The vertex of a parabola is at $(12, -4)$, and its axis of symmetry is vertical. One of the $x$-intercepts is at $(15, 0)$. What
is the $x$-coordinate of the other $x$-intercept?
1 answer:
Answer:
9
Step-by-step explanation:
Since the axis of symmetry is vertical and the vertex of the parabola is at (12,-4), the vertical line x=12 is the axis of symmertry. The x-distance between the axis of symmetry and the first x intercept (15,0) is equal to 15-12=3. Hence, this x-intercept is 3 units to the right of the axis, and because it is symmetric, the other x-intercept must be 3 units to the left of the axis, so its x-coordinate must be 12-3=9. Then, the other x-intercept is at the point (9,0)
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Answer:
Step-by-step explanation:
Hello!
So you have a new type of shoe that lasts presumably longer than the ones that are on the market. So your study variable is:
X: "Lifetime of one shoe pair of the new model"
Applying CLT:
X[bar]≈N(μ;σ²/n)
Known values:
n= 30 shoe pairs
x[bar]: 17 months
S= 5.5 months
Since you have to prove whether the new shoes last more or less than the old ones your statistical hypothesis are:
H₀:μ=15
H₁:μ≠15
The significance level for the test is given: α: 0.05
Your critical region will be two-tailed:
So you'll reject the null Hypothesis if your calculated value is ≤-1.96 or if it is ≥1.96
Now you calculate your observed Z-value
Z=<u>x[bar]-μ</u> ⇒ Z=<u> 17-15 </u> = 1.99
σ/√n 5.5/√30
Since this value is greater than the right critical value, i.e. Zobs(1.99)>1.96 you reject the null Hypothesis. So the average durability of the new shoe model is different than 15 months.
I hope you have a SUPER day!