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What is the greatest common factor shared by 70 and 15?
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Answer 1
Answer: The answer is 5
Step by step explaination
Answer 2
Answer:

Answer:

The greatest common factor of 70 and 15 is 5.

Step-by-step explanation:

First, list the prime factors for each individual number

Next, circle each common prime factor. This means that you must find the prime factors that are the same as each other. For example, if it's 1 3 4 and 2 3 5, the common prime factor would be 3.

Finally, you must multiply all of the common prime factors. Your answer will be the greatest common factor!

So, the greatest common factor of 70 and 15 is 5.

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Find two positive numbers such that the sum of the first and twice the second is 200 and their product is a maximum.

The speed of light is 300,000,000 meters per second. The sun is approximately meters 1.5 x 10¹¹ from Earth. How many seconds does it take for the sunlight to reach Earth?

Answers

Final answer:

By using the formula for time (distance divided by speed), it is found that sunlight takes approximately 500 seconds, or about 8.3 minutes, to reach the Earth from the Sun.

Explanation:

The speed of light is 300,000,000 meters per second (m/s) and the distance from the Earth to the Sun is approximately 1.5 x 10¹¹ meters. We can calculate the time it takes for sunlight to reach Earth by using the formula for time, which is distance divided by speed. Plugging these values into the formula, we have:

Time = distance/speed = (1.5 x 10¹¹ meters) / (3.0 x 10⁸ m/s) = 500 seconds.

This means that it takes approximately 500 seconds, or about 8.3 minutes, for sunlight to travel from the Sun to the Earth.

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Answer:

about 500 seconds

Step-by-step explanation:

The distances between stars across the universe are very great, so astronomers use light years as a larger unit than miles or kilometers. To calculate the actual distance of a light year, you simply need to multiply the speed of light by the number of seconds in a year. This means 300,000,000 multiplied by 500 and you would get 1.5 x 10¹¹ which is equal too 150,000,000,000

Find the components of the vertical force Bold Upper FFequals=left angle 0 comma negative 4 right angle0,−4 in the directions parallel to and normal to the plane that makes an angle of StartFraction pi Over 3 EndFraction π 3 with the positive​ x-axis. Show that the total force is the sum of the two component forces.

Answers

Answer:

F_p = < - √(3) , -3 >\n\nF_o = < √(3) , -1 >

Step-by-step explanation:

- A plane is oriented in a Cartesian coordinate system such that it makes an angle of ( π / 3 ) with the positive x - axis.

- A force ( F ) is directed along the y-axis as a vector < 0 , - 4 >

- We are to determine the the components of force ( F ) parallel and normal to the defined plane.

- We will denote two unit vectors: ( u_p ) parallel to plane and ( u_o ) orthogonal to the defined plane. We will define the two unit vectors in ( x - y ) plane as follows:

- The unit vector ( u_p ) parallel to the defined plane makes an angle of ( 30° ) with the positive y-axis and an angle of ( π / 3 = 60° ) with the x-axis. We will find the projection of the vector onto the x and y axes as follows:

                         u_o = < cos ( 60° ) , cos ( 30° ) >

                         u_o = < (1)/(2) , (√(3) )/(2) >

- Similarly, the unit vector ( u_o ) orthogonal to plane makes an angle of ( π / 3 ) with the positive x - axis and angle of ( π / 6 ) with the y-axis in negative direction. We will find the projection of the vector onto the x and y axes as follows:

                        u_p = < cos ( (\pi )/(6) ) , - cos ( (\pi )/(3) ) >\n\nu_p = < (√(3) )/(2) , -(1)/(2) >\n

- To find the projection of force ( F ) along and normal to the plane we will apply the dot product formulation:

- The Force vector parallel to the plane ( F_p ) would be:

                          F_p = u_p(F . u_p)\n\nF_p = < (1)/(2) , (√(3) )/(2) > [ < 0 , - 4 > . < (1)/(2) , (√(3) )/(2) > ]\n\nF_p = < (1)/(2) , (√(3) )/(2) > [ -2√(3) ]\n\nF_p = < -√(3) , -3 >\n

- Similarly, to find the projection of force ( F_o ) normal to the plane we again employ the dot product formulation with normal unit vector (  u_o  ) as follows:

                         F_o = u_o ( F . u_o )\n\nF_o = < (√(3) )/(2) , - (1)/(2) > [ < 0 , - 4 > . < (√(3) )/(2) , - (1)/(2) > ] \n\nF_o = < (√(3) )/(2) , - (1)/(2) > [ 2 ] \n\nF_o = < √(3) , - 1 >

- To prove that the projected forces ( F_o ) and ( F_p ) are correct we will apply the vector summation of the two orthogonal vector which must equal to the original vector < 0 , - 4 >

                       F = F_o + F_p\n\n< 0 , - 4 > = < √(3), -1 > + < -√(3), -3 > \n\n< 0 , - 4 > = < √(3) - √(3) , -1 - 3 > \n\n< 0 , - 4 > = < 0 , - 4 >  .. proven                    

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Answers

Answer:

1. The last one

2. The third one

On a coordinate plane, a line goes through (0, negative 3) and (2, 2). A point is at (2, negative 3).Complete the statements about finding the equation of the line that is parallel to line n and passes through point (2, –3).

The slope of the graphed line is
.
The slope of the parallel line is
.
An equation that can be used to find the y-intercept of the parallel line is
.
The y-intercept of the parallel line is
.
The equation of the parallel line is
.

Answers

Answer:

5/2,     5/2,     -3= (5/2)(2)+b,     -8,     y=(5/2)x-8

Step-by-step explanation:

Answer:

The slope of the graphed line is  

✔ 5/2

.

The slope of the parallel line is  

✔ 5/2

.

An equation that can be used to find the y-intercept of the parallel line is  

✔ –3 = (5/2)(2) + b

.

The y-intercept of the parallel line is  

✔ –8

.

The equation of the parallel line is  

✔ y = (5/2)x – 8

.

Step-by-step explanation:

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 139 millimeters, and a variance of 49. If a random sample of 34 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 1.8 millimeters

Answers

The probability that the sample mean would differ from the population mean by more than 1.8 millimeters is approximately 0.0668.

What is the standard deviation?

A standard deviation (σ) is a measure of the distribution of the data in reference to the mean.

The standard deviation of the population is $√(49) = 7$ millimeters. The standard error of the sample mean is then

$(7)/(√(34)) = (7)/(5.874) \approx 1.2$millimeters.

The probability that the sample mean would differ from the population mean by more than 1.8 millimeters is the probability that it falls outside of the interval $(139 - 1.8, 139 + 1.8)$. We can use the standard normal distribution to approximate this probability.

First, we need to convert the difference between the sample mean and the population means to standard units.

The difference of 1.8 millimeters is :

$(1.8)/(1.2) = 1.5$ standard units.

Then, we can use the standard normal distribution to find the probability that the sample mean falls outside of this interval.

This probability is equal to $1 - 2\Phi(-1.5) \approx 0.0668$,

where $\Phi$ is the standard normal cumulative distribution function.

Therefore, the required probability is approximately 0.0668.

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Parallel lines r and s are cut by two transversals, parallel lines t and u. Lines r and s are crossed by lines t and u to form 16 angles. Clockwise from top left, at the intersection of r and t, the angles are 1, 2, 3, 4; at the intersection of s and t, 5, 6, 7, 8; at the intersection of u and s, 9, 10, 11, 12; at the intersection of u and r, 13, 14, 15, 16. Which angles are alternate interior angles with angle 3? Angle5 and Angle13 Angle7 and Angle15 Angle6 and Angle16 Angle8 and Angle14 Mark this an

Answers

Answer:

5 and 13

Step-by-step explanation:

I got it right on edge

Answer:

5 and 13, got in right in edge 2020

Step-by-step explanation:
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