write an equation in point-slope form of the line that passes through (9, 4) and is parallel to the line y = x - 6.
WILL GIVE BRAINLIEST
Answers
Answer:
y = x - 5
Step-by-step explanation:
y = x -6
y = MX +C
.: m = 1 ( where m is the gradient of the line)
Let gradient = gradient 2 ( because the lines are parallel to each other)
m1= m2
1= y- y1 / x - x1
( 9,4) = ( x1 , y1 )
.: 1= y - 4 / x - 9
Cross multiply
1( x -9) = y - 4
x - 9 = y - 4
y = x - 9 + 4
y = x - 5
.: The equation of the line is y = x -5
The answer can also be written as y - 4 = 1( x -9)
Related Questions
PLEASE HELP!!!!!!!!!!!!!
What is the value of the expression 5x - 3y ?
3x - 4y= -24
3x +2y= -6
Answers
The value of the expression 5x - 3y, is -29 obtained by elimination method by eliminating the two equations.
The equations are :
3x - 4y= -24 ----------- A
3x +2y= -6 ----------- B
On multiplying minus sign in B equation, to eliminate the x- component in the equation.
3x +2y= -6 becomes (-3x - 2y = 6)
Then, the equation becomes,
3x - 4y= -24
-3x - 2y = 6 (+ 3x - 3x are equal and opposite becomes zero.)
------------------
-6y = -18
------------------
6y = 18 (both minus sign gets cancelled)
y = 18/6
= 3
The value of y=3.
Substitute the value of y=3 in A equation.
Equation A is, 3x - 4y= -24
3x - 4(3) = -24
3x = -24 + 12
3x = -12
x = -12 / 3
= -4
The value of x= -4.
Thus, the value of x= -4 and y = 3. By using this x and y values, the equation 5x - 3y, can be solved as,
= 5x - 3y
= 5(-4) - 3 (3)
= -20 -9
= -29
The value of the expressions 5x - 3y = -29.
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The perimeter of a rectangle is 50 inches. Its width measures 11 inches. What is its length? Let x= length of the rectangle. A.) 2x - 11 = 50
B.) 2x + 11 = 50
C.) x + 11 = 50
D.) 2x + 22 = 50
Answers
Answer: D.) 2x + 22 = 50
Step-by-step explanation:
P=2(l+w)
2x+22=50 is correct because
2 times x is 2 times the unknown length
11 times 2 is 22 so, you add that to the 2x
50 is the perimeter
Savannah recorded the grade-level and instrument of everyone in the middle school School of Rock below.
Seventh Grade Students
Instrument # of Students
Guitar 5
Bass 12
Drums 14
Keyboard 4
Eighth Grade Students
Instrument # of Students
Guitar 12
Bass 5
Drums 10
Keyboard 8
Based on these results, express the probability that a student chosen at random will play the drums as a percent to the nearest whole number.
Answers
The probability that a student chosen at random plays the drums is approximately 34%.
What is probability?
The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place. A certain event has a chance of 1, while an impossible event has a probability of 0.
The total number of students in the middle school who play the drums is 14 + 10 = 24.
The total number of students in the middle school is:
5 + 12 + 14 + 4 + 12 + 5 + 10 + 8 = 70
The probability of selecting a student who plays the drums at random is:
24/70 = 0.34285714285714286
To express this probability as a percentage, we multiply by 100 and round to the nearest whole number:
0.34285714285714286 * 100 ≈ 34
Therefore, the probability that a student chosen at random plays the drums is approximately 34%.
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The vertex of f(x)=-4.9x^(2)+26.1+65
Is the vertex a maximum/minimum?
The y-intercept and x-intercept of f(x)=-4.9x^(2)+26.1+65
Answers
$f(x) = -4.9x^2 + 26.1x + 65$
Pour trouver le sommet :
$x = -\frac{b}{2a}$
$a = -4.9$ et $b = 26.1$
$x = -\frac{26.1}{2(-4.9)}$
$x = 2,6735 $
$f(2.6735) = -4.9(2.6735)^2 + 26.1(2.6735) + 65$
$f(2.6735) = 88.7598$
Par conséquent, le sommet de la fonction donnée est $(2.6735, 88.7598)$.
Puisque le coefficient de $x^2$ est négatif ($-4.9$), la parabole s’ouvre vers le bas, et le sommet représente le point maximum de la fonction.
Pour trouver l’interception y :
$f(0) = -4.9(0)^2 + 26.1(0) + 65$
$f(0) = 65 $
Par conséquent, l’interception y est $(0, 65)$.
Pour trouver les interceptions x :
$0 = -4.9x^2 + 26.1x + 65$
En utilisant la formule quadratique:
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
$a = -4.9$, $b = 26.1$, et $c = 65$
$x = \frac{-26.1 \pm \sqrt{26.1^2 - 4(-4.9)(65)}}{2(-4.9)}$
$x = \frac{-26.1 \pm \sqrt{1521.61}}{-9.8}$
$x = 2.102$ ou $-3.117$
Par conséquent, les interceptions x sont approximativement $(2.102, 0)$ et $(-3.117, 0)$.
can you help me solve this e - 3.4 = 18.7
Answers
Answer:
evaluate: −0.68171817=18.7
Step-by-step explanation:
gregs backyard is 42 feet wide how many yards and feet is that?
pls show your work. thx
Answers
Greg's backyard is 14 yards and 1 foot wide. To summarize, we can say that 42 feet is equivalent to 14 yards and 1 foot.
To convert 42 feet to yards and feet, we need to know that there are 3 feet in 1 yard. We can divide the total number of feet (42) by 3 to get the number of yards, and then take the remainder to get the remaining feet.
So, 42 feet divided by 3 feet/yard equals 14 yards. This means that Greg's backyard is 14 yards wide.
To find the remaining feet, we can multiply the decimal part of the result by 3. So, 0.333 x 3 = 0.999. Since we cannot have a fraction of a foot, we round up to the nearest whole foot, which gives us 1 foot.
Therefore, Greg's backyard is 14 yards and 1 foot wide. To summarize, we can say that 42 feet is equivalent to 14 yards and 1 foot.
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A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 8 above 10 to 19, up to 6 above 20 to 29, up to 2 above 30 to 39, and up to 2 above 50 to 59. There is no shaded bar above 40 to 49.
Which measure of center should the charity use to accurately represent the data? Explain your answer.
The median of 22.7 is the most accurate to use to show that they have plenty of money.
The mean of 20 is the most accurate to use to show that they need more money.
The median of 20 is the most accurate to use, since the data is skewed.
The mean of 22.7 is the most accurate to use, since the data is skewed
Answers
Answer: C. The median of 20 is the most accurate to use, since the data is skewed.
The most accurate measure of center to use in this case is the median of 20. This is because the data is skewed, with a few high-value donations (such as the two donations of 55 dollars) that pull the mean up. However, most of the donations are clustered around 10 to 20 dollars. As a result, the median, which is the middle value when the data is sorted in order, is a better representation of the "typical" donation amount.
In this case, the median is 20, which means that half of the donations were less than 20 dollars and half were more. This is a more accurate representation of the central tendency of the data than the mean of 22.7, which is influenced by the high-value donations. Therefore, the charity should use the median of 20 to accurately represent the typical donations received.
Step-by-step explanation:
Jose worked for 12 hours each day for 7 days. Then the next day he worked 8 hours. How many hours did Jose work in all?
Answers
Answer:
92 hours
Step-by-step explanation:
7 * 12 + 8 = 92
approximately how many kilocalories are in a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein?
Answers
Answer:
Therefore, there are approximately 102 kilocalories in the snack bar.
Step-by-step explanation:
One gram of fat provides 9 kilocalories (kcal), while one gram of carbohydrate and protein provide 4 kcal each. So, to find the total number of kilocalories in the snack bar, we can use the following formula:
Total kcal = (grams of fat * 9) + (grams of carbohydrate * 4) + (grams of protein * 4)
Plugging in the values, we get:
Total kcal = (6 * 9) + (10 * 4) + (2 * 4)
Total kcal = 54 + 40 + 8
Total kcal = 102
Therefore, there are approximately 102 kilocalories in the snack bar.
The answer is approximately 120 kilocalories in a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein.
What are kilocalories? Kilocalories, also known as calories, are a unit of energy used to calculate the amount of energy in food. The number of kilocalories in food is calculated based on the number of grams of protein, carbohydrate, and fat it contains. Kilocalories are used by the body to fuel its processes and maintain its vital functions. The energy in food is released when it is digested, absorbed, and transported to the cells where it is used to produce ATP, the body's primary source of energy. ATP is used to power cellular processes such as metabolism, respiration, and movement. How many kilocalories are in a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein? To calculate the number of kilocalories in a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein, we need to know the number of kilocalories per gram of each macronutrient. Protein and carbohydrates each contain 4 kilocalories per gram, while fat contains 9 kilocalories per gram. To calculate the number of kilocalories in the snack bar, we multiply the number of grams of each macronutrient by the number of kilocalories per gram and then add them together. Here is the calculation:6 grams of fat x 9 kilocalories per gram of fat = 54 kilocalories10 grams of carbohydrate x 4 kilocalories per gram of carbohydrate = 40 kilocalories2 grams of protein x 4 kilocalories per gram of protein = 8 kilocalories. Total kilocalories = 54 + 40 + 8 = 102Therefore, a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein has approximately 102 kilocalories.
A snack bar with 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein has approximately 102 kilocalories. This is calculated as follows: (6 grams fat x 9 kcal/g) + (10 grams carbohydrate x 4 kcal/g) + (2 grams protein x 4 kcal/g).
Therefore, answer is 120 kilocalories.
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Jeff is purchasing a car for $28,175 that will depreciate in value 8.5% each year.
Write a function to model the value of p of the car after t years.
If he decides to sell the car after 6 years, what will be the value of his car? Express your answer as a decimal rounded to the nearest hundredth.
Answers
The function to model the value of p of the car after t years can be expressed as:
p(t) = 28,175 * (1 - 0.085)^t
where 0.085 represents the percentage of depreciation per year, and t represents the number of years.
To find the value of the car after 6 years, we substitute t = 6 into the function:
p(6) = 28,175 * (1 - 0.085)^6
p(6) = 28,175 * 0.5386
p(6) ≈ 15,199.35
Therefore, the value of Jeff's car after 6 years will be approximately $15,199.35.
what is the length of AC in the graph below
Answers
The length AC of the triangle is 4.47 units.
How to find the length on a graph?The diagram on the graph is a triangle. The question wants us to find the length AC of the triangle.
To find the length AC in the triangle, we have to use distance formula as follows:
Therefore,
A = (1, 1)
C = (3, 5)
AC = √(y₂ - y₁)² + (x₂ - x₁)²
AC = √(5 - 1)² + (3 - 1)²
AC = √4² + 2²
AC = √16 + 4
AC = √20
Hence,
AC = 4.472135955
AC = 4.47 units
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solve the system of equations
Answers
Answer:
(2, 3)
Step-by-step explanation:
9x - 7y = -3
+ -9x + 15y = 27
8y = 24 (Divide by 8 on both sides)
8 = 8
y = 3
Substitute y = 3 in any of the two equations.
9x - 7(3) = -3
9x - 21 = -3
+21 = +21 (Add 21 on both sides)
9x = 18 (Divide by 9 on both sides)
9 = 9
x = 2
Find ratio in which line joining of points A(–7, –1) and B(8, 2) is divided by x + y = 2 ?
Answers
After answering the presented question, we can conclude that As a result, the line connecting the points A(-7, -1) and B(8, 2) is divided by the line x + y = 2 in the ratio about 65.63:56.63.
what is ratio?In mathematics, ratios demonstrate how frequently one number is contained in another. For example, if there are 8 oranges and 6 lemons in a fruit dish, the ratio of oranges to lemons is 8 to 6. In a similar vein, the orange-to-whole-fruit ratio is 8, whereas the lemon-to-orange ratio is 6:8. A ratio is an ordered pair of numbers a and b represented as a / b, where b is not zero. A ratio is an equation that equates two ratios. For example, if there is one male and three girls (for every boy she has three daughters), 3/4 are girls and 1/4 are boys.
[tex]m = (y2 - y1)/(x2 - x1) = (2 - (-1))/(8 - (-7)) = 3/15 = 1/5\\y - y1 = m(x - x1)\\y - (-1) = (1/5)(x - (-7))\\y + 1 = (1/5)(x + 7)\\y = (1/5)x + 6/5 - 1\\y = (1/5)x + 1/5\\x + (1/5)x + 1/5 = 2\\(6/5)x = 9/5\\x = 3\\[/tex]
[tex]y = (1/5)(3) + 1/5\\y = 4/5\\AP = \sqrt[(3 - (-7))^2 + (4/5 - (-1))^2] = \sqrt[10^2 + 9/5^2] = \sqrt[100 + 81/25] = \Sqrt[4301]/5\\PB = \Sqrt[(8 - 3)^2 + (2 - 4/5)^2] = \sqrt[25 + 81/25] = \sqrt[3206]/5\\[/tex]
The ratio in which AB is divided by x + y = 2 is:
[tex]AP:PB = \sqrt[4301]:\sqrt[3206] = 65.63:56.63 \\[/tex]
As a result, the line connecting the points A(-7, -1) and B(8, 2) is divided by the line x + y = 2 in the ratio about 65.63:56.63.
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PLEASE HELPP
Sara is paid semi-monthly. Her annual salary is $37,560. What is her semi-monthly to the nearest cent?
A)$1,444.62
B)$1,502.40
C)$1.565,00
D)$727.31
Answers
Step-by-step explanation:
To find Sara's semi-monthly salary, we need to divide her annual salary by the number of semi-monthly periods in a year.
Since there are 24 semi-monthly periods in a year (twice a month), we can divide her annual salary by 24 to get her semi-monthly salary:
$37,560 ÷ 24 = $1,565.00
Therefore, Sara's semi-monthly salary to the nearest cent is option C) $1,565.00.
Empirical Rule Khan Academy; all, if not most, of the answers.
I didn't know how to do the assignment, nor did I want to take the time to learn how to do it- so I kept rerolling answers while documenting the question (the variables involved in each of the questions) and then noting down the answers.
Whilst doing this Khan Academy assignment (quiz or whatever) look at the first two numbers near the "less than," "more than," and "living between" part of the question. Proceed to align the next numbers to whichever ones I have on the pdf.
- The answers will be under the numbers that have "and" or "&." I put on the right, with a dash, to note whether it was the question regarding more than, less than, or living between.
This took me a while to do (I was going for 4 stars on Khan). I thought it was worth sharing. Goodluck, folks.
Answers
Answer:
dont no ok i dont konow ask an easy one
#
two different cubes of the same size are to be painted, with the color of each face being chosen independently and at random to be either black or white. what is the probability that after they are painted, the cubes can be rotated to be identical in appearance?(2020amc12b problem 20) (a) 64 9 (b) 2048 289 (c) 512 73 (d) 1024 147 (e) 4096
Answers
Step-by-step explanation:
with 2 cubes we have 12 faces to paint.
each face has 2 options (black or white).
so, we have a total of 2¹² possible outcomes.
a probability is always the ratio of
desired cases / totally possible cases
so, we need to find a way to express the desired cases of both cubes being painted the same way.
essentially that means we have a totally free choice of painting the faces of the first cube.
that is 2⁶ possible outcomes.
for the second cubes we have then only one basic choice : to repeat the choices done on the first cube.
BUT : we have 6×4 ways to orient the second cube before painting it identically.
6 ways to pick e.g. the front face, and then 4 options to rotate the cube with the same front face for the e.g. top face.
in other words, we have 2⁶ different desired patterns on the first cube and 24 options to repeat the pattern on the second cube.
that means the desired options are 2⁶×1×24
so, the probability for them to be identical is
24×2⁶ / 2¹² = 24/2⁶ = 3/2³ = 3/8 = 0.375
The probability that after they are painted, the cubes can be rotated to be identical in appearance is (a) 64/9
Probability is a branch of mathematics that deals with the study of random phenomena or events with uncertain outcomes.
Let's start by assuming that one of the cubes has the black face facing up. The other cube can be painted in any of the possible ways.
Let's list all the possible configurations for the second cube.
There are six faces, and each can be painted either black or white. Therefore, there are 2⁶ = 64 possible configurations for the second cube.
The cube with the black face facing up has been accounted for separately, so there are 63 configurations that we need to consider.
If the second cube is painted all black or all white, there is only one way to position it so that the cubes look identical, and that is to rotate it so that the black or white face is facing up.
There are two such configurations. If the second cube has exactly one white face and five black faces, there are three ways to position it so that the cubes look identical. There are three such configurations
.If the second cube has two white faces and four black faces, there are six ways to position it so that the cubes look identical. There are six such configurations.
If the second cube has three white faces and three black faces, there are eight ways to position it so that the cubes look identical. There are eight such configurations.
If the second cube has four white faces and two black faces, there are six ways to position it so that the cubes look identical. There are six such configurations.
If the second cube has five white faces and one black face, there are three ways to position it so that the cubes look identical. There are three such configurations
.If the second cube is painted all white, there is only one way to position it so that the cubes look identical, and that is to rotate it so that the white face is facing up. There are two such configurations.
In total, there are 2 + 3 + 6 + 8 + 6 + 3 + 2 = 30 ways to position the two cubes so that they look identical.
There are 63 × 64 possible configurations for the two cubes, so the probability of the cubes being able to be rotated to be identical in appearance is given by:
30/ (63×64) = 64/9
Therefore, the correct answer is (a) 64/9.
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there are 25 people competing in a rubber duck regatta. each person is allowed only one entry. if there are no ties, how many ways are there to have the first, second, and third place winners?
Answers
There are 13,800 different ways to have the first, second, and third place winners without any ties.
In a rubber duck regatta with 25 people competing and each person having only one entry, we can determine the number of ways to have the first, second, and third place winners by using permutations.
Step 1: Calculate the number of options for the first place winner.
There are 25 contestants, so there are 25 options for the first place.
Step 2: Calculate the number of options for the second place winner.
Since the first place winner has been determined, there are 24 remaining contestants to choose from for the second place.
Step 3: Calculate the number of options for the third place winner.
After determining the first and second place winners, there are 23 remaining contestants to choose from for the third place.
Step 4: Multiply the number of options for each place to get the total number of possible outcomes.
25 options (first place) × 24 options (second place) × 23 options (third place) = 13,800 possible outcomes.
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How do -4.1 and -3 1/2 compare?
Answers
Step-by-step explanation:
you have to subtract them which would be -1.05
the weather reporter stated that the probability of rain last week was 3 out of 7 days. It rained on Mont\day, Tuesday, Thursday, and Friday last week.How did the reporter's stated probabilty for rain last week compare to the actual results
Answers
If it rained on Monday, Tuesday, Thursday and Friday Last week then probability of rain would be 4/7 as there are 7 days in a week.
Total days in week = total outcome = 7days
Possible outcome = 4
P(rain) = 4/7
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will learn the potential outcomes for a random experiment using this fundamental theorem of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
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At a coffee shop, the first 100 customers'
orders were as follows.
Hot
Cold
Small Medium Large
5
48
22
8
12
5
Find the probability a customer ordered a
medium, given that they ordered a hot drink.
P(B|A) =
P(medium | hot) = [? ]
P(ANB)
P(A)
Answers
P(medium | hot) = P(hot | medium) * P(medium) / P(hot)
We can find the values we need from the table:
P(hot) = (5+48+22)/100 = 0.75
P(medium) = (8+12)/100 = 0.2
P(hot | medium) = 12/20 = 0.6
Now we can substitute these values into the formula:
P(medium | hot) = 0.6 * 0.2 / 0.75 = 0.16
Therefore, the probability that a customer ordered a medium given that they ordered a hot drink is 0.16.
Find the answer and explain
Answers
Answer:
660cm^2
Step-by-step explanation:
area of 2 triangle= 10×12
= 120cm^2
area of 3 rectangles= (13×15×2)+(10×15)
= 390+150
= 540cm^2
surface area of triangular prism
= 540+120
= 660cm^2
One rectangle is "framed" within another. Find the area of the shaded region if the "frame" is 1 unit wide.
Answers
There are [tex]18[/tex] square units in the area of the shaded rectangle.
What makes it a rectangle?The Latin words "rect" (which means "right") and "angulus" (which means "angle") are the roots of the English word "rectangle." These two words together form the term "rectangle." A rectangle has 90° straight angles at each of its four corners. A rectangular also has two equal-length diagonals that meet in the centre.
What other name does rectangle go by?In addition to rectangles, we also refer to them as geometric figures, quadrilaterals, and polygons. This is so that it is clear that a rectangle fulfils the specifications of all of these other forms.
width [tex]= 7[/tex] units
length [tex]= 10[/tex] units
We remove the frame, each measure will lose[tex]2*2[/tex] units, or [tex]4[/tex] units
[tex]width = 7 units - 4 units = 3 units[/tex]
[tex]length = 10 units - 4 units = 6 units.[/tex]
[tex]A = (3 units)*(6 units) = 18[/tex] square units.
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The completed question is:
One rectangle is "framed" within another. Find the area of the shaded region if the
"frame" is 1 unit wide.
10
5
Lily makes $8.25 an hour at her job. She has been offered a different job that pays $10.40 hour. What is the percent increase in her pay?
Answers
The percent increase in her pay is by 26.06% if she takes the new job.
What is percentage increase?A quantity's percentage increase is a way to represent how much it has grown in comparison to its starting point. The formula is as follows: take the new value, remove the original value, divide the outcome by the original value, and then multiply by 100%. When comparing two quantities, such as incomes, prices, or test scores, it is common to use the percentage increase to gauge how much has changed. A value rise is indicated by a positive percent increase, whilst a value loss is shown by a negative percent increase.
Given that, the pat increases from $8.25 an hour to $8.25 an hour.
percent increase = [(new value - old value) / old value] x 100%
Substituting the values we have:
percent increase = [(10.40 - 8.25) / 8.25] x 100%
percent increase = 26.06%
Therefore, Lily's pay would increase by 26.06% if she takes the new job.
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i need help to solve these questions step by step, PLEASEEE THIS DUES TODAY
Answers
10. x(3x+4) (2x-3
11. 8mn^2 (m-n) (m - 3n)
12. 3(5x - 2y)(2x + y)
13. x(2x - 1)(x + 3
hope this helps
6x^3 - x^2 -12x
Let’s go ahead and factor out an x:
x ( 6x^2 - x - 12)
Rewrite the 1st degree x as a difference of two values that have similar factors to 6 and 12:
x ( 6x^2 + 8x - 9x - 12 )
Factor out 2x from ( 6x^2 + 8x ):
x ( 2x ( 3x + 4) (-9x - 12) )
Factor out -3 from ( -9x - 12 ) to get the same:
x ( 2x ( 3x + 4 ) - 3 ( 3x + 4) )
Group these for your final factored form:
x (2x -3) (3x+4)
11.
Right off the bat, 8 is a factor of both 32 and 24, so divide these leading coefficients by 8:
8m^3n^2 - 32m^2n^3 + 24mn^4
m^3n^2 - 4m^2n^3 + 3mn^4
Factor out one m:
m ( m^2n^2 - 4mn^3 + 3n^4)
Now factor out an n^2:
mn^2 ( m^2 - 4mn + 3n^2)
This is the final factored form.
13.
Factor out an x:
x (2x^2 + 5x - 3)
Rewrite 5x as a difference of two terms that will factor well with 2 and 3:
x ( 2x^2 + 6x - x - 3)
Now factor out a 2x:
x ( 2x ( x + 3 ) - x - 3 )
Now factor the other part so that what’s left matches the previous factor:
x ( 2x (x + 3) -1 (x +3) )
Now group these for the final factored form:
x ( 2x - 1 ) ( x + 3 )
quartile and decile for ungrouped data
Answers
A) Quartile 1 (Q1): 2, Quartile 2 (Q2): 6, Quartile 3 (Q3): 7, Decile 1 (D1): 1, Decile 2 (D2): 2, Decile 3 (D3): 3, Decile 4 (D4): 7
B) Quartile 1 (Q1): 11, Quartile 2 (Q2): 14, Quartile 3 (Q3): 16, Decile 1 (D1): 11, Decile 2 (D2): 12, Decile 3 (D3): 14, Decile 4 (D4): 17
C) Quartile 1 (Q1): 77, Quartile 2 (Q2): 85, Quartile 3 (Q3): 94, Decile 1 (D1): 71, Decile 2 (D2): 81, Decile 3 (D3): 87, Decile 4 (D4): 98
D) Quartile 1 (Q1): 42, Quartile 2 (Q2): 66, Quartile 3 (Q3): 86, Decile 1 (D1): 28, Decile 2 (D2): 42, Decile 3 (D3): 57, Decile 4 (D4): 98
E) Quartile 1 (Q1): 100, Quartile 2 (Q2): 117, Quartile 3 (Q3): 133, Decile 1 (D1): 33, Decile 2 (D2): 100, Decile 3 (D3): 111, Decile 4 (D4): 147
F) Quartile 1 (Q1): 113, Quartile 2 (Q2): 126, Quartile 3 (Q3): 146, Decile 1 (D1): 110, Decile 2 (D2): 113, Decile 3 (D3): 121, Decile 4 (D4): 848
What is number?Number is an important part of mathematics, and it is used in virtually every aspect of life.
A) First, we need to arrange the data in order:
[1,1,2,2,2,2,2,3,3,3,3,4,5,6,6,7,7,7,7,9,9]
The median is the middle value of the data set. Since there are 21 values, the median is the average of the [tex]$10^{th}$[/tex] and [tex]$11^{th}$[/tex] values, which is 6.
The first quartile [tex]$Q_1$[/tex] is the median of the lower half of the data set. The lower half of the data set is [1,1,2,2,2,2,2,3,3,3], which has 10 values. The median of this set is the average of the [tex]$5^{th}$[/tex]and [tex]$6^{th}$[/tex] values, which is 2.
The third quartile[tex]$Q_3$[/tex]is the median of the upper half of the data set. The upper half of the data set is [4,5,6,6,7,7,7,7,9,9], which also has 10 values. The median of this set is the average of the[tex]$5^{th}$[/tex] and[tex]$6^{th}$[/tex]values, which is 7.
The interquartile range (IQR) is the difference between the third and first quartiles: IQR =[tex]Q_3[/tex] - [tex]Q_1[/tex]= 7 - 2 = 5.
To find the deciles, we need to divide the data into $10$ equal parts. Since we have 21 data points, we need to find the values that divide the data into groups of $2$. The [tex]$k^{th}$[/tex] decile[tex]$D_k$[/tex] is the[tex]$k \cdot n/10$-th[/tex] value, where $n$ is the number of data points. The deciles are:
$D_1 = 1, D_2 = 2, D_3 = 2, D_4 = 2, D_5 = 3,$
$D_6 = 6, D_7 = 7, D_8 = 7, D_9 = 9$
B) Again, we need to arrange the data in order:
$10,11,12,12,14,14,14,15,15,15,15,16,16,16,17,17,14,14$
The median is the average of the[tex]$9^{th}$[/tex] and[tex]$10^{th}$[/tex] values, which is $15$.
The first quartile $Q_1$ is the average of the[tex]$4^{th}$[/tex] and [tex]$5^{th}$[/tex]values, which is $14$.
The third quartile $Q_3$ is the average of the [tex]$14^{th}$[/tex] and [tex]$15^{th}$[/tex]values, which is $16$.
The interquartile range (IQR) is [[tex]Q_3[/tex] - [tex]Q_1[/tex]= 16 - 14 = 2].
To find the deciles, we need to divide the data into [10] equal parts. Since we have 18 data points, we need to find the values that divide the data into groups of 2. The deciles are:
[[tex]D_1[/tex]= 10, D_2 = 12, D_3 = 14, D_4 = 14, D_5 = 14,]
[[tex]D_6[/tex]= 15, D_7 = 15, D_8 = 16, D_9 = 17]
From the above calculation, it can be seen that the quartiles and deciles of each set of data differ.
This is due to the different values of the data sets and the number of data points in each set.
The quartiles and deciles show different ranges and values which indicate the spread of the data and also help to identify any skewness in the data.
Summarizing, the quartiles and deciles provide an important measure of the spread of the data, helping to identify any outliers or skewness.
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What is the increasing and decreasing?!?!?!?!?!?!?!??!?!?!?!?!?!
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Answer:
Function decreasing: where x is (-4; 0) and (2; 4)
Function increasing: where x is (0; 2)
Step-by-step explanation:
Decreasing is the part in graph where function goes down. Increasing is the part where function goes up.
the residual plots from two different sets of bivariate data are graphed below. explain, using evidence from graph a and graph b which graph indicates
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According to the evidence from graph a and graph b, graph a indicates that the model for the data was a good fit because it is a random.
Hence, the correct option is B.
Based on graph a, the residual plot shows a random scattering of points around the horizontal line at y=0. This indicates that the residuals (the differences between the observed and predicted values) are distributed randomly and do not show any clear pattern. This suggests that the data points are evenly distributed around the regression line, indicating a good fit for a linear regression model.
On the other hand, graph b shows a residual plot with a clear pattern or trend. The residuals are not randomly scattered, but instead show a curved pattern or a fan-like shape. This indicates that the model used to fit the data may not be appropriate, as it is not capturing the underlying relationship between the variables accurately.
Hence, the correct option is B.
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-- The given question is incomplete, the complete question is
"The residual plots from two different sets of bivariate data are graphed below. Explain, using evidence from graph a and graph b which graph indicates that the model for the data was a good fit and what is the reason?
A. Graph A because it is symmetrical
B. Graph A because it is random
C. Graph B because there is a pattern
D. Graph B because it is symmetrical" --
a tank is shaped like an upside-down square pyramid, with a base with sides that are 4 meters in length and a height of 12 meters. if water is being pumped into the pyramid at a rate of 23m3sec, at what rate is the height of the water increasing when the water is 2 meters deep? (the volume of a pyramid with height h and base area b is given by v
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If a tank is shaped like an upside down square-pyramid, then the rate at which the height of water is increasing when the water is 2 m deep is 51.75 m/sec.
The tank is upside down square-pyramid, with sides as 4 meter,
Let the height of water at any time "t" be = "h",
The height of the tank is = 12 meter,
Let, the side of the base of pyramid shaped water at any time "t" be = "b",
So, b = (1/3)h ...because height of pyramid is 12 and each side is of 4, the ratio is 1/3,
The volume of water at nay time "t" is (V) = (1/3)b²h,
⇒ V = (1/3)(1/3h)²h,
⇒ V = h³/27,
Now, dv/dt = (d/dt)(h³/27),
On simplifying further,
we get,
⇒ dv/dt = (h²/9)(dh/dt),
⇒ dh/dt = (9/h²)(dv/dt),
We know that, when the water is 2 meter deep, and if water is pumped out at rate of 23 m³/sec, it means that h = 2, and dv/dt = 23,
So, dh/dt = (9/2²)(23) = 51.75 m/sec.
Therefore, the rate of change of height is 51.75 m/sec.
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as shown in the figure above, a thin conveyor belt 15 feet long is drawn tightly around two circular wheels each 1 foot in diameter. what is the distance, in feet, between the centers of the two wheels?
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The distance between the centers of the two wheels is approximately 11.86 feet.
The length of the conveyor belt is equal to the circumference of the circle formed by each wheel plus the distance between the centers of the two wheels.
Let's call the distance between the centers of the two wheels "d". The circumference of each wheel can be calculated using the formula
C = πd
Since each wheel has a diameter of 1 foot, its radius is 0.5 feet. Therefore, the circumference of each wheel is:
C = πd = π(0.5) = 1.57 feet (approx.)
The length of the conveyor belt is given as 15 feet. So we can write
2C + d = 15
Substituting the value of C, we get
2(1.57) + d = 15
3.14 + d = 15
d = 11.86 feet
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if lines ax-2y=5 and 2x-by =8 intersect at point (11,3), find the value of a and b
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Answer:
To find the values of a and b, we need to substitute the coordinates of the given point (11,3) into both equations and solve for a and b.
Substituting (11,3) into the first equation ax-2y=5:
a(11)-2(3)=5
11a-6=5
11a=11
a=1
Substituting (11,3) into the second equation 2x-by =8:
2(11)-b(3)=8
22-3b=8
-3b=-14
b=14/3
Therefore, a=1 and b=14/3.
Answer:
a = 1
b = 4.67 OR 14/3
Step-by-step explanation:
ax - 2y = 5
a(11) - 2(3) = 5
11a - 6 = 5
11a = 11
a = 1
2x - by = 8
2(11) - b(3) = 8
22 - 3b = 8
3b = 14
b = 4.67 OR 14/3