 0, and different from 1, a ≠ 1.
In this case:
[tex]r(t) = 207*e^{0.005*t}[/tex]
where t is the number of years since 1960 and e is an irrational number of which it is not possible to know its exact value because it has infinite decimal places. The first figures are 2,7182818284590452353602874713527 and is often called the Euler's number. e is the base of natural logarithms.
In this case, you want to know the number of cases r (t) in 2010. So, to know t you must know how many years have passed since 1960. For that, you can simply do the following subtraction: 2010-1960 and you get as a result : 50.
Replacing in the exponential expression r (t):
[tex]r(t) = 207*e^{0.005*50}[/tex]
Solving:
r(t)=265.79 ≅ 266
The number of cases in the year 2010 is 266.
Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05.
Find an explicit solution for the initial-value problem and then fill in the following tables. (Round your answers to four decimal places. Percentages may be rounded to two decimal places.) y' = 2xy, y(1) = 1; y(1.5) y(x) = (explicit solution)
h = 0.1
xn yn Actual Value Absolute Error % Rel. Error
1.00 1.0000 1.0000 0.0000 0.00
1.10 1.2337 1.20 1.5527 1.30 1.9937
1.40 2.6117 1.50 3.4903
h = 0.05
xn yn Actual Value Absolute Error % Rel. Error
1.00 1.0000 1.0000 0.0000 0.00
1.05 1.1000 1.1079 0.0079 0.71
1.10 1.2155 1.2337 0.0182 1.48
1.15 1.3492 1.3806 0.0314 2.27
1.20 1.5044 1.5527 0.0483 3.11
1.25 1.6849 1.7551 0.0702 4.00
1.30 1.8955 1.9937 0.0982 4.93
1.35 2.1419 2.2762 0.1343 5.90
1.40 2.4311 2.6117 0.1806 6.92
1.45 2.7715 3.0117 0.2402 7.98
Answer:
see below for the tables
Step-by-step explanation:
The differential equation is separable, so the solution is ...
[tex]\displaystyle\dfrac{dy}{dx}=2xy\\\\\int{\dfrac{dy}{y}}=\int{2x}\,dx\\\\\ln{y}=x^2+C\\\\\text{Considering the initial condition, $C=-1$}\\\\\boxed{y=e^{x^2-1}}[/tex]
__
The values for yn are y+y'·h = y+2xyh. We take the "absolute error" to be the (signed) difference between the calculated yn and the actual value y(x).
Mr. Lim and Mr. Tay had $31 090 at first.Mr. Lim donated $2390 of his money and Mr. Tay spent half of his money on a holiday trip. As a result, Mr. Lim had 3 times as much money as Mr. Tay. How much money did Mr. Lim have at first?
Answer:
Mr.Lim had 19610 dollars, and Mr.Tay had 11480 dollars at first.
Step-by-step explanation:
Mr. Lim had 19610 dollars at first.
To find how much did Mr. Lim had at first.Given:
Mr. Lim and Mr. Tay had $31 090 at first.
Mr. Lim donated $2390 of his money and
Mr. Tay spent half of his money on a holiday trip.
Mr. Lim had 3 times as much money as Mr. Tay.
Step 1:
Let Mr. Tay had x
Let Mr. Lim had y
x + y=31090………..(1)
Step 2:
Mr. Tay spent on holiday = x + 2390/2
Money left with Mr. Lim = y - 2390
Given,
y - 2390 = 3(x + 2390/2) .............(2)
Step 3:
Equating equation (1) and (2)
we get,
x = 11480
y = 19610
Hence, Mr. Lim has $19610, and Mr. Tay had $11480 dollars at first.
To learn how to calculate the amount spent, refer,
https://brainly.com/question/2263981#SPJ2
What is the value of x?
Answer:
x=-14
Step-by-step explanation:
The 2 angles are opposite of each other. This means that they are vertical angles, are they are congruent.
Since they are congruent, we can set them equal to each and solve for x.
9x+184=7x+156
To solve the equation, we want to find out what x is. In order to do this, we have to get x by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.
First, subtract 7x from both sides.
9x-7x+184=7x-7x+156
9x-7x+184=156
2x+184=156
Next, subtract 184 from both sides.
2x+184-184=156-184
2x=156-184
2x=-28
Finally, divide both sides by 2.
2x/2= -28/2
x=-28/2
x= -14
The value of X is -14.
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Five crates weigh 200 pounds. One crate weighs 20 pounds but each of the other four crates weigh the same amount. What is the weight of the other 4 crates?
Subtract 20 from the total weight and divide by 4:
200 - 20 = 180
180/4 = 45
Each other crate weighs 45 pounds each.
Which describes something that is an obligation that must be paid?
A. Liability
O B. Bond
C. Liquid asset
Answer:
Liability
Step-by-step explanation:
Ap3x
What’s the correct answer for this?
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Tangents that meet at a point are equal in length so JL and LM are equal
Let's form an equation:
3x + 10 = 7x - 6
+6 to both sides
3x + 16 = 7x
-3x from both sides
16 = 4x
/4 on both sides
x = 4
Now, we can sub this value into the equation:
7(4) - 6 = 22
Thus, your answer is option B. 22
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Answer:
2ND OPTION
Step-by-step explanation:
in a circle , tangents drawn from an external point to the circle are equal.
ie JL = LM
3x+10 = 7x-6
10 + 6 = 7x- 3x
16 = 4x
x = 16/4
x=4
therefore LM = 7x -6 = 7*4 - 6
LM = 28 - 6 =22
therefore LM =22
HOPE IT HELPS. PLEASE MARK ME AS THE BRAINLIEST....
Evaluate the following Integrals ∫sin
Answer:
[tex]\displaystyle \int {xsinx} \, dx = -xcosx + sinx + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsIndefinite IntegralsIntegration Constant CIntegration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration by Parts: [tex]\displaystyle \int {u} \, dv = uv - \int {v} \, du[/tex]
[IBP] LIPET: Logs, inverses, Polynomials, Exponentials, TrigStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {xsinx} \, dx[/tex]
Step 2: Integrate Pt. 1
Identify variables for integration by parts using LIPET.
Set u: [tex]\displaystyle u = x[/tex][u] Differentiate [Basic Power Rule]: [tex]\displaystyle du = dx[/tex][dv] Trigonometric Integration: [tex]\displaystyle v = -cosx[/tex]Set dv: [tex]\displaystyle dv = sinx \ dx[/tex]Step 3: Integrate Pt. 2
[Integral] Integration by Parts: [tex]\displaystyle \int {xsinx} \, dx = -xcosx - \int {-cosx} \, dx[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {xsinx} \, dx = -xcosx + \int {cosx} \, dx[/tex][Integral] Trigonometric Integration: [tex]\displaystyle \int {xsinx} \, dx = -xcosx + sinx + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
Find the area of the figure. (Use “sq units” as the units of measure) Hints: Break it down into the triangle and 2 rectangles. Pay attention to the measurements.
Answer:
Area of the figure is 60.75 m²
Step-by-step explanation:
If we divide the given figure in three parts,
Area of the figure = Area of rectangle (1) + Area of rectangle (2) + Area of triangle (3)
Area of rectangle (1) = (Length × width)
= 3 × 4.5
= 13.5 m²
Area of rectangle (2) = (12 × 3)
= 36 m²
Area of triangle (3) = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(7.5)(3)[/tex]
= 11.25 m²
Area of the complete figure = 13.5 + 36 + 11.25
= 60.75 m²
Therefore, area of the figure is 60.75 m²
Natasha's sculpture was 5 3/16 inches tall. Mayas was 4 times as tall.How much shorter was Natasha's sculpture than Mayas
Answer:
Natasha's sculpture is 249/16 or 15.5625 or 15 9/16 inches shorter than Mayas sculpture
Step-by-step explanation:
The height of Natasha sculpture is 5 3/16 inches tall. Let us convert the height to an improper fraction.
5 3/16 = 83/16 inches tall. Therefore,
Natasha's sculpture is 83/16 inches tall.
According to the question Mayas own sculpture was 4 times as tall as Natasha's own sculpture. Mathematically, Mayas sculpture height can be expressed as follows
Mayas sculpture height = 4(83/16)
Mayas sculpture height = 4 × 83/16
Mayas sculpture height = 332/16
Mayas sculpture height = 20.75 inches or 83/4 inches
To know how much shorter was Natasha's sculpture we subtract Natasha sculpture height from Mayas sculpture height.
Therefore,
83/4 - 83/16 = (332 - 83) /16 = 249/16 or 15.5625 or 15 9/16
Natasha's sculpture is 249/16 or 15.5625 or 15 9/16 inches shorter than Mayas sculpture
The rectangle has a length of 4x+3 and a width of 3x. Show your work.
A. Find the perimeter.
B. Find the area.
C. Find the perimeter and area if x = 8.
Answer:
A. P = 14x+6
B. A = 12x^2 +9x
C. P = 118; A = 840
Step-by-step explanation:
A. The perimeter is twice the sum of length and width:
P = 2(L +W) = 2((4x+3) +(3x)) = 2(7x +3)
P = 14x +6 . . . . the perimeter of the rectangle
__
B. The area is the product of length and width:
A = LW = (4x +3)(3x)
A = 12x^2 +9x . . . . . the area of the rectangle
__
C. When x = 8, these values are ...
P = 14·8 +6 = 118 . . . . . perimeter in units
A = 12·8^2 +9·8 = 768 +72 = 840 . . . . . area in square units
Answer:
a) [tex] P = 2(4x+3) +2(3x) =8x +6 +6x = 14x +6[/tex]
b) [tex] A= 12x^2 +9x[/tex]
c) [tex] P = 14*8 +6 = 112+6 = 118[/tex]
[tex] A= 12(8)^2 +9*8 = 840[/tex]
Step-by-step explanation:
We know that the length is 4x+3 and the width is of 3x
Part a
For this case the perimeter is given by:
[tex] P = 2(4x+3) +2(3x) =8x +6 +6x = 14x +6[/tex]
Part b
The area is given by:
[tex] A= (4x+3) (3x)[/tex]
And after multiply we got:
[tex] A= 12x^2 +9x[/tex]
Part c
For this case replacing the value of x =8 we got:
[tex] P = 14*8 +6 = 112+6 = 118[/tex]
[tex] A= 12(8)^2 +9*8 = 840[/tex]
How much do you need to invest every month in an annuity to
reach a goal of $25,000 at the end of 5 years, if compounding is
done every month and the annual interest rate is 4%. Round up
to the next penny.
Answer:
A=25000 is the future value. P the value that we need to invest. r= 0.04 represent the interest rate in fraction. n = 12 represent the number of times that the rate is compounded in a year. t = 5 years.
If we solve for the value of P we got:
[tex] P= \frac{A}{(1+ \frac{r}{n})^{nt}}[/tex]
And replacing we got:
[tex] P= \frac{25000}{(1+ \frac{0.04}{12})^{12*5}} =20475.078[/tex]
And rounded to the nesrest penny we need to invest $20475.08 in order to have after 5 years $25000
Step-by-step explanation:
For this case we can use the future value with compound interest given by:
[tex] A = P (1+ \frac{r}{n})^{nt}[/tex]
Where:
A=25000 is the future value. P the value that we need to invest. r= 0.04 represent the interest rate in fraction. n = 12 represent the number of times that the rate is compounded in a year. t = 5 years.
If we solve for the value of P we got:
[tex] P= \frac{A}{(1+ \frac{r}{n})^{nt}}[/tex]
And replacing we got:
[tex] P= \frac{25000}{(1+ \frac{0.04}{12})^{12*5}} =20475.078[/tex]
And rounded to the nesrest penny we need to invest $20475.08 in order to have after 5 years $25000
Two numbers are in the ratio of 3:4. If they sum of the numbers is 63, find the numbers
Answer:
27 and 36
Step-by-step explanation:
Let's call the two numbers x and y.
[tex]3x=4y \\\\x+y=63[/tex]
If you subtract y from both sides of the second equation, you can isolate x and substitute it into the first equation:
[tex]x=63-y \\\\3(63-y)=4y\\\\189-3y=4y\\\\189=7y\\\\y=27\\\\x=63-27=36[/tex]
Hope this helps!
Compute the sample mean and sample standard deviation for private and public colleges. Round your answers to two decimal places. S1 = S2 = b. What is the point estimate of the difference between the two population means? Round your answer to one decimal place. Interpret this value in terms of the annual cost of attending private and public colleges. $ c. Develop a 95% confidence interval of the difference between the annual cost of attending private and pubic colleges. 95% confidence interval, private colleges have a population mean annual cost $ to $ more expensive than public colleges. Check My Work Icon Key Previous Question 4 of 9 NextExercise 10.13
Answer:
(1) The sample mean is = 6.98, the standard deviation is = 4.53 (2) The pint estimate difference is = 20.2 (3) The confidence interval limits are $ 15943.6 and $24456.4
Step-by-step explanation:
Solution
(A) The first step is to compute the mean sample and the standard deviation for private and public colleges.
Thus,
The mean and private colleges is computed as follows:
The mean and private colleges = The sum of derivation/The total number of observation
x= 42.5
The standard deviation is S₁ = 6.9806 = √∈ (xi - x)²/n-1
The mean of public colleges y =22.3
Standard deviation S₂ = 4.5323 = √∈ (yi - y)²/n-1
Thus,
S₁ = 6.98
S₂ =4.53
(b) We find the point estimate of the difference between two population means
Thus,
x -y = 42.5 -22.3
=20.2
Therefore, the annual cost is =$20,200
Note: Kindly find an attached copy of the option c and the complete question stated above.
Which product is negative? (Negative StartFraction 3 over 8 EndFraction) (Negative StartFraction 5 over 7 EndFraction) (one-fourth) (StartFraction 3 over 8 EndFraction) (Negative StartFraction 5 over 7 EndFraction) (Negative one-fourth) (StartFraction 3 over 8 EndFraction) (StartFraction 5 over 7 EndFraction) (one-fourth) (Negative StartFraction 3 over 8 EndFraction) (Negative StartFraction 5 over 7 EndFraction) (negative one-fourth)
Answer:
[tex](D)\left(-\dfrac38\right)\left(-\dfrac57\right)\left(-\dfrac14\right)[/tex]
Step-by-step explanation:
The given options are:
[tex](A)\left(-\dfrac38\right)\left(-\dfrac57\right)\left(\dfrac14\right)\\(B)\left(\dfrac38\right)\left(-\dfrac57\right)\left(-\dfrac14\right)\\(C)\left(\dfrac38\right)\left(\dfrac57\right)\left(\dfrac14\right)\\(D)\left(-\dfrac38\right)\left(-\dfrac57\right)\left(-\dfrac14\right)[/tex]
The key to determining which product is negative is to understand the rule of sign multiplication.
Now:
The product of even negative terms is positiveThe product of odd negative terms is negative.The product of positive will always be positive.In Options A and B, the number of negative signs is even, therefore our result is positive.
In option C, all the terms are positive, therefore our result will be positive.
In Option D, the number of negative signs is odd, therefore our result is negative.
Answer:
your answer is D
:)
Daley went to the grocery store to buy berries. Blueberries cost $1.50 a pound and strawberries cost $2.25 a pound. Daley spent $10.50 on fruit. The equation he wrote to represent the scenario is 1.5b + 2.25s = 10.5. His solution is: 1. Subtract 2.25s: 1.5b = 10.5 − 2.25s 2. Divide by 1.5: 1.5b 1.5 = 10.5 − 2.25s 1.5 3. Distribute 1.5: b = 7 − 1.5s Daley wrote an equivalent equation to determine how many pounds of blueberries he could buy. Analyze Daley’s work. Did he make an error? Yes. In step 1, he had to subtract 1.5b from both sides. Yes. In step 2, he had to multiply 1.5 to both sides. Yes. In step 3, he can only multiply the 1.5 and 12.5 together. No. He correctly solved for b.
Answer: 1.5(b)+ 2.25(s) = 10.05
Step-by-step explanation:
Answer:
B & S
Step-by-step explanation:
Can someone plz help me solved this problem I need help plz help me! Will mark you as brainiest!
Answer:
11
4
Step-by-step explanation:
3 hrs to travel 45 miles downstream
4 hrs to travel 28 miles upstream
speed of boat in still water= s
speed of the current= c
s+c= 45/3= 15s-c= 28/4=7added up the 2 equations, we get:
2s= 22s= 11 mphc= 4 mphDetermine whether the following sampling is dependent or independent. Indicate whether the response variable is qualitative or quantitative.
A researcher wishes to compare mental health of married lawyers and their spouses. She obtains a random sample of 406 such couples who take a mental health inventory and determines each spouses mental health.
1. Is this dependent or independent? Is it because one sample does or does not dictate the individual to be used in the second sample?
2. Is it quantitative or qualitative? And is that because it is an attribute classification or numerical measure?
Answer:1. Dependent
2.Qualitative Variable
Step-by-step explanation:
Step 1--- Dependent
Reason-- The researcher considers a couple as a whole and The sampling is dependent because a spouce selected for one sample dictates or determines which individual to be in the second sample.
Step 2----Qualitative variable
Reason--- it classifies the individual spouce mental health based on mental health inventory of the couple
Because Qualitative variables are variables which can be placed according to characteristic or attribute, here the characteristics is mental health.
Answer:
1) Dependent. It is becasue one sample indicates the individual to be used in another sample.
2) Quantitative. Attribute classification is numerical measure
Step-by-step explanation:
Mental health of Married lawyer and their spouses are to be compared. A married lawyers mental health is to be compared with his/her spouse only
Here attribute is mental health inventory which is quantitative.
