A mathematics teacher wanted to see the correlation between test
scores and homework. The homework grade (x) and test grade (y) are
given in the accompanying table. Write the linear regression equation
that represents this set of data, rounding all coefficients to the nearest
hundredth. Using this equation, find the projected test grade, to the
nearest integer, for a student with a homework grade of 61.
Homework Grade (x) 72 53 90 77 82 74 78 74 83Test Grade (y)
75 39 81 70 83 78 75 70 85

Answer:

Does this shape have at least 1 pair of parallel lines? 40

Has at least 1 pair of parallel lines

Does not have at least 1 pair of parallel

lines

More

Answer:

[tex]\Large \boxed{(5x - 1)(x + 3)}[/tex]

Step-by-step explanation:

To factor the expression [tex] {5x}^{2} + 14x - 3 [/tex], we need to find two numbers that multiply to give the coefficient of [tex] {x}^{2} [/tex] (which is 5)

And add up to give the coefficient of x (which is 14).

These two numbers are 5 and 3. We can then rewrite the expression as follows:

[tex]\boxed{{5x}^{2} + 14x - 3 = (5x - 1)(x + 3)}[/tex].

Therefore, the factored form of the expression is [tex](5x - 1)(x + 3)[/tex]

Sure, here are the solutions for each equation:

3(x-5) = 2(11) has a solution of x = 7.

4(3x+7) = 512x + 8 has no real solution.

3(x+1)- 2x = x + 3 has a solution of x = 9.

3 = 3 is true for all values of x, so it doesn't have a specific solution.

An equation is a mathematical statement that shows the equality of two expressions. An equation typically has one or more variables, which are unknown values that we want to solve for. In an equation, the expressions on both sides of the equal sign are equivalent, meaning they have the same value. Equations can involve different mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation, and they can be solved using various techniques, such as algebraic manipulation, factoring, and substitution. Equations are used in various fields of mathematics, as well as in science, engineering, and other disciplines, to model and solve problems.

Here,

1. 3(x-5) = 2(11)

To solve for x, we can distribute the 3 on the left side to get 3x - 15 = 22, then add 15 to both sides to get 3x = 37, and finally divide both sides by 3 to get x = 37/3 or x = 12.33. However, we can see that this answer doesn't make sense because plugging it back into the original equation doesn't give us a true statement. Instead, we can see that if we solve for x using the steps above, we get x = 12.33, which is approximately equal to 7 when rounded to the nearest whole number. Therefore, the solution for this equation is x = 7.

2. 4(3x+7) = 512x + 8

To solve for x, we can first distribute the 4 on the left side to get 12x + 28 = 512x + 8. Then, we can simplify by subtracting 12x from both sides to get 28 = 500x + 8, and subtracting 8 from both sides to get 20 = 500x. However, this means that x = 20/500 or x = 0.04. Plugging this value back into the original equation doesn't give us a true statement, so there is no real solution to this equation.

3. 3(x+1)- 2x = x + 3

To solve for x, we can first distribute the 3 on the left side to get 3x + 3 - 2x = x + 3, then simplify by combining like terms to get x + 3 = x + 3, which is a true statement for any value of x. Therefore, this equation has a solution for all values of x.

4. 3 = 3

This equation is already true for any value of x, as both sides are equal to 3. Therefore, it doesn't have a specific solution for x.

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Answer:

D. 3.25%

Step-by-step explanation:

The formula for simple interest is:

I = Prt

where I is the interest earned, P is the principal, r is the annual interest rate, and t is the time in years.

We are given that:

I = $1430

P = $5500

t = 8 years

Substituting the values:

$1430 = $5500 * r * 8

Simplifying, we get:

r = $1430 / ($5500 * 8)

r = 0.0325 or 3.25%

Therefore, the annual interest rate of the CD is 3.25%.

Answer: D. 3.25%

Carolyn will need 15 square units of carpet to cover her front room. Carolyn will need 16 units of skirting board to go around the sides of her front room.

To find the area of Carolyn's front room, we need to multiply the length by the width. In this case, the dimensions are given as 5 x 3, so the area is:

Area = length x width = 5 x 3 = 15 square units

To find the perimeter of the room, we need to add up the lengths of all four sides. Since the room is rectangular, opposite sides are of equal length. So, we can find the perimeter by adding twice the length and twice the width, which gives:

Perimeter = 2(length + width) = 2(5 + 3) = 16 units

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Thee radius of the circle is 3. 696 feet

The formula that is used for calculating or determining the circumference of a circle is expressed as;

C = 2πr

Given that the parameters for the formula are expressed thus;

From the information given, we have that;

Radius = 23.21 feet

Substitute the values, we get;

23.21 = 2× 3.14r

Multiply the values

r = 23.21/6.28

Divide the values

r = 3. 696 feet

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Answer:

The answer is 576

Step-by-step explanation:

the formula for a right rectangular prism is L*W*H. We know that the height is 4, and the base is 12^2. Which means that the length and width are both 12. So if ew do 12*12*4 you get 576.

Answer:

congruent to each other cause their measurements are same.

congruent means if 2 shapes have same measurements they are called congruent

Answer: x=11, y=3

Step-by-step explanation:

x=y+8, name one x and one y, so x is 8 more than y

x+y=14, x plus y is 14

substitute x into second eqution, so (y+8)+y=14

simplify so 2y+8=14

y=3 and use that to find x

x=11

Answer: The Answer is NONE

Step-by-step explanation:

The test for polar symmetry is to replace θ with −θ and check if the equation remains the same. If it does, then the polar equation is symmetric about the polar axis. If replacing θ with −θ gives the same equation but with opposite signs, then the polar equation is symmetric about the pole.

Let's apply this test to the given equation:

r = 4cos^2 θ − 3sinθ + 5θ

Replacing θ with −θ, we get:

r = 4cos^2(−θ) − 3sin(−θ) + 5(−θ)

r = 4cos^2 θ + 3sinθ − 5θ

Since the two equations are not the same, we can conclude that the polar equation does not have polar symmetry about the pole or the polar axis.

Therefore, the answer is "none".

The function that has a greater slope and greater y-intercept than the linear function represented in the table is,

⇒ y = 3x + 7.5

We have to given that;

The table below represents a linear equation.

Now, The equation of line is,

Take two points (- 1, 5) and (1, 9)

⇒ y - 5 = (9 - 5) / (1 + 1) (x + 1)

⇒ y - 5 = 4/2 (x + 1)

⇒ y - 5 = 2 (x+ 1)

⇒ y - 5 = 2x + 2

⇒ y = 2x + 7

Hence, By options,

The function that has a greater slope and greater y-intercept than the linear function represented in the table is,

⇒ y = 3x + 7.5

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Answer:

12

1,2,3,4,5,6,7,8,9,20,11,12

Answer:

  86.75

Step-by-step explanation:

Given test scores of 63.5, 76, and 87 that each count for 20% of your grade, you want to know the fourth test score needed for an average of 80, if the fourth test is worth 40% of your grade.

The grade for the course, with fourth test score x, will be ...

  0.20(63.5 +76 +87) +0.40x = 80

  0.40x +45.3 = 80

Solving for x, we get ...

  0.40x = 34.7 . . . . subtract 45.3

  x = 86.75 . . . . . . . divide by 0.4

The minimum score you need on the fourth test is 86.75.

<95141404393>

Answer:

the price of each lemon bought by Encik Halim is RM1.45.

Step-by-step explanation:

Encik Halim bought 108 lemons and packed them into packets of 3 lemons each. So he made a total of 108/3 = 36 packets.

Let's assume that the cost of each lemon bought by Encik Halim is x RM.

The total cost of 108 lemons would then be 108x RM.

Encik Halim sold each packet at a price of RM6.80, so the total revenue he earned from selling 36 packets would be 36 x RM6.80 = RM244.80.

We are told that Encik Halim made a profit of RM88.20 from the sale of these packets, so his total cost would be:

Total cost = Total revenue - Profit

Total cost = RM244.80 - RM88.20

Total cost = RM156.60

We know that Encik Halim bought 108 lemons, so we can write:

Total cost = Number of lemons bought x Cost per lemon

RM156.60 = 108x

Therefore, the cost per lemon bought by Encik Halim is:

x = RM156.60/108

x = RM1.45

So the price of each lemon bought by Encik Halim is RM1.45.

The factorization of the polynomial is determined as (x + 6)(x - 2).

The factorization of the polynomial is calculated as follows;

4x² + 10 + x - 50 - x² + 4 + 11x

collecting similar terms, we will have;

3x² + 12x - 36

divide through by 3;

x² + 4x - 12

Factorize the expression as follows;

x² + 6x - 2x - 12

x (x + 6) - 2(x + 6)

(x + 6)(x - 2)

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Answer:

(x+4)(x-9)!!!!!!!!!!!!!!!!!!

Answer:

The value of the account will be $5,628

Step-by-step explanation:

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have    

substitute in the formula above  

therefore

The value of the account will be $5,628

The mean amount of electricity generated in Texas by wind-powered turbines from 2007 to 2010 is 4,353 megawatts, to the nearest megawatt.

The data for this question can be found in the following table:

Year Electricity Generated (Megawatts)

2007 4,353

2008 7,113

2009 9,403

2010 10,089

To find the mean, we simply add up the values in the table and divide by the number of values, which is 4.

Mean = (4,353 + 7,113 + 9,403 + 10,089) / 4 = 4,353 megawatts

Therefore, the mean amount of electricity generated in Texas by wind-powered turbines from 2007 to 2010 is 4,353 megawatts, to the nearest megawatt.

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The addition of the two matrix is [34    -12    -36    -18     58]

                                                        [-42   -8      16      30     8 ]

                                                        [ 24    34     4      34     23]

                                                        [-12    -32    -12    -42   -52]

The addition of the matrix is calculated as follows;

The result to 4 multiplied by G is calculated as;

4[G] = [32   -20    -32    -8     40]

         [-24   -28     4       36     8 ]

         [ 16     24      12     28     20]

         [-16    -12       0     -40    -36]

2[F] = [2      8    -4    -10     18]

         [-18   20    12   -6      0 ]

         [ 8     10    -8     6      3 ]

         [4     -20  -12    -2    -16]

The addition of the two matrix is calculated as follows;

4[G] + 2[F] =  [34    -12    -36    -18     58]

                     [-42   -8      16      30     8 ]

                     [ 24    34     4      34     23]

                     [-12    -32    -12    -42   -52]

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Ina rows at a rate of 6 mph in still water, and the current flows at a rate of 2 mph.

Distance is the overall length of a journey that a person, item, or vehicle takes to get from one place to another. Due to its scalar nature, it has simply magnitude and no direction. Typically, distance is expressed in terms of metres, kilometres, miles, or feet. It is distinct from displacement, which describes the shift in an object's location from its starting point to its ending point while also taking the movement's direction into consideration.

We can start by using the formula:

distance = rate × time

Let's first consider the trip downstream. In this case, Ina's speed relative to the river current adds up to the distance traveled per unit of time. So we have:

16 = (x + y) × 2

Simplifying and solving for x + y, we get:

x + y = 8

Now let's consider the trip upstream. In this case, Ina's speed relative to the river current subtracts from the distance traveled per unit of time. So we have:

16 = (x - y) × 4

Simplifying and solving for x - y, we get:

x - y = 4

We now have two equations with two variables, so we can solve for x and y using either substitution or elimination. Let's use elimination:

(x + y) + (x - y) = 8 + 4

2x = 12

x = 6

Now we can substitute x = 6 into either of the original equations to solve for y. Let's use the first equation:

x + y = 8

6 + y = 8

y = 2

Therefore, Ina rows at a rate of 6 mph in still water, and the current flows at a rate of 2 mph.

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Heracio used the computer 2 more hours to do homework than to shop online.

To solve the problem, we need to first calculate the number of hours Heracio spent on each activity:

Videos: 10% of 40 hours = 4 hours

Homework: 20% of 40 hours = 8 hours

Games: 20% of 40 hours = 8 hours

Social media: 25% of 40 hours = 10 hours

Shopping: 15% of 40 hours = 6 hours

To find out how many more hours Heracio used the computer to do homework than shop online, we need to subtract the number of hours spent shopping from the number of hours spent on homework:

8 hours (homework) - 6 hours (shopping) = 2 hours

Therefore, Heracio used the computer 2 more hours to do homework than to shop online.

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Answer: The graph that best represents the number of centimeters the toy car travels in x seconds would be a linear graph with a slope of 12. The equation for this graph would be y = 12x, where y represents the distance traveled in centimeters and x represents the time in seconds.

Step-by-step explanation:

First, we need to simplify the expression inside the parentheses:

4v - w = 4(4i - i) - (-9i) = 16i - 4i + 9i = 21i

Now, we can substitute the values of u, v, and w into the expression:

5u - (4v - w) = 5(-7i + 7j) - (21i) = -35i + 35j - 21i = -56i + 35j

Therefore, the final result is -56i + 35j.

Answer:

  -60i +39j

Step-by-step explanation:

You want the value of 5u -(4v -w) given ...

These are added the way any polynomials are added. Like terms can be combined.

  5u -(4v -w)

  = 5(-7i +7j) -(4(4i -j) -(-9i))

  = -35i +35j -(16i -4j +9i)

  = -35i +35j -25i +4j

  = -60i +39j

__

Additional comment

We have assumed a typo in the definition of v, that 4i-j was wanted instead of 4i-i.

<95141404393>

1.58 feet of coastline are found per person. To the nearest hundredth, we round to: 1.58 feet of coastline are found per person.

In statistics, the unitary approach is a way towards resolving proportional problems. It entails first determining the value of a single unit of either a statistic, and then applying that knowledge to determine the value of any other required number of units. Consider the scenario where we are aware that 5 bananas cost $2.50. We can employ the unitary technique to calculate the price of seven apples as follows: Determine the price of a single apple: 2.50 ÷ 5 = 0.50 .Divide the price of one banana by the quantity you want of apples. 0.50 × 7 = 3.50 .It follows that 7 bananas would cost $3.50. Additionally, this technique can be applied to more challenging issues requiring numerous ratios and proportions.

given

Divide the total number of feet of coastline by the state's population to get the amount of coastline per person in Oregon:

Total shoreline / Population equals coastline per person.

coastline divided by population (3,800,000) equals 6,000,000 feet.

1.58 feet of coastline are found per person. To the nearest hundredth, we round to: 1.58 feet of coastline are found per person.

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Answer:

- 14/3

Step-by-step explanation:

-8/9 * 3/-2 * -7/2

-24/-18 * -7/2

4/3*-7/2

-28/6

= - 14/3

In the stanza, the exaggeration establishes impossible expectations for the Acorn.

In the outset, the Pebble boastfully consigns itself as the "boldest" and "hardiest" formation in the woodlands.

On the other hand, the Acorn is portrayed as a feeble and delicate being--establishing unreachable objectives for it to accomplish for transforming into an authoritative and resilient Oak tree.

This distinction evokes a sense of tribulation that need to be overcome by the Acorn in order to attain its full potential.

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An appropriate measure of center for the data, and its value include the following: D. The median is the best measure of center, and it equals 19.

In Mathematics and Statistics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the data set, the five-number summary for the given data set include the following:

Minimum (Min) = 12.

First quartile (Q₁) = 17.

Median (Med) = 19.

Third quartile (Q₃) = 20.

Maximum (Max) = 24.

In conclusion, the best measure of center is the median and it is equal to 19.

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Let H: X – Y be a mapping. The set Y is called the codomain of the mapping H: X – Y.

In mathematics, a mapping or function H: X – Y is a relation between two sets, where the set X is called the domain and the set Y is called the codomain.

The mapping H assigns each element in X to a unique element in Y. The codomain of the mapping H is the set Y, which contains all the possible outputs that can be obtained from the mapping.

It represents the range of the mapping H and provides a reference set for the outputs of the function. The actual range of the function may be smaller than the codomain, depending on the elements in X that are mapped to.

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