Answers
And 24 is 2/3 of 36
Related Questions
If we put 5 math, 6 biology, 8 engineering, and 3 physics books on a bookshelf at random, what is the probability that all the math books are together?
Answers
Answer: [tex]\dfrac{3}{4389}[/tex]
Step-by-step explanation:
Given : Number of math books = 5
Total number of books = 5+6+8+3=22
Number of books except math = 17
Number of ways to arrange 22 books in bookshelf = [tex]22![/tex]
When all math books are together , then we count whole set as one
Now, the number of objects in bookshelf = 17+1=18
Number of ways to arrange books such that all math books are together = [tex]18!5![/tex]
Now, the probability that all the math books are together :-
[tex]\dfrac{5!18!}{22!}=\dfrac{3}{4389}[/tex]
Hence, the probability that all the math books are together [tex]=\dfrac{3}{4389}[/tex]
If f(x) = 2x – 1 and g(x) = – 2, find [g ◦ f](x).
Answers
Answer:
Step-by-step explanation:
Wherever you see an x in g(x) you are supposed to put f(x).
If g(x) = x
then
g(f(x)) = f(x)
g(x) = f(x)
Since g(x) has no xs, then g(f(x)) = - 2
g(x) = -2 no matter what x is in g(x)
g(2x - 1) = - 2
Answer:
[g ◦ f](x)=-2
Step-by-step explanation:
f(x) = 2x – 1
g(x) = – 2
[g ◦ f](x)
This is a composite function. It means we take f(x) and substitute it in for x in the function g(x)
g(x) = -2
There is no x in the function, so g(x) remains the same
[g ◦ f](x)= -2
Select the correct answer.
Given: BC || DE, and ∠GAC ≅ ∠AFD.
----------------------------------------------------------
What is the missing step in the proof?
Answers
Answer:
B
Step-by-step explanation:
In step 1, we found ∠GAC ≅ ∠AFD.
In step 2, we found ∠GAC ≅ ∠AFE.
Therefore, by transitive property of equality, ∠AFD ≅ ∠AFE.
Help please?
If sin O = -sqrt3 over 2 and n < O < 3 pi over 2, what are the values of cos O and tan O?
Answers
Answer:
cos(θ) = -1/2tan(θ) = √3Step-by-step explanation:
You know that ...
cos(θ)² = 1 - sin(θ)²tan(θ) = sin(θ)/cos(θ)cosine is negative in the third quadrant (where π < θ < 3π/2)Using what you know about the relationships of these trig functions, you can find ...
cos(θ)² = 1 - ((-√3)/2)² = 1 - 3/4 = 1/4
cos(θ) = -1/2 . . . . . negative square root of 1/4
__
tan(θ) = sin(θ)/cos(θ) = ((-√3)/2)/(-1/2)
tan(θ) = √3
If five numbers are selected at random from the set {1,2,3,...,20}, what is the probability that their minimum is larger than 5? (A number can be chosen more than once, and the order in which you select the numbers matters)
Answers
Answer:
the probability that their minimum is larger than 5 is 0.2373
Step-by-step explanation:
For calculate the probability we need to make a división between the total ways to selected the 5 numbers and the ways to select the five numbers in which every number is larger than 5.
So the number of possibilities to select 5 numbers from 20 is:
20 * 20 * 20 * 20 * 20
First number 2nd number 3rd number 4th number 5th number
Taking into account that a number can be chosen more than once, and the order in which you select the numbers matters, for every position we have 20 options so, there are [tex]20^{5}[/tex] ways to select 5 numbers.
Then the number of possibilities in which their minimum number is larger than 5 is calculate as:
15 * 15 * 15 * 15 * 15
First number 2nd number 3rd number 4th number 5th number
This time for every option we can choose number from 6 to 20, so we have 15 numbers for every option and the total ways that satisfy the condition are [tex]15^{5}[/tex]
So the probability P can be calculate as:
[tex]P=\frac{15^{5} }{20^{5} } \\P=0.2373[/tex]
Then the probability that their minimum is larger than 5 is 0.2373
Sid intended to type a seven-digit number, but the two 3's he meant to type did not appear. What appeared instead was the five-digit number 52115. How many different seven-digit numbers could Sid have meant to type?
Answers
Answer:
21 ways
Step-by-step explanation:
number = 7 digit
5 digit no = 52115
to find out
How many different seven-digit numbers
solution
first we need to place the two missing 3s in the number 52115
we consider here two cases
case 1 the two 3's appear separated (like 532135 or 3521135)
case 2 the two 3's appear together (like 5332115 or 5211533)
Case 1 we can see that number type as _5_2_1_1_5_
place 3's placeholders show potential locations
( type a ) for 3's separated we will select 2 of 6 place and place 3 in every location so we do this 6C2 = (15) ways
and (type b): again use same step as _5_2_1_1_5_
here 3s together for criterion and we will select 1 of the 6 place and place both 3s here and there are 6 ways.
so that here will be 15+6=21 ways
If 3 and 3 are separate so 6C2 = 15 ways
If 3 and 3 are together so there = 6 ways
= 15 + 6 = 21 ways
In triangle ABC, mA=35, mB=40, and a=9. Which equation should you solve for b?
A. sin35/b=sin40/9
B. sin35/9=sin40/b
C. cos35/9=cos40/b
D.b sqaure=9 square-2(9)bcos40
Answers
Answer:
B. sin35/9=sin40/b
Step-by-step explanation:
The law of sines tells you ...
sin(A)/a = sin(B)/b
Filling in the given values, you get ...
sin(35°)/9 = sin(40°)/b
Answer:
B.[tex]\frac{sin 35}{9}=\frac{sin 40 }{b}[/tex]
Step-by-step explanation:
We are given that in a triangle ABC. [tex]m\angle =35^{\circ}[/tex]
[tex]m\angle B=40^{\circ}[/tex]
a=9
We have to find an equation which solve for b
We know that a sine law
[tex]\frac{a}{sine A}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]
Using above formula of sine law
Substituting all given values in the above formula of sine law
Then we get
[tex]\frac{9}{sin 35}=\frac{b}{sin 40}[/tex]
By cross multiply then we get
[tex]sin 40\times 9=sin35 \times b[/tex]
[tex] \frac{sin 40 \times 9}{b}= sin 35[/tex]
Using division property of equality
[tex]\frac{ sin 40}{b}=\frac{sin 35}{9}[/tex]
Using division property of equality
Hence, option B is true option for solving b.
Answer:B.[tex]\frac{sin 35}{9}=\frac{sin 40 }{b}[/tex]
Connie, a marketing director, lost her job when her company downsized. This is an example of what type of unemployment?
Answers
Answer:
Cyclical unemployment.
Step-by-step explanation: It is not part of the natural unemployment rate.
It's caused by the contraction phase of the business cycle. That's when demand for goods and services generated by the company fall dramatically, forcing businesses to lay off large numbers of workers to cut or reduce costs.
The number N = 100 + 100^2 + 100^3 + ... + 100^n . Find the least possible value of n such that the number N is divisible by 11. NEED QUICKLY! Thanks!!!
Answers
Answer:
Step-by-step explanation:
very interesting question. The temptation is to say that n should be 11 and that likely is divisible by 11 but it may not be the smallest.
100 + 100^2 = 100 + 10000 = 10100
The pattern of the series goes 101010101 ... 00...
100 / 11 = The remainder is 1/11
10100 / 11 = the remainder is 2/11
1010100 /11 the remainder is 3/11
The pattern suggests that the remainder will be 0 then n = 11
There might be other ways of doing this, but I don't know them.
Which is the angle of elevation from C to B?
Answers
Answer:
∠4
Step-by-step explanation:
The angle of elevation is the measure of the angle from the horizontal upwards.
The angle of elevation from C to B is ∠4
Angle of elevation from C to B will be ∠4. Option (1) will be the answer.
Angle of elevation of an object from a point:Angle of elevation of an object from a point on the ground is defined by,
"Angle between the horizontal line and line of site (line joining the observer and the object above the horizontal line)"
Following the definition,
Angle of elevation of an object at B from C will be → ∠4
Therefore, Option (1) will be the answer.
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A manufacturer of yoga pants sells them for $28 each. They hired some consultants who determined that the cost of manufacturing x pants was C\left(x\right)=x^2-2x-9 C ( x ) = x 2 − 2 x − 9 . a)Write a function for the revenue (the amount of money the company brings in). b)Write a function for the profit (the revenue – cost). c)Find the number of t-shirts they should make to maximize the profit function. Round your answer to the nearest whole number.
Answers
Answer:
a) r(x) = 28x
b) p(x) = -x^2 +30x +9
c) 15
Step-by-step explanation:
a) Let x represent the number of items sold. Each sale results in $28 of revenue, so the revenue function r(x) is ...
r(x) = 28x
__
b) p(x) = r(x) - c(x) = 28x -(x^2 -2x -9)
p(x) = -x^2 +30x +9
__
c) The axis of symmetry of ax^2 +bx +c is -b/(2a). Here, the axis of symmetry of the profit function is ...
x = -30/(2(-1)) = 15
15 is the quantity of sales that maximizes profit.
The Fibonacci numbers are a sequence of integers in which the first two elements are 1, and each following element is the sum of the two preceding elements. The mathematical definition of each kth Fibonacci number is the following:
Answers
Answer:
[tex]F_{k^{th}}=F_{(k-2)^{th}}+F_{(k-1)^{th}}[/tex]
Step-by-step explanation:
Since each number is the sum of it's 2 preceding numbers thus mathematically it can be written as
[tex]F_{k^{th}}=F_{(k-2)^{th}}+F_{(k-1)^{th}}[/tex]
Fibonacci Series can be written as
1,1,2,3,5,8,13...
A nontoxic furniture polish can be made by combining vinegar and olive oil. The amount of oil should be three times the amount of vinegar. How much of each ingredient is needed in order to make 34 oz of furniture polish?
Answers
Answer:
V=8.5
Step-by-step explanation:
o=oil. vinegar=v. furniture polish=f
O=3v
34= 3v + v
Using a system of guessing and checking if that number fits equation you can tell that 8 causes the equation to be unequal and also 9. You can learn V must be between 8 and 9 so 8.5 might fit the equation. 8.5=V
Final answer:
To make 34 oz of furniture polish, 8.5 oz of vinegar and 25.5 oz of olive oil are needed, with the olive oil being three times the amount of vinegar.
Explanation:
To create 34 oz of nontoxic furniture polish, where the amount of olive oil should be three times the amount of vinegar, we need to solve a simple algebraic equation. Let's denote the amount of vinegar as v ounces. According to the conditions, the amount of olive oil will then be 3v ounces.
The total amount of furniture polish equals the amount of vinegar plus the amount of olive oil:
v + 3v = 34 oz
This simplifies to:
4v = 34 oz
Dividing both sides by 4 gives us:
v = 8.5 oz
Therefore, the amount of olive oil needed is:
3v = 3 Times 8.5 oz = 25.5 oz
To conclude, we need 8.5 oz of vinegar and 25.5 oz of olive oil to make 34 oz of furniture polish.
Two sides of an isosceles triangle have lengths 7 and 14. Find the length of the third side.
PLS HELP
Answers
Answer:
14
Step-by-step explanation:
An isosceles triangle has two sides that are the same. If one side is 7 and another is 14, then the two possibilities are 7, 7, and 14, or 14, 14, and 7.
It can't be 7, 7, and 14, because the sum of the shortest sides of a triangle must be greater than the longest side.
Therefore, it must be 14, 14, and 7. So the third leg is 14.
The length of third side of the isosceles triangle is 14.
What is an isosceles triangle ?An isosceles triangle is a triangle that has two sides of equal length. Also the property of isosceles triangle states that the base angle of the isosceles triangle subtends angle of equal measure.
How to find the length of third side of given isosceles triangle ?It is given that the two sides of the triangle have lengths 7 and 14.
Thus for the triangle to be isosceles, the third side of the triangle will have the length as 7 or 14.
We know that the sum of any two sides of a triangle must be greater than the third side.
Thus if the third side is 7, then the sum of the sides will be (7 + 7) = 14 which is not greater than the other side. So, third side will not be of length 7 units.
The third side of the isosceles triangle is of 14 units .
Therefore, the length of third side of the isosceles triangle is 14.
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Fill in the blank.
1+8+4+7+3+_+1=24
Answers
Answer:
0
Step-by-step explanation:
if you added anything else you would be higher than 24
An object is launched upward from 62.5 meters above ground level with an initial velocity of 12 meters per second. The gravitational pull of the earth is about 4.9 meters per second squared. How long will the object take to hit the ground? 5) Explain which model would you would choose and why.An object is launched upward from 62.5 meters above ground level with an initial velocity of 12 meters per second. The gravitational pull of the earth is about 4.9 meters per second squared. How long will the object take to hit the ground? 5) Explain which model would you would choose and why.
Answers
Answer:
5 seconds
Step-by-step explanation:
This follows the pattern
[tex]h(t)=-4.9t^2+v_{0}t+h_{0}[/tex]
It is parabolic and it is used to model projectile motion. This is the model you would use. Now for the math of it.
The v₀ is the initial velocity and the h₀ is the initial height. The whole thing is negative because it is an upside down parabola. Our initial velocity is 12 and the initial height is 62.5. That means that our particular model is
[tex]h(t)=-4.9t^2+12t+62.5[/tex]
h(t) is the height of the projectile after a certain length of time, t, has gone by. We want to know how long, t, it takes the projectile to hit the ground. When something is laying on the ground, its height is 0. Therefore, in order to find how long it takes for the height to be 0, we replace h(t) with 0 and then factor to find the values of t:
[tex]0=-4.9t^2+12t+62.5[/tex]
If you plug this into the quadratic formula you will get that the values of t are
t = -2.55 and t = 5
We all know that the 2 things in math that will never EVER be negative are time and distance/measures, so we can disregard the negative value of time and say that the length of time it takes for the object to hit the ground from its initial height of 62.5 m is 5 seconds.
your bank balance is 515.50. if you write a check to buy a watch, your balance would be 496.11. how much dose the watch cost ? writ a linear equation on that models the situation
Answers
The answer is:
[tex]WatchCost=StartingBalance-EndingBalance\\\\WatchCost=515.50-496.11=19.39[/tex]
The cost of the watch is $19.39.
Why?To solve the problem, we can create a linear equation using the given information about the starting balance and the ending balance.
We know that the starting balance was $515.50, and then, after writing a check to buy the watch, the balance was $496.11, so, writing the function we have:
[tex]WatchCost=StartingBalance-EndingBalance\\\\WatchCost=515.50-496.11=19.39[/tex]
Hence, we have that the cost of the watch is $19.39.
Have a nice day!
Choose the correct answer below. A. The first step in the process of statistics is to collect the data. B. Data are typically collected from a sample because it is too difficult and expensive to collect data from an entire population. C. When the results from a sample are extended to the population, it is called inference. D. If data are not collected properly, the conclusions that are drawn will be meaningless.
Answers
Answer: The following statements are correct :
Data are typically collected from a sample because it is too difficult and expensive to collect data from an entire population.
When the results from a sample are extended to the population, it is called inference.
If data are not collected properly, the conclusions that are drawn will be meaningless.
The following statement is false: The first step in the process of statistics is to collect the data.
The first step in the process of statistics is to Plan: develop a statistical inquiry that can be answered with aggregation of data.
Which graph shows the solution set of x^2+4x-12/x>0?
Answers
Answer:
D
Step-by-step explanation:
Consider the inequality
[tex]\dfrac{x^2+4x-12}{x}>0[/tex]
First, factor the numerator:
[tex]x^2+4x-12=x^2+6x-2x-12=x(x+6)-2(x+6)=(x+6)(x-2)[/tex]
Now, the inequality is
[tex]\dfrac{(x+6)(x-2)}{x}>0[/tex]
The equivalent inequality is
[tex]x(x+6)(x-2)>0[/tex]
On the number line plot doted points -6, 0 and 2 and put signs +, -, +, - from the right to the left. Intervals with + signs are the solution of the inequality:
[tex]x\in(-6,0)\cup(2,\infty)[/tex]
that is represented by D number line.
Answer:
D
Step-by-step explanation:
Angle D is a circumscribed angle of circle O.
What is the perimeter of kite OBDE?
A) 17 units
B) 23 units
C) 27 units
D) 40 units
Answers
Answer:
The answer is 27 on edge as well!
Step-by-step explanation:
The answer is 27
This is because 15x15 is 225 plus 8x8 is 64 which is 289 and the square root of that is 17 and that is the diameter of the circle and the hypotenuse of the triangle and since the kite has two congruent sides which are both radii or half of a diameter times two would be the same as the length of the diameter which is 17 plus the two bottom sides which are both 5 and 5 plus 5 is 10 and 10 plus 17 is 27 or the perimeter of the kite.
Your Welcome!
Answer:
27
Step-by-step explanation:
im taking the test right now on edg. 2020
A phone company offers two monthly plans. Plan A costs $11 plus an additional $0.17
for each minute of calls. Plan B costs $16 plus an additional $0.13 for each minute of calls.
For what amount of calling in minutes do the two cost the same?
What is the cost when the two plans cost the same?
Answers
Answer:
125 minutes of calling
It will cost $32.25 when the plans cost the same.
Step-by-step explanation:
The first plan's expression would be:
11+.17x x being the number of minutes
The second plan's expression would be:
16+.13x
You must set the expressions equal to one another. So:
11+.17x=16+.13x
Then solve for x:
.17x=5+.13x
.04x=5
x=125
So the plans will cost the same after 125 minutes. To find the cost of the plans at that time, substitute 125 in for the x in one of the equations.
11+.17(125)=y y being the overall cost of the plan
11+21.25=y
32.25=y
To check your answer, you can substitute again in the other equation:
16+.13(125)=y
16+16.25=7
32.25=7
The revenue (in thousands of dollars) from producing x units of an item is modeled by R(x) = 12x -0.005x^2.
Find the average rate of change in revenue as x changes from 1001 to 1008.
The average rate of change in revenue is ____ dollars per unit.
(Do not round until the final answer. Then round to the nearest integer as needed.)
I just need to know how to solve this problem, I know the answer. Thank you!
Answers
Answer:
See below.
Step-by-step explanation:
Average rate of change =( R(1008) - R(1001) ) / (1008 - 1001)
=[ 12(1008) - 0.005(1008)^2 - (12(1001) - 0.005(1001)^2) ] / 7
Answer:
2
Step-by-step explanation:
Average rate of change is just the slope.
You want to find the slope of the line that goes through x=1001 and x=1008 while on R(x)=12x-0.005x^2.
So y=R(x)... R(x) will give your corresponding y values for the x's mentioned.
Just plug them in.
R(1001)=12(1001)-0.005(1001)^2=7001.995
R(1008)=12(1008)-0.005(1008)^2=7015.68
So now the question just becomes find the slope of the line that goes through
(1001,7001.995) and (1008,7015.68).
To find the slope of a line given two points: I just lined the points up and subtract vertically. Afterwards I put the second number on top of the first number.
So let's do that!
(1008 , 7015.68)
-(1001, 7001.995)
------------------------------
7 13.685
So the slope also known as the average rate of change here is 13.685/7.
Putting 13.685 divided by 7 into my calculator returns the value 1.955.
This rounded to the nearest integer is 2.
$2000 borrowed with 10% interest rate, got additional 1000 on the same rate for the same period of repayment. How much would he have saved if he borrow $3000 for the same rate and period of repayment?
Answers
Answer:
nothing
Step-by-step explanation:
Loan payments are linear in the loan amount for a given rate and period, so the payments for loans of $2000 and $1000 sum to the amount of payments for a loan of $3000.
The only possible savings (or cost) might come from rounding to the nearest cent. (In any event, the final payment on each loan should make up for any differences due to rounding.)
Answer:
nothing
Step-by-step explanation:
Loan payments are linear in the loan amount for a given rate and period, so the payments for loans of $2000 and $1000 sum to the amount of payments for a loan of $3000.
The only possible savings (or cost) might come from rounding to the nearest cent. (In any event, the final payment on each loan should make up for any differences due to rounding.)
HELPPPP!!!
Select the correct answer.
Which function is an even function?
Answers
Answer:
C.
Step-by-step explanation:
p(x)=sin(x) is an odd function since sin(-x)=-sin(x).
q(x)=cos(x) is an even function since cos(-x)=cos(x).
r(x)=tan(x) is an odd function since tan(-x)=-tan(x).
s(x)=csc(x) is an odd function since csc(-x)=-csc(x).
So the only contender seems to be C.
Let's check. To check we have to plug in (-x) in place of (x) and see if we get the same function back since we are looking for an even function.
[tex]f(x)=\cos(\frac{5\pi}{4}x)[/tex]
Replace (x) with (-x):
[tex]f(-x)=\cos(\frac{5\pi}{4}(-x)[/tex]
[tex]f(-x)=\cos(\frac{-5\pi}{4}x)[/tex]
[tex]f(x)=\cos(\frac{5\pi}{4}x)[/tex] since cosine is even; that is cos(-u)=cos(u) where u in this case is [tex]\frac{5\pi}{4}x[/tex].
So f is even.
C. f(x) = cos(x) The cosine function is an even function. So, the correct answer is C. f(x) = cos(x).
An even function is a function that satisfies the following property:
f(x) = f(-x)
Let's examine the provided functions:
A. f(x) = sin(-31)
This is not an even function because the sine function is an odd function, and negating the angle in a sine function doesn't produce an even function.
B. f(x) = tan(3x)
The tangent function is an odd function, so this function is not even.
C. f(x) = cos(x)
The cosine function is an even function. This is the correct answer.
D. f(x) = csc(-1)
The cosecant function (csc) is the reciprocal of the sine function, and as mentioned earlier, the sine function is an odd function. So, the cosecant function is also odd, and this function is not even.
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8.39+(-2.00)+161
i got 167.39 but it isnt correct
so if yall could help me plsssss
Answers
Answer:
8
Step-by-step explanation:
167.39 is right but it can be simplified.
1.61 was replaced by (161/100).
3 more similar replacement(s)
839 2 161
(——— + (0 - —)) +
100 1 100
639 + 161 8
—————————
100 1
Sorry if it looks confusing
Solve each equation by graphing. Round to the nearest tenth.
-2x^2+2=-3x
Answers
Answer:
x = -0.5 or x = 2
Step-by-step explanation:
Finding solutions graphically is often easier if the equation can be put in the form f(x) = 0. Here, we can do that by subtracting the right-side expression to give ...
(-2x^2 +2) -(-3x) = 0
This could be put in standard form, but there is no need. A graphing calculator can deal with this directly.
The solutions are x = -0.5 and x = 2.
If sine theta equals three over four, what are the values of cos θ and tan θ?
cosine theta equals plus or minus square root of seven over four, tangent theta equals plus or minus two times square root of seven over seven
cosine theta equals plus or minus seven over four, tangent theta equals negative three over seven
cosine theta equals plus or minus square root of seven over 4, tangent theta equals plus or minus three over seven
cosine theta equals plus or minus seven over four, tangent theta equals negative one over seven
Answers
Answer:
In words, Cosine theta equals plus or minus square root of seven over 4,tangent theta equals plus or minus three over root seven
Step-by-step explanation:
Given that sin ∅ =3/4 It means the ratio of the opposite side to the hypotenuse side is 3:4.
Using the Pythagoras theorem we can calculate the hypotenuse adjacent as follows.
a²+b²=c²
a²=c²-b²
a²=4²-3²
a²=16-9
a²=7
a=√7
Then Cos ∅= opposite/ adjacent
=√7/4
Then Tan ∅ = opposite/adjacent
=3/√7
In words, Cosine theta equals plus or minus square root of seven over 4,tangent theta equals plus or minus three over root seven.
Out of 100 people at a tennis match, 66% were rooting for the local champion. If two people were chosen at random from the crowd, what is the probability that at least one of them was not rooting for the champion?
Question 16 options:
22.7%
56.7%
59.2%
43.3%
Answers
Answer:
Approximately 56.7%.
Step-by-step explanation:
Choose two people at random from the crowd and there will be two cases:
Zero or one out of the two person was rooting for the champion, or both were rooting for the champion.There's no third possible outcome. In other words, the two cases are mutually exclusive. Either the first or the second event is expected to happen. The sum of their probabilities shall equal to 1.
66 out of that 100 were rooting for the champion. The probability that both were rooting for the champion will be easier to find. The probability that the first person is rooting for the champion is equal to [tex]66/100[/tex].
After that first person was chosen from the crowd, the 65 out of the remaining 99 person in the crowd were chanting. The probability that the second person is rooting as well will equal to [tex]65/100[/tex].
Both event shall take place. The probability that both were rooting for the champion will equal to
[tex]\displaystyle \frac{66}{100} \times \frac{65}{99}[/tex].
The probability that one or zero out of the two persons were rooting will equal to
[tex]\displaystyle 1 - \frac{66}{100} \times \frac{65}{99} \approx \frac{17}{30} = 56.7\%[/tex].
Answer:
56.7% is correct.
Step-by-step explanation:
A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of 34 , 000 miles and a standard deviation of 2500 miles. He wants to give a guarantee for free replacement of tires that don't wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires?
Answers
Answer:
He should word his statement as "Free replacement for tires that wear before 30875 miles."
Step-by-step explanation:
If he is willing to replace 10% of tires he should find the life of tires that gives an area of 10% in the normal distribution graph.
Now for 10% of area standard normal deviate Z can be obtained from normal distribution table
Using normal distribution table for 10% area we have Z = -1.28
Thus we have [tex]Z=\frac{X-\overline{X}}{\sigma }\\\\\therefore X=\sigma Z+\overline{X}[/tex]
Applying given values we get
[tex]X=-1.28\times 2500+34000\\\\X=30875miles[/tex]
The mechanic would replace the tires that spoil without covering up to 30800 miles.
What is z score?Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean) / standard deviation
For a mean of 34000 miles and standard deviation of 2500. The probability of 10% correspond with a z score of -1.28. Hence:
-1.28 = (x - 34000)/2500
x = 30800
The mechanic would replace the tires that spoil without covering up to 30800 miles.
Find out more on z score at: https://brainly.com/question/25638875
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Find the standard form of the equation of the hyperbola x2 − 4y2 − 2x + 16y − 31 = 0. Place the signs and values in the correct places in the standard form of the equation.
Answers
Answer:
(x - 1)²/4² - (y - 2)²/2² = 1 ⇒ The bold labels are the choices
Step-by-step explanation:
* Lets explain how to solve this problem
- The equation of the hyperbola is x² - 4y² - 2x + 16y - 31 = 0
- The standard form of the equation of hyperbola is
(x - h)²/a² - (y - k)²/b² = 1 where a > b
- So lets collect x in a bracket and make it a completing square and
also collect y in a bracket and make it a completing square
∵ x² - 4y² - 2x + 16y - 31 = 0
∴ (x² - 2x) + (-4y² + 16y) - 31 = 0
- Take from the second bracket -4 as a common factor
∴ (x² - 2x) + -4(y² - 4y) - 31 = 0
∴ (x² - 2x) - 4(y² - 4y) - 31 = 0
- Lets make (x² - 2x) completing square
∵ √x² = x
∴ The 1st term in the bracket is x
∵ 2x ÷ 2 = x
∴ The product of the 1st term and the 2nd term is x
∵ The 1st term is x
∴ the second term = x ÷ x = 1
∴ The bracket is (x - 1)²
∵ (x - 1)² = (x² - 2x + 1)
∴ To complete the square add 1 to the bracket and subtract 1 out
the bracket to keep the equation as it
∴ (x² - 2x + 1) - 1
- We will do the same withe bracket of y
- Lets make 4(y² - 4y) completing square
∵ √y² = y
∴ The 1st term in the bracket is x
∵ 4y ÷ 2 = 2y
∴ The product of the 1st term and the 2nd term is 2y
∵ The 1st term is y
∴ the second term = 2y ÷ y = 2
∴ The bracket is 4(y - 2)²
∵ 4(y - 2)² = 4(y² - 4y + 4)
∴ To complete the square add 4 to the bracket and subtract 4 out
the bracket to keep the equation as it
∴ 4[y² - 4y + 4) - 4]
- Lets put the equation after making the completing square
∴ (x - 1)² - 1 - 4[(y - 2)² - 4] - 31 = 0 ⇒ simplify
∴ (x - 1)² - 1 - 4(y - 2)² + 16 - 31 = 0 ⇒ add the numerical terms
∴ (x - 1)² - 4(y - 2)² - 16 = 0 ⇒ add 14 to both sides
∴ (x - 1)² - 4(y - 2)² = 16 ⇒ divide both sides by 16
∴ (x - 1)²/16 - (y - 2)²/4 = 1
∵ 16 = (4)² and 4 = (2)²
∴ The standard form of the equation of the hyperbola is
(x - 1)²/4² - (y - 2)²/2² = 1
Answer:
Refer to attachment below.