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3 years ago

A sphere and a cylinder have the same radius and height. The volume of the cylinder is Amie found the volume of the sphere.

Mathematics

2 answers:

vredina [299]3 years ago

7 0

Answer:

The answer is the first

Amie should have multiplied 54 by 2/3

Step-by-step explanation:

* Lets start with the rule of the volume of each solid

∵ Volume the sphere = 4/3 π r³

∵ Volume the cylinder = π r² h

∵ The radii and the heights of the sphere and the cylinder are equal

∴ The ratio between there volumes are

4/3 π r³ : π r² h

- Lets divide each part by π r²

∴ 4/3 r : h

∵ The height of the sphere = the diameter of it = 2r

∴ The height of the cylinder = 2r

∴ The ratio will be:

4/3 r : 2r

- Now divide each part by 2r

∵ (4/3)r ÷ 2r = 2/3

∵ 2r ÷ 2r = 1

∴ The ratio is 2/3 : 1

∴ The volume of the sphere = 2/3 the volume of the cylinder

∵ The volume of the cylinder = 54 m³

∴ The volume of the sphere = 2/3 × 54 = 36 m³

∴ The answer is Amie should have multiplied 54 by 2/3

Elena L [17]3 years ago

4 0

Answer:

The answer is Amie should have multiplied 54 by 2/3

Step-by-step explanation:

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Solve the inequality −4y + 6 < −14.

timama [110]

Answer:

y >5

Step-by-step explanation:

−4y + 6 < −14

Subtract 6 from each side

−4y + 6-6 < −14-6

-4y < -20

Divide by -4. Remember to flip the inequality since we are dividing by a negative

-4y/-4 >-20/-4

y >5

5 0

4 years ago

A manufacturer of a new medication on the market for Alzheimer's disease makes a claim that the medication is effective in 65% o

NeX [460]

Answer:

$z=\frac{0.639 -0.65}{\sqrt{\frac{0.65(1-0.65)}{180}}}=-0.309$

$p_v =P(z$

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults with the medication was effective is not significantly less than 0.65

Step-by-step explanation:

Data given and notation

n=180 represent the random sample taken

X=115 represent the adults with the medication was effective

$\hat p=\frac{115}{180}=0.639$ estimated proportion of adults with the medication was effective

$p_o=0.65$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that true proportion is less than 0.65.:

Null hypothesis: $p \geq 0.65$

Alternative hypothesis: $p < 0.65$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.639 -0.65}{\sqrt{\frac{0.65(1-0.65)}{180}}}=-0.309$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a left tailed test the p value would be:

$p_v =P(z$

3 0

3 years ago

1.10 The number 36 is 12% of:?

Alekssandra [29.7K]

Answer:

300

Step-by-step explanation:

12% of x = 36

12/100 x = 36

12x/100 = 36

12x=36x100

12x=3600

x=3600/12

x=300

5 0

3 years ago

Read 2 more answers

If you need how many days between two dates what function should be used

Mariana [72]

You have to do this piecemeal so there isn’t a single formula. The best way is to convert each date using a common frame of reference. Dates before October 1582 used a different calendar. Also the distance between leap years varies. It’s normally 4 years but it can be 8 years. For example, 2100 is not a leap year but 2096 and 2104 are both leap years. Similarly 1896 and 1904 but not 1900. Before October 1582 leap years occurred exactly 4 years apart.
Your next problem is to work out the day number from the beginning of the year. On average there are between 30.4 and 30.5 days in a month, but this is only an approximation because the length of each month varies. So to aid in the calculation you need a table which gives you the day number for every date in the year, and the table is different for leap years.
So, you start by subtracting the years and counting how many leap years there are between. You consult the day number table for working out how many days there are from the beginning of the year.
Another way is to have a smaller table with just the months, so in a non-leap year Jan 1 would be 1, Feb 1 would be 32, Mar 1 would be 60, Apr 1 would be 91, and so on. Then we have to add in the day date. Mar 20 would be 19 days after Mar 1 so would have a day number of 79, not 80. Some diaries and calendars include the day number.
You can speed up the calculation by using one day number table or calculation and then adding in a day for each leap year between two dates. I hope this helps.

6 0

4 years ago

Arrange in order of decreasing magnitude using the > symbol (largest number would be at the left, smallest at the right). 3.9

Yanka [14]

Since the tenths place is a greater order of magnitude than the hundredths place and .9 > .8, both 3.98 and 3.99 are greater than 3.89. Now, looking at the hundredths place, since .09 > .08, 3.99 > 3.98. Putting it all together, the numbers in decreasing magnitude are

$\bf 3.99 \ \textgreater \ 3.98 \ \textgreater \ 3.89$

6 0

4 years ago