Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

y = ln 5x, y = 2, y = 3, x = 0; about the y-axis

2.Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

y2 = 2x, x = 2y; about the y-axis

3.Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

y = x, y = 0, x = 2, x = 7; about x = 1

Answer:

It's written as

[tex]6.83 \times {10}^{ - 2} [/tex]

Hope this helps you

Answer:

6.83 × 10 -2

hopefully this helped :3

Answer:

69.9 mg

Step-by-step explanation:

A = A₀ (½)^(t / T)

where A is the final amount,

A₀ is the initial amount,

t is time,

and T is the half life.

A = 400 (½)^(4000 / 1590)

A = 69.9 mg

Answer:

a) sinx = 3/5

b) cosx = 4/5

c) line OZ = 3cm

Step-by-step explanation:

Two different questions are stated here:

The first is rectangle ABCD where two of its sides are given and we are to find line OZ

The second is on trigonometry. We have been given the tangent ratio and we are to find the sine and cosine ratio.

1) Rectangle ABCD dimensions:

AB = 2cm

CD = 6cm

So we know when we are drawing the rectangle, the smallest side = 2cm and biggest side = 6cm

AO is perpendicular to OB

Line OZ cuts line AB into two

Find attached the diagram

To determine Line OZ, we would apply tangent rule since we know adjacent but opposite is missing.

All 4 angles in a rectangle = 90°

∠OAZ = 45

tan 45 = opposite/adjacent

tan 45 = OZ/3

OZ = 3 × tan45

OZ = 3×1

OZ = 3cm

2) tanx = 3/4

Tangent ratio = opposite/adjacent

opposite = 3, adjacent = 4

see attachment for diagram

Sinx = opposite/hypotenuse

Using Pythagoras theorem

hypotenuse² = opposite² + adjacent²

hypotenuse² = 3²+4² = 9+16 = 25

hypotenuse = √25

hypotenuse = 5

Sinx = opposite/hypotenuse

Sinx = 3/5

Cosx = adjacent/hypotenuse

Cosx = 4/5

a) 3/5

b) 4/5

c) 3cm

Answer:

Rate of change of function 1: ZERO

Rate of change of function 2: TWO

The rate of change of function 2 is 2 more than the rate of change of function 1.

Step-by-step explanation:

Hope this helps and please mark as brainiest!

Answer:

The answer is 2.

Step-by-step explanation:

Answer: a) P(1&2 =defect)= 1/800

b)  P(1&2 =defect)= 1/780

Step-by-step explanation:

a) The probability that 1st of the selected fuses is defective is   2/40=1/20 =0.05

So if we replace it by the not defective the number of defective fuses is 1 and total number is 40.

So the probability that 2-nd selected fuse is defective as well is 1/40

The probability both fuses are defective is

P(1&2 =defect)= 2/40*1/40=2/1600=1/800

b) The probability that 1st of the selected fuses is defective is   2/40=1/20 =0.05

SO residual amount of the fuses is 39. 1 of them is defective.

So the probability that 2-nd selected fuse is defective as well is 1/39

The probability both fuses are defective is

P(1&2 =defect)= 2/40*1/39=2/1560=1/780

Answer:

y - 2 = (3/2)(x + 1)

Step-by-step explanation:

Start with the point-slope formula y - k = m(x - h).  With m = 3/2, h = -1 and k = 2, we get:

y - 2 = (3/2)(x + 1)

Answer:

Step-by-step explanation:

x-4 greater or equal 0

x greater or equal 4

Answer:

The actual answer is x is greater than or equal to 6 (i used the answer that was on here and got it wrong so here is the correct answer!!)

just did the test on edg 2021

Answer:

A*B= [tex]\left[\begin{array}{cc}705&80\\121&14 \end{array}\right][/tex]

Step-by-step explanation:

Given A=  [tex]\left[\begin{array}{cc}5&25\\1&4\end{array}\right] \left[\begin{array}{cc}41&6\\20&2\end{array}\right][/tex] = B

Finding A*B means multiplying the first row with the first column and first row with the second column would give the first row elements. The second ro0w elements are obtained by multiplying the second row with the 1st column and second row with the second column.

so A*B= [tex]\left[\begin{array}{cc}5*41+ 25*20&5*6 + 25*2\\ 1*41+4*20 & 1*6+ 4*2\end{array}\right][/tex]

Now multiply and add the separate elements of the matrix A*B=

[tex]\left[\begin{array}{cc}205+500&30+50\\41+80&6+8\end{array}\right][/tex]

A*B= [tex]\left[\begin{array}{cc}705&80\\121&14 \end{array}\right][/tex]

b. The 1st element of the 1st row shows the salaries of the managers and 2nd element of the 1st row the salaries of associates at the restaurant . The second row 1 st element shows the benefits of the managers and 2nd element the benefits of the associates at the food truck.

c. The total cost of salaries for all employees (managers and associates) at the restaurant = 705 + 80 = 785

Total cost of benefits for all employees at the food truck= 121 + 14= 135

Answer:

The approximate probability that the market will have a proportion of fish with dangerously high levels of mercury that is more than two standard errors above 0.15 is 0.95.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

 [tex]\mu_{\hat p}=0.15[/tex]

The standard deviation of this sampling distribution of sample proportion is:

 [tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]

As the sample size is large, i.e. n = 150 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by the normal distribution.

Compute the mean and standard deviation as follows:

[tex]\mu_{\hat p}=0.15\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.15(1-0.15)}{150}}=0.0292[/tex]

So, [tex]\hat p\sim N(0.15, 0.0292^{2})[/tex]

In statistics, the 68–95–99.7 rule, also recognized as the empirical rule, is a shortcut used to recall that 68%, 95% and 99.7% of the Normal distribution lie within one, two and three standard deviations of the mean, respectively.

Then,

                                  P (µ-σ < X < µ+σ) ≈ 0.68

                                  P (µ-2σ <X < µ+2σ) ≈ 0.95

                                  P (µ-3σ <X < µ+3σ) ≈ 0.997

Then the approximate probability that the market will have a proportion of fish with dangerously high levels of mercury that is more than two standard errors above 0.15 is 0.95.

That is:

[tex]P(\mu_{\hat p}-2\sigma_{\hat p}<\hat p<\mu_{\hat p}+2\sigma_{\hat p})=0.95\\\\P(0.15-2\cdot0.0292<\hat p<0.15+2\cdot0.0292)=0.95\\\\P(0.092<\hat p<0.208)=0.95[/tex]

Answer:

For the function [tex]f(x)=\frac{1}{x} +3[/tex]. The domain is [tex]\left(-\infty \:,\:0\right)\cup \left(0,\:\infty \:\right)[/tex] and the range is  [tex]\left(-\infty, 3\right) \cup \left(3, \infty\right)[/tex].

For the function [tex]g(x) =\sqrt{x+6}[/tex]. The domain is [tex]\left[-6, \infty\right)[/tex] and the range is [tex]\left[0, \infty\right)[/tex].

Step-by-step explanation:

The domain of a function is the set of input or argument values for which the function is real and defined.

The range of a function is the complete set of all possible resulting values of the dependent variable, after we have substituted the domain.

[tex]f(x)=\frac{1}{x} +3[/tex] is a rational function.  A rational function is a function that is expressed as the quotient of two polynomials.

Rational functions are defined for all real numbers except those which result in a denominator that is equal to zero (i.e., division by zero).

The domain of the function is [tex]\left(-\infty \:,\:0\right)\cup \left(0,\:\infty \:\right)[/tex].

The range of the function is [tex]\left(-\infty, 3\right) \cup \left(3, \infty\right)[/tex].

[tex]g(x) =\sqrt{x+6}[/tex] is a square root function.

Square root functions are defined for all real numbers except those which result in a negative expression below the square root.

The expression below the square root in [tex]g(x) =\sqrt{x+6}[/tex] is [tex]x+6[/tex]. We want that to be greater than or equal to zero.

[tex]x+6\geq 0\\x\ge \:-6[/tex]

The domain of the function is [tex]\left[-6, \infty\right)[/tex].

The range of the function is [tex]\left[0, \infty\right)[/tex].

Answer:

Step-by-step explanation:

A=2(3.14)rh+2(3.14)r^2

A=2(3.14)(4.5)(19)+2(3.14)(4.5)^2

A=536.94+127.17

A=664.11

Might want to double the math but the formula is right!

Answer:

[tex]approx. = 85.28 {ft}^{2} [/tex]

Step-by-step explanation:

You can think of this as adding the area of the rectangular portion of the deck (length x width) and the semicircular portion (πr^2)/2.

(l×w)+(πr^2)/2

(10×7)+((π2^2)/2

79+2π

[tex]approx. = 85.28 {ft}^{2} [/tex]

Answer:

 $624.90

Step-by-step explanation:

The total cost is the integral of the marginal cost. Here, you're asked to approximate that integral using 5 equal-width rectangles. The area of each rectangle is the product of its height and width. The height is given by the function value at the left end of the interval.

The table shows the function values at the left end of each of the 5 intervals. The intervals have width 1600/5 = 320. The total estimated cost is the sum of products of 320 and each of the table values. (Of course, 320 can be factored out of the sum to make the math easier.)

The estimated cost is ...

  320(58 + 50.576 + 41.104 + 29.584 +16.016) = 62,489.6 . . . cents

  ≈ $624.90 . . . . cost of manufacturing 1600 yards of fancy ribbon

Answer:

a)

The object slowing down  S = -72 centimetres after t = 4 seconds

b)

The speed is decreasing at t = -2 seconds

The objective function  S = 36 centimetres

Step-by-step explanation:

Step(i):-

Given  S = t³ - 3 t² - 24 t + 8 ...(i)

   Differentiating equation (i) with respective to 'x'

       [tex]\frac{dS}{dt} = 3 t^{2} - 3 (2 t) - 24[/tex]

     Equating Zero

      3 t ² - 6 t - 24 = 0

 ⇒   t² - 2 t - 8   = 0

 ⇒  t² - 4 t + 2 t - 8 = 0

⇒ t (t-4) + 2 (t -4) =0

⇒  ( t + 2) ( t -4) =0

⇒ t = -2 and t = 4

 Again differentiating with respective to 'x'

   [tex]\frac{d^{2} S}{dt^{2} } = 6 t - 6[/tex]

Step(ii):-

Case(i):-

Put t= -2

[tex]\frac{d^{2} S}{dt^{2} } = 6 t - 6 = 6 ( -2) -6 = -12 -6 = -18 <0[/tex]

The  maximum object

S = t³ - 3 t² - 24 t + 8

S = ( -2)³ - 3 (-2)² -24(-2) +8

S = -8-3(4) +48 +8

S = - 8 - 12 + 56

S = - 20 +56

S = 36

Case(ii):-

   put  t = 4

[tex]\frac{d^{2} S}{dt^{2} } = 6 t - 6 = 6 ( 4) -6 = 24 -6 = 18 >0[/tex]

The object slowing down at t =4 seconds

The minimum objective function

S = t³ - 3 t² - 24 t + 8

S = ( 4)³ - 3 (4)² -24(4) +8

S =  64 -48 - 96 +8

S = - 72

The object slowing down  S = -72 centimetres after t = 4 seconds

Final answer:-

The object slowing down  S = -72 centimetres after t = 4 seconds

The speed is decreasing at t = -2 seconds

The objective function  S = 36 centimetres

Answer:

D. A=(9)(4)

Step-by-step explanation:

area= length x width = 9x4

Answer:

13

Step-by-step explanation:

p^2 -6p +6

Let p=-1

(-1)^2 -6(-1) +6

1 +6+6

13

Answer:

The picture isn't very clear but I think this is the answer.

1. 15 cents

2. $1.31

3. 30 cents

Step-by-step explanation:

1. 10+5

2. 50+50+10+10+10+1

3. 25+5

Answer:

A and B are independent because P(A) * P(B) = P(A and B).

Step-by-step explanation:

If A and B are independent, then P(A) * P(B) = P(A and B)

since

P(A)*P(B) = (2/3*1/4) = 2/12 = 1 / 6 = P(A and B)

A and B are independent.

Answer:

YES THANKS FOR 30

Step-by-step explanation:

Answer:

B. No solution.

Step-by-step example

I will try to solve your system of equations.

3x−y=4;6x−2y=7

Step: Solve3x−y=4for y:

3x−y+−3x=4+−3x(Add -3x to both sides)

−y=−3x+4

−y

−1

=

−3x+4

−1

(Divide both sides by -1)

y=3x−4

Step: Substitute3x−4foryin6x−2y=7:

6x−2y=7

6x−2(3x−4)=7

8=7(Simplify both sides of the equation)

8+−8=7+−8(Add -8 to both sides)

0=−1

Therefore, there is no solution, and the lines are parallel.

Answer:

  33 units²

Step-by-step explanation:

A (graphing) calculator shows you that f(4) ≈ 8, and f(8) ≈ 8.5. The curve is almost a straight line between, so the area is approximately ...

  A = (1/2)(8 + 8.5)(4) = 33

__

If you do the integration, it gets a bit messy.

  [tex]\displaystyle\dfrac{5}{7}\int_4^8{x^{2/7}}\,dx+\dfrac{1}{2}\int_4^8{x^{4/9}}\,dx+\int_4^8{6}\,dx\\\\=\left.\left(\dfrac{5}{9}x^{9/7}+\dfrac{9}{26}x^{13/9}+6x\right)\right|_4^8\approx 33.16[/tex]

The appropriate answer choice is 33 square units.

Answer:

x = 4.5 ft

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{18}{x}[/tex] = [tex]\frac{8}{2}[/tex] ( cross- multiply )

8x = 36 ( divide both sides by 8 )

x = 4.5

Answer:

The percent of increase is 25%

Step-by-step explanation:

Percentage increase = increase in price/original price × 100 = ($250 - $200)/$200 × 100 = $50/$200 × 100 = 25%

Answer:

4

Step-by-step explanation:

25% of 25

0.25 × 25 = 6.25

15% of 15​

0.15 × 15 = 2.25

Find the difference.

6.25 - 2.25

= 4

Answer:

Step-by-step explanation:

g(x) = |x-3| is neither even nor odd; the graph is not symmetric about the y-axis (as characterizes even functions), and is not symmetric about the origin either.

g(x) = x + x is actually g(x) = 2x, which is an odd function.  The graph is symmetric about the origin.

Answer:

The 68% confidence interval is (6.3, 6.7).

The 95% confidence interval is (6.1, 6.9).

The 99.7% confidence interval is (5.9, 7.1).

Step-by-step explanation:

The Central Limit Theorem states that if we have a population with mean μ and standard deviation σ and take appropriately huge random-samples (n ≥ 30) from the population with replacement, then the distribution of the sample-means will be approximately normally distributed.

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\bar x[/tex]

And the standard deviation of the sample means (also known as the standard error)is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}} \ \text{or}\ \frac{s}{\sqrt{n}}[/tex]

The information provided is:

[tex]n=400\\\\\bar x=6.5\\\\s=4[/tex]

As n = 400 > 30, the sampling distribution of the sample-means will be approximately normally distributed.

(a)

Compute the 68% confidence interval for population mean as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]

    [tex]=6.5\pm 0.9945\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.1989\\\\=(6.3011, 6.6989)\\\\\approx (6.3, 6.7)[/tex]

The 68% confidence interval is (6.3, 6.7).

The margin of error is:

[tex]MOE=\frac{UL-LL}{2}=\frac{6.7-6.3}{2}=0.20[/tex]

(b)

Compute the 95% confidence interval for population mean as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]

    [tex]=6.5\pm 1.96\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.392\\\\=(6.108, 6.892)\\\\\approx (6.1, 6.9)[/tex]

The 95% confidence interval is (6.1, 6.9).

The margin of error is:

[tex]MOE=\frac{UL-LL}{2}=\frac{6.9-6.1}{2}=0.40[/tex]

(c)

Compute the 99.7% confidence interval for population mean as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]

    [tex]=6.5\pm 0.594\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.392\\\\=(5.906, 7.094)\\\\\approx (5.9, 7.1)[/tex]

The 99.7% confidence interval is (5.9, 7.1).

The margin of error is:

[tex]MOE=\frac{UL-LL}{2}=\frac{7.1-5.9}{2}=0.55[/tex]

Answer:

c. there might not be any causal relationship between x and y.

Step-by-step explanation:

A correlation can be defined as a numerical measure of the relationship between existing between two variables (x and y).

In Mathematics and Statistics, a group of data can either be negatively correlated, positively correlated or not correlated at all.

1. For a negative correlation: a set of values in a data increases, when the other set begins to decrease. Here, the correlation coefficient is less than zero (0).

2. For a positive correlation: a set of values in a data increases, when the other set also increases. Here, the correlation coefficient is greater than zero (0).

3. For no or zero correlation: a set of values in a data has no effect on the other set. Here, the correlation coefficient is equal to zero (0).

If two variables, x and y, have a very strong linear relationship, then there might not be any causal relationship between x and y.

A causal relation exists between two variables (x and y), if the occurrence of the first causes the other; where, the first variable (x) is referred to as the cause while the second variable (y) is the effect.

A strong linear relationship exists between two variables (x and y), if they both increases or decreases at the same time. It usually has a correlation coefficient greater than zero or a slope of 1.

Hence, if two variables, x and y, have a very strong linear relationship, then there might not be any causal relationship between x and y.

Hey there! I'm happy to help!

The domain is all of the x-values of a relation and the range is all of the y-values. When you write them out, you order the numbers from least to greatest and put it in brackets.

The domain of our relation is the x-values of these points, which are 11, 9, 7, and 5. The domain is  {5,7,9,11}.

The range is the y-values, which are 1, 2, 3, and 4. So, the range is {1,2,3,4}.

Now you can find the domain and range given a few ordered pairs!

Have a wonderful day!

Answer:

See Explanation

Step-by-step explanation:

(a)For matrices A and C, given that: [tex]CA=I_n[/tex].

We want to show that Ax=0 has only the trivial solution

If Ax=0

Multiply both sides by C

[tex]C(Ax)=C \times 0\\\implies (CA)x=0$ (Recall: CA=I_n)\\\implies I_nx=0 $ (Since I_n$ is the n\times n$ identity matrix)\\\implies x=0[/tex]

This means that the system has only the trivial solution.

(b)If the system has more columns than rows, a free variable would occur when a column does not have a pivot. This would lead to a non-trivial solution.

Answer:

A

Step-by-step explanation:

For point-slope form, you need a point and the slope.

y - y₁ = m(x - x₁)

Looking at the graph, the points you have are (4, 0) and (-4, -4).  You can use these points to find the slope.  Divide the difference of the y's by the difference of the x's/

-4 - 0 = -4

-4 - 4 = -8

-4/-8 = 1/2

The slope is 1/2.  This cancels out choices C and D.

With the point (-4, -4), A is the answer.

the equation of the line in slope-intercept form is:

y = (1/2)x - 2

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. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

From the graph, two points on the line are (-4, -4) and (4,0),

The formula for the slope of a line is:

m = (y₂ - y₁) / (x₁ - x₁)

where (x₁, y₁) and (x₂, y₂) are two points on the line.

Using the given points (-4, -4) and (4, 0), we can calculate the slope:

m = (0 - (-4)) / (4 - (-4))

m = 4 / 8

m = 1/2

Now that we know the slope, we can use the slope-intercept form of a line, which is:

y = mx + b

where m is the slope and b is the y-intercept.

To find the y-intercept, we can use one of the given points on the line. Let's use the point (-4, -4):

y = mx + b

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

-4 = -2 + b

b = -2

Therefore, the slope-intercept form of the line is y = (1/2)x - 2.

Learn more about Linear equations here:

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