Answer:
The 99% confidence interval for the percentage of people who own a tablet computer is between 71.59% and 88.41%
Step-by-step explanation:
Confidence interval for the proportion of people who own a tablet:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 150, \pi = \frac{120}{150} = 0.8[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.576[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8 - 2.575\sqrt{\frac{0.8*0.2}{150}} = 0.7159[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8 + 2.575\sqrt{\frac{0.8*0.2}{150}} = 0.8841[/tex]
Percentage:
Multiply the proportion by 100.
0.7159*100 = 71.59%
0.8841*100 = 88.41%
The 99% confidence interval for the percentage of people who own a tablet computer is between 71.59% and 88.41%
2(x + 25) HELPPPPP MEEEEE
Answer:
2x+50
Step-by-step explanation:
Distributive property: 2(x)+2(25)
Simplify: 2x+50
Answer: 2x + 50
Step-by-step explanation: In this problem, the 2 distributes through the parenthses, multiplying by each of the terms inside.
So we have 2(x) + 2(25) which simplifies to 2x + 50.
Translate the following argument in a standard form categorial syllogims then use venn diagram or rules for syllogim to determine whether each is valid or invalid.
All of the movies except the romantic comedies were exciting. Hence, the action films were exciting,because none of them is a romantic comedies.
Answer:
couldnt tell you
Step-by-step explanation:
jkj
A study of the amount of time it takes a mechanic to rebuild the transmission for a 2010 Chevrolet Colorado shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time is less than 8.9 hours.
Answer:
96.08% probability that their mean rebuild time is less than 8.9 hours.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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:
[tex]\mu = 8.4, \sigma = 1.8, n = 40, s = \frac{1.8}{\sqrt{40}} = 0.2846[/tex]
Find the probability that their mean rebuild time is less than 8.9 hours.
This is the pvalue of Z when X = 2.9.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2.9 - 2.4}{0.2846}[/tex]
[tex]Z = 1.76[/tex]
[tex]Z = 1.76[/tex] has a pvalue of 0.9608
96.08% probability that their mean rebuild time is less than 8.9 hours.
Type 11/5 in the simplest form
Answer:
[tex]2\frac{1}{5}[/tex]
Step-by-step explanation:
11 ÷ 5 = 2 R 1 → [tex]2\frac{1}{5}[/tex]
Hope this helps! :)
What is the value of x in the figure above
the value of x is 115°.
hope its helpful to uh..
Researchers studied the mean egg length (in millimeters) for a particular bird population. After a random sample of eggs, they obtained a 95% confidence interval of (45,60) in millimeters. In the context of the problem, which of the following interpretations is correct, if any?
A. We are 95% sure that an egg will be between 45 mm and 60 mm in length.
B. For this particular bird population, 95% of all birds have eggs between 45 mm and 60 mm.
C. We are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.
D. We are 95% confident that the mean length of eggs in the sample is between 45 mm and 60 mm.
E. None of the above is a correct interpretation.
Answer:
C. We are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
For 95% confidence interval, it means that we are 95% confident that the mean of the population is between the given upper and lower bounds of the confidence interval.
For the case above, the interpretation of the 95% confidence interval is that we are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.
Translate into an equation: The cost of V ounces at $2 per ounce equals $56.
Answer:
V = number of ounces
56 = 2V
Step-by-step explanation:
Answer:28
Step-by-step explanation:V times 2= 56
In ABC,if sin A=4/5 and tan A=4/3, then what I s cos A?
The function defined by w(x)=-1.17x+1260 gives the wind speed w(x)(in mph) based on the barometric pressure x (in millibars,mb). a) Approximate the wind speed for a hurricane with the barometric pressure of 900mb. b) Write a function representing the inverse of w and interpret its meaning in context. c) Approximate the barometric pressure for a hurricane with speed 90 mph.
Answer:
a) 207 mph
b) x = (1260-w)/1.17
c) 1000 mb
Step-by-step explanation:
a) Put the pressure in the equation and solve.
w(900) = -1.17(900) +1260 = 207
The wind speed for a hurricane with a pressure of 900 mb is 207 mph.
__
b) Solving for x, we have ...
w = -1.17x +1260
w -1260 = -1.17x
x = (1260 -w)/1.17 . . . . inverse function
__
c) Evaluating the inverse function for w=90 gives ...
x = (1260 -90)/1.17 = 1170/1.17 = 1000 . . . millibars
The approximate barometric pressure for a hurricane with a wind speed of 90 mph is 1000 millibars.
The average daily rainfall for the past week in the town of Hope Cove is normally distributed, with a mean rainfall of 2.1 inches and a standard deviation of 0.2 inches. If the distribution is normal, what percent of data lies between 1.9 inches and 2.3 inches of rainfall? a) 95% b) 99.7% c) 34% d) 68%
Answer:
D
Step-by-step explanation:
We calculate the z-score for each
Mathematically;
z-score = (x-mean)/SD
z1 = (1.9-2.1)/0.2 = -1
z2 = (2.3-2.1)/0.2 = 1
So the proportion we want to calculate is;
P(-1<x<1)
We use the standard score table for this ;
P(-1<x<1) = P(x<1) -P(x<-1) = 0.68269 which is approximately 68%
Answer:
68
Step-by-step explanation:
You wish to take out a $200,000 mortgage. The yearly interest rate on the loan is 4% compounded monthly, and the loan is for 30 years. Calculate the total interest paid on the mortgage. Give your answer in dollars to the nearest dollar. Do not include commas or the dollar sign in your answer.
Answer:
$143,739
Step-by-step explanation:
We must apply the formula for P0 and solve for d, that is,
P0=d(1−(1+rk)−Nk(rk).
We have P0=$200,000,r=0.04,k=12,N=30, so substituting in the numbers into the formula gives
$200,000=d(1−(1+0.0412)−30⋅12)(0.0412),
that is,
$200,000=209.4612d⟹d=$954.83.
So our monthly repayments are d=$954.83. To calculate the total interest paid, we find out the entire amount that's paid and subtract the principal. The total amount paid is
Total Paid=$954.83×12×30=$343,738.80
and therefore the total amount of interest paid is
Total Interest=$343,738.80−$200,000=$143,738.80,
which is $143,739 to the nearest dollar.
The interest paid is 2912683 dollars.
What is compound interest ?Compound interest is calculated for the principle taken as well as previous interest paid.
According to the given question Principle amount (P) taken from the bank is 2000000 dollars.
The yearly interest rate (r) compounded monthly is 4%.
Time in years (n) is 30.
We know, in the case of compound interest compounded yearly is
A = P(1 + r/100)ⁿ.
So, Amount compounded monthly will be
A = P[ 1 + (r/12)/100]¹²ⁿ.
A = 2000000[ 1 + (4/12)/100]¹²ˣ³⁰.
A = 2000000[ 1 + 0.003]³⁶⁰.
A = 2000000[ 1.003]³⁰⁰.
A = 2000000(2.456).
A = 4912583.
∴ The total interest paid on the mortgage is (4912683 - 2000000) = 2912683.
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The function f(x) = 2x^3 + 3x^2 is:
(a) even
(b) odd
(c) neither
(d) even and odd
Answer:
neither
Step-by-step explanation:
First we must determine if both x and -x are in the domain of the function
since it is a polynomial function our first condition is satisfied
Then we should calculate the image of -x :
2x(-x)^3 + 3*(-x)² = -2x^3+3x²
it is not equal to f(x) nor -f(x)
Question
An airplane is traveling at a constant speed of 585 miles per hour. How many feet does it travel in 6 seconds? Remember
that 1 mile is 5280 feet.
Convert the 6 seconds to hours:
5 seconds x x 1/60 ( minutes per seconds) x 1/60 (Hours per minute) = 6/3600 = 1/600 hours.
Distance = speed x time
Distance = 585 x 1/600 = 585/600 = 0.975 miles
Convert miles to feet:
0.975 x 5280 = 5,148 feet
The plane traveled 5,148 feet in 6 seconds.
As part of a larger project to study the behavior of stressed-skin panels, a structural component being used extensively in North America, an article reported on various mechanical properties of Scotch pine lumber specimens. Data on the modulus of elasticity (MPa) obtained 1 minute after loading in a certain configuration and 4 weeks after loading for the same lumber specimens is presented here.
Observatio 1 min 4 Week Difference
1 16,620 9,110 1380
2 17,300 13,250 3370
3 15,480 14,720 2580
4 12,970 12,740 2740
5 17,260 10,120 2850
6 13,400 14,570 2690
7 13,900 11,220 2180
8 13,630 11,100 2800
9 13,260 11,420 2210
10 14,370 10,910 2350
11 11,700 12,110 2260
12 15,470 8,620 3080
13 17,840 12,590 2880
14 14,070 15,090 2750
15 14,760 10,550 3520
Required:
Calculate and interpret an upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus; first check the plausibility of any necessary assumptions. (Use α = 0.05. Round your answer to the nearest whole number.)
Answer:
The upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus is 2933.82.
Step-by-step explanation:
Compute the mean difference and standard deviation of the difference as follows:
[tex]\bar d=\frac{1}{n}\sum d_{i}=\frac{1}{15}\times [1380+3370+2580+...+3520]=2642.67\\\\S_{d}=\sqrt{\frac{1}{n-1}\sum (d_{i}-\bar d)^{2}}\\=\sqrt{\frac{1}{15-1}[(1380-2642.67)^{2}+(3370-2642.67)^{2}+...}=525.69[/tex]
The degrees of freedom is:
df = n - 1
= 15 - 1
= 14
Th critical value of t is:
[tex]t_{\alpha/2, (n-1)}=t_{0.05/2, 14}=2.145[/tex]
*Use a t-table.
Compute the upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus as follows:
[tex]\text{Upper Confidence Bound}=\bar d+t_{\alpha/2, (n-1)}\cdot \frac{S_{d}}{\sqrt{n}}[/tex]
[tex]=2642.67+2.145\cdot \frac{525.69}{\sqrt{15}}\\\\=2642.67+291.15\\\\=2933.82[/tex]
Thus, the upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus is 2933.82.
Solve the quadratic equation x2 + 14x = 51 by completing the square.
Question 3 options:
A)
x = –17, x = –3
B)
x = –17, x = 3
C)
x = 3, x = 17
D)
x = –3, x = 17
Answer:
B
Step-by-step explanation:
Given
x² + 14x = 51
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(7)x + 49 = 51 + 49 , that is
(x + 7)² = 100 ( take the square root of both sides )
x + 7 = ± [tex]\sqrt{100}[/tex] = ± 10 ( subtract 7 from both sides )
x = - 7 ± 10
Thus
x = - 7 - 10 = - 17
x = - 7 + 10 = 3
An appliance dealer sells three different models of upright freezers having 13.5, 15.9, and 19.1 cubic feet of storage. Let X = the amount of storage space purchased by the next customer to buy a freezer. Suppose that X has pmf:
Answer:
a) E(X) = 16.09 ft³
E(X²) = 262.22 ft⁶
Var(X) = 3.27 ft⁶
b) E(22X) = 354 dollars
c) Var(22X) = 1,581 dollars
d) E(X - 0.01X²) = 13.470 ft³
Step-by-step explanation:
The complete Correct Question is presented in the attached image to this solution.
a) Compute E(X), E(X2), and V(X).
The expected value of a probability distribution is given as
E(X) = Σxᵢpᵢ
xᵢ = Each variable in the distribution
pᵢ = Probability of each distribution
Σxᵢpᵢ = (13.5×0.20) + (15.9×0.59) + (19.1×0.21)
= 2.70 + 9.381 + 4.011
= 16.092 = 16.09 ft³
E(X²) = Σxᵢ²pᵢ
Σxᵢ²pᵢ = (13.5²×0.20) + (15.9²×0.59) + (19.1²×0.21)
= 36.45 + 149.1579 + 76.6101
= 262.218 = 262.22 ft⁶
Var(X) = Σxᵢ²pᵢ - μ²
where μ = E(X) = 16.092
Σxᵢ²pᵢ = E(X²) = 262.218
Var(X) = 262.218 - 16.092²
= 3.265536 = 3.27 ft⁶
b) E(22X) = 22E(X) = 22 × 16.092 = 354.024 = 354 dollars to the nearest whole number.
c) Var(22X) = 22² × Var(X) = 22² × 3.265536 = 1,580.519424 = 1,581 dollars
d) E(X - 0.01X²) = E(X) - 0.01E(X²)
= 16.092 - (0.01×262.218)
= 16.0926- 2.62218
= 13.46982 = 13.470 ft³
Hope this helps!!!
In her backyard, Mary is planting rows of tomatoes. To plant a row of tomatoes, mary needs 20/13 square feet. There are 40 square feet in Mary's backyard, so how many rows of tomatoes can mary plant??
Answer:
26 rows
Step-by-step explanation:
[tex]number \: of \: rows \\ = \frac{40}{ \frac{20}{13} } \\ \\ = \frac{40 \times 13}{20} \\ \\ = 2 \times 13 \\ \\ = 26 \: [/tex]
5c + 16.5 = 13.5 + 10c
Answer:
Hello!
________________________
5c + 16.5 = 13.5 + 10c
Exact Form: c = 3/5
Decimal Form: c = 0.6
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
Hope this helped you!
Answer:
3000+3d=noods
Step-by-step explanation:
Help me pls I need help
Answer:
C
Step-by-step explanation:
If two lines are parallel, their slopes are the same.
Since the slope of line l is 4/9, this means that the slope of line m must also be 4/9.
Answer:
C. 4/9
Step-by-step explanation:
Parallel lines have equal slopes.
Since line l and line m are parallel, then their slopes must be the same.
[tex]m_{l} =m_{m}[/tex]
We know that the slope of line l is 4/9
[tex]\frac{4}{9} = m_{m}[/tex]
Line l has a slope of 4/9, therefore line m must also have a slope of 4/9.
The correct answer is C. 4/9
The graph of y =ex is transformed as shown in the graph below. Which equation represents the transformed function?
Answer:
B. e^x+3
Step-by-step explanation:
Y=e^x
the graph is moving 3 units up
y= y+3
y=e^x+3
answer = y=e^x+3
Answer: B
Step-by-step explanation:
Can anyone please explain? Need some help :)
A regular hexagon is inscribed in a circle with a diameter of 12 units. Find the area of the hexagon. Round your answer to the nearest tenth. (there's no picture included)
Answer:
93.5 square units
Step-by-step explanation:
Diameter of the Circle = 12 Units
Therefore:
Radius of the Circle = 12/2 =6 Units
Since the hexagon is regular, it consists of 6 equilateral triangles of side length 6 units.
Area of the Hexagon = 6 X Area of one equilateral triangle
Area of an equilateral triangle of side length s = [tex]\dfrac{\sqrt{3} }{4}s^2[/tex]
Side Length, s=6 Units
[tex]\text{Therefore, the area of one equilateral triangle =}\dfrac{\sqrt{3} }{4}\times 6^2\\\\=9\sqrt{3} $ square units[/tex]
Area of the Hexagon
[tex]= 6 X 9\sqrt{3} \\=93.5$ square units (to the nearest tenth)[/tex]
Andrew plans to retire in 36 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that over the entire 20th century, the real (that is, adjusted for inflation) annual returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal.
(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 36 years will exceed 11%?
(b) What is the probability that the mean return will be less than 5%?
Answer:
a) 24.82% probability that the mean annual return on common stocks over the next 36 years will exceed 11%
b) 13.57% probability that the mean return will be less than 5%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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:
[tex]\mu = 8.7, \sigma = 20.2, n = 36, s = \frac{20.2}{\sqrt{36}} = 3.3667[/tex]
(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 36 years will exceed 11%?
This is 1 subtracted by the pvalue of Z when X = 11.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{11 - 8.7}{3.3667}[/tex]
[tex]Z = 0.68[/tex]
[tex]Z = 0.68[/tex] has a pvalue of 0.7518
1 - 0.7518 = 0.2482
24.82% probability that the mean annual return on common stocks over the next 36 years will exceed 11%
(b) What is the probability that the mean return will be less than 5%?
This is the pvalue of Z when X = 5.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5 - 8.7}{3.3667}[/tex]
[tex]Z = -1.1[/tex]
[tex]Z = -1.1[/tex] has a pvalue of 0.1357
13.57% probability that the mean return will be less than 5%
Select two ratios that are equivalent to 7:6
Two ratios that are equal to 7:6 are 14:12 and 21:18, as they are the same, but 7 and 6 are multiplied by the same number (2 in the first, and 3 in the second.)
Maya is solving the quadratic equation by completing the square. 4x2 + 16x + 3 = 0 What should Maya do first?
Maya should Isolate the variable x² option (A) Isolate the variable x² is correct.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
The complete question is:
Maya is solving the quadratic equation by completing the What should Maya do first? square.
4x² + 16x + 3 = 0
Isolate the variable x².Subtract 16x from both sides of the equation.Isolate the constant.Factor 4 out the variable terms.We have a quadratic equation:
4x² + 16x + 3 = 0
To make the perfect square
Maya should do first:
Isolate the variable x²
To make the coefficient of x² is 1.
4(x² + 4x + 3/4) = 0
x² + 4x + 3/4 = 0
x² + 4x + 2² - 2² + 3/4 = 0
(x + 2)² - 4 + 3/4 = 0
(x + 2)² = 13/4
x + 2 = ±√(13/4)
First, take the positive and then the negative sign.
x = √(13/4) - 2
x = -√(13/4) - 2
Thus, Maya should Isolate the variable x² option (A) Isolate the variable x² is correct.
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What is the solution of (4x-16)1/3=36
(4x-16)/3 = 36
4x-16 = 108
4x = 108+16
4x = 124
x = 124/4
x = 31
Answer:
x = 31
Step-by-step explanation:
=> [tex](4x-16)\frac{1}{3} = 36[/tex]
Multiplying 3 to both sides
=> [tex]4x-16 = 36*3[/tex]
=> 4x-16 - 108
Adding 16 to both sides
=> 4x = 108+16
=> 4x = 124
Dividing both sides by 4
=> x = 31
student throws 3 coins in the air. Find the probability that exactly 2 landed on heads, given that at least 2 landed on heads.
Step-by-step explanation:
Head(H) Tails(T)
Sample space is S (HHH,HHT,HTH,THH)
Event(HHT,HTH,THH)
so the probability is 3/4
Answer:
3/4
Step-by-step explanation:
Which of the following theorems verifies that HIJ MLN?
Answer:
HL (try HL, I believe that's the right answer)
Answer:
HL
Step-by-step explanation:
BRO TRUST ME
What is the surface area of this regular pyramid? A. 230 in2 B. 304 in2 C. 480 in2 D. 544 in2
Answer:
B: 304in^2
Step-by-step explanation:
One triangle face: (8)(15) ÷ 2 = 60
Four triangle faces: 60 x 4 = 240
Bottom Face: (8)(8) = 64
Total Surface Area: Four triangle faces + Bottom Face
Total Surface Area: 240 + 64
Total Surface Area: 304in^2
The world’s population is currently estimated at 7,125,000,000. What is this to the nearest billion? billion
Answer:
7,000,000,000
Step-by-step explanation:
since the closest number is less than 5 (1<5) you round down making the nearest billion 7
Answer:
7,000,000,000 OR 7 Billion
Step-by-step explanation:
Since the 1 is millions place and its less than 5, you need to round down meaning that 7,125,000,00 rounded to the nearest billion is 7 billion.
Pls help me help me pls guys
Answer:
C
Step-by-step explanation:
[tex]-5x-49\geq 113[/tex]
[tex]-5x\geq 162[/tex]
[tex]x\leq -32.4[/tex]
(Multiplying or dividing by a negative flips the sign).