Answer:
y=9
Step-by-step explanation:
-2[(4y+1)-(2y-2)]=6(7-y)-6
-2[4y+1-2y-2]=6(7-y)-6
-2[2y-1]=6(7-y)-6
-2y+2=6(7-y)-6
-2y+2=42-6y-6
Add 6y to both sides
4y+2=42-6
4y+2=38
Subtract 2 from both sides
4y=36
Divide both sides by 4
y=9
One of the questions in a study of marital satisfaction of dual-career couples was to rate the statement, "I'm pleased with the way we divide the responsibilities for childcare." The ratings went from 1 (strongly agree) to 5 (strongly disagree). The table below contains ten of the paired responses for husbands and wives. Conduct a hypothesis test at the 5% level to see if the mean difference in the husband's versus the wife's satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife). Wife's score 2 2 3 3 4 2 1 1 2 4 Husband's score 2 1 2 3 2 1 1 1 2 4 NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)(1) State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom.)(2) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)(3) What is the p-value? (Round your answer to four decimal places.)(4) Alpha (Enter an exact number as an integer, fraction, or decimal.)α =
Answer;
1) The t-distribution is most suitable for this problem.
2) Test statistic = 2.356
3) p-value = 0.0214
4) Alpha = 5% = 0.05
5) The p-value is greater than the significance level at which the test was performed, meaning that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the husbands are happier in dual couple marriages.
Step-by-step Explanation:
Wife's score 2 2 3 3 4 2 1 1 2 4
Husband's score 2 1 2 3 2 1 1 1 2 4
To conduct a hypothesis test at the 5% level to see if the mean difference in the husband's versus the wife's satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife, we first take the difference in the respomses of wives and husbands
x = (wife's score) - (husband's score)
Wife's score 2 2 3 3 4 2 1 1 2 4
Husband's score 2 1 2 3 2 1 1 1 2 4
Difference | 0 | 1 | 1 | 0 | 2 | 1 | 0 | 0 | 0 | 0
To use the hypothesis test method, we have to make sure that the distribution is a random sample of the population and it is normally distributed.
The question already cleared these two for us that this sample size is randomly selected from the population and each variable is independent from the other.
The question also already explained that the distribution is assumed to be normally distributed.
1) The distribution to use for this test is the t-distribution. This is because the sample size isn't very large and we have no information about the population mean and standard deviation.
For any hypothesis testing, we must first define the null and alternative hypothesis
Since we want to investigate whether the husbands are happier, that the mean difference is negative, that is less than 0,
The null hypothesis, which normally counters the claim to be investigated, would be that there isnt evidence to conclude that the husbands are happier in dual couple marriages. That is, the mean difference in happiness isn't less than 0, that it is equal to or greater than 0.
And the alternative hypothesis, which usually confirms the claim to be tested, is that there is significant evidence to conclude that the husbands are happier in dual couple marriages. That is, the mean difference in happiness is less than 0.
Mathematically, if μ is the mean difference in happiness of wives and husbands,
The null hypothesis is represented as
H₀: μ ≥ 0
The alternative hypothesis is represented as
Hₐ: μ < 0
2) To obtain the test statistic, we need the mean and standard deviation first.
Mean = (sum of variables)/(number of variables) = (5/10) = 0.5
Standard deviation = σ = √[Σ(x - xbar)²/N]
Σ(x - xbar)² = 6(0 - 0.5)² + 3(1 - 0.5)² + (2 - 0.5)² = 1.5 + 0.75 + 2.25 = 4.5
σ = √(4.5/10) = 0.671
we compute the t-test statistic
t = (x - μ)/σₓ
x = sample mean difference = 0.50
μ = 0
σₓ = standard error of the sample mean = (σ/√n)
where n = Sample size = 10,
σ = Sample standard deviation = 0.671
σₓ = (0.671/√10) = 0.2122
t = (0.50 - 0) ÷ 0.2122
t = 2.356
3) checking the tables for the p-value of this t-statistic
Degree of freedom = df = n - 1 = 10 - 1 = 9
Significance level = 5% = 0.05
The hypothesis test uses a one-tailed condition because we're testing only in one direction.
p-value (for t = 2.356, at 0.05 significance level, df = 9, with a one tailed condition) = 0.021441 = 0.0214
4) Alpha = significance level = 5% = 0.05
5) The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.05
p-value = 0.0214
0.0214 < 0.05
Hence,
p-value < significance level
This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the husbands are happier in dual couple marriages.
Hope this Helps!!
What is the numerator for the simplified sum?
Answer:
The numerator would be [tex]4x+6[/tex]
Step-by-step explanation:
[tex]\frac{x}{x^{2}+3x+2 } +\frac{3}{x+1}[/tex]
= [tex]\frac{4x^{2}+10x+6 }{x^3+4x+5x+2}[/tex]
= [tex]\frac{2(2x+3)(x+1)}{(x+1)(x+1)(x+2)}[/tex]
= [tex]\frac{4x+6}{x^2+3x+2}[/tex]
the numerator is always the top number/value of a fraction thus it being [tex]4x+6[/tex]
brainliest pls
 any help would be great
Answer:
k = P - m - n
Step-by-step explanation:
The question is asking you to rearrange the equation so that k is alone on one side.
P = k + m + n
P - k = (k + m + n) - k
P - k = m + n
(P - k) - P = m + n - P
-k = m + n - P
-1(-k) = -1 (m + n - P)
k = -m - n + P
The equation is completely simplified so this is your answer.
Students are given a spinner with 5 equal sectors numbered 1-5. They are instructed to spin 50 times and record the number the arrow lands on. If there are 5 groups of students spinning, which of the following is most likely the total number of times the spinner lands in the 3 sector?
Answer: Around 50 times.
Step-by-step explanation:
If the spinner is fair, then each number should have the same probability, that is P = 1/5 = 0.20 for each of the numbers.
Now, we know that we have 5 groups, and each group spins 50 times (so we have a total of 5*50 = 250 spins)
Then we can expect to see the number 3 around:
0.20*150 = 50
Please answer this question !! Thank u tons !! Will give brainliest !!
Answer: D
Step-by-step explanation:
The key to finding the line perpendicular to the one given is teh slope. The slope is the opposite reciprocal of the original line.
m=3
perpendicular m=-1/3
Now that we know the slope, we can see which of our answer choices have -1/3 as the slope. We can see D is the only option that has -1/3 for slope.
Answer:
D) y = -1/3x - 4
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes. This means that since the slope of this line is 3, the slope of a line perpendicular to it would be -1/3 because:
Original slope: 3 (3/1)
Reciprocal (flipped): 1/3
Negative reciprocal (opposite sign): -1/3
The only equation with a slope of -1/3 is D. Therefore, that is the correct answer.
Hope this helps!
Evaluate 16x^0 if x= -3
Answer:
16
Step-by-step explanation:
[tex]16x^0= \\\\16(-3)^0= \\\\16(1)= \\\\16[/tex]
Hope this helps!
x = -3
[tex]A = 16.(-3)^{0} \\ x^{0} = 1\\A = 16.1 \\A = 16[/tex]
Remember that [tex]x^{0} = 1[/tex] ∀ [tex]x[/tex]
De un grupo de 80 niños, se sabe que 50 estudian, 40 juegan y 15 estudian y juegan, ¿cuántos solo estudian?
Answer:
Step-by-step explanation:
Portuguese - Brazil
Estudam - A
Jogam - B
A=50
B=15
A∩B = 15
Somente estudam = 50 - 15 = 35
Somente jogam = 25
Nem estudam nem jogam = 5
Write 0.00000306 in scientific notation.
Answer:
3.06×10^-6
Step-by-step explanation:
0.00000306 = 3.06×0.000001 = 3.06×10^-6
__
Your calculator or spreadsheet can display numbers in scientific notation.
The logician Raymond Smullyan describes an island containing two types of people: knights who always tell the truth and knaves who always lie. You are visiting the island and have the following encounters with natives. (a) Two natives A and B address you as follows. A says: Both of us are knights. B says: A is a knave.
Answer:
A is a knave
B is a knight
Step-by-step explanation:
If A is telling the truth, then both are knights and B cannot be lying. However, since B claims that A is a knave, they can't be both knights, and there is no possible way that A is a knight.
If A is knave and thus is lying, they aren't both knights. Since B claims A is a knave, his statement can be true and thus B can be knight and A will be knave.
There different kinds of puzzle. The option that is correct about the puzzle is option A which states that A is a knave and B is a knight.
This is known to be a type of progressively hard puzzle that is titled "knights and knaves" puzzles.It is known as a logic puzzles that took place on an island with two kinds of people. It is a puzzle by American mathematician and musician called Raymond Smullyan in his book written in 1978.
Note that knave often lie and thus A may be lying when He said he was a knight Since B claims A is a knave, his statement can be said to be true and thus B can be regarded as knight.
See full question below
The logician Raymond Smullyan describes an island containing two types of people: knights who always tell the truth and knaves who always lie. You are visiting the island and have the following encounters with natives. (a) Two natives A and B address you as follows. A says: Both of us are knights. B says: A is a knave.
What are A and B?
A. A is a knave and B is a knight.
B. A is a knave and A is a knight.
C. Both A and B are knights.
D. Both A and B are knaves.
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Please help. I’ll mark you as brainliest if correct . I don’t understand this math problem. Thank you .
Answer:
That can be factored as
(x -1 (1/3) ) * ( x +3) * (x -4/5)
and the zeroes are located at:
x = 1.33333333... x = -3 and x = .8
Step-by-step explanation:
Answer:
[tex]\boxed{\sf \ \ \ f(x)=(x+3)(5x-4)(3x-4) \ \ \ }[/tex]
Step-by-step explanation:
We need to factorise the following function
[tex]f(x)=15 x^3+13 x^2-80 x+48[/tex]
-3 is a trivial solution, we can notice that f(-3)=0
so we can factorise by (x+3)
let s note a, b and c real and let s write
[tex]f(x)=15 x^3+13 x^2-80 x+48=(x+3)(ax^2+bx+c)[/tex]
[tex](x+3)(ax^2+bx+c) = ax^3+bx^2+cx+3ax^2+3bx+3c=ax^3+(b+3a)x^2+(3b+c)x+3c[/tex]
let s identify...
the terms in [tex]x^3[/tex]
15 = a
the terms in [tex]x^2[/tex]
13 = b + 3a
the terms in x
-80 = 3b+c
the constant terms
48 = 3c
so it comes, c=48/3=16, a = 15, b = 13-3*15=13-45=-32
so [tex]f(x)=(x+3)(15x^2-32x+16)[/tex]
[tex]\Delta=32^2-4*15*16=64[/tex]
so the roots of [tex](15x^2-32x+16)[/tex] are
[tex]\dfrac{32-8}{15*2}=\dfrac{24}{30}=\dfrac{12}{15}=\dfrac{4}{5}[/tex]
and
[tex]\dfrac{32+8}{15*2}=\dfrac{40}{30}=\dfrac{20}{15}=\dfrac{4}{3}[/tex]
so [tex]f(x)=(x+3)(5x-4)(3x-4)[/tex]
the zeros are -3, 4/5, 4/3
A computer scientist is investigating the usefulness of two different design languages in improving programming tasks. Twelve expert programmers, familiar with both languages, are asked to code a standard function in both languages, and the time (in minutes) is recorded. The data follow:
Programmer Design Language 1 Design Language 2
1 17 18
2 15 14
3 21 20
4 13 11
5 18 22
6 24 21
7 15 10
8 14 13
9 21 19
10 23 24
11 13 15
12 18 20
(a) Is the assumption that the difference in coding time is normally distributed reasonable?
(b) Find a 95% confidence interval on the difference in mean coding times. Is there any indication that one design language is preferable?
(a) The assumption that the difference in coding time is normally distributed
isis not
reasonable.
(b) The 95% confidence interval is (
,
) Round your answers to 3 decimal places (e.g. 98.765).
There is no / is significant indication that one design language is preferable at a 5% significance level.
Answer:
Step-by-step explanation:
The histogram shown in the attached file show that the distribution of differences is approximately normal.
So, we can assume that the distribution is normal.
.
b)
The 95% confidence level for [tex]\mu _D=\mu_1-\mu_2[/tex] is found
[tex]\bar d \pm t_{0.025,11}\frac{S_D}{\sqrt{n} }[/tex]
[tex]=0.666667 \pm 2.201\frac{(2.964436)}{\sqrt{12} } \\\\0.666667 \pm 2.201(0.85576)\\\\=0.666667+ 1.883525474=2.5502\\\\=0.666667- 1.883525474=-1.2169\\\\=(-1.2169,2.5502)[/tex]
since 0 is in the confidence interval. we do not reject the null hypothesis.
No, there is no indication of one design language is available.
MTH 154 - DOBM
Homework: Homework 4B
Score: 0 of 1 pt
22 of 27 (21 complete)
V Score: 777
4.B.63
* Question H
Use the appropriate compound interest formula to compute the balance in the account afte
stated period of time
$14,000 is invested for 6 years with an APR of 5% and quarterly compounding.
Answer:
$18,862.91
Step-by-step explanation:
The appropriate formula is ...
A = P(1 +r/n)^(nt)
where P is the amount invested (14,000), r is the APR (.05), n is the number of times per year interest is compounded (4), and t is the number of years (6).
Filling in the numbers and doing the arithmetic, we get ...
A = 14,000(1 +.05/4)^(4·6) = 14,000·1.0125^24 ≈ 18,862.91
The balance after 6 years will be $18,862.91.
A box is filled with 6 red cards, 8 green cards and 4 blue cards what is the probability that the card is not green that is chosen
Answer:
10/18
=5/9
pls mark as brainliest
Answer:
5/9
Step-by-step explanation:
6 red cards, 8 green cards and 4 blue cards = 18 total cards
not green cards = 6 red+ 4 blue = 10 cards
P( not green) = number not green / total
= 10/18
=5/9
4(x-2+y)=
?????????????
[tex]\text{Solve:}\\\\4(x-2+y)\\\\\text{Use the distributive property:}\\\\4x-8+4y\\\\\text{Since you can't simplify it any further, that'll be your answer}\\\\\boxed{4x-8+4y}[/tex]
Answer:
4x-8+4y
Explanation:
///
What’s the correct answer for this question?
Answer:
what's the question?
it's not showing
Answer:
C.
Step-by-step explanation:
To find the perimeter, we'll use the distance formula
Distance Formula = √(x₂-x₁)²+(y₂-y₁)²
Finding Distance of AB
|AB| = √(-2+5)²+(3+1)²
|AB| = √25
|AB| = 5
Now For BC
|BC| = √(6+2)²+(-3-3)²
|BC| = √(8)²+(-6)²
|BC| = √100
|BC| = 10
FOR CA:
|CA| = √(-5-6)²+(-3+1)²
|CA| = √125
Perimeter of Triangle = 10 + 5 + √125
= 15 + √125
The area of a rectangular field is represented by the expression 14x-3x^2+2y. The width of the field is represented by the expression 5x-7x^2+7y. How much greater is the length of the field than the width?
9x+4x^2-5y
9x-10x^2-5y
19x+4x^2+9y
19x-10x^2+9y
Answer:
9x + 4x^2 - 5y
Step-by-step explanation:
It is given in the question that the length of a rectangular field is represented by the expression 14x - 3x^2 + 2y and width of the field by 5x - 7x^2 + 7y
Now we have to tell how much greater is the length of the field than the width.
That means length is greater than width and we have to subtract width from length.
Length - width = (14x - 3x^2 + 2y) - (5x - 7x^2+ 7y)
= 14x - 5x - 3x^2 + 7x^2 + 2y - 7y
= 9x + 4x^2 - 5y
Therefore expression which represents the difference between length and width of the field will be (9x + 4x^2 - 5y)
By 9x+4x²-5y length is greater than the width of a rectangle.
What is the subtraction of expressions?To subtract an algebraic expression from another, we should change the signs (from '+' to '-' or from '-' to '+') of all the terms of the expression which is to be subtracted and then the two expressions are added.
Given that, the length of rectangle is 14x-3x²+2y and width of a rectangle is 5x-7x²+7y.
To find how much greater is the length of the field than the width we need to subtract the width from the length, we get
14x-3x²+2y-(5x-7x²+7y)
= 14x-3x²+2y-5x+7x²-7y
= 9x+4x²-5y
Therefore, option A is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
The length of a rectangular field is represented by the expression14x-3x^2+2y. The width of the field is represented by the expression 5x-7x^2+7y. How much greater is the length of the field than the width?
A) 9x+4x^2-5y
B)9x-10x^2-5y
C)19x+4x^2+9y
D) 19x-10x^2+9y
A circle is centered on point B. Points A, C and D lie on its circumference.
IF ZABC measures 122, what does ZADC measure?
Answer:
61°
Step-by-step explanation:
The inscribed angle has half the measure of the central angle subtending the same arc (AC).
∠ADC = (∠ABC)/2 = 122°/2
∠ADC = 61°
Suppose you select a sample of 12 individuals and find that 10 of them do not exercise regularly. Assuming that the Surveillance System is correct, what is the probability that you would have obtained results as bad or worse than expected
Answer:
a. mean = 6.96 , standard deviation = 1.71 b. 0.0641
Step-by-step explanation:
Here is the complete question
According to the Behavioural Risk Factor Surveillance System, 58% of all Americans adhere to a sedentary lifestyle (sedentary means does not exercise).
a. If you selected repeated samples of 12 from the U.S. population, what would be the mean number of individuals per sample who do not exercise regularly? What would be the standard deviation?
b. Suppose you select a sample of 12 individuals and find that 10 of them do not exercise regularly. Assuming that the Surveillance System is correct, what is the probability that you would have obtained results as bad or worse than expected?
Solution
a. Since we can only have two types of outcomes, that is, those who exercise and those who do not exercise, the problem follows a binomial distribution.
Since the probability of those who do not exercise, p = 58 % = 0.58,
the mean of the binomial distribution μ = np where n = sample number = 12
So, μ = 12 × 0.58 = 6.96
The standard deviation of a binomial distribution σ = √(npq) where q = probability that people exercise = 1 - p = 1 - 0.58 = 0.42
So, σ = √(12 × 0.58 × 0.42) = √2.9232 = 1.71
b. To find the worst case, we consider the probability that at best, two exercise. Since two exercise, the probability that at best two exercise is ¹²C₂q²p¹⁰ + ¹²C₁qp¹¹ + ¹²C₀q⁰p¹²
= (12 × 11/2)(0.42)²(0.58)¹⁰ + 12(0.42)(0.58)¹¹ + 1 × (0.42)⁰(0.58)¹²
= 0.05 + 0.0126 + 0.00145
= 0.06405
≅ 0.0641
Select the number line model that matches the expression |8 - 1|
Answer:
Option B is correct
Step-by-step explanation:
Original expression is |8 - 1| = 7 = distance between number 1 and number 8
=> Option B is correct
Hope this helps!
The number line model that matches the expression |8 - 1| which is correct option(B)
What is the graph?The graph can be defined as a pictorial representation or a diagram that represents data or values.
What is the expression?The expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.
Given the expression as |8 - 1|,
The value of the expression would give us 7. Meaning that the distance between coordinate 8 and 1 is 7 units.
The graphs given models the expression, |8 - 1|.
Option A, would match |-8 -1| = 5 units
Option B, would match |8 - 1| = 7 units.
Therefore, the answer is option (B).
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What’s the correct answer for this question?
Answer:
y = 1/-20 (x-2) - 5
Step-by-step explanation:
Focus = (a,b) = (2,-4)
So a = 2, b = -4
Directrix: y = -6
But y = k
So k = -6
Finding Standard Form of Equation for parabola
y = (1/2(b-k))(x-a)²+(1/2)(b+k)
y = (1/2(-4-6))(x-2)+(1/2)(-4-6)
y = (1/2(-10))(x-2)+(1/2)(-10)
y = (1/-20)(x-2)+(-5)
y = 1/-20 (x-2) - 5
The weight of an organ in adult males has a bell-shaped distribution with a mean of 300grams and a standard deviation of 20 grams. Use the empirical rule to determine the following.
(a) About 95% of organs will be between what weights?
(b) What percentage of organs weighs between 280 grams and 320grams?
(c) What percentage of organs weighs less than 280 grams or more than 320 grams?
(d) What percentage of organs weighs between 240 grams and 340 grams?
Answer:
a) Within 260 grams and 340 grams.
b) 68%
c) 32%
d) 97.35%
Step-by-step explanation:
The empirical rule 68-95-99.7 for bell-shaped distributions tells us that:
Approximately 68% of the data is within 1 standard deviation from the mean.Approximately 95% of the data is within 2 standard deviation from the mean.Approximately 99.7% of the data is within 3 standard deviation from the mean.a) The data that covers 95% of the organs is within 2 standard deviations (z=±2).
Then we can calculate the bounds as:
[tex]X_1=\mu+z_1\cdot\sigma=300+-2\cdot 20=300+-40=260 \\\\X_2=\mu+z_2\cdot\sigma=300+2\cdot 20=300+40=340[/tex]
b) We have to calculate the number of deviations from the mean (z-score) we have for the values X=280 and X=320.
[tex]z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{280-300}{20}=\dfrac{-20}{20}=-1\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{320-300}{20}=\dfrac{20}{20}=1\\\\\\[/tex]
As there are the bounds for one standard devaition, it is expected tht 68% of the data will be within 280 grams and 320 grams.
c) This interval is complementary from the interval in point b, so it is expected that (100-68)%=32% of the organs weighs less than 280 grams or more than 320 grams.
d) We apply the same as point b but with X=240 and X=340 as bounds.
[tex]z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{240-300}{20}=\dfrac{-60}{20}=-3\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{340-300}{20}=\dfrac{40}{20}=2\\\\\\[/tex]
The lower bound is 3 deviations under the mean, so it is expected that (99.7/2)=49.85% of the data will be within this value and the mean.
The upper bound is 2 deviations above the mean, so it is expected that (95/2)=47.5% of the data will be within the mean and this value.
Then, within 240 grams and 340 grams will be (49.85+47.5)=97.35% of the organs.
A sample of size =n48 has sample mean x=54.6 and sample standard deviation =s9.2. Part: 0 / 20 of 2 Parts Complete Part 1 of 2 Construct a 99.9% confidence interval for the population mean μ. Round the answers to one decimal place. A 99.9% confidence interval for the population mean is:____________ .
Answer:
[tex]54.6-3.51\frac{9.2}{\sqrt{48}}=49.94[/tex]
[tex]54.6+3.51\frac{9.2}{\sqrt{48}}=59.26[/tex]
The confidence interval is given by (49.94, 59.26)
Step-by-step explanation:
Info given
[tex]\bar X=54.6[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=9.2 represent the sample standard deviation
n=48 represent the sample size
Part a
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=48-1=47[/tex]
The Confidence is 0.999 or 99.9%, and the significance is [tex]\alpha=0.001[/tex] and [tex]\alpha/2 =0.0005[/tex], and the critical value would be [tex]t_{\alpha/2}=3.51[/tex]
And replacing we got:
[tex]54.6-3.51\frac{9.2}{\sqrt{48}}=49.94[/tex]
[tex]54.6+3.51\frac{9.2}{\sqrt{48}}=59.26[/tex]
The confidence interval is given by (49.94, 59.26)
A cylindrical tank has a radius of 2 m and a height of 9 m. The tank is filled with water. Find the work needed to pump the top 3 m of water out the top of the tank. (Use 9.8 m/s2 for g and the fact that the density of water is 1000 kg/m3.)
Answer:
3,325,140 Joules
Step-by-step explanation:
Work done by the pump = Force applied to pump * distance covered by the water.
Since Force = mass * acceleration due to gravity
Force = (density of water * volume of the tank) * acceleration due to gravity
F =ρVg
Workdone = (ρVg )* d
Given ρ = 1000kg/m³, g = 9.8m/s², d = 3m
[tex]V = \pi r^{2}h\\V = \pi (2)^{2} *9\\V = 36 \pi \\V =113.10m^{3}[/tex]
Workdone by the pump = 1000 * 113.10 * 9.8 * 3
Workdone by the pump = 3,325,140Joules
Ten rugby balls are randomly selected from the production line to see if their shape is correct. Over time, the company has found that 89.4% of all their rugby balls have the correct shape. If exactly 6 of the 10 have the right shape, should the company stop the production line?
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
Ten rugby balls are randomly selected from the production line to see if their shape is correct. Over time, the company has found that 89.4% of all their rugby balls have the correct shape. If exactly 6 of the 10 have the right shape, should the company stop the production line?
1)Yes as the probability of six having the correct shape is not unusual
2)NO. as the probability of six having the correct shape is unusual
3)Yes as the probability of six having the correct shape is unusual
4) No. as the probability of six having the correct shape is not unusual
Solution:
If exactly 6 of the 10 have the right shape, it means that the probability of success for the sample is
6/10 = 0.6
Expressing the probability in terms if percentage, it becomes
0.6 × 100 = 60%
Over time, the company has found that 89.4% of all their rugby balls have the correct shape. It means that the probability of success for the population is 89.4%
Comparing both probabilities, the probability of only 6 having the right shape is unusual. Therefore, the correct option is
3)Yes as the probability of six having the correct shape is unusual
use substitution method
3x +4y+175x-2y=11
[tex]3x +4y+175x-2y=11[/tex]
[tex]4y-2y+175x+3x=11[/tex]
[tex]2y+178x=11[/tex]
[tex]2y=11-178x[/tex]
[tex]y=\frac{11-178x}{2}[/tex]
[tex]y=-89x+\frac{11}{2}[/tex]
[tex]178x=-2y+11[/tex]
[tex]x=\frac{-2y+11}{178}[/tex]
[tex]x=\frac{-1}{89} y+\frac{11}{178}[/tex]
A database system assigns a 32-character ID to each record, where each character is either a number from 0 to 9 or a letter from A to F. Assume that each number or letter being selected is equally likely. Find the probability that at least 20 characters in the ID are numbers. Use Excel to find the probability. Round your answer to three decimal places.
Answer:
Step-by-step explanation:
total number of digits= 10 (from 0 to 9)
total number of letters = 6 (from A to F)
probability of numbers = 10/(10+6)
= 0.625
this is a case of binomial distribution with fixed number trials
n = 32 and probability p = 0.625
we have to find probability of at least 20 numbers
Use the BINOM.DIST function in Excel to find the cumulative probability.
P(at least 20 numbers) = 1 - BINOMDIST(numbers, trials, probability,true)
setting numbers = 20-1, trials = 32 and probability = 0.625
we get
[tex]P(X \geq 20)=1 - BINOMDIST(20- 1, 32, 0.625, true) \\\\=1 -0.4219 \\\\=0.5781[/tex]
Alternatively,
The probability that there are exactly r letters can be found with binomial probability.
P = nCr pʳ qⁿ⁻ʳ
Given that n = 32, p = 5/8, and q = 3/8, you can use Excel to find each probability from r=20 to r=32, then add them all up.
P = ₃₂C₂₀ (⅝)²⁰ (⅜)³²⁻²⁰ + ₃₂C₂₁ (⅝)²¹ (⅜)³²⁻²¹ + ... + ₃₂C₃₂ (⅝)³² (⅜)³²⁻³²
P = 0.578
A worn, poorly set-up machine is observed to produce components whose length X follows a normal distribution with mean 14 centimeters and variance 9. Calculate the probability that a component is at least 12 centimeters long. Round your answer to four decimal places.\
Answer:
[tex]P(X>12)=P(\frac{X-\mu}{\sigma}>\frac{12-\mu}{\sigma})=P(Z>\frac{12-14}{3})=P(z>-0.67)[/tex]
And we can find this probability with the complement rule and with the normal standard table we got:
[tex]P(z>-0.67)=1-P(z<-0.67)=1-0.2514=0.7486 [/tex]
Step-by-step explanation:
Let X the random variable that represent the components whose lenghts of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(14,\sqrt{9}=3)[/tex]
Where [tex]\mu=14[/tex] and [tex]\sigma=3[/tex]
We are interested on this probability
[tex]P(X>12)[/tex]
And we can use the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we got:
[tex]P(X>12)=P(\frac{X-\mu}{\sigma}>\frac{12-\mu}{\sigma})=P(Z>\frac{12-14}{3})=P(z>-0.67)[/tex]
And we can find this probability with the complement rule and with the normal standard table we got:
[tex]P(z>-0.67)=1-P(z<-0.67)=1-0.2514=0.7486 [/tex]
Answer:
The desired probability is P(X≥12), so subtract from 1 to get P(X≥12)=1−0.2525=0.7475.
Step-by-step explanation:
(1 point) A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 25 times, and the man is asked to predict the outcome in advance. He gets 18 out of 25 correct. What is the probability that he would have done at least this well if he had no ESP
Answer:
2.16% probability that he would have done at least this well if he had no ESP
Step-by-step explanation:
For each coin toss, there are only two possible outcomes. Either he predicts the correct outcome, or he does not. The tosses are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Fair coin:
Equally as likely to be heads or tails, so [tex]p = 0.5[/tex]
Coin is flipped 25 times
So [tex]n = 25[/tex]
What is the probability that he would have done at least this well if he had no ESP?
[tex]P(X \geq 18) = P(X = 18) + P(X = 19) + P(X = 20) + P(X = 21) + P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 18) = C_{25,18}.(0.5)^{18}.(0.5)^{7} = 0.0143[/tex]
[tex]P(X = 19) = C_{25,19}.(0.5)^{19}.(0.5)^{6} = 0.0053[/tex]
[tex]P(X = 20) = C_{25,20}.(0.5)^{20}.(0.5)^{5} = 0.0016[/tex]
[tex]P(X = 21) = C_{25,21}.(0.5)^{21}.(0.5)^{4} = 0.0004[/tex]
[tex]P(X = 22) = C_{25,22}.(0.5)^{22}.(0.5)^{3} = 0.0001[/tex]
The others(23, 24 and 25) are close to 0.
[tex]P(X \geq 18) = P(X = 18) + P(X = 19) + P(X = 20) + P(X = 21) + P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25) = 0.0143 + 0.0053 + 0.0016 + 0.0004 = 0.0216[/tex]
2.16% probability that he would have done at least this well if he had no ESP
Please answer this correctly
Answer:
1-20: Make it 0 units tall (change nothing)
21-40: Make it 1 unit tall
41-60: Make it 3 units tall
61-80: Make it 2 units tall
81-100: Make it 2 units tall
Step-by-step explanation:
1-20: (0 numbers)
21-40: 33 (1 number)
41-60: 43, 44, 52 (3 numbers)
61-80: 75, 79 (2 numbers)
81-100: 86, 89 (2 numbers)
What is the rule for the reflection?
M(-5,4)
M'(5 4)
4
Ory-axis(x, y) + (-x, y)
Ory-axis(x, y) = (x, -y)
Orx-axis(x, y) - (x, y)
Orx-axis(x, y) = (x, -y)
(-6,2) N(-3,2)?
N'(32
L'6,2
2.
Answer:
The rule of reflection over y-axis is (x,y)→(-x ,y)
M(-5,4) →M¹( 5 , 4)
N(-3,2) →N¹(3 ,2)
L(-6,2) →L¹( 6,2)
Step-by-step explanation:
Explanation:-
Type of transformation change to co-ordinate point
Reflection over x-axis (x,y)→(x ,-y)
Reflection over y-axis (x,y)→(-x ,y)
Given co-ordinate is M(-5,4)
The reflection over y-axis is (x,y)→(-x ,y)
M(-5,4) →( 5 , 4)
N(-3,2) →(3 ,2)
L(-6,2) →( 6,2)
Answer: the answer is a
Step-by-step explanation:
Hope that helped