Answer:
a) 0.1587 = 15.87% probability that a battery will break down during the warranty period.
b) The expected profit of the auto store on a battery is of $15.239.
c) The expected monthly profit on batteries if the auto store sells an average of 500 batteries a month is of $7,619.50.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The life of batteries is known to be normally distributed with a mean and a standard deviation of 40 and 16 months, respectively.
This means that [tex]\mu = 40, \sigma = 16[/tex]
a. What is the probability that a battery will break down during the warranty period?
Two year warranty, that is, 24 months. This probability is the pvalue of Z when X = 24. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24 - 40}{16}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587.
0.1587 = 15.87% probability that a battery will break down during the warranty period.
b. What is the expected profit of the auto store on a battery?
1 - 0.1587 = 0.8413 probability of a profit of $20.
0.1587 probability of a loss of $10. So
[tex]E = 0.8413*20 - 0.1587*10 = 15.239[/tex]
The expected profit of the auto store on a battery is of $15.239.
c. What is the expected monthly profit on batteries if the auto store sells an average of 500 batteries a month?
Multiplying the average for a battery by 500. So
15.239*500 = $7,619.50
The expected monthly profit on batteries if the auto store sells an average of 500 batteries a month is of $7,619.50.
HELPPP What is the percent of change from 0.36 to 1.19?
Answer:
330.555556%
Step-by-step explanation:
1.19/.36=3.3305555555555555555555555555
therefore it is 330.5555%
please help!! solve ΔPQR Your answer should include the length of r and the measures of angle P and angle Q.
Include all relevant calculations, and use the correct units for all measures. Be sure explanations are written in complete sentences.
9514 1404 393
Answer:
r ≈ 15.90 mP ≈ 63.27°Q ≈ 26.73°Step-by-step explanation:
The triangle is a right triangle, so the length of r can be found using the Pythagorean theorem.
r = √(14.2² +7.15²) = √252.7625
r ≈ 15.8985 ≈ 15.90 . . . meters
__
The angles can be found from the tangent relation.
Tan = Opposite/Adjacent
tan(P) = 14.2/7.15
P = arctan(14.2/7.15) ≈ 63.2738° ≈ 63.27°
Angle Q is the complement of angle P.
Q = 90° -63.27° = 26.73°
Which of the following statistics is used to measure inflation?
Answer:
.....................
Step-by-step explanation:
As an economic indicator. The CPI is the most widely used measure of inflation and is sometimes viewed as an indicator of the effectiveness of government economic policy.
The origin is a point anywhere along the x-axis. True or False
Answer:
False
Step-by-step explanation:
The origin is at 0 on the x-axis, and 0 on the y-axis. Hence, (0,0) lies on both the axis.
hope this helps and is right. p.s. i really need brainliest :)
if my answer is wrong then i am incredibly sorry!
The statement "The origin is a point anywhere along the x-axis" is False.
What is Origin?Origin is referred to as the first point or the starting point from which we begin our calculations or measurements in mathematics, particularly in the subject of coordinate geometry. The 0 on a ruler is the point at which we begin taking measurements; as a result, it is referred regarded as the scale's origin.
As, The intersection of the x and y axes in a coordinate plane is where the origin is located.
Coordinates can be used to name any point on the coordinate plane.
The coordinates are where the origin is ( 0, 0 ).
So, the x- coordinate is 0 and y- coordinates is 0.
Hence, the given statement is False.
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An independent-samples t test was conducted to compare high-altitude exercise to exercise at sea-level. Imagine the mean comfort level of participants, rated on a 7-point scale where high values reflect high comfort, at high altitude was 3.5 while the average at sea-level was 5.1. Imagine also that values were calculated for sdifference of 1.1, 2.04 for pooled variance, and 35 for degrees of freedom total. What are the critical cutoffs for this test
Answer:
-2.03, 2.03
Step-by-step explanation:
The degree of freedom (df) ;
Df total for the two samples = 35
Therefore, obtuaking the critical value using a T-test distribution at 95% confidence level.
(1 - 95%) / 2 = (1 - 0.95) / 2 = 0.05 / 2 = 0.025
Using a T critical value calculator or t table distribution ;
Tcritical, 0.025, df = 35 = 2.03
Left tail = - 2.03
Right = 2.03
Hence, critical cutoff :
(-2.03 ; 2.03)
Suppose that in a random selection of 100 colored candies, 21% of them are blue. The candy company claims that the percentage of blue candies is equal to 29%. Use the 0.01 significance level to test that claim.
Answer:
The pvalue of the test is 0.0784 > 0.01, which means that at this significance level, we do not reject the null hypothesis that the percentage of blue candies is equal to 29%.
Step-by-step explanation:
The candy company claims that the percentage of blue candies is equal to 29%.
This means that the null hypothesis is:
[tex]H_{0}: p = 0.29[/tex]
We want to test the hypothesis that this is true, so the alternate hypothesis is:
[tex]H_{a}: p \neq 0.29[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.29 is tested at the null hypothesis:
This means that [tex]\mu = 0.29, \sigma = \sqrt{0.29*0.71}[/tex]
Suppose that in a random selection of 100 colored candies, 21% of them are blue.
This means that [tex]n = 100, X = 0.21[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.21 - 0.29}{\frac{\sqrt{0.29*0.71}}{\sqrt{100}}}[/tex]
[tex]z = -1.76[/tex]
Pvalue of the test:
The pvalue of the test is the probability of the sample proportion differing at least 0.21 - 0.29 = 0.08 from the population proportion, which is 2 multiplied by the pvalue of Z = -1.76.
Looking at the z-table, z = -1.76 has a pvalue of 0.0392
2*0.0392 = 0.0784
The pvalue of the test is 0.0784 > 0.01, which means that at this significance level, we do not reject the null hypothesis that the percentage of blue candies is equal to 29%.
pls help me forgot how to do this
find the value of x
Answer:
Step-by-step explanation:
oto begin you should know that all triangles contain 180 degrees and that a flat line contains 180 degrees as well. This means that in order to find this answer you should begin by calculating the remianing angle in the traingle. This is done by 180-(95+51) and gives and angle of 34 degrees. Then take 180-(95+35) in order to get x. This gives an x of 51.
Hope this helps!
Answer:
146°
Step-by-step explanation:
1) 180-51-95 = 34 All the angles in a triangle add up to 180.
2) A straight line is 180, so x = 180 - the interior angle.
3) We figured out in step #1 that the interior angle is 34, so all we have to do now is substitute that into step #2
4) x = 180-34 = 146
please help me i really need help please i really need help please
Answer:
(-1,-2)
Step-by-step explanation:
For a point (a,b) rotated 90° counterclockwise about the origin, it's new coordinates are (-b,a).
So since C is originally (-2,1), it's new coordinates are (-1,-2)
You are ordering a cake for your brother's birthday. You must choose between vanilla, chocolate or marble cake. You must choose between
buttercream or chocolate frosting. Finally you must choose between a cake with a 4-inch radius, 6-inch radius, 9-inch radius, or 12-inch radius. How
many difference cake options are there?
Answer:
24 different options
Step-by-step explanation:
3 cake type options
2 frosting options
4 radius sizes
3 * 2 * 4 = 24 different options
WILL NAME BRAINLIST PLEASE
Use the table to write a linear function that relates y to x . PLEASE NO HACKERS
y=
Answer:
answer: y+2/3x+5
Step-by-step explanation:
because
Plsss help mark brainlist
Answer:
17
Step-by-step explanation:
34 / 2 = 17
How much work is needed to move a 40 pound box a distance of 2 feet?
????-foot pounds
Answer:
80-foot pounds
Step-by-step explanation:
As per the given data, the work needed to move the 40 pound box a distance of 2 feet is 79.86 foot-pounds.
What is work done?In physics, work is defined as the product of force and displacement, where force is the applied force and displacement is the distance moved by the object in the direction of the applied force.
To calculate the work needed to move a 40 pound box a distance of 2 feet, we need to use the formula:
Work = Force x Distance x Cos(theta)
where Force is the amount of force applied to move the box, Distance is the distance moved, and Cos(theta) is the cosine of the angle between the force vector and the direction of motion.
Assuming that the force is applied in the same direction as the motion, the angle between the force vector and the direction of motion is 0, and thus Cos(0) = 1. Therefore, the formula simplifies to:
Work = Force x Distance
We are given that the box has a weight of 40 pounds. Since weight is a type of force, we can use the formula:
Force = Mass x Acceleration due to gravity
where Mass is the mass of the box and Acceleration due to gravity is the gravitational acceleration constant, which is approximately 32.2 feet per second squared.
Converting the weight of the box from pounds to slugs (the unit of mass in the English system of units) gives:
Mass = Weight / Acceleration due to gravity = 40 pounds / 32.2 feet per second squared = 1.24 slugs
Therefore, the force required to move the box is:
Force = Mass x Acceleration due to gravity = 1.24 slugs x 32.2 feet per second squared = 39.93 pounds-force
Finally, we can calculate the work needed to move the box a distance of 2 feet as:
Work = Force x Distance = 39.93 pounds-force x 2 feet = 79.86 foot-pounds
Therefore, the work needed to move the 40 pound box a distance of 2 feet is 79.86 foot-pounds.
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Please help me thanks
Answer:
11/13
Step-by-step explanation:
4 out of the 26 marbles are blue, meaning that the rest of the 22 marbles are not blue. (26-4=22)
This means that out of the total 26, the chance of not picking a blue marble are 22/26=11/13
Charlotte is making 20 flower bouquets 4/5 of the bouquet are daisies and the rest are tulips how many bouquets are tulips
Answer:
4 bouquets
Step-by-step explanation:
5/5 = 20 flower bouquets.
Find out how much flower bouquets there are when it's 1/5.
5/5 = 20
1/5 = 20 ÷ 5 = 4
Since tulips are 1/5 as 5/5 - 4/5 = 1/5, 4 bouquets are tulips.
a theater has 49 seats in the first row, 52 seats in the second row, 55 seats in the third row, and so on. how many seats are there in row 20
Answer:
106
Step-by-step explanation:
this question represents an arithmetic sequence problem where you can use this formula: a(n) = a(1) + d(n-1) where 'n' is value you're solving for, a(1) is the initial value, and 'd' is the common difference
a(20) = 49 + 3(20-1)
= 49 + 3(19)
= 49 + 57
= 106
Check attachment below
Answer:
[tex]170[/tex]
Step-by-step explanation:
The angle 42x+1 is the inscribed angle of Arc WX. This means Arc WX is twice of 42x+1.
[tex]wx = 2(42x + 1)[/tex]
We can add up that and the other arcs to 360.
[tex]2(42x + 1) + 29x - 1 + 65x + 3[/tex]
[tex]84x + 2 + 29x - 1 + 65x + 3 = 360[/tex]
[tex]178x + 4 = 360[/tex]
[tex]178x = 356[/tex]
[tex]x = 2[/tex]
Plug in 2 for WX.
[tex]84(2) + 2 = 170[/tex]
An item sells for $40. The sales tax on
the item is 8%. What is the sales tax and
total cost?
Answer:
$43.20 total
$3.20 sales tax
Explication:
40*1.08=43.2
Answer:
sales tax = $3.20
total cost = $43.20
Step-by-step explanation:
To calculate the sales tax on an item, multiply the price of the item by the tax percent in decimal form. To convert a percent to decimal form, divide the percent by (100).
Sales tax percent: 8%
In decimal form: 0.08
Multiply the sales tax in decimal form by the price of the item to find out the sales tax amount,
(item_price) * (sales_tax)
= (40) * (0.08)
= 3.2
Sales tax amount: $3.20
To find the total cost of the product, add the sales tax amount to the item price,
(item_price) + (sales_tax_amount)
= 40 + 3.20
= 43.20
1/5 x 3/8 x (-5) as a fraction in simplest form
Answer:
-3/8
Step-by-step explanation:
nothing can be simplified further
How does the graph of g(x) = 10x – 8 compare to the graph of f(x) = 10x?
The graphs are the same.
The graphs are translated upward 8 units.
The graphs are translated downward 8 units.
The graphs shift to the left 8 units.
Answer:
Translated down 8 units or C
Step-by-step explanation:
Can someone help me please? I forgot how to do this
Answer:
90°-33°=57°
57=2x+1
-1. -1
56=2x divide both sides by 2
28=x
x =28
Answer:
x = 28
Step-by-step explanation:
Both of these would add up to 90 degrees.
Equation → 2x + 1 + 33 = 90
Add like terms → 2x + 34 = 90
Subtract both sides by 34 → 2x + 34 - 34 = 90 - 34
Divide both sides by 2 → 2x = 56
→ x = 28
hope this helps! :)
A grain dealer sold to one customer 5 bushels of wheat, 2 of com, and 3 of ryo, for $228: to another, 2 of wheat, 3 of corn, and 5 of ryo, for $228, and to a third, 3 of wheat, 5 of com, and 2 of rye, for $228. What was the price per bushel for com?
Answer:
2.30 :) hope this helps!!!!!!! :)
Step-by-step explanation:
w = wheat c = corn r = rye
6w + 3c + 6r = 45.90
3w + 6c + 6r = 49.20
6w + 6c + 3r = 41.40
since you want the answer for c, manipulate then add 2 equations that will get rid of 1 variable:
if we multiply the first equation by -1 then add it to the second equation, it will eliminate the r
-6w - 3c - 6r = - 45.90
3w + 6c + 6r = 49.20
------------------------------------
- 3w +3c = 3.30 or w - c = - 1.10
If we multiply the 3rd equation by -2 then add it to the first equation, it will eliminate the r again:
-12w - 12c - 6r = - 82.80
6w + 3c + 6r = 45.90
------------------------------------------
- 6w - 9c = - 36.90 or 2w + 3c = 12.30
now we have 2 equations and 2 variables that we can solve by substitution:
w = c - 1.10
2(c - 1.10) + 3c = 12.30
2c - 2.20 + 3c = 12.30
5c = 14.50
c = 2.90
w = c - 1.10 or 1.80
3r = 41.40 - 6(1.80) - 6(2.90)
3r = 13.20 r = 4.40
I will pick the 2nd equation to check my answers :)!
3(1.80) + 6(2.90) + 6(4.40) = 49.20
5.40 + 17.40 + 26.40 = 49.20
As per linear equation, the price per bushel for corn is $22.8.
What is a linear equation?A linear equation is an equation that has one or multiple variable with the highest power of the variable is 1.
Given, a grain dealer sold to one customer 5 bushels of wheat, 2 of corn, and 3 of rye, for $228.
To another customer, he sold 2 of wheat, 3 of corn, and 5 of rye, for $228.
To a third customer, 3 of wheat, 5 of corn, and 2 of rye, for $228.
Let, per piece of wheat is of $x.
Per piece of corn is of $y.
Per piece of rye is of $z.
Therefore, 5x + 2y + 3z = 228 ....(1)
2x + 3y + 5z = 228 .........................(2)
3x + 5y +2z = 228 ..........................(3)
Multiplying equation(1) by '2' and equation(2) by '5' and substract, we get:
2(5x + 2y + 3z) - 5(2x + 3y + 5z) = 2(228) - 5(228)
⇒ (10x + 4y + 6z) - (10x + 15y + 25z) = - 3(228)
⇒ (- 11y - 19z) = - 684
⇒ 11y + 19z = 684 ......(4)
Multiplying equation(2) by '3' and equation(3) by '2' and substract, we get:
3(2x + 3y + 5z) - 2(3x + 5y +2z) = 3(228) - 2(228)
⇒ (6x + 9y + 15z) - (6x + 10y + 4z) = 228
⇒ - y + 11z = 228 .......(5)
Now, multiplying equation(5) by '11' and then add with equation (4), we get:
11y + 19z + 11(- y + 11z) = 684 + 11(228)
⇒ 140z = 3192
⇒ z = 22.8
Putting the value of 'z' in equation (5) we get:
- y + 11(22.8) = 228
⇒ y = 22.8
Now, putting the values of 'y' and 'z' in equation (1), we get:
5x + 2(22.8) + 3(22.8) = 228
⇒ 5x = 114
⇒ x = 22.8
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A(5, 23) and B(-2, 2) are two points.
(a) Find the co-ordinates of the midpoint of the line AB.
Answer:
The midpoint of (5,23) and (-2,2) is (3/2,25/2)
hope that helps
Step-by-step explanation:
Plss help mart brain list
Answer:
X=14
Step-by-step explanation:
Hope this helps , good luck ^^
sam bought 4kg of red apples some yellow apples and 3 kg of green apples she bought a total of 9,000 whats the mass of the yellow apples
Mr. Brown has 1/4pan of lasagna left in the refrigerator. He wants to cut the lasagna into equal slices so he can have it for dinner for 3 nights. What fraction of the whole lasagna will he eat each night?
Answer:
1/12
Step-by-step explanation:
He has a 1/4 pan left and wants to divide that into 3 equal pieces. So in night he will eat 1/3 of what he has left from the 1/4 pan. To figure out how much one slice is from an entire pan:
1/4 * 1/3 = 1/12
question 4 please, im not sure
Answer:
X=9
Step-by-step explanation:
Well since its a vertical angle, vertical angles are equal Or congruent.
So they equal the same so technically
3x+8=35
Solve
x=9
Answer:
x=9°
vertically opposite Angles are equal therefore (3x+8°)=35°
then 3x=35-8
3x=27
x=9
Which of the following ratios are equivalent?
O A. 5:7 and 10:12
O B. 2:3 and 12:20
O C. 6:7 and 18:21
O D. 8:9 and 32:27
Answer:
:::::::::
C. 6:7 = 18:21
answer: it is C
Step-by-step explanation:
6 = 18 because 6 times 3 is 18. And 7 times 3 = 21. so they are both equivalent.
hope it helps :)
Which best describes an angle?
A. Two distinct rays that originate from a common point
B. Two parallel lines on a plane
C. The set of all points equidistant from a particular point
D. A line with a starting point that extends to infinity
Will give to the brainliest!!
find the volume of a box whose length breadth and height are 28 CM 18 cm and 10cm respectively
I will mark them as brainlists all the best
Find the exact value of the expression cos-1(1/2)
Answer:
60
Step-by-step explanation:
Plug it into the calculator