a) Note that the probability that the 10th transistor produced is the first with a defect is: ≈ 0.0171
b) The probability that the machine produces no defective transistors in a batch of 100 is: ≈ 0.1338
c) The expected value of a geometric distribution is 1/p, so the expected number of transistors before the first defective one is: = 50
d) The expected value and standard deviation for the number of transistors produced before the first with a defect is ≈ 18.71
e) Increasing the probability of an event affects the mean and standard deviation of the wait time until success in opposite ways.
What is the rationale for the above responses?(a) Since each transistor is independent, the probability that the 10th transistor produced is the first with a defect is the same as the probability that the first 9 transistors are not defective and the 10th one is defective. The probability that a transistor is not defective is 1 - 0.02 = 0.98. Therefore, the probability is:
P(1st defective on 10th) = (0.98)⁹ x 0.02 ≈ 0.0171
(b) The probability that the machine produces no defective transistors in a batch of 100 is:
P(no defects in 100) = (0.98)¹⁰⁰ ≈ 0.1338
(c) The number of transistors produced before the first with a defect follows a geometric distribution with parameter p = 0.02. The expected value of a geometric distribution is 1/p, so the expected number of transistors before the first defective one is:
E(X) = 1/p = 1/0.02 = 50
The variance of a geometric distribution is (1-p)/p², so the standard deviation is:
σ = √((1-p)/p²)
= √(0.98/0.0004)
≈ 22.36
(d) The expected value and standard deviation for the number of transistors produced before the first with a defect are calculated in the same way as in (c), but with a different value of p:
E(X) = 1/p = 1/0.05 = 20
σ = √((1-p)/p₂)
= √(0.95/0.0025)
≈ 18.71
(e) Increasing the probability of an event affects the mean and standard deviation of the wait time until success in opposite ways.
As the probability of an event increases, the expected wait time until success decreases. In other words, the mean becomes smaller. However, as the probability of an event increases, the variability in the wait time until success also increases.
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Answer:
(a) 0.0167
(b) 0.1326
(c) The expected value, mean, μ = 50 SD, σ = 49.4975
(d) The expected value, mean, μ = 20 SD, σ = 19.4936
(e) Increasing the probability of an event decreases the mean and standard deviation of the wait time until success.
Step-by-step explanation:
Can you help on this math problem please
The proportional equation for the given graph would be y = 2. 5 x
How to find the proportional equation?The proportional equation takes the form :
y = mx
Where:
m = slope or the change in y as a result of x
The value of the slope is :
= Change in y / Change in x
= ( 15 - 0 ) / ( 6 - 0 )
= 15 / 6
= 2. 5
The proportional equation is:
y = 2. 5 x
In conclusion, the proportional equation would be y = 2. 5 x .
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Use this table to answer the question. Round to 2 decimal places.
Car Plane Train Total
Green 120 250 500 870
Blue 150 350 750 1250
Yellow 170 200 450 820
Red 200 300 300 800
Brown 220 450 320 990
Total 860 1550 2320 4730
What percent of the total are made up of Yellow Trains?
Therefore, Yellow Trains make up 9.5% of the total modes of transportation in the table.
It's unclear what the percentages mean.A percentage that corresponds to one tenth of an amount. One percent, represented by the symbol 1%, is equivalent to one hundredth of something; hence, 100 percent represents the complete object, and 200 percent represents twice the amount given.
According to the table:
The total number of Yellow Trains is 450.
The total number of all modes of transportation is 4730.
To calculate the percentage of the total that Yellow Trains make up, we can use the following formula:
percentage = (part/whole) x 100
Substituting the values we have:
percentage = (450/4730) x 100
percentage = 0.095 x 100
percentage = 9.5%
Therefore, Yellow Trains make up 9.5% of the total modes of transportation in the table.
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Solve the following and list any extraneous solutions
1. √30- x = x
2. x = √42 - x
3. √12-r=r
4. m = √56 - m
5. r = √-1-2r
6. √4n+8 = n +3
7. -n+√6n + 19 = 2
8. 4+√-3m + 10 = m
9. x-5=√x+1
10. n-7= √√3n - 21
The evaluation of equations by resolving into quadratic equations and factoring are presented as follows;
x = -6 and x = 5x - -7 and x = 6r = -4 and r = 3m = -8 and m = 7r = -1n = -1x = 5 and x = -3m = 3 and m = 2x = 8 and x = 3n = 10 and n = 7What are quadratic equations?A quadratic equation is an equation which can be expressed as; f(x) = a·x² + b·x + c, where a, b, and c are real numbers and a ≠ 0.
1. √(30 - x) = x
x = √(30 - x)
x² = 30 - x
x² + x - 30 = 0
Factoring the above quadratic equation, we get;
(x + 6)·(x - 5) = 0
x = -6 and x = 52. x = √(42 - x)
x² = 42 - x
x² + x - 42 = 0
(x + 7)·(x - 6) = 0
x = -7 and x = 63. √(12 - r) = r
Squaring both sides of the equation, we get;
(12 - r) = r²
r² = 12 - r
r² + r - 12 = 0
(r + 4)·(r - 3) = 0
r = -4 and r = 34. m = √(56 - m)
m² = 56 - m
m² + m - 56 = 0
(m + 8)·(m - 7) = 0
m = -8, and x = 75. r = √(-1 - 2·r)
r² = -1 - 2·r
r² + 2·r + 1 = 0
(r + 1)² = 0
r = -16. √(4·n + 8) = n + 3
4·n + 8 = (n + 3)² = n² + 6·n + 9
4·n + 8 = n² + 6·n + 9
n² + 6·n + 9 - (4·n + 8) = 0
n² + 6·n + 9 - 4·n - 8 = 0
n² + 2·n + 1 = 0
(n + 1)² = 0
n = -17. -n + √(6·n + 19) = 2
-n + √(6·n + 19) = 2
√(6·n + 19) = n + 2
(6·n + 19) = (n + 2)² = n² + 4·n + 4
6·n + 19 = n² + 4·n + 4
n² + 4·n + 4 = 6·n + 19
n² + 4·n + 4 - (6·n + 19) = 0
n² - 2·n - 15 = 0
(x - 5)·(x + 3) = 0
x = 5 and x = -38. 4 + √(-3·m + 10) = m
√(-3·m + 10) = m - 4
-3·m + 10 = (m - 4)² = m² - 8·m + 16
-3·m + 10 = m² - 8·m + 16
m² - 8·m + 16 = -3·m + 10
m² - 8·m + 16 + 3·m - 10 = 0
m² - 5·m + 6 = 0
(m - 3)·(m - 2) = 0
m = 3, and m = 29. x - 5 = √(x + 1)
Squaring both sides, we get;
(x - 5)² = (√(x + 1))²
(x - 5)² = x + 1
x² - 10·x + 25 = x + 1
x² - 10·x + 25 - (x + 1) = 0
x² - 10·x + 25 - x - 1 = 0
x² - 11·x + 24 = 0
(x - 8)·(x - 3) = 0
x = 8 and x = 310. n - 7 = √(3·n - 21)
(n -7)² = (3·n - 21)
n² - 14·n + 49 = 3·n - 21
n² - 14·n + 49 - (3·n - 21) = 0
n² - 14·n + 49 - 3·n + 21 = 0
n² - 17·n + 70 = 0
(n - 10)·(n - 7) = 0
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Point P is inside ΔABC and is equidistant from points A and B. On which of the following segments must P be located? A. AB B. The perpendicular bisector of AB C. The midsegment opposite AB D. The perpendicular bisector of AC
Answer:
Step-by-step explanation:
ASQASSA
In the year 2020, there were 14.02 billion cell phones in use worldwide. In 2022, the number
increased to 15.96 billion worldwide.
a. What is the average rate of change in the number of worldwide cell phones?
b. Using 14.02 as the initial amount, write a linear equation that models the number of
worldwide cell phones. Make sure to define the variables.
C.If the rate stays the same, predict the number of cell phones that will be in use worldwide
in the year 2027.
Answer:
Step-by-step explanation:
a. The average rate of change in the number of worldwide cell phones can be calculated as:
Average rate of change = (change in number of cell phones) / (change in time)
The change in number of cell phones is 15.96 billion - 14.02 billion = 1.94 billion, and the change in time is 2 years. Therefore,
Average rate of change = 1.94 billion / 2 years = 0.97 billion/year
So, the average rate of change in the number of worldwide cell phones is 0.97 billion per year.
b. We can use the point-slope form of a linear equation to model the number of worldwide cell phones. Let t be the time in years since 2020, and C(t) be the number of worldwide cell phones in billions. Then the equation can be written as:
C(t) - 14.02 = 0.97t
Simplifying, we get:
C(t) = 0.97t + 14.02
So, the linear equation that models the number of worldwide cell phones is C(t) = 0.97t + 14.02.
c. To predict the number of cell phones that will be in use worldwide in the year 2027, we need to find the value of C(2027 - 2020) = C(7) using the linear equation we derived in part (b).
C(7) = 0.97(7) + 14.02 = 20.83 billion
Therefore, if the rate stays the same, we can predict that there will be 20.83 billion cell phones in use worldwide in the year 2027.
You deposit $1000 each year into an account earning 6% interest compounded annually. How much will you have in the account in 25 years?
If you put $1,000 per year into an account yielding 6% interest that is compounded annually, you will have $4291.8 in the account after 25 years.
What is simple interest?Divide its principal by the risk premium, the time period and other factors to arrive at simple interest. Simple return = principal + interest + hours is the marketing formula. This process makes it easier to calculate interest. The most typical technique to figure out interests is as a portion of the principal sum. He will only pay his half of the 100% interest, for example, if he borrows $100 from a partner and agrees to repay the loan with 5% interest. $100 (0.05) = $5. When you keep borrowing, you must pay interest, and when you give it out, you must pay the interest. Interest is often set as an annual percentage of the loan total.
given:
FV = 1000(1.06)²⁵
FV = 1000 × 4.2918
FV = 4291.8
If you put $1,000 per year into an account yielding 6% interest that is compounded annually, you will have $4291.8 in the account after 25 years.
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i dont understand at all
The equation is given by 5n + 100n = 210
Peggy has 8 quarters and 2 nickels
Let's call q the number of quarters and n the number of nickels.
If Peggy has four times as many quarters as nickels, we can write the following equation:
q = 4n
Then, each quarter has a value of 0.25 dollars and each nickel has a value of 0.05 dollars, so
0.25q + 0.05n = 2.10
Because she had $2.10. Now, we can replace the first equation on the second one
0.25(4n) + 0.05n = 2.10
1n + 0.05n = 2.10
Finally, we can multiply both sides by 100, so
100n + 0.05(100)n + 2.10(100)
100n + 5n = 210
Therefore, the equation that can be used to solve the problem is
5n + 100n = 210
Now, we can solve the equation for n
105n = 210
105n/105 = 210/105
n = 2
Then, q is equal to
q = 4n
q = 4(2)
q = 8
It means that Peggy has 8 quarters and 2 nickels.
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complete question is listed below:
Peggy had four times as many quarters as nickels. She had $2.10 in all. How many nickels and how many quarters did she have?
Which of the following equations could be used to solve the problem?
On+4 n=210
5 n+100 n=210
n+4 n=2.10
5n+100 n=2.10.
Someone please help me :(
Explain in detail the process/steps you would use to factor 6x^2-11x+4. Explain how you can prove your answer is correct. Then show your work for checking your answer.
Answer:
(2x-1)(3x-4)
Step-by-step explanation:
6x²-11x+4
Now we will split the middle term so when we add the digits it will give the original number back but when we multiply them, it will give the sum of the first and the last digit
6x²-11x+4
6x²-3x-8x+4
Now you can that if we add -3 and -8, we get -11 back but if we multiple them, we get the sum of 6 and 4 (the first and the last digits), which is 24
Now we will simplify the values
3x(2x-1) - 4(2x-1)
Simplifying further, we get
(2x-1) (3x-4) which is the answer
100 POINTS WILL MARK BRAINLIEST PLEASE HELPPPP
Answer: B. 3300
Step-by-step explanation: Answers in the 5000 range would be Expenses, and 2000 would be Liabilities, which are both opposite of capital. "S.E." in accounting typically stands for "Shareholder Equity" or "Stockholder's Equity" and would be one type of capital.
Zachary invests $400 into an account that earns 3.5% simple interest for 5 years. He does not make any other deposits or withdrawals.
At the end of 5 years, Zachary invests the entire account balance into a different account that earns 5% simple interest. He leaves the money in the account for 2 years without making any additional deposits or withdrawals.
What is the new account balance at the end of 2 years?
The new account balance at the end of 2 years is $517.
Simple interest
5 yearsUsing this formula I= (P+r×t)
Where: I=Interest=?
P=Principal=$400
r=Interest rate=3.5%
t=Time=5 years
Hence: I= ($400×0.035 x 5) which makes I= $70
2 years
I=Interest=?
P=Principal=$470
r=Interest rate=5%
t=Time=2 years
I=($470+0.05×2) which makes I=$47
New balance:
New balance=$400+$70+$47
New balance=$517
Inconclusion the new account balance at the end of 2 years is $517.
help with maths problem please
The area of the shaded region is 73.5 cm square.
How to find the area of a region?Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly. Then summing all those pieces' area gives us the area of the main big region.
We are given the dimension of the shaded region.
Length = 15 cm
Breadth = 7 cm
The area of the trapezium is
Area = 1/2(sum of non parallel sides)height
Area = 1/2 (12 + 9) 7
Area = 1/2 x 21 x 7
Area = 73.5
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Number of strike outs after 20 hours
Answer:
According to the line of fit, after 20 hours of practice, the predicted number of strikeouts is 400.
Step-by-step explanation:
The equation given is:
y = 20x + 0
where y represents the number of strikeouts and x represents the number of hours of practice. To find the number of strikeouts after 20 hours of practice, we substitute x = 20 into the equation and solve for y:
y = 20(20) + 0
y = 400
Therefore, according to the line of fit, after 20 hours of practice, the predicted number of strikeouts is 400.
What is the approximate length of side a? A. 6.62 m B. 8.78 m C. 13.77 m D. 18.21 m
Answer:
C. 13.77 m
Step-by-step explanation:
The sum of the three angles of a triangle is 180°
In the given triangle, two of the angles are 37° and 90°
Third angle = 180 - (37 + 90) = 53°
By the law of sines, ratio of a side to the sine of the opposite angle is the same for all sides and their opposite angles
∴
[tex]\dfrac{a}{\sin 90} = \dfrac{11}{\sin 53}\\\\\sin 90 = 1\\\sin 53 = 0.7986\\\\\rightarrow \dfrac{a}{1} = \dfrac{11}{0.7986}\\\\a = 13.7735\\\\a\approx 13.77\; m[/tex]
Answer:i think the answer is D but it could be C but i know for a fact it is definitely not A or B
Step-by-step explanation:
I need help pleas 40 points
Answer:
x = 3
y = 6
Step-by-step explanation:
2x - y = 0
3x - 2y = -3
-----------
2x-y = 0 ---> 2x = y ---> y = 2x ----> 3x - 2(2x) = -3 ---> 3x - 4x = -3 ---->
-----> -x = -3 ---> x = -3/-1 = 3 -----> x = 3
y = 2x ----> y = 2 (3) ----> y = 6
please help me please
The values of x and y are x = 6 and y = 3√5
How to determine the values of x and yTriangle 1
From the question, we have the following parameters that can be used in our computation:
The right triangle where one of the angles is 45 degree
This is a special triangle such that
Hypotenuse = Legs * √2
So, we have
x = 3√2 * √2
Evaluate
x = 6
Triangle 2
Here, we have:
The right triangle where one of the angles is 60 degrees
So, we have
cos(60) = y/6√5
This gives
y = 6√5 * cos(60)
Evaluate
y = 3√5
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Case 1. ABY is the accounting expert for a firm that has many small clients that need monthly accounting services. ABY has been asked by the partner in charge to analyze the asset section of firms’ statements of financial positions which follow below:
2017
2018
Cash
$2,500
$3,900
Accounts receivable, net
35,000
40,000
Inventory
85,000
122,000
Other current assets
3,400
4,110
Total current assets
125,900
170,010
Property, plant & equipment, net
180,000
230,000
Other assets
15,000
26,000
Total assets
$320,900
$426,010
Required:
Prepare a Horizontal analysis of the assets section of the project statement of financial position for 2017 & 2018.and interpret any significant change in assets values. Round all percentage answers to one decimal place.
The analysis shows that the company experienced significant growth in assets from 2017 to 2018, which could be a positive sign for investors and stakeholders.
What is the Horizontal analysis of the assets section?Horizontal analysis is used to examine a company's financial statements over time. It is typically represented as a percentage increase over the same line item in the base year. Horizontal analysis enables users of financial statements to quickly identify trends and growth patterns.
To perform a horizontal analysis, we need to compare the changes in the values of assets between two years (2017 and 2018) as a percentage of the base year (2017). The analysis is as follows:
Assets 2017 2018 Change % Change
Cash $2,500 $3,900 $1,400 56%
Accounts receivable, net $35,000 $40,000 $5,000 14%
Inventory $85,000 $122,000 $37,000 44%
Other current assets $3,400 $4,110 $710 21%
Total current assets $125,900 $170,010 $44,110 35%
PPE, net $180,000 $230,000 $50,000 28%
Other assets $15,000 $26,000 $11,000 73%
Total assets $320,900 $426,010 $105,110 33%
Interpretation
The analysis shows that the total assets of the company increased by 33% from 2017 to 2018. The most significant change occurred in the other assets category, which increased by 73%, followed by inventory, which increased by 44%. The increase in other assets could be due to investments made by the company or acquisitions of other companies. The increase in inventory could indicate an increase in sales or production. The increase in property, plant & equipment, net by 28% could indicate that the company invested in new equipment or facilities to increase productivity or efficiency.Read more about Horizontal analysis
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The rectangle shown has a length of 0.9 centimeters and a width of 0.4 centimeters. A circle is drawn inside that touches the rectangle at two points. Which is closest to the area of the shaded region of the rectangle? Responses 0.14 cm2 0.23 cm2 0.28 cm2 0.49 cm2
The area of the shaded region of the rectangle is 0.23 cm², and option 2 is the correct answer.
What are complex figures?The combined shapes of one or more simple polygons and circles make up the area of the composite shapes. We can add or subtract the areas of all the fundamental shapes together to determine the area of the composite shapes. Simply calculate the area of each individual form to obtain the area of composite shapes.
The length of the rectangle is 0.9 cm.
The width of the rectangle is 0.4 cm.
The diameter of the circle us 0.4 cm, thus the radius = 0.4/2 = 0.2 cm.
The area of the rectangle is:
A = (l)(b)
Substituting the values:
A = (0.9)(0.4)
A = 0.36 sq. cm.
The area of the circle is:
A = πr²
A = (3.14)(0.2)²
A = 0.1256 sq. cm.
The area of the shaded portion is:
Area of shaded portion = area of rectangle - area of circle
Area of shaded portion = 0.36 - 0.1256 = 0.2344 sq. cm
Hence, the area of the shaded region of the rectangle is 0.23 cm², and option 2 is the correct answer.
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Si una pelota más un bate cuesta 1.10 dólares el precio del bate es 1 dólar más que la pelota
Answer:
Step-by-step explanation:
If a ball plus a bat costs 1.10 dollars and the price of the bat is 1 dollar more than the ball, what is the cost of the bat?
If we represent the price of the ball as "p", then the price of the bat will be "p + 1", since the problem tells us that the price of the bat is 1 dollar more than the price of the ball.
We also know that the sum of the price of the ball and the bat is 1.10 dollars. We can write this as an equation:
p + (p + 1) = 1.10
Simplifying and solving for p, we get:
2p + 1 = 1.10
2p = 0.10
p = 0.05
Therefore, the price of the ball is 0.05 dollars. To calculate the price of the bat, we can add 1 dollar to the price of the ball:
p + 1 = 0.05 + 1 = 1.05
So, the price of the bat is 1.05 dollars.
Explain in steps pls
Answer:
Step-by-step explanation:
2X3x2Xx
calculate the following using the long division method 8328÷ 24
Answer:
347
Step-by-step explanation:
Im not sure if that helps but thats the answer I got.
By using the long division method, The value of expression 8328 ÷ 24 after divide is,
⇒ 8328 ÷ 24
= 347
What is mean by Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, To dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
The mathematical expression for divide is,
⇒ 8328 ÷ 24
Now, We can formulate;
We can use the long division method for the expression as;
⇒ 8328 ÷ 24
⇒ 8328 / 24
24 ) 8328 ( 347
- 72
-----
112
- 96
------
168
- 168
--------
0
Therefore, We get the correct answer,
By using the long division method,
The value of expression 8328 ÷ 24 after divide is,
⇒ 8328 ÷ 24
= 347
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This is about Linear equations, please help.
Answer:
Step-by-step explanation:
line a is 5ft
Which of the following expressions are written in standard form? Choose ALL that apply.
Answer:
[tex]A. \;x^2 -7x + 1[/tex]
[tex]B.\;5x^2 + 2x[/tex]
Step-by-step explanation:
Standard Form of Polynomial
Standard form of a polynomial is written in the descending order of the power of the variable.
The standard form of polynomial is given by
[tex]f(x) = a_nx^n + a_{n-1}x^{n-1}+....... + a_1x + a_0[/tex]
where [tex]x[/tex] is the variable and [tex]a_i,\; i = 0...n[/tex] are coefficients.
The only two expressions in standard form are
[tex]A. \;x^2 -7x + 1[/tex]
and
[tex]B.\;5x^2 + 2x[/tex] (here the constant a₀ is 0)
What is the solution to this question?
Answer:
x = -3/5
Step-by-step explanation:
Given the equation:
[tex]\displaystyle{8x+9=3x+6}[/tex]
Solve for the variable x by isolating x-term, first move subtract both sides by 3x:
[tex]\displaystyle{8x+9-3x=3x+6-3x}\\\\\displaystyle{5x+9=6}[/tex]
Subtract both sides by 9:
[tex]\displaystyle{5x+9-9=6-9}\\\\\displaystyle{5x=-3}[/tex]
Divide both sides by 5:
[tex]\displaystyle{\dfrac{5x}{5}=\dfrac{-3}{5}}\\\\\displaystyle{x=-\dfrac{3}{5}}[/tex]
Therefore x = - 3/5
Answer:
x = -3/5 (or) x = -0.6
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 8x + 9 = 3x + 6
Then the value of x will be,
→ 8x + 9 = 3x + 6
→ 8x - 3x = 6 - 9
→ 5x = -3
→ x = -3 ÷ 5
→ [ x = -3/5 ]
Hence, the answer is -3/5.
What is the probability of flipping a coin 11 times and getting heads 4 times? Round your answer to the nearest tenth of a percent. O A. 8.1% O B. 22.6% O C. 16.1% ) D. 0.5%
Answer:
The answer is (A) 8.1%.
Step-by-step explanation:
The probability of flipping a coin and getting heads is 1/2 or 0.5. Assuming the coin is fair, the probability of getting heads 4 times in 11 flips is given by the binomial probability formula:
P(4 heads in 11 flips) = (11 choose 4) * (0.5)^4 * (0.5)^(11-4) = 330 * 0.5^11
Using a calculator, we get:
P(4 heads in 11 flips) ≈ 8.1%
Therefore, the answer is (A) 8.1%.
Myles writes down the distance readings from his car at the start and end of a journey.
Start of journey 12468
End of journey. 12845
Myles knows that the cost of petrol for this journey is 13p per mile.
Work out the total cost of the petrol used for this journey.
Give your answer in pounds.
Distance reading at the start of journey = 12468
Distance reading at the end of the journey = 12845
Distance traveled in the journey = 12845 - 12468 = 377 miles
Cost of petrol per mile = 13p
Cost of petrol for the journey = 13 × 377 = 4901p
Since one pound is one hundred pence, 4901p in pounds will be 4901/100 = 49.01 pounds
Cost of petrol used in the journey is 49.01 pounds
An old truck has a fuel efficiency of 12 mpg. What is the cost of gasoline if the truck uses 5 gallons to drive 60 miles?
The cost of gasoline if the truck uses 5 gallons to drive 60 miles is $18.70
How to determine the cost of gasoline if the truck uses 5 gallons to drive 60 miles?To calculate the cost of gasoline for the old truck, we can use the following formula:
Cost of gasoline = Price per gallon × Number of gallons used
Given that
Price per gallon = 3.74
Number of gallons used = 5 gallons
We have
Cost of gasoline = $3.74/gallon × 5 gallons
Evaluate
Cost = $18.70
Hence, the cost is $18.70
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Complete question
An old truck has a fuel efficiency of 12 mpg. What is the cost of gasoline if the truck uses 5 gallons to drive 60 miles if the gasoline costs $3.74 per gallon
Factorise 2 + x^3 - 3x^6
answer is (2 + 3x^3)(1 - x)(1 + x + x^2)
need working out
Let w = x^3
Square both sides to find that w^2 = (x^3)^2 = x^(3*2) = x^6
In short: w^2 = x^6
The given expression 2+x^3-3x^6 turns into 2+w-3w^2 and rearranges into -3w^2+w+2
Set this equal to zero and use the quadratic formula. We'll plug in
a = -3b = 1c = 2So,
[tex]w = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\w = \frac{-1\pm\sqrt{(1)^2-4(-3)(2)}}{2(-3)}\\\\w = \frac{-1\pm\sqrt{25}}{-6}\\\\w = \frac{-1\pm5}{-6}\\\\w = \frac{-1+5}{-6} \ \text{ or } \ w = \frac{-1-5}{-6}\\\\w = \frac{4}{-6} \ \text{ or } \ w = \frac{-6}{-6}\\\\w = -\frac{2}{3} \ \text{ or } \ w = 1\\\\[/tex]
If w = -2/3, then that rearranges to the following
w = -2/3
3w = -2
3w+2 = 0
This makes (3w+2) a factor of -3w^2+w+2
If w = 1, then it rearranges to w-1 = 0.
This makes (w-1) a factor of -3w^2+w+2
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To summarize the previous section, we found the factors of -3w^2+w+2 were:
(3w+2)(w-1)It leads to (3w+2)(w-1)
We must stick a negative out front because the leading coefficient is negative.
Therefore, -3w^2+w+2 = -(3w+2)(w-1)
You can use the FOIL rule to confirm.
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Recall we made w = x^3
Let's replace each w with x^3
-(3w+2)(w-1)
-(3x^3+2)(x^3-1)
This tells us that 2+x^3-3x^6 factors to -(3x^3+2)(x^3-1)
The next task is to factor x^3-1 using the difference of cubes factoring rule.
a^3 - b^3 = (a-b)(a^2 + ab + b^2)
x^3 - 1^3 = (x-1)(x^2 + x*1 + 1^2)
x^3 - 1 = (x-1)(x^2 + x + 1)
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So,
2+x^3-3x^6
-3x^6 + x^3 + 2
-(3x^3+2)(x^3-1)
-(3x^3+2)(x-1)(x^2 + x + 1)
-(2 + 3x^3)(-(1-x))(1 + x + x^2)
(2 + 3x^3)(1 - x)(1 + x + x^2)
Take careful notice that x-1 turned into -(1-x) in the 3rd step. The negative out front for -(1-x) cancels out with the original negative out front.
in exercises 9 and 10, (a) for what values of h is v3 in span fv1; v2g, and (b) for what values of h is fv1; v2; v3g linearly dependent? justify each answer.
The values of h is v3 in span fv1; v2g and h is fv1; v2; v3g is 4.
How to find the vector component?If we have given a vector v of initial point A and terminal point B
v = ai + bj
then the components form as;
AB = xi + yj
Here, xi and yj are the components of the vector.
We are given that;
v1 and v2 are not scalar multiples to each other
So, they are not linearly dependent
Now,
1(10h -42) -3(-14 +3h) +2 (18-20) =0
10h -9h-4 =0
h = 4
Therefore, by vectors the answer will be 4 so that the vector v3 is in {v1,v2}.
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This is a set notation I need the number of elements
The number of elements in the complement of the union set of A and B is given as follows:
12.
How to solve the operations with sets?The universal set is given as follows:
S = {1, 2, 3, ... , 23, 24, 25}.
The union between two sets is composed by the elements that belong to at least one of the sets, hence the union of sets A and B is given as follows:
A U B = {2, 3, 4, 6, 8, 12, 13, 14, 16, 18, 22, 24, 25}.
The number of elements in the union set is of:
13.
The complement of a set is composed by all the elements that belong to the universal set but to not belong to the set. As the union of A and B has 13 elements, and the universal set has 25 elements, the number of elements of the complement is given as follows:
25 - 13 = 12.
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PLS HELP!! I don’t understand
The points are as selected on the graph.
How to select points on the graph?A function is an expression that shows the relationship between the independent variable and the dependent variable. A function is usually denoted by letters such as f, g, etc.
Since f(x) = -9. What this means is that the value of f(x) will always be -9 irrespective of the value of x. That is:
x f(x)
-2 -9
0 -9
2 -9
7 -9
9 -9
Check the attached image for the points on the graph
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