b. You're looking for the probability
Pr [72,972 ≤ X ≤ 90,043]
Transform X to Z ∼ Normal(0, 1) using the rule
X = µ + σ Z
with µ = 64,436 and σ = 17,071. Then the probability is
Pr [(72,972 - µ)/σ ≤ (X - µ)/σ ≤ (90,043 - µ)/σ]
≈ Pr [0.5000 ≤ Z ≤ 1.5000]
You probably have a z-score table available, so you can look up the probabilities to be about
Pr [Z ≤ 0.5000] ≈ 0.6915
Pr [Z ≤ 1.5000] ≈ 0.9332
and then
Pr [0.5000 ≤ Z ≤ 1.5000] ≈ 0.9332 - 0.6915 = 0.2417
c. The 75th percentile word count that separates the lower 75% of the distribution from the upper 25%. In other words, its the count x such that
Pr [X ≤ x] = 0.75
Transforming to Z and looking up the z-score for 0.75, we have
Pr [(X - µ)/σ ≤ (x - µ)/σ] ≈ Pr [Z ≤ 0.6745]
so that
(x - µ)/σ ≈ 0.6745
x ≈ µ + 0.6745σ
x ≈ 75,950
d. Because the normal distribution is symmetric, the middle 60% of novels have word counts between µ - k and µ + k, where k is a constant such that
Pr [µ - k ≤ X ≤ µ + k] = 0.6
Also due to symmetry, we have
Pr [µ - k ≤ X ≤ µ + k] = 2 Pr [µ ≤ X ≤ µ + k]
⇒ Pr [µ ≤ X ≤ µ + k] = 0.3
Transform X to Z :
Pr [(µ - µ)/σ ≤ (X - µ)/σ ≤ (µ + k - µ)/σ] = 0.3
⇒ Pr [0 ≤ Z ≤ k/σ] = 0.3
⇒ Pr [Z ≤ k/σ] - Pr [Z ≤ 0] = 0.3
⇒ Pr [Z ≤ k/σ] - 0.5 = 0.3
⇒ Pr [Z ≤ k/σ] = 0.8
Consult a z-score table:
Pr [Z ≤ k/σ] ≈ Pr [Z ≤ 0.8416]
⇒ k/σ ≈ 0.8416
⇒ k ≈ 14,367
Then the middle 60% of novels have between µ - k = 50,069 and µ + k = 78,803 words.
Help show work pls :) ill mark brainliest
Answer:
52.2
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Help me!
What is 25% of 948?
Answer:
237
Step-by-step explanation:
25 percent *948
= (25/100)*948
= (25*948)/100
= 23700/100 = 237
Ruth drove 60 miles in one hour. At this rate, how many miles will she drive in 5 hours?
Answer:
Knowing that it's 60 miles per hour, that would mean we multiply 60 x 5
Meaning, it would be 300 miles in five hours
Step-by-step explanation:
Answer: 300 miles
Step-by-step explanation: 60 * 5 = 300
Directions Type your answer in the space provided.
Hunter wants to make money over the summer by selling lemonade. He has $50 in savings. He spends 520 on a pitcher and reusable cups. Doing the math, he realizes that sugar, lemons, and water will cost $. 75 per serving. What is the greatest number of cups that can be made before Hunter runs out of his budget?
Hunter can make a maximum of 59 cups before he runs out of money.
What is an inequality?An inequality is an expression that shows the non equal comparison of two or more variables and numbers.
Let x represent the number of cups that hunter can buy, He already spent 520 cents ($5.2) hence:
0.75x ≤ 50 - 5.2
x ≤ 59.7
Hunter can make a maximum of 59 cups before he runs out of money.
Find out more on inequality at: https://brainly.com/question/24372553
(2x – 4) and ( 5x²-2x+6)
Answer:
10x³ - 24x² + 20x - 24
Step-by-step explanation:
2x (5x² - 2x + 6) - 4 (5x² - 2x + 6)
10x³ - 4x² + 12x - 20x² + 8x - 24
10x³ - 24x² + 20x - 24
I hope this helps!
Select the correct answer.
Which pair of expressions are equivalent?
Answer:
D
Step-by-step explanation:
None of the others make sense. In answer D x+y is the same as x-y+2y because you add the y's and its the same thing as x+y.
Hope It Helped :)
a boat dealer sells 5 fishing boats for every 4 speed boats it sells
Answer:
Fishing boats - 5 10 15 20 25 30 35 40 45 50 55 60 65 70
Speeed Boats - 4 8 12 16 20 24 28 32 36 40 44 48 52 56
Thanks!
for some reason, your whole question isn't seen, you didn't type it in, so I just made this chart for you!
can somebody help me with this question? please and thank you
the answer to your question is 72
Determine if true:
4x8=36-4
Answer:
True
Step-by-step explanation:
4x8=32
4x8=3236-4=32
Hence, the equation is true.
A slot machine has 3 dials. Each dial has 40 positions, two of which are "Jackpot." To win the jackpot, all three dials must be in the "Jackpot" position. Assuming each play spins the dials and stops each independently and randomly, what are the odds of one play winning the jackpot?
Answer: there is a 1.2% of winning
Step-by-step explanation: there is a 1.2% chance of winning.
Step-by-step explanation:
The odds of one player that wins the jackpot should be 0.00156%.
Given that,
There are 3 dials.
In each dial, there are 40 positions.
So, the probability of receiving the jackpot should be \frac{1}{40}
40
1
Now the odds of one player that wins the jackpot should be
\begin{gathered}= \frac{1}{40} \times \frac{1}{40} \times \frac{1}{40} \\\\\end{gathered}
=
40
1
×
40
1
×
40
1
= 0.00156%
Therefore we can conclude that the odds of one player that wins the jackpot should be 0.00156%.
A music-streaming service charges $9 per month for a single user. Additional users within the same household can be added for $3 per month. Write an equation that shows how the monthly cost, y, depends on the number of additional users in the household, X. Do not include dollar signs in the equation. y=
The equation that shows the monthly cost is y = 9 + 3x
What is the equation that represents the monthly cost?
The monthly cost is a function of the charge for a single user and the cost of additional users. The monthly cost increases with the number of additional users.
The charge for a single user can be considered a fixed cost since it remains constant while the cost of the additional user can be considered a variable cost since it increases with the number of users.
Y = 9 + 3x
To learn more about fixed cost, please check: https://brainly.com/question/25879561
Answer: Y = 3x + 9
Step-by-step explanation:
A survey determined that 39% of the students at Lake Middle like math. There were 400 students in the cafeteria on Thursday. What is a good estimate for the number of students in the cafeteria who like math?
Answer:
math organization and the other one day is the best way to get a runner up
9. Which of these decimals is the LEAST in value?
0.511 0.453 0.552 0.044
O 0.453
0.511
0.552
0.044
Answer:
0.044 os the answer. brainiest pls?
Answer:
The last one 0.044
Step-by-step explanation:
what is 2 6/7 as an improper fraction
Answer:
20/7
Step-by-step explanation:
Check the picture
Mr. Miller owns two hotels and is ordering towels for the rooms. He ordered 27 hand towels and 48 bath towels for a bill of $540 for the first hotel. He ordered 50 hand towels and 24 bath towels for a bill of $416 for the other hotel.
What is the cost of one hand towel and one bath towel?
A.
The cost of one hand towel is $9 and the cost of one bath towel is $4.
B.
The cost of one hand towel is $8 and the cost of one bath towel is $5.
C.
The cost of one hand towel is $5 and the cost of one bath towel is $8.
D.
The cost of one hand towel is $4 and the cost of one bath towel is $9.
This question is based on the concept of solving a two linear equation.
Thus, the cost of one bath towel is $9 and one hand towel is $4.
Given:
Number of ordered of hand towels is 27 and bath towels is 48 and for a bill of $540 for the first hotel.
Number of ordered of hand towels is 50 and bath towels is 24 and for a bill of $416 for the other hotel.
We need tom determined the cost of one hand towel and one bath towel.
According to the question:
Let the hand towels be h and bath towels be b.
Therefore, equation of first hotel is
27h + 48b = 540........(1)
Equation of second hotel is
50h + 24b = 416.........(2)
Now, solving both equation for h and b.
Equation (2) multiplying by -2.
-100 h -48 b = - 832..................(3)
Now, solve equation (1) and (3)
27h + 48b = 540 and -100h - 48b = - 832
⇒ -73 h = - 292
⇒ h = -292 / -73
⇒ h = 4
Therefore, the cost of 1 hand towel is $4.
Now, putting the value of h = 4 in equation (1).
⇒ 27(4) + 48b = 540
⇒ 108 + 48b = 540
⇒ 48b = 540 - 108
⇒ 48b = 432
⇒ b = 432/48
⇒ b = 9
Therefore, the cost of 1 bath towel is $9.
Thus, the cost of one bath towel is $9 and one hand towel is $4.
For more details, prefer this link:
brainly.com/question/11897796
What is the value of x?
A. 15
B. 21.2
C. 10.6
D. 7.5
Answer:
c.10.6
Step-by-step explanation:
we take sin the angle on the length of the side that opposite to it ...
The value of x from the triangle is x = 10.6
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ABC
Now , the measure of hypotenuse of the triangle = 15
Let the angle be θ = 45°
From the trigonometric relations ,
sin θ = opposite / hypotenuse
On simplifying the equation , we get
sin 45° = x / 15
where sin 45° = 0.7071
So , the value of x = 0.7071 x 15
The value of x = 10.6
Hence , the value of x from the triangle is x = 10.6
To learn more about trigonometric relations click :
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#SPJ2
Select the correct answer.
A team of researchers is monitoring the population of crickets in a particular town. They do not know exactly how many crickets are remaining, but the model they use represents the minimum number of crickets remaining in the town.
According to their model, the minimum number of the species remaining, in thousands, multiplies by 10 every month. The researchers determine that right now, the population of crickets is at least 5 thousand. Once the minimum population reaches 1 million, measures are taken to stop the increase in population.
If P represents the actual population of crickets in the town, in thousands, and t represents the time, in months, which of the following systems of inequalities can be used to determine the possible number of crickets in the town over time?
Answer:
P>_5(10)^t
P<_1,000
Step-by-step explanation:
Which equation represents the graphed function?
11(u-4)
remove the parentheses
Answer: 11u - 44
Step-by-step explanation:
11u - 44.
You have to distrubute the 11 to everything inside the parenthesis. So it becomes 11*u or 11u and 11*-4 or -44.
Answer:
11u - 44
Step-by-step explanation:
11(u - 4)
We have to distribute
(11 × u) + (11 × -4)
11u - 44
Use the spinner below to find the probability of getting the following in a single spin p(9 or 2)
Answer:
1/6 or 0.1667
Step-by-step explanation:
Probability of one number out of 12 is 1/12. So the probability of getting either 9 or 2 is 2/12=1/6
The mechanic does 4 oil changes in 2 hours. How many oil changes can the mechanic do in 8 hours?
Answer:
16.
Step-by-step explanation:
^
Answer:
The mechanic does 4 oil changes in 2 hours. How many oil changes Can the mechanic do in 8 hours. My answer is16 oil changes. 4 x 2 =8 and 8+8=16.
Step-by-step explanation:
How many cubes with edge lengths of 1/4 in. will it take to fill the prism?
56 cubes
375 cubes
6000 cubes
Answer:
1560
Step-by-step explanation:
First (2 1/2)/(1/4) = (5/2)(4) = 20/2 = 10
Next, 3/(1/4) = 3(4) = 12
Lastly, (3 1/4)/(1/4) = (13/4) x 4 = 52/4 = 13
This means we need 10 rows of 12, 13 high. 10(12)(13) = 1560 cubes.
Another way is to multiply 2 1/2 x 3 x 3 1/4 = 5/2 x 3 x 13/4 = 195/8
A 1/4 inch cube is 1/4 x 1/4 x 1/4 for a volume of 1/64
(195/8)/(1/64) = (195/8)(64) = 1560 cubes.
PLS HELP I WILL MARK BRAINLIEST!!!
In a game, for every 3 enemies defeated, you earn 5 points. If you defeated 27 enemies, how many points would you have earned?
The average length of a female dolphin is about 181 inches (in).
What is this length in feet (ft) and inches (in)?
The length is ft in.
Answer:
15 ft 1 in
Step-by-step explanation:
To convert inches into feet, we divide by 12.
12 goes into 181 fifteen times, so the # of feet is 15 feet.12 x 15 = 180.181 - 180 = 1, so the # of remaining inches is 1 inchTherefore, the answer is 15 ft 1 in.
What is the slope of the line that passes through the points (1,1) and (4,4)? Write your answer in simplest form.
Answer:
The slope is 1.
Step-by-step explanation:
Slope is (y2-y1)/(x2-x1). Plug in the given points. (4-1)/(4-1) is 3/3. This reduces to 1. The slope of the line is 1.
i need help with this question asap pls
Answer:
0.01
Step-by-step explanation:
0.0
What is the distance between (2, -4) and (9,-4)?
8 units
11 units
O units
7 units
Answer:
7 units
Step-by-step explanation:
If you want to get from (2, -4) to (9, -4) you have to move 7 units to the right. (9 - 2 = 7)
Answer:
7 units.
Step-by-step explanation:
Calculus problem: A drug manufacturer has developed a time-release capsule with the number of milligrams of the drug in the bloodstream given by
S = 40[tex]x^{\frac{19}{7} }[/tex] − 560[tex]x^{\frac{12}{7} }[/tex] + 1960[tex]x^{\frac{5}{7} }[/tex]
where x is in hours and 0 ≤ x ≤ 7. Find the average number of milligrams of the drug in the bloodstream for the first 7 hours after a capsule is taken. (Round your answer to the nearest whole number.)
Solution: _____ mg
Step-by-step explanation:
You can find your answer by taking integral from 0 to 7 and then dividing it by 7.
A shipping company charges a flat rate of $3 and 1 cent for every mile traveled. What is the initial value and the rate of change?
Answer:
initial value = 3
rate of change = 0.01
Step-by-step explanation:
we can represent this as a linear equation:
y = 0.01x + 3
the initial value is the value of y when x = 0; we can find this by setting x to zero and evaluating for y, which gives us 3. Our initial value is 3.
The rate of change, of slope of this graph, is 0.01, as it is the constant multiplier of x.
Hare Krishna! :)
why does 0.5g equal 500 mg
Answer:
in kg 1.1 equals to 1gram and 100mg
so in 0.5 equals to 500 mg
hope it helps (θ‿θ)