A survey is to be conducted using a random sample of citizens in a town,
asking them if they support raising taxes to increase funding for the public school. Write the question in a way that is likely to bias the results toward more yes answers. Write the question in a way that is likely to bias the results toward more
no answers.

Answer:

[tex]r = 1.34[/tex]

Step-by-step explanation:

Given

Solid = Cylinder + 2 hemisphere

[tex]Volume = 10cm^3[/tex]

Required

Determine the radius (r) that minimizes the surface area

First, we need to determine the volume of the shape.

Volume of Cylinder (V1) is:

[tex]V_1 = \pi r^2h[/tex]

Volume of 2 hemispheres (V2) is:

[tex]V_2 = \frac{2}{3}\pi r^3 +\frac{2}{3}\pi r^3[/tex]

[tex]V_2 = \frac{4}{3}\pi r^3[/tex]

Volume of the solid is:

[tex]V = V_1 + V_2[/tex]

[tex]V = \pi r^2h + \frac{4}{3}\pi r^3[/tex]

Substitute 10 for V

[tex]10 = \pi r^2h + \frac{4}{3}\pi r^3[/tex]

Next, we make h the subject

[tex]\pi r^2h = 10 - \frac{4}{3}\pi r^3[/tex]

Solve for h

[tex]h = \frac{10}{\pi r^2} - \frac{\frac{4}{3}\pi r^3 }{\pi r^2}[/tex]

[tex]h = \frac{10}{\pi r^2} - \frac{4\pi r^3 }{3\pi r^2}[/tex]

[tex]h = \frac{10}{\pi r^2} - \frac{4r }{3}[/tex]

Next, we determine the surface area

Surface area (A1) of the cylinder:

Note that the cylinder is covered by the 2 hemisphere.

So, we only calculate the surface area of the curved surface.

i.e.

[tex]A_1 = 2\pi rh[/tex]

Surface Area (A2) of 2 hemispheres is:

[tex]A_2 = 2\pi r^2+2\pi r^2[/tex]

[tex]A_2 = 4\pi r^2[/tex]

Surface Area (A) of solid is

[tex]A = A_1 + A_2[/tex]

[tex]A = 2\pi rh + 4\pi r^2[/tex]

Substitute [tex]h = \frac{10}{\pi r^2} - \frac{4r }{3}[/tex]

[tex]A = 2\pi r(\frac{10}{\pi r^2} - \frac{4r }{3}) + 4\pi r^2[/tex]

Open bracket

[tex]A = \frac{2\pi r*10}{\pi r^2} - \frac{2\pi r*4r }{3} + 4\pi r^2[/tex]

[tex]A = \frac{2*10}{r} - \frac{2\pi r*4r }{3} + 4\pi r^2[/tex]

[tex]A = \frac{20}{r} - \frac{8\pi r^2 }{3} + 4\pi r^2[/tex]

[tex]A = \frac{20}{r} + \frac{-8\pi r^2 }{3} + 4\pi r^2[/tex]

Take LCM

[tex]A = \frac{20}{r} + \frac{-8\pi r^2 + 12\pi r^2}{3}[/tex]

[tex]A = \frac{20}{r} + \frac{4\pi r^2}{3}[/tex]

Differentiate w.r.t r

[tex]A' = -\frac{20}{r^2} + \frac{8\pi r}{3}[/tex]

Equate A' to 0

[tex]-\frac{20}{r^2} + \frac{8\pi r}{3} = 0[/tex]

Solve for r

[tex]\frac{8\pi r}{3} = \frac{20}{r^2}[/tex]

Cross Multiply

[tex]8\pi r * r^2 = 20 * 3[/tex]

[tex]8\pi r^3 = 60[/tex]

Divide both sides by [tex]8\pi[/tex]

[tex]r^3 = \frac{60}{8\pi}[/tex]

[tex]r^3 = \frac{15}{2\pi}[/tex]

Take [tex]\pi = 22/7[/tex]

[tex]r^3 = \frac{15}{2 * 22/7}[/tex]

[tex]r^3 = \frac{15}{44/7}[/tex]

[tex]r^3 = \frac{15*7}{44}[/tex]

[tex]r^3 = \frac{105}{44}[/tex]

Take cube roots of both sides

[tex]r = \sqrt[3]{\frac{105}{44}}[/tex]

[tex]r = \sqrt[3]{2.38636363636}[/tex]

[tex]r = 1.33632535155[/tex]

[tex]r = 1.34[/tex] (approximated)

Hence, the radius is 1.34cm

The radius of the cylinder that produces the minimum surface area is 1.34cm and this can be determined by using the formula area and volume of cylinder and hemisphere.

Given :

The volume of a cylinder is given by:

[tex]\rm V = \pi r^2 h[/tex]

The total volume of the two hemispheres is given by:

[tex]\rm V' = 2\times \dfrac{2}{3}\pi r^3[/tex]

[tex]\rm V' = \dfrac{4}{3}\pi r^3[/tex]

Now, the total volume of the solid is given by:

[tex]\rm V_T = \pi r^2 h+\dfrac{4}{3}\pi r^3[/tex]

Now, substitute the value of the total volume in the above expression and then solve for h.

[tex]\rm 10 = \pi r^2 h+\dfrac{4}{3}\pi r^3[/tex]

[tex]\rm h = \dfrac{10}{\pi r^2}-\dfrac{4r}{3}[/tex]

Now, the surface area of the curved surface is given by:

[tex]\rm A = 2\pi r h[/tex]

Now, the surface area of the two hemispheres is given by:

[tex]\rm A'=2\times (2\pi r^2)[/tex]

[tex]\rm A'=4\pi r^2[/tex]

Now, the total area is given by:

[tex]\rm A_T = 2\pi rh+4\pi r^2[/tex]

Now, substitute the value of 'h' in the above expression.

[tex]\rm A_T = 2\pi r\left(\dfrac{10}{\pi r^2}-\dfrac{4r}{3}\right)+4\pi r^2[/tex]

Simplify the above expression.

[tex]\rm A_T = \dfrac{20}{r} + \dfrac{4\pi r^2}{3}[/tex]

Now, differentiate the total area with respect to 'r'.

[tex]\rm \dfrac{dA_T}{dr} = -\dfrac{20}{r^2} + \dfrac{8\pi r}{3}[/tex]

Now, equate the above expression to zero.

[tex]\rm 0= -\dfrac{20}{r^2} + \dfrac{8\pi r}{3}[/tex]

Simplify the above expression in order to determine the value of 'r'.

[tex]8\pi r^3=60[/tex]

r = 1.34 cm

For more information, refer to the link given below:

https://brainly.com/question/11952845

Answer: -1 [(y-b)/m]+x=a

Step-by-step explanation:

(Y-b) / m = x-a

[(y-b)/m] -x =-a

-1 [(y-b)/m]+x=a

====================================================

Explanation:

We'll use the angle addition postulate. This is basically the idea where we can break any angle into smaller parts, or go in reverse to build up larger angles based on smaller pieces.

In this case, we can see that the smaller angles KLU and ULM combine to form the largest angle KLM. Think of it like puzzle pieces.

Let x be the measure of angle ULM

We can say the following

(angle KLU) + (angle ULM) = angle KLM

(36) + (x) = 156

36 + x = 156

To solve for x, we subtract 36 from both sides

36+x-36 = 156-36

x = 120

Angle ULM is 120 degrees.

-------------------

As a check,

(angle KLU) + (angle ULM) = 36 + 120 = 156

which matches with angle KLM, so the answer is confirmed.

Answer:

0.025

Step-by-step explanation:

Answer:

0.25 metros.

Step-by-step explanation:

cada centimetro es 0.01 metro.

Answer:

slope = 7/4

Step-by-step explanation:

slope is found by figuring the change in y-values over the change in x-values.  Look for points on the line that go through an intersection of the graph lines exactly.  I found the points (3, 4) and (-1, -3)

difference of y/difference of x = 4-(-3) / 3-(-1)   =  7/4

Answer:

I think the answer would be 125 iPhones.

Step-by-step explanation:

So basically the question is what is 2.5% of 5000.

Just multiply 5000 * 0.025 = 125

Answer:

160 in.

Step-by-step explanation:

10 *  16 = 160

Answer:

SPANISH TALK ENGLISH OK

Step-by-step explanation:

OKKK

Answer:

Growth Mindset: “In a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. This view creates a love of learning and a resilience that is essential for great accomplishment. In a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. This view creates a love of learning and a resilience that is essential for great accomplishment,” Dweck wrote.

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

the equation of the line is y=18/5x-216/5 and then find the x intercept and that is 12

The x-intercept of the line is 1.

The line intersects the x-axis at the point (1, 0).

Here,

To find the x-intercept of a line, we need to identify the point at which the line intersects the x-axis.

At the x-intercept, the y-coordinate is always 0.

Let's use the given data to find the equation of the line first using two points (x, y):

Using (22, 36) and (27, 54):

Calculate the slope (m) of the line:

m = (change in y) / (change in x) = (54 - 36) / (27 - 22) = 18 / 5

Use the slope and one of the points to find the equation of the line

(y = mx + b).

Let's use (22, 36):

36 = (18/5) * 22 + b

36 = 39.6 + b

b = 36 - 39.6

b = -3.6

So, the equation of the line is y = (18/5)x - 3.6.

Now, to find the x-intercept (where y = 0), we can set y = 0 in the equation and solve for x:

0 = (18/5)x - 3.6

(18/5)x = 3.6

x = 3.6 * 5 / 18

x = 1

Therefore, the x-intercept of the line is 1.

The line intersects the x-axis at the point (1, 0).

learn more on x-intercept :

https://brainly.com/question/1698680

#SPJ4

Answer:

0.9987

Step-by-step explanation:

Using Z score formula

z = (x-μ)/σ, where

x is the raw score = 52 inches

μ is the population mean = 94 inches

σ is the population standard deviation = 14 inches

z = 52 - 94/14

z =-3

Probability value from Z-Table:

P(x<52) = 0.0013499

P(x>52) = 1 - P(x<52)

P(x>52) = 1 - 0.0013499

= 0.99865

Therefore, the probability that, in a randomly selected year, the snowfall was greater than 52 inches is approximately 0.9987

Answer:

Step-by-step explanation:

99.87 for Knewton Alta

Answer:

The answer is 8 days.

Step-by-step explanation:

By applying the correct equations to Todd and Seth's balances for each day we end up with Todd and Seth having an equal balance in their accounts by day 8, alternatively, we can show that Todd and Seth have the same amount of money in their accounts by day 8 with this table

Day - Todd - Seth

1     -  95     - 130

2    -   90    - 120

3   -    85    -  110

4    -   80    -   100

5    -  75    -   90

6  -    70   -    80

7  -    65    -   70

8 -     60   -    60

Answer:

Step-by-step explanation:

6² + 12 × 6 = 36 + 72 = 108 m²

[tex]\frac{3*6}{2}[/tex] + 6 × 3 = 9 + 18 = 27 cm²

Answer:

108

Step-by-step explanation:

Solution:

It is that a river is flowing in the south direction with a speed of [tex]$v_r$[/tex]1.4 mi/h.

A swimmer wishes to cross the river in a horizontal direction so that he lands at a point which is due east of his starting point.

The speed of the swimmer is [tex]$v_s$[/tex] = 3 mi/h

Therefore he has to swim in such a direction that his resultant is in the direction east to his starting point.

Let this angle be θ.

Therefore, from the figure,

[tex]$\sin \theta = \frac{v_r}{v_s}$[/tex]

[tex]$\sin \theta = \frac{1.4}{3}$[/tex]

[tex]$\theta = \sin^{-1}(0.46)$[/tex]

  [tex]$=27.4^\circ[/tex]

Therefore, the swimmer has to swim in the northeast direction making an angle of (90+27.4) = 117.4° with the direction of flow of river (i.e. south).  

Answer:

I presume that 10x would be on the x axis to the right of 0.

-7y would be on the y axis under 0. Therefore in between -6 and -8

You might know this but very important

X to the decks (horizontally/straight across) and Y to the sky (vertically/ up and down)

Answer:

890.908

Step-by-step explanation:

Given that :

Median weekly salary for males :

M(x) = 0.009x3 - 0.29x2 + 30.7x + 439.6

x = number of years after 1980

Median weekly salary for all employees :

T(x) = 0.012x3 - 0.46x2 + 56.1x + 732.3

Estimate the median weekly earnings of a full-time female employee with at least a Bachelor's degree in 2006

Estimated median weekly earning for a full time female employee with at least bachelor's degree ; F(x)

F(x) = T(x) - M(x)

F(x) = (0.012x3 - 0.46x2 + 56.1x + 732.3) - (0.009x3 - 0.29x2 + 30.7x + 439.6)

F(x) = (0.012 - 0.009)x3 + (-0.46 + 0.29)x2 + (56.1 - 30.7)x + (732.3 - 439.6)

F(x) = 0.003x³ - 0.17x² + 25.4 + 292.7

x = 2006 - 1980 = 26

F(26) = 0.003x³ - 0.17x² + 25.4x + 292.7

0.003(26)^3 - 0.17(26)^2 + 25.4(26) + 292.7 = 890.908

=

Answer:

See below

Step-by-step explanation:

[tex]( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) = 1 - 2 { \cos}^{2} \theta \\ \\ LHS = ( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) \\ \\ = \sin^{2} \theta - \cos^{2} \theta \\ \\ =1 - \cos^{2} \theta - \cos^{2} \theta \\( \because \sin^{2} \theta =1 - \cos^{2} \theta) \\ \\ = 1 - 2 { \cos}^{2} \theta \\ = RHS[/tex]

Thus proved

Answer:

Step-by-step explanation:

(a).

Multiples of 4 are {4, 8, 12, 16, 20, 24, 28, ..... }

Multiples of 6 are {6, 12, 18, 24, 30, ..... }

12 and 24

(b).

Multiples of 6 are {6, 12, 18, 24, 30, 36, 42, ..... }

Multiples of 9 are {9, 18, 27, 36, 45, ..... }

18 and 36

Answer:

128

Step-by-step explanation:

If you multiply you get it.

Answer:

The GCF of these numbers are 32.

Step-by-step explanation:

All of these integers are able to be divided, and by the first number.

Hope this helps! :3

Answer:

3.5x

Step-by-step explanation:

3.5(x)=3.5x

Answer:

The number of different 7 card hands possibility is  133784560

Step-by-step explanation:

The computation of the number of different 7 card hands possibility is shown below:

Here we use the combination as the orders of choosing it is not significant

So,

The number of the different hands possible would be

= [tex]^{52}C_7[/tex]

= 52! ÷ (7! × (52 - 7)!)

= 133784560

Hence, the number of different 7 card hands possibility is  133784560

Answer:48 sq. Inches

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

30 times x all the others are incorrect so by process of elimination it is a

Answer:$35

Step-by-step explanation:well each cookie cost $3.50 so for $14 there are only 4 cookies so for ten it will cost $35 cause 14+14=28 and you need to 2 more cookies so you will add 2 more which is $7 and $7+$28=$35.Hope I’m right

Answer:

three out of the eight homes have red doors. so 3 homes have red doors

Step-by-step explanation:

Answer:

y=3x+4

Step-by-step explanation:

Answer:

A

Step-by-step explanation: