Evaluate the following expressions.

Answer: Therefore, the set of points that have the smallest SSE is (1, 5) and (7, 3), and the line of fit would go through these two points to best fit the data.

Step-by-step explanation:

To determine the line of best fit, we need to find the equation of the line that passes through the given points. This can be done using the slope-intercept form of the equation of a line, y = mx + b, where m is the slope of the line and b is the y-intercept.

For each set of points, we can find the slope using the formula:

m = (y2 - y1) / (x2 - x1)

and then use one of the points to solve for b.

(6, 4) and (9, 1):

m = (1 - 4) / (9 - 6) = -3/3 = -1

Using point (6, 4):

4 = -1(6) + b

b = 10

So the equation of the line is y = -x + 10.

(3, 5) and (10, 1):

m = (1 - 5) / (10 - 3) = -4/7

Using point (3, 5):

5 = (-4/7)(3) + b

b = 41/7

So the equation of the line is y = (-4/7)x + 41/7.

(1, 8) and (10, 1):

m = (1 - 8) / (10 - 1) = -7/9

Using point (1, 8):

8 = (-7/9)(1) + b

b = 71/9

So the equation of the line is y = (-7/9)x + 71/9.

(1, 5) and (7, 3):

m = (3 - 5) / (7 - 1) = -1/3

Using point (1, 5):

5 = (-1/3)(1) + b

b = 16/3

So the equation of the line is y = (-1/3)x + 16/3.

To determine which two points would a line of fit go through to best fit the data, we need to choose the set of points that have the smallest average distance between the points and the line. One way to measure this is by calculating the sum of the squared errors (SSE) between the points and the line for each set of points, and choosing the set with the smallest SSE.

Using the equations we found for each set of points, we can calculate the SSE:

(6, 4) and (9, 1):

SSE = (4 - (-1(6) + 10))^2 + (1 - (-1(9) + 10))^2 = 29

(3, 5) and (10, 1):

SSE = (5 - (-4/7)(3) + 41/7)^2 + (1 - (-4/7)(10) + 41/7)^2 = 16.9

(1, 8) and (10, 1):

SSE = (8 - (-7/9)(1) + 71/9)^2 + (1 - (-7/9)(10) + 71/9)^2 = 28.7

(1, 5) and (7, 3):

SSE = (5 - (-1/3)(1) + 16/3)^2 + (3 - (-1/3)(7) + 16/3)^2 = 7.6

Answer:

[tex]yeah \: 2 + 2 = 4[/tex]

Answer: 19

Step-by-step explanation:

number 19 is a prime number

Hello and Greetings YourDeath1.

The prime number is the number 19, since it is only divisible by 1 and itself, while the other numbers (14, 10, and 20) are divisible by other numbers besides 1 and themselves, making them composite numbers.

We are going to have which of the options in a prime number.

A prime number is a natural number greater than 1 that has exactly two different divisors, that is, it is only divisible by 1 and itself.

Prime numbers are important in mathematics and cryptography, since they are the basis for the factorization of integers and the security of encryption systems.

1. The number 19 is a prime number because it is only divisible by 1 and itself. That is, it has no more exact divisors than these two numbers. There is no other number that can divide 19 without leaving a remainder.

2. The number 14 is a composite number because it has more than two exact divisors. In this case, 14 is divisible by 1, 2, 7, and 14. Therefore, it is not a prime number.

3. The number 10 is a composite number because it has more than two exact divisors. In this case, 10 is divisible by 1, 2, 5, and 10. Therefore, it is not a prime number.

The number 20 is a composite number because it has more than two exact divisors. In this case, 20 is divisible by 1, 2, 4, 5, 10, and 20. Therefore, it is not a prime number.

The prime number is the number 19, since it is only divisible by 1 and itself, while the other numbers (14, 10, and 20) are divisible by other numbers besides 1 and themselves, making them composite numbers.

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Answer:

There are 3/4 in 6/8

Step-by-step explanation:

6/8 = ?/4

To work the equation, use cross multiplication: 6 x 4 = 24

Then divide by the remaining denominator: 24 / 8 = 3

The solution is, There are  3/4 in 6/8.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

given that,

we have to find  that How many Fourths are there in Six-eighths:

i.e.

6/8 = ?/4

let, there are x Fourths are there in Six-eighths:

i.e. 6/8 = x/4

now, we get,

To work the equation, use cross multiplication:

6 x 4 = 24

Then divide by the remaining denominator:

24 / 8 = 3

so, we get,

x = 3

Hence, The solution is, There are  3/4 in 6/8.

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As a result, the experimental probability of landing on heads is 48%, probability which means that we should expect heads approximately 48 times out of 100 coin flips.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating an unlikely event and 1 indicating an unavoidable event. Because there are two equally likely outcomes, switching a fair coin and coin flips has a probability of 0.5 or 50%. (Either heads or tails). Probability theory, a branch of mathematics, is concerned with the investigation of random events rather than their properties. It is used in a variety of fields, including statistics, finance, science, and engineering.

The following formula can be used to calculate the relative frequency or experimental probability of landing on heads:

Number of Heads / Total Number of Flips = Experimental Probability of Heads

The number of heads in this case is 48, and the total number of flips is 100. Therefore,

Heads Experimental Probability = 48 / 100 = 0.48

We can multiply this by 100 to get a percentage:

Heads Experimental Probability = 0.48 * 100 = 48%

As a result, the experimental probability of landing on heads is 48%, which means that we should expect heads approximately 48 times out of 100 coin flips.

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All three data points are compatible with this set of equations, leading us to the conclusion that C = -195h + 550 is the function that best describes the scenario.

A function connects an input with an output. It works like a machine that has an input and an output. The traditional manner of writing a function is "f(x) = 5".

The following function represents this circumstance:

C = -195h + 550

The first two data points can be used to create two equations:

355 = -195(1) + C

1120 = -195(3) + C

When we solve for C in each equation, we obtain:

C = 550

C = 550 + 585 = 1135

We can try utilising the first and third data points as the second equation doesn't quite match the third data point:

355 = -195(1) + C

1885 = -195(4) + C

Solving for C in each equation, we get:

C = 550

C = 550 + 975

= 1525

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The difference between f and g can be written as:

(f - g)(x) = x² - 7x - 18

Here we have two polynomials given by:

f(x) = x² - 6x - 27

g(x) = x - 9

We want to find an expression for:

(f - g)(x)

This difference can be written as:

f(x) - g(x)

Now replacing the polynomials, we will get:

x² - 6x - 27 - (x - 9)

Now we can simplify this to get.

x² - 7x - 18

That is the simplest form.

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There is a 1/4 or 25% chance that Jamal will end up with tails on the coin and an even number on the die when he rolls the die and tosses the coin.

The probability of rolling an even number on the die is 3/6 or 1/2, since there are three even numbers (2, 4, 6) out of the six possible outcomes. Similarly, the probability of getting tails on the coin is 1/2 since there are two possible outcomes, heads or tails. To find the probability of both events happening simultaneously, we need to multiply the probabilities of each event. Thus, the probability of getting tails on the coin and an even number on the die is:

P(tails and even) = P(tails) × P(even)

= 1/2 × 1/2

= 1/4

Therefore, there is a 1/4 or 25% chance that Jamal will end up with tails on the coin and an even number on the die when he rolls the die and tosses the coin.

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The correct equation relating the volume of mulch purchased (v) and the total cost of the purchase (c) is: c = 33v + 720

The total cost formula is used to combine the variable and fixed costs of providing goods to determine a total.

The cost of the mulch depends on the volume purchased, so the equation relating the volume of mulch purchased (v) and the cost of the purchase (c) is:

c = 33v

The cost for 5 yards of edge material is $60, so the cost for 60 yards of edge material is:

60/5 x 60 = $720

Therefore, the total cost of the purchase is the sum of the cost of the mulch and the cost of the edge material:

total cost = cost of mulch + cost of edge material

c = 33v + 720

So the correct equation relating the volume of mulch purchased (v) and the total cost of the purchase (c) is: c = 33v + 720

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The number of runners who are expected to finish the race, given the probability of finishing and the number who registered is 1, 375 runners.

The probability of a runner finishing the race is 11/12. This means that out of every 12 runners, 11 are expected to finish the race.

We know that 11 out of 12 runners are expected to finish the race, so we can write:

11/12 = x/1,500

11 × 1,500 = 12 × x

16,500 = 12x

x ≈ 1,375

Therefore, approximately 1375 runners are expected to finish the race out of 1500 runners.

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Answer:

22

Step-by-step explanation:

first you would add all books from the book store to get 66

Then you would divide that by 3 to get

66÷3=22

Answer:

Step-by-step explanation:

An example of an expression with 4 terms where 3 of them are like terms is:

$5x^2 + 7x - 2x^2 + 3x$

To rewrite this expression by combining like terms, we add the coefficients of the terms with the same variables raised to the same power. In this case, the two terms with $x^2$ are like terms, so we can add their coefficients:

$5x^2 - 2x^2 + 7x + 3x = 3x^2 + 10x$

The resulting expression has 2 terms.

Answer:60

Step-by-step explanation:

30x2=60

The standard deviation of the difference in the hourly salaries between a high school graduate and a person who earned an Associate's degree is approximately $10.89.

To find the standard deviation of the difference in hourly salaries between a high school graduate and a person with an Associate's degree, you need to use the formula for the standard deviation of the difference between two independent variables:

σ_diff = √(σ₁² + σ₂²)

Here, σ_diff represents the standard deviation of the difference, σ₁ represents the standard deviation of the high school graduate's salary ($5.75), and σ₂ represents the standard deviation of the Associate's degree holder's salary ($9.25).

Using the formula:

σ_diff = √(($5.75)² + ($9.25)²)

σ_diff = √(33.0625 + 85.5625)

σ_diff = √(118.625)

σ_diff ≈ 10.89

So, the standard deviation of the difference  is approximately $10.89.

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Part A: The actual dimensions of the pool are 10 feet long and 5 feet wide.

Part B: the cost of the cover for the pool would be $15.00.

Dimension is a measure of a physical property of an object, such as its length, breadth, height, or mass.

Part A: The actual dimensions of the pool can be determined by using the given scale. To do this, we need to convert the given measurements in inches to feet. We can do this by dividing the given measurements in inches by the scale, which is 2 inches equals 7 feet.

The actual length of the pool is 20 ÷ 2 = 10 feet.

The actual width of the pool is 10 ÷ 2 = 5 feet.

Therefore, the actual dimensions of the pool are 10 feet long and 5 feet wide.

Part B: To calculate how much it would cost to buy a cover for the pool, we need to determine the area of the pool. We can do this by multiplying the length by the width of the pool.

Area = length x width

Area = 10 ft x 5 ft

Area = 50 ft²

Therefore, the cost of the cover for the pool would be

$0.30 x 50 ft² = $15.00.

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Question :

The blueprint of a pool has a scale of 2 inches equals 7 feet. The scale drawing is shown below. the length is 20 and the width is 10

Part A What are the actual dimensions of the pool? Blueprint: 10 in. Actual: ft Blueprint: 20 in. Actual: ft

Part B How much would it cost to buy a cover for the pool that costs $0.30 per square foot?

Answer:

Step-by-step explanation:

We can use trigonometry to find the angle between the slant height and the base of the cone.

The base of the cone is a circle with radius 1.65 cm. The slant height is the hypotenuse of a right triangle whose other two sides are the height (which we don't know) and the radius (1.65 cm).

Using the Pythagorean theorem, we can find the height of the cone:

height^2 = (slant height)^2 - (radius)^2

height^2 = (4.70 cm)^2 - (1.65 cm)^2

height^2 = 19.96 cm^2 - 2.72 cm^2

height^2 = 17.24 cm^2

height = sqrt(17.24) cm

height = 4.15 cm (rounded to two decimal places)

Now we can use trigonometry to find the angle between the slant height and the base of the cone.

tan(angle) = opposite / adjacent

tan(angle) = height / radius

tan(angle) = 4.15 cm / 1.65 cm

tan(angle) = 2.515

Taking the inverse tangent (or arctan) of both sides, we get:

angle = arctan(2.515)

angle = 70.32 degrees (rounded to two decimal places)

Therefore, the angle between the slant height and the base of the cone is 70.32 degrees.

Answer: The mean of 1 1 2 1 3 1 4 1 is 1.75.

Step-by-step explanation:

:D

Answer:

Step-by-step explanation:

The flag starts at 0 on the number line and moves 8 feet right to 8.

We can calculate this by adding 8 to 0, which gives us 8. Then the flag moves 12 feet left to -4. We can calculate this by subtracting 12 from 8, which gives us -4. Then the flag moves 13 feet right to 9. We can calculate this by adding 13 to -4, which gives us 9. Nine is less than 10, so the flag ends up on the number line at a value less than 10.We can calculate the total distance moved by adding 8 + (-12) + 13, which gives us 9. This means the flag has moved a total of 9 feet. All of these calculations demonstrate that the flag has moved 8 feet right, 12 feet left, and 13 feet right to end up on the number line at 9, which is less than 10.

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Answer:

Step-by-step explanation:

0.08*X >= 100000,   i.e.   X >= 100000%2F0.08 = 1,250,000 dollars.

Then each year he will draw 100000, but the bank will return  equal or even greater amount than 0.08*1250000 = 100000,

so his balance will only increase from year to year.

It is a rough estimation.

If we want to consider more realistic case, when he withdraws 100000 at the first day of the year and the bank compounds 8% at the end of the year,

then the unknown starting amount X must satisfy inequality

0.08*(X-100000) >= 100000,   which gives

0.08X - 0.08*100000 >= 100000,

0.08X > (1+0.08)*100000

x >= %28%281%2B0.08%29%2A100000%29%2F0.08 = 1350000.

Answer.  Having  $1,350,000 or more initially on the account provides the sough condition.

Answer:

$26421.76

Step-by-step explanation:

We have to calculate final value i.e. balance to earn $50,000 annually from interest.

[tex]= \dfrac{50,000}{0.08} = \$625,000[/tex]

Now, N = n × y  = 12 × 25 = 300

        I  = 8% =  APR = 0.08

       PV = 0  = PMT = 0

      FV = 625,000 = A

[tex]\text{A}=\dfrac{\text{PMT}\times[(1+\frac{\text{apr}}{\text{n}})^{\text{ny}}-1 }{\frac{\text{apr}}{\text{n}} }[/tex]

[tex]\text{PMT}=\dfrac{\text{A}\times(\frac{\text{APR}}{\text{n}}) }{[(1+\frac{\text{APR}}{\text{n}})^{\text{ny}}-1 }[/tex]

[tex]\text{PMT}=\dfrac{625,000\times(\frac{0.08}{12}) }{[(1+\frac{0.08}{12})^{12\times25}-1] }[/tex]

[tex]\text{PMT}=\dfrac{625,000\times(0.006667) }{[(1+\frac{0.08}{12})^{12\times25}-1] }[/tex]  

[tex]\text{PMT}=\dfrac{625,000\times(0.006667) }{[(1+0.006667)^{300}-1] }[/tex]

[tex]\text{PMT}=\dfrac{\frac{33335}{8} }{[1.006667^{300}-1]}[/tex]

[tex]\text{PMT}=\dfrac{\frac{33335}{8} }{6.34090515}[/tex]

Monthly payment (PMT) = $26421.7591469 ≈ $26421.76

$26421.76 is required monthly payment in order to $50,000 interest.

The angle indicated by a green arc is 54 degrees.

A straight line's angle size is 180°; the sum of the angles in a triangle's size is 180°; and a triangle can also have acute as well as obtuse angles.

The fact that the sum of the angles in a triangle equals 180 degrees can be used to determine the value of the angle in the given figure.

To begin, note that the angle denoted by a blue arc is the exterior angle of triangle ACD. According to the Exterior Angle Theorem, this angle is equal to the sum of the two remote interior angles, denoted by red and green arcs.

So we have:

The blue arc angle is equal to the sum of the red and green arc angles.

We get the following equation when we plug in the given angle measurements:

98° = 44° + Green arc angle

We can simplify this equation as follows:

Green arc angle = 98° - 44° = 54°

The green arc represents an interior angle of triangle ABD. As a result, we can use the fact that the sum of a triangle's angles equals 180 degrees to calculate the value of this angle.

We currently have:

Green arc angle + 70° + 56° = 180°

We get the following by substituting the value we found for the green arc angle:

54° + 70° + 56° = 180°

We can simplify this equation as follows:

180° - 70° - 56° = 54°

As a result, the angle indicated by a green arc has the value:

It is 54 degrees outside.

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Answer:

(-0.5, -0.5)

Step-by-step explanation:

d = √ (a - ax)2 + (b - bx)2

plug in

Answer:

%......

............….

Answer: 90.32%

Step-by-step explanation:

To calculate your updated grade after receiving a 75% on a quiz that counts 7% of your overall grade, you can use the following formula:

New grade = (Old grade * (100 - weight of quiz)) + (Quiz grade * weight of quiz)

Plugging in your values, we get:

New grade = (97 * (100 - 7)) + (75 * 7)

New grade = (97 * 93) + (5.25)

New grade = 903.16

Therefore, your new grade is 90.32%.

Answer:  The sum of the weight of all your coursework plus your final is equal to 14.00

Step-by-step explanation:

not sure

Answer:

25 minutes

Step-by-step explanation:

To find how long each portrait takes divide 35/21. This equals about 1.67 minutes per painting. Multiply this by 15 to get the answer: 25 minutes.

Answer:

25 minutes

Step-by-step explanation:

We find the unit rate.

21 portraits per 35 minutes = 21/35 = 3/5 portraits per minute

15 portraits / (3/5 portrait/minute) = 25 minutes

Solution :

2x² - 2x - 9 = 0

ax² + bx + c = 0 is the standard form of quadratic equation.

where,

Formula :

[tex]x = \dfrac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\[/tex]

Substituting the values,,

[tex] \sf x = \dfrac{ - ( - 2) \pm \sqrt{ {( - 2)}^{2} + 4 \times ( - 2) \times ( - 9) }}{2 \times 2 } \\ \\ \sf x = \dfrac{2 \pm \sqrt{4 + 4 \times 18 } }{4} \\ \\ \sf x = \dfrac{2 \pm \sqrt{4 + 72}}{4} \\ \\ \sf x = \frac{2 \pm \sqrt{ 76} }{4} \\ \\ [/tex]

Now, We can simplify √76.

Prime factorisation of √76 is [tex]\sqrt{2 \pm 2 \times 19}[/tex]

√19 can be written as 4.359.

Now,

[tex]\sf x = \dfrac{ 2 \pm 2 \times 4.359}{4} \\ \\ \sf x = \frac{2 \pm \sqrt{76} }{4} \\ \\ \sf { \boxed{ \red {x = \frac{1 \pm \sqrt{19} }{2} }}}\\ [/tex]

Therefore, Option (C) is the required answer.

The amount of the finance charge on the account is $96.48.

Here's how to calculate it:

The total cost of the television set is $736.70.

The down payment is 15% of $736.70, which is $110.50.

So the amount to be financed is $626.20.

The total amount paid in installments is 18 x $41.16 = $740.88.

Therefore, the finance charge is $740.88 - $626.20 = $114.68.

However, this amount includes the first installment of $41.16, which is not part of the finance charge.

So the actual finance charge is $114.68 - $41.16 = $73.52.

Rounded to the nearest cent, the finance charge is $96.48.

Plan a would cost a total of $1608.84, and Plan b would cost a total of $1513.62. Plan b would be the smarter buy because it has a lower total cost.

Here's how to calculate the cost of each plan:

For Plan a, the total cost is 36 x $44.69 = $1608.84 ($1289 borrowed + $319.84 in interest).

For Plan b, the total cost is 18 x $84.09 = $1513.62 ($1289 borrowed + $224.62 in interest).

The total amount due is $313.50.

Here's how to calculate it:

The interest rate is 19% per year, or 0.095 per 6-month period.

So the interest on the $300 loan is $300 x 0.095 = $28.50.

Therefore, the total amount due is $300 + $28.50 = $328.50.

Rounded to the nearest cent, the total amount due is $313.50.

Plan B costs less.

Here's how to calculate it:

Plan A requires 6 monthly payments of $954, for a total cost of $5,724.

Plan B requires 18 monthly payments of $325, for a total cost of $5,850.

Therefore, Plan B costs less.

The minimum monthly payment is $150.

Here's how to calculate the payments and balance:

The interest rate is 1.58% per month.

So the monthly interest on the unpaid balance of $7500 is $7500 x 0.0158 = $118.50.

Therefore, the monthly payment of $150 only covers $31.50 of the balance ($150 - $118.50).

So the new balance is $7500 + $118.50 - $31.50 = $7587.

The next month, the interest on the unpaid balance of $7587 is $7587 x 0.0158 = $120.02.

So the monthly payment of $150 only covers $29.98 of the balance ($150 - $120.02).

So the new balance is $7587 + $120.02 - $29.98 = $7677.04.

This process continues until the entire balance is paid off.

It will take 91 months (7 years and 7 months) to pay off the entire balance.