Answer:
The quotient is 8.25 to the nearest hundredth.
Step-by-step explanation:
If we approximate the 2 numbers
55.6875 = approximately 60 and 6.75 = approximately 7.
The division becomes 60 / 7 = approximately 9.
So 0.825 is not correct. The Decimal point must be after the first number.
If we divide the original numbers the quotient is 8.2496 or 8.25 to the nearest hundredth.
Answer:
Just substitute each number into the expression:
5(5) - 6(3) + 20(1/4)/4(3)(1/4) = 25 - 18 + 5/3 = 7 + 5/3 = 26/3 or 8 and 2/3.
Step-by-step explanation:
Answer:
![h(x)\leq 5](https://tex.z-dn.net/?f=h%28x%29%5Cleq%205)
Step-by-step explanation:
<u>Piecewise Function</u>
The given function has a point where its behavior changes. At the left side of x=3 the function is
![h(x)=x+2](https://tex.z-dn.net/?f=h%28x%29%3Dx%2B2)
While at the right side the function is
![h(x)=-x+8](https://tex.z-dn.net/?f=h%28x%29%3D-x%2B8)
We need to find the range of h, i.e. the values h takes when x moves along its domain. Let's analyze what values takes h when x decreases without limit.
![\lim\limits_{x \rightarrow -\infty }(x+2)=-\infty](https://tex.z-dn.net/?f=%5Clim%5Climits_%7Bx%20%5Crightarrow%20-%5Cinfty%20%7D%28x%2B2%29%3D-%5Cinfty)
When x=3
![h(3)=-3+8=5](https://tex.z-dn.net/?f=h%283%29%3D-3%2B8%3D5)
When x increses without limit
![\lim\limits_{x \rightarrow \infty }(-x+8)=-\infty](https://tex.z-dn.net/?f=%5Clim%5Climits_%7Bx%20%5Crightarrow%20%5Cinfty%20%7D%28-x%2B8%29%3D-%5Cinfty)
As shown, the values of h run from
to 5, i.e.
![Range \ h=(-\infty , 5]](https://tex.z-dn.net/?f=Range%20%5C%20h%3D%28-%5Cinfty%20%2C%205%5D)
Or, equivalently
![\boxed{h(x)\leq 5}](https://tex.z-dn.net/?f=%5Cboxed%7Bh%28x%29%5Cleq%205%7D)
Answer:
ST = 12 units
Step-by-step explanation:
As RA is parallel to ET, the angle in R is equal to the angle in T, and the angle in A is equal to the angle in E, so the triangle RAS is similar to the triangle SET.
If RT is 21 units, we have that RS + ST = 21 -> RS = 21 - ST
Using a rule of three with the sides of the triangle (as they are proportional), we have:
RS / ST = AR / ET
(21 - ST) / ST = 6 / 8
4 * (21 - ST) = 3*ST
84 - 4*ST = 3*ST
7*ST = 84
ST = 12 units
Kindly check complete question in the attached picture below.
Answer:
2.2236
Step-by-step explanation:
From the R output given, we can obtain the linear regression model in the form ;
y = bx + c
Intercept, c = 9.4764
Slope, b = 0.0315
x = number of manufacturing enterprise employing 20 or more workers
y = annual mean concentration of Sulphur dioxide
Hence, The regression equation model as obtained from the R output is :
y = 0.0315x + 9.4764
For the city of Duarte;
x = 200
Actual annual mean concentration of Sulphur dioxide is 18 micrograms per cubic meter.
Residual = Actual value - predicted value
Prediction using the regression equation to obtain the predicted annual mean concentration ;
The predicted y value, when x = 200
y = 0.0315(200) + 9.4764
y = 15.7764
The residual, if actual annual concentration = 18
Y residual = 18 - 15.7764 = 2.2236