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
Please answer this question now
Answer:
1109.12
Step-by-step explanation:
The value of which of these expressions is closest to e?
Answer:
b
Step-by-step explanation:
Megan leaves her house at 4:15 to go soccer practice. It takes her 35 minutes to get there. Her practice is two hours long. Then, she drives home, which takes 40 minutes. What time does she get back home?
Answer:
7:35
Step-by-step explanation:
we take the 35 and 45 and add it together, then take out the 60 minutes and put that in as an hour. the practice is two hours long plus the hour we took out. then the remaining minutes are 20. we add 20 minutes and three hours
Subtract the matrices
Answer:
pleas learn subtraction
Step-by-step explanation:
so it can make you better in math
Answer:
[tex]\large \boxed{\mathrm{Option \ A}}[/tex]
Step-by-step explanation:
[tex]{\mathrm{view \ attachment}}[/tex]
PLS ANSWER I WILL GIVE YOU BRAINLIST AND A THANK YOU!!
Answer:
x=45
Step-by-step explanation:
2x+45+x=180
Combine 2x and x to get 3x.
3x+45=180
Subtract 45 from both sides.
3x=180−45
Subtract 45 from 180 to get 135.
3x=135
Divide both sides by 3.
x=135/3
Divide 135 by 3
x=45
what is the change in each term of the sequence? 0.8, 1, 1.2, 1.4, 1.6
Begin by studying the pattern.
Notice that the difference between 0.8 and 1 is 0.2.
In other words, 0.8 + 0.2 is 1.
In the same way, 1 + 0.2 is 1.2.
1.2 + 0.2 is 1.4 and 1.4 + 0.2 is 1.6.
So we can see that the difference
between each of the terms is 0.2.
Answer:
+.2
Step-by-step explanation:
To find the common difference, take the second term and subtract the first term
1 - .8 = .2
Check by subtracting the second term from the third term
1.2 - 1 = .2
The common difference is .2
I need help factoring this question, Factor 4(20) + 84.
Answer:
164
Step-by-step explanation:
B for brackets
O for of
D for division
M for multiplication
A for addition
S for subtraction
You first start with the brackets (20) and multiply with 4 which is equal to 80 and then add it to 84 which makes 164
I hope this helps
FWML is a parallelogram. Find the values of x and y. Solve for the value of z, if z=x−y.
Answer:
x = 5, y = 8, z = -3
Step-by-step explanation:
Opposite sides of a parallelogram are congruent so to find x:
x + 7 = 3x - 3
-2x = -10
x = 5
To find y:
y + 2 = 2y - 6
-y = -8
y = 8
Therefore, z = x - y = 5 - 8 = -3.
How do I even start this? And how to i order the equation to solve
[tex]f(g(h(x)))=f(g(\sqrt x))=f(\sqrt x-1)=\boxed{(\sqrt x-1)^4+4}[/tex]
This is because
[tex]h(x)=\sqrt x[/tex]
[tex]g(x)=x-1[/tex]
[tex]\implies g(h(x))=\sqrt x-1[/tex]
(that is, replace any instance of x in the definition of g with √x )
and
[tex]f(x)=x^4+4[/tex]
[tex]\implies f(\sqrt x-1)=(\sqrt x-1)^4+4[/tex]
(replace any x in f with √x - 1)
Also acceptable:
[tex](\sqrt x-1)^4+4=((\sqrt x)^4-4(\sqrt x)^3+6(\sqrt x)^2-4\sqrt x+1)+4[/tex]
[tex]=\boxed{x^2-4x\sqrt x+6x-4\sqrt x+5}[/tex]
(assuming x is not negative)
Determine what type of model best fits the given situation: The height of a tree increases by 2.5 feet each growing season.
Answer: Linear model
The fact the height increases the same amount each time indicates we have a linear model. The slope is the rate of growth, so it is 2.5 feet per season.
Keep in mind that the linear model only works for a specific interval and doesn't work forever (the tree can't grow forever and at the same rate). A more realistic scenario is that the tree's height grows quickly at first and then slows down over time. For this type of scenario we would use a logarithmic model.
The linear model best fits the given situation option (B) linear is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
The height of a tree increases by 2.5 feet each growing season.
Let h is the height and s be the number of seasons.
The relation between h and s:
h = 2.5s
Thus, the linear model best fits the given situation option (B) linear is correct.
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Combine the radicals. 2√24+5√54 A) 53√6 B) 5√6 C) 19√6 D) 93√6
Answer:
The answer is option CStep-by-step explanation:
2√24 + 5√54
To combine the radicals first make sure the radicals have the same square root
That's
For 2√24[tex]2 \sqrt{24} = 2 \sqrt{4 \times 6} = 2 \times 2 \sqrt{6} [/tex][tex] = 4 \sqrt{6} [/tex]For 9√54[tex]5 \sqrt{54} = 5 \sqrt{9 \times 6} = 5 \times \sqrt{9} \times \sqrt{6} [/tex][tex] = 5 \times 3 \times \sqrt{6} [/tex][tex] = 15 \sqrt{6} [/tex]Since they have the same square root we can combine them
That's
[tex]4 \sqrt{6} + 15 \sqrt{6} = (4 + 15) \sqrt{6} [/tex]We have the final answer as
[tex]19 \sqrt{6} [/tex]Hope this helps you
What value(s) of x make the equation x2 - 18x + 81 = 0 true?
Answer:
By factoring we get:
(x -9) * (x -9) = 0
The answers are
x = 9 and x = 9
Step-by-step explanation:
Answer:it’s A
Step-by-step explanation:
70 POINTS! PLEASE HELP! Explain the difference between the following equation formats: Slope-Intercept, Point-Slope and Standard
Answer and Step-by-step explanation:
1. slope intercept
2. point-slope form
3. standard
Explanation:
1. A slope intercept form equation is when it's set up as y = m x + b
m = slope
b = y-intercept
2. A point-slope form is when a line passes through a point
and the equation is set up as y −b = m ( x−a)
m = slope
(a, b) A point that the line passes through
3. standard lope form is when the equation is set up as
Ax + By = C
please help on 30–31
Step-by-step explanation:
30-option c
because only crows r black in appearance
31-option d
thats the option which represents the question asked
HELP! URGENT!
Alice wrote three consecutive even numbers. The sum of these numbers was 252.
Pat wrote three consecutive odd numbers. Pat's numbers were larger than Alice's numbers.
The difference between the largest of Pat's numbers and the largest of Alice's numbers was 25.
What was the sum of Pat's numbers?
Answer:
333
Step-by-step explanation:
Let a represent Alice's numbers and p represent Pat's numbers.
Alice wrote three consecutive even numbers. The sum of the three is 252. This means:
[tex]a+(a+2)+(a+4)=252[/tex]
The first term is even. Each consecutive even term is two more than the previous term. Simplify:
[tex]3a+6=252\\3a=246\\a=84[/tex]
In other words, Alice's first number was 84.
Pat wrote three consecutive odd numbers. His numbers were larger than Alice's numbers. Similar to Alice, we can write:
[tex](p+1)+(p+3)+(p+5)=x[/tex]
The first term is odd. Each consecutive odd term will be 1 more, then 3 more, then 5, etc. We want to find Pat's sum, or x.
We are told that the difference between the largest of Pat's and Alice's numbers is 25. Therefore:
[tex](p+5)-(a+4)=25[/tex]
Simplify. Substitute a. Solve for p:
[tex]p-a+1=25\\p-84=24\\p=108[/tex]
Therefore, Pat's sum is:
[tex](108+1)+(108+3)+(108+5)=333[/tex]
Someone please help me fast !!
10 points to the person who answers this whole thing and I will mark you as brainliest.
Answer:
Step-by-step explanation:
Perimeter is found by adding together all the lengths of the sides. For us, that is x + (2x + 5) + (6x - 17) + (3x + 2). Now we will just combine like terms. We can also drop the parenthesis because they do nothing for us and mean nothing to the problem.
x + 2x + 5 + 6x - 17 + 3x + 2 becomes
12x - 10
What is the volume of this rectangular prism?
2 cm
7/3 cm
2 cm
Answer:
28\3
Step-by-step explanation:
What is negative sqrt 64?
Answer:
8i. In real numbers only, this isnt possible, but if immagenary numbers are allowed then 8i is your answer
What is the rule for the transformation from triangle EFG to triangle E'F'G'?
Answer:
The rule of the transformation is 6 units up and 3 units to the right [tex]T_{(3, \ 6)}[/tex] and an horizontal dilation of 2 as well as a vertical dilation of 4.
Step-by-step explanation:
The given coordinates of EFG and E'F'G' from the chart are;
E(3, 2)
F(9, 5)
G(9, 2)
E'(6, 8)
F'(18, 20)
G'(18, 8)
Therefore, we have, given that the y-coordinates of E and G are the same, the length of segment EG = 9 - 3 = 6 units
Similarly, given that the x-coordinates of F and G are the same, the length of segment FG = 5 - 2 = 3 units
The length of segment FE = [tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex] which gives;
Length from E(3, 2) to F(9, 5) = [tex]l = \sqrt{\left (5-2 \right )^{2}+\left (9-3 \right )^{2}} = 3 \cdot \sqrt{5}[/tex]
For similarly oriented E'F'G', we have;
E'G' = 18 - 6 = 12
F'G' = 20 - 8 = 12
E'F' = 12·√2
Therefore, the transformation is 6 units up and 3 units to the right and an horizontal dilation of 2 as well as a vertical dilation of 4.
if the first step of the equation -8 - 7x = -5x - 10 is " add 10" then what should be done next?
Answer:
Add 7x to each side
Step-by-step explanation:
-8 - 7x = -5x - 10
Add 10 to each side
-8 - 7x+10 = -5x - 10+10
2 -7x = -5x
Add 7x to each side
2-7x+7x = -5x+7x
2 = 2x
Answer: See below
Step-by-step explanation:
[tex]-8 - 7x = -5x - 10[/tex]
I believe it is adding 8 on both sides
The next step after adding 8 on both sides is adding 5x on both sides
[tex]-7x=-5x-2[/tex]
[tex]-7x+5x=-5x-2+5x[/tex]
[tex]-2x=-2[/tex]
x=1
What is the best first step to begin simplifying the expression - } (x + 4) = 6?
A.
Distribute -1/2
B.
Distribute -2
c. Multiply both sides of the equation by-2.
D.
Subtract 4 from both sides of the equation.
E.
Subtract 6 from both sides of the equation.
Hi how do I solve this simultaneous equation
Answer:
for the first one find a common dinominator which is 6 because you multiplied 2 times 3 which is 6 you have to do the same for the top so 3 multiplyed by 3 is 9 than the same for the other side than for x
Step-by-step explanation:
The product of 2 rational numbers is -16/9 . If one of the numbers is -4/3 find the other plz fast
Answer:
4/3
Step-by-step explanation:
let the other number be x.
-4/3 x=-16/9
x=-16/9×-3/4=4/3
In March, Mateo ran 19 miles. In April, he ran twice as many miles as he ran in March. In May, he ran four times as many miles as he did in April. How many total miles did Mateo run in the three months? Enter your answer in the box.
Answer:
209
Step-by-step explanation:
march = 19 miles
april = 19 times 2 = 38
may = 38 times 4 = 152
so that'd be 19 + 38 + 152 = 209 miles in total.
209 miles Mateo ran in the three months.
What is Simplification?Simplification in mathematical terms is a process to convert a long mathematical expression in simple and easy form.
Given that,
Mateo ran in March = 19 miles,
Also,
Mateo ran in April = 2 times of ran in March = 2 x 19 = 38 miles
Mateo ran in May = 4 times of ran in April = 4 x 38 = 152 miles.
Total distance ran by Mateo in all three months
= ran in March + ran in April + ran in May
= 19 + 38 + 152
= 209 miles.
Mateo ran 209 miles in all three months.
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Kelli swam upstream for some distance in one hour. She then swam downstream the same river for the same distance in only 6 minutes. If the river flows at 5 km/hr, how fast can Kelli swim in still water?
Answer:
6.11km/hr
Step-by-step explanation:
Let the speed that Kelli swims be represented by Y
Speed of the river = 5km/hr
Distance = Speed × Time
Kelli swam upstream for some distance in one hour
Swimming upstream takes a negative sign, hence:
1 hour ×( Y - 5) = Distance
Distance = Y - 5
She then swam downstream the same river for the same distance in only 6 minutes
Downstream takes a positive sign
Converting 6 minutes to hour =
60 minutes = 1 hour
6 minutes =
Cross Multiply
6/60 = 1/10 hour
Hence, Distance =
1/10 × (Y + 5)
= Y/10 + 1/2
Equating both equations we have:
Y - 5 = Y/10 + 1/2
Collect like terms
Y - Y/10 = 5 + 1/2
9Y/10 = 5 1/2
9Y/ 10 = 11/2
Cross Multiply
9Y × 2 = 10 × 11
18Y = 110
Y = 110/18
Y = 6.1111111111 km/hr
Therefore, Kelli's can swim as fast as 6.11km/hr still in the water.
PT.1 Kelli swam upstream for some distance in one hour. She then swam downstream the same river for the same distance in only 6 minutes. If the river flows at 5 km/hr, how fast can Kelli swim in still water?
Choose the most logical value for the variable to represent.
Let x = Kelli's swimming speed in still water
PT.2 Which expression represents the distance Kelli traveled upstream?
1(x – 5)
PT.3 Which expression represents the distance Kelli traveled downstream?
0.1(x + 5)
PT.4 Solve the equation x – 5 = 0.1(x + 5) for x. Round your answer to the nearest hundredth. Kelli can swim about 6.11 km/hour.
3 friends Mary, Peter, John have 10 flowers. Mary has the most flowers, Peter has the least. Know that the number of John's flowers is double Peter's . How many flowers that Peter, John and Mary got? (Detail Solution pls) Thanks
Answer:
Mary has 7 flowers
Peter has 1 flower
John has 2 flowers
Step-by-step explanation:
M + P + J = 10
J = 2P
M + P + 2P = 10
M + 3P = 10
P = 1
M + 3 = 10
M = 7
Find the rectangular coordinates of the point with the polar coordinates. ordered pair negative 7 comma 2 pi divided by 3
Answer:
The rectangular coordinates of the point with polar coordinates (7, 2·π/3) is (-3.5, 3.5·√3)
Step-by-step explanation:
The given polar coordinates is (7, 2·π/3)
Where, the 7 represent the distance, r, from the point of reference and 2·π/3, the angle, θ, from the reference point.
Polar coordinates are represented in rectangular form by the equivalence transformation equation given as follows;
The x-coordinate = Radius, r × cos(θ), which gives
We note that 2·π/3 radians = 2 × 180/3 = 120°
x = 7 × cos(2·π/3) = 7 × cos(120°) = 7 × (-0.5) = -3.5
x = -3.5
The y-coordinate = Radius, r × sin(θ), which gives
x = 7 × sin(2·π/3) = 7 × sin(120°) = 7 × (√3)/2 = 3.5·√3
y = 3.5·√3
Therefore, the rectangular coordinates of the point with polar coordinates (7, 2·π/3) is (-3.5, 3.5·√3).
Last year, there were 245 pies baked for the bake sale. This year, there were k pies baked . Using k, write an expression for the total number of pies baked in the two years.
Answer:
245 + k
Step-by-step explanation:
Since we know that,
245 = amt. of pies baked for the bake sale last year.
--> and k = (unknown) amt. of pies baked for the bake sale this year.
Using k, we need to write the total amt. of pies baked for bake sales in the 2 years.
last year + this year =>
respectively, 245 and k
Thus, we get 245 + k
n urn contains 3 red balls, 9 green, 2 yellow, 2 orange, and 4 purple balls. Two balls aredrawn, one at a time with replacement. Find the probability of drawing a green ball and an orangeball.
Answer:
[tex]\frac{9}{100}[/tex]
Step-by-step explanation:
Given:
Number of red balls, n(R) = 3
Number of green balls, n(G) = 9
Number of yellow balls, n(Y) = 2
Number of orange balls, n(O) = 2
Number of purple balls, n(P) = 4
Two balls are drawn one at a time with replacement.
To find:
Probability of drawing a green ball and an orange ball ?
Solution:
Total number of balls, n(Total) = 3 + 9 + 2 + 2 + 4 = 20
Formula for probability of an event E is given as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Probability that a green ball is drawn at first:
[tex]P(Green) = \dfrac{\text{Number of Green balls}}{\text {Total number of Balls}}[/tex]
[tex]P(Green) = \dfrac{9}{20}[/tex]
Now, the ball is replaced , so total number of balls remain the same i.e. 20.[tex]P(Orange) = \dfrac{\text{Number of Orange balls}}{\text {Total number of Balls}}[/tex]
[tex]P(Orange) = \dfrac{2}{20} = \dfrac{1}{10}[/tex]
[tex]P(Green\ then\ orange) = P(Green) \times P(Orange)\\\Rightarrow P(Green\ then\ orange) = \dfrac{9}{10} \times \dfrac{1}{10}\\\Rightarrow P(Green\ then\ orange) = \bold{ \dfrac{9}{100} }[/tex]
