Answer:
Length of pipe to Chesterville is 8.376 miles and
Length of pipe to Denton is 5.46 miles
Step-by-step explanation:
Here we have
The distance of Chesterville from the river is 3 miles, while the distance of Denton from the river is 5 miles
The bank of the river is 10 miles long
Therefore, we have
If x is the distance from the point directly opposite to Chesterville to the location of the water works, the equation is;
Cost to Chesterville = [tex]3000\times \sqrt{x^2 + 3^2}[/tex]
Cost to Denton = [tex]7000\times \sqrt{(10-x)^2 + 5^2}[/tex]
Total cost is then;
[tex]7000\times \sqrt{(10-x)^2 + 5^2} + 3000\times \sqrt{x^2 + 3^2}[/tex]
We differentiate the above equation and equate it to zero to get the minimum cost as
[tex]\frac{\mathrm{d} (7000\times \sqrt{(10-x)^2 + 5^2} + 3000\times \sqrt{x^2 + 3^2})}{\mathrm{d} x}[/tex] = 0
[tex]7000\frac{2x-20}{2\sqrt{x^2-20x+125} } +3000\frac{2x}{2\sqrt{x^2+9} } = 0[/tex]
[tex]3500\frac{2x-20}{\sqrt{x^2-20x+125} } = -1500\frac{2x}{\sqrt{x^2+9} }[/tex]
[tex]3500\frac{\sqrt{x^2+9}}{\sqrt{x^2-20x+125} } = -1500\frac{2x}{2x-20 }[/tex]
[tex]x^4-20x^3+10.54x^2-22.05x+110.25 =0[/tex]
Solving the quartic equation we get
x = 7.82 miles
Therefore the length of is given as
Length of pipe to Chesterville [tex]\sqrt{7.82^{2} +3^2 } = 8.376 \, miles[/tex]
Length of pipe to Denton = [tex]\sqrt{(10-7.82)^2 + 5^2} = 5.46 \, miles[/tex].
A conical perfume bottle has a radius of 3.4 centimeters and a height of 4.8 centimeters . Using 3.14 for pi, approximately how much perfume can the bottle hold ?
Answer:
58.077 cubic cm
Step-by-step explanation:
Given that:
height : 4.8 cm radius: 3.4 cmAs we know that, the volume of a conical perfume bottle is as following:
V = (1/3) * π * r² * h
So perfume can the bottle hold is:
V = (1/3) * 3.14 * 3.4² * 4.8 = 58.077 cubic cm
Hope it will find you well
Answer:
[tex]V \approx 58.107\,cm^{3}[/tex]
Step-by-step explanation:
The volume of a cone is:
[tex]V = \frac{1}{3}\pi\cdot r^{2}\cdot h[/tex]
Where:
[tex]r[/tex] - Radius, in centimeters.
[tex]h[/tex] - Height, in centimeters.
The volume of liquid that bottle can hold is:
[tex]V = \frac{1}{3}\pi \cdot (3.4\,in)^{2}\cdot (4.8\,cm)[/tex]
[tex]V \approx 58.107\,cm^{3}[/tex]
A bag contains 100 cubes that are black, yellow, and white. A student randomly selects a cube without looking and replaces it in the bag. If the student selected 9 black cubes, 4 yellow cubes, and 7 white cubes, which of the options below show a reasonable estimate for the total number of a certain cube in the bag? Select all that apply.
A) 45 black cubes
B) 20 yellow cubes
C) 70 white cubes
D) 90 black cubes
E) 35 white cubes
Answer:
The answer is..
A) 45 black cubes
B) 20 yellow cubes
E) 35 white cubes
Step-by-step explanation:
Final answer:
To estimate the total number of a certain cube in the bag, we can use the proportion of the selected cubes to the total number of cubes. The estimates for the total number of a certain cube in the bag are 45 black cubes and 20 yellow cubes.
Explanation:
To estimate the total number of a certain cube in the bag, we can use the proportion of the selected cubes to the total number of cubes. In this case, the proportion of black cubes to the total number of cubes is 9/20. So, if there are 100 cubes in total, we can estimate that there are approximately 45 black cubes in the bag. Similarly, the proportion of yellow cubes to the total number of cubes is 4/20, so we can estimate that there are approximately 20 yellow cubes in the bag. However, the proportion of white cubes to the total number of cubes is 7/20, which is less than the proportion of yellow cubes. Therefore, we cannot estimate that there are 70 white cubes in the bag. The estimates for the total number of a certain cube in the bag are A) 45 black cubes and B) 20 yellow cubes.
The diagonal of a rectangle is 25 in. The width is 15 inches. What is the length
Answer:
a= 20
Step-by-step explanation:
We can use the Pythagorean theorem to solve
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
The diagonal is the hypotenuse and the length and width are the legs
a^2 + 15^2 =25^2
a^2 +225 = 625
Subtract 225 from each side
a^2+225-255=625-225
a^2 = 400
Take the square root of each side
sqrt(a^2) =sqrt(400)
a = 20
a circle is centered on point B. Points a, c and d lie on its circumference.
if angle ADC measures 23°, what does angle ABC measure?
Answer:
[tex]m\angle ABC=46^o[/tex]
Step-by-step explanation:
step 1
we know that
The inscribed angle is half that of the arc it comprises.
so
[tex]m\angle ADC=\frac{1}{2}(arc\ AC)[/tex]
we have
[tex]m\angle ADC=23^o[/tex]
so
[tex]23^o=\frac{1}{2}(arc\ AC)\\arc\ AC=46^o[/tex]
step 2
we know that
Central angle is the angle that has its vertex in the center of the circumference and the sides are radii of it
so
[tex]m\angle ABC=arc\ AC[/tex] ----> by central angle
therefore
[tex]m\angle ABC=46^o[/tex]
At the bulk food store, Stacey bought 7 pounds of nuts. She used 8 ounces of nuts in a recipe and then put the rest of the nuts into small bags to use for snacks. If each small bag contained 4 ounces of nuts, how many small bags of nuts did Stacey make
Stacey made 26 small bags of nuts.
To solve this problem, let's first convert all measurements to the same unit, ounces, so we can compare them easily.
Stacey bought 7 pounds of nuts. Since 1 pound is equal to 16 ounces, 7 pounds would be 7×16=112 ounces.
She used 8 ounces of nuts in a recipe.
So, the amount of nuts she had left after using them in the recipe would be 112−8=104 ounces.
Now, if each small bag contains 4 ounces of nuts, we can find out how many small bags she made by dividing the remaining nuts by the amount in each bag:
[tex]\begin{aligned}& \text { Number of small bags }=\frac{\text { Remaining nuts }}{\text { Nuts per bag }}=\frac{104 \text { ounces }}{4 \text { ounces per bag }} \\& =\frac{104}{4} \\& =26\end{aligned}[/tex]
So, Stacey made 26 small bags of nuts.
2) A pharmacist has 60 ml of an 8% alcohol solution. How much water should be evaporated so that the solution that remains is 10% alcohol?
Answer:
let water evaporated be x ml
...
acid 8% ------60 ml
...
final quantity = 10% ----(60-x)
..
60*8 = 10(60-x)
480=600-10x
10x=600-480
10x= 120
/10
x=12 ml should be evaporated.
Step-by-step explanation:
Robin and Evelyn are playing a target game. The object
of the game is to get an object as close to the center as
possible. Each player's score is the number of
centimeters away from the center. Robin's mean is 107,
and Evelyn's mean is 138. Compare the means. Explain
what this comparison indicates in the context of the data.
Who is winning the game? Why?
Answer:
The mean is all the numbers added together divided by the number of numbers. Greater the numbers the greater the mean. Since the goal of the game is to have as few centimeters away as possible the lowest number (107 or Robin) is winning
Step-by-step explanation:
Answer:
Evelyn has the greater mean. It indicates that, on average, her objects landed farther away from the center than Robin’s. This difference means that Robin is winning the game.
Step-by-step explanation:
this is the answer on the curst platform
A letter is selected from the word EXAMINATIONS. What is the probability that the letter selected is N?
Answer:
2/1
then simplify it
= 1/6
The probability of selecting the letter 'N' from the word EXAMINATIONS is 1/6 or approximately 16.67%.
The word EXAMINATIONS consists of 12 letters, and the letter 'N' appears twice in this word. The probability of selecting an 'N' from the word is calculated by dividing the number of occurrences of 'N' by the total number of letters in the word. Therefore, the probability is 2/12, which simplifies to 1/6.
To express this mathematically, the probability P of selecting 'N' from EXAMINATIONS is given by P = n/N, where n is the number of times the event 'selecting N' occurs, and N is the total number of possible outcomes (total letters in the word).
So, P = 2/12 = 1/6. Therefore, the probability of selecting 'N' is approximately 0.1667, or 16.67%.
The question is Fiona's swimming pool is a right rectangular prism. It holds 137 1/2 cubic feet of water. The length of the pool is 6 1/4 feet. The width of the pool is 5 1/2 feet. What is the height of the pool? I searched it up but it gave me different questions that have the name Fiona. I was wondering if you were able to answer it.
Answer:
The width is 4 feet
Step-by-step explanation:
Yes, I might be able to answer it! Hello there!
In this question, we are asked to calculate the height of a pool which has a shape of right rectangular prism.
The key to solving this problem is simply by knowing the formula for the volume of a right rectangular prism.
Mathematically the volume V is w * h * l where w , h and l are the width, height and length respectively.
Now let’s input these values and get what the height of the pool is.
It would be easier if you had the measurements are in decimals;
137 1/2 becomes 137.5
6 1/4 becomes 6.25
5 1/2 becomes 5.5
kindly note the fraction 1/2 is 0.5 in decimals while the fraction 1/4 is 0.25 in decimals
So now let’s compute the height;
137.5 = w * 6.25 * 5.5
w = 137.5/(6.25 * 5.5)
w = 137.5/(34.375)
w = 4 feet
The time t required to empty a tank varies inversly as the rate r of pumping. If a pump can empty a tank in 35 min at the rate of 800kL per minute, how long will it atake the pump to empty the same tanks at the rate of 1400kL per minute?
Answer: It will take the pump 20 min
Step-by-step explanation: Please see the attachments below
find the missing side length
please help :)
Answer:
14
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
So we know that triangle ABC and QRS are similar.
There is a theorem that states that corresponding sides of similar triangles are proportional.
This means that we can set up a proportion to find the missing side of the triangle.
3/7=6/n
Cross multiply.
3*n=7*6
3n=42
Divide both sides by 3.
n=14
Alexis is knitting a blanket 6 meters long. Every 3 decimeter, she changes the color of the yarn to make stripes. How many stripes will the blanket have?
Answer:
There are 20 color strips in the blanket.
Step-by-step explanation:
We are given the following in the question:
Length of blanket = 6 meter
A new color strip is added every 3 decimetres
We have to find the number of color strips in the blanket.
1 decimetre = 0.1 meter
Number of color strips =
[tex]=\dfrac{\text{Length of blanket}}{\text{Color strip every 3 decimeter}}\\\\=\dfrac{6}{3\times 0.1}\\\\=20[/tex]
Thus, there are 20 color strips in the blanket.
Why x and 4x -10 are factors of the expression x(4x - 10)3 rather than terms of the expression.what are the terms of the factor 4x - 10?
Answer:
4x-10Step-by-step explanation:
A "term" is a (signed) number, variable, or product of numbers and variables, separated from other terms by + or - signs. That is, it is the largest such product that includes any given number or variable.
A "factor" is a piece of a product. It is multiplied by other factors to form a product. It can be a (signed) number or variable or some expression.
One way to think of it is that terms are delimited (separated) by + or - signs. Factors are delimited by × or / signs.
__
The terms of 4x -10 are "4x" and "-10".
_____
The sign typically goes with the term. That is, an expression is a sum of terms.
What’s the dependent probability of this?
"A spinner has an equal chance of landing on each of its six numbered regions. You spin twice. The first spin lands in region one and the second spin lands in region three"
i believe the answer is independant.
if i'm wrong, please tell me so i can fix my mistake =)
Final answer:
The probability of a spinner, with equal chances of landing on any of its six regions, landing on Region 1 first and then on Region 3 in a second spin is 1/36, reflecting independent events.
Explanation:
The question concerns the concept of dependent probability, which involves calculating the likelihood of a sequence of events where the outcome of one event affects the outcome of another.
Since the spinner has an equal chance of landing on each of its six numbered regions, the probability of the first spin landing in region one is 1/6.
However, the second spin is independent of the first, making the probability of landing in region three also 1/6. Since these are independent events, the combined probability of both events happening in sequence is the product of their probabilities, which is 1/6 x 1/6 = 1/36.
If P=x²-yz , Q=y²-x² ,R=z²-xy, Then find PQR
[tex]PQR=( {x}^{2} - yz)( {y}^{2} - {x}^{2} )( {z}^{2} - xy) = \\ = {x}^{2} {y}^{2} {z}^{2} - {x}^{3} {y}^{3} - {x}^{4} {z}^{2} + {x}^{5} y - {y}^{3} {z}^{3} + \\ + x {y}^{4} z + xy {z}^{3} - {x}^{2} {y}^{2} z[/tex]
I don't know if it was necessary to open the brackets, but I think you can write it like this:
[tex]PQR=( {x}^{2} - yz)( {y}^{2} - {x}^{2} )( {z}^{2} - xy) \\ [/tex]
There are about 31{,}500{,}00031,500,00031, comma, 500, comma, 000 seconds in a year.
Choose the best approximation of the number of seconds in a year.
The closest approximation to the number of seconds in a year is [tex]3\times10^7[/tex], which is option B.
There are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day. So, to find the number of seconds in a day, you would multiply these values together:
[tex]\[60 \text{ seconds/minute} \times 60 \text{ minutes/hour} \times 24 \text{ hours/day} = 86,400 \text{ seconds/day}.\][/tex]
In a year, there are typically 365 days. So, to find the total number of seconds in a year, you would multiply the number of seconds in a day by the number of days in a year:
[tex]\[86,400 \text{ seconds/day} \times 365 \text{ days/year} = 31,536,000 \text{ seconds/year}.\][/tex]
Since [tex]\(31,536,000\)[/tex] is closest to [tex]\(3 \times 10^7\)[/tex], the best approximation among the given options is B) [tex]\(3 \times 10^7\).[/tex]
Complete Question:
There are about 31,500,000 seconds in a year ?
Choose the best approximation of the number of seconds in a year
A) 3x[tex]10^6[/tex]
B) [tex]\(3 \times 10^7\).[/tex]
Perry sells TVs at an electronics store. He makes a 15% commission for every TV he sells. How much would he have to sell a single TV for to make a $72 commission?
Answer:
$480
Step-by-step explanation:
Perry makes 15% commission for each TV he sells.
How much would he have to sell a TV to get $72
First of all, let's call the unknown variable x
So 15% of x= $72
Mathematically, this would be represented as 15/100 * x= 72
15/100x= 72
Breaking down further,
15/100 can be broken down to 3/20
3/20x= 72
So to find the value of x, we divide both sides by 3/20
x= 72 ÷ 3/20
x= 72 * 20/3 (using the law of indices)
x= 1440/3
x= $480 dollars.
So, Perry would have to sell a TV for $480 to make a $72 commission.
What is a possible measure of an angle that has a terminal side in Quadrant III and makes a 60degree angle with the x -axis
Answer:
[tex]240^\circ[/tex]
Step-by-step explanation:
See the attached picture. One possible angle measure is [tex]60^\circ+180^\circ=240^\circ[/tex]
The possible measure of an angle with terminal side in 3rd quadrant and making an angle of 60°with the X-axis is 240°.
What is the terminal side of an angle?When the vertex of an angle is at the origin and one ray is on the positive x-axis, it is said to be in standard position. The ray on the x-axis is known as the starting side, while the ray on the y-axis is known as the terminal side.
The question is shown in the figure below:
The angle made with X - axis = 60°
Angle is lying in 3rd quadrant
If we start moving in the anticlockwise direction then the measure of the total angle will be 180° + 60° = 240°.
Hence, the total angle for an angle lying in 3rd quadrant is 240°.
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What is the radius and diameter of the following circle?
7 cm
Diameter =
-
Answer:
Radius =
Diameter =
Answer:
Diameter = 7cm
Radius = 3.5cm
Step-by-step explanation:
The diameter is the distance across the circle; shown as 7cm.
The radius is half the distance of the diameter, or half the distance across the circle.
Answer:
Radius = 3.5
Diameter = 7
Step-by-step explanation:
Radius = half of diameter
Diameter is the 7 cm you see on the image.
30+30-2 hi brainly people and I
Answer:
58
Step-by-step explanation:
Order of operations.
Additions and subtractions, in the order they appear, from left to right.
30 + 30 - 2 =
= 60 - 2
= 58
This is a building on the grounds of the us Air Force academy in Colorado featuring a glass skylight resembling the tail of a jet fighter that points towards the North Star the building is 150 feet tall and to estimate its area we should use which geometric solid
Answer:
Pyramid
Step-by-step explanation:
Which is the simplified form of the expression (x^-3)(y^2)/(x^4)(y^6)
Pls mark Brainliest.
Answer:
If we write the final answer with negative exponents, then it will be:
(x^-7)(y^-4)
If we write this as a fraction, it will be:
1/(x^7)(y^4)
Step-by-step explanation:
x^-3 is equivalent to 1/x^3. We can put this in the denominator expression and calculate the product:
[tex]\frac{y^{2} }{(x^4)(x^3)(y^6)}[/tex] This simplifies into:
[tex]\frac{y^{2} }{(x^7)(y^6)}[/tex] after the denominator simplifies.
If we write the final answer with negative exponents, then it will be:
(x^-7)(y^-4)
If we write this as a fraction, it will be:
1/(x^7)(y^4)
The simplified form of [tex]\(\frac{{x^{-3} \cdot y^2}}{{x^4 \cdot y^6}}\)[/tex] is [tex]\(\frac{1}{{x^7 \cdot y^4}}\)[/tex], with all exponents as positive values in the denominator.
To simplify the expression [tex]\(\frac{{x^{-3} \cdot y^2}}{{x^4 \cdot y^6}}\)[/tex], we can apply the rules of exponents. First, we subtract the exponent in the denominator from the exponent in the numerator for each variable (x and y).
For x, we have [tex]\(x^{-3 - 4} = x^{-7}\)[/tex], and for y, we have [tex]\(y^{2 - 6} = y^{-4}\)[/tex].
So, the expression simplifies to [tex]\(x^{-7} \cdot y^{-4}\).[/tex]
To express this in a more conventional form, we can move the negative exponents to the denominator, resulting in [tex]\(\frac{1}{{x^7 \cdot y^4}}\).[/tex]
In this simplified form, the expression has all positive exponents and represents the same mathematical relationship as the original expression but in a more compact and manageable format.
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2/3=z/15 what is z?
Please help
Answer:
z=10 because 3x5=15 and you do the same to the other number.
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
To get from 3 to 15 you multiply by 5 so if you multiply 2 by 5 you get 10
Noah randomly selects one of his eight different pairs of shoes to wear each day. Of his eight pairs of shoes, Noah has two pairs of boots and one pair of loafers. For how many days of the next 264 is it expected that Noah will wear either boots or loafers?
Answer:
The expected number of times that Noah wears either boots or loafers is 99.
Step-by-step explanation:
Given:-
- Noah has 8 different pairs of shoes to wear, Out of 8 pairs:
two pairs of boots
one pair of loafers
Find:-
For how many days of the next 264 is it expected that Noah will wear either boots or loafers?
Solution:-
- Denote an Event (A) that Noah selects a pair of boots.
- Denote an Event (B) that Noah selects a pair of loafers.
- The probability of each event is to be determined:
p ( A ) = Pair of boots / Total pair of shoes
p ( A ) = 2 / 8
p ( A ) = 1/4
p ( B ) = Pair of loafers / Total pair of shoes
p ( B ) = 1 / 8
- The probability that Noah selects a pair of boot or loafers is independent from each other:
p ( A U B ) = P (A) + P (B)
p ( A U B ) = 0.25 + 0.125
= 0.375
- The expected number of days out n = 264 days do we expect Noah to wear either boots or loafers.
- The number of days (trials) n = 264 days
- The probability of success = p ( A U B ) = 0.375
- The expected value = n*p
= 264*0.375
= 99 days
Big guy up there done wrote a whole pg. The answer is 99 days. Have a good day.
Lucia is making invisibility potions. Each potion requires 222 eyes of newt. How many invisibility potions can Lucia make with 161616 eyes of newt? Lucia has all of the other ingredients she needs.
We have been given that Lucia is making invisibility potions. Each potion requires 2 eyes of newt. We are asked to find the number of invisibility potions that Lucia can make with 16 eyes of newt.
We will use proportions to find the number of potions that Lucia can make with 16 eyes of newt as:
[tex]\frac{\text{Invisibility potions}}{\text{Number of Newt eyes}}=\frac{1}{2}[/tex]
[tex]\frac{\text{Invisibility potions}}{16}=\frac{1}{2}[/tex]
[tex]\frac{\text{Invisibility potions}}{16}\times 16=\frac{1}{2}\times 16[/tex]
[tex]\text{Invisibility potions}=8[/tex]
Therefore, Lucia can make 8 invisibility potions with 16 eyes of newt.
A line with a slope of -2 passes through the point (4, 7).
What is an equation for this line in point-slope form? ( the brackets are blanks, fill in the blanks)
y - 7 = [ ] (x - [ ])
Answer:
y-7= -2 (x-4)
Step-by-step explanation:
We can use the point slope formula, since we have a point, and a slope
[tex]y-y_{1} =m(x-x_{1})[/tex]
m is the slope, y1 is the y coordinate of the point, and x1 is the x coordinate of the point
We know -2 is the slope, 7 is the y coordinate, and 4 is the x coordinate, so we can substitute them in
y-7= -2 (x-4)
Since we don't need to solve, this is the answer. The first bracket is -2, and the second is 4
Point-slope form: y - y₁ = m(x - x₁)
(m is the slope, (x₁, y₁) is the point you are given that's on the line)
You know:
m = -2
(x₁, y₁) = (4, 7) So plug it into the equation
y - y₁ = m(x - x₁)
y - 7 = -2(x - 4)
[so the first bracket is -2, the second bracket is 4]
PLEASE ANSWER THIS QUICKLY!! I WILL GIVE BRAINLIEST!!!
The monthly demand for a company's sports caps varies directly as the amount spent on advertising and inversely as the square of the price per cap. At $15 per cap, when $2750 is spent each week on ads, the demand is 330 caps. When advertising is increased to $3250, what price yields a demand of 330 caps? (Round your answer to the nearest cent.)
I think it's $16.432 but I'm not sure.
The price per cap yielding demand of 330 caps when advertising is increased to $3250 is 16.51 per cap.
What is algebra ?
Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.
It is given that at $15 per cap , $2750 is spent each week on ads , and demand is 330 caps.
So , we can find how much money earn if cost is $15 per cap.
As 330 is the demand , then total earning is :
= 330 × 15
= $ 4950
Out of this , $2750 is spent per week on ads. So , total profit is :
= 4950 - 2750
= $ 2200
Now , If advertising is increased to $3250 then , money more spent on ads is :
= 3250 - 2750
= 500
So , total earning will be :
= 3250 + 2200
= 5450
And price per cap for demand of 330 caps will be :
= 5450 ÷ 330
= 16.51 per cap
Therefore , the price per cap yielding demand of 330 caps when advertising is increased to $3250 is 16.51 per cap.
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(3x2 - 4x +8)+(-x2 – 2x – 8)
Hey there,
The question given is as follows:
(3x² - 4x + 8) + (-x² - 2x - 8)When we add polynomials we add like terms (e.x. we add 3x² with -x²) and combine the two to make one polynomial. When we add the two polynomials given above:
2x² - 6x + 0So our answer to the problem would be 2x² - 6x.
Hope I helped,
Amna
The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds. The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition from the fitness association
Answer:
The time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.
Step-by-step explanation:
We are given that the time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds.
The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition.
Let X = time for this event for boys in secondary school
SO, X ~ Normal([tex]\mu=460,\sigma^{2} =40^{2}[/tex])
The z-score probability distribution for normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean time = 460 seconds
[tex]\sigma[/tex] = standard deviation = 40 seconds
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, it is given that the fitness association wants to recognize the fastest 10% of the boys with certificates of recognition, which means;
P(X > x) = 0.10 {where x is the required time which boy need to beat}
P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-460}{40}[/tex] ) = 0.10
P(Z > [tex]\frac{x-460}{40}[/tex] ) = 0.10
So, the critical value of x in the z table which represents the top 10% of the area is given as 1.2816, that is;
[tex]\frac{x-460}{40} =1.2816[/tex]
[tex]{x-460}{} =1.2816\times 40[/tex]
[tex]x[/tex] = 460 + 51.264 = 511.264 seconds
Hence, the time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.
Megan's quiz scores for the quarter are 85%, 99%, 98%, and 87%. What would Megan have to score
on the fifth quiz to have an overall average of 93%?
Answer:
96%
because if you add all of them up then add 96 then divid by 5 you get 93 which is the average.
hope this helps :)