Using the normal distribution, it is found that:
a) 4.46% of finish times was higher than 72 minutes.
b) 55.11% of finish times was between 52 and 70 minutes.
c) The 40th percentile of finish times is 52.5 minutes.
d) The 95th percentile of finish times is 71.45 minutes.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
The mean is of 55 minutes, hence [tex]\mu = 55[/tex].The standard deviation is of 10 minutes, hence [tex]\sigma = 10[/tex]Item a:
The proportion is 1 subtracted by the p-value of Z when X = 72, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{72 - 55}{10}[/tex]
[tex]Z = 1.7[/tex]
[tex]Z = 1.7[/tex] has a p-value of 0.9554
1 - 0.9554 = 0.0446
0.0446 x 100% = 4.46%
4.46% of finish times was higher than 72 minutes.
Item b:
Th proportion is the p-value of Z when X = 70 subtracted by the p-value of Z when X = 52, hence:
X = 70:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70 - 55}{10}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a p-value of 0.9332.
X = 52:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{52 - 55}{10}[/tex]
[tex]Z = -0.3[/tex]
[tex]Z = -0.3[/tex] has a p-value of 0.3821.
0.9332 - 0.3821 = 0.5511
0.5511 x 100% = 55.11%
55.11% of finish times was between 52 and 70 minutes.
Item c:
The 40th percentile is X when Z has a p-value of 0.4, so X when Z = -0.253.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.253 = \frac{X - 55}{10}[/tex]
[tex]X - 55 = -0.253(10)[/tex]
[tex]X = 52.5[/tex]
The 40th percentile of finish times is 52.5 minutes.
Item d:
The 95th percentile is X when Z has a p-value of 0.95, so X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 55}{10}[/tex]
[tex]X - 55 = 1.645(10)[/tex]
[tex]X = 71.45[/tex]
The 95th percentile of finish times is 71.45 minutes.
A similar problem is given at https://brainly.com/question/24663213
The expression on the left side of an equation is shown below.
-4(x-2)+5x=0
If the equation has no solution, which expression can be written in the box on the other side of the equation?
2(x+4) - x
O x + 8
O 4(x + 2) - 5x
Ο Χ
Answer:
x + 8
Step-by-step explanation:
Expanding the equation
-4(x-2)+5x = -4(x-2)+5x
= -4x+8+5x
= -4x+5x + 8
= x+8
IMG World of Adventures sold 350 children's tickets last month . If this made up 12.5% of its yearly children's ticket sales, how many children's tickets did IMG World of Adventures sell all year? (WRITE ONLY THE NUMBER)
I'm sorry if I'm wrong
A farmer wants to increase the area of His rectangular pen but keep the pen a rectangular shape. He decides to a 5.7 yards of fencing
to the width of the pen but the length will remain 9.5 yards. The new area will be 77.9 square yards.
Which can be used to determine the original width of the pen?
5.7 (W+9.5) = 77.9
S95219
9.5 (W + 5.7) = 77.9
Using the equation for the area of a rectangle, the original width of the pen is determined by:
9.5 (W + 5.7) = 77.9
The area of a rectangle of length l and width w is given by:
[tex]A = lw[/tex]
In this problem:
Increases the width by 5.7 yards, hence [tex]w = w + 5.7[/tex], in which w is the original width.The length remains at 9.5 yards, hence [tex]l = 9.5[/tex].The area is of 77.9 square yards, hence [tex]A = 77.9[/tex]Then:
[tex]A = lw[/tex]
[tex]9.5(w + 5.7) = 77.9[/tex]
For a similar problem, also involving the area of a rectangle, you can check https://brainly.com/question/10489198
Are the expressions 0.85b-0.2b and 0.65b equivalent?
Hello!
0.85b-0.2b
0.65b
0.65b=0.65b
So these expressions are equivalent.
Hope it helps!
~Just a determined gal
#CarryOnLearning
[tex]MysteriousNature[/tex]
Tamara bought a $22 mailbox using a 10% off coupon David bought an identical mailbox for $19.95 at a different store
Which statement is true?
Thank you
Answer:
I don't see any statements, but Tamara paid less. She paid 19.8 after the discount. David spent a little more at 19.95
The ratio of boys to girls in the class is 4 to 5. If there are 18 boys and girls in the
class, how many of each are there?
Answer:
8 boys and 10 girls
Step-by-step explanation:
If the ratio is 4:5,
4x2 + 5x2 equal 8+10 =
18.
4:5=8:10
Answer:
8 boys
10 girls
Step-by-step explanation:
4:5
8:10
8+10=18
Use Pythagoras Theorem to determine which of the following shapes are rectangles. please awnser
Answer:
(a) - no, (b) - yesStep-by-step explanation:
Use equation and compare results:
d² = a² + b²(a)
10.15² = 8.1² + 6.3²103.0 ≠ 105.3, no(b)
15.31² = 14.4² + 5.2²234.4 = 234.4, yes#a
[tex]\\ \sf\longmapsto H^2=P^2+B^2[/tex]
[tex]\\ \sf\longmapsto (10.15)^2=(8.1)^2+(6.3)^2[/tex]
[tex]\\ \sf\longmapsto 103=65.61+39.69[/tex]
[tex]\\ \sf\longmapsto 103\neq 105.3[/tex]
No
#b
[tex]\\ \sf\longmapsto H^2=P^2+B^2[/tex]
[tex]\\ \sf\longmapsto (15.31)^2=(14.4)^2+(5.2)^2[/tex]
[tex]\\ \sf\longmapsto 234.4=207.3+27.1[/tex]
[tex]\\ \sf\longmapsto 234.4\neq 234.4[/tex]
Yes
6. Jasper pays $42.8 for his cell phone. Marco pays $38.15 for his cell phone plan.
How much more does Jasper pay? Do not use a $ sign. Just type in the numbers.
Answer: 4.65
Step-by-step explanation: 42.80 - 38.15 = 4.65
Derrick earns $14 per hour working at Pizza Palace. What will Derrick's new hourly rate be after a 4.5% raise.
14x4,5÷100=0,63
14+0,63=14,63
2x5 what would 2x5=?
Answer:
10
Step-by-step explanation:
Answer:
10 would be the answer.
Step-by-step explanation:
2+2+2+2+2 Hope this helps!
What is 10 plus 5 to the 3 power minus 1? Order of operation
Step-by-step explanation:
(10+5)³-1 = 3375-1 = 3374.
a pacific seahorse eats about 56 shrimp per week how much does it eat per day
see image above ^^^^
Answer: A reflection, and then a translation.
SOLVE THE CORRECT ANSWER!
1.234.45 added to the difference of 89 and 23.765
2. increase 234.57 by the difference of 5.23 and 2.678
3.subtract 68.501 from the sum of 21.54
and 80.27
please paki answer po ng maayos need ko po ng solution
Step-by-step explanation:
1.
123445+(89-23765)=99769
2.
234.57+(5.23-2.678)=237.122
3
(21.54+ 80.27)-68.501=33.309
Helen counted six dollars and four cents in her purse. She recorded this amount in decimal form as $6.40. Did she record it correctly? If she made a mistake, what is the correct way
to record this amount of money as a decimal?
Pls answer will give brainiest
Answer:
6 dollars and 4 cents
Step-by-step explanation:
15.
The number of calories in a 100-g serving of fruit varies by the type of fruit. A snack consisting of
on serving each of peach, apple, and banana contains 124 calories. A snack consisting of two
servings of peach and one serving of banana contains 160 calories. A snack consisting of one
serving of peach, 2 servings of apple, and two servings of banana contains 188 calories. How
many calories are in a 100-g serving of each type of fruit?
Answer:
A=24, B=40, P=60
Step-by-step explanation:
given:
P+A+B=124
2P+B=160
P+2A+2B=188
___________
P=188-2A-2B
P=124-A-B
188-2A-2B=124-A-B
188-A-B=124
188=124+A+B
A+B=64
___
P+A+B=124
P=60
___
2P+B=160
120+B=160
B=40
___
A+B=64
A=24
___
If we substitute each variable in the three given equations for these values, the equations hold true. Therefore, these are the correct values.
You may use a calculator for this item,
Zach, Kolby, and Peyton are investing a total of $360,000 to open a cottee shop Their investments are in the radio
1:2:0.5, respectively
How much has Zach invested, in dollars?
Enter your answer in the space provided
Based on the investment ratio and the amount invested, the amount that Zach invested is $102,857.14.
First thing to do is to add up the numbers in the ratio:
= 1 + 2 + 0.5
= 3.5
The amount that Zach invested is:
= Zach's ration/ Sum of ratio x Amount invested
= 1 / 3.5 x 360,000
= $102,857.14
In conclusion, Zach invested $102,857.14.
Find out more at https://brainly.com/question/17061956.
consider the system of equations. which shows an equivalent system of equations?
see attatched
Answer:
A.
Step-by-step explanation:
All choices show the first original equation.
Each choice shows a different second equation.
Take the second original equation:
6x + 5y = 30
Multiply both sides by -5.
-30x - 25y = -150
Answer: A.
Will give brainliest to whoever helps pls
Answer:
for me the picture is blurry sorry
Step-by-step explanation:
Answer:
-23
Step-by-step explanation:
Solve the equation 3x - 2(x + 1) = 2x - 7
Answer:
X=5
Step-by-step explanation:
Collect like terms then move the terms. Then collect liked terms. Calculate and Chang signs
Answer:
X = 5
Remember, x has a hidden one behind it, so it would be 1x
3x - 2(x + 1) = 2x - 7
Use the distributive property to multiply −2 by x+1.
3x−2x−2=2x−7
Combine 3x and −2x to get x
x−2=2x−7
Subtract 2x from both sides
x−2−2x=−7
Combine x and −2x to get −x
−x−2=−7
Add 2 to both sides
−x=−7+2
Add −7 and 2 to get −5
−x=−5
multiply both sides by -1
x=5
how do I make this as simplest form
qns: 5 2/3 + 3 1/10
pls answer
the prod. is 8 23/30
Answer:
That is the final product
Step-by-step explanation:
According to all sites I used, they all said that was in the simplest form and cannot be simplified lower than that.
HELPPP LAST ATTEMPT!!
Answer:
Here’s something I wrote that can help you. I don’t really wanna do transformations but this should help you get the answer in a snap.
ONLY FOR REFLECTIONS
Over the x-axis: (x, y) — > (x, –y)
Over the y-axis: (x, y) — > (–x, y)
Over the line y = x: (x, y) — > (y, x)
Through the origin: (x, y) — > (–x, –y)
So for example E is (6,-1)
Over the y axis so following the coordinate plane rules, (6,-1) — > (-6, -1)
(-6, -1) over x axis which is following the rules
(-6, -1) — > (-6, 1)
Final answer (-6,1)
Answer:
(-6, 1)
Step-by-step explanation:
If you reflect over y-axis and x-axis it is just the opposite of each number.
5. Mohan and Sohan have the same storybook. Mohan has read 2/5 of the book and Sohan has read 2/7 of the book. Who has read more pages? 6. Sonali and Priya are classmates Sonali completed her homework in a of an hour and Priya in of an hour 3/4 . Who was faster?
#5
Mohan read =2/5Sohan read=2/7Compare
[tex]\\ \sf\longmapsto \dfrac{2}{5}>\dfrac{2}{7}[/tex]
Mohan read more pages.#6
Sonali completed in=1/2Priya completed in=3/4[tex]\\ \sf\longmapsto \dfrac{1}{2}=\dfrac{2}{4}[/tex]
Compare
[tex]\\ \sf\longmapsto \dfrac{2}{4}<\dfrac{3}{4}[/tex]
Sonali was faster
Roger’s office building has a $320,000 value, a 2 rating, and a B building classification. The contents in the building are valued at $105,000. Calculate his total annual premium.
Answer:
2,230
Step-by-step explanation:
In year one the population of rabbits is 100. In year three the population is 300. Assuming the population is to go unchecked and is linear what will be the population in year 10? Construct a formula for this.
Answer:
the rabbits ran away
Step-by-step explanation:
now its 300 rabbits
a. Does it take more cups or gallons to measure the amount of water in a large
a
pot? Explain.
Which relation is not a function?
The number of eggs Mia can sell varies directly with the number of chickens she owns. The more hens she owns, the more
eggs she can sell. If she has 38 eggs each week when she owns 6 chickens, then how many eggs will she get if she has 15
chickens?
If there are 15 chickens. Then the number of eggs will be 95.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
The number of hens Mia has directly affected how many eggs she can sell. She can sell more eggs if she has more chickens. If she has 6 hens and produces 38 eggs every week.
Let the number of eggs be x. Then the equation is written as,
x / 15 = 38 / 6
x = 95
If there are 15 chickens. Then the number of eggs will be 95.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ2
Given (x – 7)2 = 36, select the values of x.
x = 13
x = 1
x = –29
x = 42
Answer:
x = 13 and x = 1
Step-by-step explanation:
(x-7)² = 36
simplify left side of equation
x² - 14x + 49 = 36
Our object now is to get every thing on the left side of the equal sign so we can factor. To do this, we subtract 36 from both sides
x² - 14x + 13 = 0
we then factor the left side of the equation
( x - 1 ) ( x - 13 ) = 0
we then set factors equal to 0 and solve both factors for x
x - 1 = 0
add 1 to both sides
x = 1
x - 13 = 0
add 13 to both sides
x = 13
The values of x are x = 13 and x = 1
I will give Brainliesttttt :D!
A car's gas mileage is the distance it can go using 1 gallon of gas (measured in miles per gallon).
Based on the graph, what is this car's gas mileage? Explain.
Answer:
20 mpg
Step-by-step explanation:
Answer:
The car is traveling 20 miles per gallon.
Step-by-step explanation:
There are two ways you can solve this.
1) Since this is a graph of the car's gas mileage, all you have to do is look to find the miles for one gallon, which is plotted in this case. As you can see, for one, it is plotted halfway between 0 and 40, so that means the mile number would be 20. Looking at this, the car travels 20 miles per gallon.
2) You can also look at the point at the top that is clearly defined, and the point is (12, 240), 12 gallons used for 240 miles. To get the exact number of miles for one mile, you would divide 12 and 240 both by 12, which results in (1, 20). Since it is miles per gallon, the car gas mileage is 20 miles per gallon.
Hope this helped and have a great day!
