Answer:
b = 16
Step-by-step explanation:
Answer:
-6b-12+8 which simplifies to -6b-4
Step-by-step explanation:use distrubutive property and then combine like terms
Several years ago, 50% of parents who had children in grades K-12 were satisfied with the quality of education the students receive. A recent poll asked 1 comma 095 parents who have children in grades K-12 if they were satisfied with the quality of education the students receive. Of the 1 comma 095 surveyed, 478 indicated that they were satisfied. Construct a 95% confidence interval to assess whether this represents evidence that parents' attitudes toward the quality of education have changed.
Answer:
The 95% confidence interval for the proportion of parents that are satisfied with their children's education is (0.4118, 0.4618). 0.5 is not part of the confidence interval, so this represents evidence that parents' attitudes toward the quality of education have changed.
Step-by-step explanation:
We have to see if 50% = 0.5 is part of the confidence interval.
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 = 1095, \pi = \frac{478}{1095} = 0.4365[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4365 - 1.96\sqrt{\frac{0.4365*0.5635}{1095}} = 0.4118[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4365 + 1.96\sqrt{\frac{0.4365*0.5635}{1095}} = 0.4612[/tex]
The 95% confidence interval for the proportion of parents that are satisfied with their children's education is (0.4118, 0.4618). 0.5 is not part of the confidence interval, so this represents evidence that parents' attitudes toward the quality of education have changed.
PLEASE HELP
Jan writes an e-mail to a co-worker asking her to provide information about the budget for the upcoming year. Which type of routine message is she using?
A: informational
B: appreciation
C: request
D: goodwill
Jon and Jim painted a fence Jon painted a quarter of the fence and Jim painted five twelfths of the fence how much of the fence did they paint
Answer: jon & jim painted 8/12 of the fence
Step-by-step explanation: first, convert. one quarter is equal to 1/4, & 1/4 of 12 (since Jim painted 5/12) is 3/12. now we know that Jon painted 3/12 of the fence & that Jim painted 5/12 of the fence (we already knew this, didn't we?). all you have to do now is add: 3/12 + 5/12 = 8/12. so, jon & jim painted 8/12 of the fence.
- hope this helps
:)
Jon and Jim painted a total of two thirds of the fence together. We found this by converting 1/4 to 3/12 and then adding it to 5/12, which gave us 8/12, or 2/3.
Explanation:The question involves understanding the addition of fractions. Jon painted a quarter of the fence which is equal to 1/4 and Jim painted five twelfths of the fence which is equal to 5/12.
To find out how much of the fence they painted together, we simply add these fractions. The lowest common multiple of 4 and 12 is 12. So, we convert 1/4 to 3/12 to make the denominators the same. Now, we have 3/12 (Jon's part) and 5/12 (Jim's part). The total part of the fence they painted together is 3/12 + 5/12 = 8/12 = 2/3.
So, Jon and Jim painted two thirds of the fence together.
Learn more about Addition of Fractions here:https://brainly.com/question/34825764
#SPJ2
Which step should richard perform last? Will choose brainliest. Any absurd answers will be reported.
Answer:
A
Step-by-step explanation:
Our equation is: 9² + 2[(5 + 2)² - 4]. We need to use PEMDAS: parentheses, exponents, multiplication, division, addition, and subtraction.
The first thing to do is to add the 5 and 2 in the parentheses:
9² + 2[(5 + 2)² - 4]
9² + 2[(7)² - 4]
Then square the 7:
9² + 2[(7)² - 4]
9² + 2[49 - 4]
Do the subtraction operation within the parentheses/brackets:
9² + 2[49 - 4]
9² + 2[45]
Square 9:
9² + 2[45]
81 + 2[45]
Multiply 2 by 45:
81 + 2[45]
81 + 90
Thus, the answer is A.
Answer:
A
Step-by-step explanation:
9² + 2[(5+2)² - 4]
81 + 2[(7)² - 4]
81 + 2[49 - 4]
81 + 2(45)
81 + 90
Yet another variation: A better packet switched network employs the concept of acknowledgment. When the end user’s device receives a packet correctly it sends an acknowledgment to the sender. Here too, a packet is received correctly with probability p, but the sender keeps sending copies of a given packet until a copy is correctly received (signaled by acknowledgment). Let random variable N be the number of times the same message packet is sent. a) Find the PMF PN (n).
Answer:
P(N = n) = [tex](1-P)^{n-1} \times P[/tex]
Step-by-step explanation:
to find out
Find the PMF PN (n)
solution
PN (n)
here N is random variable
and n is the number of times
so here N random variable is denote by the same package that is N (P)
so here
probability of N is
P(N ) = Ф ( N = n) .................. 1
here n is = 1, 2,3, 4,...................... and so on
so that here P(N = n) will be
P(N = n) = [tex](1-P)^{n-1} \times P[/tex]
What is the product?
[tex] \frac{5}{4 {k}^{2} } [/tex]
Answer:5/4k^2
Step-by-step explanation:
5k/6 x 3/2k^3
(5k x 3) ➗ (6 x 2k^3)
15k/12k^3=5/4k^2
Using intervals of width 10, how many intervals
are needed for this graph to be drawn correctly?
O 5 or fewer
O between 6 and 10
O between 11 and 19
0 25 or more
DONE
saaled
Answer:D
Step-by-step explanation:
4 2/5 divided by 1 1/3
Answer:
3.3
Step-by-step explanation:
[tex] = > \frac{4 \frac{2}{5} }{1 \frac{1}{3} } \\ \\ = > \frac{ \frac{20 + 2}{5} }{ \frac{3 + 1}{3} } \\ \\ = > \frac{ \frac{22}{5} }{ \frac{4}{3} } \\ \\ = > \frac{22}{5} \times \frac{3}{4} \\ \\ = > \frac{11}{5} \times \frac{3}{2} \\ \\ = > \frac{33}{10} \\ \\ = > 3.3[/tex]
What is a solution to the equation (x-2)(x+5)=18
Answer:
x= -7 x=3
Step-by-step explanation:
(x-2)(x+5)=18
FOIL
x^2 +5x -2x-10 = 18
Subtract 18 from each side
x^2 +5x -2x-10-18 = 18-18
x^2 +3x -28 =0
Factor
What 2 numbers multiply to -28 and add to 3
7*-4 = -28
7-4 =3
(x+7) (x-3) =0
Using the zero product property
x+7 =0 x-3 =0
x= -7 x=3
When a bactericide is added to a nutrient broth in which bacteria are growing, the bacterium population continues to grow for a while, but then stops growing and begins to decline. The size of the population at time t (hours) is b equals 8 Superscript 6 Baseline plus 8 Superscript 5 Baseline t minus 8 Superscript 4 Baseline t squared .b=86+85t−84t2. Find the growth rates at t equals 0 hours commat=0 hours, t equals 4 hours commat=4 hours, and t equals 8 hours.t=8 hours.
Answer:
The growth rates at t = 0 is 8⁵.
The growth rates at t = 4 is 0.
The growth rates at t = 8 is -8⁵.
Step-by-step explanation:
The expression representing the size of the population at time t hours is:
[tex]b(t)=8^{6}+8^{5}t-8^{4}t^{2}[/tex]
Differentiate b (t) with respect to t to determine the growth rate as follows:
[tex]\frac{db(t)}{dt}=\frac{d}{dt} (8^{6}+8^{5}t-8^{4}t^{2})[/tex]
[tex]=0+8^{5} (1)-8^{4}(2t)\\=8^{4}(8-2t)[/tex]
The growth rate is:
R (t) = 8⁴ (8 - 2t)
Compute the growth rates at t = 0 as follows:
[tex]R (0) = 8^{4} (8 - 2\times 0)\\=8^{4}\times 8\\=8^{5}[/tex]
Thus, the growth rates at t = 0 is 8⁵.
Compute the growth rates at t = 4 as follows:
[tex]R (4) = 8^{4} (8 - 2\times 4)\\=8^{4}\times 0\\=0[/tex]
Thus, the growth rates at t = 4 is 0.
Compute the growth rates at t = 8 as follows:
[tex]R (4) = 8^{4} (8 - 2\times 8)\\=8^{4}\times (-8)\\=-8^{5}[/tex]
Thus, the growth rates at t = 8 is -8⁵.
The growth rates at t=0 hours, t=4 hours, and t=8 hours can be calculated using the given equation.
When a bactericide is added to a nutrient broth in which bacteria are growing, the bacterium Population Growth in Bacteria continues to grow for a while, but then stops growing and begins to decline.
The size of the population at time t (hours) is b equals 8 Superscript 6 Baseline plus 8 Superscript 5 Baseline t minus 8 Superscript 4 Baseline t squared .b=86+85t−84t2.
Find the growth rates at t equals 0 hours commat=0 hours, t equals 4 hours commat=4 hours, and t equals 8 hours.t=8 hours.
Learn more about Population Growth in Bacteria here:
https://brainly.com/question/1152024
#SPJ3
The probable question may be:
When a bactericide is added to a nutrient broth in which bacteria are growing, the bacterium population continues to grow for a while, but then stops growing and begins to decline. The size of the population at time t (hours) is b equals 8 Superscript 6 Baseline plus 8 Superscript 5 Baseline t minus 8 Superscript 4 Baseline t squared .b=86+85t−84t2. Find the growth rates when
t equals 0 hours commat=0 hours,
t equals 4 hours commat=4 hours,
t equals 8 hours.t=8 hours.
Suppose a simple random sample of size nequals1000 is obtained from a population whose size is Nequals1 comma 000 comma 000 and whose population proportion with a specified characteristic is p equals 0.44 . Complete parts (a) through (c) below. (a) Describe the sampling distribution of ModifyingAbove p with caret. A. Approximately normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0005 B. Approximately normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0002 C. Approximately normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0157 (b) What is the probability of obtaining xequals460 or more individuals with the characteristic? P(xgreater than or equals460)equals nothing (Round to four decimal places as needed.) (c) What is the probability of obtaining xequals410 or fewer individuals with the characteristic? P(xless than or equals410)equals nothing (Round to four decimal places as needed.)
Question:
Suppose a simple random sample of size n = 1000 is obtained from a population whose size is N = 1,000,000 and whose population proportion with a specified characteristic is p = 0.44 . Complete parts (a) through (c) below.
(a) Describe the sampling distribution of ModifyingAbove p with caret.
A.)Approximately normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0002
B.)Approximately normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0005
C.)Approximately normal, mu Subscript ModifyingAbove p with caretequals0.44 and sigma Subscript ModifyingAbove p with caretalmost equals0.0157
(b) What is the probability of obtaining xequals480 or more individuals with the characteristic?
P(xgreater than or equals480)equals
nothing (Round to four decimal places as needed.)
(c) What is the probability of obtaining xequals410 or fewer individuals with the characteristic?
P(xless than or equals410)equals
nothing (Round to four decimal places as needed.)
Answer:
a) Option C.
b) 0.1021
c) 0.0280
Step-by-step explanation:
Given:
Sample size, n = 1000
p' = 0.44
a) up' = p' = 0.44
The sampling distribution will be:
[tex] \sigma _p' = \sqrt{\frac{p' (1 - p')}{n}}[/tex]
[tex] = \sqrt{\frac{0.44 (1 - 0.44)}{1000}}[/tex]
[tex] = \sqrt{\frac{0.44*0.56}{1000}} = 0.0157 [/tex]
Option C is correct.
b) The probability when x ≥ 460
[tex] P' = \frac{x}{n} = \frac{460}{1000} = 0.46[/tex]
p'(P ≥ 0.46)
[tex] 1 - P = \frac{(p' - up')}{\sigma _p'} < \frac{0.46 - 0.44}{0.0157} [/tex]
[tex] = 1-P( Z < 1.27) [/tex]
From the normal distribution table
NORMSDIST(1.27) = 0.898
1-0.8979 = 0.1021
Therefore, the probability = 0.102
c) x ≤ 410
[tex] P' = \frac{x}{n} = \frac{410}{1000} = 0.41[/tex]
p'(P ≤ 0.41)
[tex] P = \frac{(p' - up')}{\sigma _p'} < \frac{0.41 - 0.44}{0.0157} [/tex]
[tex] = P( Z < - 1.9108) [/tex]
From the normal distribution table
NORMSDIST(-1.9108) = 0.0280
Probability = 0.0280
Carl bought a DVD that cost $24.00 plus 8.25% sales tax. How much did Carl pay for this DVD in dollars and cents?
Answer: Carl paid $25.98 for this DVD in dollars and cents.
Step-by-step explanation:
The original cost of the DVD was $24.00. If a sales tax of 8.25% was charged, it means that the original cost of the DVD would increase by 8.25%.
The value in dollar and cents of an 8.25% increment(sales tax) would be
8.25/100 × 24 = 0.0825 × 24
= $1.98
Therefore, the amount that Carl would pay for this DVD in dollars and cents is
24 + 1.98 = $25.98
Help. Best answer = Brainiest
Answer:
10
Step-by-step explanation:
Answer:
-10
Step-by-step explanation
By substituting -2 in for all the X's you have (-2)^2+2(-2)-10. After ths is simplified you have 4+(-4)-10. -4+4 =0 and 0-10= -10
A machining company needs to manufacture more than 20 fixtures in a day. The company uses five identical machines to make the fixtures. If each machine produces x fixtures, which inequality represents this situation?
A.
5x > 20
B.
5x < 20
C.
5x > 20 + 5
D.
5x < 20 + 5
(I NEED AN EXPLANATION ON HOW YOU GOT THE ANSWER
PLEASE AND thank you)
Answer:
A
Step-by-step explanation:
We know that each machine makes x fixtures and we have 5 machines. So we need to use multiplication:
5 * x = 5x
The above expression indicates how many fixtures the 5 machines can make. We want the total to be more than 20, so we need to use the greater than sign: >.
5x > 20
The answer is A.
Answer:
A. 5x > 20
Step-by-step explanation:
Total production by 5 machines: 5x
5x > 20
Reggie works for an accounting firm. He earns $18,000 per year plus 8% of all money he saves his clients. How much money must he save his clients to earn $2,000 per month
Answer:
He has to save his clients $75,000.
Step-by-step explanation:
$2,000 per month is 2*2,000 = $24,000
He eanrs a fixed rate of $18,000 per year. So in bonuses, he has to earn 24,000 - 18,000 = $6,000.
His bonuses are 8% of the money he saves his clients.
So this 8% must be $6,000. How much his 100%?
0.08 - $6,000
1 - $x
[tex]0.08x = 6000[/tex]
[tex]x = \frac{6000}{0.08}[/tex]
[tex]x = 75000[/tex]
He has to save his clients $75,000.
What is the y-intercept of this quadratic function?
f(x)=-x2+10x-22
Answer:
The y intercept is (0,-22)
Step-by-step explanation:
To find the y intercept, set x =0 and solve for y
f(0)=-0^2+10*0-22
= -22
Final answer:
To find the y-intercept of a quadratic function, substitute x = 0 into the function and calculate the value. In this case, the y-intercept of the function [tex]f(x) = -x^2 + 10x - 22[/tex] is at y = -22.
Explanation:
The y-intercept of a quadratic function is the point where the graph intersects the y-axis, and it occurs when x = 0. To find the y-intercept of the quadratic function [tex]f(x) = -x^2 + 10x - 22[/tex], substitute x = 0 into the function.
Replace x with 0: f(0) =[tex]-(0)^2 + 10(0) - 22[/tex]
Calculate the value: f(0) = 0 + 0 - 22 = -22
Therefore, the y-intercept of the quadratic function is at y = -22.
There are ten kids in a class. When any two meet, they shake their hands.Before the class starts, how many handshakes are there?
Answer: 45
Step-by-step explanation:
Ok, Kid 1 can meet other 9 kids, so we have 9 handshaks.
Kid 2 can also meet other 9 kids, but he already meet kid 1, so we are not counting that handshake, this means that now we have 8 handshakes.
Kid 3 can also meet 9 kids, but we already counted the handshake with kid 1 and kid 2, so here we have other 7 andshakes.
And so on, so we have a total of:
9 + 8 + 7 + 6 + 5 + 4 +3 + 2 + 1 = 45 handshakes in total.
Answer:
45 handshakes
Step-by-step explanation:
4.
a) Name the highlighted arc and determine if it is a major arc, minor arc, or semicircle.
b) Find the measure of the highlighted arc.
Answer: 4.067units.
Step-by-step explanation:
(a) The highlighted arc is the major arc. That is , it covers from G to I.
(b) The length of the major arc will be
πr0°/180 where the angle substended at the center by the highlighted arc is
360° - 127° ( the angles if the arc not highlighted)
= 233°
Though this radius of the circle was not given so we are going to find the arc length without necessarily defining the radius.
Arc length = π × r × 233°
---------------
180
= 3.142 × r × 233°
------------------
180
= 4.067runits.
The arc that is highlighted is the major arc
The measure of the highlighted arc is 4.067runits.
How to solve for the arcThe formula for the length of major arc
πr0°/180
Without highlioghts the angles are
360° - 127°
= 233 degrees
Formula for lenght of arc Arc length = π × r × 233° / 180
= = 3.142 × r × 233° / 180
= 4.067runits.
Read mroe on Arc length here https://brainly.com/question/29860198
#SPJ2
Carmen is planning rail lines for a new train station. Help her find m<1. Explain how you found that solution. Parallel lines a and b are cut by transversal t to form 8 angles. Clockwise from top left, the angles formed with line a are blank, 17 degrees, 2, blank; with line b are 1, blank, blank, blank.
Answer:
m<1 =163 degrees163,17,163,17 (all in degrees)163,17,163,17 (all in degrees)Step-by-step explanation:
I have reproduced and attached a diagram (in figure 1) of the problem.
For ease of understanding, I have attached a second diagram which is labelled.
On line a
17+<CBE=180 (Linear Pair Postulate)
m<2=<CBE=180-17=163 degrees
<ABG=<CBE=163 degrees (Vertically Opposite Angles)
<ABE=<GBC= 17 degrees(Vertically Opposite Angles)
On line b
m<1=<DEB=<ABG=163 degrees (Corresponding Angles)
<BEF=<GBC= 17 degrees (Corresponding Angles)
<HEF=<DEB=163 degrees (Vertically Opposite Angles)
<DEH=<BEF=17 degrees (Vertically Opposite Angles)
Therefore:
m<1 =163 degreesClockwise from top left, the angles formed with line a are: 163 degrees, 17 degrees, m<2=163 degrees and 17 degrees.Clockwise from top left, the angles formed with line b are: m<1=163 degrees, 17 degrees, 163 degrees, and 17 degrees.Answer:
Sample response: Angle 2 is a supplementary angle with 17°, so m∠2 = 163°. Since ∠1 and ∠2 are alternate interior angles of parallel lines, they are congruent, and the m ∠1 = m ∠2. Thus, m∠1 = 163°.
Step-by-step explanation:
PLZ GIVE BRAINLIEST!!!!!!!!!!!!!
1. How many solutions does the following equation have?
3x + 9 + 14x = 4x + 5
No solutions
Exactly one solution
Infinitely many solutions
Answer:
no solutions
because it
Step-by-step explanation:
10.15 + 31.60 + 34.75 + 40 + 69.25 + 54.75 =
Answer:
The sum of 10.15 + 31.60 + 34.75 + 40 + 69.25 + 54.75 equals to 185.75
Step-by-step explanation:
10.15 + 31.6 + 34.75 + 40 + 69.25
= 41.75 + 104 + 40
= 145.75 + 40
= 185.75
Alternate forms:
743/4 , 185 3/4
\frac{743}{4} 185\frac{3}{4}
Answer:
240.5
Step-by-step explanation:
Suppose a team of researchers is studying the half-life of a drug in the human body (i.e. how long it takes for 1 2 of the drug to be broken down by the body). They take 50 people, administer a standard dose of the drug, and measure the half-life for each of these people. They find the average half-life to be 7.4 hours. Suppose the variance of half-life is known to be 0.16. Find the 95% confidence interval for population half-life based on this sample. What is the length of this interval?
Answer:
95% confidence interval for the population half-life based on this sample is [7.29 , 7.51].
Step-by-step explanation:
We are given that the average half-life to be 7.4 hours. Suppose the variance of half-life is known to be 0.16.
They take 50 people, administer a standard dose of the drug, and measure the half-life for each of these people.
Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample average half-life = 7.4 hours
[tex]\sigma[/tex] = population standard deviation = [tex]\sqrt{0.16}[/tex] = 0.4 hour
n = sample of people = 50
[tex]\mu[/tex] = population mean
Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] <
P( [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]
= [ [tex]7.4-1.96 \times {\frac{0.4}{\sqrt{50} } }[/tex] , [tex]7.4+1.96 \times {\frac{0.4}{\sqrt{50} } }[/tex] ]
= [7.29 , 7.51]
Therefore, 95% confidence interval for the population half-life based on this sample is [7.29 , 7.51].
The length of this interval is = 7.51 - 7.29 = 0.22
Suppose that n units are randomly sampled and x number of the sampled units are found to have the characteristic of interest. A survey of n = 540 pet owners revealed that x = 243 buy their pets holiday presents. For p = proportion of pet owners who revealed that they buy their pets holiday presents, provide a point estimate of p and determine its 95% error margin. Carry out all calculations exactly, round the final answers only. Point estimate =
Answer:
The point estimate is 0.45.
The 95% error margin is 0.042 = 4.2 percentage points.
Step-by-step explanation:
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].
The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
Point estimate
We have that [tex]n = 540, x = 243[/tex]
So the point estimate is:
[tex]\pi = \frac{243}{540} = 0.45[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
Error margin:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{0.45*0.55}{540}}[/tex]
[tex]M = 0.0420[/tex]
The 95% error margin is 0.042 = 4.2 percentage points.
Find the volume of the cone. Round your answer to the nearest tenth.
Answer:
45π or 141.4 [tex]cm^{3}[/tex]
Step-by-step explanation:
The volume of a cone is [tex]V=\frac{1}{3} \pi r^{2} h[/tex]
Here we have a diameter of 6 cm which means we have a radius of 3 (dividing by 2)
Our height here is 15 cm
Plugging in all our values we get [tex]\frac{1}{3}\pi[/tex][tex](3)^{2} (15)[/tex] which gives us 45π or 141.4 [tex]cm^{3}[/tex]
1. To evaluate the effect of a treatment, a sample (n = 16) is obtained from a population with a mean of µ = 30 and a treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 31.3 with a sample standard deviation of s = 3. Are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α = .05?
Answer:
We conclude that the treatment does not has a significant effect.
Step-by-step explanation:
We are given that to evaluate the effect of a treatment, a sample (n = 16) is obtained from a population with a mean of µ = 30 and a treatment is administered to the individuals in the sample.
After treatment, the sample mean is found to be M = 31.3 with a sample standard deviation of s = 3.
Let [tex]\mu[/tex] = population mean.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 30 {means that the treatment does not has a significant effect}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 30 {means that the treatment has a significant effect}
The test statistics that would be used here One-sample t test statistics as we don't know about population standard deviation;
T.S. = [tex]\frac{M-\mu}{\frac{s}{\sqrt{n}}}[/tex] ~ [tex]t_n_-_1[/tex]
where, M = sample mean = 31.3
s = sample standard deviation = 3
n = sample size = 16
So, test statistics = [tex]\frac{31.3-30}{\frac{3}{\sqrt{16}}}[/tex] ~ [tex]t_1_5[/tex]
= 1.733
The value of t test statistics is 1.733.
Now, at 0.05 significance level the t table gives critical values of -2.131 and 2.131 at 15 degree of freedom for two-tailed test. Since our test statistics lie within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the treatment does not has a significant effect.
The data are not sufficient to conclude that the treatment has a significant effect. The calculated test statistic is less than the critical value for a two-tailed test with a significance level of α = 0.05, hence we fail to reject the null hypothesis.
Explanation:To determine if the treatment had a significant effect, we must conduct a hypothesis test. This falls under the field of statistics.
First, let's state our null hypothesis (H₀) and alternative hypothesis (H₁). H₀: µ = 30 (i.e., the treatment has no effect) and H₁: µ ≠ 30 (treatment has an effect).
Next, we find the standard error (SE) of the mean, which is s/√n = 3/√16 = 0.75.
We then calculate our test statistic, which is the difference between M (sample mean) and µ (population mean) divided by the SE: (31.3 - 30) / 0.75 = approximately 1.73.
Given a two-tailed test with a significance level of α = 0.05, the critical z-values would be -1.96 and +1.96. As our calculated test statistic falls between these two critical values (-1.96reject the null hypothesis.
Consequently, the data are not sufficient to conclude that the treatment has a significant effect.
Learn more about Hypothesis Testing here:https://brainly.com/question/34171008
#SPJ3
Two sides of a triangle are 7 and 11 the length of the third side x is expressed
Answer:
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. ... No; The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. ANSWER: No; 9.
A bag contains 50 marbles, 28 red ones and 22 blue ones. A marble is picked at random from the bag. 17 What is the probability of picking a red marble after a blue marble had been picked first and not replaced?
After a blue marble is drawn and not replaced, the probability of drawing a red marble from the bag containing initially 28 red and 22 blue marbles is 9/16.
Explanation:The question is asking for the probability of picking a red marble after a blue marble has been picked first and not replaced. The bag originally contains 50 marbles, 28 red ones, and 22 blue ones. After removing one blue marble, there would be 27 red marbles and 21 blue ones left, making a total of 48 marbles.
To find the probability of now drawing a red marble, we divide the number of red marbles by the new total number of marbles:
Probability = Number of Red Marbles / Total Number of Marbles
Probability = 27 / 48
Probability = 9 / 16
Therefore, the probability of drawing a red marble after having already drawn a blue marble and not replacing it is 9/16.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ2
what is the fraction for 4.5
Answer:
4 [tex]\frac{1}{2}[/tex]
OR
[tex]\frac{9}{2}[/tex]
Step-by-step explanation:
I'm not exactly sure which type of fraction you're asking for, so I'll put both.
This would be the fraction for 4.5 because the 0.5 is half of 1, while we already have a whole number, being 4.
OR
9 divided by 2 is 4.5, making the fraction for 4.5, [tex]\frac{9}{2}[/tex]
Answer:
9/2
Step-by-step explanation:
Please answer this correctly
Answer:
all of them are valid solutions
Step-by-step explanation:
So we plug in values of t below and get:
18 is < 107
54 is < 107
36 is < 107
27 is <107
The on-line access computer service industry is growing at an extraordinary rate. Current estimates suggest that 20% of people with home-based computers have access to on-line services. Suppose that 15 people with home-based computers were randomly and independently sampled. What is the probability that at least 1 of those sampled have access to on-line services at home?
Answer:
Probability that at least 1 of those sampled have access to on-line services at home is 0.9648.
Step-by-step explanation:
We are given that current estimates suggest that 20% of people with home-based computers have access to on-line services.
Suppose that 15 people with home-based computers were randomly and independently sampled.
The above situation can be represented through binomial distribution;
[tex]P(X=r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ;x=0,1,2,3,......[/tex]
where, n = number of trials (samples) taken = 15 people
r = number of success = at least one
p = probability of success which in our question is % of people
who have access to on-line services at home, i.e.; p = 20%
Let X = Number of people who have access to on-line services at home
So, X ~ Binom(n = 15, p = 0.20)
Now, probability that at least 1 of those sampled have access to on-line services at home is given by = P(X [tex]\geq[/tex] 1)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= [tex]1- \binom{15}{0}\times 0.20^{0} \times (1-0.20)^{15-0}[/tex]
= [tex]1- (1\times 1 \times 0.80^{15})[/tex]
= 1 - 0.0352 = 0.9648
Hence, the required probability is 0.9648.
The following problem can be solved using the binomial distribution.
Binomial distributionA common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
[tex]P(x) = ^nC_x p^xq^{(n-x)}[/tex]
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
There is 96.481% chance that at least 1 of those sampled have access to online services at home.
Given to usThe online access computer service industry is growing at an extraordinary rate. Current estimates suggest that 20% of people with home-based computers have access to online services.Suppose that 15 people with home-based computers were randomly and independently sampled. SolutionFor the values,As given, 20% of people with home-based computers have access to online services. therefore, the probability of a person having access to online services is also 20%. thus, p = 20% = 0.2We know that for any event the sum of all probability is 1. therefore, the probability of a person not having access to online services is (1-p). thus, q = (1-0.20) = 0.80It is already stated in the sentence that the sample is been done on 15 people. therefore, the sample size is n = 15.We need the probability that at least 1 of those sampled have access to online services at home, therefore, x ≥ 1.ProbabilitySubstituting the values in a binomial distribution,
[tex]P(x\geq 1) = 1- P(0)[/tex]
[tex]P(x\geq 1) = 1-\ ^{15}C_0\times [0.20^0]\times [0.80^{(15-10)}]\\\\ P(x\geq 1)=1-\ 0.032\\\\ P(x\geq 1) = 0.96481\\\\ [/tex]
Hence, there is 96.481% chance that at least 1 of those sampled have access to online services at home.
Learn more about Binomial Distribution:
https://brainly.com/question/12734585