5. Use quadratic regression to find
a quadratic equation that fits the
given points.
X
0 1 2 3
y 6.1 71.2 125.9 89.4
Oy 25.4z +106.66z+ 2.06
Oy 25.42-106.66x + 2.06
Oy -25.42 +106.66x + 2.06
Oy -25.42-106.66x-2.06

Answer:

A)  6x - 27

Step-by-step explanation:

Given expression:

[tex]-9(x + 3) + 15x[/tex]

Apply the distributive property:

[tex]\implies -9 \cdot x -9 \cdot 3+15x[/tex]

[tex]\implies -9x -27+15x[/tex]

Collect like terms:

[tex]\implies -9x+15x -27[/tex]

Combine like terms:

[tex]\implies 6x -27[/tex]

Answer:

[tex] \sf \: a) \: 6x - 27[/tex]

Step-by-step explanation:

Now we have to,

→ simplify the given expression.

The expression is,

→ -9(x + 3) + 15x

Let's simplify the expression,

→ -9(x + 3) + 15x

→ -9x - 27 + 15x

→ (-9x + 15x) - 27

→ (6x) - 27

→ 6x - 27

Hence, the answer is 6x - 27.

The required equation is y=x/3+3

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here the line passes through the points (3,4) and (0,3)

Thus the slope intercept form of the line passing through these points is

y=x/3+3 where m=4-3/3-0 is the slope of the line

Hence, The required equation is y=x/3+3

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The journal entries required on February 28, 2021, for Selkirk Company to accrue interest and to record the discounting are as follows:

Debit Interest Receivable $225

Credit Interest Revenue $225

Debit Cash $15,048

Debit Interest Expense $177

Credit Note Receivable $15,000

Credit Interest Receivable $225

When a note receivable is discounted, the following steps are followed:

February 28, 2021

Interest Receivable $225 Interest Revenue $225

Cash $15,048 Interest Expense $177 Note Receivable $15,000 Interest Receivable $225

Note receivable = $15,000

Interest = 9%

Maturity period = 6 months (Jan 1, 2021, to July 1, 2021) or 180 days

Discount date = February 28, 2021

Maturity value = $15,675 ($15,000 + $15,000 x 9% x 6/12)

Discount = $627 ($15,675 x 12% x 120/360)

Proceeds = $15,048 ($15,675 - $627)

Accrued interest = $225 ($15,000 x 9% x 60/360)

Note's carrying value on February 28, 2021, = $15,225 ($15,000 + $225)

Interest expense = $177 ($15,048 - $15,225)

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Angles in parallel lines are formed when two parallel lines intersect with another line known as a transversal. So here ∠y is 40° and ∠z is 140°.

We know that sum of angles over a straight line is 180°

So here ∠x + 140° = 180°

So ∠x = 180 - 140

Therefore ∠x = 40°

So in this figure ∠x = ∠y , Since they are corresponding angles are equal.

Therefore ∠y = 40°

So ∠z will be 140° . Since ∠y = 40° its opposite angle will also be 40°.

So ∠z + 40° = 180°

Therefore ∠z = 140°

So the angles ∠y = 40° and ∠z = 140°.

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Answer:

[tex]\frac{35}{12}[/tex]

Step-by-step Explanation:

The tangent of an acute angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Answer:

Step-by-step explanation:

A typical geometric sequence can be represented as

c

0

a

,

c

0

a

2

,

⋯

,

c

0

a

k

and a typical arithmetic sequence as

c

0

a

,

c

0

a

+

Δ

,

c

0

a

+

2

Δ

,

⋯

,

c

0

a

+

k

Δ

Calling

c

0

a

as the first element for the geometric sequence we have

⎧

⎪

⎨

⎪

⎩

c

0

a

2

=

c

0

a

+

2

Δ

→

First and second of GS are  the first and third of a LS

c

0

a

+

3

Δ

=

10

→

The fourth term of the linear sequence is 10

5

c

0

a

+

10

Δ

=

60

→

The sum of its first five term is 60

Solving for

c

0

,

a

,

Δ

we obtain

c

0

=

64

3

,

a

=

3

4

,

Δ

=

−

2

and the first five elements for the arithmetic sequence are

{

16

,

14

,

12

,

10A typical geometric sequence can be represented as

c

0

a

,

c

0

a

2

,

⋯

,

c

0

a

k

and a typical arithmetic sequence as

c

0

a

,

c

0

a

+

Δ

,

c

0

a

+

2

Δ

,

⋯

,

c

0

a

+

k

Δ

Calling

c

0

a

as the first element for the geometric sequence we have

⎧

⎪

⎨

⎪

⎩

c

0

a

2

=

c

0

a

+

2

Δ

→

First and second of GS are  the first and third of a LS

c

0

a

+

3

Δ

=

10

→

The fourth term of the linear sequence is 10

5

c

0

a

+

10

Δ

=

60

→

The sum of its first five term is 60

Solving for

c

0

,

a

,

Δ

we obtain

c

0

=

64

3

,

a

=

3

4

,

Δ

=

−

2

and the first five elements for the arithmetic sequence are

{

16

,

14

,

12

,

10

Answer:67/24

Step-by-step explanation:

i did it

Answer:

providing goods

Step-by-step explanation:

i need 20 words so here, you can you go without the hard rock you can you go without it is not the first half way to you by the

Answer:

Out of all possible choices you've shown, I'd say the best answer would be C

Step-by-step explanation:

The car can go 44.25 miles on one gallon of gas

Xavier's car used 1 1/3 gallons to travel for 59 miles

The number of miles travelled on one gallon of gas can be calculated as follows

1 1/3 gallons= 59 miles

1 gallon= x

Cross multiply both sides

4/3x= 59

4x= 177

x= 177/4

x= 44.25

Hence Xavier's car can travel 44.25 miles on one gallon of gas

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Answer:

7 and 40

Step-by-step explanation:

for you to get the next number you have to add 7 to that number...then add 1 to the number you have gotten then continue like that

eg: to get 8 you had to add 7 to 1 now to get the next number add 1 to 8 to get 9 then add 7 to 9 to get 16 then continue like that

47 percent of the sandwiches had turkey.

Find the whole amount of what you're looking for to get a percentage of.

To calculate the percentage, divide the number.

Add 100 to the value.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. It's frequently represented by the sign "%" or just "percent" or "pct." For instance, 35% is equal to the fraction 0.35 or the decimal 0.35.

The value of the number out of 100 is the proportion of the number. For instance, there are 26 females and 24 boys in a class. As a result, 52 out of 100 students in the class are females, or 52% of the class.

The Latin word "per centum," which meaning "by the hundred," was the source of the English word "percentage." Percentages.

According to our question

47+53= 100%,

So 1= 1%

= 47x1= 47, So it equals 47%.

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Upon solving the decimals, The expression which is equivalent to 0.125 are -12.5 ÷ 10²⇒ 0.125 and 1,250 ÷ 10⁴ ⇒ 0.125.

A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

Decimal fractions and recurring (repeating or non-terminating, like) decimals are the three different sorts of decimals (a.k.a. converting a decimal into a fraction whose denominator is a power of ten).

1.25 ÷ 10       ⇒ 0.125

Upon solving the decimals,

12.5 ÷ 10²       ⇒ 0.125

0.125 ÷ 100    ⇒ 0.00125

1,250 ÷ 10⁴     ⇒ 0.125

12.5 ÷ 1           ⇒ 12.5

125 ÷ 1,000    ⇒ 0.0125

The expression which is equivalent to 0.125 are -

12.5 ÷ 10²       ⇒ 0.125

1,250 ÷ 10⁴     ⇒ 0.125

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The expression 5 - g has two terms in it, "5" and "g" where 5 is a constant and g is a variable.

To find the number of terms in an algebraic expression, you find out the number of signs that separate the terms and these signs only include the plus and minus signs. In this case 5 - g has two terms, 5 and g.

A term can be a number, a variable, a product of two or more variables, or a number and a variable product. An algebraic expression can be made up of a single term or a group of terms. For example, the two terms in the expression 4x + y are 4x and y. It should be noted that the terms combine to form the expression.

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The equation formed by the sentence is 9b - 7 = 8.

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

Let the variable be b

By the given sentence we get the equation

9b - 7 = 8

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The  probability of selecting a boy then a girl is 24/91

Probability is defined as the chance of occurrence of an event

E.  It is the ratio of the number of required outcome over the total of all possible outcomes in an even.

the given parameters that will help us to determine the probabilities are

The probability of the event is

P(E) = Pr(B) Then Pr(G)

Pr(E) = 8/14 *6/13

Simplify the fractions to have  48/182

= 24/91

Conclusively the selection is 24/91

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The values of maximum and minimum values are  11i + 3 and √5+ 3 .

Function can be defined in which it relates an input to the output. Functions are relationships in mathematics where each input has a particular output. Functions are often used in science and mathematics. In this section, we will learn the definitions of functions, various kinds of functions, and properties, along with examples to help us understand.

Given,

The function is f(x) = √x+3.

We have to find the maximum and minimum values on the interval [-11,5]

So,

f'(x) = 1/2√x

As when,

f'(x) = 0

has no solution than,

f(-11)  =  √-11 + 3

= 11i + 3

f(5) = √5+ 3 .

Therefore, The values of maximum and minimum values are 11i + 3 and √5+ 3 .

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By simply dividing the reduced value by 12, the value of 120 decreases by 12%, yielding a percentage drop of 102.

In mathematics, a ratio or number expressed as a fraction of 100 is called a percentage. Also occasionally used are the acronyms "pct.," "pct," and "pc." However, the percentage symbol "%" is widely used to represent it. The % quantity is dimensionally empty. Basically, percentages are fractions when the denominator is 100. A percent symbol (%) should be placed next to a number to indicate that it is a percentage. For instance, you score a 75% on a test if you properly answer 75 out of 100 questions (75/100). When calculating percentages, multiply the result by 100 after dividing the amount by the total. By multiplying (value/total) by 100%, the percentage is determined.

given

The value of the percentage decrease

= · 120 - (15% × 120)

=  120 - 15% × 120

=  85 ÷ 100 × 120

= 85 × 120 ÷ 100 = 102

You may calculate the percentage drop by simply dividing the lowered value by the original value and multiplying the result by 100.

In this case, Reduced Value equals Original Value - New Value.

By simply dividing the reduced value by 12, the value of 120 decreases by 12%, yielding a percentage drop of 102.

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a) The Corresponding minimum UGPA = 3.70

b) The range of middle 50% values will be: (3.28, 3.52).

What is the z-score?

A z-score (also known as a standard score) is a measure of how many standard deviations an individual data point is from the mean of a distribution. A z-score is calculated by subtracting the population mean from an individual data point, and then dividing that number by the population standard deviation.

a) z score corresponding to top 5% area = 1.645

Hence,

Corresponding minimum UGPA = 3.40 + 1.645*0.18 = 3.70

b) z score corresponding to middle 50% area = -0.67, 0.67

Hence,

The range of middle 50% values will be:

(3.40 - 0.67*0.18, 3.40 + 0.67*0.18)

(3.28, 3.52)

Hence,

a) The Corresponding minimum UGPA = 3.70

b) The range of middle 50% values will be: (3.28, 3.52).

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Answer: Pretend the function g(x)=4x+1 is x and replace x in f(x) with it

Step-by-step explanation:

The new points of the trapezoid are P'(4, -8), Q'(8, -8), R'(8, 4) and S'(-8, 4)

An equation is an expression relating two or more numbers and variables.

Dilation is the increase or decrease in size of a figure by a scale factor. The rule for dilation is:

(x, y) ⇒ (kx, ky)

The vertices of the trapezoid is P(1, -2), Q(2, -2), R(2, 1) and S(-2, 1)

If the trapezoid is dilated by a scale factor of 4 about the origin, the new points are:

P'(4, -8), Q'(8, -8), R'(8, 4) and S'(-8, 4)

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The indices for the directions are indicated by the two vectors in the following sketch - [1 0 0] and [ 2 0 3].

Miller Indices of Direction Vector:

The Miller indices of direction are rationalized components of the direction vectors taken in all crystallographic directions. They are indicated by [[u v w ]]. They are always defined as the smallest integers, so if they occur in fractional or decimal form, we need to convert them into the smallest integral value by algebraic manipulation.

The indices of direction 1.

Let the length of direction 1 along the x-axis be X units. The length of the vectors along the y and z axes is 0.

[ X 0 0 ]

⇒ [tex]\left[\begin{array}{ccc}0&0&0\\X'&X'&X'\\\end{array}\right][/tex]

Divide each length by X to convert it into the smallest integer.

⇒ [1 0 0]

And, this is the Miller indices of the direction vector 1.

So, the Miller indices of the direction vector 1 are [ 1 0 0].

Direction 2

The indices of direction 2.

Let the length of direction 2 along the x-axis be X units. The length of the vector along the y and z axes are 0.

[ 0.2 0 0.3 ]

⇒[ 2 0 3 ]

Multiply each fractional length by 10 to convert it into the smallest integer.

So, the Miller indices of the direction vector 2 are [ 2 0 3].

Therefore, The indices for the directions are indicated by the two vectors in the following sketch - [1 0 0] and [ 2 0 3].

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Answer:

y = 0.20x + 12.5

Lets set the cost of the cost as the y-axis and the amount of fish as the x-axis. 12.50, a constant and the y-intercept, is the price when you don't have any fish.

0.2 is the slope and in this case, the amount of 1 fish.

0.2x + 12.5 is the total amount as every fish added adds 20 cents. 12.5 is the fishtank which you need to get before getting any fish.

Answer:

8

Step-by-step explanation:

Let the AP numbers be: ( a - 3d ), ( a - d ), a, ( a + d ), ( a + 3d )

We are given that sum of all these numbers is 40.

⇒ a - 3d + a - d + a + a + d + a + 3d = 40

⇒ 5a + 4d - 4d = 40

⇒ 5a = 40

⇒ a = 40 / 5 = 8

We know that the middle term of the five numbers given is 'a'.

As a result, the given AP's middle term is 8.

Good luck <3

Answer:

the third one

Step-by-step explanation:

an open circle means it does not include that number. therefore, it needs to be x is less than -2. a closed circle means it includes that number. therefore, x is greater than or equal to 4

The integral[tex]∫20(45t^3-34t^2+25t)dt[/tex] can be evaluated by using the power rule of integration, which states that the derivative of x^n is [tex]nx^(n-1)[/tex]. This rule can be applied to each term of the integral separately.

The first step is to integrate [tex]∫20(45t^3-34t^2+25t)dt[/tex] with respect to t. By using the power rule, we can find the antiderivative of each term inside the parentheses:

[tex]∫45t^3 dt = (45/4)t^4 + C[/tex]  (the antiderivative of 45t^3 is (45/4)t∧4)

[tex]∫34t^2 dt = (34/3)t^3 + C[/tex] (the antiderivative of 34t^2 is (34/3)t∧3)

[tex]∫25t dt = (25/2)t^2 + C[/tex] (the antiderivative of 25t is (25/2)t∧2)

Now, we can substitute these results back into the original integral:

[tex]20(∫45t^3 dt - ∫34t^2 dt + ∫25t dt) = 20((45/4)t^4 + (34/3)t^3 + (25/2)t^2) + C= 20(15t^4-11t^3+25t^2) + C[/tex]

So, the evaluated integral for [tex]∫20(45t^3-34t^2+25t)dt[/tex] is [tex]20(15t^4-11t^3+25t^2) + C.[/tex]

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The one-sided limit that does not exist is given as follows:

lim x -> -6^- f(x).

A one sided limit will not exist when it is outside the domain of the function.

The domain of a function is composed by the set of all the input values of the function, hence on the graph it is given by the values of x.

For this problem, the domain is then given as follows:

-6 ≤ x ≤ 8.

To the left of -6, the function is not defined, hence the one-sided limit that does not exist is given as follows:

lim x -> -6^- f(x).

Meaning that the correct option is given by the last option.

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The points to be graphed are (0, -3) and (1.8, 0). The graph of the equation is shown in the attached image

In order to graph the equation of the line 3y-5x=-9:

First, find the value of x when y = 0:

3y-5x=-9, when y = 0:

3(0) - 5x=-9

- 5x = -9

x = 9/5

x = 1.8

Also, find the value of y when x = 0:

3y-5x=-9, when x = 0:

3y - 5(0) = -9

3y = -9

y = -9/3

y = -3

Therefore,  the values to be plotted on our graph are (0, -3) and (1.8, 0). The image of the graph is attached

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Answer: It will take 7 more years for George’s sister to be taller than him.

Step-by-step explanation:

Answer:

Step-by-step explanation:

7 years

Answer:

.........,..........,.

Step-by-step explanation:

.................. .....