Answer:
2/27
Step-by-step explanation:
Probability to get an even number on a spinner is 4/9.
Probability of getting a 5 on a die is 1/6.
4/9*1/6=4/54=2/27
7.5 km/h
Step-by-step explanation:
Let's assign the speed of Jerry in still air as <em>x </em> (in km/h)
Let's assign the speed of the wind as <em>y </em>(in km/h)
With the wind as Jerry’s back, he takes 10 minutes to get to the library. We can create the following equation. (<em>we are converting the minutes to hours by dividing by 60</em>);
2.5 / (x + y) = 10/60
10x + 10y = 150
x + y = 15
With the wind against Jerry, he takes 15 minutes from the library. We can create the following equation;
2.5 / (x-y) = 15/60
15x – 15y = 150
x – y = 10
We can now solve the simultaneous equation by subtraction;
x + y = 15
x – y = 10
2y = 5
y = 5/2 = 2.5
y = 2.5 km/h
x = 7.5 km/h
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The lower quartile is 60. Quartiles are the numbers in the middle of the median and lowest/highest number.
A) The empirical rule tells you the probability of being within 1 standard deviation of the mean is 68%.
b) The probability that the sample mean falls within 3 standard deviations* of the mean is 99.7%.
___
* The standard deviation of the sample mean is 1/√9 = 1/3 of the standard deviation of an individual sample. Hence the same limits (90-110) now cover 3 standard deviations of the sample mean.
Answer:
y=7/3x²-13/3x+2
Step-by-step explanation:
<u>Determine the value of c:</u>
y=ax²+bx+c
2=a(0)²+b(0)+c
2=c
<u>Substitute (1,0) into the quadratic and create an equation with a and b:</u>
y=ax²+bx+2
0=a(1)²+b(1)+2
0=a+b+2
-2=a+b
<u>Do the same with (3,10) to get a second equation:</u>
y=ax²+bx+2
10=a(3)²+b(3)+2
10=9a+3b+2
8=9a+3b
<u>Set the two equations equal to each other and solve for a and b:</u>
-2=a+b
8=9a+3b
<u>Multiply first equation by 3 and eliminate b to find a:</u>
-6=3a+3b
- (8=9a+3b)
_______
-14=-6a
14/6=a
7/3=a
<u>Substitute 7/3=a into the first equation:</u>
-2=7/3+b
-2-(7/3)=b
-13/3=b
<u>Final equation:</u>
y=7/3x²-13/3x+2
See the graph for a visual representation