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3 years ago

What is the least perfect square which is divisible by 24 30 and 60?

2 answers:

6 0

Step 1: LCM of 24 , 30 and 60 = 120

so 120 is the least no which is divisible by all 24 , 30 and 60

Step 2: factors of 120 will be 2^3 * 3 * 5

so the least perfect square, which is divisible by 24, 30 and 60 will be
(2^3 * 3 * 5) x ( 2 * 3 * 5 ) = 3600

3600

exis [7]3 years ago

5 0

Answer: 3600 is the least perfect square number which is divisible by 24,30 and 60.

Step-by-step explanation:

Since we have given that

The numbers are 24,30 and 60.

We need to find the least perfect square.

First we find the L.C.M. of 24, 30 and 60 .

So, L.C.M. of 24, 30 and 60 = 120

But 120 is not a perfect square because:

120=2×2×2×3×5

Since 2,3 and 5 has no pair.

We will multiply with 2,3,and 5.

So, it becomes,

2×2×2×3×5×2×3×5

=3600

Hence, 3600 is the least perfect square number which is divisible by 24,30 and 60.

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In a survey of 603 adults, 98 said that they regularly lie to people conducting surveys. Create a 99% confidence interval for th

marysya [2.9K]

Answer:

The population proportion is estimated to be with 99% confidence within the interval (0.1238, 0.2012).

Step-by-step explanation:

The formula for estimating the population proportion by a confidence interval is given by:

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

Where:

$\hat{p}$ is the sample's proportion of success, which in this case is the people that regularly lie during surveys,

$z_{\alpha /2}$ is the critical value needed to find the tails of distribution related to the confidence level,

$n$ is the sample's size.

<u>First</u> we compute the $\hat{p}$ value:

$\hat{p}=\frac{successes}{n}=\frac{98}{603}=0.1625$

<u>Next</u> we find the z-score at any z-distribution table or app (in this case i've used StatKey):

$z_{\alpha /2}=2.576$

Now we can replace in the formula with the obtained values to compute the confidence interval:

$\hat{p}\pm z_{\alpha /2}\times\sqrt{\frac{\hat{p}\times(1-\hat{p})}{n}}=0.1625\pm 2.576\times\sqrt{\frac{0.1625\times(1-0.1625)}{603}}=(0.1238, 0.2012)$

5 0

3 years ago

Determine the relationships between the following lines: *

Dennis_Churaev [7]

9514 1404 393

Answer:

the lines are perpendicular

Step-by-step explanation:

You can tell something by looking at the differences of coordinates:

B-A = (6-2, -11-5) = (4, -16) . . . . . Δy/Δx = -16/4 = -4

D-C = (-1-3, 9-10) = (-4, -1) . . . . . Δy/Δx = -1/-4 = 1/4

The product of the slopes of these lines is (-4)(1/4) = -1, so ...

the lines are perpendicular

4 0

3 years ago

A family decides to put tiles in the entryway of their home. The entryway has an area of 7 square meters. If each tile is 5 cent

lyudmila [28]

9514 1404 393

Answer:

2800 tiles

Step-by-step explanation:

Each tile has an area of (0.05 m)² = 0.0025 m². Then the number of tiles required to cover 7 square meters is ...

(7 m²)/(0.0025 m²/tile) = 2800 tiles

It will take 2800 tiles to cover the entryway.

8 0

3 years ago

The local oil changing business is very busy on Saturday mornings and is considering expanding. A national study of similar busi

eimsori [14]

Answer:

$t=\frac{4.2-3.6}{\frac{1.4}{\sqrt{16}}}=1.714$

Reject the null hypothesis if the observed "t" value is less than -2.131 or higher than 2.131

Rejection Zone: $t_{calculated}$ or $t_{calculated}>2.131$

In our case since our calculated value is not on the rejection zone we don't have enough evidence to reject the null hypothesis at 5% of significance.

Step-by-step explanation:

Previous concepts and data given

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".

$\bar X=4.2$ represent the sample mean

$s=1.4$ represent the sample standard deviation

n=16 represent the sample selected

$\alpha=0.05$ significance level

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is different from 3.6, the system of hypothesis would be:

Null hypothesis: $\mu = 3.6$

Alternative hypothesis: $\mu \neq 3.6$

If we analyze the size for the sample is < 30 and we know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{4.2-3.6}{\frac{1.4}{\sqrt{16}}}=1.714$

Critical values

On this case since we have a bilateral test we need to critical values. We need to use the t distribution with $df=n-1=16-1=15$ degrees of freedom. The value for $\alpha=0.05$ and $\alpha/2=0.025$ so we need to find on the t distribution with 15 degrees of freedom two values that accumulates 0.025 of the ara on each tail. We can use the following excel codes:

"=T.INV(0.025,15)" "=T.INV(1-0.025,15)"

And we got $t_{crit}=\pm 2.131$

So the decision on this case would be:

Reject the null hypothesis if the observed "t" value is less than -2.131 or higher than 2.131

Rejection Zone: $t_{calculated}$ or $t_{calculated}>2.131$

Conclusion

In our case since our calculated value is not on the rejection zone we don't have enough evidence to reject the null hypothesis at 5% of significance.

3 0

4 years ago

I don’t know the answer to that one can you help me please

dybincka [34]

Answer:

16/45

Step-by-step explanation:

Step 1: When dividing fractions, use “KFC”. It means Keep the first fraction, Flip the second one, and

Change it to multiplication

-4/20 ÷ -9/16 → -4/20 ∙ 16/-9

Step 2: Reduce any fractions if necessary, it makes multiplying them easier and you will have to reduce anyway at the end. It’s easier arithmetic to reduce at this step. The first fraction reduces because both the numerator and denominator are divisible by 4.

-1/5 ∙ 16/-9

Step 3: Multiply numerators and denominators together to get one fraction

(-16)/(-45)

Step 4: Cancel out the negatives, a negative divided by a negative is a positive. Our final answer is

16/45

4 0

4 years ago