pls help!! What is an equation of the line that passes through the (8, −7) and is parallel to the line x+2y=18?

Step-by-step explanation:

Given

5c + 9 - 2c - 7

= 3c + 2

Hope it will help :)❤

Answer:

We conclude that not more than 500 gallons of wastewater per hour, on average, is discharged into a neighboring lake.

Step-by-step explanation:

We are given that an industrial plant can discharge not more than 500 gallons of wastewater per hour, on average, into a neighboring lake.

Four one-hour periods are selected randomly over a period of one week. The following are observed:

1384, 683, 1534, 405

Let \(\mu\) = population average gallons of wastewater discharged per hour

So, Null Hypothesis, \(H_0\) : \(\mu \leq\) 500 gallons      {means that not more than 500 gallons of wastewater per hour, on the average, is discharged into a neighboring lake}

Alternate Hypothesis, \(H_A\) : \(\mu\) > 500 gallons     {means that more than 500 gallons of wastewater per hour, on the average, is discharged into a neighboring lake}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                                T.S.  =  \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\)  ~ \(t_n_-_1\)

where, \(\bar X\) = sample mean = \(\frac{\sum X}{n}\) = 1001.5 gallons

             s = sample standard deviation = \(\sqrt{\frac{\sum (X - \bar X)^{2} }{n-1} }\) = 543.79

             n = sample of periods = 4

So, the test statistics =  \(\frac{1001.5-500}{\frac{543.79}{\sqrt{4} } }\)  ~ \(t_3\)

                                    =  1.844

The value of t-test statistics is 1.844.

Since in the question we are not given with the level of significance so we assume it to be 5%. Now, at 0.05 level of significance, the t table gives a critical value of 2.353 at 3 degrees of freedom for the right-tailed test.

Since the value of our test statistics is less than the critical value of z as 1.844 < 2.353, so we have insufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that not more than 500 gallons of wastewater per hour, on average, is discharged into a neighboring lake.

The most appropriate choice for compound interest will be given by-

1) If compounded monthly, amount = $9160

2)If compounded continuously, amount = $218

What is compound interest?

If the interest on a certain principal at a certain rate over a certain period of time increases exponentially (not linearly), the interest earned is known as compound interest.

If P is the principal, r is the rate and t is the time in years,

\(A = P(1+\frac{r}{100})^n\)

Here,

Principal = $28

Rate = 4%

Time = 2010 - 1855

         = 145 years

a) If compounded monthly

Amount =

\(28(1 + \frac{4}{1200})^{145\times 12}\\28(1 + \frac{1}{300})^{1740}\\28(\frac{300+1}{300})^{1740}\\28(\frac{301}{300})^{1740}\\28 \times 327.13\\\)

$9159.56

$9160

b) If compounded continuously

Amount =

\(28 \times e^{4\times 145}\\28e^{580}\\28 \times 7.78\\\)

$217.84

$218

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Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

Answer:

177 pounds

Step-by-step explanation:

Create an equation to represent the system.

Since it's 18% more than what was used last month an equation can be written such as the one below:

(118%)( last month's cheese ) = this month's cheese

Convert the percentages into decimals by moving the decimal place at the end of 118.00 two places to the left

118% = 1.18

( 1.18 )( last month's cheese ) = this month's cheese

Next, plug in the number for last month's cheese

( 1.18 )( 150 pounds) =

177 pounds

Answer:

35

area of traingle b xh/2 5x4/2 - 10

area of square lxl - 5x5 -25

add- 35

Answer:

The answer would be 35.

Step-by-step explanation:

The area of the shape would be 35 square centimeters because if we divide the shape into 3 different shapes, a square on the bottom and 2 triangles at the top, we can multiply the square's length and width to get an area of 25. Next, we'll multiply the 2 triangles length of 4 with the width of 5 to get a total area of 20 from both of them, we'll then divide the area of 20 by 2 to get 10. Now add 20 and 10 to get 35.

The data correlation in the scatter plot above include the following: B. positive.

In Mathematics, a positive correlation is used to described a scenario in which two variables move in the same direction and are in tandem.

This ultimately implies that, a positive correlation exist when two variables have a linear relationship or are in direct proportion. Therefore, when one variable increases, the other variable generally increases, as well.

By critically observing the scatter plot shown in the image attached above, we can reasonably infer and logically deduce that there is a positive correlation between the x-values and y-values because they both increase simultaneously.

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Answer:

The derivative does not exist at the extremum (-2, 0).

Step-by-step explanation:

Given function:

\(f(x)=(x+2)^{\frac{2}{3}}\)

To differentiate the given function, use the chain rule and the power rule of differentiation.

\(\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule of Differentiation}\\\\If $y=f(u)$ and $u=g(x)$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\boxed{\begin{minipage}{5.4 cm}\underline{Power Rule of Differentiation}\\\\If $y=x^n$, then $\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}$\\\end{minipage}}\)

\(\begin{aligned}\textsf{Let}\;u &= x+2& \implies f(u) &= u^{\frac{2}{3}}\\\\\implies \dfrac{\text{d}u}{\text{d}{x}}&=1 &\implies \dfrac{\text{d}y}{\text{d}u}&=\dfrac{2}{3}u^{(\frac{2}{3}-1)}=\dfrac{2}{3}u^{-\frac{1}{3}}\end{aligned}\)

Apply the chain rule:

\(\implies f'(x) = \dfrac{\text{d}y}{\text{d}{u}} \cdot \dfrac{\text{d}u}{\text{d}{x}}\)

\(\implies f'(x) = \dfrac{2}{3}u^{-\frac{1}{3}} \cdot1\)

\(\implies f'(x) = \dfrac{2}{3}u^{-\frac{1}{3}}\)

Substitute back in u = x + 2:

\(\implies f'(x) = \dfrac{2}{3}(x+2)^{-\frac{1}{3}}\)

\(\implies f'(x) = \dfrac{2}{3(x+2)^{\frac{1}{3}}}\)

An extremum is a point where a function has a maximum or minimum value. From inspection of the given graph, the minimum point of the function is (-2, 0).

To determine the value of the derivative at (-2, 0), substitute x = -2 into the differentiated function.

\(\begin{aligned}\implies f'(-2) &= \dfrac{2}{3(-2+2)^{\frac{1}{3}}}\\\\ &= \dfrac{2}{3(0)^{\frac{1}{3}}}\\\\&=\dfrac{2}{0} \;\;\;\leftarrow \textsf{unde\:\!fined}\end{aligned}\)

As the denominator of the differentiated function at x = -2 is zero, the value of the derivative at (-2, 0) is undefined.  Therefore, the derivative does not exist at the extremum (-2, 0).

Answer:

Step-by-step explanation:

To differentiate the function y = x^4 - x, we will use the power rule of differentiation. The power rule states that if f(x) = x^n, then the derivative of f(x) is f'(x) = nx^(n-1).

So, for y = x^4 - x, we can find the derivative as follows:

y' = 4x^3 - 1

So, the derivative of the function y = x^4 - x is y' = 4x^3 - 1.

Rounding to two decimal places, the Z-score corresponding to the youngest senator of age 39 is -1.40.

To find the Z-score corresponding to a particular value in a normal distribution, we use the formula:

Z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation.

Part 1 of 2: For the oldest senator of age 85:

Z = (x - μ) / σ = (85 - 56.5) / 12.5 ≈ 2.28

Rounding to two decimal places, the Z-score corresponding to the oldest senator of age 85 is 2.28.

Part 2 of 2: For the youngest senator of age 39:

Z = (x - μ) / σ = (39 - 56.5) / 12.5 ≈ -1.4

Rounding to two decimal places, the Z-score corresponding to the youngest senator of age 39 is -1.40.

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The ratio of boxes to the circles is 7: 10

Answer:

It's option B, (f • g)(x) = 3x^3 + 6x^2 - 5x - 10

Step-by-step explanation:

In this problem, we are dealing with a branch of functions called composite functions. What the difference is between normal and composite functions is that we instead of defining a value for f(x), take two functions, f(x) and g(x), in the form of f and g. For instance, h(x) = g.

• Take the products of both functions.

f(x)g(x) = 3x²+5 • x-2

• Next, expand the functions. We expand by combining like terms.

= 3x^3 - 6x^2 + 5x - 10

Since the function cannot be simplified further, this leads to option B being our answer.

Hope this helps!

Answer:

x = 3 and x = -2

Step-by-step explanation:

The given equation is :

\(x^2-x-6=0\)

We need to solve the given equation.

We can solve it using Completing the Square method.

We take two numbers such that their product is -6 and sum is -1.

So,

\(x^2-x-6=0\\\\x^2+2x-3x-6=0\\\\x(x+2)-3(x+2)=0\\\\(x-3)(x+2)=0\\\\x=3\ and\ x=-2\)

so, the values of x are 3 and -2.

Altogether they have 85 marbles.

Given,

Randy's marbles = 50

Randy's marbles is 5/2 of Andy's marbles.

Randy's marbles is 10/3 of Peter's marbles.

Now form the linear equations,

Let Andy has x marbles.

So,

5/2 × x = 50

x = 20

Andy's marbles = 50

Let Peter has y marbles.

So,

10/3 × y = 50

y = 15

Peter's marbles = 15

Thus total marbles of Randy , Andy , Peter is 85.

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Answer:

85 marbles

Step-by-step explanation:

Andy has 20

Randy has 50

Peter has 15

Answer:

2,600.6

I think its 2,600.6 because 6% is 6 dollers I dont know if I am correct lol! but have a nice day! =)

Answer:

The points  -3, 5 and 8 are included in the solution set

Step-by-step explanation:

2 ≤ |x-3| ≤ 6

x-3 ≥ 2 or x-3 ≤ -2       -->      x ≥ 5 or x ≤ 1

-6 ≤ x-3 ≤ 6   -->  -3 ≤ x ≤ 9

-9  and -5 are smaller than -3 so they don't hold for the second inequality. -3  fits in both. but 0 and 2 don't fit in the first one.

then 5 does and 8 is included too.

The points  -3, 5 and 8 are included in the solution set

Answer:

g(x) = f(x–3) + 2

Step-by-step explanation:

If g(x) is just 3 spaces to the right and 2 spaces up from f(x), then g(x) = f(x–3) + 2

Answer:

x=√715

Step-by-step explanation:

Using Pythagorean Theorem,,

(34) ^2= (21)^2+x^2

⇒x^2= 1156-441

⇒x^2= 715

⇒x= √715

Answer:

There is no solution to the systems of equation.

Step-by-step explanation:

Graph the system by using y=mx+b

Both systems are y=2/5x+5/2.

Answer:

that guy is wrong. its the first option.

Step-by-step explanation:

i just took it

Answer:

66/8

Explanation

8x8+2=66/8  

66/8 simplafied is 33/8

Answer:

No answer do u today

Step-by-step explanation:

Lol

H hi ha job un hi is ihnihniuniunihn como te quiero

The product obtained by multiplying the numbers 0.102 and 7.3 is 0.7446.

Multiplication is one of the most elementary mathematical operations along with addition, subtraction, and division. Two numbers on being multiplied yield a number known as their product.

The multiplication of two decimal numbers always results in a decimal number.

The given numbers are 0.102 and 7.3.

The decimal 0.102 can be written as a fraction as follows:

\(0.102 = \dfrac{102}{1000}\)

        \(= \dfrac{51}{500}\)

The decimal 7.3 can be written as a fraction as follows:

\(7.3 = \dfrac{73}{10}\)

The product of both numbers is obtained as follows:

\(0.102 \times 7.3 = \dfrac{51}{500}\times \dfrac{73}{10}\)

                 \(= \dfrac{51\times73}{500\times10}\\= \dfrac{3723}{5000}\\= 0.7446\)

Thus, the given numbers on multiplication give 0.7446.

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so, we know the diameter is 8, so that means its radius is half that, or 4.

\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4\\ \theta =45 \end{cases}\implies A=\cfrac{(45)\pi (4)^2}{360}\implies A=2\pi ~ft^2\)

Answer:

The amount of fabric needed to create one quilting square is 8 inches.

Answer:

The amount of fabric needed to create one quilting square is 8 inches.

Step-by-step explanation:

162

Step-by-step explanation:

(12 square - 15 + 17) + 16

=(144 - 15 + 17) + 16

=146 + 16

=162

f the gray suitcase weighs 11 lb more than the pink suitcase, the pink suitcase weighs 5 lb than the blue suitcase, and the total of 3 suitcases is 127 lb, then the blue suitcase weighs 35.3 lb

Let the gray suitcase be represented by g

Let the pink suitcase be represented by p

Let the blue suitcase be represented by b

The gray suitcase weighs 11 lb more than the pink suitcase

g    =   p   +   11........(1)

The pink suitcase weighs 5 lb than the blue suitcase.

p   =  b  +  5

b  =  p  -  5...........(2)

Total of 3 suitcases = 127 lb

p  +  b  +  g    =  127............(3)

Substitute equations (1) and (2) into equation (3)

p  +  p  - 5 + p  +  11   =  127

3p  +  6   =  127

3p   =  127  -  6

3p   =  121

p  =  121/3

p  = 40.3 lb

Substitute p = 40.3 into equation (2)

b = p - 5

b  = 40.3  - 5

b  =  35.3

The blue suitcase weigh 35.3 lb

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Answer:

22 degrees

Step-by-step explanation:

Just do arccos(0.9272) on your calculator or just do 90 minus 68.

The solution to the inequality expression is -8/9 ≤ x ≥ 4/9

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

|3x + 6/9| ≥ 2

Expand the inequality expression

So, we have

-2 ≤ 3x + 6/9 ≥ 2

Subtract 6/9 from both sides

So, we have

-24/9 ≤ 3x ≥ 12/9

Divide through the equation by 3

-8/9 ≤ x ≥ 4/9

Hence, the solution to the inequality expression is -8/9 ≤ x ≥ 4/9

The graph is attached

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