Answer:
2a) -2
b) 8
Step-by-step explanation:
<u>Equation of a parabola in vertex form</u>
f(x) = a(x - h)² + k
where (h, k) is the vertex and the axis of symmetry is x = h
2 a)
Using the equation of a parabola in vertex form, a parabola with vertex (2, -6):
f(x) = a(x - 2)² - 6
If one of the x-axis intercepts is 6, then
f(6) = 0
⇒ a(6 - 2)² - 6 = 0
⇒ 16a - 6 = 0
⇒ 16a = 6
⇒ a = 6/16 = 3/8
So f(x) = 3/8(x - 2)² - 6
To find the other intercept, set f(x) = 0 and solve for x:
f(x) = 0
⇒ 3/8(x - 2)² - 6 = 0
⇒ 3/8(x - 2)² = 6
⇒ (x - 2)² = 16
⇒ x - 2 = ±4
⇒ x = 6, -2
Therefore, the other x-axis intercept is -2
b)
Using the equation of a parabola in vertex form, a parabola with vertex (2, -6):
f(x) = a(x - 2)² - 6
If one of the x-axis intercepts is -4, then
f(-4) = 0
⇒ a(-4 - 2)² - 6 = 0
⇒ 36a - 6 = 0
⇒ 36a = 6
⇒ a = 6/36 = 1/6
So f(x) = 1/6(x - 2)² - 6
To find the other intercept, set f(x) = 0 and solve for x:
f(x) = 0
⇒ 1/6(x - 2)² - 6 = 0
⇒ 1/6(x - 2)² = 6
⇒ (x - 2)² = 36
⇒ x - 2 = ±6
⇒ x = 8, -4
Therefore, the other x-axis intercept is 8
You can ask Siri. Answer is Increased 75%. “What percent is 56 out of 32.”
The probability that the mean clock life would differ from the population mean by greater than 12.5 years is 98.30%.
Given mean of 14 years, variance of 25 and sample size is 50.
We have to calculate the probability that the mean clock life would differ from the population mean by greater than 1.5 years.
μ=14,
σ=
=5
n=50
s orσ =5/
=0.7071.
This is 1 subtracted by the p value of z when X=12.5.
So,
z=X-μ/σ
=12.5-14/0.7071
=-2.12
P value=0.0170
1-0.0170=0.9830
=98.30%
Hence the probability that the mean clock life would differ from the population mean by greater than 1.5 years is 98.30%.
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There is a mistake in question and correct question is as under:
What is the probability that the mean clock life would differ from the population mean by greater than 12.5 years?
The equation of the line in slope-intercept form would be y = m(x - 1/5) - 8.
<h3>What is slope intercept form a straight line?</h3>
The slope-intercept form of a straight line is used to get the equation of a line. We need to know the slope of the line and the intercept where the line crosses the y-axis in order to use the slope-intercept formula.
One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfills.
Since the slope is undefined in the given question, let us consider it as m.
Therefore, slope=m
Given points are 1/5 and -8, so x₁ = 1/5 and y₁ = -8
We know the formula is, y - y₁ = slope × (x - x₁)
Putting the values of x₁, y₁ and slope in the given formula we get,
y -(-8) = m × (x-1/5)
y = m(x-1/5) - 8
Hence, we get the required equation.
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Answer:
A) 0.4255
B) 0.5813
C) 0.5588
D) 0.7241
Step-by-step explanation:
Assuming that the probability for each case is the same, we can calculate the probability by dividing the number of favourable cases with the total amount of cases. You can find the total amount of cases by adding the favourable ones with the non favourable ones, so, the probability of each case would be:
A) 20/(27+20) = 20/47 = 0.4255
B) 25/(18+25) = 25/43 = 0.5813
C) 19/(15+19) = 19/34 = 0.5588
D) 21((8+21) = 21/29 = 0.7241
