Answer:
B
Step-by-step explanation:
Answer:
![\textsf{(a)} \quad (3x)^{\circ}+(x+14)^{\circ}=90^{\circ}](https://tex.z-dn.net/?f=%5Ctextsf%7B%28a%29%7D%20%5Cquad%20%283x%29%5E%7B%5Ccirc%7D%2B%28x%2B14%29%5E%7B%5Ccirc%7D%3D90%5E%7B%5Ccirc%7D)
![\textsf{(b)} \quad m \angle 1=\boxed{57}\:^{\circ}](https://tex.z-dn.net/?f=%5Ctextsf%7B%28b%29%7D%20%5Cquad%20m%20%5Cangle%201%3D%5Cboxed%7B57%7D%5C%3A%5E%7B%5Ccirc%7D)
![m \angle 2=\boxed{33}\:^{\circ}](https://tex.z-dn.net/?f=m%20%5Cangle%202%3D%5Cboxed%7B33%7D%5C%3A%5E%7B%5Ccirc%7D)
Step-by-step explanation:
From inspection of the given diagram:
<h3><u>Part (a)</u></h3>
A right angle is 90° and is represented by the ∟ symbol.
To find x, <u>equal</u> the sum of the angles to 90° and solve for x:
![\implies m \angle 1+m\angle2=90^{\circ}](https://tex.z-dn.net/?f=%5Cimplies%20m%20%5Cangle%201%2Bm%5Cangle2%3D90%5E%7B%5Ccirc%7D)
![\implies (3x)^{\circ}+(x+14)^{\circ}=90^{\circ}](https://tex.z-dn.net/?f=%5Cimplies%20%283x%29%5E%7B%5Ccirc%7D%2B%28x%2B14%29%5E%7B%5Ccirc%7D%3D90%5E%7B%5Ccirc%7D)
![\implies 3x+x+14=90](https://tex.z-dn.net/?f=%5Cimplies%203x%2Bx%2B14%3D90)
![\implies 4x+14=90](https://tex.z-dn.net/?f=%5Cimplies%204x%2B14%3D90)
![\implies 4x+14-14=90-14](https://tex.z-dn.net/?f=%5Cimplies%204x%2B14-14%3D90-14)
![\implies 4x=76](https://tex.z-dn.net/?f=%5Cimplies%204x%3D76)
![\implies 4x \div 4=76 \div 4](https://tex.z-dn.net/?f=%5Cimplies%204x%20%5Cdiv%204%3D76%20%5Cdiv%204)
![\implies x=19](https://tex.z-dn.net/?f=%5Cimplies%20x%3D19)
<h3><u>Part (b)</u></h3>
To find the degree measure of each angle, substitute the found value of x into the expression for each angle.
![\implies m \angle 1=(3 \cdot 19)^{\circ}=57^{\circ}](https://tex.z-dn.net/?f=%5Cimplies%20m%20%5Cangle%201%3D%283%20%5Ccdot%2019%29%5E%7B%5Ccirc%7D%3D57%5E%7B%5Ccirc%7D)
![\implies m \angle 2=(19+14)^{\circ}=33^{\circ}](https://tex.z-dn.net/?f=%5Cimplies%20m%20%5Cangle%202%3D%2819%2B14%29%5E%7B%5Ccirc%7D%3D33%5E%7B%5Ccirc%7D)
Answer:
43
Step-by-step explanation:
Estimate the area under the curve f(x) = 16 - x^2 from x = 0 to x = 3 by using three inscribed (under the curve) rectangles
First we find out the width of the rectangle
Δx=b−a/n, a= 0 and b= 3, n= 3
so Δx= 1
Divide the interval [0,3] into 3 sub intervals of width=1
[0,1] [1,2] [2,3]
Now we plug in end point and evaluate the function
We take left endpoints
![f(x) = 16 - x^2](https://tex.z-dn.net/?f=f%28x%29%20%3D%2016%20-%20x%5E2)
f(0) = 16 - 0^2=16
f(1) = 16 - 1^2= 15
f(2) = 16 - 2^2= 12
Now sum = Δx(f(0) + f(1)+f(2))
= 1 (16+15+12)= 43
Answer:
47
Step-by-step explanation:
Because x is 47
Thank you so much
Maximum height of a bar in a relative frequency histogram ranges from
0<Height of bar in a relative frequency histogram≤1
So a) 1 is the correct answer.
So let me start from here , in frequency histogram on X axis we draw bars and on vertical axis we represent frequencies.
But in relative frequency histogram we represent bars on X axis but relative frequency on Y axis i.e vertical axis.
Let me start by taking an example.Consider 20 observations
Interval frequency Relative frequency
0-5 4 4/20
5-10 8 8/20
10-15 5 5/20
15-20 3 3/20
As you can see from above example the height of bar can't extend than 1.
and sum of all relative frequency=4/20 +8/20 +5/20+3/20 =1