Answer:
The length of the circular arc is 8.64 inches
Step-by-step explanation:
Length of circular arc (L) = central angle/360° × 2πr
central angle = pie/4 = 45°, r (radius) = 11 inches
L = 45°/360° × 2 × 3.142 × 11 = 8.64 inches (to two decimal places)
Answer:
x = 0, y = 7
Step-by-step explanation:
Solving a system of equations using substitution requires one side to be equal to a variable present in the equation, in this case x or y. We should simplify the equation using elimination before substituting to reduce the chance of error.
In order to use the elimination method, you have to create variables that have the same coefficient—then you can eliminate them. These equations arew already aligned for us.
3x - 10y=-70
-<u> 4x +9y = 63</u>
-x + y = 7
Now, for substitution, the equation must be set to a variable.
-x + y = 7
y = x + 7
Next, plug the equation in where applicable in another equation.
4x +9(x + 7) = 63
4x + 9x + 63 = 63
13x = 0
x = 0
The final step of substitution is to plug the known variable into an equation to find the other variable.
3(0) - 10y=-70
0 - 10y = -70
10y = 70
y = 7
I guarantee you this answer is correct, I worked it out using other methods and graphing prior to submitting this answer.
A. T= d/r
A good way to remember this is by making a pyramid with 3 parts and putting distance at the top and rate and time in the other two parts. This way you can visibly see the equation and use it if you need to find one for rate.
B. It's reasonable to write distance as a positive number because distance is always positive. You are not able to have a negative distance. Imagine someone standing on a side walk. Even if they are not moving, their distance is 0 which is positive. If they move backwards or forwards, their distance is still positive because it is more than that 0 and they are gaining something.
C. Just plug in the numbers into the formula.
T= d/r
T= 32.12 m /<span>8.8 m/min
T= 3.65 min
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Answer:
Probability that the cost will be less than $500 is 0.95994 .
Step-by-step explanation:
We are given that Money magazine reported that a visit to a hospital emergency room for something as simple as a sore throat has a mean cost of $348 with a standard deviation of $87.
Let X = cost of a hospital emergency room visit for this medical service
So, X ~ N(
)
The standard normal z score distribution is given by;
Z = 
~ N(0,1)
(a) Probability that the cost will be less than $500 = P(X < $500)
P(X < 500) = P( < 
) = P(Z < 1.75) = 0.95994 {from z table}
Therefore, the probability that the cost will be less than $500 is 0.95994 .
