What is the equation of the line through (1, 6) and (0, 2)?

Y=4x - 2

Y= -4x - 2

Y= -4x + 2

Y= -4x + 2

Statistical analyses are least likely to be found in a (D) qualitative research.

Therefore, statistical analyses are least likely to be found in a (D) qualitative research.

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The sum of all five numbers in the list is 25.

According to the question,

The first number on my list of five numbers is 1, and the fifth is 5. The other figures are all one more than their two nearest neighbors' averages.

Let the list of numbers be 1,x,y,z,5.

As each of the other numbers is equal to one more than the average of its two neighbors.

x=(1+y)/2+1

2x=3+y   -(1)

Similarly,

y=(x+z)/2+1

2y=x+z+2   -(2)

z=(y+5)/2+1

2z=y+7    -(3)

Multiply equation (2) by 2 and then substitute equations (1) and (3),

4y=3+y+y+7+4

4y=2y+14

2y=14

y=14/2

y=7

From equation (1),

2x=3+7

2x=10

x=5

From equation (3),

2z=7+7

2z=14

z=14/2

z=7

The list is: 1,5,7,7,5

Sum of the numbers of list = 1+5+7+7+5 = 25

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Answer:

Negative.

Step-by-step explanation:

b is above zero. So, it is positive.

c is below zero. So, it is negative.

A positive divided by negative number results in negative.

Answer:

B. negative

Step-by-step explanation:

-2 is negative. That's why.

Answer:

A = (0, b)

B = (a, b)

Step-by-step explanation:

A is straight up from the origin and is the same height as b so it's (0, b)

B is straight up from C so the x is the same so it's (a, b)

Answer:

[tex]\displaystyle \int \dfrac{\ln x}{x^8}\:\:\text{d}x=-\dfrac{\ln x}{7x^7}- \dfrac{1}{49x^7}+\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given integral:

[tex]\displaystyle \int \dfrac{\ln x}{x^8}\:\:\text{d}x[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{1}{a^n}=a^{-n}[/tex]

[tex]\implies \displaystyle \int x^{-8}\ln x\:\:\text{d}x[/tex]

[tex]\boxed{\begin{minipage}{4.8 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}[/tex]

Using Integration by parts:

[tex]\textsf{Let }u=\ln x \implies \dfrac{\text{d}u}{\text{d}x}=\dfrac{1}{x}[/tex]

[tex]\textsf{Let }\dfrac{\text{d}v}{\text{d}x}=x^{-8} \implies v=-\dfrac{1}{7}x^{-8+1}=-\dfrac{1}{7}x^{-7}=-\dfrac{1}{7x^7}[/tex]

Therefore:

[tex]\begin{aligned}\displaystyle \int u \dfrac{dv}{dx}\:dx & =uv-\int v\: \dfrac{du}{dx}\:dx\\\\\implies \displaystyle \int x^{-8}\ln x\:\:\text{d}x & = -\dfrac{1}{7x^7}\ln x- \int -\dfrac{1}{7x^7} \cdot \dfrac{1}{x}\:\:\text{d}x\\\\& = -\dfrac{\ln x}{7x^7}+ \int \dfrac{1}{7x^8}\:\:\text{d}x\\\\& = -\dfrac{\ln x}{7x^7}+ \int \dfrac{1}{7}x^{-8}\:\:\text{d}x\\\\& = -\dfrac{\ln x}{7x^7}-\dfrac{1}{7 \cdot 7}x^{-8+1}+\text{C}\\\\& = -\dfrac{\ln x}{7x^7}- \dfrac{1}{49x^7}+\text{C}\end{aligned}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Differentiating $\ln x$}\\\\If $y=\ln x$, then $\dfrac{\text{d}y}{\text{d}x}=\dfrac{1}{x}$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

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Substitute [tex]y=\ln(x) \iff e^y = x[/tex] and [tex]dy=\frac{dx}x[/tex] to get

[tex]\displaystyle \int \frac{\ln(x)}{x^8} \, dx = \int ye^{-7y} \, dy[/tex]

Integrate by parts with

[tex]u = y \implies du = dy[/tex]

[tex]dv = e^{-7y} \, dy \implies v = -\dfrac17 e^{-7y}[/tex]

Then

[tex]\displaystyle \int u\,dv = uv - \int v\,du \\\\ \implies \int y e^{-7y} \, dy = -\dfrac17 ye^{-7y} + \frac17 \int e^{-7y} \, dy + C \\\\ ~~~~~~~~~~~~ = -\frac17 ye^{-7y} - \frac1{49} e^{-7y} + C \\\\ ~~~~~~~~~~~~ = \boxed{-\frac{\ln(x)}{7x^7} - \frac1{49x^7} + C}[/tex]

Answer: the area of the triangle is 5.

Step-by-step explanation:

[tex]A(0;0) \ \ \ \ B(1;3) \ \ \ \ C(4;2) \ \ \ \ S_{ABC}=?\\Use \ the\ formula:\\\displaystyle\\\boxed{S=\frac{1}{2}*|[(x_A-x_C)*(y_B-y_C)-(x_B-x_C)*(y_A-y_c)] |}\\x_A=0\ \ \ \ x_B=1\ \ \ \ x_C=4\ \ \ \ y_A=0\ \ \ \ \ y_B=3\ \ \ \ \ y_C=2.\\S=\frac{1}{2}*|[(0-4)*(3-2)-(1-4)*(0-2)]|\\S=\frac{1}{2}*| [(-4)*1-(-3)*(-2)]|=\\ S=\frac{1}{2}*| (-4-6)|\\S=\frac{1}{2}*|(-10)|\\S= \frac{1}{2} *10\\S=5.[/tex]

The equation y=[tex]-1/2\sqrt{x^{3} }[/tex] does not give result to y=-2/[tex]x\sqrt{x}[/tex].

Given two equations y=[tex]-1/2\sqrt{x^{3} }[/tex] and y=-2/[tex]x\sqrt{x}[/tex].

We are required to find that how the first equation will result in second equation.

Equation is like a relationship between two or more variables that are expressed in equal to form.Equation of two variables look like ax+by=c. It may be a linear equation,cubic or quadratic equation or many more depending on the power if variable.

Taking the first equation.

y=[tex]-1/2\sqrt{x^{3} }[/tex]

Interchange the power of x.

y=-1/2[tex]\sqrt{x} ^{3}[/tex]

Now multiply [tex]\sqrt{x}[/tex] three times.

y=-1/2[tex]\sqrt{x} \sqrt{x} \sqrt{x}[/tex]

Now [tex]\sqrt{x} \sqrt{x}[/tex] will result in x.

y=-1/2x[tex]\sqrt{x}[/tex]

You can see our result is not matching the second equation.

Hence the equation y=[tex]-1/2\sqrt{x^{3} }[/tex] does not give result to y=-2/[tex]x\sqrt{x}[/tex].

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Answer:

B

Step-by-step explanation:

It's B

Answer:

Option B

Step-by-step explanation:

The equation is:

[tex]y=10-2x[/tex]

when x=2

[tex]y=10-2(2)010-4=6[/tex]

When x = 3

[tex]y=10-2(3)=10-6=4[/tex]

When x=4

[tex]y=10-2(4)=10-8=2[/tex]

Hope this helps

The examples of exponential growth include bacteria population growth and compound interest and a real life example of exponential decay is radioactive decay.

Exponential growth is the pattern of data that shows sharper increases over time. Savings accounts with a compounding interest rate can show exponential growth.

There are many real-life examples of exponential decay. An example, is thatsuppose that the population of a city was 100,000 in 1980. Then every year after that, the population has decreased by 3% as a result of heavy pollution. This is an example of exponential decay.

One of the best examples of exponential growth is the observed in bacteria. It takes bacteria roughly an hour to be able to reproduce through prokaryotic fission. In this case, if we placed 100 bacteria in an environment and recorded the population size each hour, we would observe an exponential growth.

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The work done (in foot-pounds) in stretching the spring from its natural length to 0.7 feet beyond its natural length is 1.23 foot-pound

From the question given above, the following data were obtained:

F = Ke

Divide both sides by e

K = F/ e

K = 3 / 0.6

K = 5 pound/foot

Thus, the spring constant of the spring is 5 pound/foot

Wd = ½Ke²

Wd = ½ × 5 × 0.7²

Wd = 2.5 × 0.49

Wd = 1.23 foot-pound

Therefore, the work done in stretching the spring 0.7 feet is 1.23 foot-pound

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Based on the given parameters of a = 1.7 cubic feet and concrete for first 4 steps as 17 cubic feet, the concrete is required for the first 12 steps is 132.6 cubic feet

Sn = n/2 {2a + (n - 1) d}

17 = 4/2{2×1.7 + (4 - 1)d}

17 = 2{3.4 + (3)d}

17 = 2(3.4 + 3d)

17 = 6.8 + 6d

17 - 6.8 = 6d

10.2 = 6d

d = 10.2/6

Concrete required for first 12 steps;

Sn = n/2 {2a + (n - 1) d}

= 12/2{2×1.7 + (12-1)1.7}

= 6{3.4 + (11) 1.7}

= 6(3.4 + 18.7)

= 6(22.1)

= 132.6

Concrete required for first 12 steps = 132.6 cubic feet

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Answer:

132.6 cubic feet

Step-by-step explanation:

The first quartile of the dataset {1, 2, 3, 4, 5, 6} is 2.

Given data set: {1,2,3,4,5,6}

Median of the given data set =3.5

The data set can be split into 2 parts as, {1,2,3} and {4,5,6}. The first quartile is calculated by simply finding the median of the first part of the data set.

Thus, the first quartile is 2.

The quarter divides the distribution into four groups and calculates the range of values above and below the mean.

A quartile separates the dataset into four categories by dividing the data into three points: the lowest, median, and upper quartiles.

The interquartile range, a measurement of variation around the median, is calculated using quartiles.

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Answer:

  (f +g)(2) = -7

Step-by-step explanation:

Functions are added by adding their values.

  (f +g)(2) = f(2) +g(2)

  = (2 -8) +(4(2) -9) . . . . . evaluate f and g with z=2

  = -6 +(-1)

  (f +g)(2) = -7

Answer:

x = 55°

Step-by-step explanation:

x , 35° , 90° lie on a straight line and sum to 180° , that is

x + 35° + 90° = 180°

x + 125° = 180° ( subtract 125° from both sides )

x = 55°

Hi there,

please see below for solution steps :

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

⨠ add 8 and 6

[tex]\sf{2x^2+14}[/tex]

⨠ factor the 2 out

[tex]\sf{2(x^2+7)}[/tex]

Since we cannot simplify this more, we know that we've simplified completely.                                                                                   [tex]\small\pmb{\sf{Frozen \ melody}}[/tex]

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

Answer:

It gets more complicated with a six-sided die. In this case if you roll the die, there are 6 possible outcomes (1, 2, 3, 4, 5 or 6). Can you figure out what the theoretical probability for each number is? It is 1/6 or 0.17 (or 17 percent).

Answer:

600 and 200

Step-by-step explanation:

kofi  : kweku     is   3 :1

   so Kofi gets   3 out of ( 3 +1)  = 3/4 of 800  = 3/4 * 800 = 600

         kweku get s the rest   800- 600 = 200  

Step-by-step explanation:

The turn of the 20th century = 1900

So it is 1900 + 107 years ago, hence, 2007

The form of deductive reasoning used in the given argument is; Law of Syllogism

The argument we are given is;

If a number ends in 0, then it is divisible by 10.

If a number is divisible by 10, then it is divisible by 5.

If a number ends in 0, then it is divisible by 5.

The law used for the deductive reasoning in the given argument is called Law of Syllogism. This is because this law of mathematical logic states that;

If the following two statements are true:

(1) If p , then q .

(2) If q , then r .

Then we can derive a third true statement:

(3) If p , then r .

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The approximate year at which two revenues were equal is; 7.5 years

From the graph attached, we see that in the year 10, the revenue for printed ads was 2 million dollars & 3 million dollars for printed ads and online ads revenue respectively.

Thus, printed ad. Revenue line equation is;

(y - 2) = (3 - 2)(x - 10)/(0 - 10)

y - 2 = (x - 10)/-10

x - 10 = -10(y - 2)

x - 10 = -10y + 20

x - 10 = -10y + 20

x  + 10y = 30   -----(1)

At x = 12 years from the graph, we have;

12 + 10y = 30

10y = 18

y = 1.8

Thus, online ad. Revenue line equation is;

(y - 0) = ((3 - 0)/(10 - 0))(x - 0)

y = 3x/10

10y = 3x

10y - 3x = 0 -----(2)

At x = 12, we have;

10y = 3*12

10y = 36

y = 3.6

In year '12' the online ad revenue got doubled as that of printed ad revenue and afterward more than doubled.

B) The approximate year at which two revenues were equal is gotten by solving equation 1 and 2 simultaneously to get;

x = 7.5

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Answer:

7

Step-by-step explanation:

You take the corresponding side that you know which is 10.5 and you multiply that by your scale factor of 2/3.

Another name for 10.5 is 10 [tex]\frac{1}{2}[/tex]  and that can be changed to [tex]\frac{21}{2}[/tex]

([tex]\frac{21}{2}[/tex])([tex]\frac{2}{3}[/tex])  The two's cancel out and we are left with [tex]\frac{21}{3}[/tex]  Which is the same as 7.

The numerical expression, 2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3 = 67/24 on simplification using the BODMAS rule.

In the question, we are asked to simplify the numerical expression:

2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3.

To simplify the expression, we will follow the BODMAS rule, where B means Brackets, O means Of, D means Divide, M means Multiplication, A means Addition, and S means Subtraction.

2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3

= 2/3 ÷ 16 + (3/4 + 1/6) ÷ 1/3 {Solving 2⁴ = 16, before proceeding BODMAS}.

= 2/3 ÷ 16 + ((9+2)/12) ÷ 1/3 {Solving Brackets by taking LCM}

= 2/3 ÷ 16 + 11/12 ÷ 1/3 {Simplifying}

= 2/3 * 1/16 + 11/12 * 3/1 {Solving divisions by taking reciprocals}

= 1/24 + 11/4 {Multiplying}

= (1 + 66)/24 {Adding using LCM}

= 67/24 {Simplifying}.

Thus, the numerical expression, 2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3 = 67/24 on simplification using the BODMAS rule.

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The provided question is incomplete. The complete question is:

"Type the correct answer in the box. Use numerals instead of words. For this item, a non-integer answer should be entered as a fraction using / as the fraction bar.

Simplify the numerical expression.

2/3 ÷ 2⁴ + (3/4 + 1/6) ÷ 1/3

The expression has a value equal to."

The original amount of ida's rent is $56.

First consider the unknown original amount as 'x'. To find the increase or decrease, multiply the rate by the original amount 'x'. To find the final amount, add or subtract the increase or decrease to the original amount 'x' and equate this to given final amount. Solve the equation and find the original amount 'x'.

Let the original amount be x. This amount increase by 5% after increasing the amount is $59.

[tex]x+x(\frac{5}{100})=59\\\\[/tex]

[tex]x+x(\frac{1}{20})=59\\\\[/tex]

[tex]\frac{21x}{20}[/tex]  = 59

x = $56.19

Hence, The original amount be x =$56.19.

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Answer:

= – 5 – 7

Step-by-step explanation:

= –5 – 7

Answer:

1: Linear

2: Linear

Step-by-step explanation:

Scenario 1:

Equation: y=8x  (where x represents # of hours worked)

The graph would be linear.

Scenario2:

Equation: y=5x (where x is the # of boxes of donuts purchased)

The graph would be linear. ( I assumed that each box is $5 since 5/1=10/2 )

A similar situation could be: In an art shop, crayons are sold. It costs $7 for 1 box of crayons.

- The graph would be linear, and it would be constant as long as the price for each box of crayons is not changed. Equation is: y=7x

I'm not sure if this is exactly what the last question asked, pretty sure this would be an okay example.

The value of a₃₁ of the arithmetic sequence exists 77.4.

Given: a₅ = 12.4 and a₉ = : 22.4

For the arithmetic sequence a₁, a₂, a₃, ..., the n-th term exists

where d = common difference

a₅ = 12.4,

a₁ + 4d = 12.4 .........(1)

Because a₉ = 22.4,

a₁ + 8d = 22.4 .........(2)

Subtract (1) from (2), we get

a₁ + 8d - (a₁ + 4d) = 22.4 - 12.4

4d = 10

Dividing throughout by 4, we get

d = 2.5

From (1), we get

a₁ = 12.4 - 4 [tex]*[/tex] 2.5 = 2.4

a₃₁ = 2.4 + 30 [tex]*[/tex] 2.5 = 77.4

Therefore, the correct answer is a₃₁ = 77.4

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Answer:

x=10.5

Step-by-step explanation:

if the two triangles were ratios it would be like

19.3:7.2 to x:3.9

so 75.27 = 7.2x

whcih is 10.45 which is approximately 10.5

Answer:

Discount =40\%

Selling price of headphone =\$36

Solution --

we know that,

MP=SP * 100/(100-D\%)

putting values now we get,

MP = 36 * 100 / 60=60$

so, initial price of Headphone was =$60