What is the greatest common factor of 30 and 18

Three cyclists simultaneously start racing on a circular track at 7 am. It takes them 10 minutes, 25 minutes and 15 minutes resp

slega [8]

Answer:

9:30 am

Step-by-step explanation:

factors of 10; 5 and 2

factors of 15; 5 and 3

factors of 25; 5 and 5

calculate lcm so, 5x5x3x2 =150

150 mins = 2hr 30mins

7am+2hr30min = 9:30 am

6 0

4 years ago

Read 2 more answers

Use the distance formula to calculate the length of the leg CD

Karo-lina-s [1.5K]

To calculate the distance between two points on the coordinate system you have to use the following formula:

$d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}$

Where

d represents the distance between both points.

(x₁,y₁) are the coordinates of one of the points.

(x₂,y₂) are the coordinates of the second point.

To determine the length of CD, the first step is to determine the coordinates of both endpoints from the graph

C(2,-1)

D(-1,-2)

Replace the coordinates on the formula using C(2,-1) as (x₁,y₁) and D(-1,-2) as (x₂,y₂)

$\begin{gathered} d_{CD}=\sqrt[]{(2-(-1))^2+((-1)-(-2))}^2 \\ d_{CD}=\sqrt[]{(2+1)^2+(-1+2)^2} \\ d_{CD}=\sqrt[]{3^2+1^2} \\ d_{CD}=\sqrt[]{9+1} \\ d_{CD}=\sqrt[]{10} \end{gathered}$

The length of CD is √10 units ≈ 3.16 units

6 0

1 year ago

In speech class, Carolyn needs at least a B + to keep her financial aid. To earn a B+, the average of her four speeches must be

Arada [10]

Answer:

<h3>The minimum score speech to get a B+ is 89.</h3>

Step-by-step explanation:

Average of the first 3 = 85 + 77 + 81 / 3

= 243 / 3

= 81

The fourth score ( to get 85 ) = 81 + 89

= 170 / 2

= 85

4 0

3 years ago

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Write a description of this inequality: <br> -5a+3>1

iren [92.7K]

The sum of -5a and 3 is greater than 1.

8 0

3 years ago

In an examination of purchasing patterns of shoppers, a sample of 16 shoppers revealed that they spent, on average, $54 per hour

Lesechka [4]

Answer:

$54-1.64\frac{21}{\sqrt{16}}=45.39$

$54 +1.64\frac{21}{\sqrt{16}}=62.61$

So on this case the 90% confidence interval would be given by (45.39;62.61)

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".

$\bar X=54$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=21$ represent the sample standard deviation

n=16 represent the sample size

Solution to the problem

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

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.90 or 90%, the value of $\alpha=1-0.9=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$

Now we have everything in order to replace into formula (1):

$54-1.64\frac{21}{\sqrt{16}}=45.39$

$54 +1.64\frac{21}{\sqrt{16}}=62.61$

So on this case the 90% confidence interval would be given by (45.39;62.61)

4 0

4 years ago