Factor this expression using the GCF (greatest common factor) and then explain how you can verify your answer:

If a student mixes 3.5 ml of yellow paint and 5.25 ml of blue paint to make the same shade of green, how many ml used in total

PSYCHO15rus [73]

Step-by-step explanation:

8.75 ml i think is correct

6 0

3 years ago

Suppose y varies directly as x, and y=16 when x=8. Find y when x=16

Fudgin [204]

We can make a proportion here, 8/16, where the proportion is x/y. We can make another proportion that says 16/y, and y would be 32, because twice the number of x is y.

3 0

3 years ago

Find the vertex, focus, directrix, and focal width of the parabola.

ANEK [815]

Answer:

Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16 ⇒ answer (a)

Step-by-step explanation:

* Lets revise some facts about the parabola

- Standard form equation for a parabola of vertex at (0 , 0)

- If the equation is in the form x² = 4py, then

- The axis of symmetry is the y-axis, x = 0

- 4p equal to the coefficient of y in the given equation to

solve for p

- If p > 0, the parabola opens up.

- If p < 0, the parabola opens down.

- Use p to find the coordinates of the focus, (0 , p)

- Use p to find equation of the directri , y= − p

- Use p to find the endpoints of the focal diameter, (±2p , p)

* Now lets solve the problem

- The vertex of the parabola is (0 , 0)

∵ -1/16x² = y ⇒ multiply each side by -16

∴ x² = -16y

∴ 4p = -16 ⇒ ÷ 4 tbe both sides

∴ p = -4

∵ The focus is (0 , p)

∴ The focus is (0 , -4)

∵ The directrix is y = -p

∴ The directrix is y = -(-4) = 4 ⇒ y = 4

∵ The endpoints of the focal diameter, (±2p , p)

∴ The focal width = 2p - (-2p) = 4p

∴ The focal width = 4 × I-4I = 16

* Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16

6 0

3 years ago

Read 2 more answers

PLEASE HELP ASAP!!! WILL MARK BRAINLIEST!!!!

xxMikexx [17]

Answer:

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Step-by-step explanation:

5 0

3 years ago

A church group is interested in estimating the true proportion of Americans who attend weekly religious services. How large a sa

artcher [175]

Answer:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can use an estimatior for the population proportion as $\hat p=0.5$ since we don't know previous info. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11$

And rounded up we have that n=1068

Step-by-step explanation:

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since the confidence level is 99%, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.03$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can use an estimatior for the population proportion as $\hat p=0.5$ since we don't know previous info. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11$

And rounded up we have that n=1068

8 0

3 years ago