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vagabundo [1.1K]
3 years ago
11

Two spheres, one of radius 15 and the other of radius 33, have the same center. Find the side length of the largest cube that fi

ts between them.

Mathematics
1 answer:
Sophie [7]3 years ago
6 0

Answer: 18

Step-by-step explanation:

The detailed explanation is in the attached picture.

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Let D = {-48, -14, -8, 0, 1, 3, 16, 23, 26, 32, 36} Determine which of the following statements are true and which are false. a)
morpeh [17]

Answer:

\forall x\in D if x is odd then x> 0 is true statement.

\forall x\in D if x is odd then x> 0 is true statement.

\forall x\in D if x is even then x≤0 is false statement.

\forall x\in D If the ones digit of x is 2, then the tens digit is 3 or 4 is true statement.

\forall x\in D if the ones digit of x is 6, then the tens digit is 1 or 2 is false statement.

Step-by-step explanation:

Consider the provided information.

D = {-48, -14, -8, 0, 1, 3, 16, 23, 26, 32, 36}

Part (A) \forall x\in D if x is odd then x> 0

Here only even numbers are less than 0 that means the statement is true.

\forall x\in D if x is odd then x> 0 is true statement.

Part (B) \forall x\in D if x is less than 0 then x is even.

Here only even numbers are less than 0 that means the statement is true.

\forall x\in D if x is odd then x> 0 is true statement.

Part (C) \forall x\in D if x is even then x≤0

Here we can see that 16, 26, 32, 36 are even number and also greater than 0. Thus the statement is false.

\forall x\in D if x is even then x≤0 is false statement.

Part (D) \forall x\in D If the ones digit of x is 2, then the tens digit is 3 or 4.

There is only one number whose ones digit is 2. i.e. 32 also the tens digit of the number 32 is 3. Which makes the above statement true.

\forall x\in D If the ones digit of x is 2, then the tens digit is 3 or 4 is true statement.

Part (E) \forall x\in D if the ones digit of x is 6, then the tens digit is 1 or 2.

Numbers having ones digit 6 are: 16, 26 and 36

Here, the tens digits are 1, 2 and 3 which is contradict to our statement. Hence the provided statement is false.

\forall x\in D if the ones digit of x is 6, then the tens digit is 1 or 2 is false statement.

8 0
3 years ago
Find the area someone please help
a_sh-v [17]

Answer:

33.3cm²

Step-by-step explanation:

9 multiplied by 3.7 is equal to 33.3cm²

5 0
2 years ago
Read 2 more answers
What number is indicated on the number line
g100num [7]
Depends on the number line my guy
3 0
3 years ago
Read 2 more answers
Find (3.3 × 10^4) + (1.9 × 10^5)
scoundrel [369]

Answer:

2.23 \times 10^{5}

Step-by-step explanation:

We have to find the sum of two numbers following the steps as described in the question.

The question is in the form of fill in the blanks.

Now, the given sum is (3.3 \times 10^{4} )+(1.9 \times 10^{5} )

= (3.3 \times 10^{4} )+(19 \times 10^{4} )

= (3.3+19) \times 10^{4}

= 22.3 \times 10^{4}

= 2.23 \times 10^{5} (Answer)

5 0
3 years ago
Suppose a lawn and garden company wants to determine the current percentage of customers who use fertilizer on their lawns. How
marishachu [46]

Answer:

n=601

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.04 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

Since we don't have a prior estimation for the proportion we can use 0.5 as estimation. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.96})^2}=600.25  

And rounded up we have that n=601

3 0
3 years ago
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