Y is a random variable that is distributed N(-16, 1.21). Find k such that Prob(-15.043 < Y ≤ k) = 0.1546. (Round your answer with 4 digits after the decimal.)
Answers
Transform Y to Z, which is distributed N(0, 1), using the formula
Y = µ + σZ
where µ = -16 and σ = 1.21.
Pr[-15.043 < Y ≤ k] = 0.1546
Pr[(-15.043 + 16)/1.21 < (Y + 16)/1.21 ≤ (k + 16)/1.21] = 0.1546
Pr[0.791 < Z ≤ (k + 16)/1.21] ≈ 0.1546
Pr[Z ≤ (k + 16)/1.21] - Pr[Z < 0.791] = 0.1546
Pr[Z ≤ (k + 16)/1.21] = 0.1546 + Pr[Z < 0.791]
Pr[Z ≤ (k + 16)/1.21] ≈ 0.1546 + 0.786
Pr[Z ≤ (k + 16)/1.21] ≈ 0.940
Take the inverse CDF of both sides (Φ(x) denotes the CDF itself):
(k + 16)/1.21 ≈ Φ⁻¹ (0.940) ≈ 1.556
Solve for k :
k + 16 = 1.21 • 1.556
k ≈ -14.118
Related Questions
The initial number of bacteria cells in a culture is 1000, and this number increases by 6% every hour. Approximately how many bacteria would be in the culture after 4 hours?
Answers
Answer:
1,264
Step-by-step explanation:
a = 1000(1.06)^4
a = 1,262.47696
1,264
The circumference of a circle is 15π centimeters. What is the area of the circle in terms of π?
Answers
Answer: 7.5²π square centimeters. OR 56.25π cm²
Step-by-step explanation:
Circumference = diameter × π
So the diameter is 15 cm
Area = πr²
Radius is half the diameter, so 15/2 or 7.5
Area = (15/2)²π cm²
what is the standard form for graphs of y-5=4/5(x-30)
Answers
Answer:
y=0.8*x -19
Step-by-step explanation:
y-5=4/5(x-30)
5*(y-5)=5*(4/5(x-30))
5y-25=4x-120
5y=4x-120+25
5y=4x-95
y=(4/5)*x -19
y=0.8*x -19
The first used 20 gal of fuel and the second used 25 gal. The 2 drove 1450 miles and the sum of their fuel efficiencies was 65 miles per gal. What we’re each car fuel efficiency?
Answers
Answer: there you go :)
Car 1 consumes 30 gallons of gas.
Car 2 consumes 20 gallons of gas.
Step-by-step explanation:
Let x = gallons consumed by car 1
Let y = gallons consumed by car 2
We set up our equations:
35x+40y = 1850 eq1
x+y = 50 eq2
Substituting eq 2 into eq 1,
35x+40(50-x) = 1850
35x+2000-40x = 1850
-5x+2000 = 1850
-5x = -150
x = 30
Substitute value of x into eq 2.
x+y = 50
30+y = 50
y = 20
Car 1 consumes 30 gallons of gas.
Car 2 consumes 20 gallons of gas.
The area of Mrs. Crocker's rectangular
pantry floor can be expressed as x2 + 11x + 24
units2. List a possible expression for the length
and the width of her pantry floor.
Answers
Possible expressions for the length and the width of her pantry floor are x + 3 and x + 8
How to determine the expressionsThe function given for the area of the rectangular pantry floor is expressed as;
Area = x2 + 11x + 24
Now, let's solve the quadratic equation using the factorization method
Multiply the coefficient of x squared by the constant + 24
Then, find the pair factors of product that sums up to 11 and substitute the values
We get;
x² + 8x + 3x + 24
Factor in pairs, we have;
(x² + 8x) + (3x + 24)
Now, factor the common terms, we have;
x( + 8) + 3(x + 8)
Then, the expression for x are;
Length = x + 3
Width = x + 8
Hence, the expressions are x + 3 and x + 8
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ANSWER THE QUESTION FOR BRAINLIEST
Answers
Answer:
stight line
Step-by-step explanation:
Owen receives $10 and puts it into his saving account. He adds $0.50 to the account each day for a number of day, d, after that. He writes the expression 10+ 0.5(d-1) to find the amount of money in his account after d days. Which statement about his expression is true?
Answers
The true expression about the account is D.) It is the sum of the initial amount and the additional amount after d days.
What does the expression 10+0.5(d−1) represent in Owen's savings account?The answer is D because it represents the sum of the initial amount and the additional amount after d days. The initial amount is $10 and Owen adds $0.50 to the account each day for a number of days, represented by d.
By subtracting 1 from d, the expression ensures that on the first day (when d=1), only the initial $10 is counted. On each subsequent day, the additional amount of $0.50 is added to the total. Therefore, the expression 10+0.5(d−1) gives the amount of money in Owen's account after d days.
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If z varies directly with the square of x and inversely with the cube of y, when x = 8, y = 2, and z = 12, what is x when y = 1 and z = 24?
PLEASE HELP!!! :))))
Answers
Step-by-step explanation:
it just means
z = k×x²/y³
12 = k×8²/2³ = k×64/8 = k×8
k = 12/8 = 3/2
24 = k×x²/1³ = 3/2 × x²/1 = 3/2 × x²
24/(3/2) = x²
48/3 = x²
16 = x²
x = 4 or
x = -4
Philip has been experimenting with new recipes at his bakery for the past 8 months. This month, he tried a recipe for lavender vanilla muffins and gave samples to his customers. He asked them to rate the muffins on a scale of 1 to 10 stars. The median rating was 7 stars, and the interquartile range was 4 stars. ) What can you conclude from these data and statistics? Select all that apply. () No customer gave the muffins fewer than 8 stars. A typical rating for the muffins was 7 stars. The middle 50% of customer ratings had a range of 4 stars. Submit
Answers
- A typical rating for the muffins was 7 stars, since the median rating was 7 stars.
- The middle 50% of customer ratings had a range of 4 stars, since the interquartile range was 4 stars.
- We cannot conclude that no customer gave the muffins fewer than 8 stars, as the median is not necessarily equal to the mean, and it is possible that some customers rated the muffins below 8 stars. Therefore, this statement is not necessarily true.
Will give crown thingy 5 stars a thanks and 10 points to whoever helps me with this!!!!!!!
Answers
Answer:29.15
Step-by-step explanation:
You just divide 21.20 by 8 then multiply
Use the diagram of the right triangle above and round your answer to the nearest hundredth.
If Measure of angle B = 60 degreesº and a = 10 meters, find b.
a.17.32 m
b6.93 m
c.14 m
d.9.99 m
Answers
The calculated value of the side length b is 17.32 meters
Finding the side length bFrom the question, we have the following parameters that can be used in our computation:
Angle B = 60 degrees
Length a = 10 meters
The side length b is calculated as
tan(60) = b/a
So, we have
tan(60) = b/10
Make b the subject
b = 10 * tan(60)
Evaluate
b = 17.32
Hence, the side length b is 17.32 meters
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A four-ounce serving of Campbell's Pork & Beans contains 5 grams of protein and 21 grams of carbohydrates A typical slice of "lite" rye bread contains 4 grams of protein and 12 grams of carbohydrates.
(a) I am planning a meal of "beans-on-toast" and I want it to supply 20 grams of protein and 80 grams of carbohy- drates. How should I prepare my meal?
(b)If I require A grams of protein and B grams of carbohy- drates, give a formula that tells me how many slices of bread and how many servings of Pork & Beans to use.
Answers
(a) To meet the desired 20g protein and 80g carbohydrate intake, prepare 4 servings of Pork & Beans and combine with 15 slices of "lite" rye bread.
(b) Bread: A/4 slices, Beans: B/21 - (A/4) * (12/21) servings.
(a) To prepare a meal of "beans-on-toast" that supplies 20 grams of protein and 80 grams of carbohydrates, you can use the following combination:
- Servings of Campbell's Pork & Beans: 4 servings.
- Slices of "lite" rye bread: 15 slices.
By using 4 servings of Campbell's Pork & Beans, you will obtain a total of 20 grams of protein (5 grams per serving) and 84 grams of carbohydrates (21 grams per serving).
Combining this with 15 slices of "lite" rye bread will contribute an additional 60 grams of carbohydrates (12 grams per slice) and 4 grams of protein (4 grams per slice). Thus, your meal will meet the desired nutritional requirements of 20 grams of protein and 80 grams of carbohydrates.
(b) The formula to determine the number of slices of bread and servings of Pork & Beans needed to meet specific protein and carbohydrate requirements is as follows:
- Number of slices of bread (Bread): A divided by 4.
- Number of servings of Pork & Beans (Beans): (B divided by 21) minus ((A divided by 4) multiplied by (12 divided by 21)).
Using this formula, you can calculate the appropriate quantities of bread and beans based on the desired protein (A) and carbohydrate (B) values.
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An expression is given.
16
−
14
÷
2
+
(
3
+
2
)
2
What is the value of the expression?
46
46
34
34
26
26
16
Answers
9514 1404 393
Answer:
34
Step-by-step explanation:
Maybe you want to evaluate ...
16 - 14 ÷ 2 + (3 +2)²
The parentheses are evaluated first.
16 -14÷2 +5²
Then the exponential term.
16 -14÷2 +25
The division is evaluated next.
16 -7 +25
Finally, the sum is evaluated.
= 9 +25
= 34
____
Your calculator can do this arithmetic for you.
The formula for finding the area of a square that has a side length, s, is A = s2. If a square has an area of 40 square units,
what is the length of a side?
A. 2./10
B. 10.12
C. 20
Answers
Answer:
2./10
Step-by-step explanation:
It's simply by finding the square root of its area which is √40 giving 6.325 for an answer
If simplified by dividing each side with 3 then the answer would be 2./10
A ratio defined as
Answers
Answer:
, a ratio indicates how many times one number contains another.
Step-by-step explanation:
Answer:
the quantitative relation between two amounts showing the number of times one value contains or is contained within the other
Step-by-step explanation:
The ratio of carrots to peas is 3 to 5
How to find p-value from z-score?
Answers
The procedure to calculate the p-value from z-score depends on one of two choices: one-tailed (which may be Left-tailed or Right-tailed) or two-tailed tests.
How to find the p-value from the z-score?A z-table, otherwise termed the standard normal table, provides the area under the curve to the left of a z-score.
The technique for using z-tables to find p-values depends on the test being carried out; which may be; one- or two-tailed test.
For one-tailed tests, the directionality is also a factor.
It therefore follows that;
For a Left-tailed z-test: the p-value = Φ(Zscore)
For a Right-tailed z-test: the p-value = 1 - Φ(z-score).
For a Two-tailed z-test: the p-value = 2 * Φ(−|z-score|).
The procedure described above represents how to calculate p-value from z-score.
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The following equations are used to find the p-value from its z-score
Left-tailed test: Φ(z-score)Right-tailed test: 1 - Φ(z-score)Two-tailed test: 2Φ(−|z-score|)How to find p-value from its z-score?From the question, the parameters are given as
p-valuez-scoreAlso, from the question, we understand that:
The p value depends on the z-score for its own value
There are three formulas for calculating the p-value from the z-score, depending on the type of test (i.e. left-tailed test, right-tailed test and two-talied test)
These formulas are:
Left-tailed test: Φ(z-score)Right-tailed test: 1 - Φ(z-score)Two-tailed test: 2Φ(−|z-score|)Read more about p-value at
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Problem-work-interest-total
Rita needs to take out a loan for a new
car. Her loan is for $25,000. The interest
rate on the loan is 6%, and is
compounded yearly. She plans to pay off
the loan in 5 years. What will she owe
after she factors in interest?
Answers
The amount that she owes after she factors in interest will be $33,455.64.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
Rita necessities to apply for a line of credit for another vehicle. Her advance is $25,000. The financing cost on the advance is 6% and is accumulated yearly. She intends to take care of the advance in 5 years.
Then the amount is given as,
A = $25,000 x (1 + 0.06)⁵
A = $25,000 x (1.06)⁵
A = $25,000 x 1.3382
A = $33,455.64
The amount that she owes after she factors in interest will be $33,455.64.
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which table best classifies the following numbers as rational and irrational?
-4/5, √2, 2.5,0.4,√16
Answers
Answer:
√2 is the only irrational number here. Others are rational
Step-by-step explanation:
Which of the following is a rational number but is NOT an integer?
F. 8
G. 24
H. 40/4
J. 6.2
Answers
Solve the following questions by showing the necessary steps.
1. DISPOSAL The Meyer family uses a kitchen trash can shaped like a
cylinder. It has a height of 12 inches and a base radius of 6 inches. What is
the volume of the trash can? Round your answer to the nearest tenth of a
cubic inch.
Answers
Answer:
The volume of the trash can is approximately 3,618.2 cubic inches.
Step-by-step explanation:
The volume V of a cylinder is given by the formula:
V = πr^2h
where r is the radius of the base and h is the height of the cylinder.
In this case, the height is 12 inches and the base radius is 6 inches, so we have:
V = π(6)^2(12)
= 1,152π
≈ 3,618.2 cubic inches (rounded to the nearest tenth of a cubic inch)
Therefore, the volume of the trash can is approximately 3,618.2 cubic inches.
Answer:
Volume of trash can is 1375.7 cubic inch.Step-by-step explanation:
The Meyer family uses a kitchen trash can shaped like a cylinder. It has a height of 12 inches and a base radius of 6 inches.
Height of trash can = 12 inches
Height of trash can = 12 inchesRadius of trash base = 6 inches.
Volume of cylinder = πr²h
= 22/7 × 6² × 12
= 22/7 × 36 × 12
= 9504/7
= 1375.7 inch³
Hence, Volume of the trash can is 1375.7 cubic inch.
What is the area of a sector when 0=pi/2 radians and r=8/3
Answers
\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =\frac{\pi }{2}\\[1em] r=\frac{8}{3} \end{cases}\implies A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot\left( \cfrac{8}{3} \right)^2 \\\\\\ A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot \cfrac{64}{9}\implies A=\cfrac{16\pi }{9}\implies A\approx 5.59\)
Order the tiles to match the scenario of the graph of the
Answers
Answer:
i dont see a graph...
Step-by-step explanation:
???
At a local college, only 30% of students live off campus. Of those who live off campus, 62% of those students get a part-time job. Of those who live on campus, 65% work part-time. The tree diagram shows how the college students are divided into subgroups.
The tree diagram shows college students branching off into two categories, off campus and on campus students. Off campus students branches off into two sub-categories, work part-time and do not work. On campus branches off into two subcategories, work part-time and do not work.
What is the percentage of students who live on campus who do not have a part-time job?
18.6%
24.5%
35%
38%
Answers
Answer:
24.5%
Step-by-step explanation:
Given
P(Off-Campus) = 0.30
P(Part-Time Job | Off-Campus) = 0.62
P(Part-Time Job | On-Campus) = 0.65
Inferred
P(On-Campus) = 0.70
P(No Part-Time Job | Off-Campus) = 0.38
P(No Part-Time Job | On-Campus) = 0.35
Calculation
P(No Part-Time Job | On-Campus) = P(No Part-Time Job ∩ On-Campus)/P(On-Campus)
0.35 = P(No Part-Time Job ∩ On-Campus)/0.70
0.245 = P(No Part-Time Job ∩ On-Campus)
Therefore, 24.5% of students that live on campus do not have a part-time job.
Xavier earns a yearly salary of $16,500. If he gets a raise or $110 per month, what is the percent of increase
Answers
Answer
approximately 0.0067
Step-by-step explanation:
If you multiply 0.0067 with 16,500 you get about 110.55 and the more you keep going with the 6, the closer it gets to 110$.
A regional survey found that 60% of all families who indicated an intention to buy a new car bought a new car within 3 months, that 10% of families who did not indicate an intention to buy a new car bought one within 3 months, and that 26% indicated an intention to buy a new car. If a family chosen at random bought a car, find the probability (as a percent) that the family had not previously indicated an intention to buy a car. (Round your answer to two decimal places.)
Answers
Let A be the event that a family chose at random indicated an intention to buy a new car and let B be the event that a family chose at random bought a new car within 3 months.
We are asked to find P(A'), which is the probability that a family chosen at random had not previously indicated an intention to buy a car.
We can use the given information to write the following conditional probabilities:
P(B | A) = 60%
P(B | A') = 10%
P(A) = 26%
We can use these probabilities to apply Bayes' theorem to find P(A' | B), which is:
P(A' | B) = P(B | A') * P(A') / P(B)
Substituting the values from the problem, we have:
P(A' | B) = (10%) * (100% - 26%) / (60% * 26% + 10% * (100% - 26%))
= (10%) * (74%) / (60% * 26% + 10% * 74%)
= (10%) * (74%) / (15.4% + 7.4%)
= (10%) * (74%) / (22.8%)
= 43.86%
Therefore, the probability that a family chosen at random had not previously indicated an intention to buy a car is 43.86%.
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19-x²
if x = -5
How would you solve this math problem?
Answers
The solution to the math problem is -6.
A math problem is a problem that can be represented, analyzed, and probably solved, with the techniques of arithmetic. This will be an actual-world problem, inclusive of computing the orbits of the planets inside the solar gadget, or trouble of a greater summary nature, such as Hilbert's problems.
The Collatz Conjecture is the only math problem no person can resolve it is straightforward and sufficient for almost every person to recognize but notoriously difficult to resolve.
= 19 - ( - 5 ) ²
= 19 - ( 25 )
= 19 - 25
= - 6
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For the question of total area of the cuboid is 200cm^.
I understand where we divide 150 by 4.
But why do I need to multiply by 5, when there are 6 faces.
Answers
You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.
When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.
A cuboid has six faces, but each face has a pair that is identical in size and shape.
Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.
To find the surface area of a cuboid, you can add up the areas of all its faces.
However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:
(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.
By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.
Essentially, you are considering one face from each pair and then summing their areas.
Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.
When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.
Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.
Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.
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Greg is saving to buy a tablet that costs $235. He already has $25 saved up. Each week, Greg earns $15 babysitting and $25 as a cashier, but he spends $10 on lunches. Write and solve an equation to find how many weeks it will take Greg to have enough money saved to buy the tablet.
Answers
Answer:
235=30x-25
Step-by-step explanation:
235+25=30x-25+25
260=30x
260/30=30x/30
x=8.66 or 9 weeks
The equation is 30x + 25 = 235. And the number of weeks will be 7.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
Greg is saving to purchase a tablet that costs $235. He as of now has $25 set aside. Every week, Greg procures $15 looking after children and $25 as a clerk, however, he burns through $10 on snacks.
Let x be the number of weeks. Then the equation is given as,
25x + 15x - 10x + 25 = 235
Simplify the equation, then the number of weeks is given as,
25x + 15x - 10x + 25 = 235
30x = 235 - 25
30x = 210
x = 210 / 30
x = 7 weeks
The equation is 30x + 25 = 235. And the number of weeks will be 7.
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20 miles is equal to how many kilometers? (1 mile ≈ 1.6 km)
Answers
Answer:
32.1869 or 32
Step-by-step explanation:
The math term for this topic would be conversions
In order to get the answer for this question we will be using fraction form.
Solving the question:
\(\frac{x}{20}\) = \(\frac{1.6}{1}\) the top is for the km and the bottom is the miles 20 x 1.6------------------------- < multiply across to get this
1
X = 32km
Statement:
Therefore, 20 miles is equaled to 32 kilometers.
Plz need helppp Quick !!!!!!!
Answers
Step-by-step explanation:
A. 1 cup of blue rate for 3/5 cup of red paint
B. 1 cup of flour for 2.5 muffins
C. r = d/t = 420 miles/7 hours = 60 miles per hour.
D. 48/3 = $16 for every hour
E. $15/6 = $2.5 for every hot dog