The purchaser rejects 26.01% of the lots that contain five or more defective components, and the conditional probability of having four defective components given that the lot was rejected is 0.1653.
How do we calculate the probability?The percentage of defective lots that the purchaser rejects can be found by using the given formula. We can also calculate the conditional probability of having four defective components, given that the lot was rejected. Here's how to do it.
Let p be the probability that any component is defective. Then the probability that any component is non-defective is 1-p.
According to the given data, a lot is rejected if and only if there are at least five defective components in it. Let q be the probability that a lot is defective, i.e. the probability that there are five or more defective components in a lot.
Then, q = P(X ≥ 5), where X is the number of defective components in the lot. We can find the probability of rejecting a lot by subtracting the probability of accepting the lot from 1. So, we have:
P(reject) = 1 - P(accept)
P(accept) = P(X ≤ 4)
Now, we need to find q. We can do this by using the binomial distribution:
[tex]P(X = k) = C(n, k) * pk * (1-p)n-k[/tex]
where C(n, k) is the number of ways to choose k items out of n items. Here, n = 20 (the number of components in a lot). So,
[tex]q = P(X \geq 5) = 1 - P(X\leq 4) = 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)][/tex]
[tex]q = 1 - [C(20, 0) * p0 * (1-p)20-0 + C(20, 1) * p1 * (1-p)20-1 + C(20, 2) * p2 * (1-p)20-2 + C(20, 3) * p3 * (1-p)20-3 + C(20, 4) * p4 * (1-p)20-4][/tex]
[tex]q = 1 - [1 * p0.2 * (1-0.2)20-0 + 20 * p0.2 * (1-0.2)20-1 + 190 * p0.2 * (1-0.2)20-2 + 1140 * p0.2 * (1-0.2)20-3 + 4845 * p0.2 * (1-0.2)20-4][/tex]
[tex]q = 0.2601[/tex] (rounded to four decimal places)
So, the purchaser rejects 26.01% of the lots that contain five or more defective components.
Now, we need to find the conditional probability that a lot contained four defective components given that it was rejected. Let R be the event that a lot is rejected, and let F be the event that a lot contains four defective components.
Then, we have to find P(F | R), the conditional probability of F given R. We can use Bayes' theorem to find this:
P(F | R) = P(R | F) * P(F) / P(R)
where P(R | F) is the probability of rejecting a lot given that it contained four defective components, P(F) is the prior probability of a lot containing four defective components, and P(R) is the overall probability of rejecting a lot.
[tex]P(F) = C(20, 4) * p4 * (1-p)20-4 = 0.186[/tex]
[tex][tex]P(R) = P(X \geq 5) = q = 0.2601[/tex][/tex]
[tex]P(R | F) = P(X \geq 5 | X = 4) = P(X = 5) / P(X = 4) = C(20, 5) * p5 * (1-p)20-5 / C(20, 4) * p4 * (1-p)20-4[/tex]
[tex]P(R | F) = 0.2308[/tex]
So, we have:
[tex]P(F | R) = P(R | F) * P(F) / P(R)[/tex]
[tex]P(F | R) = 0.2308 * 0.186 / 0.2601[/tex]
[tex]P(F | R) = 0.1653[/tex] (rounded to four decimal places)
Therefore, the conditional probability of having four defective components given that the lot was rejected is 0.1653.
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A gardener wants to divide a square piece of lawn in half diagonally. What is the length of the diagonal if the side of the square is 8 ft? Leave your answer in simplest radical form.A. 16B. 2C. 8D. 4
The length of the diagonal is 8√2 ft.
How to find the length of the diagonal if the side of the square is 8 ft?If the side of the square is 8 ft, then the diagonal will form a right triangle with legs of length 8 ft. We can use the Pythagorean theorem to find the length of the diagonal (hypotenuse).
Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
In this case, we have:
a = 8 ft (one leg)
b = 8 ft (the other leg)
c = ? (the hypotenuse)
Using the Pythagorean theorem, we have:
c² = a² + b²
c² = 8² + 8²
c² = 64 + 64
c² = 128
c = √128
c = 8√2 ft
Therefore, the length of the diagonal is 8√2 ft.
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Which mathematical term is best defined as two lines that intersect each other at 90 ° angles?
Answer:
Perpendicular
Step-by-step explanation:
suppose a jar contains 6 red marbles and 13 blue marbles. if you reach in the jar and pull out 2 marbles at random, find the probability that both are red. write your answer as a reduced fraction.
From the given jar, the probability that both are red marbles is 15/171.
What is the probability?Suppose a jar contains 6 red marbles and 13 blue marbles.
If you reach in the jar and pull out 2 marbles at random, find the probability that both are red. Write your answer as a reduced fraction.
Let's first find out the total number of marbles in the jar:
Total number of marbles in the jar = 6 + 13 = 19
Since we need to find the probability of picking out two red marbles, we need to calculate the total number of ways we can pick 2 marbles from 19:
n(S) = (¹⁹C₂)
we need to calculate the total number of ways to pick out two red marbles from 6:
n(E) = (⁶C₂)
We can use the formula for probability:
[tex]P(picking two red marbles) = \frac{n(E) }{n(S)} \\ = \frac{6C2 }{19C2} \\= \frac{15}{171}[/tex]
So, the probability of both marbles being red is 15/171. This fraction cannot be reduced any further.
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ADEF-AABC. What is the sequence of transformations that maps AABC to ADEF?
A reflection across the y-axis and a translation 4 units down
A rotation of 180* about the origin and a dilation with center (0,0) and scale factor 2
A reflection across the y-axis and a translation 2 units down.
A rotation of 90° about the origin and a translation 2 units down
The series of transformations consists of a translation down two units and a reflection across the y-axis. Thus, option C is correct.
What is transformation?The points A and C will be replaced with D and F, respectively, by a reflection across the y-axis, leaving B in the same location. As a result, the image of AABC is given, A'D'BCF.
The final image, denoted by the letters ADEF, is produced by translating all the points of the image A'D'BCF' down by two units.
ADEF and AABC are not in the same location, even if they are the same height and shape.
The first thing we notice is that ADEF and AABC are oriented the same way, so we don't need to rotate them. Instead, by utilising a reflection over the y-axis, we may swap out the places where A and B were for D and E, respectively.
A'B'C' is still not in the appropriate place even though it is 2 units to the left of ADEF. Hence, we must translate 2 units down in order to position A'B'C' where ADEF is.
Therefore, A reflection across the y-axis and a translation 2 units down.
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Amy, Beth, and Cassandra were carpeting 4 identically sized rooms. It would take Amy 6 hours to carpet one of the rooms; it would take Beth 4 hours to carpet one room; and it would take Cassandra 8 hours to carpet one room. Together, how long would it take them to carpet the 4 rooms (round to the nearest thousandth of an hour;
It would take the three of them about 6 hours to paint the four rooms.
How to solve an equation?Let t represent the time that it would take all three of them to paint one room.
It would take Amy 6 hours to carpet one of the rooms; it would take Beth 4 hours to carpet one room; and it would take Cassandra 8 hours to carpet one room.
Therefore:
(1/6 + 1/4 + 1/8)t = 1
(2/3)t = 1
t = 1.5 hours
It would take all of them 1.5 hours each to paint one room.
For 4 rooms:
Total time = 1.5 hours * 4 = 6 hours
It would take the three of them about 6 hours to paint the four rooms.
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What is 6x+2y=-4 in slope-intercept form
Answer:
y = -3x - 2
Step-by-step explanation:
To write the equation 6x + 2y = -4 in slope-intercept form, we need to solve for y.
First, we can isolate the y-term by subtracting 6x from both sides:
6x + 2y = -4
2y = -6x - 4
Next, we can divide both sides by 2 to isolate y:
2y/2 = (-6x - 4)/2
y = -3x - 2
So the slope-intercept form of the equation 6x + 2y = -4 is y = -3x - 2.
2 HCl + CaCO3 → CaCl2 + H2O + CO2
If 1.8392 moles of HCl are reacted, how many grams of CaCO3 will also be reacted?
A diagonal of rectangle is inclined to one side of the rectangle at 25 degree the acute angle between diagonal is
Answer:
A diagonal of a rectangle is inclined to one side of the rectangle at 25º Angle between a side of the rectangle and its diagonal = 25º Consider x as the acute angle between diagonals
Step-by-step explanation:
Which expression represents the perimeter of a triangle in simplest form that has side lengths: 2x, 3x + 5, x + 2
Answer:
6x + 7
Step-by-step explanation:
triangle has 3 sides right, which is 2x, 3x+5 and x+2
so basically you just have to add everything up since perimeter is just the total number of each sides combined
2x + (3x+5) + (x+2)
expand from the brackets
2x + 3x + 5 + x + 2
rearrange the numbers to avoid confusion
2x + 3x + x + 5 + 2
add everything up
6x + 7
Suppose X and Y are independent N(0; 1) random variables.
(a) Find P(X^2 < 1).
(b) Find P(X^2 + Y^2 < 1)
The required probability is obtained as:
(a) P(X^2 < 1) = 0.8413.
(b) P(X^2 + Y^2 < 1) = 0.7854.
(a) We know that X^2 follows a chi-squared distribution with 1 degree of freedom, which can be written as X^2 ~ chi-squared(1). Therefore, we can find P(X^2 < 1) as:
P(X^2 < 1) = P(Z < √1) (where Z ~ chi-squared(1))
Since the square of a standard normal distribution is a chi-squared distribution with 1 degree of freedom, we can rewrite the above equation as:
P(X^2 < 1) = P(Z < 1) (where Z ~ N(0,1))
Using a standard normal distribution table or calculator, we can find that P(Z < 1) = 0.8413. Therefore, P(X^2 < 1) = 0.8413.
(b) We can rewrite X^2 + Y^2 < 1 as the inequality r^2 < 1, where r is the distance from the origin to the point (X,Y) in the xy-plane. Therefore, we need to find the probability that the point (X,Y) falls within the unit circle centered at the origin.
We can use polar coordinates to express X and Y as:
X = Rcosθ
Y = Rsinθ
where R is the distance from the origin to (X,Y), and θ is the angle between the positive x-axis and the line connecting the origin and (X,Y). Since X and Y are independent N(0,1) random variables, R^2 = X^2 + Y^2 follows a chi-squared distribution with 2 degrees of freedom, which can be written as R^2 ~ chi-squared(2).
Therefore, we can find P(X^2 + Y^2 < 1) as:
P(X^2 + Y^2 < 1) = P(R^2 < 1) (where R^2 ~ chi-squared(2))
Using the cumulative distribution function (CDF) of the chi-squared distribution with 2 degrees of freedom, we can find that:
P(R^2 < 1) = 0.7854
Therefore, P(X^2 + Y^2 < 1) = 0.7854.
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Which angles would the Alternate Exterior Angles Theorem state are congruent?
Which angles would the Alternate Exterior Angles Theorem state are congruent?
Answer:
Choice 2
∠1 and ∠7, ∠2 and ∠8
Step-by-step explanation:
This is a good example of a problem that can be solved by POE(process of elimination)
First choice: ∠2 and ∠3 are on the same straight line so they cannot be congruent. They are supplementary in that they add up to 180°
The same applies for ∠3 and ∠4 (third choice)
The same applies for ∠1 and ∠4 (fourth choice)
That leaves choice 2
We can prove ∠1 ≅ ∠7 as follows:
∠1 ≅ ∠3 since they are vertically opposite angles
∠3 ≅ ∠7 since they are exterior angles
So ∠1 ≅ ∠7
By similar reasoning,
∠2 ≅ ∠8
So correct choice is Choice 2
A certain computer loses half of its value every four years. If the value of the computer after 6 years is $835, what was the initial value of the computer?
The PC is initially worth $3,340.
Given that a computer loses half of its worth after six years, and assuming that value is $835, we must determine the device's original value.
What does the term "starting value" mean?
The starting output value is the initial value.
Let's say that computer's starting value is x.
As a result, after four years,
It is X/2 for the fourth year.
It is X/2 for the fifth year.
It's X/4 in the sixth year.
We stated that the PC will be worth $835 after six years. Hence, we may express it as,
X/4 = $835
X=4( $835)
X= $3,340
Hence, the initial value of the computer is $3,340.
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(3882+3561+3459+2587+ 2817
+2068+2516+3590+2740+2572) ÷ 10
Mean =
X^2+9x+20/x+3 • x^2-x-12/x^2+3x-4
What is the product in simplest form? State any restrictions on the variable
To find the product, we need to first factor the numerators and denominators of both fractions:
x^2 + 9x + 20 = (x + 5)(x + 4)
x^2 - x - 12 = (x - 4)(x + 3)
x^2 + 3x - 4 = (x + 4)(x - 1)
Substituting these into the expression, we get:
[(x + 5)(x + 4)/(x + 3)] * [(x - 4)(x + 3)/(x + 4)(x - 1)]
Now, we can simplify the product by cancelling out common factors:
[(x + 5) * 1/(x - 1)] * [(x - 4) * 1/1]
= (x + 5)(x - 4)/(x - 1)
So the product in simplest form is (x + 5)(x - 4)/(x - 1).
However, there is a restriction on the variable because the expression involves division by (x + 3), (x - 1), and (x - 4). Therefore, x cannot be equal to -3, 1, or 4, since these values would make the denominators zero and the expression undefined.
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A garden is shaped like a right-angled triangle.
Work out the perimeter of the garden.
Give your answer in metres (m) to 1 d.p.
Answer:
Step-by-step explanation:
First , we would add 10 + 4 = 14 then ,
using Pythagoras Theorem , a^2 + b^2 = c^2 to find out the hypotenuse so
10^2+4^2= 116
Finally , add the square root of 116 to 14 to get
24.8 metres rounded to 1 decimal place.
The population of a city increases by 5% per year. What should we multiply the current population by to find the next year's population in one step? Answer:
Answer:
Step-by-step explanation:
Tο find the pοpulatiοn οf the city after οne year, we shοuld multiply the current pοpulatiοn by 1.05.
What is the percentage?A percentage that represents a tenth οf a quantity. One percent, denοted by the symbοl 1%, is equal tο οne-hundredth οf sοmething; hence, 100 percent denοtes the full thing, and 200 percent designates twice the amοunt specified. A pοrtiοn per hundred is what the percentage denοtes. The percentage refers tο οne in a hundred. The % sign is used tο denοte it.
We can express a 5% increase as a decimal by dividing 5 by 100, which gives 0.05. This means that the pοpulatiοn after οne year will be the current pοpulatiοn plus 5% οf the current pοpulatiοn. Mathematically, we can write:
Next year's pοpulatiοn = Current pοpulatiοn + 0.05 * Current pοpulatiοn
We can simplify this expressiοn by factοring οut the current pοpulatiοn:
Next year's pοpulatiοn = Current pοpulatiοn * (1 + 0.05)
Simplifying further, we can add 1 tο the decimal tο get:
Next year's pοpulatiοn = Current pοpulatiοn * 1.05
Therefοre, tο find the pοpulatiοn οf the city after οne year, we shοuld multiply the current pοpulatiοn by 1.05.
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Part A Which solution do you get when you use the quadratic formula to solve the equation –4x2 – 12x – 9 = 0?
Answer:
A: -3/2
Step-by-step explanation:
-4x²-12x-9=0 First split the b value so that it equals a×c, or -4×-9
-4x²-6x-6x-9=0 Factor by grouping
(-2x-3)(2x+3)=0 Solve for x
x= -3/2
A 2014 Ford F150 was purchased new for $35,000. If the truck's current value in 2021
is $26,796.88 what is the annual rate of depreciation? (round answer to the nearest
tenth of a percent)
According to the solving the annual rate of depreciation is approximately 4.77%.
What does "annual rate" refer to?Annual percentage rate (APR) is the word used to define the annual interest that is generated by a payment that is due to investors or assessed to borrowers. The annual percentage rate, or APR, is a gauge of how much it actually costs to borrow cash over the duration of a loan or the income from an investment.
According to the given information:V = V0 * e[tex]^(^-^r^t^)[/tex]
where:
V0 is the initial value of the asset (in this case, $35,000)
V is the current value of the asset (in this case, $26,796.88)
r is the annual rate of depreciation (what we want to find)
t is the time elapsed (in years)
We know that the time elapsed is 2021 - 2014 = 7 years.
26,796.88 = 35,000 * e[tex]^(^-^7^r^)[/tex]
Dividing both sides by 35,000, we get:
0.766195 = e[tex]^(^-^7^r^)[/tex]
ln(0.766195) = -7r
Solving for "r", we get:
r = -ln(0.766195) / 7
r ≈ 0.0477
the annual rate of depreciation is approximately 4.77%.
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Factor 1/3x - 1/3, if it cannot be factorized write cannot be factorized
Answer: [tex]1/3(x-1)[/tex]
Step-by-step explanation: In this case, factoring cannot be done at a large scale because there is no degree higher than one on both terms. However, you can factor out the gcf on both terms which is one-half to make the equation in factorized form.
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Answer:
Not sure what the expression actually is, but it is is either:
1.
[tex] \frac{1}{3x} - \frac{1}{3} [/tex]
Then:
[tex] \frac{1}{3x} - \frac{1}{3} = \frac{1}{3} ( \frac{1}{x} - 1)[/tex]
Or
2.
[tex] \frac{1}{3} x - \frac{1}{3} [/tex]
Then:
[tex] \frac{1}{3} x - \frac{1}{3} = \frac{1}{3} (x - 1)[/tex]
I dont know the answer helpppo
For all values of x the function is decreasing function because as x increases the value of the function decreases.
What is derivative?One of the core ideas of calculus is the derivative, which shows how quickly a function is changing at any given moment. It offers a means of determining the slope of a curve at a certain location, which may be used to address a variety of issues in physics, engineering, economics, and social sciences. The derivative may be used to predict the behaviour of physical systems, discover the maximum and lowest values of a function, and improve a process or system.
From the given table we observe that as x increases the value of the function decreases.
That is for all values of x the function is decreasing function.
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Kendall will find the total surface area of the prism below. Assuming the base is the shaded surface (the bottom), drag an
drop the correct values for the variables P, h, B that she should use in her formula.
1.2 ft
P.⠀
h:
B:
feet
feet
8.8 ft
square feet
nwore mangslugnsits arts to come sostua eri bait of absan y
So
2 ft
Answer:
Step-by-step explanation:
is 8,15,24
The probability of drawing a black ball from a bag containing 5 black and 3 red ball is
Answer:
The probability of drawing a black ball can be calculated using the following formula:
Probability of drawing a black ball = Number of black balls / Total number of balls
In this case, there are 5 black balls and 3 red balls, so the total number of balls in the bag is:
Total number of balls = 5 + 3 = 8
Therefore, the probability of drawing a black ball is:
Probability of drawing a black ball = 5/8
So, the answer is the probability of drawing a black ball from a bag containing 5 black and 3 red balls is 5/8.
Step-by-step explanation:
the life of light bulbs is distributed normally. the variance of the lifetime is 225 and the mean lifetime of a bulb is 530 hours. find the probability of a bulb lasting for at most 540 hours. round your answer to four decimal places.
The probability of a bulb lasting for at most 540 hours is 0.7521, rounded to four decimal places.
The life of light bulbs is distributed normally. The variance of the lifetime is 225 and the mean lifetime of a bulb is 530 hours. Find the probability of a bulb lasting for at most 540 hours. Round your answer to four decimal places.
Using the z-score formula z = (x - μ) / σ, where x is the value in question (540 hours in this case), μ is the mean (530 hours in this case) and σ is the standard deviation (15 hours in this case), we can calculate the z-score:
z = (540 - 530) / 15
z = 10 / 15
z = 0.67
Using a z-table, we can look up the probability of a value being less than or equal to 0.67, which is 0.7521.
Therefore, the probability of a bulb lasting for at most 540 hours is 0.7521, rounded to four decimal places.
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the population of a community is known to increase at a rate proportional to the number of people present at time t. if an initial population p0 has doubled in 5 years, how long will it take to triple? (round your answer to one decimal place.) yr how long will it take to quadruple? (round your answer to one decimal place.) yr
It will take approximately 8.5 years to triple the population and approximately 10 years to quadruple the population.
Given that the population of a community is known to increase at a rate proportional to the number of people present at time t, and an initial population p0 has doubled in 5 years.
To calculate:
How long will it take to triple?
How long will it take to quadruple?
Let p be the population of a community at any time t. According to the given information, the population p is proportional to the number of people present at time t. Therefore, we have p ∝ p_0 …… (1)
where p_0 is the initial population of the community. It is given that the initial population p_0 has doubled in 5 years.
So, we have 2p_0 = p_0e^(rt) 2 = e^(5r)
Taking natural logarithm on both sides, ln 2 = ln e^(5r) = 5rln 2/5 = r …… (2)
Using equation (1) and (2), we can write population p asp = p_0e^(rt) = p_0e^(ln2/5 t) = p_0 2^(t/5)
Now, we have to find for how many years (t) we need to wait until the population of the community triples, i.e.
3p_0 = p_0 2^(t/5) 3 = 2^(t/5)
Taking logarithm (with base 2) on both sides,
log_2 3 = log_2 2^(t/5)log_2 3 = (t/5)log_2 2t = 5 log_2 3t ≈ 8.5 (Rounded to one decimal place)
Therefore, it will take approximately 8.5 years to triple the population.
Now, we need to find for how many years (t) we need to wait until the population of the community quadruples, i.e. 4p_0 = p_0 2^(t/5) 4 = 2^(t/5)
Taking logarithm (with base 2) on both sides,
log_2 4 = log_2 2^(t/5)
log_2 4 = (t/5)log_2 2t = 5 log_2 4t ≈ 10 (Rounded to one decimal place)Therefore, it will take approximately 10 years to quadruple the population.
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Stock sold at 23 7/8 at the start of
trading. It was up 3 1/2 points at the
end of trading. What was the price
at the end of trading?
Answer:
To solve the problem, we need to add 23 7/8 and 3 1/2 to find the final price.
First, we need to convert 3 1/2 to an improper fraction:
3 1/2 = (2 x 3) + 1/2 = 7/2
Next, we need to find a common denominator between 8 and 2:
8 = 8/1
2 = 2/1 x 4/4 = 8/4
Now we can add the two fractions:
23 7/8 + 3 1/2
= 23 14/16 + 3 8/16 (using 16 as the common denominator)
= 27 6/16
= 27 3/8
Therefore, the stock was priced at $27 3/8 at the end of trading.
0
2
Given the function f(x) = x-2, draw a line from the value of
to the corresponding value of f(x).
16
undefined
The graph of the function f(x) = x - 2 is a straight line that passes through the origin and has a slope of 1.
What is function in math?Function is a mathematical concept which refers to a rule or set of rules that takes an input and produces an output. Its purpose is to map out a relationship between two distinct sets of data. The input is called the argument, and the output is called the value. Functions are used to model real-world situations, to discover patterns, and to solve problems. Functions help to organize data and make it easier to interpret and analyze. They are also used to predict the effects of changes in the input.
This means that for every unit increase in x, the value of f(x) increases by 1 unit. Therefore, when x is equal to 0, the value of f(x) is equal to -2. When x is equal to 1, the value of f(x) is equal to -1. When x is equal to 2, the value of f(x) is equal to 0. When x is equal to 16, the value of f(x) is equal to 14. As you can see, for every increase in x, the value of f(x) increases by 2 units. This is the reason why the line drawn from the value of x to the corresponding value of f(x) increases by 2 units when x is increased by 1 unit.
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In this case, there is no corresponding point on the line, so the line does not extend from (2, 4) to (4, 2).
What is function ?Function is a mathematical concept which refers to a rule or set of rules that takes an input and produces an output. Its purpose is to map out a relationship between two distinct sets of data. The input is called the argument, and the output is called the value. Functions are used to model real-world situations, to discover patterns, and to solve problems. Functions help to organize data and make it easier to interpret and analyze. They are also used to predict the effects of changes in the input.
In this example, the function f(x) = x-2 is being represented by a line that connects each value of x to the corresponding value of f(x).
When x = 4,
then f(x) = 4-2
f(x) = 2,
so the line extends from (4, 2) to the origin (0, 0).
Similarly, when x = 0,
then f(x) = 0-2
f(x) = -2,
so the line extends from (0, -2) to (4, 2).
When x = 1,
then f(x) = 1-2
f(x) = -1,
so the line extends from (1, -1) to (4, 2).
Finally,
when x = 2,
then f(x) is undefined.
In this case, there is no corresponding point on the line, so the line does not extend from (2, 4) to (4, 2).
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Bethany wants to build a wooden deck on her patio, which is in the shape of a parallelogram. The area of the patio is 580 ft2. Find the base. Round your answer to the nearest foot.
The base of the parallelogram is 18. 3 feet
How to determine the base of the parallelogramFrom the information given, we have that;
Area = 280ft^2
height = 5x
Base = 6x
Note that he formula that is used for calculating the area of the parallelogram is represented with the equation;
Area = bh
Given that the parameters are;
b is the base of the parallelogramh is the height of the parallelogramSubstituting the values of area, base and height.
280 = 5x × 6x
280 = 30x^2
Divide both sides by 30
x^2 = 280/30
Find the square root of both sides
x = √(280/30)
We have that the base = 6x
Substitute the value of x, we get;
Base = 6x = 6(√(280/30))
Base = 18.3ft
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Find the amount of the following ordinary annuities rounded to the nearest cent. Find the tot
Amount of Deposited
Interest
Rate Time (Years) Amount of an
Annuity
Earned
each deposit
$1050
annually
5%
14
Answer:I=(PxRxT)/100
I=(10000x20x1)/100x2
I=200000/200
I=1000I=(
Step-by-step explanation:
The newspaper in Haventown had a circulation of 80,000 papers in the year 2000. In 2010, the circulation was 50,000. With x=0 representing the year 2000, the graph below models this scenario.
What number will complete the point-slope equation that models this scenario?
Answer:
The answer to your problem is, -3000
Step-by-step explanation:
:Write down the points through which the line passes through
:The line is passing through a point at (0, 80000) and (10, 50000)
Next, ( important )
Find the slope of the line
Since the line is passing through the point (0, 80000) and (10, 50000)
So the slope of the line:
= m
[tex]\frac{80,000 - 50,000}{0 - 10}[/tex]
= [tex]\frac{30,000 }{-10}[/tex]
= -3,000
Techniquelly the answer is, 30,000 but for more explanation here it is :)
Find the number that will complete the point-slope equation that models this scenario
The required point-slope equation that models this scenario is
[tex]y - y_{1} - m( x - x_{1} )[/tex]
y - 50,000 = -30,000 ( x - 10 )
Thus the answer to your problem is, - 3,000
Any questions? Write them down below \/
Here is a hanger that is in balance. We don't know how much any of its shapes weigh. How
could you change the number of shapes on it, but keep it in balance? Describe in a couple
sentences
We can change the number of shapes on it by putting one rectangle to the right and put two triangles to the left.
A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Let's say the circle is A, Triangle is B, and Rectangle is C.
2A + 4C = 2A + 4B + 2C
So, C = 2B ( 4C = 4B + 2C, 2C = 4B, C = 2B)
That one rectangle and two triangles are equally weighed. So, put one rectangle to the right and put two triangles to the left. The hanger is still in the balance.
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