Answer:
Step-by-step explanation:
i. The parameter the manager is interested in is number of defective bulbs in a case.
ii. Null hypothesis: u <= 20
Alternative hypothesis: u > 20
iii. The critical value the manager should use to determine the rejection region is 1.645.
iv. Using the p value which is 0.021 at 0.10 significance level we will reject the null as the p value is less than 0.1. Thus, we will conclude that there is enough statistical evidence to prove that the mean number of defective bulbs per case is greater than 20.
v. Our risk of committing type one error is alpha which is the level of significance set for the hypothesis test. An alpha level of 0.1 shows that we are willing to accept a 10% chance that we are wrong when you reject the null hypothesis.
vi. With a low p value, the data has enough evidence to prove that the mean number of defective bulbs per case is greater than 20 during the morning shift
vii. The manager will conclude that there is sufficient statistical evidence to prove that mean number of defective bulbs per case is greater than 20 during the morning shift.
viii. the p value if this is a two tail test would be 0.03662
Helen wants to buy 8 boxes of crayons at $1.94 per box for the day care center that she runs estimate the total cost of the crayons
Answer: $16
Step-by-step explanation:
1.94 * 8 = 15.52
$15.52 rounds up to $16
PLZZZZ HELPPP FOR BRAINLIEST! COMPARING EXPONENTIAL FUNCTIONS WHICH STATEMENT CORRECTLY COMPARES FUNCTIONS F AND G
Answer:
B. Left limits are the same; right limits are different.
Step-by-step explanation:
When we talk about "end behavior," we are generally concerned with the limiting behavior of the function for x-values of large magnitude. Decreasing exponential functions all have the same end behavior: they approach infinity on the left (for large negative values of x), and they approach a horizontal asymptote on the right (for large positive values of x).
If we are to write the end behavior in terms of specific limiting values, we would have to say that ...
as x → -∞, f(x) → ∞
as x → -∞, g(x) → ∞ . . . . . . the same end behavior as f(x)
__
and ...
as x → ∞, f(x) → -4
as x → ∞, g(x) → (some constant between 0 and 5) . . . . . different from f(x)
__
So, in terms of these limiting values, the left-end behavior is the same; the right-end behavior is different for the two functions, matching choice B.
An animal shelter has 5 times as many cats as it has dogs. There are 75cats at the shelter
Answer: 15 dogs
Step-by-step explanation:
75 / 5 = 15
Answer:
15 dogs
Step-by-step explanation:
Let the number of dogs be x
number of cats be y
5 times the number of cats = number of dogs
y = x*5
Since y = 75
75 = 5x
Bring 5 to the other side n divide
x= 75/5
= 15
Which are the possible side lengths of a triangle?
O 3 cm, 5 cm, 9 cm
O 4 cm, 8 cm, 10 cm
O 6 cm, 9 cm, 17 cm
O 8 cm, 10 cm, 18 cm
Answer:
4 cm, 8 cm, 10 cm
Step-by-step explanation:
For a triangle to exist, two sides added up must be greater than the third side. The only quantities that satisfy this relationship is the second option.
Please answer this correctly
Answer:
5/7
Step-by-step explanation:
There are 7 cards, all of which have an equal chance of being chosen.
And in this case, because there are 7 cards in total, they each have a 1/7 chance of being chosen. Because there are 5 cards greater than 4, you have a 5x1/7 chance =5/7 chance of choosing a number greater than 4.
P.S. If you need it as a percentage, then it is 71.428571%.
P.P.S. Remember if you like the answer then mark as brainliest thank you!
How many arrangements of the letters in the word olive can you make if each arrangement must use three letters
Answer:
60
Step-by-step explanation:
There are 5 letters that can be first.
There are 4 letters that can be second.
There are 3 letters that can be third.
The number of permutations is 5×4×3 = 60.
Find the length of a rectangle with a diagonal of 10 and a height of 8.
Answer:
The length of the rectangle is 6.
Step-by-step explanation:
Given: The diagonal of a rectangle is 10 and the height is 8.
Please understand, that a diagonal, divides the rectangle into two tringles.
To find the length of the rectangle, you can use Pythagoras on one of the right sided triangles, because the length of the triangle, is also the length of the rectangle!
EXTRA:
If you know the special 3 4 5 triangle, a so called Pythagorean Triple, then you can "see" the simularity between the numbers.
Instead of 5, a diagonal of 10 is given (factor of 2 bigger).
Instead of 4, the height of 8 is given (factor of 2 bigger). By scaling the Pythagorean Triple 3 4 5 by a factor of 2, you get the numbers 6 8 10. Could it be, that the number we need to find, is six?
Try to verify, by calculating the missing number (which is the length of the rectangle we are looking for).
a² + b² = c²
a = length (and is unknown)
b = height = 8
c = hypothenusa/diagonal = 10
Substitute the numbers given:
a² + 8² = 10²
Subtract 8² left and right of the = sign.
a² +8² -8² = 10² - 8²
a² + 0 = 100 - 64
a² = 36
a = + - √36
a = + - 6
EXTRA:
You can ignore the -√36 = -6 part of the solution, because a length of -6 has no meaning here.
a = 6
So, the length of the triangle is 6 and thus, the length of the rectangle is also 6.
Fill in the blanks.
In a normal distribution, ____________ percent of the data are above the mean, and___________ percent of the data are below the mean. Similarly, _____________ percent of all data points are within 1 standard deviation of the mean, ___________percent of all data points are within 2 standard deviations of the mean, and___________ percent are within 3 standard deviations of the mean.
Answer:
In a normal distribution, 50 percent of the data are above the mean, and 50 percent of the data are below the mean. Similarly, 68 percent of of all data points are within 1 standard deviation of the mean, 95 percent of all data points are within 2 standard deviations of the mean, and 99.7 percent are within 3 standard deviations of the mean.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
Also:
The normal distribution is symmetric, which means that 50% of the data is above the mean and 50% is below.
Then:
In a normal distribution, 50 percent of the data are above the mean, and 50 percent of the data are below the mean. Similarly, 68 percent of of all data points are within 1 standard deviation of the mean, 95 percent of all data points are within 2 standard deviations of the mean, and 99.7 percent are within 3 standard deviations of the mean.
In a normal distribution, 50 percent of the data are above the mean, and 50 percent of the data are below the mean. Similarly, 68 percent of all data points are within 1 standard deviation of the mean, 95 percent of all data points are within 2 standard deviations of the mean, and 99.9 percent are within 3 standard deviations of the mean.
The normal distribution is a probability distribution that is important in many areas. It is, in fact, a family of distributions of the same form, each with different location and scale parameters: the mean and standard deviation respectively. The standard normal distribution is the normal distribution with mean equal to zero, and standard deviation equal to one. The shape of its probability density function is similar to that of a bell.
Learn more in https://brainly.com/question/12421652
Consider the function f(x) = 3x and the function g, which is shown below. G(x)=F(x)-2=3^x-2 How will the graph of g differ from the graph of f? A. The graph of g is the graph of f shifted 2 units up. B. The graph of g is the graph of f shifted 2 units to the right. C. The graph of g is the graph of f shifted 2 units down. D. The graph of g is the graph of f shifted 2 units to the left. Reset Next
H E L P
Answer:
C. The graph of g is the graph of f shifted 2 units down
Step-by-step explanation:
The transformation ...
g(x) = f(x -h) +k
represents a translation h units right and k units up.
You have h=0 and k=-2, so the graph is shifted 0 units right and 2 units the opposite of up.
The graph of g is the graph of f shifted 2 units down.
Answer:
C
Step-by-step explanation:
I just took the test on edmentum
Please answer this correctly.
Answer:
m=(3+f)/(f-4)
Step-by-step explanation:
To make m the subject of the formula, we want to isolate m. That is, we want to move m to one side of the equation.
First, the fractions need to be taken away. Multiply both sides by m-1 to get: f(m-1)=4m+3.
The distributive property of subtraction tells us a(b-c)=ab-ac. Thus, from this equation we have fm-f=4m+3.
Subtracting 4m, we have fm-4m-f=3
Now, we work the distributive property backwards, where we have ab-ac=a(b-c). Rearrange the terms of fm and 4m, to get mf, and m4. Thus, this can be simplified to m(f-4).
Going back to the equation, we have m(f-4)-f=3.
Add f on both sides, so we have m(f-4)=3+f.
Divide by f-4, so we have m=(3+f)/(f-4)
5:36, 2:9, 3:18, 1:3 what is the largest ratio? please help me!
Answer:
[tex]1:3[/tex]
Step-by-step explanation:
[tex]5:36=5/36[/tex]
[tex]\approx 0.13888888888[/tex]
[tex]2:9=2/9[/tex]
[tex]\approx 0.22222222222[/tex]
[tex]3:18=1/6[/tex]
[tex]\approx 0.16666666666[/tex]
[tex]1:3=1/3[/tex]
[tex]\approx 0.33333333333[/tex]
Answer:
1:3
Step-by-step explanation:
GCF of 36, 9, 18, 3 is 36
5:36
2:9= 8:36
3:18= 6:36
1:3= 12:36
1:3 is the largest ratio.
EXREAMLY URGENT!! WILL FOREVER THANK YOU!!!! PLS JUST TAKE A LOOK!!!!!
17. Find the measure of DE
A) 14.5
B) 13.4
C) 12.3
D) 15.9
Answer:
C. 12.3
Step-by-step explanation:
We should use Law of Cosines: c² = a² + b² -2abcosC
If that is the case, then EF is a, DF is b, and ∠F is c. We then plug the known variables in:
c² = 12² + 13² - 2(12)(13)cos59°
Plug that into the calc and you should get 12.2313, rounded to 12.3 as your final answer!
100 POINTS!!!!! PlZ help Find all possible values of the digits Y, E, A, R if YYYY - EEE + AA - R = 1234, and different letters represent different digits.
Answer:
Y = 1, E = -1, A= 1, R = -1
Step-by-step explanation:
YYYY - EEE + AA - R = 1234
First we would break down the digits in the whole numbers into their place value (thousands, hundreds, tens and units).
YYYY = 1000Y + 100Y +10Y + Y
EEE = 100E + 10E + E
-EEE = -100E - 10E - E
AA = 10A + A
R = R
-R = -R
1234 = 1000+200+30+4
Let's equate each place value for each of the numbers.
Thousands: 1000Y = 1000
Y = 1000/1000 = 1
Hundreds: 100Y - 100E = 200
100(1) - 100E = 200
-100E = 200-100
-100E= 100
E = -1
-EEE = -E(111)
Tens: 10Y - 10E + 10A = 30
10(1) - 10(-1) + 10A = 30
20+ 10A = 30
A = 10/10
A= 1
Units: Y - E + A - R = 4
1 - (-1) + 1 - R = 4
3-R = 4
R = 3-4 = -1
YYYY - EEE + AA - R = 1234
1111 - (-111) + 11 - (-1) = 1111+111+11+1 = 1234
All possible values of the digits Y, E, A, R are Y = 1, E = -1, A= 1, R = -1
Answer:
Y=2
E=9
A=1
R=0
Step-by-step explanation:
Let's check our work.
2,222 - 999 + 11 - 0
1,223 + 11 - 0
1,234 - 0
1,234
Also previous answerer how can digits be negative?
Square 100 * square 25 simplified
Answer:
50
Step-by-step explanation:
Both √100 and √25 are perfect squares:
√100 = 10
√25 = 5
10(5) = 50
a personality test maybe given to assess what
Answer:
A personality test may be given to assess individual behavior patterns. A personality test may be given to assess individual behavior patterns. This answer has been confirmed as correct and helpful.
Step-by-step explanation:
hopes this helps
Answer:
Interests, values, skill set and basic personality
Step-by-step explanation:
Personality tests are mostly used as an assessment tool be HR managers and employers during the interview process. They can provide a potential employer with information about your interests, values, skill set and even basic personality, which can be very useful to help an employer make a decision about whether you are the best fit for a position.
I hope this helped. I am sorry if you get this wrong.
two technicians regularly make repairs when breakdowns occur on an automated production line. the first technican, who services 40% of the breakdowns, has 5% chance of making incomplete repair. the second technican, who services 60% of the breakdowns, has 3% chance of making an incomplete repair. given that there is a problem with the production line due to an incomplete repair, what is the probability that thids intial repair was made by the first technican
Answer:
52.63% probability that thids intial repair was made by the first technican
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Incomplete repair
Event B: Made by the first technican.
The first technican, who services 40% of the breakdowns, has 5% chance of making incomplete repair.
This means that [tex]P(B) = 0.4, P(A|B) = 0.05[/tex].
Probability of an incomplete repair:
5% of 40%(first technican) or 3% of 60%(second technican). So
[tex]P(A) = 0.05*0.4 + 0.03*0.6 = 0.038[/tex]
Given that there is a problem with the production line due to an incomplete repair, what is the probability that thids intial repair was made by the first technican
[tex]P(B|A) = \frac{0.4*0.05}{0.038} = 0.5263[/tex]
52.63% probability that thids intial repair was made by the first technican
Which is the better buy?. Store A $180 at 1/3 off Or Store B $110 at 10% off
Answer: Store B
Step-by-step explanation:
180 / 3 = 60. 180 - 60= $120. Store A cost is $120.
110 * 0.9 = $99. Store B's cost is $99.
Answer:
Store B
Step-by-step explanation:
Store A the price would be about $120.60
Store B price would be about $99
To find store a price, you first find the discount, so
0.33 x 180 = 59.40
Then subtract this from the original price to know the total after the discount
180-59.40=120.60
Do the same thing with the other Store
110 x 0.10 = 11
110-11=99
4. (07.04 MC)
An observer (0) spots a plane (P) taking off from a local airport and flying at a 23° angle horizontal to her line of sight and located directly above a tower (T). The observer also notices a bird (B)
circling directly above her. If the distance from the plane (P) to the tower (T) is 5,000 ft., how far is the bird (B) from the plane (P)? Round to the nearest whole number.
Answer:
11779 ft
Step-by-step explanation:
We are given that
[tex]\theta=23^{\circ}[/tex]
Distance between tower and plane,d=5000 ft
We have to find the distance between the plane and bird.
Let x be the distance between bird and plane
We know that
[tex]tan\theta=\frac{perpendicular\;side}{Base}[/tex]
Using the formula
[tex]tan23=\frac{5000}{x}[/tex]
[tex]x=\frac{5000}{tan23}=11779.3 \approx 11779ft[/tex]
Hence, the distance between the plane and bird=11779 ft
Answer:
11779 ft
Step-by-step explanation:
We are given that
Distance between tower and plane,d=5000 ft
We have to find the distance between the plane and bird.
Let x be the distance between bird and plane
We know that
Using the formula
Hence, the distance between the plane and bird=11779 ft
A large school district notices that about 26% of its sophomore students fail Algebra I. An online education supplier suggests the district try its new technology software, which is designed to improve Algebra 1 skills and, thus, decrease the number of students who fail the course. The new technology software is quite expensive, so the company offers a free, one-year trial period to determine whether the Algebra 1 pass rate improves. If it works, the district will pay for continued use of the software. What would happen if the school district makes a Type I error
Answer:
In the case of a Type I error, the null hypothesis would be wrongly rejected and the school district will conclude that the new technology is effective when it is not.
They will start to pay for the software when in fact it does not improve Algebra 1 skills.
Step-by-step explanation:
A Type I error happens when a true null hypothesis is rejected.
The probability of a Type I error is equal to the significance level, as it is the probabilty of getting an sample result with low probability but only due to chance, as the null hypothesis is in fact true.
In this scenario, the null hypothesis would represent the claim that the new technology does not make significant improvement.
In the case of a Type I error, this null hypothesis would be wrongly rejected and the school district will conclude that the new technology is effective when it is not.
They will start to pay for the software when in fact it does not improve Algebra 1 skills.
If three times a number, added to 2 is divided by the number plus 5, the result is eight thirds.
Answer:
Number = 34
Step-by-step explanation:
We are looking for our mystery "number". I will call this number N.
We can find out what our equation looks like based on what the question tells us.
"three times a number" is 3N
"added to 2" is + 2
Which so far is 3N + 2
"divided by the number plus 5" is ÷ [tex]{N+5}[/tex]
Combined with the first two parts to give us (3N + 2) ÷ (N + 5)
"the result is eight third" So the above equation is equal to 8/3
Combining all these comments together to get the following equation
(3N + 2) ÷ (N + 5) = 8/3
Rearrange by multiplying both sides of the = by (N+5)
3N + 2 ÷ (N + 5) × (N + 5) = 8/3 × (N + 5)
Simplify
3N + 2 = 8/3 × (N + 5)
3N + 2 = 8N/3 + 40/3
Bring the N numbers to one side and the non N numbers to the other side, by subtracting 2 from both sides of the =
3N + 2 - 2 = 8N/3 + 40/3 - 2
Simplify
3N = 8N/3 + 34/3
and then subtracting 8N/3 from both sides
3N - 8N/3 = 8N/3 - 8N/3 + 34/3
Simplify
1N/3 = 34/3
Simplify for our final answer by multiplying both sides of the = by 3
1N/3 x 3 = 34/3 x 3
N = 34
Many of these steps can be skipped when solving for yourself but I wanted to be thorough
explain why the solution to the absolute value inequality |4x-9|>-12 is all real numbers
Answer:
Step-by-step explanation:
Hello,
by definition the absolute value is always positive
so |4x-9| >= 0
so the equation |4x-9| > -12 is always true
so all real numbers are solution of this equation
hope this helps
Find the exact value of each of the following under the given conditions.
a. cosine left parenthesis alpha plus beta right parenthesis b. sine left parenthesis alpha plus beta right parenthesis c. tangent left parenthesis alpha plus beta right parenthesis
tangent alpha equals one half
, pi less than alpha less than StartFraction 3 pi Over 2 EndFraction
, and cosine beta equals three fifths
, StartFraction 3 pi Over 2 EndFraction less than beta less than 2 pi
Answer:
[tex](a)-\dfrac{11\sqrt{5}}{25} \\(b) -\dfrac{2\sqrt{5}}{25} \\(c)\dfrac{11}{2}[/tex]
Step-by-step explanation:
[tex]\tan \alpha =\dfrac12, \pi < \alpha< \dfrac{3 \pi}{2}[/tex]
Therefore:
[tex]\alpha$ is in Quadrant III[/tex]
Opposite = -1
Adjacent =-2
Using Pythagoras Theorem
[tex]Hypotenuse^2=Opposite^2+Adjacent^2\\=(-1)^2+(-2)^2=5\\Hypotenuse=\sqrt{5}[/tex]
Therefore:
[tex]\sin \alpha =-\dfrac{1}{\sqrt{5}}\\\cos \alpha =-\dfrac{2}{\sqrt{5}}[/tex]
Similarly
[tex]\cos \beta =\dfrac35, \dfrac{3 \pi}{2}<\beta<2\pi\\\beta $ is in Quadrant IV (x is negative, y is positive), therefore:\\Adjacent=$-3\\$Hypotenuse=5\\Opposite=4 (Using Pythagoras Theorem)[/tex]
[tex]\sin \beta =\dfrac{4}{5}\\\tan \beta =-\dfrac{4}{3}[/tex]
(a)
[tex]\cos(\alpha + \beta)=\cos\alpha\cos\beta-\sin \alpha\sin \beta\\[/tex]
[tex]=-\dfrac{2}{\sqrt{5}}\cdot \dfrac{3}{5}-(-\dfrac{1}{\sqrt{5}})(\dfrac{4}{5})\\=-\dfrac{2\sqrt{5}}{5}\cdot \dfrac{3}{5}+\dfrac{\sqrt{5}}{5}\cdot\dfrac{4}{5}\\=-\dfrac{2\sqrt{5}}{25}[/tex]
(b)
[tex]\sin(\alpha + \beta)=\sin\alpha\cos\beta+\cos \alpha\sin \beta[/tex]
[tex]\sin(\alpha + \beta)=\sin\alpha\cos\beta+\cos \alpha\sin \beta\\=-\dfrac{1}{\sqrt{5}}\cdot\dfrac35+(-\dfrac{2}{\sqrt{5}})(\dfrac{4}{5})\\=-\dfrac{\sqrt{5}}{5}\cdot\dfrac35-\dfrac{2\sqrt{5}}{5}\cdot\dfrac{4}{5}\\=-\dfrac{11\sqrt{5}}{25}[/tex]
(c)
[tex]\tan(\alpha + \beta)=\dfrac{\sin(\alpha + \beta)}{\sin(\alpha + \beta)}=-\dfrac{11\sqrt{5}}{25} \div -\dfrac{2\sqrt{5}}{25} =\dfrac{11}{2}[/tex]
Pleasssseeee hheeelllppp
Answer:
No
Step-by-step explanation:
They are not congruent or similar because the figures themselves indicate no similar or congruent parts. Although they may seem congruent or similar, without telling us one thing, we cannot assume that they are similar or congruent.
Assume A, B, P, and D are n times n matrices. Determine whether the following statements are true or false. Justify each answer.
A matrix A is diagonalizable if A has n eigenvectors.
The statement is false. A matrix is diagonalizable if and only if it has n -1 linearly independent eigenvectors.
The statement is true. A diagonalizable matrix must have more than one linearly independent eigenvector.
The statement is true. A diagonalizable matrix must have a minimum of n linearly independent eigenvectors.
The statement is false. A diagonalizable matrix must have n linearly independent eigenvectors.
If A is diagonalizable, then A has n distinct eigenvalues.
The statement is false. A diagonalizable matrix can have fewer than n eigenvalues and still have n linearly independent eigenvectors.
The statement is true. A diagonalizable matrix must have n distinct eigenvalues.
The statement is false. A diagonalizable matrix must have more than n eigenvalues.
The statement is true. A diagonalizable matrix must have exactly n eigenvalues.
If AP = PD, with D diagonal, then the nonzero columns of P must be eigenvectors of A.
The statement is true. AP = PD implies that the columns of the product PD are eigenvalues that correspond to the eigenvectors of A.
The statement is false. If P has a zero column, then it is not linearly independent and so A is not diagonalizable.
The statement is true. Let v be a nonzero column in P and let lambda be the corresponding diagonal element in D. Then AP = PD implies that Av = lambda v, which means that v is an eigenvector of A.
The statement is false. AP = PD cannot imply that A is diagonalizable, so the columns of P may not be eigenvectors of A.
Answer:
The correct answers are (1) Option d (2) option a (3) option a
Step-by-step explanation:
Solution
(1) Option (d) The statement is false. A diagonalizable matrix must have n linearly independent eigenvectors: what it implies is that a matrix is diagnostic if it has linearity independent vectors.
(2) Option (a) The statement is false. A diagonalizable matrix can have fewer than n eigenvalues and still have n linearly independent eigenvectors: what this implies is that a diagonalizable matrix can have repeated eigenvalues.
(3) option (a) The statement is true. AP = PD implies that the columns of the product PD are eigenvalues that correspond to the eigenvectors of A : this implies that P is an invertible matrix whose column vectors are the linearity independent vectors of A.
6 people will attend a lunch 2 cans of juice should be provided per person determine the total number of cans of juice required
Answer:
12
Step-by-step explanation:
it's 6 people and 2 cans of juice goes to each person so you can multiply 6× 2 and you get 12 . 12 cans of juice would be required to provide 6 people with 2 cans each .
Suppose that the thickness of one typical page of a book printed by a certain publisher is a random variable with mean 0.1 mm and a standard deviation of 0.002 mm. A new book will be printed on 500 sheets of this paper. Approximate the probability that the
Answer:
The probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm is 0.97.
Step-by-step explanation:
The complete question is:
Suppose that the thickness of one typical page of a book printed by a certain publisher is a random variable with mean 0.1 mm and a standard deviation of 0.002 mm Anew book will be printed on 500 sheets of this paper. Approximate the probability that the thicknesses at the entire book (excluding the cover pages) will be between 49.9 mm and 50.1 mm. Note: total thickness of the book is the sum of the individual thicknesses of the pages Do not round your numbers until rounding up to two. Round your final answer to the nearest hundredth, or two digits after decimal point.
Solution:
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e S, will be approximately normally distributed.
Then, the mean of the distribution of the sum of values of X is given by,
[tex]\mu_{S}=n\mu[/tex]
And the standard deviation of the distribution of the sum of values of X is given by,
[tex]\sigma_{S}=\sqrt{n}\sigma[/tex]
The information provided is:
[tex]n=500\\\mu=0.1\\\sigma=0.002[/tex]
As n = 500 > 30, the central limit theorem can be used to approximate the total thickness of the book.
So, the total thickness of the book (S) will follow N (50, 0.045²).
Compute the probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm as follows:
[tex]P(49.9<S<50.1)=P(\frac{49.9-50}{0.045}<\frac{S-E(S)}{SD(S)}<\frac{50.1-50}{0.045})[/tex]
[tex]=P(-2.22<Z<2.22)\\\\=P (Z<2.22)-P(Z<-2.22)\\\\=0.98679-0.01321\\\\=0.97358\\\\\approx 0.97[/tex]
Thus, the probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm is 0.97.
Mary pays income tax according to the graduated schedule shown below. A 3-column table with 6 rows. Column 1 is labeled If taxable income is over with entries 0 dollars, 7,825 dollars, 31,850 dollars, 77,100 dollars, 160,850 dollars, 349,700 dollars. Column 2 is labeled but not over with entries 7,825 dollars, 31,850 dollars, 77,100 dollars, 160,850 dollars, 349,700 dollars, no limit. Column 3 is labeled the tax is with entries 10 percent of the amount of 0 dollars, 782 dollars and 50 cents plus 15 percent of the amount of 7,825 dollars, 4,386 dollars and 25 cents plus 25 percent of the amount of 31,850 dollars, 15,698 dollars and 75 cents plus 28 percent of the amount over 77,100 dollars, 39,148 dollars and 75 cents plus 33 percent of the amount of 160,850 dollars, 101,469 dollars and 25 cents plus 35 percent of the amount over 349,700 dollars. If Mary’s taxable income is $68,562, how much income tax does she owe, rounded to the nearest dollar?
Answer:
$13564
Step-by-step explanation:
[tex]\left|\begin{array}{c|c|c}$If taxable&& \\$income&&\\$ is over&$but not over&$the tax is\\---&---&---\\$0 &7,825 &$10\% of the amount over 0\\7,825 &31,850 &$782.50 plus $15\% $ of the amount over 7,825$ \end{array}\right|[/tex][tex]\left|\begin{array}{c|c|c}31,850 &77,100 &$4,386.25 plus 25\% of the amount over 31,850 \\77,100 &160,850 &$15,698.75 plus 28\% of the amount over 77,100\end{array}\right|[/tex]
[tex]\left|\begin{array}{c|c|c}160,850 &349,700 &$39,148.75 plus 33\% of the amount over 160,850 \\349,700 &$no limit&$101,469.25 plus 35\% of the amount over 349,700\end{array}\right|[/tex]
Mary’s taxable income= $68,562
From the table, If taxable income is over $31,850 but not over $77,100
The tax = $4386.25 + 25% of the amount over 31,850
Amount over $31,850=$68,562-$31,850
=$36,712
Therefore:
Mary's tax = $4386.25 + (25% of $36,712)
=$4386.25 +9,178
=$13564.25
=$13564 (to the nearest dollar)
Income tax is the tax charged on individual's or entities' income
Mary owes $13564 income tax
Given that the taxable income is $68,562.
Using the table as a guide, $68,562 falls within the income range $31,850 - $77,100
So, the tax is $4386 added to 25% of the excess over $31850
This is calculated as:
[tex]Tax = \$4386 + 25\% \times (Income -\$31850)[/tex]
Substitute $68,562 for income
[tex]Tax = \$4386 + 25\% \times (\$68562 -\$31850)[/tex]
Solve the expression in the bracket
[tex]Tax = \$4386 + 25\% \times \$36712[/tex]
Evaluate the product
[tex]Tax = \$4386 + \$9178[/tex]
Add the terms of the expression
[tex]Tax = \$13564[/tex]
Hence, Mary owes $13564 income tax
Read more about income tax at:
https://brainly.com/question/1720419
A consumer group surveyed 146 airplane travelers after a flight and found that 132 of them would fly that airline again. Find the standard error for the sample proportion of airline travelers who would fly on that airline again. Enter your answer as a decimal rounded to three decimal places.
Answer:
[tex]\hat p =\frac{X}{n}[/tex]
And replacing we got:
[tex]\hat p =\frac{132}{146}= 0.904[/tex]
And for this case the standard error assuming normality would be given by:
[tex] SE= \sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
And replacing we got:
[tex]SE= \sqrt{\frac{0.904*(1-0.904)}{146}}= 0.024[/tex]
Step-by-step explanation:
For this problem we know the following notation:
[tex] n= 146 [/tex] represent the sample size selected
[tex] X= 132[/tex] represent the number of airplane travelers who after a flight would fly that airline again
The estimated proportion for this case would be:
[tex]\hat p =\frac{X}{n}[/tex]
And replacing we got:
[tex]\hat p =\frac{132}{146}= 0.904[/tex]
And for this case the standard error assuming normality would be given by:
[tex] SE= \sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
And replacing we got:
[tex]SE= \sqrt{\frac{0.904*(1-0.904)}{146}}= 0.024[/tex]
WORK OUT THE VALUE of 19+7⌹2-5
Answer:
17.5
Step-by-step explanation:
Remember PEMDAS
step 1 : divide 7 by 2
7 ÷ 2 = 3.5
step 2 : rewrite the equation
19 + 3.5 - 5
step 3 : add 19 + 3.5
19 + 3.5 = 22.5
step 4 : subtract 22.5 - 5
22.5 - 5 = 17.5
The image of ABC after a reflection across EG is ABC which statement is true about point F
Answer: First option.
Step-by-step explanation:
As the triangle is reflected over the line EG, this means that the distance between each common point of the triangles and the line must be the same for both triangles.
This means that the distance between B and E, is the same distance as the distance between B' and E.
Now, as you know, the midpoint of a segment is a point such that the distance between that point and each endpoint is the same.
So, in the linea AA', the points A and A' are the endpoints, and because F lies in the line of reflection, the distance between A and F is the same distance than in between A' and F.
So F is the midpoint in the line AA'
The correct option would be the first one, F is the midpoint of AA' because the line EG bisects AA', and F is colinear to E and G.