Answer:
[tex]$ \text {Sample mean} = \bar{x} = \mu = 500 \: hours $[/tex]
Step-by-step explanation:
What is Normal Distribution?
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
For the given scenario, it is known from numerous previous samples that when this service life is in control it is normally distributed with a mean of 500 hours and a standard deviation of 20 hours.
On three recent production batches, he tested service life on random samples of four headlamps.
We are asked to find the mean of the sampling distribution of sample means when the service life is in control.
Since we know that the population is normally distributed and a random sample is taken from the population then the mean of the sampling distribution of sample means would be equal to the population mean that is 500 hours.
[tex]$ \text {Sample mean} = \bar{x} = \mu = 500 \: hours $[/tex]
Whereas the standard deviation of the sampling distribution of sample means would be
[tex]\text {standard deviation} = s = \frac{\sigma}{\sqrt{n} } \\\\[/tex]
Where n is the sample size and σ is the population standard deviation.
[tex]\text {standard deviation} = s = \frac{20}{\sqrt{4} } \\\\ \text {standard deviation} = s = \frac{20}{2 } \\\\ \text {standard deviation} = s = 10 \: hours \\\\[/tex]
The following data summarizes results from 945 pedestrian deaths that were caused by accidents. If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated or the driver was intoxicated.
Pedestrian
intoxicated not intoxicated
Driver intoxicated 64 68
not intoxicated 292 521
Answer:
37.67% probability that the pedestrian was intoxicated or the driver was intoxicated.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
945 accidents.
In 64 of them, the pedestian was intoxicated.
In 292 of them, the driver was intoxicated.
Probability that the pedestrian was intoxicated or the driver was intoxicated.
(64+292)/945 = 0.3767
37.67% probability that the pedestrian was intoxicated or the driver was intoxicated.
Solve the inequality and graph the solution set. Write the answer in interval notation. Write your answer in exact simplified form
0> 20x+2>-32
what is the solution?
Answer:
The solution is [tex]\:\left(-\frac{17}{10},\:-\frac{1}{10}\right)[/tex].
Step-by-step explanation:
An inequality is a mathematical relationship between two expressions and is represented using one of the following:
≤, "less than or equal to"<, "less than">, "greater than" ≥, "greater than or equal to"To find the solution of the inequality [tex]0>\:20x+2>\:-32[/tex] you must:
[tex]\mathrm{If}\:a>u>b\:\mathrm{then}\:a>u\quad \mathrm{and}\quad \:u>b\\\\0>20x+2\quad \mathrm{and}\quad \:20x+2>-32[/tex]
First, solve [tex]0>20x+2[/tex]
[tex]\mathrm{Switch\:sides}\\\\20x+2<0\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\\\20x+2-2<0-2\\\\\mathrm{Simplify}\\\\20x<-2\\\\\mathrm{Divide\:both\:sides\:by\:}20\\\\\frac{20x}{20}<\frac{-2}{20}\\\\\mathrm{Simplify}\\\\x<-\frac{1}{10}[/tex]
Next, solve [tex]20x+2>-32[/tex]
[tex]20x+2-2>-32-2\\\\20x>-34\\\\\frac{20x}{20}>\frac{-34}{20}\\\\x>-\frac{17}{10}[/tex]
Finally, combine the intervals
[tex]x<-\frac{1}{10}\quad \mathrm{and}\quad \:x>-\frac{17}{10}\\\\-\frac{17}{10}<x<-\frac{1}{10}[/tex]
The interval notation is [tex]\:\left(-\frac{17}{10},\:-\frac{1}{10}\right)[/tex] and the graph is:
The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four 10s, etc., down to four 2s in each deck.
You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. (a) Are the outcomes on the two cards independent? Why?
1. No. The events cannot occur together. 2. Yes. The events can occur together. 3. No. The probability of drawing a specific second card depends on the identity of the first card. 4. Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.
(b) Find P(ace on 1st card and jack on 2nd). (Enter your answer as a fraction.)
(c) Find P(jack on 1st card and ace on 2nd). (Enter your answer as a fraction.)
(d) Find the probability of drawing an ace and a jack in either order. (Enter your answer as a fraction.)
Answer:
(a)No. The probability of drawing a specific second card depends on the identity of the first card.
(b)4/663
(c) 4/663
(d) 8/663
Step-by-step explanation:
(a)The events are not independent because we are drawing cards without replacement and the probability of drawing a specific second card depends on the identity of the first card.
(b) P(ace on 1st card and jack on 2nd).
[tex]P$(Ace on 1st card) =\dfrac{4}{52}\\ P$(Jack on 2nd card)=\dfrac{4}{51}\\\\$Therefore:\\P(ace on 1st card and jack on 2nd) =\dfrac{4}{52}\times \dfrac{4}{51}\\=\dfrac{4}{663}[/tex]
(c)P(jack on 1st card and ace on 2nd)
[tex]P$(Jack on 1st card) =\dfrac{4}{52}\\ P$(Ace on 2nd card)=\dfrac{4}{51}\\\\$Therefore:\\P(jack on 1st card and ace on 2nd) =\dfrac{4}{52}\times \dfrac{4}{51}\\=\dfrac{4}{663}[/tex]
(d)Probability of drawing an ace and a jack in either order.
We can either draw an ace first, jack second or jack first, ace second.
Therefore:
P(drawing an ace and a jack in either order) =P(AJ)+(JA)
From parts (b) and (c) above:
[tex]P$(jack on 1st card and ace on 2nd) =\dfrac{4}{663}\\P$(ace on 1st card and jack on 2nd) =\dfrac{4}{663}\\$Therefore:\\P(drawing an ace and a jack in either order)=\dfrac{4}{663}+\dfrac{4}{663}\\=\dfrac{8}{663}[/tex]
The following are daily outputs from shift A and shift B at a factory.
Shift A: {77, 91, 82, 68, 75, 72, 85, 65, 70, 79, 94, 86}
Shift B: {68, 93, 53, 100, 77, 86, 91, 88, 72, 74, 66, 82}
Q. Compare the means of the shift outputs. The workers in the shift with the highest mean will earn a bonus. Which shift will earn the bonus?
Answer:
shift B
Step-by-step explanation:
shift a is 78.6 repeating
shift b is 79.3 repeating
mean is when you add them all then divide it by the numbers it has
Answer:
shift B
Step-by-step explanation:
To calculate the mean for a set of data, add all the numbers in that set, then divide by the number of data points in the set.
Please help!!! Which of the following is equal to the rational expression when x ≠ -2 or 3? x^2+5x+6/x^2-x-6
Answer:
see below
Step-by-step explanation:
These are always simplified by cancelling common factors from numerator and denominator. In order to do that, you have to factor the expressions. The restrictions on x give a clue as to the factors of the denominator.
[tex]\dfrac{x^2+5x+6}{x^2-x-6}=\dfrac{(x+3)(x+2)}{(x-3)(x+2)}=\boxed{\dfrac{x+3}{x-3}}[/tex]
The best possible statement to your question is x+3 / x-3
divide 41000 into two parts such that their amounts at 50% compound interest compounded annually in 2 and 3 years are equal
Answer:24600 , 16400
Step-by-step explanation:
Let the first part be x
So, second part will be 41000 - x
For amount x
SI = prt / 100
SI = x * 0.50 * 2
SI = 1x
For amount 41000 - x
SI = (41000-x) * 0.50 * 3
SI = 61500 - 1.5x
1x = 61500 - 1.5x
1.5x + x = 61500
2.5x = 61500
x = 61500 / 2.50 = 24600 for 2 years
2nd part = 41000 - 24600 = 16400 for three years
Serena wants to determinethe area of the lawn the grass part of her front yard using the information given in the diagram below Serena knows that she needs to divide by 9 to change the units from square yards so she writes the expression below to determine the area of grass in square yards
Answer:
The answer is 295 square yards.
Step-by-step explanation:
[48(72-12)-15^2] divide by 9
3456-576-225 divide by 9
Subtract 3456 by 576
2880-255
2655 divide by 9
=295 square yards.
Hope this helped!
The answer is 295 square yards.
What is the area of square space?To find the area of square , take the square of side.
Given expression is [48(72-12)-15^2] divide by 9 .
Let the unknown area is x.
x = {48 * 60 - 15^2 } divide by 9
x = 2880 - 225 divide by 9
x = 2655 divide by 9
x =295 square yards.
Hence, The answer is 295 square yards.
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3/5 of a juice drink is made of real juice. What percent of the drink is
real juice?
Answer:
60%
Step-by-step explanation:
Percent means out of 100
Changing 3/5 to a denominator of 100
3/5*20/20
60/100
The percent is 60 %
"A 12-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 33 feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 55 feet from the wall?"
Answer:
Step-by-step explanation:
The question has typographical errors. The correct question is:
"A 12-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 3 feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 5 feet from the wall?
Solution:
The ladder forms a right angle triangle with the ground. The length of the ladder represents the hypotenuse.
Let x represent the distance from the top of the ladder to the ground(opposite side)
Let y represent the distance from the foot of the ladder to the base of the wall(adjacent side)
The bottom of the ladder is sliding along the pavement directly away from the building at 3ft/sec. This means that y is increasing at the rate of 3ft/sec. Therefore,
dy/dt = 3 ft/s
The rate at which x is reducing would be
dx/dt
Applying Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side², it becomes
x² + y² = 12²- - - - - - - -1
Differentiating with respect to time, it becomes
2xdx/dt + 2ydy/dt = 0
2xdx/dt = - 2ydy/dt
Dividing through by 2x, it becomes
dx/dt = - y/x ×dy/dt- - - - - - - - - - 2
Substituting y = 5 into equation 1, it becomes
x² + 5 = 144
x² = 144 - 25 = 119
x = √119 = 10.91
Substituting x = 10.91, dy/dt = 3 and y = 5 into equation 2, it becomes
dx/dt = - 5/10.91 × 3
dx/dt = - 1.37 ft/s
Solve the system of equations.
3x + 3y + 6z = 6
3x + 2y + 4z = 5
7x + 3y + 32 = 7
a. (x = 2, y = -2, z = 0)
b. (x = 3, y=-3, z = 3)
c. (x = 1, y = - 1,2= 1)
d. (x = 0, y = 0, z = 2)
Answer:
The answer is option c
x = 1 y = - 1 z = 1
Hope this helps.
x=(y+2)^2 solve the equation
Answer:
x= y^2+4y+4
Step-by-step explanation:
x= (y+2)(y+2)
x= y^2+2y+2y+4
x= y^2+4y+4
Answer:
X = y^2 + 4y + 4
Y= (√X) -2
Step-by-step explanation:
X = (Y+2)^2
X = (Y+2)(Y+2)
X = Y^2 + 4y + 4
X = (Y+2)^2
√X = √(Y+2)^2 (taking the root of both sides cancels the exponent)
√X = Y+2
-2 -2
(√X) - 2 = Y
or
Y = (√X) - 2
On Sunday, a local hamburger shop sold a combined of 572 hamburger and cheeseburger. The number of cheeseburgers sold was three times the number of hamburger sold. How many hamburger were sold on Sunday
What is the value of y ??????????????
Answer & Step-by-step explanation:
For this problem we can just set up an equation and equal it to 180.
(2y) + (y + 10) + 50 = 180
Combine like terms.
3y + 60 = 180
Subtract 60 from 180.
3y = 120
Divide 120 by 3.
y = 40
So, the value of y is 40°
Graph the line y=-2x+5
Hope this helps!! :)
math question is attached below
and show your work
Answer:
[tex]V = \frac13 \pi r^2 h[/tex]
117.81
Step-by-step explanation:
r is half the diameter so 2.5 cm
h is 18
fill in and get:
V = [tex]\frac13 \pi \cdot 6.25 \cdot 18 \approx 117.81 cm^3[/tex]
Louis had 19 dogs. He feeds them with 38 pounds of biscuits. If there are 4 more
dogs, then how much more pounds of biscuit are needed?
Answer:
14
Step-by-step explanation:
Answer:
Which of these factors will affect the friction on a road
Step-by-step explanation:
7+2x/3=5 im stuck on this question pls hhelp my homework is due soon pls help
The value of X is 4
please see the attached picture for full solution
Hope it helps
Good luck on your assignment..
I need help please help me
Answer:
Option 2
Step-by-step explanation:
Cost of book= 6.50
Shipping= 4.99
Total= 82.99
Equation:
6.50x+4.99= 82.99
Option 2 is correct
A cell phone company
charges a $20 fee every
month and $0.01 for ten
minutes spent talking on
the phone. Write an
equation to model the cost
of a monthly cell phone bill
for the linear function.
Answer:
C = 20 + 0.001x
C = $20 + $0.001x
Step-by-step explanation:
Let x represent the number of minutes spent talking on the phone.
Given;
Fixed monthly charge F = $20
Charge per 10 minutes V = $0.01
Charge per minute = V/10 = $0.01/10 = $0.001
The equation to model the cost of a monthly cell phone bill;
Total cost = fixed cost + variable cost
C = F + (V/10)x
Substituting the values;
C = 20 + 0.001x
Suppose you
earn $10.30 per hour and work 24 eight-hour
days in a month. How much do you earn in that month?
Answer:1977.60
Step-by-step explanation:
24x8= 192
192x 10.30= 1977.60
got another math problem.. please help
the correct answer is 59.
Answer:
59
Step-by-step explanation:
[2+ (4-2)+8²]-[2-(-1)][2+2+64]-[2-(-1)]²68-3²68-959In a lottery, you pay $1 and pick a number from 000 to 999. If your number comes up, you win $350, which is a profit of $349. If you lose, you lose $1. Your probability of winning is 0.001. What is the expected value of your profit
Answer:
The expected value of profit is -$0.65.
Step-by-step explanation:
The rules of the lottery are as follows:
You pay $1 and pick a number from 000 to 999.If your number comes up, you win $350, which is a profit of $349.If you lose, you lose $1.The probability of winning is, P (W) = 0.001.
Then the probability of losing will be,
P (L) = 1 - P (W)
= 1 - 0.001
= 0.999
Let the random variable X represent the amount of profit.
The probability distribution table of the lottery result is as follows:
Result X P (X)
Win +349 0.001
Lose -1 0.999
The formula to compute the expected value of X is:
[tex]E(X)=\sum X\cdot P(X)[/tex]
Compute the expected value of profit as follows:
[tex]E(X)=\sum X\cdot P(X)[/tex]
[tex]=(349\times 0.001)+(-1\times 0.999)\\\\=0.349-0.999\\\\=-0.65[/tex]
Thus, the expected value of profit is -$0.65.
Can someone please help me on this?
Answer:
(0, 3/2)
Step-by-step explanation:
The equation can be put in the form ...
x^2 = 4py
where p = 3/2.
In this form, the focus is distance "p" from the vertex in the direction the parabola opens.
The vertex is at (0, 0); the parabola opens upward. So, the focus is 3/2 units above the vertex, at ...
focus = (0, 3/2) . . . . . matches choice A
What does the “equity” of a tax mean?
Answer:
Equity of taxation means each citizen pays an amount of tax equal to their income and ability to pay the tax.
Answer:
C) The tax is paid equally by everyone
Step-by-step explanation:
Please answer this question I give brainliest thank you! Number 16
Answer:
4a
Step-by-step explanation:
The mean is found by adding all of the data set together and then dividing by the amount of individual pieces of data in the set.
(2+3+3+8) = 16
16/4=4
The answer is 4a.
A box on a 20 degree incline is shown with vectors radiating from a point in the center of the box. The first vector points up and parallel to the surface of the incline, labeled F Subscript f s Baseline. A second vector points toward the center of the earth, labeled F Subscript g Baseline = 735 N. A third vector is perpendicular to and away from the surface of the incline from the point, labeled F Subscript N Baseline. A fourth vector is broken into 2 components, one parallel to the surface and down the incline, labeled F Subscript g x Baseline, and one perpendicular to the surface and into the surface, labeled F Subscript g y Baseline.
A box at rest on a ramp is in equilibrium, as shown.
What is the force of static friction acting on the box? Round your answer to the nearest whole number. N
What is the normal force acting on the box? Round your answer to the nearest whole number.
The images to solve this problem is in the attachment.
Answer: [tex]F_{fs}[/tex] = 671.0 N; [tex]F_{N}[/tex] = 300 N
Step-by-step explanation: From the image in the attachment and knowing that the box is in equilibrium, i.e., the "sum" of all the forces is 0, it is possible to conclude that:
[tex]F_{fs}[/tex] = [tex]F_{gx}[/tex] and [tex]F_{N}[/tex] = [tex]F_{gy}[/tex]
Using trigonometry, shown in the second attachment, the values for each force are:
Force of Static Frictionsin 20° = [tex]\frac{F_{gx} }{F_{g} }[/tex]
[tex]F_{gx}[/tex] = [tex]F_{g}[/tex]. sin(20)
[tex]F_{gx}[/tex] = 735.0.913
[tex]F_{gx}[/tex] = 671.0
Normal Forcecos 20° = [tex]\frac{F_{gy} }{F_{g} }[/tex]
[tex]F_{gy}[/tex] = [tex]F_{g}[/tex]. cos (20)
[tex]F_{gy}[/tex] = 735.0.408
[tex]F_{gy}[/tex] = 300
The force of static friction is 671N and normal force is 300N
Answer:
Static force is 251 and the Normal force is 691.
Step-by-step explanation:
Hope this helps!! Have a great day!! :)
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
D. F(x) = 2(x-3)^2 + 3
Step-by-step explanation:
We are told that the graph of G(x) = x^2, which is a parabola centered at (0, 0)
We are also told that the graph of the function F(x) resembles the graph of the function G(x) but has been shifted and stretched.
The graph of F(x) shown is facing up, so we know that it is multiplied by a positive number. This means we can eliminate A and C because they are both multiplied by -2.
Our two equations left are:
B. F(x) = 2(x+3)^2 + 3
D. F(x) = 2(x-3)^2 + 3
Well, we can see that the base of our parabola is (3, 3), so let's plug in the x value, 3, and see which equation gives us a y-value of 3.
y = 2(3+3)^2 + 3 =
2(6)^2 + 3 =
2·36 + 3 =
72 + 3 =
75
That one didn't give us a y value of 3.
y = 2(3-3)^2 + 3 =
2(0)^2 + 3 =
2·0 + 3 =
0 + 3 =
3
This equation gives us an x-value of 3 and a y-value of 3, which is what we wanted, so our answer is:
D. F(x) = 2(x-3)^2 + 3
Hopefully this helps you to understand parabolas better.
Twice the length of the rectangle exceeds three times the width of the rectangle by one centimeter and if one-third of the difference of the length and the width is one centimeter.find the dimension.
The dimensions of the rectangle are given as 4cm and 1cm respectively.
What is a rectangle?A rectangle is a type of parallelogram having equal diagonals.
All the interior angles of a rectangle are equal to the right angle.
The diagonals of a rectangle do not bisect each other.
Suppose the length of rectangle be x.
And, the width be y.
Then, the following equations can be written as per the information given as,
2x - 3y = 1 (1)
And, 1/3(x - y) = 1
⇒ x - y = 3 (2)
Multiply equation (2) by 2 and subtract from (1) to get,
2x - 3y - 2(x - y) = 1 - 2 × 3
⇒ -5y = -5
⇒ y = 1
Substitute y = 1 in equation (2) to get,
x - 1 = 3
⇒ x = 4
Hence, the dimensions are 4cm and 1cm respectively.
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A supervisor records the repair cost for 14 randomly selected refrigerators. A sample mean of $79.20 and standard deviation of $10.41 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the refrigerators. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
( $74.623, $83.777)
The 90% confidence interval is = ( $74.623, $83.777)
Critical value at 90% confidence = 1.645
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = $79.20
Standard deviation r = $10.41
Number of samples n = 14
Confidence interval = 90%
Using the z table;
The critical value that should be used in constructing the confidence interval.
z(α=0.05) = 1.645
Critical value at 90% confidence z = 1.645
Substituting the values we have;
$79.20+/-1.645($10.42/√14)
$79.20+/-1.645($2.782189528308)
$79.20+/-$4.576701774067
$79.20+/-$4.577
( $74.623, $83.777)
The 90% confidence interval is = ( $74.623, $83.777)
A box plot is shown below:
What is the median and Q1 of the data set represented on the plot?
Median = 31; Q1 = 26
Median = 30; Q1 = 26
Median = 31; Q1 = 20
Median = 30; Q1 = 20
Answer:
Step-by-step explanation:
Hello!
I didn't find the exact box plot for this exercise but I've found one that'll help you identify the required values
When constructing a box plot the box lower and upper limits are defined by the first and third quartiles and the line separating it in two represents the median.
In this case, the box is lying on the side, the first quartile is represented by the left side of the box. If you see the graphic this one corresponds to 25.
The median, as said, is represented by the line drawn inside the box, it is not necessarily in its middle but it will always be inside it.
Watching the example, the median is 33
I hope this helps!
Answer: D
Step-by-step explanation: