Answer:
a) The error bound of the confidence interval is of 0.66.
b) The confidence interval will be narrower.
Step-by-step explanation:
Question a:
We have to find the margin of error. Considering that we have the standard deviation for the sample, the t-distribution is used.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 71 - 1 = 70
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 70 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.9944
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
For this problem, [tex]s = 2.8, n = 71[/tex]. So
[tex]M = T\frac{s}{\sqrt{n}} = 1.9944\frac{2.8}{\sqrt{71}} = 0.66[/tex]
The error bound of the confidence interval is of 0.66.
b. What will happen to the level of confidence obtained if 1,000 male Swedes are surveyed instead of 48? Why?
The margin of error is inversely proportional to the square root of the sample size, so increasing the sample size leads to a smaller margin of error and a narrower confidence interval.
Which of the following pairs of functions are inverses of each other?
O A. f(x) = 8x? - 10 and g(x) = x +10
8
B. f(x) = {+8 and g(x) = 2x - 8
O C. f(x) = 18 - 9 and g(x) =
O D. f(x) = 3x2 +16 and g(x) = -
18
X+9
16
Answer:
A is the answer I guess so...
The functions f(x) = 18/x -9 and g(x) = 18/x+9 are inverse to each other.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function f(x)= 18/x - 9
Let us replace f(x) by y
y=18/x - 9
Now x=18/y-9
Add 9 on both sides
x+9=18/y
Apply cross multiplication
y(x+9)=18
Divide both sides by x+9
y=18/(x+9)
f⁻¹(x)=18/(x+9)
Hence, the functions f(x) = 18/x -9 and g(x) = 18/x+9 are inverse to each other.
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A G.P is such that the 3rd term minus a first term is 48. The 4th term minus 2nd term 144. Find: (i) Common ratio ii) The first term (ii) 6th term of the sequence
Answer:
Step-by-step explanation:
r is the common ratio.
Third term minus first term is 48.
a₃ - a₁ = 48
a₃ = a₁r²
a₁r² - a₁ = 48
a₁(r²-1) = 48
r²-1 = 48/a₁
Fourth term minus second term is 144.
a₄ - a₂ = 144
a₂ = a₁r
a₄ = a₁r³
a₁r³ - a₁r = 144
a₁r(r²-1) = 144
r²-1 = 144/(a₁r)
48/a₁ = 144/(a₁r)
r = 3
:::::
r²-1 = 48/a₁
a₁ = 6
:::::
a₆ = a₁r⁵ = 1458
(i) The common ratio for the given condition is 3.
ii) The first term of the sequence is 6.
iii) The 6th term of the sequence is 1458.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity,
It is given that a is a geometric progression such that the 3rd term minus a first term is 48. The 4th term minus the 2nd term 144.
Each number following the first in a geometric sequence is multiplied by a particular number, known as the common ratio.
As the third term minus the first term is 48.
a₃ - a₁ = 48
a₃ = a₁r²
a₁r² - a₁ = 48
a₁(r²-1) = 48
r²-1 = 48/a₁
The fourth term minus the second term is 144.
a₄ - a₂ = 144
a₂ = a₁r
a₄ = a₁r³
a₁r³ - a₁r = 144
a₁r(r²-1) = 144
r²-1 = 144/(a₁r)
48/a₁ = 144/(a₁r)
r = 3
r²-1 = 48/a₁
a₁ = 6
a₆ = a₁r⁵ = 1458
Thus the common ratio for the given condition is 3, the first term of the sequence is 6 and the 6th term of the sequence is 1458.
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Which equation could represent a linear combination of the systems?
9514 1404 393
Answer:
(b) 0 = -78
Step-by-step explanation:
Subtracting 6 times the first equation from the second will give ...
(4x +15y) -6(2/3x +5/2y) = (12) -6(15)
0 = -78
Answer:
the answer is b
Step-by-step explanation:
Which equation is true?
f of negative 10 = 1
f of 2 = negative 10
f of 0 = 6
f of 1 = negative 10
Answer:
f(0) = 6
Step-by-step explanation:
Complete question:
The function f (x) is given by the set of ordered pairs 1,0 (-10,2), (0,6) (3,17) (-2,-1) which equation is true
f(-10)=1
f(2)=-10
f(0)=6
f(1)=-10
Given the coordinate (x, y). This shows that the input function is x and the output function is y, i.e. f(x) = y
From the pair of coordinates given, hence;
f(1) = 0
f(-10) = 2
f(0) = 6
f(3) = 17
f(-2) = -1
From the following options, this shows that f(0) = 6 is correct
Answer:
f(0) = 6
Step-by-step explanation:
EDGE
1/4 + 4/10 what is the answer plz give correct
Answer:
0.65 is the correct answer
Step-by-step explanation:
hopes it helps
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]\boxed{\frac{13}{20}}[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the answer...}}\\\\\frac{1}{4} +\frac{4}{10}\\------------\\LCM(4,10) = 20\\\\\rightarrow \frac{1}{4}=\frac{1*5}{4*5} = \frac{5}{20}\\\\\rightarrow \frac{4}{10}=\frac{4*2}{10*2}=\frac{8}{20}\\\\\\\rightarrow\frac{5}{20}+ \frac{8}{20} = \boxed{\frac{13}{20}}\\\\\\\text{The answer is in it's simplest form.}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
To make concrete, the ratio of cement to sand is 1 : 3. If cement and sand are sold in bags of equal mass, how many bags of cement are required to make concrete using 15 bags of sand?
Answer:
5 bags of cement are required.
Step-by-step explanation:
Since to make concrete, the ratio of cement to sand is 1: 3, if cement and sand are sold in bags of equal mass, to determine how many bags of cement are required to make concrete using 15 bags of sand the following calculation must be done:
Cement = 1
Sand = 3
3 = 15
1 = X
15/3 = X
5 = X
Therefore, 5 bags of cement are required.
A survey of 77 teenagers finds that 30 have 5 or more servings of soft drinks a week. a. Give a 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week. b. In the general population, 30% have 5 or more servings of soft drinks a week. Is there evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population
Answer:
a) The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).
b) 30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.
Step-by-step explanation:
Question a:
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 z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
A survey of 77 teenagers finds that 30 have 5 or more servings of soft drinks a week.
This means that [tex]n = 77, \pi = \frac{30}{77} = 0.3896[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 - 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.2982[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 + 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.481[/tex]
The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).
Question b:
30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.
See above. okokokoookkokokokokkkkokokkokokkok
Answer:
B
Step-by-step explanation:
B is the correct answer
please help
Find the missing side of this right
triangle.
X
7
12
X
= [?]
Answer:
13.9 (if x is the Hypotenuse)
Step-by-step explanation:
which one is the Hypotenuse (the side opposite of the 90 degree angle) ?
because that determines the calculation.
if x is the Hypotenuse then Pythagoras looks like this
x² = 7² + 12² = 49 + 144 = 193
x = sqrt(193) = 13.9
if 12 is the Hypotenuse, then it looks like this
12² = 7² + x²
144 = 49 + x²
95 = x²
x = sqrt(95) = 9.75
The temperature at 5 a.m. was −7.4°C. By 9 a.m., the temperature was −4.7°C. How much warmer was the temperature at 9 a.m.?
Answer:
2.7°C.
Step-by-step explanation:
If it was -7.4°C. at 5 am, then -4.7°C. at 9am, then the temperature rose by 2.7°C.
Proof:
-7.4
-4.7
--------
2.7
Brendan has $65 worth of balloons and flowers delivered to his mother. He pays the bill plus an 8.5% sales tax and an 18% tip on the total cost including tax. He also pays a $10 delivery fee that is charged after the tax and tip. How much change does he receive if he pays with two $50 bills? Round to the nearest cent.
Answer:
its 6.78 i believe
Step-by-step explanation:
Rectangle QRST with vertices Q(-3,2), R(-1,4), S(2,1), and T(0,-1)) in the x-axis
Answer:
D
Step-by-step explanation:
The coordinate of the new rectangle after the reflection across will be Q'(-3, -2), R'(-1, -4), S'(2, -1), and T'(0, 1). Then the correct option is D.
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
The reflection does not change the shape and size of the geometry. But flipped the image.
Rectangle QRST with vertices Q(-3, 2), R(-1, 4), S(2, 1), and T(0, -1).
The coordinate of the new rectangle after the reflection across is given as,
Q' = (-3, -2)
R' = (-1, -4)
S' = (2, -1)
T' = (0, 1)
The coordinate of the new rectangle after the reflection across will be Q'(-3, -2), R'(-1, -4), S'(2, -1), and T'(0, 1). Then the correct option is D.
More about the transformation of a point link is given below.
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Question 7(Multiple Choice Worth 1 points)
(07.02 MC)
Jason has two bags with 6 tiles each. The files in each bag are shown below
1
2
3
4
5
6
Without looking, Jason draws a file from the first bag and then a file from the second bag What is the probability of Jason drawing the file numbered 5 from the first bag and an odd file from the second bag?
0
영
o
Answer:a.3/6
Step-by-step explanation:
Because there’s a total of 12 files in each bag which is 6 in each
Any help would be very appreciated
Answer:
21
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 60 = x / 7 sqrt(3)
7 sqrt(3) tan 60 = x
7 sqrt(3) sqrt(3) = x
7*3 = x
21 = x
The average monthly salary of a worker is ₹8200. If there are 45 workers in a factory, then total expenditureincurred on expenditure is:
Answer: [tex]Rs.3,69,000[/tex]
Step-by-step explanation:
Given
average monthly salary of a worker is [tex]Rs.8200[/tex]
If there are 45 workers in a factory
Total expenditure is calculated by taking the product of Average monthly salary and no of workers in the factory
[tex]\Rightarrow 8200\times 45\\\Rightarrow Rs.3,69,000[/tex]
This is a list of the heights ( each nearest cm ) of 12 children
150 134 136 139 131 141
132 134 136 137 150 146
Select the type of the data.
Discrete
Continuous
Categorical
Qualitative
choose one
NO FAKE ANSWERS
FIRST MARKED BRAINLIST
qualitative
Step-by-step explanation:
b cos the question is in quality format
Answer:
cutee!
SUP???
Hiii friend :]
cuteee~!
prettyyy
Which explains whether or not the graph represents a direct variation?
Answer:
The slope is 3 and equation of the line is y=3x. I think the answer is the 1st option
Step-by-step explanation:
Given:
y=3x
Direct variation equations have the form:
y=kx,
where
k is the constant of proportionality
so k=3
1. In 2020, the populations of City A and City B were equal. From 2015 to 2020, the population of City A increased by 20% and the population of City B decreased by 10%. If the population of City A was 120,000 in 2015, what is the population of City B in 2015?
2. A chef is preparing a sauce for a steak she offers as a key dish in her menu. To prepare the sauce she needs to prepare a mix with 40% butter, with the rest being egg yolk. In the kitchen right now, she only has a sauce that has 20% butter (rest is egg yolk) and a sauce that has 50% butter (rest is egg yolk) in stock. In what ratio should she mix the 20% sauce with the 50% sauce in order to obtain the 40% sauce that she needs to prepare her famous recipe?
3. A book was on sale for 30% off its original price. If the sale price of the book was $28, what was the original price of the book? (Assuming there is no sales tax)
4. At a retail store, they needed to do surveys of 32 stores which equals 40% of all their stores. How many stores does the retailer have in total?*
Answer:
180000 people
1 : 2
$40
80 stores
Step-by-step explanation:
1.)
Population in 2020 are equal : Let population =
City A increased by 20% From 120,000 in 2015
(1 + 0.2) * 120,000 = (1.2 * 120,000) = 144,000
Hence, city A = 144,000.
Since, city A and B have equal population ; city B also has a population of 144000 in 2020.
Let population in 2015 = x
(1 - 0.2) * x = 144000
0.8x = 144000
x = 144000/0.8
x = 180,000
2.)
Let proportion of 20% butter = x and proportion of 50% butter = 1 - x
0.2x + 0.5(1 - x) = 0.4
0.2x + 0.5 - 0.5x = 0.4
-0.3x + 0.5 = 0.4
-0.3x = 0.4 - 0.5
-0.3x = - 0.1
x = 0.1/0.3
x = 0.3333
(1-x) = 1 - 0.33333 = 0.6666%
0.3333% of 20% butter
0.6666% of 50% butter
Hence ;
0.3333 : 0.6666
1 : 2
3.)
Let original price of book = x
Discount on sale = 30%
Sale price = $28
Sale price = original price * (1 - discount)
$28 = (1 - 0.3) * x
$28 = 0.7x
x = $28/0.7
x = $40
4.)
Let total number of stores = x
Store surveys needed = 32
40% of total stores = 32 stores
0.4x = 32
x = 32 / 0.4
x = 80
which of the following tables represents an inverse variation between x and y
Answer:
I think that d is the answer
HELP. Need help on this
Answer:
what are the answers
Step-by-step explanation:
Simplify to the extent possible:
(logx16)(log2 x)
Answer:
Step-by-step explanation:
Use the change-of-base rule.
A half-century ago, the mean height of women in a particular country in their 20s was inches. Assume that the heights of today's women in their 20s are approximately normally distributed with a standard deviation of inches. If the mean height today is the same as that of a half-century ago, what percentage of all samples of of today's women in their 20s have mean heights of at least inches?
Answer:
0.26684
Step-by-step explanation:
Given that :
Mean, μ = 62.5
Standard deviation, σ = 1.96
P(Z ≥ 63.72)
The Zscore = (x - μ) / σ
P(Z ≥ (x - μ) / σ)
P(Z ≥ (63.72 - 62.5) / 1. 96) = P(Z ≥ 0.6224)
P(Z ≥ 0.6224) = 1 - P(Z < 0.6224)
1 - P(Z < 0.6224) = 1 - 0.73316 = 0.26684
Which of the following describes an angle with a vertex at Z?
About 9% of the population has a particular genetic mutation. 400 people are randomly selected. Find the mean for the number of people with the genetic mutation in such groups of 400
Answer:
36 people
Step-by-step explanation:
The expected value E(X) = mean of sample = np
Where, p = population proportion, p = 9% = 0.09
n = sample size, = 400
The mean of the number of people with genetic mutation, E(X) = np = (400 * 0.09) = 36
36 people
William's assembly unit has decided to use a p-Chart with 2-sigma control limits to monitor the proportion of defective castings produced by their production process. The quality control manager randomly samples 150 castings at 10 successively selected time periods and counts the number of defective castings in the sample.
Sample Defects
1 9
2 14
3 9
4 9
5 13
6 8
7 12
8 10
9 12
10 11
Required:
a. What is the Center Line of the control chart?
b. What value of z should be used to construct the control chart?
c. What is the Upper Control Limit?
d. What is the Lower Control Limit?
Answer: attached below is the missing p chart
a) 0.07133
b) 2
c) 0.098
d) 0.045
Step-by-step explanation:
sample size = 150 castings
number of periods = 10
a) Determine the center Line of the control chart
( 0.06 + 0.0933 + 0.06 + 0.06 + 0.0867 + 0.0533 + 0.08 + 0.067 + 0.08 + 0.073) / 10
mean = 0.07133
standard deviation = 0.01335
b) Determine the value of Z to be used
Given that we are using 2sigma limits .
the value of Z to be used = 2
c) Upper limit control
= mean value + z-value * std
= 0.0713 + 2*0.01335 = 0.098
d) Lower Control Limit
= mean value - z-value * std
= 0.0713 - 2*0.01335 = 0.045
7/9 - 2/3 and 2/3 - 1/6
Answer:
The answer is 1/9 and 1/2
write √3 x √6 in the form b√2 where b is an integer
Answer:
[tex]3 \sqrt{2} [/tex]
Step-by-step explanation:
[tex] \sqrt{(9 \times 2)} [/tex]
Take the square root of 9 out of the square root and leave the 2 in.
Answer:
3[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the rules of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then
[tex]\sqrt{3}[/tex] × [tex]\sqrt{6}[/tex]
= [tex]\sqrt{3(6)}[/tex]
= [tex]\sqrt{18}[/tex]
= [tex]\sqrt{9(2)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex]
= 3[tex]\sqrt{2}[/tex]
Please help me thank you
9514 1404 393
Answer:
y = 32.1x +779.91165 cases in 2010Step-by-step explanation:
A suitable statistics calculator can tell you the coefficients of the linear regression equation. In the attached, we put the given x- and y-values into a table and asked for the best fit equation. Rounded to tenths, the equation is ...
y = 32.1x +779.9
The year 2010 is 12 years after 1998, so we can find the desired projection using x=12.
y = 32.1×12 +779.9 = 385.2 +779.9 = 1165.1
The number of cases is projected to be 1165 in 2010.
_____
We wonder if using the button "Open Statistics Calculator" will let you solve this question yourself.
What is the value of cot ø= 2/3 what is the value of csc ø
Answer:
Step-by-step explanation:
cotθ = cosθ/sinθ = 2/3
sinθ = 3/√(2²+3²) = 3/√13
cscθ = 1/sinθ = √13/3
Help Please ASAP!!! Not sure how to solve this problem. Can someone help me please? Thank you for your help!
Answer:
This question is formatted incorrectly
Step-by-step explanation:
