The correct answer is $15
Explanation:
The first step is to determine the total of oil that was used for the 5 batches. To find this, you just need to multiply the amount of oil used for one batch by the total batches.
1 cup of oil per batch x 5 batches = 5 cups of oil
This means, in the 5 batches the oil Dinesh used was 5 cups of oil. Additionally, you know the total of cups in the bottle of oil is 12 cups, and these 12 cups or total costs $36. Now to find what is the cost of the 5 cups use the rule of three and cross multiplication.
12 cups of oil = $36 1. Write the values
5 cups of oil = x
12 x = 180 2. Cross multiply this means 36x 5 and 12 multipy by x
x = 180 ÷ 12 3. Solve the equation
x= 15 - Cost for 5 cups used in the batches
At which times could rory phone have been plugged into the charger?select three options
Answer:
9hrs 11hrs 19hrs
Step-by-step explanation:
just took the quiz on edge 2020
Answer:
9 hours, 11 hours, 19 hours.
Will has 2 quarters, 6 dimes, some nickels, and 4 pennies. If the ratio of pennies to the total number of coins he has is 1:5, how many nickels are there?
Answer:
8 nickels
Step-by-step explanation:
Let n be the number of nickels.
4: (2+ 6 + 4 + n) = 1:5
4÷(12 + n) = 1÷5
4 x 5 = 1 x (12 + n)
20 = 12 + n
n = 8
Meguel does not understand which digit is in the tenths location in the number 514.196 Where would it be located at
Answer:
first number after the decimal point
Step-by-step explanation:
after the decimal point is the tenths, hundredths, and thousandths place.
0.1 - tenths
0.09 - hundredths
0.006 - thousandths
-8+4x-12=-4(2x-8) help me plz
Answer:
x = 13/3Step-by-step explanation:
[tex]-8+4x-12=-4\left(2x-8\right)\\\\\mathrm{Group\:like\:terms}\\\\\mathrm{Subtract\:the\:numbers:}\:-8-12=-20\\\\4x-20=-4\left(2x-8\right)\\\\\mathrm{Expand\:}-4\left(2x-8\right):\quad -8x+32\\4x-20=-8x+32\\\\\mathrm{Add\:}20\mathrm{\:to\:both\:sides}\\4x-20+20=-8x+32+20\\\\Simplify\\\\4x=-8x+52\\\\\mathrm{Add\:}8x\mathrm{\:to\:both\:sides}\\\\4x+8x=-8x+52+8x\\\\\mathrm{Simplify}\\\\12x=52\\\\\mathrm{Divide\:both\:sides\:by\:}12\\\\\frac{12x}{12}=\frac{52}{12}\\\\x=\frac{13}{3}[/tex]
Answer:
Step-by-step explanation:
-8+4x-12 =-8x+32
4x+8x=32+8+12
12x=52
x=52\12
x=41.3
Ernesto solves the equation below by first squaring both sides of the equation. \sqrt{\dfrac{1}{2}w+8}=-2 2 1 w+8 =−2square root of, start fraction, 1, divided by, 2, end fraction, w, plus, 8, end square root, equals, minus, 2 What extraneous solution does Ernesto obtain?
Answer:
w = -8Step-by-step explanation:
Given the equation solved by Ernesto expressed as [tex]\sqrt{\dfrac{1}{2}w+8}=-2[/tex], the extraneous solution obtained by Ernesto is shown below;
[tex]\sqrt{\dfrac{1}{2}w+8}=-2\\\\square\ both \ sides \ of \ the \ equation\\(\sqrt{\dfrac{1}{2}w+8})^2=(-2)^2\\\\\dfrac{1}{2}w+8 = 4\\\\Subtract \ 8 \ from \ both \ sides\\\\\dfrac{1}{2}w+8 - 8= 4- 8\\\\\dfrac{1}{2}w= -4\\\\multiply \ both \ sides \ by \ 2\\\\\dfrac{1}{2}w*2= -4*2\\\\w = -8[/tex]
Hence, the extraneous solution that Ernesto obtained is w = -8
Father's age is 3 times the sum of ages of his two children. After 5 years his age will be twice the sum of ages of two children. Find the age of father.
Answer:
45 is the father's age
Step-by-step explanation:
solution for 2x is equal to 10
Answer:
The answer is 5
Step-by-step explanation:
divide 10 by two and get 5
Answer:
[tex]x = 5[/tex]
Step-by-step explanation:
We have the equation [tex]2x = 10[/tex], we can try and isolate x by dividing both sides by 2.
[tex]2x \div 2 = 10\div2\\x = 5[/tex]
Hope this helped!
Archer receives a day's work of pay, p, for 5 days of mowing lawns. He spent half of his money on gas. Then he spent $5 on water. Now, he has $40 left. Which equation represents how much Archer would get paid each day of mowing lawns?
Answer:
Daily pay= $18
5 days pay = $90
Step-by-step explanation:
Archer's daily pay =p
Pay for 5 days= 5p
Gas = 1/2 of 5p
= 1/2 × 5p
= 5p/2
Water = $5
Balance = $40
5p = 5/2p + 5 + 40
5p - 5/2p = 45
10p -5p /2 = 45
5/2p = 45
p= 45÷ 5/2
= 45 × 2/5
= 90/5
P= $18
5p= 5 × $18
=$90
The equation to determine Archer's daily pay is
5p = 5/2p + 5 + 40
Divide both sides by 5
p = 5/2p + 45 ÷ 5
= (5/2p + 45) / 5
p= (5/2p + 45) / 5
What are the solutions to the equation 3(x – 4)(x + 5) = 0? x = –4 or x = 5 x = 3, x = 4, or x = –5 x = 3, x = –4, or x = 5 x = 4 or x = –5
Answer:
x= 4 x = -5
Step-by-step explanation:
3(x – 4)(x + 5) = 0
Using the zero product property
(x – 4)=0 (x + 5) = 0
x= 4 x = -5
What are the solutions to the equation 3(x – 4)(x + 5) = 0?
x = –4 or x = 5
x = 3, x = 4, or x = –5
x = 3, x = –4, or x = 5
x = 4 or x = –5
Answer:
D. x = 4 or x = –5
Step-by-step explanation:
A model of a wedge of cheese is used in a display for a deli. All the sides of the model are covered in yellow construction paper. A rectangular prism has a rectangular base with length of 15 centimeters and height of 5 centimeters. Another rectangle has length of 15 centimeters and height of 13 centimeters. Another rectangle has length of 15 centimeters, and height of 12 centimeters. The triangular sides have a base of 5 centimeters and heights of 12 centimeters. How much construction paper is needed for the model? 45 square cm 330 square cm 510 square cm 570 square cm
Answer:
510 cm²
Step-by-step explanation:
To find how much construction paper is needed for the model, we calculate the total areas of each of its sides.
The area of the first triangular sides is A₁ = 15 cm × 5 cm = 75 cm²
The area of the second triangular sides is A₂ = 15 cm × 13 cm = 195 cm²
The area of the third triangular sides is A₃ = 15 cm × 12 cm = 180 cm²
The area of each triangular side is A₄ = 1/2 × 5 cm × 12 cm = 30 cm²
The area of the two triangular sides is A₅ = 2A₄ = 2 × 30 cm² = 60 cm²
The total surface area of a wedge of cheese is A = A₁ + A₂ + A₃ + A₅ = 75 cm² + 195 cm² + 180 cm² + 60 cm² = 510 cm²
So the amount of construction paper needed equals the total surface area of the wedge of cheese = 510 cm²
Answer:
510
Step-by-step explanation:
What are the domain and range of the real-valued function f(x)=2/(x+5)?
Answer:
Domain is all real numbers, x ≠ -5
Range is all real numbers, y ≠ 0
Step-by-step explanation:
The Fairy Tale Spectacular is coming to town. Admission to the fair costs $32.50 and each ride costs $0.80. You have $50 to spend at the Fairy Tale Spectacular including admission. Write and solve an inequality to determine the maximum number of rides you can enjoy at the Fairy Tale Spectacular?
Answer:21
Step-by-step explanation:
50-32.5=17.5
17.5/0.8=21.875
Cody is a lifeguard and spots a drowning child 40 meters along the shore and 70 meters from the shore to the child. Cody runs along the shore for a while and then jumps into the water and swims from there directly to the child. Cody can run at a rate of 4 meters per second and swim at a rate of 1.1 meters per second. How far along the shore should Cody run before jumping into the water in order to save the child? Round your answer to three decimal places.
Answer:
Cody should run approximately 19.978 meters along the shore before jumping into the water in order to save the child.Thus,
Step-by-step explanation:
Consider the diagram below.
In this case we need to minimize the time it takes Cody to save the child.
Total time to save the child (T) = Time taken along the shore (A) + Time taken from the shore (B)
The formula to compute time is:
[tex]time=\frac{distance}{speed}[/tex]
Compute the time taken along the shore as follows:
[tex]A=\frac{x}{4}[/tex]
Compute the time taken from the shore as follows:
[tex]B=\frac{\sqrt{70^{2}+(40-x)^{2}}}{1.1}[/tex]
Then the total time taken to save the child is:
[tex]T=\frac{x}{4}+\frac{\sqrt{70^{2}+(40-x)^{2}}}{1.1}[/tex]
Differentiate T with respect to x as follows:
[tex]\frac{dT}{dx}=\frac{d}{dx}[\frac{x}{4}]+\frac{d}{dx}[\frac{\sqrt{70^{2}+(40-x)^{2}}}{1.1}][/tex]
[tex]=\frac{1}{4}-\frac{1}{1.1}\cdot \frac{(40-x)}{\sqrt{70^{2}+(40-x)^{2}}}[/tex]
Equate the derivative to 0 to compute the value of x as follows:
[tex]\frac{dT}{dx}=0[/tex]
[tex]\frac{1}{4}-\frac{1}{1.1}\cdot \frac{(40-x)}{\sqrt{70^{2}+(40-x)^{2}}}=0\\\\\frac{1}{1.1}\cdot \frac{(40-x)}{\sqrt{70^{2}+(40-x)^{2}}}=\frac{1}{4}\\\\4\cdot (40-x)=1.1\cdot [\sqrt{70^{2}+(40-x)^{2}}]\\\\\{4\cdot (40-x)\}^{2}=\{1.1\cdot [\sqrt{70^{2}+(40-x)^{2}}]\}^{2}\\\\16\cdot (40-x)^{2}=1.21\cdot [70^{2}+(40-x)^{2}}]\\\\16\cdot (40-x)^{2}-1.21\cdot (40-x)^{2}=5929\\\\14.79\cdot (40-x)^{2}=5929\\\\(40-x)^{2}=400.88\\\\40-x\approx 20.022\\\\x\approx 40-20.022\\\\x\approx 19.978[/tex]
Thus, Cody should run approximately 19.978 meters along the shore before jumping into the water in order to save the child.
The polygons in each pair are similar. find the scale factor of the smallest figure to larger figure.
Greetings from Brasil...
It is said that polygons are similar, so we can use the expression of similarity.
BIG/small = BIG/small
35/14 = 25/X
X = 10
But the scale factor is questioned. Just use one of the expressions. We conclude that the largest is 2.5 times the value of the smallest
35/14 OR 40/16 OR 25/10
We get 2.5x-----------------------------------------------------------
BIG/small = BIG/small
25/5 = 40/Y
Y = 8
25/5 OR 25/5 OR 40/8
We get 5xtimes the value of the smallest
Rearrange the equation so x is the independent variable. y+6=5(x-4)
Answer:
x = (y + 26)/5
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out equation
y + 6 = 5(x - 4)
Step 2: Distribute
y + 6 = 5x - 20
Step 3: Isolate x
y + 26 = 5x
Step 4: Isolate variable x
(y + 26)/5 = x
Step 5: Rewrite
x = (y + 26)/5
Answer:
y = 5x - 26
Step-by-step explanation:
Since x is the independent variable, you have to solve for y.
y + 6 = 5(x-4)
Now distribute:
y + 6 = 5x - 20
subtract the 6 from both sides
y + 6 - 6 = 5x - 20 - 6
y = 5x - 26
For a ,a relationship to be a function, which values cannot repeat: the x-
values or the y-values? *
Answer:
The x - valuesThe y-values repeat in various functions (for example: quadratic function: y=x²; y=4 for x=2 and for x=-2)
What is the 6th row of Pascal's triangle?
Answer:
1, 6, 15, 20, 15, 6, 1
A 250.0 kg rock falls off a 40.0 m cliff. What is the kinetic energy of the rock just before it hits the ground (hint: conservation of energy)?
Answer:
kinetic energy body when it hits the ground is 98000 joule
1000joule = 1 kilojoule
, kinetic energy body when it hits the ground is 98 kilo-joule
Step-by-step explanation:
conservation of energy states that total energy of a system remains constant.
Potential energy of body = mgh
m = mass
g = gravitational pull = 9/8 m/s^2
h = height
kinetic energy = 1/2 mv^2
where v is the velocity of body
________________________________________
Total energy for this at any point is sum of potential energy and kinetic energy
total energy at height h
v= 0
PE = 250*9.8*40= 98,000
KE = 1/2 m0^2 = 0
total energy at when ball hits the ground
h=0
PE = 250*9.8*0 =
KE = 1/2 mv^2
_______________________________________\
Applying conservation of energy
Total energy at height h = total energy at ground
98000 = KE
Thus, kinetic energy body when it hits the ground is 98000 joule
1000joule = 1 kilojoule
, kinetic energy body when it hits the ground is 98 kilo-joule
Complex numbers
[ = square root symbol
-[-64
How would I find this?
[tex]-\sqrt{-64}=-\sqrt{8^2\cdot (-1)}-8\sqrt{-1}=-8i[/tex]
4:3=x:6, find the value of x please help me
Answer:
x=8
Step-by-step explanation:
4:3=x:6
Multiply the first set by 2
4*2 : 3*2
8:6
That means x =8
what's the square footage of 12'3" * 18'4"
Answer:
multiply length time width
Compute the range and interquartile range for the data collected for boys and girls. Describe their differences in detail using specific terms of spread. (4 points)
Answer:
The measure of central tendency, mean and median are approximately equal for the boys indicating that the data of the boys is more evenly spread while standard deviation of the girls data is less than those of the boys indicating that the data for the girls is less widely spread.
Step-by-step explanation:
The given data are;
, 1 2 3 4 5 6 7 8 9 10
Girls, 50 32 15 56 81 50 18 81 22 55
Boys, 75 41 25 22 7 0 43 12 45 70
Sorting the data gives;
Girls, 15, 18, 22, 32, 50, 50, 55, 56, 81, 81
Boys, 0, 7, 12, 22, 25, 41, 43, 45, 70, 75
For the even numbered sample data size, the first quartile, Q₁ is found by sharing the data into two and finding the median of the left half which gives;
10/2 = 5 on each half
The first quartile, Q₁, is the median of the left 5 data points which is the 3rd data point = 22 for girls and 12 for boys
The third quartile, Q₃, is found in similar method to be the 8th data point which is 56 for girls and 45 for boys
The median = 50 for girls and 33 for boys
Therefore, the interquartile ranges are;
IQR = 56 - 22 = 34 for girls, 45 - 12 = 33 for boys
We check for outliers.
Q₁ - 1.5×IQR = 22 - 1.5*34 = -29
Q₃ + 1.5×IQR = 56 + 1.5*34 = 107
We check the mean of both data samples as follows;
Average for the girls = 46
Average for the boys = 34
Standard deviation for girls = 23.99
Standard deviation for girls = 25.43
Therefore, the measure of central tendency is more accurate for the boys indicating that the data of the boys is more evenly spread while the data for the girls is less widely spread.
Which of the following best describes the graph shown below?
16
A1
1
14
O A This is the graph of a linear function
B. This is the graph of a one-to-one function
C. This is the graph of a function, but it is not one to one
D. This is not the graph of a function
The vertical line test helps us see that we have a function. Note how it is not possible to draw a single straight line through more than one point on the curve. Any x input leads to exactly one y output. This graph passes the vertical line test. Therefore it is a function.
The function is not one-to-one because the graph fails the horizontal line test. Here it is possible to draw a single straight horizontal line through more than one point on the curve. The horizontal line through y = 2 is one example of many where the graph fails the horizontal line test, meaning the function is not one-to-one.
The term "one-to-one" means that each y value only pairs up with one x value. Here we have something like y = 2 pair up with multiple x values at the same time. This concept is useful when it comes to determining inverse functions.
The axis of symmetry for a quadratic equation can be found using the formula x equals StartFraction negative b Over 2 a EndFraction, where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane. What is the equation when solved for a?
Answer:
[tex]a=-\frac{b}{2x}[/tex]
Step-by-step explanation:
The equation of a quadratic function is given as:
ax² + bx + c = 0
where a, b and c are the coefficient in the quadratic equation.
The axis of symmetry of the quadratic equation is given as:
[tex]x=-\frac{b}{2a}[/tex]
To get the equation for a, we have to make a the subject of formula:
[tex]x=-\frac{b}{2a}\\\\multiply\ both\ sides\ by \ 2a:\\\\x*2a=-\frac{b}{2a}*2a\\\\2ax=-b\\\\Divide\ through\ by\ 2a\\\\2ax/2a=-b/2a\\\\a=-\frac{b}{2x}[/tex]
The value of a when solved from x = -b/2a is;
a = -b/2x
We are given the formula for axis of symmetry of a quadratic equation to be;
x = -b/2a
Where;
a and b are coefficients in the quadratic equation
x represents the values along a vertical line on the coordinate plane.
Now, we want to solve for a which means we make it the subject of the equation;
Using multiplication property of equality, we multiply both sides by 2a to get;
2ax = -b
We now use division property of equality by dividing both sides by 2x to get;
a = -b/2x
Read more at; https://brainly.com/question/3528055
1 liter of ink can print 5000 pages of text. If you had 100 gallons of ink then how many pages could you print?
Answer:
500,000 pages
Step-by-step explanation:
1 / 5000 = 100 / x
x = 5000(100)
x = 500,000
Answer:
1892705 pages of text.
Step-by-step explanation:
g=Gallon
L=Liters
P=Pages
1L=5000p
1g=3.78541L
100g·3.78541L=378.541L
378.541L·5000=1892705
Michael is drawing a card from a standard 52-card deck, which includes 4 aces: the ace of clubs, the ace of diamonds, the ace of hearts, and the ace of spades. For each trial, he drews a card, records which cards he drew, and returns it to the deck. He draws an ace 240 times
Michael is drawing a card from a standard 52-card deck, which includes 4 aces: the ace of clubs, the ace of diamonds, the ace of hearts, and the ace of spades. For each trial, he draws a card, records which cards he drew, and returns it to the deck. He draws an ace 240 times
Of the times he draws an ace, which of the following would be a good estimate for the number of times the ace drawn is the ace of hearts?
Answer:
Step-by-step explanation:
From the information:
Let consider the following variables,
assume p to be the number of times an ace was drawn,
also, q should be the number of aces and r to be the number of outcomes.
Thus ;
[tex]\mathtt{r = \dfrac{p}{q}}[/tex]
where;
p = 240
q = 4
[tex]\mathtt{r = \dfrac{240}{4}}[/tex]
r = 60
It is literally unlikely that exactly 25% of the drawings are going to be the ace of hearts, therefore, the best answer will be 60 or the value closest to 60
Newly planted seedlings approximately double their weight every week. If a seedling weighing 5 grams is planted at time t=0 weeks, which equation best describes its weight, W, during the first few weeks of its life?
Answer:
[tex]W(t)=5(2^t)[/tex]
Step-by-step explanation:
Given that the Newly planted seedlings approximately double their weight every week and a seedling weighing 5 grams is planted at time t = 0 weeks. This represent an exponential function with an equation in the form:
[tex]W(t)=ab^t[/tex].
W(t) is the weight in t weeks, t is the weeks and a is the weight when t = 0. At t = 0, W = 5 g:
[tex]W(t)=ab^t\\W(0)=ab^0\\5=ab^0\\a=5[/tex]
Since the weight double every week, b = 2. The exponential function is given as:
[tex]W(t)=ab^t\\\\W(t)=5(2^t)[/tex]
Mia’s average driving speed is 6 kilometers per hour faster than Kirk’s. In the same length of time it takes Mia to drive 558 kilometers, Kirk drives only 522 kilometers. What is Mia’s average speed?
Answer:
93km/hr
Step-by-step explanation:
Using the formula Speed = Distance/Time. From the formula we can substitute for time as shown;
Time = Distance/Speed
Let the distance and speed travelled by Mia be Dm ans Ds respectively
Distance travelled by Kirk be Km and and Ks respective.
Time taken be Mia to travel Tm = Dm/Sm
Time taken be Kirk to travel Tk = Dk/Sk
Since it takes the same length of time for both of them to travel, then Tm = Tk. Hence Dm/Sm = Dk/Sk
Given parameters
Dm = 558 kilometers
Dk = 522 kilometres
If Mia’s average driving speed is 6 kilometers per hour faster than Kirk’s, then Mia's driving speed Sm = 6 + Sk
Required
Mia’s average speed (Sm)
Since Dm/Sm = Dk/Sk
Substituting the given values to get Sk first we have;
558/6+Sk = 522/Sk
Cross multiply
558Sk = 522(6+Sk)
open the parenthesis
558Sk = 3132 + 522SK
558Sk-522Sk = 3312
36Sk =3132
Sk = 3132/36
Sk =87km/hr
SInce Sm = 6+Sk
Sm = 6+87
Sm = 93km/hr
Hence Mia's average speed is 93km/hr
A circle is circumscribed around a square and another circle is inscribed in the square. If the area of the square is 9 in2, what is the ratio of the circumference of the circumscribed circle to the one of the inscribed?
Answer:
√2:1
Step-by-step explanation:
First we need to know that the length of the side of the square is equal to the diameter of the inscribed circle i.e
L = di
Given the area of the square to be 9in², we can get the length of the square.
Area of a square = L²
L is the length of the square.
9 = L²
L = √9
L = 3in
Hence the length of one side of the square is 3in
This means that the diameter of the inscribed circle di is also 3in.
Circumference of a circle = π×diameter of the circle(di)
Circumference of inscribed circle = π×3
= 3π in
For the circumscribed circumscribed circle, diameter of the outer circle will be equivalent to the diagonal of the square.
To get the diagonal d0, we will apply the Pythagoras theorem.
d0² = L²+L²
d0² = 3²+3²
d0² = 9+9
d0² = 18
d0 = √18
d0 = √9×√2
d0 = 3√2 in
Hence the diameter of the circumscribed circle (d0) is 3√2 in
Circumference of the circumscribed circle = πd0
= π(3√2)
= 3√2 π in
Hence, ratio of the circumference of the circumscribed circle to the one of the inscribed will be 3√2 π/3π = √2:1
The body paint, an automobile body paint shop, has determined that the painting time of automobiles is uniformly distributed and that the required time ranges between 45 minutes to 11/2hours.
What is the probability that the painting time will be less than or equal to an hour?
What is the probability that the painting time will be more than 50 minutes?
Determine the expected painting time and its standard deviation.
Answer:
a. [tex]\mathbf{P(Y \leq 60) = 0.3333}[/tex]
b. P(Y>50) = 0.8889
c. E(y) = 67.5 and Standard deviation [tex]\sigma[/tex] = 12.99
Step-by-step explanation:
From the information given :
an automobile body paint shop, has determined that the painting time of automobiles is uniformly distributed and that the required time ranges between 45 minutes to [tex]1\frac{1}{2}[/tex]hours.
The objective is to determine the probability that the painting time will be less than or equal to an hour?
since 60 minutes make an hour;
[tex]1\frac{1}{2}[/tex]hours = 60 +30 minutes = 90 minutes
Let Y be the painting time of the automobile; then,
the probability that the painting time will be less than or equal to an hour ca be computed as :
[tex]P(Y \leq 60) = \int ^{60}_{45} f(y) dy \\ \\ \\ P(Y \leq 60) = \int ^{60}_{45} \dfrac{1}{45} dy \\ \\ \\ P(Y \leq 60) = \dfrac{1}{45} \begin {pmatrix} x\end {pmatrix}^{60}_{45} \\ \\ \\ P(Y \leq 60) = \dfrac{60-45}{45 } \\ \\ \\ P(Y \leq 60) = \dfrac{15}{45} \\ \\ \\ P(Y \leq 60) = \dfrac{1}{3} \\ \\ \\ P(Y \leq 60) = 0.3333[/tex]
What is the probability that the painting time will be more than 50 minutes?
The probability that the painting will be more than 50 minutes is P(Y>50)
So;
[tex]P(Y>50) = \int \limits ^{90}_{50} f(y) dy[/tex]
[tex]P(Y>50) = \int \limits ^{90}_{50} \dfrac {1}{45} dy[/tex]
[tex]P(Y>50) = \dfrac{1}{45}[x]^{90}_{50}[/tex]
[tex]P(Y>50) = (\dfrac{90-50}{45})[/tex]
[tex]P(Y>50) = \dfrac{40}{45}[/tex]
P(Y>50) = 0.8889
Determine the expected painting time and its standard deviation.
Let consider E to be the expected painting time
Then :
[tex]E(y) = \int \limits ^{90}_{45} y f(y) dy \\ \\ \\ E(y) = \int \limits ^{90}_{45} y \dfrac{1}{45} dy \\ \\ \\ E(y) = \dfrac{1}{45} [\dfrac{y^2}{2}]^{90}_{45} \\ \\ \\ E(y) = \dfrac{1}{45}[\dfrac{(90^2-45^2)}{2}] \\ \\ \\ E(y) = \dfrac{1}{45} (\dfrac{6075}{2}) \\ \\ \\ E(y) = \dfrac{1}{45} \times 3037.8 \\ \\ \\ \mathbf{E(y) = 67.5}[/tex]
[tex]E(y^2) = \int \limits ^{90}_{45} y^2 f(y) dy \\ \\ \\ E(y^2) = \int \limits ^{90}_{45} y^2 \dfrac{1}{45} dy \\ \\ \\ E(y^2) = \dfrac{1}{45} [\dfrac{y^3}{3}]^{90}_{45} \\ \\ \\ E(y^2) = \dfrac{1}{45}[\dfrac{(90^3-45^3)}{3}] \\ \\ \\ E(y^2) = \dfrac{1}{45} (\dfrac{637875}{3}) \\ \\ \\ E(y^2) = \dfrac{1}{45} \times 2126.25 \\ \\ \\ \mathbf{E(y^2) = 4725}[/tex]
To determine the standard deviation, we need to first know what is the value of our variance,
So:
Variance [tex]\sigma^2[/tex] = E(x²) - [E(x)]²
Variance [tex]\sigma^2[/tex] = 4725 - (67.5)²
Variance [tex]\sigma^2[/tex] = 4725 - 4556.25
Variance [tex]\sigma^2[/tex] = 168.75
Standard deviation [tex]\sigma[/tex] = [tex]\sqrt{variance}[/tex]
Standard deviation [tex]\sigma[/tex] = [tex]\sqrt{168.75}[/tex]
Standard deviation [tex]\sigma[/tex] = 12.99
