Solution :
Given information :
A sample of n = 10 adults
The mean failure was 24 and the standard deviation was 3.2
a). The formula to calculate the 95% confidence interval is given by :
[tex]$\overline x \pm t_{\alpha/2,-1} \times \frac{s}{\sqrt n}$[/tex]
Here, [tex]$t_{\alpha/2,n-1} = t_{0.05/2,10-1}$[/tex]
= 2.145
Substitute the values
[tex]$24 \pm 2.145 \times \frac{3.2}{\sqrt {10}}$[/tex]
(26.17, 21.83)
When the [tex]\text{sampling of the same size}[/tex] is repeated from the [tex]\text{population}[/tex] [tex]n[/tex] infinite number of [tex]\text{times}[/tex], and the [tex]\text{confidence intervals}[/tex] are constructed, then [tex]95\%[/tex] of them contains the [tex]\text{true value of the population mean}[/tex], μ in between [tex](26.17, 21.83)[/tex]
b). The formula to calculate 95% prediction interval is given by :
[tex]$\overline x \pm t_{\alpha/2,-1} \times s \sqrt{1+\frac{1}{n}}$[/tex]
[tex]$24 \pm 2.145 \times 3.2 \sqrt{1+\frac{1}{10}}$[/tex]
(31.13, 16.87)
(1+y²)dx + (1+x²)dy = 0
This differential equation is separable:
(1 + y²) dx + (1 + x²) dy = 0
(1 + y²) dx = - (1 + x²) dy
dy/(1 + y²) = -dx/(1 + x²)
Integrating both sides gives
arctan(y) = -arctan(x) + C
and solving for y gives (over an appropriate domain)
y = tan(C - arctan(x))
(the domain being -1 ≤ y ≤ 1).
What is the common ratio for this geometric sequence?
27, 9, 3, 1, ...
Answer:
a multiple of 3.
Step-by-step explanation:
1x3=3
3x3=9
9x3=27
A survey showed that, in one city, 20.7% of the population used
product X, 50% use product Y and among users Y, 36.5% use X. Randomized interview
However, a resident in that city, calculate the probability that that person
a) Use both X and Y;
b) Neither X nor Y
Answer:
Step-by-step explanation:
a) 0.5*0.365=18.25%
b) (100%-20,7%-50%)=29.3
g According to a report from a particular university, % of female undergraduates take on debt. Find the probability that of the female undergraduates have taken on debt if female undergraduates were selected at random. What probability should be found
Answer:
P(0 female undergraduate takes on debt) ;
0.00635
Step-by-step explanation:
Probability of taking on debt, p = 0.43
q = 1 - p = 1 - 0.43 = 0.57
Number of samples, number of trials, n = 9
To obtain the probability that none of the female undergraduate take on debt :
P(0 female undergraduate takes on debt)
P(x = 0) ; using the binomial probability relation :
P(x = x) = nCx * p^x * q^(n-x)
P(x = 0) = 9C0 * 0.43^0 * 0.57^(9-0)
P(x = 0) = 9C0 * 0.43^0 * 0.57^9
P(x = 0) = 1 * 1 * 0.006351461955384057
P(x = 0) = 0.006351461955384057
P(x = 0) = 0.00635
Suppose that a group of 10 people join a weight loss program for 3 months. Each person's weight is recorded at the beginning and at the end of the 3-month program. To test whether the weight loss program is effective, the data should be treated as:
To test the effectiveness of the weight loss program, a PAIRED SAMPLE test distribution is used.
The weight loss data collated for the program for both the beginning and end of the program period was obtained with one subject or person having two separate readings, these shows that the samples are NOT INDEPENDENT.
When performing a test which involves DEPENDENT or MATCHED samples, whereby means of two measurements taken from the SAME subject are involved, a PAIRED SAMPLE TEST DISTRIBUTION IS ADOPTED.
Therefore, the effectiveness of the weight loss programme will be accurately evaluated using a PAIRED SAMPLE TEST.
Learn more : https://brainly.com/question/17143411
Imagine that you are given two linear equations in slope-intercept form. You
notice that both the slopes and the y-intercepts are the same. How many
solutions would you expect for this system of equations?
O A. 1
ОВ. о
C. infinitely many
O D. cannot be determined
SURAT
Answer:
C. infinitely many
Step-by-step explanation:
If two equations in slope-intercept form have the same slope and y-intercept they must be the same line. Additionally, the solutions of a system of equations are wherever the two lines intersect. Since the lines are the same they must intersect at every point. Therefore, there are infinitely many solutions.
what are the answers to the questions below?
Answer:
You have to follow PEMDAS or parenthesis, exponents, multiplication, division, addition, and subtraction. It's an order to solve equations. I listed the steps and the answers for you below :) I have throughly checked them so they should be correct! yw :D
Step-by-step explanation:
1. 5x + 4x - 6x = 24
9x - 6x = 24
3x = 24
24/3 = 8
x = 8
2. 8y + 5 - 4y + 1 = 46
8y - 4y = 4y
5 + 1 = 6
4y + 6 = 46
4y = 46 - 6
4y = 40
40/4 = 10
y = 10
3. 33 = 5 ( x + 8 ) + 3
33 = 5x + 40 + 3 (because we distributed)
33 = 5x + 43
5x + 43 = 33 (just rewriting it to make it easier)
5x = 33 - 43
5x = -10
-10/5 = -2
so x = - 2
4. 2m + 3 ( m - 8 ) = 1
2m + 3m - 24 = 1
we got 3m - 24 because we distributed the 3
5m - 24 = 1
5m = 25
25/5 = 5
m = 5
5. p + p - 2p + 4p = - 48
2p - 2p + 4p = - 48
4p = - 48
- 48 / 4 = - 12
p = - 12
6. 2 ( y + 5 ) + 3y = 25
2y + 10 + 3y = 25
5y + 10 = 25
5y = 25 - 10
5y = 15
15/5 = 3
y = 3
7. 1/4 h + 3/4 h + 1/2 h + 2 = 5
1/4 h + 3/4 h + 1/2 = 3/2 h
3/2 h + 2 = 5
3/2 h = 5 - 2
3/2 h = 3
h = 2
8. 60 = 4 ( k + 3 ) + 2 ( k - 3 )
60 = 4k + 12 + 2k - 6
4k + 12 + 2k - 6 = 60
6k + 6 = 60
6k = 60 - 6
6k = 54
k = 9
9. - 2 ( d + 1.4 ) - 1.8 = 20.6
-2d + - 2.8 - 1.8 = 20.6
-2d - 2.8 = 22.4
-2d = 25.2
d = - 12.6
10. 8 - 2 ( w + 4 ) = 10
8 + - 2 w + - 8 = 10
-2w + 9 + - 8 = 10
-2w = 10
10 / -2 = -5
w = -5
40 percent of the teachers at a meeting are male.
Of the male teachers at the meeting, 20 percent
teach mathematics. Which of the following
could be the possible number of teachers at the
meeting?
(A) 60
(B) 64
(C) 72
(D) 75
(E) 80
Answer:
D. 75
Step-by-step explanation:
To find the possible number of teachers at the meeting, find which answer choice creates a whole number answer when calculating the 40% of teachers that are male and the 20% of them that teach math.
This number is answer choice D, 75.
40% of 75 is 30.
Of those 30 teachers, 20% of 30 is 6.
So, since each quantity is a whole number, this could be the possible number of teachers at the meeting.
The correct answer is D. 75
how do i convert 134five to base ten
Answer:
44
Step-by-step explanation:
1×5² + 3×5¹ +4×5⁰
25+15+4
44
Ted wanted to determine if one brand of paper towels (Brand A) was stronger than another brand (Brand B). He performed a study where he randomly selected 25 sheets from each of the two brands, placed each sheet in an embroidery hoop (and tightened the hoop), placed 30 drops of water on each paper towel, and placed weights on each sheet until the sheet broke. He recorded the maximum weight on the paper towel before it broke. Which of the following statements is correct?
A) A two-tail test will be performed since the alternative hypothesis contains a "less than"
B) A one-tail test will be performed since the alternative hypothesis contains a "not equal to".
C) A one-tail test will be performed since the alternative hypothesis contains a "less than".
D) A two-tail test will be performed since the null hypothesis contains a "not equal to"
E) A two-tail test will be performed since the alternative hypothesis contains a "not equal to".
Answer:
C) A one-tail test will be performed since the alternative hypothesis contains a "less than".
Step-by-step explanation:
Test may be categorized as being one tailed or two tailed depending on the inequality sign used when defining the hypothesis ` ; Hypothesis whereby the alternative hypothesis takes a not equal to (≠) are categorized as two talked as the direction of does not point to either the left or right. Conversely, alternative hypothesis which takes a less Than sign or takes a greater Than sign are classed as being one tailed as the they point to a specified direction..
For the scenario given : we are to test the claim that one is stronger than the other ;
For this knid if test it has been stated explicitly that one is greater than another ;
H0 : μ = μ
H0 : μ < μ
The table below shows the educational attainment of a country's population, aged 25 and over. Use the data in the table, expressed in millions to find the probability that a randomly selected citizenaged 25 or over , was a man with 4 years of college (or more)
Answer:
The answer is "[tex]\bold{\frac{22}{171}}[/tex]"
Step-by-step explanation:
There are 22 million males that have completed four years of undergraduate, according to the data below: (or more). This is predicated on a population of 171 million.
The chances we're searching about [tex]\frac{(22\ million)}{(171\ million)} = \frac{22}{171}[/tex]
however
This proportion could be further reduced because 22 and 171 have no common features (other than 1).
The Susan B. Anthony dollar has a radius of 0.52 inches. Find the area of one side of the coin to the nearest
hundredth.
Answer:
0.85 in²
Step-by-step explanation:
really ? you need help with that ? you could not find the formula for the area of a circle on the internet and type it into your calculator ? I can't do anything else here.
a circle area is
A = pi×r²
r being the radius.
and pi being, well, pi (3.1415....)
r = 0.52 in
so,
A = pi×0.52² = pi×0.2704 = 0.849486654... in²
the area of one side of the coin is 0.85 in²
Suppose a six-sided die is tossed 1200 times and a 6 comes up 419 times. (a) Find the empirical probability for a 6 to occur. (Enter your probability as a fraction.) (b) On the basis of a comparison of the empirical probability and the theoretical probability, do you think the die is fair or biased
Answer:
Here both probabilities are not equal.
Therefore the die is not fair and biased.
Step-by-step explanation:
Now n= 1200 times and x = 419 times.
a) Empirical Probability:
[tex]=\frac{x}{n} \\\\= \frac{419}{1200}\\ \\=0.349[/tex]
Probability = 0.349
b) Theoretical Probability:
[tex]=\frac{1}{6}[/tex]
Here both probabilities are not equal.
Therefore the die is not fair and biased.
In 1990, the average math SAT score for students at one school was 498. Five years later, a teacher wants to perform a hypothesis test to determine whether the average SAT score of students at the school has changed from the 1990 mean of 498.
The hypotheses are shown below. Identify the Type II error.
H0:μ=498
Ha:μ≠498
A. Fail to reject the claim that the average math SAT score is 498 when in fact it is not 498.
B. Reject the claim that the average math SAT score is 498 when in fact it is not 498.
C. Reject the claim that the average math SAT score is 498 when in fact it is 498.
D. Fail to reject the claim that the average math SAT score is 498 when in fact it is 498.
Answer:
A. Fail to reject the claim that the average math SAT score is 498 when in fact it is not 498.
Step-by-step explanation:
Type II Error:
A type II error happens when there is a non-rejection of a false null hypothesis.
In this question:
The null hypothesis is H0:μ=498.
Since there is a type II error, there was a failure to reject the claim that the average math SAT score is 498 when in fact it is not 498, and thus, the correct answer is given by option A.
Find the range of the function f(x) = 2 cos πx:
A) R
B) [-π,π]
C)[-2,2]
D) [-1,1]
PLEASE I NEED HELP IM REALLY BAD AT FINDING RANGES , I WILL MARK BRAINLIEST!!!
Answer:
A) R
Step-by-step explanation:
f(x) = 2 cos π x, but cos π = -1 therefore
f(x) = -2x, this is a line that has the slope m= -2, and goes trough the origin
the range is given by all the values of y so is R
Hello my ''brainiest intelligent minds'' once again I'm counting on you, lol, I'm trying to figure this out.
f(x)=2x+3
g(x)=3x+2
What does (f+g)(x) equal?
Answer:
(f + g)(x) = 5x + 5
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = 2x + 3
g(x) = 3x + 2
Step 2: Find
Substitute in function values: (f + g)(x) = 2x + 3 + 3x + 2Combine like terms: (f + g)(x) = 5x + 525 scores from all of the students who took the test. She sees that the mean score is 134 with a standard deviation of 6.0547. The superintendant wants to know if the standard deviation has changed this year. Previously, the population standard deviation was 13. Is there evidence that the standard deviation of test scores has decreas
Answer:
WE fail to reject the Null and conclude that ; Standard deviation of test hasn't decreased.
Step-by-step explanation:
The hypothesis :
H0 : σ = 13
H1 : σ < 13
Using the Chisquare Square statistic :
χ² = (n-1)*s²/σ²
Sample size, n = 25
s² = 6.0547²
σ² = 13²
χ² = (25 - 1)*6.0547² / 13²
χ² = 879.82541016 / 169
χ² = 5.206
The degree of freedom, df = 25 - 1 = 24
The Pvalue(5.206, 24) = 0.99981
Reject H0, if Pvalue < α ;
Since Pvalue > α ; WE fail to reject the Null and conclude that ; Standard deviation of test hasn't decreased.
For the graph find a) b) c) and d)
Answer:
[tex]f(0) = -1[/tex]
[tex]f(\pi) = 1[/tex]
Domain: All real numbers
[tex]Range = [-1,1][/tex]
Step-by-step explanation:
Given
The attached graph
Solving (a): f(0)
On the attached graph
[tex]f(x) = -1[/tex] when [tex]x =0[/tex]
So:
[tex]f(0) = -1[/tex]
Solving (b): f(pi)
On the attached graph
[tex]f(x) = 1[/tex] when [tex]x =\pi[/tex]
So:
[tex]f(\pi) = 1[/tex]
Solving (c): Domain
There is no restriction on x.
Hence, the domain is the set of all real numbers
Solving (d): Range
In the attached graph
[tex]y_{min} = -1[/tex]
[tex]y_{max} = 1[/tex]
So, the range is:
[tex]Range = [-1,1][/tex]
What is the inverse of the function ? f(x)=x+1 over x?
plato
Answer:
[tex]f { - 1}^{} = \frac{1 - x}{x - 1} [/tex]
Step-by-step explanation:
bxhrrrhi5u44ftj7gttjoy
Answer:
x = (y+1)/y
xy = (y+1)
xy -y = 1
y(x-1)=1
y = 1/(x-1)
Step-by-step explanation:
Find f such that f'(x) = 8x – 3. f(4) = 0
Answer: y=29 / (4,29)
Step-by-step explanation:
By graphing [tex]f(x)=8x-3[/tex] and [tex]f(4)=0[/tex] on Desmos. You'll be able to find that when x is 4, y is 29.
Similarly, you can plugin 4 into the original equation ([tex]f(x)=8x-3[/tex]) Which looks like:
[tex]8(4)-3\\32-3=29[/tex]
Additionally, you can change [tex]f(x)=[/tex] to [tex]y=[/tex] as it is the exact same thing. With that in mind, you can do the same with [tex]f(x)=0[/tex] and just change it to x=4. As you're wanting to know what the y-value is when x=4.
Answer:
4x²-3x+c is our original equation
Step-by-step explanation:
we have an independent number I called this number c
put 4 from x and try to find c
f(4)=4*(4²)-3*(4)+c=0
we have to be careful about f(4) is 0
64-12+c=0 and c is -52 so our original equation is 4x²-3x-52
please help me with geometry
Answer:
x = 7
Explaination:
ABC = 40°
and BD bisects the angle so ABD = 20°
so 3x-1=20
solving for x gets us
x = 7
Teacher gives 2 questions to a class of 50 student. 30 students correctly answer ther first question, 25 students correctly answer the second question, 7 wongly answer both question, there are _ students correctly answer both question
Answer:
43
Step-by-step explanation:
only 7 out of the 50 got both wrong
Answer:
Step-by-step explanation:
Write the options so they are homogeneous in content. • Use answers given in previous open-ended exams to provide realistic distractors. 2. Use a Question ...
PLS HELP !! Is the following a fair sampling of the contents of the jar? Why?
Pour a 2” layer of lentils into a jar. Then pour a 2” layer of kidney beans into the jar. Then pour a 2” layer of pinto beans into the jar. Stir the contents of the jar well. Then pull out a handful of beans.
What is a8 for the geometric sequence 6,561;−2,187;729;−243;….
Answer:
In geometric sequence you divide the terms. As I will show you the calculations step by step. Hopefully this becomes clear and helpful to you
Step-by-step explanation:
-2187÷6561
= -0.3333...
a8=a1 r^8-1
=(4374)(-0.3)^8-1
=(4374)(-0.3)^7
=(4374)(-4.572473708×10^-4)
=-2
Therefore a8= -2
The National Oceanic and Atmospheric Administration tracks the amount of oysters harvested from the Chesapeake Bay each year:
Find the exponential regression equation that models this data.
The EXPONENTIAL REGRESSION equation obtained by fitting the data is [tex]y = 58.031(0.964)^x[/tex]
To obtain the exponential regression equation which models the data, we could use technology, we involves Inputting the data into an EXPONENTIAL REGRESSION CALCULATOR or EXCEL
Using an exponential regression calculator :
The regression equation obtained is :
[tex]y = 58.031(0.964)^x[/tex]
The general function of an exponential regression function is : [tex]AB^x[/tex]
A = 58.031 = Initial value ; B = Decay factor
Hence, the EXPONENTIAL REGRESSION EQUATION obtained using technology is : [tex]y = 58.031(0.964)^x[/tex]
Learn more :
https://brainly.com/question/11169800
What is the inverse of the function g (x) = 5 (x - 2)
Answer:
g − 1 ( x ) = x/ 5 + 2
Step-by-step explanation:
See the pic for solutions :)
 evaluate P(6,2) or 6p2
Answer:
30
Step-by-step explanation:
Permutation equation: [tex]\frac{n!}{(n-r)!}[/tex]
n = Total number of objects, r = Number of objects selected
[tex]_6P_2=\frac{6!}{(6-2)!}=30[/tex]
Ian and Keith make extra money in the summer picking strawberries. Yesterday, they picked 384 pounds of strawberries altogether. Ian is more experienced and picked 3 times as many pounds as Keith. How many pounds of strawberries did Keith pick yesterday?
Find the length of BC again
Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.
Remember: SOH-CAH-TOA
Looking from the angle, we know the opposite side and want to know the adjacent side. Therefore, we should use the tangent function.
tan(61) = 47 / BC
BC = 47 / tan(61)
BC = 26.05 units
Hope this helps!
Answer:
BC = 26.05
Step-by-step explanation:
SOH CAH TOA
tan 61 = 47/BC
BC = 47/tan 61
4. A solution of 60% fertilizer is to be mixed with a solution of 21% fertilizer to form 234 liters of a 43% solution. How many liters of the 60% solution must be used?
SHOW YOUR WORK
Given:
A solution of 60% fertilizer is to be mixed with a solution of 21% fertilizer to form 234 liters of a 43% solution.
To find:
The quantity of the 60% solution in the mixture.
Solution:
Let x be the quantity of the 60% solution and y be the quantity of the 21% solution.
Quantity of mixture is 234. So,
[tex]x+y=234[/tex]
[tex]x=234-y[/tex] ...(i)
The mixture has 43% fertilizer. So,
[tex]\dfrac{60}{100}x+\dfrac{21}{100}y=\dfrac{43}{100}\times 234[/tex]
Multiply both sides by 100.
[tex]60x+21y=10062[/tex] ...(ii)
Using (i) and (ii), we get
[tex]60(234-y)+21y=10062[/tex]
[tex]14040-60y+21y=10062[/tex]
[tex]-39y=10062-14040[/tex]
[tex]-39y=-3978[/tex]
Divide both sides by -39.
[tex]\dfrac{-39y}{-39}=\dfrac{-3978}{-39}[/tex]
[tex]y=102[/tex]
Putting this value in (i), we get
[tex]x=234-102[/tex]
[tex]x=132[/tex]
Therefore, 132 liters of the 60% solution must be used.
