Answer:
The standard error of your estimate of the average height in the city is 0.5 inches.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes 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.
You begin by collecting the heights of a random sample of 196 people from the city.
This means that [tex]n = 196[/tex]
The standard deviation of the heights in your sample is 7 inches.
This means that [tex]\sigma = 7[/tex]
The standard error of your estimate of the average height in the city is
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{7}{\sqrt{196}} = 0.5[/tex]
The standard error of your estimate of the average height in the city is 0.5 inches.
write each equation explicitly in terms of x. then indicate whether the equation is a function.
3xy+x=y-6
We usually write explicit functions as one variable in terms of another variable. A simple example of an explicit function is a linear function, such as y = 4x - 7. This function is written as the dependent variable y in terms of the independent variable x.
A bank quotes an interest rate as 0.06341 annual effective yield. What interest rate, compounded monthly, will provide that
annual effective interest rate? Round your answer to five decimal places and do not round any intermediate calculations to
less than seven decimal places.
9514 1404 393
Answer:
0.06164
Step-by-step explanation:
The effective annual rate obtained by compounding nominal annual rate r monthly is ...
eff rate = (1 +r/12)^12 -1
Then the value of r is ...
r = 12×((eff rate) +1)^(1/12) -1)
For the given effective rate, that is ...
r = 12×(1.06341^(1/12) -1) ≈ 0.06164 . . . . nominal annual interest rate
Use the differential to approximate the expression. Then use a calculator to approximate the quantity, and give the absolute value of the difference in the two results to four decimal places.
√
53
9514 1404 393
Answer:
0.0056
Step-by-step explanation:
f(x) = √(49 +x)
f'(x) = 1/(2√(49 +x))
A linear approximation of f(x) expanded about x=0 is ...
f(x) ≈ f(0) + f'(0)x = 7 +x/(2·7)
Then for √53, we have x=4
f(4) ≈ 7 +4/14 = 7 2/7 . . . . . approximate √53 using differentials
__
The calculator value of √53 is about 7.280110, so the difference in results is ...
approx - actual ≈ 7.285714 -7.280110 = 0.005604 ≈ 0.0056
Solve for x
X-8 = -10
A) X = 2
B) X = -2
C) X = 18
D) X = -18
Answer:
x=–2
Step-by-step explanation:
x-8=-10
x=-10-8
x=–2
Answer:
-8= -10
, = -10+8
, = -2
16: The temperature yesterday at noon was 68.5 degrees. Today at noon
it was 59.9 degrees. What was the difference in temperature?
O A. 8.4 degrees
OB. 8.5 degrees
C. 8.6 degrees
O D. 8.7 degrees
Answer:
C
Step-by-step explanation:
It is 8.6 because we are finding the difference and using subtraction.
So I did 68.8-59.9 and I got 8.6
What is $124,503 rounded to the nearest thousand?
Answer:
124,503 round to 125,000
Step-by-step explanation:
4 is in the thousands place
We look at the hundreds place
5 is in the hundreds place. Since 5 is 5 or greater, we round the 4 up
124,503 round to 125,000
Tìm vi phân toàn phần của các hàm số sau:
ln(x+√(x^2+y^2 ) ) ln(sin(y/x))
Let f = ln(x + √(x ² + y ²)) ln(sin(y/x)).
Then the total differential is
[tex]\mathrm df = \dfrac{\mathrm d\left(x+\sqrt{x^2+y^2}\right)}{x+\sqrt{x^2+y^2}}\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}\right)\dfrac{\mathrm d\left(\sin\left(\frac yx\right)\right)}{\sin\left(\frac yx\right)}[/tex]
[tex]\mathrm df = \dfrac{\mathrm dx + \frac{\mathrm d(x^2+y^2)}{\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}}\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}\right)\dfrac{\cos\left(\frac yx\right)\,\mathrm d\left(\frac yx\right)}{\sin\left(\frac yx\right)}[/tex]
[tex]\mathrm df = \dfrac{\mathrm dx + \frac{2x\,\mathrm dx+2y\,\mathrm dy}{\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}\right)\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}}\right)\dfrac{\cos\left(\frac yx\right)\frac{x\,\mathrm dy-y\,\mathrm dx}{x^2}}{\sin\left(\frac yx\right)}[/tex]
[tex]\mathrm df = \dfrac{\left(2x+\sqrt{x^2+y^2}\right)\,\mathrm dx +2y\,\mathrm dy}{x\sqrt{x^2+y^2}+x^2+y^2\right)\ln\left(\sin\left(\dfrac yx\right)\right) \\\\ \indent + \dfrac1{x^2}\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}}\right)(x\,\mathrm dy-y\,\mathrm dx)[/tex]
[tex]\mathrm df = \left(\left(\dfrac{2x+\sqrt{x^2+y^2}}{x\sqrt{x^2+y^2}+x^2+y^2}\right)\ln\left(\sin\left(\dfrac yx\right)\right) - \dfrac y{x^2}\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}\right)\right)\,\mathrm dx \\\\ \indent + \left(\dfrac{2y}{x\sqrt{x^2+y^2}+x^2+y^2}\ln\left(\sin\left(\dfrac yx\right)\right)+\dfrac1x\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}\right)\right)\,\mathrm dy[/tex]
Find hyperbola equation. center (0,0) vertex (-2,0) focus (-5,0)
[tex] \frac{ {x}^{2} }{4} - \frac{ {y}^{2} }{21} = 1[/tex]
[tex] \frac{(x - h)^{2} }{ {a}^{2} } - \frac{(y - k) ^{2} }{ {b}^{2} } = 1 \\ [/tex]
a= (–2, 0) ; Center =(0,0)[tex]distance = \sqrt{(x2 - x1)^{2} + (y2 - y1) ^{2} } \\ a = \sqrt{(( - 2) - 0)^{2} + (0 - 0) ^{2} } \\ a = \sqrt{ {2}^{2} } \\ a = 2[/tex]C = (–5,0) ; Center =(0,0)[tex]distance = \sqrt{(x2 - x1) ^{2} + (y2 - y1) ^{2} } \\ c = \sqrt{(( - 5) - 0)^{2} + (0 - 0) ^{2} } \\ c = \sqrt{ {5}^{2} } \\ c = 5[/tex]
C²= a²+ b²(5)²= (2)² + b²b²= 25–4 —> b² = 21[tex]b = + \sqrt{21} , - \sqrt{21} [/tex]
[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{0 - 0}{0 - ( -5 )} = 0[/tex]
[tex] \frac{(x - h)^{2} }{ {a}^{2} } - \frac{(y - k) ^{2} }{ {b}^{2} } = 1 \\ [/tex]
[tex]\frac{(x - 0)^{2} }{ {2}^{2} } - \frac{(y - 0) ^{2} }{ { \sqrt{2} }^{2} } = 1 \\ [/tex]
[tex] \frac{ {x}^{2} }{4} - \frac{ {y}^{2} }{21} = 1[/tex]
I hope I helped you^_^
Solve the system of equations.
4x + 3y + 5z = 6
6x + 8y + 6z = 4
4x + 2y + z = 8
(x = 1, y = -1,2 = 1)
b. (x = 3, y = -3,2 = 3)
a.
C. (x = 0, y = 0, 2 = 2)
d. (x - 2, y --2, z = 0)
urgent !!!!!! plz image below
Answer:
[tex]216\ km^2[/tex]
Step-by-step explanation:
1. Approach
The surface area of a three-dimensional figure is the two-dimensional distance around the figure. The easiest way to find the surface area of a figure is to find the area of each of its facets, then add up the area to get the total surface area. The given pyramid is composed of four congruent triangles and a square. Find the area of one of the triangles, and then the area of the rectangle. Multiply the area of the triangle by four to account for the fact that there are four congruent triangles. Then add the area of the base to the result, the result attained is the surface area of the prism.
2. Find the area of the triangles
The formula to find the area of a triangle is the following:
[tex]A_t=\frac{b*h}{2}[/tex]
Where (b) represents the base and (h) represents the height of the triangle. Substitute the given values into the formula and solve for the answer.
[tex]A_t=\frac{b*h}{2}[/tex]
[tex]A_t=\frac{9*7.5}{2}[/tex]
[tex]A_t=\frac{67.5}{2}[/tex]
[tex]A_t=33.75[/tex]
3. Find the area of the rectangle
The formula to find the area of a rectangle is the following,
[tex]A_r=b*h[/tex]
Substitute the given values in and solve,
[tex]A_r=b*h[/tex]
[tex]A_r=9*9[/tex]
[tex]A_r=81[/tex]
4. Find the total surface area
Multiply the area of the triangle by four to account for the fact that there are four triangles. Then add its area to the area of the rectangle.
[tex]A_t+A_t+A_t+A_t+A_r=A[/tex]
[tex]4(A_t)+(A_r)=A[/tex]
[tex]4*33.75+81=A[/tex]
[tex]135+81=A[/tex]
[tex]216=A[/tex]
Which best describes the process of selecting a cluster sample?
Clusters that each represent the population are sampled from such that no two members of the same cluster are included in the sample.
Members of a population are organized in clusters, each of which is representative of the population, and then whole clusters are randomly selected to make up the sample.
Members of a population are ordered by some characteristic, and then a cluster sample is formed by selecting every kth member.
Members of a population are separated into clusters based on a characteristic important to the study and a random sample is selected from each cluster.
Answer:
"Members of a population are organized in clusters, each of which is representative of the population, and then whole clusters are randomly selected to make up the sample"
Step-by-step explanation:
In cluster random sampling, "the population is divided, usually geographically, into groups that generally have the same size. A certain number of groups are randomly chosen, and every individual in the chosen groups are chosen for the sample."
In accord with this logic, the second choice, "Members of a population are organized in clusters, each of which is representative of the population, and then whole clusters are randomly selected to make up the sample" seems to be correct.
NOTE: This may not be the correct answer. I am simply basing my answer on the definition I have learnt.
Answer:
B
Step-by-step explanation:
PLEASE HELP
Write the equation of the line that is perpendicular to the given segment and that passes through the point (-6, -3). A. 1 V=--x-3 2 B. 1 V=--X-6 2 C. y = 2x + 9 D. = 2x-6.
Answer:
C
Step-by-step explanation:
The slope of the line will be (2) and the equation will be C
Students in a statistics class are conducting a survey to estimate the mean number of units students at their college are enrolled in. The students collect a random sample of 48 students. The mean of the sample is 12.4 units. The sample has a standard deviation of 1.7 units.
Required:
What is the 95% confidence interval for the average number of units that students in their college are enrolled in?
Answer:
[11.906 ; 12.894]
Step-by-step explanation:
Given :
Sample mean, xbar = 12.4
Sample standard deviation, s = 1.7
Sample size, n = 48
We use the T distribution since we are using the sample standard deviation;
α - level = 95% ; df = n - 1 = 48 - 1 = 47
Tcritical = T(1 - α/2), 47 = 2.012
Using the confidence interval for one sample mean
Xbar ± Tcritical * s/√n
12.4 ± (2.012 * 1.7/√48)
12.4 ± 0.4936922
C. I = [11.906 ; 12.894]
find the value of z, angles related to a circle
There are 4 windows in the living room. Each window has 1 set of blinds and 2 panels of curtains. The blinds cost $20 each. Each curtain panel cost $28. How much do the window treatments cost?
Answer:
$304
Step-by-step explanation:
4 Windows (each window has 1 blind and 2 panels of curtains)
1 blind = $20 * 4 = $80
1 panels curtains = $28 * 2 = $56 * 4 = $224
$80 + $224 = $304
help me now where are you all helppppp
A fraction means division.
To find the decimal equivalent of a fraction, divide the top number by the bottom number.
If f(x)=logx, show that f(x+h)-f(x)/h=log[1+h/x]^1/h, h=/=0 (Picture attached, thank you!)
Answer:
Step by step proof shown below.
Step-by-step explanation:
To prove the equation, you need to apply the Logarithm quotient rule and the Logarithm power rule. Here's how the quotient rule looks like.
[tex]log_b(x/y) = log_b(x) - log_b(y)[/tex]
And here's how the power rule looks like
[tex]log_a(x)^n = nlog_a(x)[/tex]
First let's apply the quotient rule.
[tex]\frac{f(x+h)-f(x)}{h} = \frac{log_a(x+h)-log_a(x) }{h} = \frac{log_a(\frac{x+h}{x} )}{h}[/tex]
Now we can do some quick simplification, and apply the power rule.
[tex]\frac{1}{h} log_a(1 + \frac{h}{x} ) = log_a(1+\frac{h}{x} )^\frac{1}{h}[/tex]
A truck is said to get 18 miles per gallon on a highway, but this value can fluctuate, at most, by 4 miles per gallon. Which of the following absolute value inequalities matches this scenario? Question 23 options: |x + 18| ≤ 4 |x – 18| ≤ 4 |x – 4| > 18 |x + 18| > 4
Answer:
the correct answer is |x – 18| ≤ 4
just took the test
Step-by-step explanation:
If an angle of a right angle triangle is 81 find the remaining angle in grades
Answer:
9
Step-by-step explanation:
90+81+mising angle=180, missing angle is 9
What is the solution for the quadratic equation?
you buy butter at 3 dollars a pound one portion requires 2oz of butter how much for one portion
Answer:
0.375 dollars
Step-by-step explanation:
1 pound = 16 oz
1 oz = 1/16 pound
2 oz = 2/16
2/16 * 3 = 0.375
The following section is a statement from the rental agreement Tim signed when he rented his car this past weekend. “Upon checkout, the fuel level of the vehicle will be determined by turning the vehicle on and visually inspecting the fuel gauge. The approximate fuel level will be recorded on the Check-Out sheet and verified with initials by the vehicle Renter. One copy of the Check-Out sheet will be given to the customer. Another copy will be kept with the on-site records of the vehicle. The rented vehicle must be returned with a minimum fuel level the same as that indicated on the Check-Out sheet. A vehicle returned with a fuel level less than the approximate level indicated on the Check-Out sheet will be completely refueled with on-site pumps. The price of the fuel used to refuel the vehicle will be added to the Renter’s total charge at a cost of $4.50 per gallon plus a $5.00 re-fueling charge.” As a part of the check-out process, it is customary for a car rental agency to look over the car with the customer and fill out the Check-Out sheet together. As Tim was walking around the car looking for damages that he didn’t want to be held responsible for, the agency representative turned on the car, took note of the fuel level, and indicated it on the Check-Out sheet. Since Tim didn’t have any questions, the clerk handed him the keys and a copy of the Check-Out sheet and wished him well. Which action invalidates the contract Tim signed with the rental agency? a. Tim failed to notice a dent under the right front fender. b. The representative failed to give Tim a copy of the Check-Out sheet. c. The representative failed to have Tim initial by the fuel level on the Check-Out sheet. d. Neither Tim nor the representative checked the oil level in the car.
Answer:
C. The representative failed to have Tim initial by the fuel level on the Check-Out sheet.
Step-by-step explanation:
After reading the paragraph, we can eliminate B, by seeing that the representative did give him a copy of the Check-Out sheet, as quoted. "Since Tim didn’t have any questions, the clerk handed him the keys and a copy of the Check-Out sheet and wished him well.".
We can also eliminate A and D, as the contract stated nothing about dents or the oil level in the car.
The answer is C, as the representative failed to have Tim initial on the Check-Out sheet. That is a requirement for the contract to be valid, as stated. "The approximate fuel level will be recorded on the Check-Out sheet and verified with initials by the vehicle Renter.". However, Tim never initialed by the fuel level, as stated here. "...the agency representative turned on the car, took note of the fuel level, and indicated it on the Check-Out sheet. Since Tim didn’t have any questions, the clerk handed him the keys and a copy of the Check-Out sheet and wished him well.". No where here does it state that Tim initialed on the Check-Out sheet, meaning that he didn't. Him not doing so invalidates the contract.
How high is a tree that cast a 26ft shadow at the same time a6ft post casts a shadow which is 11ft long
Set up a ratio:
6/11 = x/26
Cross multiply:
11x = 156
Divide both sides by 11:
X = 14.18 feet ( round answer as needed.)
Decimal divison need answer no pdf
Answer:
1.84
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
A psychologist conducted a survey of the attitude towards the sustainability of American energy consumption with 250 randomly selected individuals several years ago. The psychologist believes that these attitudes have changed over time. To test this he randomly selects 250 individuals and asks them the same questions. Can the psychologist confirm his theory that the attitudes have changed from the first survey to the second survey?
Attitude 1st Survey 2nd Survey
Optimistic 7% 6%
Slightly Optimistic 9% 6%
Slightly Pessimistic 31% 37%
Pessimistic 53% 51%
Step 4 of 10: Find the expected value for the number of respondents who are optimistic. Round your answer to two decimal places.
Answer:
Yes. the Psychologist can confirm his theory that the attitudes have changed over time, based on the first and second surveys.
The expected value for the number of respondents who are optimistic is:
= 16.25
Step-by-step explanation:
Attitude 1st Survey 2nd Survey
Optimistic 7% 6%
Slightly Optimistic 9% 6%
Slightly Pessimistic 31% 37%
Pessimistic 53% 51%
Expected value of optimistic respondents:
Attitude
Optimistic Expected Value
1st Survey 8.75 (250 * 7% * 50%)
2nd Survey 7.50 (250 * 6% * 50%)
Total EV 16.25
work out the value of y when x = 4 30 points
Answer:
y = 54/25 when x = 4.
Step-by-step explanation:
y is given by the equation:
[tex]\displaystyle y = p\times q^{x-1}[/tex]
Where p and q are numbers.
We are also given that when x = 1, y = 10 and when x = 6, y = 0.7776.
And we want to determine the value of y when x = 4.
Since y = 10 when x = 1:
[tex]\displaystyle (10) = p\times q^{(1)-1}[/tex]
Simplify:
[tex]10 = p \times q^0[/tex]
Any number (except for zero) to the zeroth power is one. Hence:
[tex]p=10[/tex]
Thus, our equation is now:
[tex]y = 10\times q^{x-1}[/tex]
When x = 6, y = 0.7776. Thus:
[tex](0.7776) = 10\times q^{(6)-1}[/tex]
Simplify and divide both sides by ten:
[tex]\displaystyle 0.07776 = q^5[/tex]
Take the fifth root of both sides:
[tex]\displaystyle q = \sqrt[5]{0.07776}[/tex]
Use a calculator. Hence:
[tex]\displaystyle q = \frac{3}{5} = 0.6[/tex]
Our completed equation is:
[tex]\displaystyle y = 10\times \left(\frac{3}{5}\right)^{x-1}[/tex]
Then when x = 4, y equals:
[tex]\displaystyle \begin{aligned} y &= 10\times \left(\frac{3}{5}\right)^{(4)-1} \\ \\ &= 10\times \left(\frac{3}{5}\right)^3 \\ \\ &= 10\times \left(\frac{27}{125}\right) \\ \\ &= \frac{54}{25}\end{aligned}[/tex]
A lab technician needs 35 ml of 15% base solution for a certain experiment,
but she has only 10% solution and 20% solution. How many milliliters of
the 10% and the 20% solutions should she mix to get what she needs?
Answer:
17.5ml- of 10 percent solution, 17.5ml- of 20 percent solution
Step-by-step explanation:
35:100*15=5.25- ml of alkali in the base solution
Suppose we need x ml of 10 percents solution and 35-x - of 20 percents.
Then The quantity of alkali in the first one (10 percents) is x/100*10=0.1x
when in the second one we have (35-x)/100*20= 7-0.2x of alkali
0.1x+7-0.2x=5.25
7-0.1x= 5.25
0.1x=1.75
x=17.5- 0f 10 percents
35-17.5=17.5 - of 20 percents
Mrs Lee had $7500 in her bank account. The bank paid 4% interest at the
end of each year. How much did she have in the bank at the end of 1 year?
Answer:
$7800
Step-by-step explanation:
1. Principal x interest x rate
So: $7500 + 4% (0.04) x 1 year = $300
2. Interest + Principal
So: $7500 + $300
Mrs Lee had $7800 in the bank.
Write these numbers in expanded form 132 480 302
Step-by-step explanation:
132 = 100×1+3×10+2×1
480 = 100×4+8×10+0×1
302 = 100×3+0×10+2×1
I conducted a poll and asked 1012 students how many books they read last year. The data indicates x = 12.1 books and s = 16.6 books. Construct a 90% confidence interval for the number of books the students read. Z = 1.645
Answer:
(11.242 ; 12.958)
Step-by-step explanation:
The confidence interval is obtained using the relation :
C. I = xbar ± Zcritical * s/√n
Given that ::
xbar = 12.1 ;
Standard deviation, s = 16.6
n = 1012
C. I = 12.1 ± 1.645 * (16.6/√1012)
C.I = 12.1 ± 0.8583881
C. I = 11.242 ; 12.958
