Number 26? Geometry anyone please I don’t understand

A parabola is the locus of a point such that the distance from a fixed line called directrix and the distance from a fixed point called focus is constant.

The equation of a parabola with a vertex at (h, k) with axis of symmetry parallel to the y axis is given as:

$4p(y-k)=(x-h)^2$

The directrix is at y = k - p, and focus is at (h, k + p).

Given an equation -1/16(x-3)^2 + 4 = y, expressing it in standard form is:

$-\frac{1}{16}(x-3)^2+4=y\\\\(y-4)= -\frac{1}{16}(x-3)^2\\\\-16(y-4)=(x-3)^2\\\\$

Comparing with the standard form:

The center = (h, k) = (3, 4)

Also, -16 = 4p

p = -4

Directrix is at y = k - p = 4 - (-4) = 8

Directrix is at y = 8

The focus is at (h, k + p) = (3, 4 + (-4)) = (3, 0)

The focus is at (3, 0)

3 0

3 years ago

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 100100 engin

Margaret [11]

Answer:

Null hypothesis: $\mu \geq 7.3$

Alternative hypothesis: $\mu < 7.3$

$z=\frac{7.2-7.3}{\frac{0.81}{\sqrt{100}}}=-1.235$

$p_v =P(z$

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so then we can conclude that the mean pressure for the automobile engines is not significantly less than 7.3 at 1% of significance.

Step-by-step explanation:

1) Data given and notation

$\bar X=7.2$ represent the sample mean

$\sigma=0.81$ represent the population standard deviation

$n=100$ sample size

$\mu_o =7.3$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

2) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean pressure is lower than the specificated value 7.3, the system of hypothesis are :

Null hypothesis: $\mu \geq 7.3$

Alternative hypothesis: $\mu < 7.3$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

3) Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{7.2-7.3}{\frac{0.81}{\sqrt{100}}}=-1.235$

4) P-value

Since is a one-side lower test the p value would given by:

$p_v =P(z$

5) Conclusion

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the mean pressure for the automobile engines is not significantly less than 7.3 at 1% of significance.

7 0

3 years ago

Can you solve this math minigame first?

Margarita [4]

4
16
10
100
81
64
30
56
10,000

7 0

3 years ago