Answer:
37 and 38
Step-by-step explanation:
let the consecutive integers be x-1 and x
If their sum is 75
x-1+x = 75
2x - 1 = 75
2x = 75+1
2x = 76
x = 76/2
x = 38
First integer = x - 1
First integer = 38-1 = 37
Second integer is 38
Hence the integers are 37 and 38
Using the given equation y-3 = 3/4(x+2)
Give Y a value and then solve for x:
If y = 0 the equation is now:
0 -3 = 3/4(x+2)
Solve for x:
-3 = 3/4x + 1.5
-4.5 = 3/4x
x = -4.5 / 3/4
x = -6
So the first point would be (-6,0)
Now make x 0 and solve for y:
y -3 = 3/4(0+2)
y-3 = 0 + 1.5
y = 4.5
So the 2nd point would be (0,4.5)
You are close, but the dot you have on y=4, needs to be moved up to 4.5.
The length of the rope needed is 15 feet
Given the following parameters;
- Height of the pole = 9 foot
- The distance from the <u>rope away from the base </u>of the pole is 12 feet
Required
To get the length of the rope, you will use the pythagoras theorem expressed as:
Substituting the given parameters:
c² = 9² + 12²
c² =81 + 144
c² = 225
c = √225
c = 15 feet
Therefore the length of the rope needed is 15 feet
Learn more on Pythagoras theorem here: brainly.com/question/231802
Answer:
The standard deviation of the following data set is 32.2
Step-by-step explanation:
step 1
Find the mean
we have
![[56,78,123,34,67,9,20]](https://tex.z-dn.net/?f=%5B56%2C78%2C123%2C34%2C67%2C9%2C20%5D)
Sum the data and divided by the number of elements
![[56+78+123+34+67+91+20]/7=469/7=67](https://tex.z-dn.net/?f=%5B56%2B78%2B123%2B34%2B67%2B91%2B20%5D%2F7%3D469%2F7%3D67)
step 2
For each number: subtract the Mean and square the result
![[(56-67)^{2},(78-67)^{2},(123-67)^{2},(34-67)^{2},(67-67)^{2},(91-67)^{2},(20-67)^{2}]](https://tex.z-dn.net/?f=%5B%2856-67%29%5E%7B2%7D%2C%2878-67%29%5E%7B2%7D%2C%28123-67%29%5E%7B2%7D%2C%2834-67%29%5E%7B2%7D%2C%2867-67%29%5E%7B2%7D%2C%2891-67%29%5E%7B2%7D%2C%2820-67%29%5E%7B2%7D%5D)
![[121,121,3,136,1,089,0,576,2,209]](https://tex.z-dn.net/?f=%5B121%2C121%2C3%2C136%2C1%2C089%2C0%2C576%2C2%2C209%5D)
step 3
Work out the mean of those squared differences
![[121+121+3,136+1,089+0+576+2,209]/7=1,036](https://tex.z-dn.net/?f=%5B121%2B121%2B3%2C136%2B1%2C089%2B0%2B576%2B2%2C209%5D%2F7%3D1%2C036)
This value is called the "Variance"
step 4
Take the square root of the variance
