To divide the given polynomial by a binomial, use polynomial long division, resulting in a quotient of -2x² - 10x - 30 and a remainder of 92.
Dividing a Polynomial by a Binomial
To divide the polynomial -2x³ – 4x² + 3x + 2 by the binomial x - 3, we will use polynomial long division, which is a process similar to long division with numbers. It involves subtracting multiples of the divisor from the dividend to get a quotient and possibly a remainder.
First, divide the first term of the dividend, -2x³, by the first term of the divisor, x, to get -2x².
Multiply the divisor x - 3 by the first term of the quotient, -2x², to get -2x³ + 6x².
Subtract this result from the dividend to obtain the new dividend -4x2 (adjusting the original terms), which becomes -10x².
Repeat this process with the remaining terms of the new dividend.
Continue until all terms of the dividend have been divided.
This process results in the quotient -2x² - 10x - 30 and a remainder of 92. The complete division statement is -2x³ – 4x² + 3x + 2 = (x - 3)(-2x² - 10x - 30) + 92.
Find three consecutive even integers such that the sum of the first, twice the second, three times the third is -76. What is the number?
(the three numbers is the same number)
Answer:
The numbers are -14,-13 and -12
Step-by-step explanation:
The correct question is
Find three consecutive integers such that the sum of the first, twice the second and three times the third is -76. What is the number?
Let
x ----> the first consecutive integer
x+1 ---> the second consecutive integer
x+2 ---> the third consecutive integer
we have that
[tex]x+2(x+1)+3(x+2)=-76[/tex]
solve for x
apply distributive property
[tex]x+2x+2+3x+6=-76[/tex]
Combine like terms
[tex]6x+8=-76[/tex]
subtract 8 both sides
[tex]6x=-76-8[/tex]
[tex]6x=-84[/tex]
Divide by 6 both sides
[tex]x=-14[/tex]
so
[tex]x+1=-14+1=-13[/tex]
[tex]x+2=-14+2=-12[/tex]
therefore
The numbers are -14,-13 and -12
If g = 3, evaluate (solve) the following expression. 2g + 7= _____
Answer:
13.
Step-by-step explanation:
2g + 7
= 2(3) + 7
= 6 + 7
= 13.
Answer: 13
Step-by-step explanation: In this problem, we have the xpression 2g + 7 and we want to evaluate the expression when g is equal to 3.
To evaluate an expression, we simply plug the value of the variable into the expression and solve. So here, since g is equal to 3, we have 2 (3) + 7. 2 × 3 is equal to 6 so we have 6 + 7 which is equal to 13.
So the value of our expression when g is equal to 3 is 13.
Remember, when we see a variable like g next to a number, it means multiplication so you want to multiply by the value of the variable.
which property is shown by the rails of a railway track?
The correct answer is :
B) parallelism
The rails of a railway track demonstrate parallelism because they run alongside each other without intersecting, maintaining a constant distance apart. This allows trains to travel smoothly along the track without veering off course.
The complete question is here:
Which property is shown by the rails of a railway track?
A) perpendicularity
B) parallelism
C) intersecting lines
D) opposites
How can you use the point-slope form of a line when only given two points?
Answer:
If we already have two points of the line, we can find its slope ([tex]m[/tex]), its intersection with the y-axis ([tex]b[/tex]), hence its point-slope form equation in the following way:
Let's call Point 1: [tex](x_{1},y_{1})[/tex] and Point 2: [tex](x_{2},y_{2})[/tex]
The Slope equation is:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Now, the equation of the line in its point-slope form is:
[tex]y=mx+b[/tex]
And we can find the intersection with the y-axis ([tex]b[/tex]) by evaluating the equation with any of the two given points and then isolating [tex]b[/tex].
a 2015 Gallup poll of 1,627 adults found that only 22% felt fully engaged with their mortgage provider ?
1. Population: All adults with a mortgage provider.
2. Sample size: 1,627.
3. Margin error: Approximately 0.02.
4. Confidence interval (95%): 0.204 to 0.236
5. Proportion of adults fully engaged with their mortgage provider falls from 0.204 to 0.236.
Given that,
Gallup poll conducted in 2015
Sample size: 1,627 adults
Population: All adults with a mortgage provider
Percentage of adults who felt fully engaged with their mortgage provider: 22%
Confidence level: 95%
1. Population: All adults who have a mortgage provider.
2. Sample size: 1,627 adults.
3. Margin of error:
To calculate the margin error,
The sample size (n) and the confidence level.
Given that, the confidence level = 95%,
The margin error can be calculated using the formula:
The Margin of Error [tex]= Z \sqrt{(p (1-p) / n)}[/tex]
Assume a conservative estimation for p = 0.5 (since we don't have the sample proportion), and using a Z-value of 1.96 for a 95% confidence level,
The margin error would be:
The margin of error is,
[tex]1.96\sqrt{(0.5 (1-0.5) / 1627)} \approx 0.02[/tex]
Therefore, the 95% margin error is approximately 0.02.
4. 95% Confidence Interval:
Without the sample proportion, we cannot provide a specific confidence interval.
Assume a conservative estimate of p = 0.5,
Calculate the interval using the formula:
Confidence Interval = Sample Proportion ± Margin of Error
Given that,
The sample proportion is 0.22
The margin error is 0.016,
The 95% of the confidence interval is,
0.22 ± 0.016 = 0.24 or 0.2
5. Expressing the answer in a meaningful sentence:
With a 95% confidence level,
It can be estimated that the proportion of adults who feel fully engaged with their mortgage provider falls between 0.2 to 0.24.
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The complete question is:
A 2015 Gallup poll of 1627 adults found that only 22% felt fully engaged with their mortgage provider. 1. What is the population? 2. What is the sample size? 3. What is the 95% margin of error? 4. What is the 95% confidence interval? 5. Express your answer to 4 in a meaningful sentence.
Ollie used 852 heads to make 4 bracelets he put the same number of beads on each bracelet how many beads does each bracelet have
Answer: 213
Step-by-step explanation:
852/4 = 213
Answer:
213
Step-by-step explanation:
852/4 = 213
He is splitting 852 beads into 4 bracelets (groups)
jamal's age is 3 more than 3 times Mike's age. Mike's age is 17 years less than Jamals agee. What is the sum of the ages of Mike and Jamal?
Jamal's age is 24
Mikes age is 7
so their ages together would equal 31
Answer:
The sum of the ages of Mike and Jamal is 31
Step-by-step explanation:
First we need to translate the questions into mathematical equation and then solve.
Let x be Jamal's age and y be Mike's age.
"Jamal's age is 3 more than 3 times Mike's age" can be written mathematically as;
x =3 + 3y ---------------------------------------------------------------(1)
"Mike's age is 17 years less than Jamal's age" can be written mathematically as ;
y = x - 17 -----------------------------------------------------------------(2)
Substitute equation (1) into equation (2)
y = 3 + 3y - 17
y = 3y - 14
subtract 3y from both-side of the equation
y - 3y = 3y - 3y - 14
-2y = -14
Divide both-side of the equation by -2
[tex]\frac{-2y}{-2}[/tex] = [tex]\frac{-14}{-2}[/tex]
y = 7
Mike is 7 years old
Substitute y = 7 into equation (1)
x = 3 + 3y
= 3 + 3(7)
= 3+21
=24
Jamal is 24 years old
The sum of their ages is = x + y = 24 + 7 = 31
Therefore, The sum of the ages of Mike and Jamal is 31
Use the example above and determine the fraction of total interest owed.
After the fifth month of a 12-month loan:
the numerator is: ((n +
) + (n +
) + (n +
3 =
, and
, and
the denominator is: [(n) + (n + 1) + ... + (n
Therefore, the fraction is numerator/denominator (to the nearest tenth)
Answer:
11
10
9
8
7
50
----------------
11
78
-----------------
64.1
Hope this helps :) -Zach
Step-by-step explanation:
To determine the fraction of total interest owed on a loan after the fifth month of a 12-month loan, calculate the numerator by adding the interest paid in each of the first five months, and the denominator by summing the interest amounts for all twelve months. Divide the numerator by the denominator to get the fraction (to the nearest tenth).
Explanation:To determine the fraction of total interest paid after the fifth month of a 12-month loan, we can use the Rule of 78. This rule states that the majority of the interest on a loan is paid in the early months of the term.
The formula for the Rule of 78 is:
(n + 5)(n + 4)(n + 3)(n + 2)(n + 1) / (n × (n + 1) × (n + 2) × (n + 3) × (n + 4))
where 'n' represents the number of payments remaining.
In this case, we have 7 payments remaining after the fifth month. Plugging this value into the formula, we get:
(7 + 5)(7 + 4)(7 + 3)(7 + 2)(7 + 1) / (7 × (7 + 1) × (7 + 2) × (7 + 3) × (7 + 4)) = 0.505
Therefore, after the fifth month of a 12-month loan, approximately 50.5% of the total interest has been paid.
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The ratio of boys to girls in a math class is 18 to 11. Is that proportional to the science class with a ratio of 16 girls to 14 boys?
Question 10 options:
154 ≠ 288
224 ≠ 198
176 ≠ 252
Answer:
The ratio of boys to girls in a math class is not proportional to the ratio of boys to girls in a science class
154=288
Step-by-step explanation:
Let
x ----> the number of boys
y ----> the number of girls
we know that
The ratio of boys to girls is x/y
we have
Math class
[tex]\frac{x}{y}=\frac{18}{11}[/tex]
Science class
[tex]\frac{x}{y}=\frac{14}{16}[/tex]
equate both ratios
[tex]\frac{14}{16}=\frac{18}{11}[/tex]
Multiply in cross
[tex]14(11)=18(16)[/tex]
[tex]154=288[/tex] ----> is not true
therefore
The ratio of boys to girls in a math class is not proportional to the ratio of boys to girls in a science class
Dr. Johnson treated 1134 patients in 63 days.
About how many patients did she treat each day on the average?
Answer:
Dr. Johnson treated about 18 patients a day.
Step-by-step explanation:
1134 ÷ 63 = 18
On average, Dr. Johnson treated 18 patients each day.
Why?
1134/63=18
I hope this helped! If so, please mark brainliest!
Which of the following are NOT vector directions?
A. 35 degrees north of east
B. north
C. outside 45 degrees
D. 35 degrees inside
Final answer:
The correct answer is C. outside 45 degrees. In this question, we are asked to identify which directions are NOT vector directions. Options A, B, and D all describe vector directions, but option C does not.
Explanation:
The correct answer is C. outside 45 degrees.
In this question, we are asked to identify which directions are NOT vector directions. A vector direction is a specific direction or angle that describes the orientation of a vector.
Options A, B, and D all describe vector directions:
A. 35 degrees north of east: This describes a vector direction that is 35 degrees north of the east direction.
B. north: This is a vector direction that points directly north.
D. 35 degrees inside: This describes a vector direction that is 35 degrees inside the reference angle.
Option C, outside 45 degrees, does not describe a specific vector direction. It is not clear whether the direction is outside 45 degrees to the left or right. Therefore, option C is NOT a vector direction.
Multiply and simplify (x-9)(x-3)
Answer:
x2-12x+3
Step-by-step explanation:
=x(x-3)-9(x-3)
=x2-3x-9x+3
=x2-12x+3
HOPE IT HELPS U.............
Rashid has been purchasing bonds from a company that has recently gotten poor ratings for its ability to pay Its vendors. As a resu
Increased risk, the bond's interest rate has increased. What type of risk does Rashid face as an Investor?
A
taxability risk
• B.
Inflationary risk
C.
currency risk
D.
credit risk
Answer:
The answer is letter D, credit risk.
Step-by-step explanation:
A bond is considered to be a contract between two occurring parties. It allows companies to borrow money from people (investors). These investors purchase the bond and are given a certain interest for a particular period of time. The rate varies according to the economic situation or the company's standing. This affects the supply and demand for the bond.
Remember that the price of the bond and the interest rate are indirectly proportional. This means that as the price of the bond increases, the interest rate decreases and vice-versa.
In the situation above, Rashid is facing a credit risk as an investor. He has been purchasing bonds from a company that has recently gotten a poor rating. This means that the company is not performing well. This can affect the amount of money (including the interest) that will be paid back to Rashid. There is a chance that some of the amount of money he invested will not be returned to him. It was also mentioned that the bond's interest rate has increased. This means that the bond prices will decrease and thus the number of bond investors will also decrease. The issuer of the bond in this situation can have a hard time paying the investor back.
Answer:
D
Step-by-step explanation:
what is the distance from 10 To 0
Answer:
10
Hope this helps :)
Answer:
rthw aeenser is 20
Step-by-step explanation:
A diagram of a concrete patio is shown, where each small square represents one square meter. Find the total area of the concrete patio.
Answer:
C
Step-by-step explanation:
The red bordered area is the patio. We need to find its area.
We will consider
If this was a square, full red square. Then we find the area of the square.
After that, we will subtract the white part that is not there to create the patio shape.
Hence,
Area of Patio = Area of Square - Area of White Portion
So,
Area of Square is Side * Side
If we look at the coordinates, x goes from 5 to 15, so side is 15 - 5 = 10
also, y goes from 5 to 15, so same, that is 10
Area of Square = 10 * 10 = 100
Now, the small white portion is also a square with length 5 (looking at coordinates),
So,
Area of White Portion = 5 * 5 = 25
Hence,
Area of Patio = 100 - 25 = 75 sq. meters
Correct answer is C
(10x - 17)
(6y + 29)\(8x + 1)
the product of (10x - 17) and (6y + 29)(8x + 1) is:
[tex]\[ 480xy^2 - 756xy + 2320x^2 - 3654x - 102y - 493 \][/tex]
you want to multiply the expressions (10x - 17) and (6y + 29)(8x + 1). Let's proceed with the multiplication:
First, distribute (6y + 29) into (8x + 1):
[tex]\[ (6y + 29)(8x + 1) = 6y \cdot 8x + 6y \cdot 1 + 29 \cdot 8x + 29 \cdot 1 \]\[ = 48xy + 6y + 232x + 29 \][/tex]
Now, multiply the result by (10x - 17):
[tex]\[ (10x - 17)(48xy + 6y + 232x + 29) \]\[ = 10x \cdot (48xy + 6y + 232x + 29) - 17 \cdot (48xy + 6y + 232x + 29) \]\[ = 480xy^2 + 60xy + 2320x^2 + 290x - 816xy - 102y - 3944x - 493 \]\[ = 480xy^2 - 756xy + 2320x^2 - 3654x - 102y - 493 \][/tex]
So, the product of (10x - 17) and (6y + 29)(8x + 1) is:
[tex]\[ 480xy^2 - 756xy + 2320x^2 - 3654x - 102y - 493 \][/tex]
The probable question maybe:
multiply the expressions (10x - 17) and (6y + 29)(8x + 1).
The product of (10x - 17) and (6y + 29)(8x + 1) is: = [tex]\[ 480xy^2 - 756xy + 2320x^2 - 3654x - 102y - 493 \][/tex]
You have to multiply the expressions (10x - 17) and (6y + 29)(8x + 1). Let's proceed with the multiplication:
First, distribute (6y + 29) into (8x + 1):
[tex]\[ (6y + 29)(8x + 1) = 6y \cdot 8x + 6y \cdot 1 + 29 \cdot 8x + 29 \cdot 1 \]\[[/tex]
= 48xy + 6y + 232x + 29
Now, multiply the result by (10x - 17):
[tex]\[ (10x - 17)(48xy + 6y + 232x + 29) \]\\\\ = 10x \cdot (48xy + 6y + 232x + 29) - 17 \cdot (48xy + 6y + 232x + 29) \]\\\\ = 480xy^2 + 60xy + 2320x^2 + 290x - 816xy - 102y - 3944x - 493 \]\\\\ = 480xy^2 - 756xy + 2320x^2 - 3654x - 102y - 493 \][/tex]
So, the product of (10x - 17) and (6y + 29)(8x + 1) is:
[tex]\[ 480xy^2 - 756xy + 2320x^2 - 3654x - 102y - 493 \][/tex]
The complete question is:
Multiply the expressions (10x - 17) and (6y + 29)(8x + 1).
Write a linear equation that gives the rule for this table.
x y
1 24
2 48
3 72
Equation :
Answer:
y=24x
Step-by-step explanation:
(48-24)/(2-1)=24/1
24=24(1)+b
24=24+b
b=0
The linear equation with points (1, 24), (2, 48), and (3, 72) is y = 24x.
What are linear and non-linear functions?A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.
Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.
An example of a non-linear function is a quadratic function.
From the table,
At x = 1, y = 24 ⇒ (1, 24).
At x = 2, y = 48 ⇒ (2, 48).
At x = 3, y = 72 ⇒ (3, 72).
Therefore the linear equation representing the table is y = 24x.
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Astronaut that weighs 180 pounds at what distance from the center earth the astronaut weigh 1 pound.
Answer:
The height of the astronaut from the center of the Earth is 85865 km.
Step-by-step explanation:
It is assumed that the astronaut will be going towards space, so we have to find out that at what height from the center of the earth would the value of g will be [tex]\frac{g}{180}[/tex].
The weight of astronaut on the surface of Earth 180 pounds.
g=9.81 [tex]m/s^{2}[/tex]
Required value of g'=[tex]\frac{g}{180}[/tex]
g'=[tex]\frac{gR^{2} }{h^{2} }[/tex]
where R=Radius of the Earth
h=Height of the point from the center of the earth
[tex]\frac{g}{180} = \frac{gR^{2} }{h^{2} } \\\\h^{2} =180R^{2} \\h=\sqrt{180} R\\[/tex]
h=13.42
The value of R is approximately 6400 km.
So, h=85865 km.
The astronaut would need to be approximately 85,552 kilometers from the center of the Earth to weigh 1 pound.
Newton's law of universal gravitation is given by the formula:
[tex]F = G \frac{m_1 m_2}{r^2}[/tex]
Where:
[tex]F[/tex] is the gravitational force,[tex]G[/tex] is the gravitational constant [tex](6.674 \times 10^{-11} \text{Nm}^2/\text{kg}^2)[/tex],[tex]m_1[/tex] is the mass of the first object (the astronaut),[tex]m_2[/tex] is the mass of the second object (Earth),[tex]r[/tex] is the distance between the centers of the two objects.On Earth's surface, the weight of the astronaut is the gravitational force exerted by the Earth. This can also be expressed as:
[tex]Weight = m_1 \cdot g[/tex]
Where [tex]g[/tex] is the acceleration due to gravity (approximately [tex]9.8 \text{m/s}^2[/tex]).
Given that the astronaut weighs 180 pounds on Earth, we use the following relation to find the new distance where the astronaut's weight would be 1 pound:
[tex]180 \text{ pounds} \div r^2 = 1 \text{ pound}[/tex]
[tex]r^2 = 180[/tex]
[tex]r = \sqrt{180}[/tex]
However, we need this distance in terms of the Earth's radius [tex]( R_E )[/tex]. The Earth's radius is approximately 6,371 km.
Let's form the ratio:
[tex]\left( \frac{d}{R_E} \right)^2 = 180[/tex]
[tex]\frac{d}{R_E} = \sqrt{180} \approx 13.42[/tex]
Thus, the astronaut would need to be approximately 13.42 times the Earth's radius away from the center of the Earth to weigh 1 pound.
To convert this to an actual distance:
[tex]d = 13.42 \cdot R_E[/tex]
[tex]d \approx 13.42 \cdot 6371 \text{ km} \approx 85,552 \text{ km}[/tex]
How do you find the least common multiple or the lcm of 10 and 8
Answer:
40
Step-by-step explanation:
Least common multiple (lcm) = the smallest multiple that both numbers have.
Let's figure it out.
10 = 2 x 5
8 = 2 x 2 x 2
the ones I have highlighted, we will multiply them all together, except for a 2.
we didn't multiply one of the 2's because they both have a two, so we only keep one of them.
so it is 2 x 5 x 2 x 2
let me say it again, because they both share a same 2, that one is eliminated.
so the answer is 40 because:
2 x 5 x 2 x 2
= 10 x 4
= 40
Answer:
Step-by-step explanation:
list the multiples of 8 and 10 and mark wich one is the lowest number
Simon took out an unsubsidized student loan of $43,000 at a 2.4% APR,
compounded monthly, to pay for his last six semesters of college. If he will
begin paying off the loan in 33 months with monthly payments lasting for 20
years, what will be the amount of his monthly payment?
The amount of Simon's monthly payment, rounded to the nearest cent, is approximately $240.17.
To calculate the monthly payment for Simon's loan, we need to use the formula for an annuity, which is derived from the amortization formula for loans. The formula to find the monthly payment (M) is:
[tex]\[ M = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1} \][/tex]
where:
- [tex]\( P \)[/tex] is the principal amount of the loan ($43,000)
- [tex]\( r \)[/tex] is the monthly interest rate (APR divided by 12)
- [tex]\( n \)[/tex] is the total number of payments (20 years times 12 months per year)
First, we need to convert the annual percentage rate (APR) to a monthly interest rate by dividing by 12:
[tex]\[ r = \frac{2.4\%}{12} = \frac{0.024}{12} = 0.002 \][/tex]
Next, we calculate the total number of payments:
[tex]\[ n = 20 \text{ years} \times 12 \text{ months/year} = 240 \text{ months} \][/tex]
Now we can plug these values into the formula:
[tex]\[ M = \frac{43000 \times 0.002 \times (1 + 0.002)^{240}}{(1 + 0.002)^{240} - 1} \][/tex]
[tex]\[ M = \frac{43000 \times 0.002 \times (1.002)^{240}}{(1.002)^{240} - 1} \][/tex]
Using a calculator, we find:
[tex]\[ (1.002)^{240} \approx 1.558 \][/tex]
Now we can calculate the monthly payment:
[tex]\[ M = \frac{43000 \times 0.002 \times 1.558}{1.558 - 1} \][/tex]
[tex]\[ M = \frac{43000 \times 0.002 \times 1.558}{0.558} \][/tex]
[tex]\[ M = \frac{134.034}{0.558} \][/tex]
[tex]\[ M \approx 240.17 \][/tex]
Therefore, the amount of Simon's monthly payment, rounded to the nearest cent, is approximately $240.17.
Answer:
241.16
Step-by-step explanation:
The perimeter of a rectangle is 74 cm. The length of a rectangle is 5cm less than twice the width. Find the dimensions of the rectangle.
The width of the rectangle is 14 cm and the length is 23 cm.
Explanation:Let's assume the width of the rectangle is x cm. According to the question, the length is 5 cm less than twice the width, so the length would be 2x - 5 cm. The perimeter of a rectangle is calculated by adding up the lengths of all its sides. In this case, the perimeter is given as 74 cm, so the equation becomes:
2(x + 2x - 5) = 74
Simplifying the equation, we get:
6x - 10 = 74
Adding 10 to both sides:
6x = 84
Dividing both sides by 6:
x = 14
So the width of the rectangle is 14 cm, and the length is 2(14) - 5 = 23 cm.
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Carey has already knit 2 centimeters of scarf, and can knit 1 centimeter each night. After
45 nights of knitting, how many centimeters of scarf will Carey have knit in total?
ensed
91
centimeters
Time
Answer:
47cm
Step-by-step explanation:
if she already has 2cm and can knit 1 more very night after 45 nights that leaves you with 45cm in scarf then you add the 2cm you already had.
If x+y=11 and xy=15, find the value of x^2 + y^2
There is actually some tactics to this. I tried to find x and y first but they are very messy numbers but...
We know...
(x+y)²=x²+2xy+y²
In this case, (x+y)² = 11² = 121.
So, x²+2xy+y²=121
We also know that xy=15 and furthermore that 2xy=30.
x²+y² = 121-30 = 91
answer: 91
The value of x^2 + y^2 is 91.
To find the value of x^2 + y^2 given that x+y=11 and xy=15, we can use algebraic identities. We will use the fact that (x+y)^2 = x^2 + 2xy + y^2. We know that x+y=11, so (x+y)^2 = 11^2 = 121. Also given is xy=15, which we'll use in the identity mentioned.
Now, let's substitute the values into the identity:
(x+y)^2 = x^2 + 2xy + y^2
121 = x^2 + 2(15) + y^2
121 = x^2 + 30 + y^2
121 - 30 = x^2 + y^2
91 = x^2 + y^2
The table shows the average cost, in dollars, of a movie ticket in the United States for different years. Calculate the correlation coefficient. Round to the nearest hundredth.
Year Cost
1948 0.36
1963 0.86
1974 1.89
1978 2.34
1985 3.55
1991 4.21
1997 4.59
2005 6.41
2010 7.89
0.12
0.96
0.93
1
Answer:
The correlation coefficient is 0.96
Step-by-step explanation:
The Given Table showing year and cost:
Year Cost
1948 0.36
1963 0.86
1974 1.89
1978 2.34
1985 3.55
1991 4.21
1997 4.59
2005 6.41
2010 7.89
Regression table:
Regression table can be made if we rewrite the year column by associating
1948 with 0, and the years after 1948 to be associated with the number of years after 1948. For example, if 1948 is associated with 0, then 1963 would come after 15 years, hence 1963 would be represented by 15, and with the same way, we can associate other years as well. Have a look:
Year (X) Cost (Y) X² XY
0 0.36 0 0
15 0.86 225 12.9
26 1.89 676 49.14
30 2.34 900 70.2
37 3.55 1369 131.35
43 4.21 1849 181.03
49 4.59 2401 224.91
57 6.41 3249 365.37
62 7.89 3844 489.18
∑X= 319 ∑Y= 32.1 ∑X²= 14513 ∑XY= 1524.08
As the correlation coefficient (r) can be determined as follows:
r = n (∑ XY) - (∑X) (∑Y) ÷ √[n(∑X²)-(∑Y)²][n(∑Y²)-(∑Y)²]
But, we need an additional column Y²
So,
Y²
0.1296
0.7396
3.5721
5.4756
12.6025
17.7241
21.0681
41.0881
62.2521
∑Y² = 164.6518
As,
r = n (∑ XY) - (∑X) (∑Y) ÷ √[n(∑X²)-(∑Y)²][n(∑Y²)-(∑Y)²]
So,
r = 9 (524.08) - (319)(32.1) ÷ √[9(14513 )-(319)²][9(164.6518)-(32.1)²]
[tex]r = \frac{3476.82}{\sqrt{(28856)(451.4562)}}[/tex]
[tex]r = \frac{3476.82}{\sqrt{(13027220.11)}}[/tex]
[tex]r = \frac{3476.82}{\sqrt{(3609.32)}} = 0.96[/tex]
So, the correlation coefficient is 0.96.
Keywords: correlation coefficient
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If value of x is 5, help me solve the area of this geometry figure :)
Answer:
102
Step-by-step explanation:
X=5 so from A to E is 5. 5 squared is 25 plus 4 = 29 then add 29 to 5 you get 34. Then multiply 34 times 6 you get 204 then divide by 2 because area of triangle is base times height divided by 2 you get 102.
what is the distance between the y-intercept and the x-intercept of the line whose equation is y=3x+12
The distance between the y-intercept and the x-intercept of the line is 12.64911 units or [tex]\sqrt{160}[/tex] units
Solution:
Given equation is y = 3x + 12
We have to find the distance between y-intercept and the x-intercept of the line whose equation is y = 3x + 12
Let us first find the x - intercept and y - intercept
The x-intercept is the point at which the line crosses the x-axis. At this point, the y-coordinate is zero.
The y-intercept is the point at which the line crosses the y-axis. At this point, the x-coordinate is zero
Finding x - intercept:
To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'.
Substitute y = 0 in given equation
y = 3x + 12
0 = 3x + 12
3x = -12
x = -4
Thus the x - intercept is (-4, 0)
Finding y - intercept:
To find the y-intercept, plug 0 in for 'x' and solve for 'y'
Substitute x = 0 in given equation
y = 3x + 12
y = 3(0) + 12
y = 12
Thus the y - intercept is (0, 12)
Now let us find the distance between x intercept and y intercept
Distance between two points [tex]P(x_1, y_1) \text{ and } Q(x_2, y_2)[/tex] is given by:
[tex]d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}[/tex]
Here the distance between (-4, 0) and (0, 12) is given as:
[tex]\begin{aligned}&d=\sqrt{(0-(-4))^{2}+(12-0)^{2}}\\\\&d=\sqrt{4^{2}+12^{2}}\\\\&d=\sqrt{16+144}=\sqrt{160}\\\\&d=12.64911\end{aligned}[/tex]
Thus the distance between the y-intercept and the x-intercept of the line is 12.64911 units or [tex]\sqrt{160}[/tex] units
The y-intercept of the line y=3x+12 is (0,12) and the x-intercept is (-4,0). The distance between these two points is approximately 12.65 units.
Explanation:The equation given is y=3x+12. The x-intercept is the point where the line crosses the x-axis (where y=0), and the y-intercept is where the line crosses the y-axis (where x=0).
For the y-intercept, we simply replace x with 0, so y = 3(0) + 12 = 12. Thus, the y-intercept is (0,12).
For the x-intercept, we replace y with 0, so 0 = 3x + 12. Solving this equation for x gives x = -4. Thus, the x-intercept is (-4,0).
The distance between two points in the coordinate plane is given by the formula √[(x2-x1)² + (y2-y1)²]. Therefore, the distance between the x-intercept and the y-intercept is √[(-4-0)² + (0-12)²] = √(16 + 144) = √160 = 12.65.
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Laura sees a horse pulling a buggy. She wonders how it can accelerate if the action of the horse pulling the cart would causes an equal and opposite reaction of the cart pulling on the horse. Which explanation best answers her question
Answer:
The net forces exerted on the horse and cart are not the same, so they are not balanced forces.
Step-by-step explanation:
Please see the Newton's 2nd Law which states that an object accelerates if there is a net or unbalanced force on it. In this scenario there is just one force exerted on the wagon i.e: the force that the horse exerts on it. The wagon accelerates because the horse pulls on it. And the amount of acceleration equals the net force on the wagon divided by its mass.
As there are two forces the push and pull the horse; the wagon pulls the horse backwards, and the ground pushes the horse forward. The net force is determined by the relative sizes of these two forces.
If the ground pushes harder on the horse than the wagon pulls, there is a net force in the forward direction, and the horse accelerates forward, and if the wagon pulls harder on the horse than the ground pushes, there is a net force in the backward direction, and the horse accelerates backward.
If the force that the wagon exerts on the horse is the same size as the force that the ground exerts, the net force on the horse is zero, and the horse does not accelerate.
Answer:
The net forces exerted on the the horse and cart are not the same, so they are not balanced forces.
Step-by-step explanation:
According to Newton's 2nd Law, an object accelerates if there is a net or unbalanced force on it. For a body to accelerate, two factors are involved which are the mass of the object and the net force acting upon the body. In this situation, there is just one force exerted on the cart i.e: the force that the horse exerts on it. The cart accelerates because the horse pulls on it. The amount of acceleration can be calculated by dividing the net force on the cart by its mass.
In this scenario, we can clearly see the actions of the pull and push forces. The pull force brings an object closer while the push moves an object away from something. The cart pulls the horse backwards, and the ground pushes the horse forward. They both work in opposite directions. The net force is determined by the relative sizes of these two forces.
If the push force is greater(i.e the ground pushes harder on the horse than the cart pulls), then there is a net force in the forward direction, and the horse accelerates forward. But if the pull force is greater( the cart pulls harder on the horse than the ground pushes), then there is a net force in the backward direction, and the horse accelerates backward.
If the force that the cart exerts on the horse is the same size as the force that the ground exerts, the net force on the horse is zero, and the horse does not accelerate.
What is an equation of the line that passes through the point (4, -1) and has
slope -5?
This is what my teacher says to do and i dont know how to solve it. Can anyone help?
Answer:
y + 1 = -5(x - 4)
y + 1 = -5x + 20
y = -5x + 19
12-2/3x=x-18 so how do you answer this question
Answer:
Step-by-step explanation:
I think I've already answered this question.
The point (2, 3) is in which quadrant?