write an equation for the graph shown in the form $y=ax b.$

Answer:

(-41, 30)

Step-by-step explanation:

The midpoint of a segment lies on the segment.

x: (-88 + 6)/2 = -41

y: (61 + (-1)) = 30

Answer: (-41, 30)

The summation notation of the sum is given as follows:

[tex]\sum_{i = 1}^{6} \frac{(-1)^{i-1}}{3^i}[/tex]

The summation notation of the sum is written considering the patterns of the terms that compose the terms.

First we look at the fact that the sum has six terms, and the first term is considered as having index 1, hence:

[tex]\sum_{i = 1}^{6}[/tex]

Then we consider that the signal is alternating, with the terms with odd indices being positive and those with even indices being negative, hence the numerator is of:

[tex](-1)^{i - 1}[/tex]

(any of -1 or +1 would work here).

Then we considering that the denominator is composed by the powers of 3, hence it is given by:

[tex]3^i[/tex]

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Answer:

3 x y (y + x)

Step-by-step explanation:

Factor the following:

(y + x)^3 - (y^3 + x^3)

Factor the sum of two cubes. y^3 + x^3 = (y + x) (y^2 - x y + x^2):

(y + x)^3 - ((y + x) (y^2 - x y + x^2))

Factor y + x out of (y + x)^3 - (y + x) (y^2 - x y + x^2), resulting in (y + x) ((y + x)^(3 - 1) - (y^2 - x y + x^2)):

(y + x) ((y + x)^(3 - 1) - (y^2 - x y + x^2))

3 - 1 = 2:

(y + x) ((y + x)^2 - (y^2 - x y + x^2))

(y + x) (y + x) = (x) (x) + (x) (y) + (y) (x) + (y) (y) = x^2 + x y + x y + y^2 = y^2 + 2 x y + x^2:

(y + x) ((y^2 + 2 x y + x^2) - (y^2 - x y + x^2))

-(y^2 - x y + x^2) = -y^2 + x y - x^2:

(y + x) (x^2 + 2 x y + y^2 + (-y^2 + x y - x^2))

Grouping like terms, y^2 - y^2 + 2 x y + x y + x^2 - x^2 = (2 x y + x y) + (y^2 - y^2) + (x^2 - x^2):

((2 x y + x y) + (y^2 - y^2) + (x^2 - x^2)) (y + x)

x y 2 + x y = x y×3:

(3 x y + (y^2 - y^2) + (x^2 - x^2)) (y + x)

y^2 - y^2 = 0:

(3 x y + (x^2 - x^2)) (y + x)

x^2 - x^2 = 0:

Answer: 3 x y (y + x)

The scientific notation is  [tex]1.45*10^{11}[/tex]

Scientific notation is a way to present extremely large or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place after the decimal. This makes it challenging to represent a small number of integers in their enlarged form. We, therefore, employ scientific notations.

We need to move the decimal point 11 places to the left therefore the exponent for the 10s term will be positive:

[tex]145,000,000,000=145,000,000,000.0=1.45*10^{11}[/tex]

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To simplify the expression 2-x+1/x-2-x-4/x+2, you can first simplify the fractions 1/x-2 and -x-4/x+2.

To simplify the fraction 1/x-2, you can rewrite it as (x+2)/(x-2)(x+2). This simplifies to x+2.

To simplify the fraction -x-4/x+2, you can rewrite it as (-x-4)/(x+2)(-x+2). This simplifies to -(x+2).

Next, you can simplify the rest of the expression by combining like terms:

2-x+1/x-2-x-4/x+2 = 2-x+(x+2)-(x+2) = 2-2x = -2x+2

Therefore, the simplified expression is -2x+2.

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Answer:

y = 51.2

Step-by-step explanation:

y/32=16/10

First, we time 32 on both sides to get y alone

y = 32(16/10)

y = 32(1.6)

y = 51.2

Let's check:

51.2/32 =  16/10

1.6 = 1.6

The answer y = 51.2 is correct!

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Answer:

To prove the given identity, we can start by multiplying both sides of the equation by (cosθ - sinθ) to obtain:

(cosθ/1 - tanθ) (cosθ - sinθ) - sin^2θ/(cosθ - sinθ) = (cosθ + sinθ)(cosθ - sinθ)

Expanding both sides of the equation gives us:

cos^2θ - tanθcosθ - sin^2θ = -sin^2θ + cos^2θ

We can simplify this equation to:

-tanθcosθ = -sin^2θ + cos^2θ

We can simplify this further by using the identity cos^2θ + sin^2θ = 1:

-tanθcosθ = 1 - 2sin^2θ

We can rearrange this equation to solve for sin^2θ:

sin^2θ = (1 + tanθcosθ)/2

This is the desired result, so we have successfully proved the given identity.

I hope this helps! Let me know if you have any questions.

Step-by-step explanation:

SELF EXPLANATORY

(1) The measure of the angle CFD = 48°.

(2) The measure of the angle AFE = 48°.

(3) Pair of supplementary angles: Angle BFC and angle CFD.

(4) Pair of adjacent angles: Angle AFB and angle BFD.

What are the properties of angles?

The angle properties of lines are:

Vertically opposite angles are equal, for example, a = d, b = c.

Adjacent angles add to 180, for example, a + b = 180, a + c = 180. Corresponding angles are equal, for example, a = e, b = f, c = g, d= h.

(2) In the given figure, m∠BFC = 42°

By using the property of linear pair, we can write

       ∠BFC + ∠CFD = 180

         42 + ∠CFD = 180

        ∠CFD = 58.

(2) Angle CFD and angle AFE are opposite angles and opposite angles are same in measurement so we can write

             m∠AFE = 58°.

(3) Pair of supplementary angles: Angle BFC and angle CFD.

(4) Pair of adjacent angles: Angle AFB and angle BFD.

Hence,

(1) The measure of the angle CFD = 48°.

(2) The measure of the angle AFE = 48°.

(3) Pair of supplementary angles: Angle BFC and angle CFD.

(4) Pair of adjacent angles: Angle AFB and angle BFD.

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By information provided in the question, we can say that It is the probability of a Type I error.

The proportion of favorable outcomes to all possible outcomes for an event is known as the probability. The quantity of positive outcomes in an experiment with 'n' outcomes is represented by x. The following equation can be used to determine the likelihood of an event:

Probability (event) = positive outcome / overall outcome = x/n

It refers to the likelihood of a Type I mistake.

The likelihood that a Type I error will occur, or the likelihood that a null hypothesis will be rejected when it is true, determines the degree of significance.

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At least one patient will arrive in the following 15 minutes if the next patient arrives before 11:45 a.m.= ​∗e −1.5 ≈0.777.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

According to our question-

I If X indicates the number of patients who arrived in 1.5 hours at random, then X = Pois(6*1.5) = Pois (9)

P(X=7)=frac 9/7/7!e-9/approximately 0.17P(X=7)= 7! 9/7

​ \s ∗e \s−9 \s ≈0.117

(ii) If X indicates the number of patients who arrived in 15 minutes or less, then X = Pois(6*0.25) = Pois (1.5)

At least one patient will arrive in the following 15 minutes if the next patient arrives before 11:45 a.m.

P(X≥1)=1-P(X<1)

=1-P(X=0)

=1-frac 1.5 0 0!*e 1.5 Approximately 0.777P(X1)

=1−P(X<1)

=1−P(X=0)=1− \s0! \s1.5 \s0

​ \s ∗e \s−1.5 \s ≈0.777

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The linear function represents the total cost is y = 15 + 35x and the money made by 8 lawns will be $295.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given,

For x number of lawn mows,

Total earning y = 15 + 35x

For x = 8

y = 15 + 35 x 8 = 295

Hence "The linear function represents the total cost is y = 15 + 35x and the money made by 8 lawns will be $295".

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The correct B. 495.

A group of k elements can be chosen from a group of n elements in  ways.

n = 12

r = 4

Probability

Probability is the branch of mathematics concerning the occurrence of a random event, and four main types of probability exist: classical, empirical, subjective and axiomatic. Probability is synonymous with possibility, so you could say it's the possibility that a particular event will happen

nCr = n1 / (n-r)! r1

12C4 = 12! / (12-4)! 4!

12C4 = 12x11x10x9x8! / 8! 4!

12C4 = 11880 / 24

12C4 = 495

The correct B. 495.

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The ratio of a : b : c in the linear equation is 2 : -1 : -1

From the question, we have the following equation that can be used in our computation:

ax + by + c = 0

The points on the line are given as

(2 ,3) and (8 , 15)

A linear equation is represented as

y = mx + c

Where

Slope = m

y-intercept = c

This means that

3 = 2m + c

15 = 8m + c

Subtract the equations

So, we have the following representation

6m = 12

Divide by 6

m = 2

Substitute m = 2 in 3 = 2m + c

3 = 2 * 2 + c

So, we have

c = -1

Substitute m = 2 and c = -1 in y = mx + c

y = 2x - 1

So, we have

2x - y - 1 = 0

Recall that

ax + by + c = 0

This means that

a : b : c = 2 : -1 : -1

Hence, the ratio is 2 : -1 : -1

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Answer:

(x-1)(2x+5)

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2x^2 −3x +9=0 is the given equation that is quadratic.

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax^2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable.

Quadratic expressions are those involving powers of x up to the second power, not the fourth power, hence the prefix quad signifies "four" rather than "two."

As highest power of variable is 2 so the expression 2x^2 −3x +9=0 is quadratic.

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The expression that can be used to determine how long it will take for the tank to fill completely is C. 1 over 4 . 12.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B). This indicates that you're dividing information A by B. For instance, the ratio will be 5/10 if A is 5 and B is 10.

In this case, the oil company fills 1 over 12 of a tank in 1 over 4 hour with gasoline.

The rate will be:

= 1/4 ÷ 1/12

= 1/4 × 12

= 3

The correct option is C

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Answer:

Nelson's average speed was 8 miles per hour.

Step-by-step explanation:

To find Nelson's average speed, you need to divide the distance he traveled by the time it took him to travel that distance. In this case, Nelson traveled 20 miles in 2 1/2 hours, so his average speed was 20 miles / 2.5 hours = <<20/2.5=8>>8 miles per hour.

Answer:

8 miles per hour

Step-by-step explanation:

In order to find Nelson's average speed, we can set up a proportion. To solve for x, x being miles traveled in one hour.

[tex]\frac{20 miles}{2.5hours} =\frac{x miles }{1 hour}[/tex]

x= 8

Answer:

p=500

Step-by-step explanation:

18/100=90/p

First, set up equation

90x100=18xp

9000=18p

9000/18=18p/18

500=p

Answer:

[tex]p = 500[/tex]

Step-by-step explanation:

Use the cross-multiplication method. Multiply 18 with p, and 90 with 100, respectively:

[tex]\frac{18}{100} = \frac{90}{p} ; \\ 18p = 90 * 100\\ 18p = 9000[/tex]

Isolate the variable, p. Note the equal sign, what you do to one side, you do to the other. Divide 18 from both sides of the equation:

[tex]\frac{(18p)}{18} = \frac{(9000)}{18} \\p = \frac{9000}{18} \\p = 500[/tex]

[tex]p = 500[/tex] is your answer.

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Length of wall = 10km

side of square= 10km

area of square= 10²= 100km²

radius of circle = 10/2 = 5km

area of circle = 3.14 × 5²

area of circle = 3.14 × 25

area of circla = 78.5 km²

area of square >>> area of circle

The probability of selecting exactly three clubs from a standard deck is 0.088. Where n = 5; p = 0.25; q = 0.75; and x = 3 . It is calculated by using binomial probability.

The binomial probability formula is

P(X = x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾ = [tex]\frac{n!}{(n-x)!x!} p^xq^{(n-x)}[/tex]

Where n is the number of trials, p i is the probability of success, and q is the probability of failure.

And q = 1 - p

It is given that, a card is selected from a standard deck and replaced.

This experiment has repeated a total of five times. i.e., trials n = 5

So, the probability of success is p = 1/4 = 0.25

(Since one card is to be selected from the five trials where each time the card is replaced)

Then, the probability of failure is q = 1 - 0.25 = 0.75

And it is given that we need to find the probability of selecting exactly three clubs. So, the required random variable is x = 3.

Then, using the binomial probability formula, we get

P(X = x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾

⇒ P(X = 3) = ⁵C₃ p³q⁽⁵⁻³⁾ = ⁵C₃(0.25)³(0.75)² = 0.0878

On rounding off, we get the required probability as 0.088.

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Answer:

A. [tex] {5}^{7} [/tex]

B. [tex] ( { - 7})^{5} [/tex]

C. [tex] {3}^{9} [/tex]

D. [tex] {27}^{2} [/tex]

E. [tex] ({ - 2})^{9} [/tex]

F. [tex] {3}^{14} [/tex]

G. [tex] {( - 4)}^{14} [/tex]

H. [tex] {2}^{8} [/tex]

I. [tex] {(0.25)}^{5} [/tex]

J. [tex] {7}^{6} [/tex]

Step-by-step explanation:

A.

[tex] {5}^{3} \times {5}^{4} \\ = {5}^{3 + 4} \\ = {5}^{7} [/tex]

B.

[tex]( { - 7})^{2} \times ( { - 7})^{3} \\ = ( { - 7})^{2 + 3} \\ = ( { - 7})^{5} [/tex]

C.

[tex] {3}^{6} \times {3}^{3} \\ = {3}^{6 + 3} \\ = {3}^{9} [/tex]

D.

[tex] {27}^{0} \times {27}^{2} \\ = {27}^{0 + 2} \\ = {27}^{2} [/tex]

E.

[tex]( { - 2})^{2} \times ( { - 2})^{3} \times ( { - 2})^{4} \\ = ( { - 2})^{2 + 3 + 4} \\ = ({ - 2})^{9} [/tex]

F.

[tex] {3}^{4} \times {9}^{2} \times ( { - 3})^{6} \\ = {3}^{4} \times {3}^{2 \times 2} \times {3}^{6} \\ = {3}^{4} \times {3}^{4} \times {3}^{6} \\ = {3}^{4 + 4 + 6} \\ = {3}^{14} [/tex]

G.

[tex] {( - 4)}^{6} \times {( - 4)}^{5} \times {( - 4)}^{3} \\ = {( - 4)}^{6 + 5 + 3} \\ = {( - 4)}^{14} [/tex]

H.

[tex] ( - 8) \times ( - 8) \times {2}^{2} \\ = 8 \times 8 \times {2}^{2} \\ = {2}^{3} \times {2}^{3} \times {2}^{2} \\ = {2}^{3 + 3 + 2} \\ = {2}^{8} [/tex]

I.

[tex] 0.25 \times {(0.25)}^{4} \times {(0.25)}^{0} \\ = {(0.25)}^{1} \times {(0.25)}^{4} \times {(0.25)}^{0} \\ = \times {(0.25)}^{1+4+0} \\ = \times {(0.25)}^{5} [/tex]

J.

[tex] {7}^{3} \times {7}^{2} \times 7 \\ = {7}^{3} \times {7}^{2} \times {7}^{1} \\ = {7}^{3+2+1} \\ = {7}^{6} [/tex]

The number is 17.

The first part is "Fifteen less than twice a number".

Let us say that n represents the unknown number.

Twice a number is the same as two times the number or 2n, and fifteen less than 2n is 2n−15.

The next part "is the same as the" part of the word problem indicating that the two parts are equal. So we use an equal sign to represent it⇒2n−15 =

The third part of the problem is "the number plus two". This is the same as n+2

The final equation is 2n-15=n+2

To solve for n, we would add 15 to both sides: 2n=n+17

Then subtract 1n from both sides: n=17

The number is 17.

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The alkali metals, which are located in Group 1A of the periodic table, are the most reactive metals.

The blue column on the left of the periodic table contains the alkali metals, which are the most reactive metals. As we move down column (group) one, which is depicted in blue, their responsiveness improves.

What are Alkali metals ?

Alkali metals are those that react with water to produce strong bases.

It is composed of six elements collectively referred to as the lithium family. These metals have one electron in their outermost shell, making them extremely reactive elements of the periodic table.

A few instances of alkali metal

lithium (Li), sodium (Na), rubidium (Rb), potassium (K), francium (Fr) and  Caesium  (Cs).

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The odds that the chosen cookies being chocolate chip cookies is 1/7

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

We are given that

A cookie jar contains six chocolate chip cookies, four peanut butter cookies and five oatmeal cookies

Hence the total number of cookies are 15

Two cookies are selected from the jar

This can be done in 15c2 ways that is 105

Now we have six Choco chip cookies in the same jar

Number of ways in which we can select 2 cookies is 6c2

That is 15

Hence the odds are 15/105

That is 1/7.

The odds that the chosen cookies being chocolate chip cookies is 1/7.

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The Missing number for each fraction is ---

a) 3/7 = 12/28

b)5/8 = 25/40

c)3/4 =12/16

d)7/3 = 14/6

Fraction:

A fraction (from Latin: fracturs, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction (examples {1}/{2}} and ) consists of a numerator, displayed above a line (or before a slash like 1⁄2), and a non-zero denominator, displayed below (or after) that line. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals.

Given that

a) [tex]\frac{3}{7}[/tex] = 12/_

  let x

3/7 = 12/x

3x = 84

x = 28

3/7 = 12/28

b) x/8 = 25/40

40x = 200

x = 5

5/8 = 25/40

c)3/4 = x/16

4x =48

x =12

3/4 =12/16

d)7/x = 14/6

42 = 14x

x = 3

7/3 = 14/6

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Answer:

Therefore, the equation of the line that is parallel to the given line and passes through the point ( − 6 , 9 ) (−6,9) is y = 4x + 33.

Step-by-step explanation:

To find the equation of a line that is parallel to a given line and passes through a given point, you can use the point-slope form of a linear equation. The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

Where (x1, y1) is the point through which the line passes, and m is the slope of the line.

The slope of a line is given by the difference in the y-coordinates of two points on the line, divided by the difference in the x-coordinates of those points. The slope of a line is also the coefficient of the x-term in the standard form of a linear equation (y = mx + b).

In this case, the given line is x − 6y = −60 − 9x. To find the slope of this line, you can rearrange the equation to standard form:

x − 6y = −60 − 9x

−9x + x − 6y = −60

−8x − 6y = −60

y = 4x + 15

The slope of this line is m = 4.

To find the equation of a line parallel to this line that passes through the point ( − 6 , 9 ) (−6,9), you can use the point-slope form of a linear equation with (x1, y1) = ( − 6 , 9 ) (−6,9) and m = 4:

y - 9 = 4(x - (-6))

y - 9 = 4(x + 6)

y - 9 = 4x + 24

y = 4x + 33

An equation which suggests how the range of skeins of yarn remaining, y, relies upon at the range of hats Anna knits, x is y =6- 1.2x.

An expression is a mathematical equation that is used to reveal the connection present among or extra variables and numerical quantities.

Let y constitute the range of skeins of yarn remaining. Let x constitute the range of hats Anna knits.

Mathematically, an equation which fashions the connection among x and y is given by: Mathematically, an equation which fashions the connection among x and y is given by

Remaining yarn = Total quantity of yarns -

Number of yarns used in keeping with hats

Substituting the given parameters into the formula, we have;

y = 6 - 1.2x

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Power Query solve the problem b) Cleaning messy data

Power Query is a Microsoft Excel feature that is designed to help users extract, transform, and load data from a variety of sources. It is particularly useful for solving the problem of cleaning messy data.

Cleaning messy data is a common challenge that many people face when working with large or complex datasets. Data can be messy for a variety of reasons, such as being in an inconsistent format, having errors or typos, or containing duplicates or missing values. Cleaning up this data can be time-consuming and error-prone, especially if it is done manually.

Power Query provides a set of tools and features that make it easier to clean and transform data in Excel. It allows users to easily extract data from various sources, remove unwanted columns or rows, split or merge columns, apply filters and transformations, and more. This helps users save time and effort when working with large or complex datasets, and ensures that their data is clean and ready for analysis.

In summary, Power Query helps users solve the problem of cleaning messy data by providing a set of tools and features that make it easier to extract, transform, and load data in Excel.

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A linear equation is used to prove the mathematical result that two linear expressions, or a linear expression and a constant, are not equivalent.

The mathematical assertion that two linear expressions, or a linear expression and a constant, are not equal is made via a linear equation.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

A mathematical equation must take the form y=mx+b in order to be classified as a linear function (in which m is the slope and b is the y-intercept).

Therefore, a linear equation is used to prove the mathematical result that two linear expressions, or a linear expression and a constant, are not equivalent.

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