Refer to the diagram shown below.
The dimensions of the outside of the picture rame are:
Width = x + 1 + 1 = x + 2 inches
Length = (x+2) + 1 + 1 = x + 4 inches.
The perimeter of the outside of the picture frame is 28 inches.
Therefore
2(x + 2) + 2(x+4) = 28
Solve for x.
2x + 4 + 2x + 8 = 28
4x + 12 = 28
4x = 16
x = 4 inches
Answer: 4 inches
Answer:
#3
20tan(53) + 5 feet OR 31.54 feet (rounded to nearest hundredth)
#4
6tan(32) feet OR 3.75 km (rounded to nearest hundredth)
Step-by-step explanation:
#3
The horizontal line is at Chloe's eye level, which is 5 feet.
She looks up at an angle of 53 degrees, and is 20 feet away from the statue. This creates a right triangle that you can use basic trigonometry to solve.
Let's call the shorter leg (upper half of statue) as x and the longer leg (distance between Chloe and statue) is 20 feet. We are given the opposite and adjacent sides (from the given angle) so we can use tan.
tan = opp/adj, so tan(53)=x/20
If you plug 20 tan 53 into your calculator to find x, you get 26.54089643
But you have to add 5 feet to your answer because that is her eye level.
#4
The horizontal distance from airplane to raft is 6km, the angle of depression is 32 degrees from the airplane, and we are asked to find the altitude of the plane (x).
We are given an adjacent side and are tasked to find the opposite side, so we will use tan.
tan 32=x/6
Plug this into your calculator and you get x=3.749216111 km.
The correct answer is A.
Please mark as brainliest!
Answer:
![y=0.00673(253) +90.190=91.894](https://tex.z-dn.net/?f=y%3D0.00673%28253%29%20%2B90.190%3D91.894)
And the difference is given by:
![r_i =91.894-83=8.894](https://tex.z-dn.net/?f=r_i%20%3D91.894-83%3D8.894)
Step-by-step explanation
We assume that th data is this one:
x: 242-255 -227-251-262-207-140
y: 91- 81 -91 - 92 - 102 - 94 - 91
Find the least-squares line appropriate for this data.
For this case we need to calculate the slope with the following formula:
![m=\frac{S_{xy}}{S_{xx}}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7BS_%7Bxy%7D%7D%7BS_%7Bxx%7D%7D)
Where:
![S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}](https://tex.z-dn.net/?f=S_%7Bxy%7D%3D%5Csum_%7Bi%3D1%7D%5En%20x_i%20y_i%20-%5Cfrac%7B%28%5Csum_%7Bi%3D1%7D%5En%20x_i%29%28%5Csum_%7Bi%3D1%7D%5En%20y_i%29%7D%7Bn%7D)
![S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}](https://tex.z-dn.net/?f=S_%7Bxx%7D%3D%5Csum_%7Bi%3D1%7D%5En%20x%5E2_i%20-%5Cfrac%7B%28%5Csum_%7Bi%3D1%7D%5En%20x_i%29%5E2%7D%7Bn%7D)
So we can find the sums like this:
![\sum_{i=1}^n x_i =242+255+227+251+262+207+140=1584](https://tex.z-dn.net/?f=%5Csum_%7Bi%3D1%7D%5En%20x_i%20%3D242%2B255%2B227%2B251%2B262%2B207%2B140%3D1584)
![\sum_{i=1}^n y_i =91+ 81 +91 + 92 + 102 + 94 + 91=642](https://tex.z-dn.net/?f=%5Csum_%7Bi%3D1%7D%5En%20y_i%20%3D91%2B%2081%20%2B91%20%2B%2092%20%2B%20102%20%2B%2094%20%2B%2091%3D642)
![\sum_{i=1}^n x^2_i =242^2 +255 ^2 +227^2 +251^2 +262^2 +207^2 +140^2=369212](https://tex.z-dn.net/?f=%5Csum_%7Bi%3D1%7D%5En%20x%5E2_i%20%3D242%5E2%20%2B255%20%5E2%20%2B227%5E2%20%2B251%5E2%20%2B262%5E2%20%2B207%5E2%20%2B140%5E2%3D369212)
![\sum_{i=1}^n y^2_i =91^2 + 81 ^2 +91 ^2 + 92 ^2 + 102 ^2 + 94 ^2 + 91^2=59108](https://tex.z-dn.net/?f=%5Csum_%7Bi%3D1%7D%5En%20y%5E2_i%20%3D91%5E2%20%2B%2081%20%5E2%20%2B91%20%5E2%20%2B%2092%20%5E2%20%2B%20102%20%5E2%20%2B%2094%20%5E2%20%2B%2091%5E2%3D59108)
![\sum_{i=1}^n x_i y_i =242*91 +255*81 +227*91 +251*92 +262*102 +207*94 +140*91=145348](https://tex.z-dn.net/?f=%5Csum_%7Bi%3D1%7D%5En%20x_i%20y_i%20%3D242%2A91%20%2B255%2A81%20%2B227%2A91%20%2B251%2A92%20%2B262%2A102%20%2B207%2A94%20%2B140%2A91%3D145348)
With these we can find the sums:
![S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=369212-\frac{1584^2}{7}=10775.429](https://tex.z-dn.net/?f=S_%7Bxx%7D%3D%5Csum_%7Bi%3D1%7D%5En%20x%5E2_i%20-%5Cfrac%7B%28%5Csum_%7Bi%3D1%7D%5En%20x_i%29%5E2%7D%7Bn%7D%3D369212-%5Cfrac%7B1584%5E2%7D%7B7%7D%3D10775.429)
![S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=145348-\frac{1584*642}{7}=72.571](https://tex.z-dn.net/?f=S_%7Bxy%7D%3D%5Csum_%7Bi%3D1%7D%5En%20x_i%20y_i%20-%5Cfrac%7B%28%5Csum_%7Bi%3D1%7D%5En%20x_i%29%28%5Csum_%7Bi%3D1%7D%5En%20y_i%29%7D%7Bn%7D%3D145348-%5Cfrac%7B1584%2A642%7D%7B7%7D%3D72.571)
And the slope would be:
![m=\frac{72.571}{10775.429}=0.00673](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B72.571%7D%7B10775.429%7D%3D0.00673)
Now we can find the means for x and y like this:
![\bar x= \frac{\sum x_i}{n}=\frac{1584}{7}=226.286](https://tex.z-dn.net/?f=%5Cbar%20x%3D%20%5Cfrac%7B%5Csum%20x_i%7D%7Bn%7D%3D%5Cfrac%7B1584%7D%7B7%7D%3D226.286)
![\bar y= \frac{\sum y_i}{n}=\frac{642}{7}=91.714](https://tex.z-dn.net/?f=%5Cbar%20y%3D%20%5Cfrac%7B%5Csum%20y_i%7D%7Bn%7D%3D%5Cfrac%7B642%7D%7B7%7D%3D91.714)
And we can find the intercept using this:
![b=\bar y -m \bar x=91.714-(0.00673*226.286)=90.190](https://tex.z-dn.net/?f=b%3D%5Cbar%20y%20-m%20%5Cbar%20x%3D91.714-%280.00673%2A226.286%29%3D90.190)
So the line would be given by:
![y=0.00673 x +90.190](https://tex.z-dn.net/?f=y%3D0.00673%20x%20%2B90.190)
The prediction for 253 seconds is:
![y=0.00673(253) +90.190=91.894](https://tex.z-dn.net/?f=y%3D0.00673%28253%29%20%2B90.190%3D91.894)
And the difference is given by:
![r_i =91.894-83=8.894](https://tex.z-dn.net/?f=r_i%20%3D91.894-83%3D8.894)
Answer:
He has surveyed the students who are already participating in the choir. So naturally the number of students who likes the choir class will be higher than in other classes. You can see it reflected in the data.
Step-by-step explanation:
He has surveyed the students who are already participating in the choir. So naturally the number of students who likes the choir class will be higher than in other classes. You can see it reflected in the data.
If he needs to make an inference on the whole school he needs to randomly pick people from the school and ask the same question. Then he can make a better inference about the favorite class of students.