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Levart [38]
3 years ago
14

What’s the answer to this please?

Mathematics
1 answer:
MAVERICK [17]3 years ago
8 0
The answer is c I think
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Emmanuel carves a cone-shaped hollow out of a solid clay cylinder. What is the approximate volume of the solid portion of the cy
bixtya [17]

Answer:

3.14r^2(h-\frac{1}{3}h_1)

Step-by-step explanation:

Let h be the cylinders height and r the radius.

-The volume of a cylinder is calculated as:

V=\pi r^2h

-Since the cone is within the cylinder, it has the same radius as the cylinder.

-Let h_1be the height of the cone.

-The area of a cone is calculated as;

V=\pi r^2 \frac{h}{3}\\\\=\frac{1}{3}\pi r^2h_1

The volume of the  solid section of the cylinder is calculated by subtracting the cone's volume from the cylinders:

V=V_{cy}-V_{co}\\\\=\pi r^2h-\frac{1}{3}\pi r^2 h_1, \pi=3.14\\\\=3.14r^2(h-\frac{1}{3}h_1)

Hence, the approximate area of the solid portion is 3.14r^2(h-\frac{1}{3}h_1)

5 0
3 years ago
A solution initially contains 200 bacteria. 1. Assuming the number y increases at a rate proportional to the number present, wri
GuDViN [60]

Answer:

1.\frac{dy}{dt}=ky

2.543.6

Step-by-step explanation:

We are given that

y(0)=200

Let y be the number of bacteria at any time

\frac{dy}{dt}=Number of bacteria per unit time

\frac{dy}{dt}\proportional y

\frac{dy}{dt}=ky

Where k=Proportionality constant

2.\frac{dy}{y}=kdt,y'(0)=100

Integrating on both sides then, we get

lny=kt+C

We have y(0)=200

Substitute the values then , we get

ln 200=k(0)+C

C=ln 200

Substitute the value of C then we get

ln y=kt+ln 200

ln y-ln200=kt

ln\frac{y}{200}=kt

\frac{y}{200}=e^{kt}

y=200e^{kt}

Differentiate w.r.t

y'=200ke^{kt}

Substitute the given condition then, we get

100=200ke^{0}=200 \;because \;e^0=1

k=\frac{100}{200}=\frac{1}{2}

y=200e^{\frac{t}{2}}

Substitute t=2

Then, we get y=200e^{\frac{2}{2}}=200e

y=200(2.718)=543.6=543.6

e=2.718

Hence, the number of bacteria after 2 hours=543.6

4 0
3 years ago
Compare the functions.
marshall27 [118]

Function h has the largest y-intercept which is 44

Step-by-step explanation:

Any linear function is represented in the form

f(x) = mx+b

Here b is the y-intercept of the linear function i.e. the constant term in the function.

We will compare all the functions with the general form we get

y-intercept of f(x) = 1

y-intercept of g(x) = 8

y-intercept of h(x) = 44

y-intercept of j(x) = 0

Hence,

Function h has the largest y-intercept which is 44

Keywords: intercepts, linear functions

Learn more about intercepts at:

  • brainly.com/question/9532142
  • brainly.com/question/9590016

#LearnwithBrainly

5 0
3 years ago
The following results come from two independent random samples taken of two populations.
photoshop1234 [79]

Answer:

(a)\ \bar x_1 - \bar x_2 = 2.0

(b)\ CI =(1.0542,2.9458)

(c)\ CI = (0.8730,2.1270)

Step-by-step explanation:

Given

n_1 = 60     n_2 = 35      

\bar x_1 = 13.6    \bar x_2 = 11.6    

\sigma_1 = 2.1     \sigma_2 = 3

Solving (a): Point estimate of difference of mean

This is calculated as: \bar x_1 - \bar x_2

\bar x_1 - \bar x_2 = 13.6 - 11.6

\bar x_1 - \bar x_2 = 2.0

Solving (b): 90% confidence interval

We have:

c = 90\%

c = 0.90

Confidence level is: 1 - \alpha

1 - \alpha = c

1 - \alpha = 0.90

\alpha = 0.10

Calculate z_{\alpha/2}

z_{\alpha/2} = z_{0.10/2}

z_{\alpha/2} = z_{0.05}

The z score is:

z_{\alpha/2} = z_{0.05} =1.645

The endpoints of the confidence level is:

(\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}

2.0 \± 1.645 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}

2.0 \± 1.645 * \sqrt{\frac{4.41}{60}+\frac{9}{35}}

2.0 \± 1.645 * \sqrt{0.0735+0.2571}

2.0 \± 1.645 * \sqrt{0.3306}

2.0 \± 0.9458

Split

(2.0 - 0.9458) \to (2.0 + 0.9458)

(1.0542) \to (2.9458)

Hence, the 90% confidence interval is:

CI =(1.0542,2.9458)

Solving (c): 95% confidence interval

We have:

c = 95\%

c = 0.95

Confidence level is: 1 - \alpha

1 - \alpha = c

1 - \alpha = 0.95

\alpha = 0.05

Calculate z_{\alpha/2}

z_{\alpha/2} = z_{0.05/2}

z_{\alpha/2} = z_{0.025}

The z score is:

z_{\alpha/2} = z_{0.025} =1.96

The endpoints of the confidence level is:

(\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}

2.0 \± 1.96 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}

2.0 \± 1.96* \sqrt{\frac{4.41}{60}+\frac{9}{35}}

2.0 \± 1.96 * \sqrt{0.0735+0.2571}

2.0 \± 1.96* \sqrt{0.3306}

2.0 \± 1.1270

Split

(2.0 - 1.1270) \to (2.0 + 1.1270)

(0.8730) \to (2.1270)

Hence, the 95% confidence interval is:

CI = (0.8730,2.1270)

8 0
3 years ago
Lines that meet or cross each other to form square corners are called ______.
Viefleur [7K]

The lines that intersect to form square corners that are right angles are called: C. perpendicular lines.

<h3>What are Perpendicular Lines?</h3>

Perpendicular lines are lines that intersect each other at a point and forms for square corners that are right angles at that point of intersection.

An example of perpendicular lines is shown in the image attached below.

Thus, the lines that meet to form right angles are called: C. perpendicular.

Learn more about perpendicular lines on:

brainly.com/question/1202004

#SPJ1

5 0
1 year ago
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