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3 years ago

4. What is the formula to find the volume of a sphere?

Mathematics

1 answer:

adell [148]3 years ago

5 0

Answer:

The formula of the volume of the sphere is V = (4/3)×π×r³ where r is the radius of the sphere.

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Find the slope of the line (2,1) and (3,1)

DochEvi [55]

The slope is 0, it is a straight line.
Hope this helps!

3 0

3 years ago

The function shown below was created to track the different intervals of speed that an automobile travels over a period of 28 se

Ksenya-84 [330]

Answer:

1. The car is slowing down at a rate of 2.5mph/s

2. The greatest acceleration is 10 mph/s.

3. In the interval 4s to 16s the speed remains constant and has magnitude 25 mph.

Step-by-step explanation:

1. The deceleration of the car is from 16 seconds to 24 seconds is the slope $m$ of the graph from 16 to 24:

$m=\dfrac{\Delta speed }{\Delta time } = \dfrac{5-25}{24-16} =-2.5mph/s$

the negative sign indicates that it is deceleration.

2. The automobile experiences the greatest change in speed when the slope is greatest because that is when acceleration/deceleration is greatest.

From the graph we see that the greatest slope of the graph is between 28 and 24 seconds. The acceleration the interval is the slope $m$ :

$m= \dfrac{45-5}{28-24}= 10mph/s$

3. The automobile experiences no acceleration in the interval 4 s to 16 s—that's the graph is flat.

The speed of the automobile in that interval, as we see from the graph, is 25 mph.

7 0

3 years ago

Read 2 more answers

Two angles are supplementary and have a ratio of 1:4. what is the size of the smaller angle

Dima020 [189]

Supplementary angles add up to 180 degrees
ratio of 1:4.....added = 5

1/5(180) = 180/5 = 36 <=== smaller angle
4/5(180) = 720/5 = 144 .... larger angle

4 0

3 years ago

Read 2 more answers

Dennis spent $5 less on lunch than he spent on dinner. Dennis spent at most $12 on dinner. Write and solve an inequality to find

Vinil7 [7]

12>x-5 is the answer your looking for. Make sure to put a line under the more than sign, my computer wouldn't allow me to plug that part in.

7 0

3 years ago

A healthcare provider monitors the number of CAT scans performed each month in each of its clinics. The most recent year of data

Rasek [7]

Answer: a. 1.981 < μ < 2.18

b. Yes.

Step-by-step explanation:

A. For this sample, we will use t-distribution because we're estimating the standard deviation, i.e., we are calculating the standard deviation, and the sample is small, n = 12.

First, we calculate mean of the sample:

$\overline{x}=\frac{\Sigma x}{n}$

$\overline{x}=\frac{2.31=2.09+...+1.97+2.02}{12}$

$\overline{x}=$ 2.08

Now, we estimate standard deviation:

$s=\sqrt{\frac{\Sigma (x-\overline{x})^{2}}{n-1} }$

$s=\sqrt{\frac{(2.31-2.08)^{2}+...+(2.02-2.08)^{2}}{11} }$

s = 0.1564

For t-score, we need to determine degree of freedom and $\frac{\alpha}{2}$ :

df = 12 - 1

df = 11

$\alpha$ = 1 - 0.95

α = 0.05

$\frac{\alpha}{2}=$ 0.025

Then, t-score is

$t_{11,0.025}$ = 2.201

The interval will be

$\overline{x}$ ± $t.\frac{s}{\sqrt{n} }$

2.08 ± $2.201\frac{0.1564}{\sqrt{12} }$

2.08 ± 0.099

The 95% two-sided CI on the mean is 1.981 < μ < 2.18.

B. We are 95% confident that the true population mean for this clinic is between 1.981 and 2.18. Since the mean number performed by all clinics has been 1.95, and this mean is less than the interval, there is evidence that this particular clinic performs more scans than the overall system average.

8 0

3 years ago