Find the equation of the line passing through the points (2, 4) and (3, 2).​

Answer:

[tex]A=603.18\ cm^2[/tex]

Step-by-step explanation:

The length of a blade, r = 24 cm

The sweeping angle is 120°.

We need to find the total area cleaned at one sweep of the blade. The area of sector is given by :

[tex]A=\dfrac{\theta}{360}\times \pi r^2[/tex]

[tex]A=\dfrac{120}{360}\times \pi \times 24^2\\\\=603.18\ cm^2[/tex]

So, the total area cleaned at one sweep of the blade is [tex]603.18\ cm^2[/tex].

Answer:

[tex]\displaystyle \frac{d}{dx} = \frac{3x - 5}{2x^\bigg{\frac{3}{2}}}[/tex]

General Formulas and Concepts:

Algebra I

Calculus

Derivatives

Derivative Notation

Derivative Property [Addition/Subtraction]:                                                            [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

Derivative Rule [Quotient Rule]:                                                                               [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \frac{3x + 5}{\sqrt{x}}[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

Answer:

108 meters with the formula lxhxw

Options:

(2, 2), (3, 1), (4, 2)

(2, 2), (3, –1), (4, 1)

(2, 2), (1, –2), (0, 2)

(2, 2), (1, 2), (2, 0)

Answer:

A. (2, 2), (3, 1), (4, 2)  

Step-by-step explanation:

Given

[tex]y > -\frac{1}{3}x + 2[/tex]

[tex]y < 2x + 3[/tex]

Required

Solve for x and y

To solve this, we make use of graphical method (see attachment for graph)

All points that lie on the shaded region are true for the inequality

Next, we plot each of the given options on the graph

A. (2, 2), (3, 1), (4, 2)

All 3 points lie on the shaded region.

Hence, (a) is true

Answer:

A. (2, 2), (3, 1), (4, 2)  

Step-by-step explanation:

Answer:

The correct answer is:

        30 = 10 + 3h - 6

        26 = 3h

        h = 8.67

Step-by-step explanation:

We're gonna calculate by our part the hours a new costumer can rent a bike and pay a total of $30, using the original function:

Where:

We know The total money spent must be $30, by this reason, the function change to:

Now, we must clear the h variable, by this reason, we multiply 3 by h and 2:

We pass the 10 and the -6 to the left side of the equality:

Finally, we pass the 3 to the left side of the equality:

26 / 3 = h (the 3 pass to divide because is multiplying the x)

If we just use two decimals, the number of hours is:

How the third option is the one that shows this calculation and result, that is the correct answer.

9514 1404 393

Answer:

  1/3

Step-by-step explanation:

The slope of a line is the ratio of its "rise" to its "run." The "rise" is the change in vertical distance, and the "run" is the corresponding change in horizontal distance between two points on the line. The formula for the slope is ...

  [tex]m=\dfrac{y_2-y_1}{x_2-x_1}\qquad\text{where $(x_1,y_1)$ and $(x_2,y_2)$ are points on the line}[/tex]

In this problem, you are told the line passes through the origin, which is point (x, y) = (0, 0), and through point (6, 2). Using these coordinates in the slope formula gives ...

  [tex]m=\dfrac{2-0}{6-0}=\dfrac{2}{6}=\boxed{\dfrac{1}{3}}[/tex]

__

You may notice that when the line passes through the origin, the slope is simply the ratio y/x of any point on the line. Here, that ratio is 2/6 = 1/3.

_____

Additional comment

A line through the origin is the graph of a proportional relationship. That is, y is proportional to x. The slope of the line is the constant of proportionality. The equation of the line is ...

  y = kx . . . . . . where k is the constant of proportionality.

The line in this problem statement will have the equation ...

  y = (1/3)x

Answer:

sin²2θ. (cos θ sin θ). cos 2θ

Step-by-step explanation:

finding g'(x)

g'(x)

= 4 (cosθsinθ)³ . { cosθ. (sinθ)' + sinθ. (cosθ)' }

= 4 (cosθsinθ)³ { cosθ. cos θ + sinθ.(-sin θ)}

= 4 (cosθsinθ)³{ cos²θ - sin²θ}

= (4 cosθ sinθ)². (cosθ sinθ). { cos²θ - sin²θ}

= sin²2θ. (cos θ sin θ). cos 2θ

Answer:

[tex]2\frac{3}{4} +(-4\frac{1}{4} )=-1\frac{2}{4}[/tex]

Step-by-step explanation:

That's the only equation that makes sense to the number line

Answer:

Approximately [tex]4.75[/tex].

Step-by-step explanation:

Remark: this approach make use of the fact that in the original solution, the concentration of  [tex]\rm CH_3COOH[/tex] and [tex]\rm CH_3COO^{-}[/tex] are equal.

[tex]{\rm CH_3COOH} \rightleftharpoons {\rm CH_3COO^{-}} + {\rm H^{+}}[/tex]

Since [tex]\rm CH_3COONa[/tex] is a salt soluble in water. Once in water, it would readily ionize to give [tex]\rm CH_3COO^{-}[/tex] and [tex]\rm Na^{+}[/tex] ions.

Assume that the [tex]\rm CH_3COOH[/tex] and [tex]\rm CH_3COO^{-}[/tex] ions in this solution did not disintegrate at all. The solution would contain:

[tex]0.3\; \rm L \times 0.2\; \rm mol \cdot L^{-1} = 0.06\; \rm mol[/tex] of [tex]\rm CH_3COOH[/tex], and

[tex]0.06\; \rm mol[/tex] of [tex]\rm CH_3COO^{-}[/tex] from [tex]0.2\; \rm L \times 0.3\; \rm mol \cdot L^{-1} = 0.06\; \rm mol[/tex] of [tex]\rm CH_3COONa[/tex].

Accordingly, the concentration of [tex]\rm CH_3COOH[/tex] and [tex]\rm CH_3COO^{-}[/tex] would be:

[tex]\begin{aligned} & c({\rm CH_3COOH}) \\ &= \frac{n({\rm CH_3COOH})}{V} \\ &= \frac{0.06\; \rm mol}{0.5\; \rm L} = 0.12\; \rm mol \cdot L^{-1} \end{aligned}[/tex].

[tex]\begin{aligned} & c({\rm CH_3COO^{-}}) \\ &= \frac{n({\rm CH_3COO^{-}})}{V} \\ &= \frac{0.06\; \rm mol}{0.5\; \rm L} = 0.12\; \rm mol \cdot L^{-1} \end{aligned}[/tex].

In other words, in this buffer solution, the initial concentration of the weak acid [tex]\rm CH_3COOH[/tex] is the same as that of its conjugate base, [tex]\rm CH_3COO^{-}[/tex].

Hence, once in equilibrium, the [tex]\rm pH[/tex] of this buffer solution would be the same as the [tex]{\rm pK}_{a}[/tex] of [tex]\rm CH_3COOH[/tex].

Calculate the [tex]{\rm pK}_{a}[/tex] of [tex]\rm CH_3COOH[/tex] from its [tex]{\rm K}_{a}[/tex]:

[tex]\begin{aligned} & {\rm pH}(\text{solution}) \\ &= {\rm pK}_{a} \\ &= -\log_{10}({\rm K}_{a}) \\ &= -\log_{10} (1.76 \times 10^{-5}) \\ &\approx 4.75\end{aligned}[/tex].

Answer:

6 : 24

Step-by-step explanation:

If we are in the ratio of 1 to 4, the total is 1+4 = 5

Divide 30 by 5

30/5 = 6

Multiply each term in the ratio by 6

1  :4

1*6 : 4*6

6 : 24

Answer:

total ratio:

[tex] = 1 + 4 \\ = 5[/tex]

For the portion of 1:

[tex] = 30 \div \frac{1}{5} \\ = 30 \times 5 \\ = 150[/tex]

For the portion of 4:

[tex] = 30 \div \frac{4}{5} \\ = 30 \times \frac{5}{4} \\ = 37.5[/tex]

= 30 : 7.5

Answer:

for each dress she used 6/3 of material

=2

then for a curtain =2x4=8 materials

Answer:

RA = 24

Step-by-step explanation:

Since the triangle is isosceles ( 2 equal sides ) , then LU is a perpendicular bisector , so

AU = RU , that is

4r = 18 - 2r ( add 2r to both sides )

6r = 18 ( divide both sides by 6 )

r = 3

Then

RA = 18 - 2r + 4r = 18 + 2r = 18 + 2(3) = 18 + 6 = 24

Answer:

∠ BCA = 90°

Step-by-step explanation:

∠ BCA is an angle in the semicircle and equals 90°

Answer:

is opposite line BC. Answer is letter E.

Answer:

13.4 cubic feet and 23040 inches

Step-by-step explanation:

Answer:

In cubic feet =  13.3 ft^3 ...........or 13.33ft^3

In cubic inches = 23040in^3

Step-by-step explanation:

In cubic feet it becomes

4(5) = 20 feet ^2   ................but we need volume in feet

so 8 inches = .............2/3 of a foot = 0.666667

Answer therefore is   (4) x (5) x (0.666667) = 13.32ft^3

In cubic inches it becomes

4 x 12 = 48 inches

5  x 12  = 60 inches

and 8 inches

48 x 60 x 8 = 23040 in^3

We check by squaring the divider

23040/12^3 = 13.333

We only square and square again to find a cube but to square once we do this with area too.

Area 1. =  4 x 5 = 20 feet^2

Area 2. =  48 x 60 = 2880 in ^2  / 12^2 = 20

Answer: yes

Step-by-step explanation:

Answer: 12

Step-by-step explanation: Whenever you have a minus a negative in a problem, you can change it to plus a positive.

So we can think of 7 - (-5) as 7 + (+5).

Whenever we have two negatives in a row, we can think of those

negatives as being multiplied together and a negative times a negative

will always result in a positive.

So just add 7 + 5 to get 12.

Answer:

A. c = -7

Step-by-step explanation:

Standard form of a quadratic equation is given as ax² + bx + c = 0, where,

a, b, and c are known values not equal to 0,

x is the variable.

Given a quadratic equation of -x² + 4x - 7, therefore,

a = -1

b = 4

c = -7

Answer:

-3a+3bx+2ab

Step-by-step explanation:

Hi there!

[tex]\large\boxed{\frac{dy}{dx} = \frac{1}{2\sqrt{x}}sec^{-1}(\sqrt{x}) + \frac{1}{2|\sqrt{x}|\sqrt{{x} - 1}}}[/tex]

[tex]y = \sqrt{x} * sec^{-1}(-\sqrt{x}})[/tex]

Use the chain rule and multiplication rules to solve:

g(x) * f(x) = f'(x)g(x) + g'(x)f(x)

g(f(x)) = g'(f(x)) * 'f(x))

Thus:

f(x) = √x

g(x) = sec⁻¹ (√x)

[tex]\frac{dy}{dx} = \frac{1}{2\sqrt{x}}sec^{-1}(\sqrt{x}) + \sqrt{x} * \frac{1}{\sqrt{x}\sqrt{\sqrt{x}^{2} - 1}} * \frac{1}{2\sqrt{x}}[/tex]

Simplify:

[tex]\frac{dy}{dx} = \frac{1}{2\sqrt{x}}sec^{-1}(\sqrt{x}) + \sqrt{x} * \frac{1}{2|x|\sqrt{{x} - 1}}[/tex]

[tex]\frac{dy}{dx} = \frac{1}{2\sqrt{x}}sec^{-1}(\sqrt{x}) + \frac{1}{2|\sqrt{x}|\sqrt{{x} - 1}}[/tex]

Answer:

[tex]\displaystyle y' = \frac{arcsec(\sqrt{x})}{2\sqrt{x}} + \frac{1}{2|\sqrt{x}|\sqrt{x - 1}}[/tex]

General Formulas and Concepts:

Algebra I

Calculus

Derivatives

Derivative Notation

Basic Power Rule:

Derivative Rule [Product Rule]:                                                                             [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Arctrig Derivative:                                                                                                 [tex]\displaystyle \frac{d}{dx}[arcsec(u)] = \frac{u'}{|u|\sqrt{u^2 - 1}}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = \sqrt{x}sec^{-1}(\sqrt{x})[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

Answer:

a) 0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

b) 0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

c) 0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

d) None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.

This means that [tex]\mu = 273, \sigma = 100[/tex]

A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?

Sample of 30 means that [tex]n = 30, s = \frac{100}{\sqrt{30}}[/tex]

The probability is the p-value of Z when X = 273 + 16 = 289 subtracted by the p-value of Z when X = 273 - 16 = 257. So

X = 289

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{289 - 273}{\frac{100}{\sqrt{30}}}[/tex]

[tex]Z = 0.88[/tex]

[tex]Z = 0.88[/tex] has a p-value of 0.8106

X = 257

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{257 - 273}{\frac{100}{\sqrt{30}}}[/tex]

[tex]Z = -0.88[/tex]

[tex]Z = -0.88[/tex] has a p-value of 0.1894

0.8106 - 0.1894 = 0.6212

0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?

Sample of 30 means that [tex]n = 50, s = \frac{100}{\sqrt{50}}[/tex]

X = 289

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{289 - 273}{\frac{100}{\sqrt{50}}}[/tex]

[tex]Z = 1.13[/tex]

[tex]Z = 1.13[/tex] has a p-value of 0.8708

X = 257

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{257 - 273}{\frac{100}{\sqrt{50}}}[/tex]

[tex]Z = -1.13[/tex]

[tex]Z = -1.13[/tex] has a p-value of 0.1292

0.8708 - 0.1292 = 0.7416

0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?

Sample of 30 means that [tex]n = 100, s = \frac{100}{\sqrt{100}}[/tex]

X = 289

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{289 - 273}{\frac{100}{\sqrt{100}}}[/tex]

[tex]Z = 1.6[/tex]

[tex]Z = 1.6[/tex] has a p-value of 0.9452

X = 257

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{257 - 273}{\frac{100}{\sqrt{100}}}[/tex]

[tex]Z = -1.6[/tex]

[tex]Z = -1.6[/tex] has a p-value of 0.0648

0.9452 - 0.0648 =

0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?

None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

C is actually 0.8904

for anybody else stuck on this wondering why cengage is telling you c is wrong

Answer:

262.5 miles

Step-by-step explanation:

Correct me if I am wrong

Answer:

150 dollars. if I am wrong correct me

Answer:

C and D

Step-by-step explanation:

15 to 30 galons at $9.95 to $21.00

the minimum amount can be found by calculating the minimum amount sold at a minimum price 15*9.95 = $149.25

the maximum amount can be found by calculating the maximum amount sold at a maximum price 30*21 = $630

there are 2 choices that are between 149.25 and 630, C, and D

Answer:

The correct answer is "1668". A further solution is provided below.

Step-by-step explanation:

According to the question,

Estimated proportion,

[tex]\hat{p} = \frac{574}{1007}[/tex]

  [tex]=0.57[/tex]

Margin of error,

E = 0.02

Level of confidence,

= 90%

= 0.90

Critical value,

[tex]Z_{0.10}=1.65[/tex]

Now,

⇒  [tex]0.02=1.65\times \sqrt{\frac{0.57\times 0.43}{n} }[/tex]

 [tex]0.0004=2.7225\times \frac{0.2451}{n}[/tex]

         [tex]n=\frac{2.7225\times 0.2451}{0.0004}[/tex]

             [tex]=1668.21[/tex]

or,

         [tex]n \simeq 1668[/tex]

Answer:

b.

Graph B

Step-by-step explanation:

We are given the following linear equation:

[tex]6x = y + 8[/tex]

When x = 0:

[tex]6(0) = y + 8[/tex]

[tex]y = -8[/tex]

Thus, the line goes through (0,-8).

When y = 4:

[tex]6x = y + 8[/tex]

[tex]6x = 4 + 8[/tex]

[tex]6x = 12[/tex]

[tex]x = \frac{12}{6} = 2[/tex]

So also through (2,4).

Thus means that the correct answer is given by Graph B.

Volume of the 3d composite figure is,

(7×6×5)+(7×6×5)/3

= 210+70

= 280 cm³

Relationship between the two volumes,

Volume of the rectangular prism is 3 times the volume of the pyramid.

Answered by GAUTHMATH

Answer:

I was gonna anwer it but somone already did.

Step-by-step explanation:

Hi there!  

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I believe your answer is:  

Quadrant III

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Here’s why:  

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See the attached picture for reference.

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»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.