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3 years ago

What are the domain and range of the function f(x)=- square root x+3 - 2?

Mathematics

1 answer:

mars1129 [50]3 years ago

5 0

Answer:

Domain: x>= -3

Range: y <= -2

Step-by-step explanation:

Domain is all the x's on the graph or allowed in the equation.

Range is all the y's on the graph or able to come from the equation.

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Use the least commom denominator of 10 and 15 to solve 2/10+ 7/15

Juli2301 [7.4K]

The least common denominator of 10 and 15 is 30. It's easiest to use trial and error to find the LCD. In this case, just multiply both numbers by 2 and see if that works. Since 15 doesn't go into 20, I tried multiplying 15 by 2 instead, and got 30, which is divisible by 2. If that doesn't work, move on to multiplying them by 3, then 4 four, and so on. However, in this case, it did work, so, since you multiplied 15 by two to get 30, multiply 7 by two to get the fraction 14/30. Then, since you multiplied 10 by 3 to get 30, multiply 2 by 3 to get 6/30. Then, add the two together to get 20/30 and simplify the fraction to 2/3.

2/10 + 7/15 Given.
6/30 + 14/30 LCD.
20/30 Add.
2/3 Simplify.

6 0

3 years ago

A cone is inverted and filled with water to of its height. What percent of the cone's volume is filled with water

wlad13 [49]

The 75% of the cone's volume is filled with water.

According to the statement

we have to find that the What percent of the cone's volume is filled with water.

So, For this purpose, we know that the

Cone is the surface traced by a moving straight line that always passes through a fixed point (the vertex).

So, Form given information

Let's call the height of the cone " h " and the area of its base " a ".

volume of cone = (1/3)(a)(h)

The water will also be in the shape of a cone, with a height that is 3/4 that of the container.

volume of water = (1/3)(a)(3/4 * h)

volume of water = (3/4) * (1/3)(a)(h)

volume of water = (3/4) * volume of cone

volume of water = 75% of the volume of cone

So, 75% of the cone's volume is filled with water.

Learn more about cone's volume here

brainly.com/question/1082469

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Question:

A cone is inverted and filled with water to 3/4 of its height. What percent of the cone's volume is filled with water?

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1 year ago

(g-7)=-8g-52 what is the value of g?

lozanna [386]

(0,2) is the answer

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2 years ago

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Aliun [14]

<span>D. The distance traveled by a truck driving at a constant speed compared with time</span>

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3 years ago

Read 2 more answers

The following data represent the pH of rain for a random sample of 12 rain dates. A normal probability plot suggests the data co

Travka [436]

Answer:

a) Point estimate of the population mean = 4.883

b) B.There is 95% confidence that the population mean pH of rain water is between 4.646 and 5.120.

c) C.There is 99% confidence that the population mean pH of rain water is between 4.549 and 5.217.

d) As the level of confidence increases, the width of the interval increases.

This makes sense since the margin of error increases as well.

Step-by-step explanation:

We have a sample for the pH of rain.

The mean of the sample is:

$M=\dfrac{1}{12}\sum_{i=1}^{12}(5.3+5.72+4.38+4.8+5.02+...+4.56+4.68)\\\\\\ M=\dfrac{58.59}{12}=4.883$

The sample standard deviation is:

$s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{12}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{11}\cdot [(5.3-4.883)^2+(5.72-4.883)^2+...+(4.68-4.883)^2]}\\\\\\$

$s=\sqrt{\dfrac{1}{11}\cdot [(0.17)+...+(0.1)+(0.04)]}\\\\\\s=\sqrt{\dfrac{1.526625}{11}}=\sqrt{0.1387841}\\\\\\s=0.373$

a) The point estimation for the population mean is the sample mean and has a value of 4.883.

b) We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=4.883.

The sample size is N=12.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=\dfrac{s}{\sqrt{N}}=\dfrac{0.373}{\sqrt{12}}=\dfrac{0.373}{3.464}=0.108$

The t-value for a 95% confidence interval is t=2.201.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_M=2.201 \cdot 0.108=0.237$

Then, the lower and upper bounds of the confidence interval are:

$LL=M-t \cdot s_M = 4.883-0.237=4.646\\\\UL=M+t \cdot s_M = 4.883+0.237=5.12$

The 95% confidence interval for the mean is (4.646, 5.120).

B.There is 95% confidence that the population mean pH of rain water is between 4.646 and 5.120.

c) We have to calculate a 99% confidence interval for the mean.

The t-value for a 99% confidence interval is t=3.106.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_M=3.106 \cdot 0.108=0.334$

Then, the lower and upper bounds of the confidence interval are:

$LL=M-t \cdot s_M = 4.883-0.334=4.549\\\\UL=M+t \cdot s_M = 4.883+0.334=5.217$

The 99% confidence interval for the mean is (4.549, 5.217).

C.There is 99% confidence that the population mean pH of rain water is between 4.549 and 5.217.

d) When the confidence level is increased, the width also increases as it has to include more possible values for the true mean of the population.

As the level of confidence increases, the width of the interval increases.

This makes sense since the margin of error increases as well.

5 0

3 years ago

What are the domain and range of the function f(x)=- *square root* x+3 - 2?

What are the domain and range of the function f(x)=- square root x+3 - 2?