Which of the following is an x-intercept of the graph of the function shown below?
2 answers:
Answer: Second option.
Step-by-step explanation:
By defintion, a Quadratic function is a polynomial of degree 2 and it has the following form:
Therefore, the function given is Quadratic. This is:
The steps to find the roots (or the x-intercepts) of the function, are:
1. You must substitute :
2. Now, you can factor the Quadratic equation. Choose two numbers whose sum is 6 and whose product is 9. Notice that:
Therefore, you will get a "Double root".
4. So the solution is:
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Answer:
(a) P(X > $57,000) = 0.0643
(b) P(X < $46,000) = 0.1423
(c) P(X > $40,000) = 0.0066
(d) P($45,000 < X < $54,000) = 0.6959
Step-by-step explanation:
We are given that U.S. Bureau of Economic Statistics reports that the average annual salary in the metropolitan Boston area is $50,542.
Suppose annual salaries in the metropolitan Boston area are normally distributed with a standard deviation of $4,246.
<em>Let X = annual salaries in the metropolitan Boston area</em>
SO, X ~ Normal()
The z-score probability distribution for normal distribution is given by;
Z = ~ N(0,1)
where, = average annual salary in the Boston area = $50,542
= standard deviation = $4,246
(a) Probability that the worker’s annual salary is more than $57,000 is given by = P(X > $57,000)
P(X > $57,000) = P( >
) = P(Z > 1.52) = 1 - P(Z
1.52)
= 1 - 0.93574 = <u>0.0643</u>
<em>The above probability is calculated by looking at the value of x = 1.52 in the z table which gave an area of 0.93574</em>.
(b) Probability that the worker’s annual salary is less than $46,000 is given by = P(X < $46,000)
P(X < $46,000) = P( <
) = P(Z < -1.07) = 1 - P(Z
1.07)
= 1 - 0.85769 = <u>0.1423</u>
<em>The above probability is calculated by looking at the value of x = 1.07 in the z table which gave an area of 0.85769</em>.
(c) Probability that the worker’s annual salary is more than $40,000 is given by = P(X > $40,000)
P(X > $40,000) = P( >
) = P(Z > -2.48) = P(Z < 2.48)
= 1 - 0.99343 = <u>0.0066</u>
<em>The above probability is calculated by looking at the value of x = 2.48 in the z table which gave an area of 0.99343</em>.
(d) Probability that the worker’s annual salary is between $45,000 and $54,000 is given by = P($45,000 < X < $54,000)
P($45,000 < X < $54,000) = P(X < $54,000) - P(X $45,000)
P(X < $54,000) = P( <
) = P(Z < 0.81) = 0.79103
P(X $45,000) = P(
) = P(Z
-1.31) = 1 - P(Z < 1.31)
= 1 - 0.90490 = 0.0951
<em>The above probability is calculated by looking at the value of x = 0.81 and x = 1.31 in the z table which gave an area of 0.79103 and 0.9049 respectively</em>.
Therefore, P($45,000 < X < $54,000) = 0.79103 - 0.0951 = <u>0.6959</u>
The number of bags of chips sold is 8 and the number of packs of cookies sold is 12
<em><u>Solution:</u></em>
Let "a" be the number of bags of chips sold
Let "b" be the number of packs of cookies sold
Given that,
Cost of one bag of chips = $ 1.50
Cost of one pack of cookies = $ 1.25
Yesterday Abigail made $27 from selling a total of 20 bags of chips and packs of cookies
<em><u>So we can frame a equation as:</u></em>
Number of bags of chips sold + number of packs of cookies sold = 20
a + b = 20 ---- eqn 1
Also given that Abigail made $27 from selling
number of bags of chips sold x Cost of one bag of chips + number of packs of cookies sold x Cost of one pack of cookies = $ 27
1.5a + 1.25b = 27 ---- eqn 2
<em><u>Let us solve eqn 1 and eqn 2 to find values of "a" and "b"</u></em>
From eqn 1,
a = 20 - b ---- eqn 3
Substitute eqn 3 in eqn 2
1.5(20 - b) + 1.25b = 27
30 - 1.5b + 1.25b = 27
-0.25b = -3
<h3>b = 12</h3>Therefore from eqn 3,
a = 20 - b = 20 - 12 = 8
<h3>a = 8</h3><em><u>Thus we have:</u></em>
number of bags of chips sold = 8
number of packs of cookies sold = 12