Let s be the solid obtained by rotating the region shown in the figure about the y-axis (Assume a = 5 and b = 2)


Sketch a typical approximating shell.


What are its circumference c and height h?


c(x) =


h(x) =


Use shells to find the volume V of S.


V =

Answer:

The smallest angle of the triangle is 33.030°.

Step-by-step explanation:

The angles of triangle can be determined with the help of the Law of Cosine and the fact that sum of all angles equals to 180°:

[tex]\cos A = -\frac{6^{2}-9^{2}-11^{2}}{2\cdot (9)\cdot (11)}[/tex]

[tex]\cos A = 0.838[/tex]

[tex]A \approx 33.030^{\circ}[/tex]

[tex]\cos B = -\frac{9^{2}-6^{2}-11^{2}}{2\cdot (6)\cdot (11)}[/tex]

[tex]\cos B = 0.575[/tex]

[tex]B \approx 54.847^{\circ}[/tex]

[tex]C = 180^{\circ} - A - B[/tex]

[tex]C = 180^{\circ} - 33.030^{\circ} - 54.847^{\circ}[/tex]

[tex]C = 92.123^{\circ}[/tex]

The smallest angle of the triangle is 33.030°.

Answer:

[tex] t = \frac{504.9m}{49.5 m/h}= 10.2[/tex]

And the best option would be:

10.2 h

Step-by-step explanation:

We have the following formula for the distance:

[tex] d = rt[/tex]

And we want to find the value of t with r = 49.5 m/h and d = 504.9 m. If we solve from t we got:

[tex] t = \frac{d}{r}[/tex]

And replacing the info given we got:

[tex] t = \frac{504.9m}{49.5 m/h}= 10.2[/tex]

And the best option would be:

10.2 h

Answer:

[tex]\bold{METHOD\ 2:}\\\\\text{Substitute the values of}\ r=49.5\ \dfrac{m}{h}\ \text{and}\ d=504.9\ m\ \text{to the formula}\ d=rt:\\\\504.9\ m=49.5\ \dfrac{m}{h}\cdot t\\\\\text{solve for}\ t:\\\\49.5\ \dfrac{m}{h}\cdot t=504.9\ m\qquad\text{divide both sides by}\ 49.5\ \dfrac{m}{h}\\\\t=504.9\ m:\left(49.5\ \dfrac{m}{h}\right)\\\\t=\dfrac{504.9}{49.5}\ m\!\!\!\!\!\diagup\cdot\dfrac{h}{m\!\!\!\!\!\diagup}\\\\t=10.2\ h[/tex]

Step-by-step explanation:

[tex]\bold{METHOD\ 2:}\\\\\text{Substitute the values of}\ r=49.5\ \dfrac{m}{h}\ \text{and}\ d=504.9\ m\ \text{to the formula}\ d=rt:\\\\504.9\ m=49.5\ \dfrac{m}{h}\cdot t\\\\\text{solve for}\ t:\\\\49.5\ \dfrac{m}{h}\cdot t=504.9\ m\qquad\text{divide both sides by}\ 49.5\ \dfrac{m}{h}\\\\t=504.9\ m:\left(49.5\ \dfrac{m}{h}\right)\\\\t=\dfrac{504.9}{49.5}\ m\!\!\!\!\!\diagup\cdot\dfrac{h}{m\!\!\!\!\!\diagup}\\\\t=10.2\ h[/tex]

Answer:

Actually, a loaf of bread costs 1.5. Barbara was wrong but only by 10 pence

Step-by-step explanation:

1 box of eggs = 1.2

3 boxes of eggs =3*1.2=3.6

1 jar of mayonnaise =1.8

2 loves of bread=2x

Total price of her purchases =10-1.6=8.4

Setting up the equation:

3.6+1.8+2x=8.4

Solving for x

2x=8.4-3.6-1.8

2x=3

x=3/2=1.5

Answer:

(x-8)(x^2-2)

Step-by-step explanation:

take x common from the first 2 terms and take -2 common from the last two terms. Then, take (x-8) common.

x^2(x-8)-2(x-8) = (x-8)(x^2-2)

Answer:

4,775.329156626506‬

Step-by-step explanation:

Answer:

-6x-10=20

Collect like terms

-6x=20+10

-6x=30

Divide both sides by -6

x=30/6

x=5

Answer:

-2+2x=y

Step-by-step explanation:

got it correct on imagine math

Answer:

x = 2, y = 1

Step-by-step explanation:

2x+3y = 7

y = 6x -11

Substitute the second equation in for y in the first equation

2x +3( 6x - 11) = 7

Distribute

2x+18x - 33 = 7

Combine like terms

20x - 33 = 7

Add 33 to each side

20x -33+33= 7+33

20x = 40

Divide each side by 20

20x/20 = 40/20

x= 2

Now find y

y = 6x-11

y = 6*2-11

y = 12-11

y =1

Answer:

B (2,1)

Step-by-step explanation:

X = 2, y = 1

$285×15/100

= $42.75 and this is the discount

$285-42.75 = $242.25

Sally will buy the bicycle at $ 242.25

Answer:

There are two limo companies that charge based on the number of people, x, that they carry. Limo A charges $30 plus $4 per person. Limo B charges $70 plus $2 per person. How many people can ride to make the two companies charge the same amount?

Step-by-step explanation:

The correct situation is the third one, this is because the expression we have is:

[tex]30+4x=70+2x[/tex]

let's take the left side as the charge of the company limo A, and the left side as the charge of limo B.

Since 'x' is the number of people, the left side tells us that limo A charges $4 per person (hence the 4x) and adds an additional $30 (hence the 30 added on the left side).

And the right side tells us that limo B charges $2 per person (hence the 2x) and adds an additional $70 (hence the 70 added on the right side).

And since we have an equal sign this means that the expression represents the number of people that can ride and will pay an equal amount in each company.

This is the situation that the third option describes:

There are two limo companies that charge based on the number of people, x, that they carry. Limo A charges $30 plus $4 per person. Limo B charges $70 plus $2 per person. How many people can ride to make the two companies charge the same amount?

Answer:

7 + 5a

Step-by-step explanation:

3-(- 2a -4)+3a = 3+2a +4 +3a = 7 + 5a

Answer:

Step-by-step explanation:

Answer:

A(1) = -7

A(4) = -48

A(8) = -769

Step-by-step explanation:

[tex]A(n) = -3.2 ^n - 1.....(1)\\\\Plug \: n= 1\: in \: (1)\\A(1) = -3.2 ^1 - 1 =-3.2-1= -6 -1 \\\huge\red{\boxed{A(1) = -7}}\\\\Plug \: n= 4\: in \: (1)\\A(4) = -3.2 ^4 - 1 =-3.16-1= -48 -1 \\\huge\purple{\boxed{A(4) = -49}}\\\\Plug \: n= 8\: in \: (1)\\A(8) = -3.2 ^8 - 1 =-3.256-1= -768 -1 \\\huge\orange{\boxed{A(8) = -769}}[/tex]

Answer:

976

Step-by-step explanation:

this is literally the exact same question

Answer:

-24

Step-by-step explanation:

goes by -5

Answer:

-24

Step-by-step explanation:

We are subtracting 5 each time

1-5 = -4

-4-5 = -9

-9-5=-14

-14-5=-19

-19-5 =-24

The fifth term is -24

c number answer is the correct answer

Answer:

The solution is: [tex](-\infty, \infty)[/tex], that is, all real values of x.

Step-by-step explanation:

The modulus of a value x(|x|) is the distance of x to the origin.

A distance is a positive measure, or zero, so |x| is never a negative value.

In this problem:

|10x| > -2

Remembering that the modulus is never negative, which means that for every value of x in the real set, |10x| > -2.

So the solution is: [tex](-\infty, \infty)[/tex], that is, all real values of x.

Answer:

  G. y-intercept

Step-by-step explanation:

Both of Marcus's functions are lines in slope-intercept form:

  y = mx +b

where b is the y-intercept.

In his first function, b=2; in his second, b=-2. The value of the y-intercept is what changed.

Answer:

Hope this is correct

Answer:

d

Step-by-step explanation:

Answer:

[tex]\frac{5(x+y)}{-8x}[/tex]

Step-by-step explanation:

Given the description below;

-The expression is quotient of 2 quantities

-The numerator of the expression is 5 and the sum of x and y

-The denominator is the product of -8 and x

Let the given two quantities be a and b

The quotient of the expression will be expressed as [tex]\frac{a}{b}[/tex] where 'a' is the numerator and 'b' is the denominator

If the numerator of the expression is 5 and the sum of x and y , then;

[tex]a = 5(x+y)[/tex]

If the denominator is the product of -8 and x, then;

[tex]b =-8x[/tex]

The quotient of both expression will be [tex]\frac{a}{b} = \frac{5(x+y)}{-8x}[/tex]

The expression that fits the description is [tex]\frac{5(x+y)}{-8x}[/tex]

Answer:

V(x) = (f ∙ g)(x)

Step-by-step explanation:

Note. There is no table attached.

However it can solved with remaining information given.

The volume of a prism is

If we have a function for the volume V(x) it has to be equal to a product of functions for the area and the height

Therefore the function will be similar to:

So the correct option is the first one

Answer:

p ≥ -14

Step-by-step explanation:

Subtract 4 from both sides:

p + 4 ≥ -10

   - 4     - 4

________

p ≥ -14

Answer:

95​% confidence interval for the mean difference in leisure time between adults with no children and adults with children (μ1 - μ2).

(0.4144 , 2.3256)

Step-by-step explanation:

Given sample size 'n' =n₁ = n₂ = 40

The mean of the first sample  (x₁⁻) = 5.69 hours

The standard deviation of the first sample (S₁)= 2.42 hours

The mean of the second sample( x₂⁻) = 4.32 hours

The standard deviation of the second sample (S₂)= 1.83 hours

95% of confidence intervals for (μ₁ - μ₂)are determined by

[tex](X^{-} _{1} - X^{-} _{2} - t_{\frac{\alpha }{2} } Se(X^{-} _{1} - X^{-} _{2} ) , X^{-} _{1} - X^{-} _{2} + t_{\frac{\alpha }{2} } se(X^{-} _{1} - X^{-} _{2} ))[/tex]

where

The standard error of the difference between two means

[tex]se(X^{-} _{1} - X^{-} _{2} ) = \sqrt{\frac{S^{2} _{1} }{n_{1} }+\frac{S^{2} _{2} }{n_{2} } }[/tex]

[tex]se(X^{-} _{1} - X^{-} _{2} ) = \sqrt{\frac{(2.42)^2 }{40 }+\frac{(1.83)^2 }{40 } }[/tex]

[tex]se(X^{-} _{1} - X^{-} _{2} ) = \sqrt{0.2301325} = 0.47972[/tex]

Degrees of freedom γ = n₁ +n₂ -2 = 40+40 -2 =78

[tex]t_{\frac{\alpha }{2} } = t_{\frac{0.05}{2} } = t_{0.025}[/tex]

t₀.₀₂₅ = 1.992

95% of confidence intervals for (μ₁ - μ₂)are determined by

[tex](X^{-} _{1} - X^{-} _{2} - t_{\frac{\alpha }{2} } Se(X^{-} _{1} - X^{-} _{2} ) , X^{-} _{1} - X^{-} _{2} + t_{\frac{\alpha }{2} } se(X^{-} _{1} - X^{-} _{2} ))[/tex]

(5.69 -4.32)- 1.992(0.47972)), (5.69-4.32)+1.992(0.47972))

(1.37 -0.9556 , 1.37+0.9556)

(0.4144 , 2.3256)

Conclusion:-

95​% confidence interval for the mean difference in leisure time between adults with no children and adults with children (μ1 - μ2).

(0.4144 , 2.3256)

Following are the calculation to the confidence interval:

Given:

[tex]\bar{x_1}= 5.69\\\\\bar{x_2}= 4.32\\\\s_1=2.42\\\\s_2=1.83\\\\n_1=40\\\\n_2=40\\\\[/tex]

To find:

confidence interval=?

Solution:

[tex]\to a=0.1\\\\ \to Z(0.05)=1.645[/tex]            (from standard normal table)

Calculating the confidence interval when its value is [tex]95\%[/tex]:

[tex]\to (\bar{x_1}-\bar{x_2}) \pm Z \times \sqrt{(\frac{s^2_{1}}{n_1}+ \frac{s^2_{2}}{n_2})}[/tex]  

[tex]\to (5.69-4.32)\pm 1.645 \times \sqrt{(\frac{2.42^2}{40}+\frac{1.83^2}{40})}\\\\\to (1.37)\pm 1.645 \times \sqrt{(\frac{5.8564}{40}+\frac{3.3489}{40})}\\\\\to (1.37)\pm 1.645 \times \sqrt{(\frac{5.8564+3.3489}{40})}\\\\\to (1.37)\pm 1.645 \times \sqrt{(\frac{9.2053}{40})}\\\\\to (1.37)\pm 1.645 \times \sqrt{0.2301325}\\\\\to (1.37)\pm 1.645 \times 0.4797212 \\\\\to (1.37)\pm 0.789\\\\\to (2.159, 0.581 )[/tex]

Therefore, the final answer is "(2.159 and 0.581)".

Learn more about the confidence interval:

brainly.com/question/24131141

Answer:

The central angle measure of the sector in radians is [tex]\theta=\frac{13}{9}[/tex].

Step-by-step explanation:

A sector of a circle is the portion of a circle enclosed by two radii and an arc. It resembles a "pizza" slice.

The area of a sector when the central angle is in radians is given by

                                                    [tex]A=(\frac{\theta}{2})\cdot r^2[/tex]

where

r = radius

θ = central angle in radians

We know that the area of the sector is [tex]26 \:cm^2[/tex] and the radius is 6 cm. Applying the above formula and solving for the central angle ([tex]\theta[/tex]) we get that

                                                   [tex]26=(\frac{\theta}{2})\cdot (6)^2\\\\\left(\frac{\theta}{2}\right)\left(6\right)^2=26\\\\\frac{\frac{\theta}{2}\cdot \:6^2}{36}=\frac{26}{36}\\\\\frac{\theta}{2}=\frac{13}{18}\\\\\theta=\frac{13}{9}[/tex]

Answer:

Estimations of π/4:

100 points: 0.75

1,000 points: 0.768

10,000 points: 0.7819

Step-by-step explanation:

To get an estimate of π/4 you can place random points in the square [0, 1] × [0, 1] and estimate it as the ratio of the points that landed inside the unit circle to the total number of points (because the ratio of the area of the circle to the area of the square is π/4).

We do it for 100 xy points and we get:

Point inside the circle area = 75

Estimation of π/4 = 0.75

[tex]\pi/4\approx=\dfrac{\text{points inside circle area}}{\text{total points}}=\dfrac{75}{100}=0.75[/tex]

We do it for 1,000 xy points and we get:

Point inside the circle area = 768

Estimation of π/4 = 0.768

[tex]\pi/4\approx=\dfrac{\text{points inside circle area}}{\text{total points}}=\dfrac{768}{1000}=0.768[/tex]

If we do it fo 10,000 xy points, we get

Point inside the circle area = 768

Estimation of π/4 = 0.768

[tex]\pi/4\approx=\dfrac{\text{points inside circle area}}{\text{total points}}=\dfrac{7819}{10000}=0.7819[/tex]

The value of π/4 (4 decimals) is 0.7854.

The simulation gets more precise with the increase in the number of points.

The spreadsheet and the graphs are attached.

Hey there! I'm happy to help!

First, let's find the slope of the two lines. To find the slope, you divide the difference in the y-values by the difference in the x-values.

LINE M

7-12/3-6=-5/-3= 5/3

LINE N

1-6/-5+2=-5/-3=5/3

If lines have the same slopes, they are parallel because they are always moving at the same incline and therefore will never meet. This matches what answer A says.

Therefore, the correct answer is A) Lines m and n have the same slope so they are parallel.

I hope that this helps! Have a wonderful day!

Answer:

Option C is correct

Step-by-step explanation:

The equation, when graphed with the given  equation (y = -x + 4), will form a system that has an infinite number of solutions MUST have same form as given equation.

y = (-1/2)(2x - 8) = (-1/2)*2x + (-1/2)*8 = -x + 4 (same form as given equation)

Hope this helps!

:)

Answer:

A. Inscribed Angle Theorem

Step-by-step explanation:

Because the angles are inscribed in the circle, the angle lie on arcs which mean that the angles have to add up to 360 degrees just like a circle is 360 degrees, making it a quadrilateral that is inscribed!

Hope this helps actually explain the answer,

                                                   Matthew Keister aka Mattsawesome 5000 YT

The missing information in the paragraph proof is  inscribed angle theorem that if an angle is inscribed in a circle, the measure of the inscribed angle is half the measure of the intercepted arc.

Inscribed angle in a circle is formed by two chords that have a common end point on the circle. This common end point is the vertex of the angle.

We have,

Quadrilateral [tex]A B C D[/tex] inscribed in Circle.

Measure of Arc [tex]B C D = a^0[/tex].

Arc [tex]B C D[/tex] and Arc [tex]B A D[/tex] form a circle, and a circle measures [tex]360^0[/tex],

Measure of Arc [tex]B A D = 360 - a^0[/tex]

Because of the theorem that if an angle is inscribed in a circle, the measure of the inscribed angle is half the measure of the intercepted arc.

Therefore,

[tex]\angle A = \frac{a}{2}^0[/tex]  and    

[tex]\angle C = (\frac{360-a}{2}) ^0[/tex]

The sum of the measures of angles [tex]A[/tex] and [tex]C[/tex] is,

[tex]\angle A + \angle C = \frac{a}{2}^0 +(\frac{360-a}{2}) ^0=180^0[/tex]

Therefore, angles  [tex]A[/tex] and [tex]C[/tex] are supplementary because their measures add up to [tex]180^0[/tex].

Angles [tex]B[/tex] and [tex]D[/tex] are supplementary because the sum of the measures of the angles in a quadrilateral is[tex]360^0[/tex].

[tex]\angle A + \angle C + \angle B + \angle D = 360^0[/tex]

and using substitution,

[tex]180^0 + \angle B + \angle D = 360^0[/tex]

So,

[tex]\angle B + \angle D = 180^0[/tex]

So, from the above provided proof we can say that the missing information in the proof was inscribed angle theorem.

Hence, we can say that the missing information in the paragraph proof is  inscribed angle theorem that if an angle is inscribed in a circle, the measure of the inscribed angle is half the measure of the intercepted arc.

To know more about inscribed angle click here

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