Answer:
C
Step-by-step explanation:
Calculate the standard error of the sample proportion estimate. (SEest.) Give your answer to three decimal places.
A. The sample proportion is 0.52.
B. The standard error of the sample proportion is approximately 0.041.
C. The standard error of the sample proportion estimate is approximately 0.041.
A. To calculate the sample proportion, we divide the number of people who support the special transportation tax (78) by the total number of people surveyed (150):
Sample proportion = 78 / 150 = 0.52
B. To calculate the standard error of the sample proportion (SE), we use the formula:
[tex]SE = \sqrt{(p * (1 - p)) / n}[/tex]
where p is the sample proportion and n is the sample size. Substituting the values into the formula:
[tex]SE = \sqrt{(0.52 * (1 - 0.52)) / 150}\\\\SE = \sqrt{0.2496 / 150}\\\\SE = \sqrt{0.001664}\\\\SE = 0.0407[/tex]
Therefore, the standard error of the sample proportion is approximately 0.041 (rounded to three decimal places).
C. The standard error of the sample proportion estimate (SEest) is the same as the standard error of the sample proportion (SE) calculated in part B. Hence, the standard error of the sample proportion estimate is also approximately 0.041 (rounded to three decimal places).
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the amount of gas in sarahs car is uniformly distributed between 1 and 16 gallons. Calculate the probability that the amount of gas is exactly 7 gallons
Answer:
The probability that the amount of gas in Sarah's car is exactly 7 gallons is 0.067.
Step-by-step explanation:
Let the random variable X represent the amount of gas in Sarah's car.
It is provided that [tex]X\sim Unif(1, 16)[/tex].
The amount of gas in a car is a continuous variable.
So, the random variable X follows a continuous uniform distribution.
Then the probability density function of X is:
[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b[/tex]
For a continuous probability distribution the probability at an exact point is 0.
So, to compute the probability that the amount of gas in Sarah's car is exactly 7 gallons use continuity correction on both sides:
P (X = 7) = P (7 - 0.5 < X < 7 + 0.5)
= P (6.5 < X < 7.5)
[tex]=\int\limits^{7.5}_{6.5} {\frac{1}{16-1}} \, dx \\\\=\frac{1}{15}\times |x|^{7.5}_{6.5}\\\\=\frac{1}{15}\times (7.5-6.5)\\\\=\frac{1}{15}\\\\=0.0666667\\\\\approx 0.067[/tex]
Thus, the probability that the amount of gas in Sarah's car is exactly 7 gallons is 0.067.
Write the null and alternative hypotheses you would use to answer this question. Are Americans getting fatter? Researchers interested in this question take a random sample of 500 people and record an average weight of 190 pounds. Ten years ago, the average weight was 185 pounds.
Answer:
H0: u = 185 against Ha: u > 185
or
H0: u ≤ 185 against Ha: u > 185
Step-by-step explanation:
The null and alternative hypotheses for this experiment would be
H0: u = 185 against Ha: u > 185
or
H0: u ≤ 185 against Ha: u > 185
This is a one tailed test .
If the results are such that we reject the null hypothesis and accept the alternative hypothesis it means that the Americans are getting fatter as the mean weight is increasing day by day.
The null hypothesis deals with all the values equal to or less than 185 pounds and the alternative with all the values greater than 185 pounds.
A multiple choice test contains 10 questions with 5 answer choices. What is the probability of correctly answering 5
questions if you guess randomly on each question?
The answer is 1/2 because there are total 10 questions. So, the probability of getting 5 correct answers is 5/10 that is 1/2.
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15 POINTS AND BRAINLIEST JUST HELP ME PLZZZZZ 4x^2 + 28x + 49 = 0 Rewrite equation (x + __ )^2 = __
Answer:
[tex]\boxed{(x+7)^2 =-3x^2-14x}[/tex]
Step-by-step explanation:
[tex]4x^2 + 28x + 49 = 0[/tex]
[tex]\sf Subtract \ 3x^2 \ and \ 14x \ from \ both \ sides.[/tex]
[tex]4x^2 + 28x + 49 -3x^2-14x= 0-3x^2-14x[/tex]
[tex]x^2 + 14x + 49 = -3x^2-14x[/tex]
[tex]\sf Factor \ left \ side \ of \ the \ equation.[/tex]
[tex](x+7)^2 =-3x^2-14x[/tex]
Answer:
(x+7)² = -3x² -14x
Step-by-step explanation:
4x^2 + 28x + 49 = 0
Subtract 3x² and 14x from each sides.
x^2 + 14x + 49 = -3x² -14x
Next step will be factoring.
(x+7)² = -3x² -14x
f(x)=−5x^3−4x^2+8x and g(x)=−4x^2+8, find (f−g)(x) and (f−g)(−2).
Answer:
see explanation
Step-by-step explanation:
(f - g)(x) = f(x) - g(x) , that is
f(x) - g(x)
= - 5x³ - 4x² + 8x - (- 4x² + 8) ← distribute parenthesis by - 1
= - 5x³ - 4x² + 8x + 4x² - 8 ← collect like terms
= - 5x³ + 8x - 8
Substitute x = - 2 into this expression, thus
(f - g)(- 2)
= - 5(- 2)³ + 8(- 2) - 8
= - 5(- 8) - 16 - 8
= 40 - 16 - 8
= 16
Determine the area of the shape above. The formula for the area of a polygon is: Area = 1/2 (a n s) *
Step-by-step explanation:
Area of a regular polygon is half the apothem times the perimeter, or A = ½ a n s, where a is the apothem, n is the number of sides, and s is the side length.
A = ½ (8.5705 in) (8) (7.1 in)
A = 243.4022 in²
what is the domain of this
Answer:
[tex]\boxed{\sf B. \ All \ real \ numbers}[/tex]
Step-by-step explanation:
The domain is all possible values for x.
[tex]f(x)=(\frac{1}{4} )^x[/tex]
There are no restrictions on x.
The domain is all real numbers.
Answer:
B.All real number
hope you have unterstand
michaela has h hair ties. michaela's sister has triple the number of hair ties that michaela has. choose the expression that shows how many hair bows michaela's sister has
Answer:
[tex]S = 3 h[/tex]
Step-by-step explanation:
Let M represent Michaela hair tier and S represents Michaela sister's
Given
M = h
S = Triple of M
Required
Determine an expression for S
From the given parameters, we have that;
S = Triple of M
Mathematically, this implies;
[tex]S = 3 * M[/tex]
Substitute h for M
[tex]S = 3 * h[/tex]
[tex]S = 3 h[/tex]
Hence, the expression for Michaela sister' is [tex]S = 3 h[/tex]
An engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 3.6 mm, how many of these components should she consider to be 90% sure of knowing the mean will be within ± 0.1 ±0.1 mm?
Answer:
She must consider 3507 components to be 90% sure of knowing the mean will be within ± 0.1 mm.
Step-by-step explanation:
We are given that an engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 3.6 mm.
And she considers to be 90% sure of knowing the mean will be within ±0.1 mm.
As we know that the margin of error is given by the following formula;
The margin of error = [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]
Here, [tex]\sigma[/tex] = standard deviation = 3.6 mm
n = sample size of components
[tex]\alpha[/tex] = level of significance = 1 - 0.90 = 0.10 or 10%
[tex]\frac{\alpha}{2} = \frac{0.10}{2}[/tex] = 0.05 or 5%
Now, the critical value of z at a 5% level of significance in the z table is given to us as 1.645.
So, the margin of error = [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]
0.1 mm = [tex]1.645 \times \frac{3.6}{\sqrt{n} }[/tex]
[tex]\sqrt{n} = \frac{3.6\times 1.645}{0.1 }[/tex]
[tex]\sqrt{n}[/tex] = 59.22
n = [tex]59.22^{2}[/tex] = 3507.0084 ≈ 3507.
Hence, she must consider 3507 components to be 90% sure of knowing the mean will be within ± 0.1 mm.
Brainly help me Kelly made fruit punch to serve at a party for her chess team. She mixed 1 2/5 liters of cranberry juice and 1 3/5 liters of pineapple juice together. Then, she split the fruit punch evenly among 9 glasses. How much fruit punch did Kelly pour into each glass? Write your answer as a whole number, fraction, or mixed number. Simplify any fractions.
Answer:
1/3
Step-by-step explanation:
1[tex]\\1\frac{2}{5} =1.4\\\\[/tex]
[tex]1\frac{3}{5} =1.6[/tex]
[tex]1.6+1.4=3[/tex]
3 Liters of Fruit Punch.
3/9=1/3 Fruit Punch among the 9 glasses.
=
Graphing an integer function and finding its range for a given...
The function h is defined as follows for the domain given.
h(x) = 2 -2x, domain = {-3, -2, 1, 5}
Write the range of h using set notation. Then graph h.
Answer:
Step-by-step explanation:
● h(x) = 2-2x
The domain is {-3,-2,1,5}
● h(-3) = 2-2×(-3) = 2+6 = 8
● h(-2) = 2 -2×(-2) = 2+4 = 6
● h(1) = 2-2×1 = 2-2 = 0
● h(5) = 2-2×5 = 2-10 = -8
The range is {-8,0,6,8}
WHat is the solution to the system of linear equations graphed below answers 3 1/2-4
Answer:
(3 1/2, -4)
Step-by-step explanation:
The solution is the point on the graph that the two lines intersect. The point that the lines intersect in the graph is (3 1/2, -4).
Answer:
3 1/2 , -4
Step-by-step explanation:
yes
John receives a perpetuity paying 2 at the end of year 4, 4 at the end of year 6, 6 at the end of year 8, etc. The present value of this perpetuity at an annual effective rate of 10% equals X. Calculate X
Answer:
45.35
Step-by-step explanation:
From the above question, we are told that the annual effective rate = 10% = 0.10
Note also that payment is been made every 2 years
Hence , we apply the formula of effective interest rate for a period of 2 years.
Effective Interest rate(j) = (1 + r)² - 1
= (1 + 0.10)² - 1
= 1.10² - 1
= 1.21
= 0.21
Present value of perpetuality = t/[j × j/(1 + r)²]
Where t = time in years = 2
r = 0.10
= 2/ [0.21 × 0.21/(1 + 0.10)²
= 54.87528
Present value at time t = 0
= 54.87528(1 + r)^-2
= 54.87528(1 + 0.10) ^-2
= 54.87528(1.10)^-2
= 45.35
Therefore, the present value at time (t) is 0 = 45.35
what is empowerment and radication please that is not from google
Answer:
In MATH:
Empowerment - Gaining the skills required in language and practices to fully understand math.
Radication - The process of extracting a number's root.
In ENGLISH:
Empowerment - The process of gaining more power over anything, including yourself, others, society, government, and corporations.
Ex - In the spirit of empowerment, the company has implemented a new system that asks employees to nominate one another for bonuses.
Radication - The process of establishing, fixing, or creating.
Ex - The high prestige of the premier is radicated in the hearts of the people.
Vu is three times as old as Wu. In 25 years Wu will be twice as old as Vu. How old is Vu now?
Answer: Vu is 15 years old now.
Step-by-step explanation:
Let present age of WU be x.
Then, the present age of Vu = 3x
Also, After 25 years
Age of Wu = x+25
According to the question:
[tex](x+25)=2(3x)\\\\\Rightarrow\ x+25=6x\\\\\Rightarrow\5x=25\\\\\Rightarrow\ x=5[/tex]
Present age of Vu = 3(5) = 15
Hence, Vu is 15 years old now.
Answer:
j
Step-by-step explanation:j
Decide all proper subsets of A { 8 ,7 ,6 ,5 ,4 ,3 ,2 ,1} = A 1- { 4 ,3 ,2 ,1} 2- { } 3- { 9 ,8 ,7 } 4- { 11 ,2} 5- { 5 }
Answer:
A, E
Step-by-step explanation:
There should be 2^8-1 proper subsets of A. Its every one besides { }
A ladder leans against a vertical at angle of 60° to the wall of the foot of the ladder is 5m away from the wall calculate the length of the ladder
Answer:
Your question indicates the ladder is at an angle of 60° to the wall, meaning the angle between the wall and the ladder is 60° and the angle between the ladder and the ground must be 30°. Not a very efficient way to set up a ladder.
5.7735 meters. The top of the ladder is 2.8868 meters off the ground.
Now, if you meant the ladder is 60° from the ground, that’s a different story.
Then, the ladder is 10 meters long and reaches 8.6603 meters from the ground.
A 30–60–90 right triangle is half of an equalateral triangle. Therefore the hypotenuse is double the length of the short leg, and by the Pythagorean theorum, we can determine that the other leg is the length of the short leg times the square root of 3.
All lengths in this answer are rounded to the nearest tenth of a millimeter.
Step-by-step explanation:
Compute using long division: 1,234÷68
Answer:
Quotient = 18
Remainder = 10
Step-by-step explanation:
1234/68
=> 68 x 1 = 68
=> 123 - 68 = 55
=> Take the 4 down
=> 554/68
=> 68 x 8 = 544
=> 554 - 544 = 10
So, the quotient = 18.
Remainder = 10
According to the United States Golf Association, the diameter of a golf ball should not be less than 42.67 millimeters. What is the estimate of this value rounded to the nearest tenth of a millimeter?
Answer:
42.7 mm
Step-by-step explanation:
To the nearest tenth of a mm, 42.67 mm would be 42.7 mm.
After estimate of this value rounded to the nearest tenth of a millimeter,
⇒ 42.67 ≈ 42.7
We have to given that,
According to the United States Golf Association, the diameter of a golf ball should not be less than 42.67 millimeters.
Hence, After estimate of this value rounded to the nearest tenth of a millimeter, we get;
⇒ 42.67
As, 7 is grater than 5, so we can add 1 to the tenth place.
⇒ 42.67 ≈ 42.7
Therefore, After estimate of this value rounded to the nearest tenth of a millimeter,
⇒ 42.67 ≈ 42.7
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Please answer this correctly without making mistakes
Answer:
1,377/2 and 688 1/17
Step-by-step explanation:
Suppose you have read two different books on world war 2 and each book has different arguments about how the war started which of the following sources provides the best support for the authors arguments
Answer:
Well this is my opinion I would try to compared both them and see if they have something familiar in their arguments. If not I would try to view their different point of view and write your own opinion about it. I would check out another book about the World War 2 because there's infinite of books about it.
Mr. Vazquez determines that the area of a bathroom in his house is 25 square feet less than 1/5 of the area of the living room. If the bathroom measures 35 square feet, what is the area of the living room?\
Answer:
300 SF
Step-by-step explanation:
just took the test
Design a nonlinear system that has at least two solutions. One solution must be the ordered pair: (-2, 5). Tell how you came up with your system and give the entire solution set for the system.
Answer:
[tex] \begin{cases} (x - 2)^2 + (y - 2)^2 = 25 \\ y = 5 \end{cases} [/tex]
Solutions: x = 6, y = 5 or x = -2, y = 5
Step-by-step explanation:
Use a graph.
Plot point (-2, 5). That will be a point on a circle with radius 5.
From point (-2, 5), go right 4 and down 3 to point (2, 2). (2, 2) is the center of the circle.
You now need the equation of a circle with center (2, 2) and radius 5.
Use the standard equation of a circle:
[tex] (x - h)^2 + (y - k)^2 = r^2 [/tex]
where (h, k) is the center and 5 is the radius.
The circle has equation:
[tex] (x - 2)^2 + (y - 2)^2 = 25 [/tex]
To have a single solution, you need the equation of the line tangent to the circle at (-2, 5), but since you want more than one solution, you need the equation of a secant to the circle. For example, use the equation of the horizontal line through point (2, 5) which is y = 5.
System:
[tex] \begin{cases} (x - 2)^2 + (y - 2)^2 = 25 \\ y = 5 \end{cases} [/tex]
To solve, let y = 5 in the equation of the circle.
(x - 2)^2 + (5 - 2)^2 = 25
(x - 2)^2 + 9 = 25
(x - 2)^2 = 16
x - 2 = 4 or x - 2 = -4
x = 6 or x = -2
Solutions: x = 6, y = 5 or x = -2, y = 5
An example of a nonlinear system that has at least two solutions, one of which is (-2,5) are,
⇒ x² + y² = 29
⇒ 3x + 4y = -2
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now, This system by starting with the equation of a circle centered at the origin with radius sqrt(29), which is,
⇒ x² + y² = 29.
Then, Added a linear equation that intersects the circle at (-2,5) to create a system with two solutions.
The entire solution set for this system is: (-2, 5) and (7/5, -19/10)
Thus, An example of a nonlinear system that has at least two solutions, one of which is (-2,5) are,
⇒ x² + y² = 29
⇒ 3x + 4y = -2
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Volume 1 (3)3 = 367
SSCE/JME-TYPE OF
2
The area of an equilateral triangle of side 8 cm is
A. 16V3 cm? B. 32/3 cm
B.
48 cm
cm?
D.
36V3 cm
A
parallelogram
of area 425 cmhas a height o
Answer:
[tex]A.\ 16\sqrt3\ cm^2[/tex] is the correct answer.
Step-by-step explanation:
Given that:
Side of an equilateral triangle = 8 cm
To find:
Area of the triangle will be:
[tex]A.\ 16\sqrt3\ cm^2[/tex]
[tex]B.\ \dfrac{32}{3} cm^2[/tex]
[tex]C.\ 48\ cm^2[/tex]
[tex]D.\ 36\sqrt3\ cm^2[/tex]
Solution:
First of all, let us have a look at the formula for area of an equilateral triangle:
[tex]A =\dfrac{\sqrt3}{4}a^2[/tex]
Where [tex]a[/tex] is the side of equilateral triangle and an equilateral triangle is a closed 3 sided structure in 2 dimensions which has all 3 sides equal to each other.
Here, we are given that side, [tex]a=8\ cm[/tex]
Putting the value in formula:
[tex]A =\dfrac{\sqrt3}{4}\times 8^2\\\Rightarrow A =\dfrac{\sqrt3}{4}\times 64\\\Rightarrow A =\sqrt3\times 16\\OR\\\Rightarrow \bold{A =16\sqrt3\ cm^2}[/tex]
Hence, [tex]A.\ 16\sqrt3\ cm^2[/tex] is the correct answer.
Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. Listed below are the weights in pounds of 1111 players randomly selected from the roster of a championship sports team. Are the results likely to be representative of all players in that sport's league?
278 303 186 292 276 205 208 236 278 198 208
a. Find the mean.
The mean is ? pound(s).
(Type an integer or a decimal rounded to one decimal place asneeded.)
b. Find the median.
The median is ? pound(s).
(Type an integer or a decimal rounded to one decimal place asneeded.)
c. Find the mode.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The mode(s) is(are) ? pound(s).
(Type an integer or a decimal. Do not round. Use a comma to separate answers as needed.)
B. There is no mode.
d. Find the midrange.
The midrange is ? pound(s).
(Type an integer or a decimal rounded to one decimal place asneeded.)
e. Are the results likely to be representative of all players in that sport's league?
A. The results are not likely to be representative because the median is not equal to the mode.
B. The results are likely to be representative because a championship team is most likely representative of the entire league.
C. The results are not likely to be representative because the median is not equal to the mean.
D. The results are not likely to be representative because the championship team may not be representative of the entire league.
Answer:
Mean= 242.5 pounds
Median= 236 pounds
Mode= 208 and 278 pounds
Range=117 pounds
Mid-range= 58.5 pounds
B. The results are likely to be representative because a championship team is most likely representative of the entire league.
Step-by-step explanation:
278 303 186 292 276 205 208 236 278 198 208
Arranged in ascending order is
186 198 205 208 208 236 276 278 278 292 303
Mean = (186 +198+ 205+ 208 +208 +236 + 276+ 278 +278+ 292 +303)/11
Mean =2668/11
Mean= 242.5 pounds
Median = the middle number
Median= 236 pounds
Mode = highest occuring number(s)
Mode= 208 and 278 pounds
Range= highest number- smallest number
Range=303-186
Range=117 pounds
Mid-range= range/2
Mid-range= 117/2
Mid-range= 58.5 pounds
Find the mass and center of mass of the solid E with the given density rho. E is the cube 0 ≤ x ≤ a, 0 ≤ y ≤ a, 0 ≤ z ≤ a; rho(x, y, z) = 9x2 + 9y2 + 9z2.
Answer:
mass = 9a^5
center of mass = [tex]\frac{7a}{12}, \frac{7a}{12}, \frac{7a}{12}[/tex]
Step-by-step explanation:
Finding the mass of the solid E
given density function : p ( x,y,z ) = [tex]9x^2 + 9y^2 + 9z^2[/tex]
Mass = [tex]\int\limits^a_0 \int\limits^a_0 \int\limits^a_0 {9(x^2+y^2+z^2)} \, dx dydz[/tex] [tex]= \int\limits^a_0 \int\limits^a_0 {9(\frac{a^3}{3}+ay^2+az^2 )} \, dydz[/tex]
[tex]= \int\limits^a_0 {9(\frac{a^4}{3}+\frac{a^4}{3} +a^2z^2 )} \, dz[/tex] [tex]= \int\limits^a_0 {9(\frac{2a^4}{3}+a^2z^2 )} \, dz[/tex] [tex]= 9 ( \frac{2a^5}{3} + \frac{a^5}{3} )[/tex]
( taking limits as a and 0 )
hence Mass = 9 [tex](a^5)[/tex]
finding the center of mass
attached below is solution
Please answer my question
Step-by-step explanation:
The inequality shows by line is
i) 1<=x<=6
OR,
x is an positive integer.
I need help on this question, can someone please answer it correctly?
Answer:the one area < with line underneath then -4
St-by-step explanation: I’m pretty sure this is correct
Answer:
[tex] \boxed{x \leqslant - 4}[/tex]Step-by-step explanation:
[tex] \mathrm{16x - 7 \leqslant - 71}[/tex]
Move constant to Right hand side and change its sign
[tex] \mathrm{16x \leqslant - 71 + 7}[/tex]
Calculate
[tex] \mathrm{16x \leqslant - 64}[/tex]
Divide both sides of the equation by 16
[tex] \mathrm{ \frac{16x}{16} \leqslant \frac{ - 64}{16} }[/tex]
Calculate
[tex] \mathrm{x \leqslant - 4}[/tex]
Hope I helped!
Best regards!
On a map, two locations are 0.75 centimeter apart. Their actual distance is 15 kilometers apart. What scale could be
shown on the map? Select three options.
Answer:
20
Step-by-step explanation:
It is 20 because 0.75 is on the map and its actualy distance is 15 so 15/0.75 is 20
Find the sum of 1 + 3/2 + 9/4 + …, if it exists.
Answer:
Option (4)
Step-by-step explanation:
Given sequence is,
[tex]1+\frac{3}{2}+\frac{9}{4}..........[/tex]
We can rewrite this sequence as,
[tex]1+\frac{3}{2}+(\frac{3}{2})^2.............[/tex]
There is a common ratio between the successive term and the previous term,
r = [tex]\frac{\frac{3}{2}}{1}[/tex]
r = [tex]\frac{3}{2}[/tex]
Therefore, it's a geometric sequence with infinite terms. In other words it's a geometric series.
Since sum of infinite geometric sequence is represented by the formula,
[tex]S_{n}=\frac{a}{1-r}[/tex] , when r < 1
where 'a' = first term of the sequence
r = common ratio
Since common ratio of the given infinite series is greater than 1 which makes the series divergent.
Therefore, sum of infinite terms of a series will be infinite Or the sum is not possible.
Option (4) will be the answer.
