What is the smallest number with the factors 1,2,3,4, and 5? What is the special name for it?

It costs Doug $30 to set up a cupcake stand. He charges $2 for every cupcake he sells. If Doug makes $48 of profit in one day, h

Lunna [17]

Answer:

It is 39 cupcakes.

Since he charges $2 per cupcake (39), it is 78.

He makes profit so subtract 30 from 78 and you get $48.

6 0

3 years ago

Select the items the crusaders brought back with them from the East.

gulaghasi [49]

Answer:Jewels, WOOL, SILK

Step-by-step explanation:

sorry for the caps

4 0

3 years ago

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The base of an isosceles triangle is one and a half times the length of the other two sides.A smaller triangle has a perimeter t

Anna11 [10]

Answer:

Perimeter of the smaller triangle = 1.75x

Step-by-step explanation:

Let the two equal sides of an isosceles triangle = x

Therefore, length of the base = $(1\frac{1}{2})x$

Perimeter of this isosceles triangle = x + x + $(1\frac{1}{2})x$

= 2x + $(1+\frac{1}{2})x$

= 2x + x + $\frac{x}{2}$

= $\frac{5x}{2}$

Since, smaller triangle has a perimeter that is half the perimeter of the larger triangle,

Length of each corresponding side of smaller triangle will be half of the larger triangle.

Length of sides of the smaller triangle = $\frac{x}{2},\frac{x}{2},(1\frac{1}{2})\frac{x}{2}$

Perimeter of the smaller triangle = $\frac{x}{2}+\frac{x}{2}+(1\frac{1}{2})\frac{x}{2}$

= x + $\frac{x}{2}+\frac{x}{4}$

= $\frac{3}{2}x+\frac{x}{4}$

= $\frac{6}{4}x+\frac{x}{4}$

= $\frac{7}{4}x$

= 1.75x

Therefore, expression that represents the perimeter of the smaller triangle is (1.75x)

4 0

3 years ago

f the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability, how many

Oksanka [162]

Answer:

n=1849

Step-by-step explanation:

Previous concepts

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

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

Solution to the problem

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 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58$

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 $ME =\pm 0.03$ 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)

Assuming that the proportion is estimated $\hat p =0.5$ . And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{2.58})^2}=1849$

And rounded up we have that n=1849

7 0

3 years ago

Given the length of three sides of a triangle, which is a right triangle?

RSB [31]

The aides of a right triangle will always satisfy the Pythagorean relationship ...

 a² + b²= c²

We can take each of these and try it out:

(1) ... 10² + 24² = 100 + 576 = 676
 √676 = 26 Yes.

(2) ... 12² + 18² = 144 + 324 = 468
 √468 = 21.6, not 20. No.

(3) ... 15² + 26² = 225 + 676 = 901
 √901 = 30.017 Awfully close. As an engineer, I'll buy this one. Yes.

(4) ... 40² + 50² = 1,600 + 2,500 = 4,100
 √4,100 = 64.03, not 80. No.

8 0

3 years ago

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