An effective visual representation of a function or a mapping between two sets is a mapping diagram. It consists of two vertical columns, one of which represents the domain set items and the other of which represents the range set elements. The items in the range set that match to those in the domain set are listed in the right column, and vice versa.
I assume you are given a mapping rule that relates elements in a set to other elements in another set, and you are asked to complete a mapping diagram based on this rule.
If the mapping rule is not specified, we cannot determine the values of a and b. However, assuming that the mapping rule is such that each element (x, y) in the set R is mapped to [tex](x + a, y + b)[/tex], we can complete the mapping diagram as follows:
The given set R is:
R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}
If we apply the mapping rule to each element in R, we get:
(-3, -2) → (-3 + a, -2 + b)
(-3, 0) → (-3 + a, 0 + b)
(-1, 2) → (-1 + a, 2 + b)
(1, 2) → (1 + a, 2 + b)
To complete the mapping diagram, we need to find the values of a and b such that each mapped element is in the set R. That is, we need to find a and b such that:
(-3 + a, -2 + b) ∈ R
(-3 + a, 0 + b) ∈ R
(-1 + a, 2 + b) ∈ R
(1 + a, 2 + b) ∈ R
Substituting the values of R into each of these equations, we get:
(-3 + a, -2 + b) = (-3, -2), which gives a = 0 and b = 0
(-3 + a, 0 + b) = (-3, 0), which gives a = 0 and b = 0
(-1 + a, 2 + b) = (-1, 2), which gives a = 0 and b = 0
(1 + a, 2 + b) = (1, 2), which gives a = 0 and b = 0
Therefore, the values of a and b that complete the mapping diagram are a = 0 and b = 0.
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I need it simplified help
The answer is 23/40
To simplify this expression, we need to find a common denominator for each pair of fractions that are being added or subtracted.
The common denominator for 1/4 and 1/5 is 20, so we can rewrite 1/4 as 5/20 and 1/5 as 4/20. Then, we can subtract these fractions to get 1/20.
The common denominator for -3/4 and 1/8 is 8, so we can rewrite -3/4 as -6/8. Then, we can add these fractions to get -5/8.
Now, we can combine the two simplified fractions by finding a common denominator of 40. We can do this by multiplying 20 and 8, which gives us 160.
Then, we can rewrite 1/20 as 2/40 and -5/8 as -25/40. Adding these fractions together gives us:
2/40 - 25/40 = -23/40.
The absolute value of any number is always positive so it becomes 23/40.
The simplified version of (1/4 - 1/5) + (-3/4 + 1/8) is 23/40.
how many ways can rudy choose 5 pizza toppings from a menu of 20 toppings if each topping can only be chosen once?
in a deli, the ratio of ham subs to cheese subs sold in a day was 9:4. If 36 cheese subs were sold, how many ham subs were sold?
Answer: 81 ham subs
Step-by-step explanation:
4 times 9 is 36. That means you have to multiply 9 by 9, to get 81 ham subs. The ratio is 81:36. :)
The pilot, Sully Sullenberger, made the decision to land on the Hudson river when he was 1650 feet above the ground descending at 2° degrees, which was 30 seconds after the bird strike.
6a) Would he have been able to make it back to LaGuardia Airport? Remember he landed within 8 miles from making the decision to land in the Hudson River. Support your answer by finding the horizontal distance back to LaGuardia Airport.
The Airbus A320 Sullenberger was piloting typically cruises at about 550 miles, or 807 ft per minute. His greatest horizontal range would have been between 4.4 and 6.0 nautical miles.
How are miles used?In certain circumstances, you may trade your miles for items like cash back and gift cards in addition to using them to pay for flights. Most of the time, redeeming airline points is straightforward. By entering into your account while making your reservation with most flights, you may use your points to get a free ticket.
Where do miles come from?You may also determine distance in miles unless you already know your speed and how long it takes to go a particular distance. Just double the time by the speed.
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suppose men always married women who were exactly 3 years younger. what would the correlation between their ages be?
The correlation between the ages of men and women in this situation would be +1. This means that for every one-year increase in the age of the man, the age of the woman would increase by one year as well. The correlation coefficient of +1 signifies a perfect positive linear correlation between the two variables.
In other words, if a man is 40 years old, the woman he is married to would be 37. If the man was 50, then the woman would be 47, and so on. This would remain true for any age, regardless of the difference in their ages. Therefore, the correlation between their ages would always remain +1.
It is important to note that this correlation coefficient is not necessarily reflective of traditional or even natural social or biological behavior. Rather, it is simply a mathematical relationship that would exist in this specific situation. In reality, the age gap between married couples can vary widely depending on various social and cultural factors.
To summarize, the correlation between the ages of men and women in this scenario would be +1, signifying a perfect positive linear correlation. This means that for any given age of the man, the age of the woman would be exactly three years younger.
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Compared to smaller firms, larger companies tend to:Multiple Choicedelay exporting until after their domestic market is fully saturated.systematically scan foreign markets to see where export opportunities lie.be intimidated by the complexities and mechanics of exporting to foreign countries.hesitate to seek export opportunities because they do not know how big the opportunities actually are.be reactive about seeking opportunities for profitable exporting.The main reason most international transactions require full payment before the buyer receives the merchandise is:Multiple Choicestrict government regulations.an underlying lack of trust.an excess of factor endowments.to trigger lower tariffs.the inability to charge interest on the cost of goods.b
Compared to smaller firms, larger companies tend to option (B) systematically scan foreign markets to see where export opportunities lie.
Larger companies tend to systematically scan foreign markets to identify potential export opportunities due to their greater resources, including financial and human capital. This allows them to invest in researching and analyzing foreign markets, and to create effective exporting strategies. Furthermore, larger companies often have established distribution networks and greater brand recognition, which can make exporting a more viable option.
In contrast, smaller firms may lack the necessary resources and expertise to effectively navigate the complexities of exporting to foreign countries, and may therefore be more hesitant to seek out export opportunities.
Therefore, the correct option is (B) systematically scan foreign markets to see where export opportunities lie.
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The given question is incomplete, the complete question is:
Compared to smaller firms, larger companies tend to
Multiple Choice
A) delay exporting until after their domestic market is fully saturated.
B) systematically scan foreign markets to see where export opportunities lie.
C) be intimidated by the complexities and mechanics of exporting to foreign countries.
D) hesitate to seek export opportunities because they do not know how big the opportunities actually are
E) be reactive about seeking opportunities for profitable exporting.
Which of the following equations could be the function pictured in the graph?
A. y= (x-1)(x+3)
B. y= (x+1)(x-3)
C. y= (x+1)(x+3)
D. y= (x+1)(x-1)
Answer:
B. y = (x+1)(x-3)
Step-by-step explanation:
Bbecause when y intersect the x axis, y = 0
so (x+1)(x-3) = 0, which we get x = -1 and x = 3
As shown in the graph this is true, because the function does indeed also intersect with the x axis at x = -1 and x = 3 as well.
if customer interarrival times are exponentially distributed with rate 6 customers per hour, then to simulate the minutes between customer arrives in excel, one would use: group of answer choices
To simulate the minutes between customer arrivals in Excel, one would use the Exponential distribution function in Excel.
This function is part of the Statistical functions category and can be found under the "Statistical" tab in Excel.
An exponential distribution is a probability distribution that describes the time between events in a Poisson process, where events occur continuously and independently at a constant average rate.
The Exponential distribution function in Excel takes two arguments: Lambda and x.
Lambda is the rate parameter, which describes the average number of events per unit of time.
In this case, the rate is 6 customers per hour, so Lambda would be equal to 6.
X is the time interval, and in this case, it would be the time between customer arrivals in minutes.
Therefore, to simulate the minutes between customer arrivals, one would use the following formula in Excel: =EXPON.DIST(x/60,1/6,TRUE)
The "x/60" part of the formula is used to convert the time interval from minutes to hours, as the rate is given in customers per hour.
The "1/6" part of the formula is used to set the Lambda value to 6.
The "TRUE" part of the formula is used to specify that we want the cumulative distribution function (CDF), which gives the probability that the time between events is less than or equal to x.
To simulate the minutes between customer arrivals in Excel, we would use the Exponential distribution function with Lambda = 6 and x being the time interval between customer arrivals in minutes.
The formula would be = EXPON.DIST(x/60,1/6,TRUE).
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When George Washington became president in 1789, the army he had commanded in the American Revolution had
disbanded
ARMY DISBANDED MEANS SOLDIERS WERE RELEASED FROM SERVICE
When George Washington became president in 1789, the army he had
commanded in the American Revolution had disbanded. This means that
the soldiers were released from service and the military units were
dissolved after the end of the war.He pursued two intertwined interests:
military arts and western expansion. At 16 he helped survey Shenandoah
lands for Thomas, Lord Fairfax. Commissioned a lieutenant colonel in 1754,
he fought the first skirmishes of what grew into the French and Indian War.
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Please help this is my last question on my unit test and I do not know it
Find and explain the error in the student’s work below.
Solve 2x² - 5x -12 = 0 using the Quadratic Formula.
The roots of the given quadratic equation are x= 4, [tex]\frac{-3}{2}[/tex]
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:
ax² + bx + c = 0The roots of a quadratic equation are found using the quadratic formula. In place of the factorization method, this formula aids in evaluating the quadratic equations' solutions. The quadratic formula aids in identifying the problem's fictitious roots when a quadratic equation lacks actual roots. Shreedhara Acharya's formula is another name for the quadratic formula.
2x² - 5x -12 = 0
The Shridharacharya formula or quadratic formula -
[tex]x=\frac{-b\ +-\sqrt{b^2-4ac}}{2a}[/tex]
we have a=2, b=-5 and c=-12
[tex]x=\frac{5+-\sqrt{5^2-4*2*12}}{2*2}\\\\x=\frac{5+-\sqrt{25+96}}{4}\\\\x=\frac{5+\sqrt{121}}{4}\\\\x=\frac{5+-11}{4}\\now, \\x=\frac{5+11}{4}=\frac{16}{4}\\x=4\\x=\frac{5-11}{4}\\x=-6/4\\x=-3/2[/tex]
The mistake in your solution is we have the value of b=-5 so , when we put the value of b in a formula then -5 will be 5.
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pleaseee help super confused, and if you can please explain it i don’t understand
Answer:
China's top ten famous flowers are: the queen of flowers - plum blossom, the king of flowers - peony, frost blooming - chrysanthemum, gentleman's flower - orchid, the queen of flowers - rose, blooming flowers - Rhododendron, delicate flowers - camellia, water hibiscus - lotus, ten miles of fragrance - osmanthus, Lingbo fairy - daffodil 10 kinds of precious and beautiful local flowers.
Plum blossom is known as the "top ten famous flowers in China". These ten kinds of flowers respectively contain different levels of Chinese spiritual and cultural deposits, with profound and strong historical connotation. They are unique in the flower industry, marking the extraordinary significance of Chinese traditional culture. However, among China's top 10 traditional famous flowers, only the plum blossom, osmanthus and lotus have international registration rights.
Como resolver ecuaciones que tienen diferentes incógnitas
Ej: -x-4z=-15
To solve an equation with multiple unknowns, you need to have as many equations as there are unknowns.the solution to the system of equations is [tex]x = 13/11 and z = 37/11.[/tex]
What is the system of equations?For the equation you provided, [tex]-x - 4z = -15[/tex] , there are two unknowns: x and z. To solve for both, you need another equation that involves x and z.
If you have another equation that involves x and z, you can use a method like substitution or elimination to solve for both variables simultaneously.
For example, let's say you have the equation [tex]2x + 3z = 7.[/tex] You can use substitution to solve for one variable in terms of the other and substitute the result into the other equation.
To solve for x, rearrange the first equation to get x in terms of z:
[tex]-x - 4z = -15[/tex]
[tex]x = -15 + 4z[/tex]
Substitute the expression for x into the second equation:
[tex]2x + 3z = 7[/tex]
[tex]2(-15 + 4z) + 3z = 7[/tex]
Distribute the 2:
[tex]-30 + 8z + 3z = 7[/tex]
Simplify:
[tex]11z = 37[/tex]
Solve for z:
[tex]z = 37/11[/tex]
Substitute the value of z back into the equation for x:
[tex]x = -15 + 4z[/tex]
[tex]x = -15 + 4(37/11)[/tex]
[tex]x = -15 + 148/11[/tex]
Simplify:
[tex]x = 13/11[/tex]
Therefore, the solution to the system of equations is x = 13/11 and z = 37/11.
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karla paid $200 for an item that was originally priced at $350. what percent of the original price did karla pay? round your answer to the nearest tenth of a percent.
Karla paid 57.1% of the original price for an item that was originally priced at $350.
The explanation is that we can find the percentage that Karla paid by dividing the amount she paid by the original price and then multiplying by 100.
Percentage is a fraction out of 100. The formula for finding the percentage is as follows: (part / whole) × 100.
So, if Karla paid $200 for an item that was originally priced at $350, we can find the percentage she paid as follows: (200/350) × 100 = 57.1%.
Therefore, Karla paid 57.1% of the original price. To round it to the nearest tenth of a percent, we can simply round the answer to one decimal place, which is 57.1%.
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There are 14 muffins in a basket Tina put some on a plane now there are six in the basket. How many muffins does Tina put on the plate?
Answer:
Step-by-step explanation:
All you have to do is subtract 6 from 14. The answer is 8. If the question is something like this one, always take the remainder and subtract it from how many you had in the beginning to get the answer.
Good luck
Peyton
HARD 30 points please help me :(
A liner function goes through the points (1, 2) and (-3, 5) Calculate the slope of the line in simplest form
M = Y2 - Y1
X2 - X1
Show your work, please
Slope (m) =
Answer:
To calculate the slope of the line that passes through the points (1, 2) and (-3, 5), we use the slope formula:
m = (Y2 - Y1) / (X2 - X1)
where (X1, Y1) = (1, 2) and (X2, Y2) = (-3, 5).
Substituting the values into the formula, we get:
m = (5 - 2) / (-3 - 1)
m = 3 / (-4)
Simplifying the fraction by dividing both the numerator and denominator by their greatest common factor of 1, we get:
m = -3/4
Therefore, the slope of the line in simplest form is -3/4.
Find the areas of the figures whose vertices are
(a) (0,0), (3,7), (5,1)
(c) (-4,2), (0,-8), (5,11)
(e) (-2,-4), (3,1), (-1,5), (6,-3)
(b) (-1,-2), (-2,3), (4,-4)
(a) The area of the triangle is 16 square units.
(b) The area of the triangle is 54 square units.
(c) the area of the quadrilateral is 20 square units.
(d) The area of the triangle is 12.5 square units.
What is the area of the figures?(a) To find the area of the triangle with vertices (0,0), (3,7), and (5,1), we can use the formula:
A = 1/2 | x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) |
Plugging in the values, we get:
A = 1/2 | 0(7 - 1) + 3(1 - 0) + 5(0 - 7) |
= 1/2 | 0 + 3 - 35 |
= 1/2 |-32|
= 16
(b) To find the area of the triangle with vertices (-4,2), (0,-8), and (5,11), we can again use the same formula:
A = 1/2 | x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) |
Plugging in the values, we get:
A = 1/2 | (-4)(-8 - 11) + (0)(11 - 2) + (5)(2 - (-8)) |
= 1/2 | 108 |
= 54
(c) To find the area of the quadrilateral with vertices (-2,-4), (3,1), (-1,5), and (6,-3), we can divide it into two triangles and find the area of each triangle.
We can use the formula for the area of a triangle:
A = 1/2 | x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) |
For the triangle with vertices (-2,-4), (3,1), and (-1,5), we get:
A1 = 1/2 | (-2)(1 - 5) + (3)(5 + 4) + (-1)(-4 - 1) |
= 1/2 | (-8 + 35 + 5) |
= 16
For the triangle with vertices (3,1), (-1,5), and (6,-3), we get:
A2 = 1/2 | (3)(5 + 3) + (-1)(-3 - 1) + (6)(1 - 5) |
= 1/2 | (24 + 4 - 20) |
= 4
Therefore, the area of the quadrilateral is:
A = A1 + A2
= 16 + 4
= 20 square units
(d) To find the area of the triangle with vertices (-1,-2), (-2,3), and (4,-4), we can use the same formula:
A = 1/2 | x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) |
Plugging in the values, we get:
A = 1/2 | (-1)(3 + 4) + (-2)(-4 + 2) + (4)(-2 - 3) |
= 1/2 | (-7 - 4 - 14) |
= 12.5
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how far will 560J raise a block weighing 8 N
a force of 560J can raise a block weighing 8 N to a height of 70 meters. It's important to note that this calculation assumes no energy is lost due to friction or other factors, so in reality, the block may not reach exactly 70 meters.
How to calculate work?
To calculate the height to which a block weighing 8 N can be raised by a force of 560J, we need to use the formula for work done:
Work (W) = force (F) x distance (d) x cos(theta)
where theta is the angle between the force and the displacement. In this case, the force is the weight of the block (8 N), the distance is the height the block is raised (h), and theta is 0 degrees because the force is acting vertically upward and the displacement is in the same direction.
So, we can rearrange the formula to solve for the height (h):
h = W / (F x cos(theta))
Substituting the values we have, we get:
h = 560 J / (8 N x cos(0 degrees))
Since the cosine of 0 degrees is 1, we can simplify to:
h = 560 J / 8 N
h = 70 meters
Therefore, a force of 560J can raise a block weighing 8 N to a height of 70 meters. It's important to note that this calculation assumes no energy is lost due to friction or other factors, so in reality, the block may not reach exactly 70 meters.
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(20points) phone camera took the pictures in the aspect ratio of 3:2. Luckily, Naomi can enlarge, shrink or rotate the pictures, but she doesn't want to have to crop the pictures at all or leave any extra space on the sides.
Which print sizes will she be able to order without leaving any extra space or having to cut off any extra material?
Which print sizes will she be able to order without leaving any extra space or having to cut off any extra material?
2x3
4x4
4x5.3
4x6
5x7
D 8x8
8x10
11x14
16x20
20x30
24x36
Solve for the missing angle measures
(4x-7)°
(3x-15)°
plss help
The measure of the missing angles of the right triangle are 57 degree and 33 degrees.
What are the measures of the missing angles?The sum of the interior angles of a triangle equals 180 degrees.
From the diagram:
Angle A = (4x - 7) degrees
Angle B = (3x - 15) degrees
Angle C = 90 degrees
In a right triangle, the sum of the two acute angles is 90 degrees.
So, we have:
angle A + angle B + 90 = 180 (sum of angles in a triangle)
(4x - 7) + (3x - 15) + 90 = 180
Solve for x
4x - 7 + 3x - 15 + 90 = 180
4x + 3x - 15 - 7 + 90 = 180
7x - 15 - 7 + 90 = 180
7x + 68 = 180
7x = 180 - 68
7x = 112
x = 112/7
x = 16
Therefore, the missing angles will be:
angle A = (4x - 7) = 4(16) - 7 = 57 degrees
angle B = (3x - 15) = 3(16) - 15 = 33 degrees.
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Answer:
The measure of the missing angles of the right triangle are 57 degree and 33 degrees.
Step-by-step explanation:
a statistics professor wants to see if more than 80% of her students enjoyed taking her class. at the end of the term, she takes a random sample of students from her large class and asks, in an anonymous survey, if the students enjoyed taking her class. which set of hypotheses should she test?
To test if more than 80% of her students enjoyed taking her class, the statistics professor should use a hypotheses test.
The null hypotheses (H0) would be that the proportion of students who enjoyed taking her class is equal to or less than 80%, while the alternative hypothesis (Ha) would be that the proportion is greater than 80%.
H0: p <= 0.80
Ha: p > 0.80
Where p: proportion of students who enjoyed taking the class.
To test this hypothesis, the professor would need to collect a random sample of students from her class and ask them if they enjoyed taking the class. She could then use a test statistic, such as the z-score, to determine the probability of obtaining the observed proportion of students who enjoyed the class, assuming the null hypothesis is true.
If the probability of obtaining the observed proportion is very low (typically, less than 0.05), then the professor would reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that more than 80% of her students enjoyed taking her class.
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1. Make a box plot of the ticket prices shown and identify the median price.
$25.50 $45.00
$24.00
$32.50 $32.00 $20.00
$38.50 $50.00 $45.00
Answer:
Step-by-step explanation:
A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production. Which of the following would result in the smallest margin of error in estimating the mean salt content, u? A. 90% confidence, n = 25 B. 90% confidence, n = 50 C. 95% confidence, n = 25 D. 95% confidence, n = 50 E. n = 100 at any confidence level
The option that would result in the smallest margin of error in estimating the mean salt content, u, is 95% confidence, n = 50. The correct answer is Option D.
What is the margin of error?The margin of error is the amount by which a statistic is expected to differ from the true value of the population parameter. The interval estimate is calculated with the help of a margin of error. The margin of error and the interval estimate are inversely related to each other. If we want a small margin of error, we must increase the sample size.
What is the confidence level?The confidence level is the likelihood that a population parameter will fall within a specified range of values. The confidence level is determined by the sample size and margin of error. The sample size and margin of error are directly related to each other. When the sample size is smaller, the margin of error is larger. When the sample size is larger, the margin of error is smaller.
How to determine the smallest margin of error?The margin of error is the highest at a confidence level of 50%. In general, as the confidence level increases, the margin of error decreases, and vice versa. As the sample size increases, the margin of error decreases. It follows that a 95% confidence level, n = 50 would yield the smallest margin of error in estimating the mean salt content, u. Hence, option D) 95% confidence, n = 50 would result in the smallest margin of error in estimating the mean salt content, u.
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someone please help meee!! ASAPPP
Hi so you have to do grid for the equation
Helppp.. also show work pls
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
in a survey, 69% of americans said they own an answering machine. if 15 americans are selected at random, find the probability that exactly 7 own an answering machine. round your answer to three decimal places.
Rounding to three decimal places, the probability that exactly 7 Americans out of a sample of 15 own an answering machine is approximately 0.170.
To find the probability that exactly 7 of the 15 Americans selected at random own an answering machine, we can use the binomial distribution formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
where P(X = k) is the probability of getting exactly k successes, n is the sample size, p is the probability of success, and (n choose k) is the binomial coefficient which represents the number of ways to choose k successes out of n trials.
In this case, n = 15, p = 0.69 (the proportion of Americans who own an answering machine), and k = 7. Thus, the probability of getting exactly 7 Americans who own an answering machine out of a sample of 15 is:
P(X = 7) = (15 choose 7) * 0.69^7 * (1 - 0.69)^(15 - 7)
Using a calculator or statistical software, we can evaluate this expression to find:
P(X = 7) ≈ 0.170
This means that if we were to repeat this survey many times with samples of size 15, we would expect approximately 17% of the samples to have exactly 7 Americans who own an answering machine.
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Find the new y-intercept by writing an equation in slope-intercept form that
is parallel to the line y = -3x + 8 and goes through the point (5, 3).
Answer:
y- intercept = 18
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 3x + 8 ← is in slope- intercept form
with slope m = - 3
• Parallel lines have equal slopes , then
y = - 3x + c ← is the partial equation
to find c substitute (5, 3 ) into the partial equation
3 = - 3(5) + c = - 15 + c ( add 15 to both sides )
18 = c
y = - 3x + 18 ← equation of parallel line
with y- intercept c = 18
pl z help ill give brianliest
Answer:
The correct answer is 21 km.
Step-by-step explanation:
Because
A = (1/2) · (p + q) · h
Where p is 9 and q is 5 (the bases)
and h is the height (3)
Then:
A = (1/2) · (p + q) · h
A = (1/2) · (9 + 5) · 3
A = (1/2) · (14) · 3
A = (1/2) · 42
A= 21
Brainliest Please!
answer: 21
7 times 3 = 21
11. if 3 men can dig a 3 x 2 x 4 meter hole in 20 minutes, how long will it take 6 men to dig a 4 x 4 x 3 meter hole?
it would take 6 men 20 minutes to dig a hole that is 4 x 4 x 3 meters
To solve this problem, we can use the formula that relates the time taken to do a job to the number of workers available, assuming that all workers have the same productivity. This formula is given by the equation:Work Done = Productivity x Time Taken x Number of Workers available. If we let the work done be W, the productivity be P, and the time taken be T, then the equation becomes:W = P x T x N. We are given that 3 men can dig a hole that is 3 x 2 x 4 meters in 20 minutes. We can find the volume of this hole by multiplying its dimensions:V = 3 x 2 x 4 = 24 cubic metersThis means that 3 men can dig a volume of 24 cubic meters in 20 minutes.
To find their productivity, we can use the formula: Productivity = Work Done / (Time Taken x Number of Workers)P = W / (T x N) = 24 / (20 x 3) = 0.4 cubic meters per minute per worker. Now we can use this productivity to find the time taken for 6 men to dig a hole that is 4 x 4 x 3 meters. We can find the volume of this hole by multiplying its dimensions:V = 4 x 4 x 3 = 48 cubic meters.
To dig this hole, the amount of work done would be 48 cubic meters. The productivity per worker is still 0.4 cubic meters per minute, but the number of workers is now 6. Therefore, the time taken would be:T = W / (P x N) = 48 / (0.4 x 6) = 20 minutes.Therefore, it would take 6 men 20 minutes to dig a hole that is 4 x 4 x 3 meters, given that 3 men can dig a hole that is 3 x 2 x 4 meters in 20 minutes.
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100 points please help!
The quadratic equation x² + 2 - 4x = -4 in standard form is x² - 4x + 6 = 0
What is a quadratic equation in standard form?A quadratic equation in standard form is given by ax² + bx + c = 0
Now, given the equation x² + 2 - 4x = -4, we desire to write it in standard form, we proceed as follows.
Since we have the quadratic equation x² + 2 - 4x = -4 writing it in standard form, we have
x² + 2 - 4x = -4
Adding 4 to both sides of the equation, we have that
x² + 2 - 4x + 4 = -4 + 4
x² + 2 + 4 - 4x = 0
x² + 6 - 4x = 0
Re-arranging, we have that
x² - 4x + 6 = 0
So, in equation in standard form is x² - 4x + 6 = 0
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if n > 30 , then the sampling distribution of the mean will have a shape of symmetric , the mean will be equal to [ select ] and the standard error will be equal to
When n > 30, the sampling distribution of the mean will have a shape of symmetric, the mean will be equal to the population mean (μ), and the standard error will be equal to σ/√n.
The shape of a sampling distribution of the mean is always symmetric when n > 30. This is because the Central Limit Theorem (CLT) states that the sampling distribution of the mean is approximately normal when the sample size is greater than 30. Therefore, when n > 30, the shape of the sampling distribution of the mean will be symmetric.
The mean of the sampling distribution of the mean is equal to the population mean, μ. This is because the sampling distribution of the mean is a probability distribution of all the possible sample means, and it is centered around the population mean. Therefore, the mean of the sampling distribution of the mean is equal to μ.
The standard error (SE) of the sampling distribution of the mean is equal to the population standard deviation (σ) divided by the square root of the sample size (n). This is because the standard error is a measure of how accurately the sample mean estimates the population mean. Since the sample size is greater than 30, the sample mean will accurately estimate the population mean and the standard error will be equal to σ/√n.
In summary, when n > 30, the sampling distribution of the mean will have a shape of symmetric, the mean will be equal to the population mean (μ), and the standard error will be equal to σ/√n.
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