Answer: a) To find the mean and standard deviation of the difference of their times, we need to use the properties of normal distributions. When two independent normal random variables are subtracted, the mean and standard deviation of the difference can be found using the following formulas:
Mean of the difference = Mean of x - Mean of y
Standard deviation of the difference = √(Standard deviation of x^2 + Standard deviation of y^2)
Plugging in the given values:
Mean of the difference = Mean of Molesky - Mean of Liberty = 100 - 110 = -10
Standard deviation of the difference = √(8^2 + 10^2) = √(64 + 100) = √(164) = 12.8
So the mean of the difference of their times is -10 minutes and the standard deviation is 12.8 minutes.
b) To find the probability that Mr. Molesky will finish his game before Mr. Liberty on any given day, we need to find the probability that the difference of their times is less than 0. Since the difference of their times is normally distributed with a mean of -10 and a standard deviation of 12.8, we can use the standard normal distribution table to find this probability.
To calculate the probability, we will standardize the distribution of the difference by subtracting the mean and dividing by the standard deviation.
z = (x - mean) / standard deviation
z = (-10) / 12.8 = -0.78125
Using a standard normal table we can find that P(z<-0.78125) = 0.22 or 22%
So the probability that Mr. Molesky will finish his game before Mr. Liberty on any given day is 22%.
Step-by-step explanation:
3. Find the area of the circle below.
Help the circle is 3
Answer:
28.26 [tex]in^{2}[/tex]
Step-by-step explanation:
a = [tex]\pi r^{2}[/tex]
a = 3.14([tex]3^{2}[/tex])
a = 3.14(9)
a = 28.26
a box contains 90 balls numbered from 1 to 90. if 8 balls are drawn with replacement, what is the probability that at least two of them have the same number?
The probability that at least two of the balls have the same number is 27.40%
What is probability?Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.
Probability requested is equivalent to:
P(at least 2 have same number) = 1 - P(no 2 have the same number)
P(no 2 have same number) = No. of ways to succeed / No. of possible outcomes
No. of ways to succeed = 90P8
No. of possible outcomes = 90^8
No. of ways to succeed =
nPr = n! / (n-r)!
90P8 = 90! / (90-8)!
90P8 = 90! / (82)!
90P8 = 90*89*88*87*86*85*84*83*82! / [(82)!
90P8 = 90*89*88*87*86*85*84*83
90P8 = 3.13x10^15
P(no 2 have same number) = 3.13x10^15 / 90^8
P(no 2 have same number) = 0.73
P(at least 2 have same number) = 1 - P(no 2 have the same number)
P(at least 2 have same number) = 1 - 0.73
P(at least 2 have same number) = 0.2740 = 27.40%
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Timmy buys four T-shirts costing t dollars. For buying four T-shirts he gets a 25% discount on each T-shirt. Write two expressions to represent the cost of the four T-shirts
Expression 1: 4t - (4t x 0.25) = 4t - (t) = 3t
Expression 2: 4 x (t - (t x 0.25)) = 4 x (t x 0.75) = 3t
where 't' is the cost of one T-shirt.
In expression 1, the original cost of the four T-shirts (4t) is multiplied by 25% (0.25) which is the given discount percent, and then subtracted from the original cost.
In expression 2, the original cost of one T-shirt (t) is multiplied by 25% (0.25) and subtracted from the original cost, and then the resulting cost (t x 0.75) is multiplied by four to represent the cost of four T-shirts.
Both expressions represent the cost of the four T-shirts after a 25% discount has been applied. they both yield the same result of 3t, which represents the final cost of the four T-shirts after the discount has been applied.
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As part of a project about response bias, Ellery surveyed a random sample of 25 students from her school. One of the questions in the survey required students to state their GPA aloud. Based on the responses, Ellery said she was 90% confident that the interval from 3. 14 to 3. 52 captures the mean GPA for all students at her school.
Required:
a. Interpret the confidence level.
b. Explain what would happen to the length of the interval if the confidence level were increased to 99%.
c. How would a 90% confidence interval based on a sample of size 200 compare to the original 90% interval?
d. Describe one potential source of bias in Ellery's study that is not accounted for by the margin of error
It should be emphasized that this suggests that we are 90% certain that the mean GPA for all students at the institution is between 3.14 and 3.52
Sampling
If the confidence level were raised to 99%, something would happen to the interval's length, increasing it.
The difference between a 90% confidence interval based on a 200-person sample and the original 90% interval is that the latter is narrower.
Last but not least, having the students say their grades aloud could have introduced bias into Ellery's study, which is not taken into account by the margin of error. Some of them with lesser grades will start to lie as a result.
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16 - x + x + 19 - x = 31
Answer:
X = 4
Step-by-step explanation:
We have to add like variables, so all the x variables will be added together. We get this:
-x + 35 = 31
Get x by itself.
-x = -4
Get rid of the negatives since what you do on one side you do to both sides.
x = 4
I hope this was able to help you out :D
16 (-x +x ) +19 + x = 31
16+19+x = 31
35+x = 31
x= -4
hey buddy i hope uh got an answer
a smaller square of side length feet is cut out of a square board. what is the approximate area (shaded region) of the remaining board in square feet?
If a smaller square of side length 17 feet is cut out of a square board , then the approximate area of remaining board in square feet is x² - 289 square feet .
le the side length of the big square board be = "x" ft ;
the side length of smaller square is = 17 ft ;
So , the area of the smaller square is = (side length) × (side length)
= 17 × 17
= 289 ft² .
and , the area of the larger square is = (x) × (x) ;
= x² .
So , the approximate area of the remaining board is calculated as :
= x² - 289 ;
Therefore , area of remaining board is "x² - 289" .
The given question is incomplete , the complete question is
A smaller square of side length 17 feet is cut out of a square board. What is the approximate area of the remaining board in square feet ?
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A student is standing, with her arms outstretched, on a platform that is rotating at 1.6 rev/s. She pulls her arms in and the platform now rotates at 2.2 rev/s. Her original moment of inertia (I0) is 25 kg m2.
What is her final moment of inertia (If)?
The student's final moment of inertia is 18.18 kgm².
What is moment of inertia?The moment of inertia of an objecr is the property of an object which shows its ability to rotate.
How to find the final moment of inertia?Since a student is standing with her arms outstretched, on a platform that is rotating at 1.6 rev/s. She pulls her arms in and the platform now rotates at 2.2 rev/s. Her original moment of inertia (I0) is 25 kgm². To find the r final moment of inertia, we use the law of conservation of angular momentum.
What is the law of conservation of angular momentum?The law of conservation of angular momentum states that for any rotation, angular momnetum is constant.
So, Iω = constant where
I = moment of inertia and ω = angular speed.So, Iω = I'ω' where
I = initial moment of inertia of student = 25kgm²ω = initial angular speed of student = 1.6 rev/s I' = final moment of inertia of student ω' = final angular speed of student = 2.2 rev/sMaking I' subject of the formula, we have that
I' = Iω/ω'
So, substituting the values of the variables into the equation, we have that
I' = Iω/ω'
I' = 25 kgm² × 1.6 rev/s ÷ 2.2 rev/s
= 40 kgm²rev/s ÷ 2.2 rev/s
= 18.18 kgm²
So, the final moment of inertia is 18.18 kgm².
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Does someone mind helping me with problem? Thank you!
The number of people that attended the school play is given as follows:
Adults: 325.Students: 612.How to model the situation?The situation is modeled by a system of equations, for which the variables are given as follows:
Variable a: number of adults.Variable s: number of students.There was a total of 937 people, hence:
a + s = 937.
s = 937 - a.
The total sales were of $1,109, hence:
2a + 0.75s = 1109.
Replacing s = 937 - a in the second equation, the number of adults is obtained as follows:
2a + 0.75(937 - a) = 1109
1.25a = 406.25
a = 406.25/1.25
a = 325.
Then the number of students is obtained as follows:
s = 937 - a
s = 937 - 325
s = 612.
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How do I find the median of this trapezoid?
The median of the trapezoids is given by QR = 23.5 and VW = 15.2
What is a trapezoid?The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.
There are three types of trapezoids , and those are given below:
a) Isosceles Trapezoid
b) Scalene Trapezoid
c) Right Trapezoid
The area of the Trapezoid is given by
Area of Trapezoid = ( ( a + b ) h ) / 2
where , a = shorter base of trapezium
b = longer base of trapezium
h = height of trapezium
Given data ,
Let the first trapezoid be represented as A
Let the second trapezoid be represented as B
Now , the median of the trapezoid M = ( 1/2 ) ( sum of longer base and shorter base )
Substituting the values in the equation , we get
a)
The length of longer base = 35.6
The length of shorter base = 11.4
So , the median of A is QR = ( 1/2 ) ( 35.6 + 11.4 )
On simplifying the equation , we get
The median of trapezoid QR = ( 1/2 ) 47
The median of trapezoid QR = 23.5
b)
The length of longer base = 19.1
The length of shorter base = 11.3
So , the median of B is VW = ( 1/2 ) ( 19.1 + 11.3 )
On simplifying the equation , we get
The median of trapezoid VW = ( 1/2 ) 30.4
The median of trapezoid VW = 15.2
Hence , the median of trapezoid is solved
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What is the slope of the line shown in the graph?
Someone please help me :/
Answer: It's the third down. (-1/-2) - PLEASE TAKE THIS WITH A GRAIN OF SALT. I'm not very good at this type of math.
Step-by-step explanation:
the time t needed to paint a fence varies directly as the length L and inversely as the number of workers w if it takes 10 hours to paint 400 feet of fence with six workers how long it will take for 10 workers to paint 1000 ft fence
Using the direct and inverse variations, the time taken by 10 workers to paint a fence of 1000 ft is 15 hours.
What is proportionality constant?The ratio between two proportional quantities' constant values is known as the constant of proportionality. When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship. The Direct Variation and Inverse Variation types of proportions between the two provided values determine the proportionality constant's value.
Given that the time t needed to paint a fence varies directly as the length L and inversely as the number of workers w.
This is represented as follows:
t = k(l/p)
Where, k is the proportionality constant.
Given that, it takes 10 hours to paint 400 feet of fence with six workers.
Substitute the value of t = 10, l = 400 and w = 6 in the equation we have:
10 = k (400 / 6)
10 = k (66.66)
k = 10 / 66.66
k = 0.15
Now, for or 10 workers to paint 1000 ft fence, take l = 1000, w = 10, and k - 0.15:
t = (0.15) (1000 / 10
t = (0.15) (100)
t = 15
Hence, the time taken by 10 workers to paint a fence of 1000 ft is 15 hours.
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URGENT!!
Which of the 3 graphs to the left best models the path
of a firework given it didn't explode?
Note: The path may be going in a different direction,
perhaps reflected or translated vertically or horizontally
while maintaining the same shape.
Linear
Quadratic
Exponential
Explain your thinking.
The path may be Quadratic in nature.
What is a graph?The path of a firework is modeled by a quadratic function. The firework ascends from point of launch with decreasing speed (negative acceleration due to gravity) until it reaches its maximum height and then starts dropping back to the ground at increasing speeds due to positive acceleration exerted by the force of gravity.
The flight path of the parabola can thus be modeled by height as a function of elapsed time
h = f(t) where f(t) is a quadratic equation in t with the general form being
a · t² +b · t + c
We can easily eliminate the linear model since that implies the firework will ascend at a constant speed forever
The exponential model indicates that at the moment of launch the speed of the firework is constant and then it suddenly accelerates. However, we know from observation that the firework has the highest speed at the moment of launch
Do not be confused by the shape of the graph - it seems to indicate the firework shoots down and up.
Note: The path may be going in a different direction, perhaps reflected or translated vertically or horizontally while maintaining the same shape.
Indeed the actual path of the firework is a reflection of the graph about the x-axis. so that it is a downward-facing parabola. The vertex of the parabola is the highest y-value which is the maximum height the firework would reach.
The height would be the y-axis and the time t the x-axis.
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Ella went on a walk that was 12/5 miles long. She
stopped to have lunch when she had walked 15/16 of
the way.
How far, in miles, did Ella walk before lunch?
Give your answer as a fraction in its simplest form.
Answer:
12/5 = 2.4 miles
2.4 x (15/16) = 2.25 miles.
2.25, or 9/4 miles
need the answer asap ! thank you to anyone who helps !
Answer:
Step-by-step explanation:
D
4x(5x+3)
Find the product
Answer:
[tex]20x^{2} + 12x[/tex]
Step-by-step explanation:
We can expand this equation:
(4x * 5x) + (4x * 3)
= [tex]20x^{2} + 12x[/tex]
If simplified/factored further, we can take out the common variable, x, as well as 4, which is a common number shared between 20 and 12:
4x(5x + 3)
PLEASE HELP 100 POINTS!!
A line has a slope of 0 and a y-intercept of –5/3. Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
the answer is 0= -5/3x + c
Answer: non
as a wordf 2 b geven
If you work 32 hours cleaning, how many hours do you need to work babysitting to get $420 for the week?
to write and solve each inequality.
and
9. Seven more than the quotient of a number b
and 45 is greater than 5..
+15
45
5
Multimedia
E
45
An algebraic equation which represents this word description "Seven more than the quotient of a number b and 45 is greater than 5" is b > -90.
What is a quotient?In Mathematics, a quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number.
In order to translate this word problem into algebraic equation, we would assign a variable to the unknown number and then translate the word problem into algebraic equation as follows:
Let the variable b represent the unknown number.
Translating the word problem into an algebraic equation, we have the following;
7 + b/45 > 5
By collecting like terms, we have the following:
b/45 > 5 - 7
b/45 > -2
By cross-multiplying, we have the following:
b > -2 × 45
b > -90
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The perimeter of an isosceles trapezoid is 40 ft. The bases of the trapezoid are 11 ft and 19 ft. Find the area of the trapezoid. Hint: Think characteristics of isosceles trapezoid
The area of an isosceles trapezoid is 45 square ft.
We have to evaluate the area of trapezoid.
The perimeter of an isosceles trapezoid is 40 ft.
The bases of the trapezoid are 11 ft and 19 ft.
The perimeter of an isosceles trapezoid = a + b + c + d
a, b, c and d all are sides of an isosceles trapezoid.
a + b + c + d = 40
According to question, c = d
11 + 19 + c + c = 40
30 + 2c = 40
Subtract 30 on both side, we get
2c = 10
Divide by 2 on both side, we get
c = 5 = d
The formula of area of an isosceles trapezoid is
A = [tex]\frac{1}{2}[/tex](a+b)h, where a and b are bases and h is the height.
We can see on the diagram that we can use Pythagorean theorem to find the height.
According to theorem;
[tex]c^2=a^2+b^2[/tex]
[tex](5)^2 = h^2+(4)^2[/tex]
25 = [tex]h^2[/tex] + 16
Subtract 16 on both side, we get
[tex]h^2[/tex] = 9
Taking square root on both side, we get
h = 3
The height of an isosceles trapezoid is 3 ft.
Now, the area of an isosceles trapezoid is
A = [tex]\frac{1}{2}[/tex](11+19)×3
A = [tex]\frac{1}{2}[/tex] × 30 × 3
A = 15 × 3
A = 45 square ft
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Need help please !!
Ian often takes his dog to the park. He estimates that 30% of the other dogs he sees are retrievers, 20% are terriers,and 20% are German shepherds. He designs a simulation.
Let 0,1, and 2 represent retrievers.
Let 3 and 4 represent terriers.
Let 5 and 6 represent German shepherds.
Let 7,8, and 9 represent other dogs.
The table shows the simulation results
The probability that at least one of the next five dogs he sees is a German shepherd is 0.75.
We have from the question.
0,1, and 2: retrievers
3 and 4: terriers
5 and 6: German shepherds
7,8 and 9: other dogs
In these results, 5 and 6 represent a german shepherd "at least one of the next five dogs he sees is a German shepherd." this means that at least one of the five numbers is 5 or 6.
There are a total of 20 results among them; 12 results include at least one 5 or 6.
∴P = 12/20 = 0.75
Hence, the correct option is B.
--The given question is incomplete; the complete question is
"Ian often takes his dog to the park. He estimates that 30% of the other dogs he sees are retrievers, 20% are terriers, and 20% are German shepherds. He designs a simulation. Let 0,1 and 2 represent retrievers. Let 3 and 4 represent terriers. Let 5 and 6 represent German shepherds. Let 7,8, and 9 represent other dogs. The table shows the simulation results. According to this simulation, what is the probability that at least one of the next five dogs he sees is a German shepherd?
A. 0.70
B. 0.75
C. 0.65
D. 0.60"--
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Popcorn sales at a Saturday afternoon matinee were 108% of the sales at the 8:00 showing of the movie. Calvin expressed 108% as 10.8. is Calvin correct? Explain.
Calvin representation of 108% as 10.8 is incorrect
How to determine if the statement is correctFrom the question, we have the following parameters that can be used in our computation:
Percentage increase = 108%
Express the percentage as a fraction
So, we have the following representation
Percentage increase = 108/100
Evaluate the quotient
This gives
Percentage increase = 1.08
Hence, the expression is 1.08 and Calvin is wrong
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Please help me out on my homework
Answer: No Solution is the answer
Step-by-step explanation:
Have a photo attached with the work
What will be the length of the south, west and north side of the scale drawing?
Answer:
See below
Step-by-step explanation:
North, 50
West, 28
South, 71
Answer: i got North, 50
West, 28
South, 71
but have a good day
Step-by-step explanation:
What are given?Php 45.50 - cot of 1 kilo of mango Php 35.00 - cot of a pineapple Php 19.50 -change Php100.00-Amount given to the fruit vendor with olution
It is right to receive a change of 19.50 if Juan gave php 100.00 to the fruit vendor
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
Mango = 45.50Pineapple = 35.00Amount given = 100Calculating how many Juan spend we have:
Total cost = mango + pineapple
Total cost = 45.50 + 35.00
Total cost = 80.5
Calculating how much Juan should receive in change:
Change = Amount given - Total cost
Change = 100 - 80.5
Change = 19.5
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Correctly written question:
Juan bought a kilo of mango at 45.50 and pineapple at 35.00 is it right to receive a change of 19.50 if he gave php 100.00 to the fruit vendor?
Select the correct answer
Consider this absolute value function.
f(x)=[x+3]
if function f is written as piece wise function which piece will include?
Absolute value function f(x) = | x + 3 | written in piece wise function includes the piece given by option B . x + 3, x > -3.
Function f(x) is represented as absolute value function:
f(x) = | x + 3 |
Absolute function is always positive when the included variable is greater than zero.
| x + 3 | > 0
⇒ ( x + 3 ) > 0
Subtract three from both the sides we get,
⇒ x + 3 - 3 > 0 - 3
⇒ x > -3
Here piecewise function incudes the piece :
x + 3, x > -3.
Therefore, the absolute function f(x) = | x + 3 | includes the piece after written in piecewise function form is equal to option B. x + 3, x > -3.
The above question is incomplete , the complete question is:
Select the correct answer.
Consider this absolute value function.
f(x) = | x + 3 |
If function f is written as a piecewise function, which piece will it include?
A. x + 3, x > 3
B. x + 3, x > -3
C. -x + 3, x < -3
D. -x - 3, x < 3
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Create a proportion for each set of similar triangles, that can be used to find the missing side lengths indicated. Then solve the proportion.
Using the created proportion for each set of similar triangles, the missing side lengths are 3√29 units and 24 units respectively
How to create a proportion for a set of similar triangles?Similar triangles are triangles that have the same shape, but not necessarily the same size. Two triangles are similar if and only if they have the same shape, meaning they have the same angle measures.
For the 1st triangles, we can write the proportion as follows:
proportion = (√29)/5
(√29)/5 = x/15
x = 15 × (√29)/5
x = 3√29 units
Thus, the missing side length is 3√29 units
For the 2nd triangles, we can write the proportion as follows:
proportion = 12/13
12/13 = x/26
x = 26 × (12/13)
x = 24 units
Thus, the missing side length is 24units
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i need help please i have been stuck on this problem for 2 months
Answer:
$8
Step-by-step explanation:
I just don't understand any of this because I'm dyslexic.
Answer:
HI = 9
Step-by-step explanation:
HJ = HI + IJ
2x + 10 = x + 9 + 1
2x - x = 10 - 10
∴ x = 0
∴ HI = x + 9
= 0 + 9
= 9
Find the perimeter of a rectangle measuring 4.1263cm long and 2.8315cm. Correct the answer to 3d.p and 3s.f
The perimeter of a rectangle measuring 4.1263cm long and 2.8315cm is 13.9 cm
How to determine the perimeter of the rectanglefrom the question, we have the following parameters that can be used in our computation:
Length = 4.1263 cm
Width = 2.8315 cm
The perimeter of a rectangle can be calculated using tge following equation
Perimeter = 2 x (Length + Width)
substitute the known values in the above equation, so, we have the following representation
Perimeter = 2 x (4.1263 + 2.8315)
Evaluate
Perimeter = 13.9156
Approximate
Perimeter = 13.9 to 3 significant figures
Perimeter = 13.916 to 3 decimal places
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−n + (−3) + 3n + 5
please help its due tmrw