Answer:
Step-by-step explanation:
Both 115 and 145 mph are above the mean. Draw a normal curve and mark these speeds. 115 mph is 1 standard deviation above the mean; 130 would be 2 standard deviations above the mean; and 145 would be 3 s. d. above it.
We need to find the area under the standard normal curve between 115 and 145. This is equivalent to the area under the standard normal curve between z = 1 and z = 3.
I used my TI-83 Plus calculator's DISTR function "normalcdf(" to calculate this area: normalcdf(1, 3) = 0.1573.
The area between z = 1 and z = 3 is 0.1573. In other words, the percentage of serves that were between 115 and 145 mph was 15.73%.
Answer:
210.82
Step-by-step explanation:
arc length= 2pi r (Ø/360)
= 2x 3.14 x 47(257/360)=210.82
Answer:
-36
Step-by-step explanation:
Just plug in -12 for x
f(x) = 4 x (-12) -12
-48 - 12 = -36
The equation of the transformation of the exponential function <em>y</em> = 2ˣ in the form <em>y</em> = A·2ˣ + k, obtained from the simultaneous found using the points on the graph is <em>y</em> = (-2)·2ˣ + 3
<h3>What is an exponential equation?</h3>
An exponential equation is an equation that has exponents that consists of variables.
The given equation is <em>y</em> = 2ˣ
The equation for the transformation is; <em>y</em> = A·2ˣ + k
The points on the graphs are;
(0, 1), (1, -1) and (2, -5)
Plugging the <em>x </em>and <em>y</em>-values to find the value <em>A</em> and <em>k</em> gives the following simultaneous equations;
When <em>x</em> = 0, <em>y</em> = 1, therefore;
1 = A·2⁰ + k = A + k
1 = A + k...(1)
When <em>x</em> = 1, <em>y</em> = -1, which gives;
-1 = A·2¹ + k
-1 = 2·A + k...(2)
Subtracting equation (1) from equation (2) gives;
-1 - 1 = 2·A - A + k - k
-2 = A
1 = A + k, therefore;
1 = -2 + k
k = 2 + 1 = 3
k = 3
Which gives;
y = -2·2ˣ + 3 = 3 - 2·2ˣ
Learn more about the solutions to simultaneous equations here:
brainly.com/question/26310043
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Your answer would be:
The fourth option ---> 12