Given Information:
Mean clear height = μ = 22 feet
Standard deviation of clear height = σ = 4 feet
Required Information:
a) P(X > 16) = ?
b) P(X < 14) = ?
c) P(25 < X < 30) = ?
Answer:
a) P(X > 16) = 93.12%
b) P(X < 14) = 2.27%
c) P(25 < X < 30) = 20.39%
Step-by-step explanation:
What is Normal Distribution?
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
a) We want to find out the probability that the clear height is greater than 16 feet.
[tex]P(X > 16) = 1 - P(X < 16)\\\\P(X > 16) = 1 - P(Z < \frac{x - \mu}{\sigma} )\\\\P(X > 16) = 1 - P(Z < \frac{16 - 22}{4} )\\\\P(X > 16) = 1 - P(Z < \frac{-6}{4} )\\\\P(X > 16) = 1 - P(Z < -1.5)\\\\[/tex]
The z-score corresponding to -1.5 is 0.0668
[tex]P(X > 16) = 1 - 0.0668\\\\P(X > 16) = 0.9312\\\\P(X > 16) = 93.12 \%[/tex]
Therefore, the probability that the clear height is greater than 16 feet is 93.12%
b) We want to find out the probability that the clear height is less than 14 feet
[tex]P(X < 14) = P(Z < \frac{x - \mu}{\sigma} )\\\\P(X < 14) = P(Z < \frac{14 - 22}{4} )\\\\P(X < 14) = P(Z < \frac{-8}{4} )\\\\P(X < 14) = P(Z < -2)\\\\[/tex]
The z-score corresponding to -2 is 0.02275
[tex]P(X < 14) = 0.02275\\\\P(X < 14) = 2.27 \%[/tex]
Therefore, the probability that the clear height is less than 14 feet is 2.27%
c) We want to find out the probability that the clear height is between 25 and 30 feet.
[tex]P(25 < X < 30) = P( \frac{x - \mu}{\sigma} < Z < \frac{x - \mu}{\sigma} )\\\\P(25 < X < 30) = P( \frac{25 - 22}{4} < Z < \frac{30 - 22}{4} )\\\\P(25 < X < 30) = P( \frac{3}{4} < Z < \frac{8}{4} )\\\\P(25 < X < 30) = P( 0.75 < Z < 2 )\\\\[/tex]
The z-score corresponding to 0.75 is 0.7734 and 2 is 0.9773
[tex]P(25 < X < 30) = P( Z < 2 ) - P( Z < 0.75 ) \\\\P(25 < X < 30) = 0.9773 - 0.7734 \\\\P(25 < X < 30) = 0.2039\\\\P(25 < X < 30) = 20.39 \%[/tex]
Therefore, the probability that a child spends more than 4 hours and less than 8 hours per day unsupervised is 20.39%
How to use z-table?
Step 1:
In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.5, 2.2, 0.5 etc.)
Step 2:
Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 1.50 then go for 0.00 column)
Step 3:
Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.
You're choosing between two car rental companies. Company A charges an initial fee of $15 with $.25 per mile, while Company B only charges $.50 per mile. How many miles will it take for both companies to have the same service price? What's this price amount? Use the following systems of linear equations to solve by graphing. Company A: y = 0.25x + 15 Company B: y = 0.50x
Name
Date
SHARE THE TREASURE 3
Captain Salamander and his crew have found 24 bars of gold.
The captain decides that he is going to share all the treasure out.
He puts 1/3 of the bars to aside for himself.
He gives 1/4
of the bars to his friend Bill
He shares out 7 bars with the rest of his crew.
How many bars does he have left?
Z
/ 17
.
Answer:
3 bars
Step-by-step explanation:
Total no. of gold bars = 24.
Fraction of bar captain allocated to himself = 1/3 of the bars
no. of bars he allocated to himself = 1/3 of 24 = 1/3 * 24 = 8
Fraction of bar captain allocated to his friend bill = 1/4 of the bars
no. of bars he allocated to his friend bill = 1/4 of 24 = 1/4 * 24 = 6
No . of bars captain allocated to rest of crew = 7
Total no of bars which are allocated altogether =
no. of bars he allocated to himself +no. of bars he allocated to his friend bill +No . of bars captain allocated to rest of crew
substituting the value of above summation variable as calculated above we have
Total no of bars which are allocated altogether = 8+6+7 = 21
No. of bars left = total no. of bars - Total no of bars which are allocated altogether = 24 - 21 = 3
Thus 3 gold bars are left.
The Tip Top Tennis Balls manufacturing company makes and sells tennis balls. The revenue (in dollars) that the company receives in selling x cases (12 cans per case, three balls per can) of tennis balls in one week is given by The cost (in dollars) is given by All of the following questions refer to a one-week period, and only full cases of balls are sold. Write an equation for the profit P the company makes in producing and selling x cases. (Remember the profit = revenue – cost.) How many tennis balls need to produced and sold for the profit to be greater than zero? Choose the correct answer.
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
Which statement correctly compares the spreads of the distributions?
Answer:
b. the ranges of penguin heights are the same.
Step-by-step explanation:
Hello!
Statements:
Which statement correctly compares the spreads of the distributions?
a. the mode of penguin heights at county side zoo is greater than the mode at city view zoo.
b. the ranges of penguin heights are the same.
c. the range of penguin heights is greater at city view zoo than at county side zoo.
d. the range of penguin heights is greater at county side zoo than at city view zoo.
The mode and mean are measurements of central tendency, these indicate the position of a data set but don't show any information concerning the distribution of said data.
The range on the other had is a measurement of variance, it shows the difference between the maximum and minimum values of the data set and indicates its total dispersion.
City view Zoo R= 44-37= 7 cm
County side Zoo: R= 45-38= 7 cm
Both ranges are the same.
I hope this helps!
Susan works as a hostess where she makes $8.75 per hour. She also babysits and earns $10.00 per hour. Last week she made $165.00. If she worked 6hour more as a hostess than she did babysitting, how many hours did she babysit last week?
Answer:
6 hours as a babysitter and 12 hours as a hostess
54,36,24 whats the next term in the geometric sequence
Answer:
16
Step-by-step explanation:
The common ratio is 36/54 = 2/3.
So the next term is 2/3 (24) = 16.
Answer:
16
Step-by-step explanation:
sorry no step by step explanation because I was in a rush anyway I did the quiz and here u go anyway have a great day I hope this helps :D
What’s the correct answer for this?
Answer:
B = 15 units ²
Step-by-step explanation:
In the attached file
in a basketball game . Tina made 9 baskets . each dasket was worth either 2 or 3 points how many different numbers could represent the total points that Tina could have made?? answer me
Answer:
Tina could make are 10 Possible total points.
They number of possible total points are; 18, 19, 20, 21, 22, 23, 24, 25, 26 and 27.
Step-by-step explanation:
This is a zero-sum sort of deal. If tina makes 9 baskets, they can be all 2 points or all 3 points.
Let's make some number of 2 points "n". Then, the number of 3 points has to be 9 - n. The logic is exactly the same if we considered the number of 3 points made to be "n".
Thus, the maximum of this relationship is when n = 0.
Hence, 9 baskets gives the following possible permutations:
1) 0 number of 2 points and 9 number of 3 points = 27 points
2) 1 number of 2 points and 8 number of 3 points = 26 points
3) 2 number of 2 points and 7 number of 3 points = 25 points
4) 3 number of 2 points and 6 number of 3 points = 24 points
5) 4 number of 2 points and 5 number of 3 points = 23 points
6) 5 number of 2 points and 4 number of 3 points = 22 points
7) 6 number of 2 points and 3 number of 3 points = 21 points
8) 7 number of 2 points and 2 number of 3 points = 20 points
9) 8 number of 2 points and 1 number of 3 points = 19 points
10) 9 number of 2 points and 0 number of 3 points = 18 points
So the number of possible points Tina could make are; 18, 19, 20, 21, 22, 23, 24, 25, 26 and 27.
please help with this
Answer:
x^2 + 10x +21
Step-by-step explanation:
Your multiplying the Squares together and then adding them
Blue Square : x*x= x^2
Pink Square : x*7= 7x
Green Square: x*3= 3x
Orange Square: 3*7= 21
Now we add all the squares together to get the total area.
x^2+7x+3x+21
x^2+ 10x +21
HELPPPPP What is the combine legth of all the buttons longer than 1 inch
On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these
flowers rapidly increases as the trees blossom.
The relationship between the elapsed time, t, in days, since the beginning of spring, and the total number of
locusts, L(t), is modeled by the following function:
t
L(t) = 750 - (1.85)^t
Complete the following sentence about the daily rate of change of the locust population.
Every day, the locust population
grows/shrinks
by a factor of______?
Answer:5
Step-by-step explanation:
Answer:
if it is the percentage question, the answer is 65% and added
Step-by-step explanation:
khan
Select one of these options for each of the 4 questions
A. Exactly one pair of opposite sides of a trapezoid is parallel.
B. Slope formula
C. Two distinct lines are parallel if and only if they have equal slopes.
D. Midpoint formula
E. Given
F. Distance formula
G.Both sets of opposite sides of a trapezoid are parallel.
Answer:
1. Given
2. Slope Formula
3. Two distinct lines are parallel if and only if they have equal slopes.
4. Both sets of opposite sides of a trapezoid are parallel.
Step-by-step explanation:
Hope this helps.
Answer:
1. Given
2. Slope Formula
3. C
4. A. Exactly one pair of a trapezoid is parallel
The solution to 2x2 – 11 = 87 is .
Step-by-step explanation:
Step 1: Subtract 87 from both sides
[tex]2x^2 - 11 - 87 = 87 - 87[/tex]
[tex]2x^2 - 11 - 87 = 0[/tex]
Step 2: Factor
[tex]2x^2 - 11 - 87 = 0[/tex]
[tex]2(x + 7)(x - 7) = 0[/tex]
[tex]x + 7 = 0[/tex] and [tex]x - 7 = 0[/tex]
[tex]x = -7[/tex] and [tex]x = 7[/tex]
Answer: [tex]x = -7, 7[/tex]
Answer:
x = 7, -7
Step-by-step explanation:
2x² - 11 = 87
2x² = 98
x² = 49
x = +/-7
In order to multiply fractions, the ______(s) are multiplied together, the_______(s) are multiplied together, and the fractions is simplified
Answer:
Numerators and denominators
Step-by-step explanation:
Upper part of fraction is referred to as numerator while lower part as denominator.
Answer:
In order to multiply fractions, the numerator(s) are multiplied together, the denominator(s) are multiplied together, and the fractions is simplified
Step-by-step explanation:
I remember it like this: numerator - up; denominator - down
Please give me brainliest
ABCD is a quadrilateral with vertices at (-2,3), (-1,7), (3,9), and (2,5). Is it a rectangle
Answer:
No
Step-by-step explanation:
It is a parallelogram but it does not contain at least 2 right angles.
The multiplicative identity element for integers is _______________________.
Answer:
The multiplicative identity of the ring of integers and of its extension rings such as the ring of Gaussian integers , the field of rational numbers , the field of real numbers , and the field of complex numbers .
The answer is 1
Hope this helps
Answer: 1
Step-by-step explanation: Any no. multiplied by 1 is no. itself
i.e. x × 1= x
Wesson Company sold 10,000 units of its only product in the first half of the year. If sales increase by 12% in the second half of the year, which cost will increase?
Answer:
Direct materials
Step-by-step explanation:
In this case we must bear in mind that as more products are sold, more material is needed to manufacture those additional final products
.
Therefore, in this case the cost would be related mainly to the materials, mainly the direct materials, since they are essential in the production of the product.
Solve plzzzz As attached
Answer:
Step-by-step explanation:
Basically, we're solving for a.
w = 3(2a + b) - 4
w = 6a + 3b - 4
-6a + w = 3b - 4
-6a = -w + 3b - 4
a = (w - 3b + 4)/6
Hope this helps!
Solve: -(1/4)m + 5 = 16
Answer:
m=-44
Explanation: distribute the negative and add -1/4 to m and then take the 5 away from 16 and then multiply both sides
Answer:
M = - 44
Step-by-step explanation:
You will start by subtracting 5 on both sides of the equation.
- (1/4)m + 5 =16
-5 -5
Simplify
- 1/4 m =11
Multiple both sides by - 4
(-1/4m)(-4)= 11 (- 4)
The final result is m equals negitive 4.
M = -44
Paul had 65 marbles. He gave 26 marbles to his sister and 19 to his brother. How many marbles did Paul have left
A)
12
B)
15
C)
18
D)
20
Answer:
D) 20
Step-by-step explanation:
26+19=45
65-45=20
Answer:
D. 20 would be your answer.
Step-by-step explanation:
[tex]65-26=39[/tex]
[tex]39-19= 20[/tex]
Paul had [tex]20[/tex] marbles left.
:)
The graph shows equivalent ratios. Khalid plots a point to show a fourth equivalent ratio. If the x-value of Khalid’s point is 35, what is the y-value? 20 25 28 35
Answer:
25
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing. Show your work or give an explaination.
Answer:
The Answer is B
Step-by-step explanation:
Why, Because it is saying graph the equation by a number of units so it will most likely be going down. Hope it helps.
A circle has a circumference of 452.16. What is the radius of the circle
Formula: r = C/2π
Solve with the given values.
r = 452.16/2(3.14)
r = 452.16/6.28
r = 72
Therefore, the radius is approximately 72 units.
Best of Luck!
Solve the equation by completing the square. x2 + 20x + 82 = 7
Answer:
{-15, -5}
Step-by-step explanation:
The constant on the left needs to be the square of half the x-coefficient:
(20/2)^2 = 100
To get it to that value, we can add 18 to both sides of the equation:
x^2 +20x +100 = 25 . . . add 18 to both sides of the equation
(x +10)^2 = 25 . . . . . . . . write the left side as a square
x +10 = ±√25 = ±5 . . . . . take the square root
x = -10 ±5 = {-15, -5}
The solutions are x = -15 and x = -5.
_____
The attached graph shows the solutions to ...
x^2 +20x +82 -7 = 0 . . . . . the result of subtracting 7 from both sides
Answer:
sqdancefan
Genius
40.3K answers
503.3M people helped
Answer:
{-15, -5}
Step-by-step explanation:
The constant on the left needs to be the square of half the x-coefficient:
(20/2)^2 = 100
To get it to that value, we can add 18 to both sides of the equation:
x^2 +20x +100 = 25 . . . add 18 to both sides of the equation
Step-by-step explanation:
please answer my question
Answer:
0π
Step-by-step explanation:
After you add 5 and divide by 7, you find you're looking for solutions to ...
cos(θ) = 1
Your knowledge of the cosine function tells you the solution is ...
θ = 0 . . . . . matches the last choice (only)
___
Any multiple of 2π is a solution, but the only one in the allowed domain is 0π.
WILL GIVE BRAINLIEST ANSWER TO WHOEVER ANSWERS FIRST AND CORRECT PLEASE EXPLAIN WHY YOU ARE CORRECT
Answer:
AB is mid-segment of this trapezoid, then we have:
2 x AB = DG + EF
=> 2 x 12 = 5x - 4 + 8x + 2
=> 24 = 13x - 2
=>13x = 26
=> x = 2
=> Option A is correct
Hope this helps!
:)
A sales man earns 6% commission on all the merchandise that he sells last month he sold $7000 worth of merchandise how much commission and daughters did he earn last month
Answer:
$420
Step-by-step explanation:
You just say commission = 6% of $7000
commission = (6/100) * 7000
commission = 0.06 * 7000 = $420
Answer:
$420
Step-by-step explanation:
6/100 x 7000 = 420
Al stop app weep woop so eery ya wet
Twelve and sixty-eighty thousandths
Answer:
12,60800000
hope it is not help full
Answer:
12 80000 I hope this helps buddy
Step-by-step explanation:
good luck
Given
Principal 1500
Intrest 6%
Time 240 days
Partial payments for 100th day 7,000
For 180th day 4,000
A. Use the u.s rule to solve for total intrest cost
B. Use the u.s rule to solve the balance after payments for the 100th and 180th
C use the u.s rules to solve final payment
Joe went to the bank and withdrew $358 from his checkings account and his balance is now at -$96. He later deposited ¾ of his $800 check and put the rest in his savings account. How much money does he have in his checking account?
Answer:
$504
Step-by-step explanation:
In this case you're solving for his checking account. In the beginning due to him withdrawing $358 he was left with -$96, assuming that he grabbed more than he could take. But later, he deposited 3/4 of $800 into his checking account.
So you need to find what 3/4 of 800 is first to see how much money he put into his checking account
3/4x800/1=600
But thats not the answer since thats only how much he put into his checking account, not how much he has.
So according to the question he had -96 left in the checking account. Therefore, you have to add the 600 in.
600+-96=504
In case you are wondering why there was a lower number when adding, it was a negative number which causes you to start from -96, but go more right into the number line 600 times.
If you have any questions please ask and I hope this helped! :)