Giving brainlist to whoever answers

At what point on the curve x^2 + y^2 = 9 is the tangent line vertical?

Gemiola [76]

x² + y² = 9 is the equation of a circle with center (0, 0) and radius 3.

This puts the vertices at (-3, 0), (3, 0), (0, -3), and (0, 3).

When is the tangent line vertical? <em>when it passes through the x-axis.</em>

Answer: (-3, 0), (3, 0)

7 0

3 years ago

A rectangular prism measures 4 ½ inches long, 6 ½ inches wide, and 2 ½ high. How many cubes with side length of ½ inch are neede

natita [175]

Answer:

it's a volume question

Explanation:

First, find the volume of the small shape.

(

1

4

×

1

4

×

1

4

)

=

1

64

Then, divide the volume of the bigger shape.

(

4.1

2

×

5

×

3.3

4

)

=

675

8

Finally, divide the big shape volume by the small shape volume.

(

675

8

÷

1

64

)

=

5400

Smaller shapes will fit into bigger shapes.

Step-by-step explanation:

5 0

3 years ago

Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car. Whe

kherson [118]

Answer:

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

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

And rounded up we have that n=1068

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

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 our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by: