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2 years ago

Graph the inequality on the axes below.

Mathematics

1 answer:

gtnhenbr [62]2 years ago

3 0

Answer:

See attached

Step-by-step explanation:

<u>Given inequality:</u>

y < 1/3x - 6

Find the x- and y- intercepts and connect with a dotted line.

x = 0 ⇒ y = -6
y = 0 ⇒ x = 18

Shade the region below the y- intercept.

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The average heights of a random sample of 400 people from a city is 1.75 m. It is known that the heights of the population are r

Dimas [21]

Answer:

The 95% confidence interval for the average heights of the population is between 1.7108m and 1.7892m.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.025 = 0.975$ , so $z = 1.96$

Now, find M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

The standard deviation is the square root of the variance. So

$\sigma = \sqrt{0.16} = 0.4$

Then

$M = 1.96*\frac{0.4}{\sqrt{400}} = 0.0392$

The lower end of the interval is the mean subtracted by M. So it is 1.75 - 0.0392 = 1.7108m

The upper end of the interval is the mean added to M. So it is 1.75 + 0.0392 = 1.7892m

The 95% confidence interval for the average heights of the population is between 1.7108m and 1.7892m.

4 0

3 years ago

As part of a sixth-grade class project, the teacher brings to class a large jar containing 200 gumballs of two different colo

Rudiy27

Answer:

There would be 40 red gumballs

Step-by-step explanation:

Since, out of 40 gumballs there are 8 red gumballs,

So, the ratio of red gumballs and total gumballs = $\frac{8}{40}$

$=\frac{1}{5}$

Now, let there are x red gumballs in 200 gumballs,

The ratio of red gumballs and total gumballs = $\frac{x}{200}$

$\implies \frac{x}{200}=\frac{1}{5}$

$x =\frac{200}{5}=40$

Hence, the possible number of red gumballs in the jar would be 40.

7 0

2 years ago

Point A has coordinates (3,4). After a translation 4 units left, a reflection across the x-axis, and a translation 2 units down,

jeka94

Answer:

The coordinates of the image of point A are (-1, -6)

Step-by-step explanation:

Let us revise the rule of translation to the left, down, and reflection across the x-axis

If the point (x, y) translated horizontally to the left by h units then its image is (x - h, y) ⇒ T (x, y) → (x - h, y)

If the point (x, y) translated vertically down by k units then its image is (x, y - k) ⇒ T (x, y) → (x, y - k)

If the point (x, y) reflected across the x-axis, then its image is (x, -y), the rule of reflection is rx-axis (x, y) → (x, -y)

∵ The coordinates of point A are (3, 4)

∵ It is translated 4 units left

∴ h = 4

→ By using the 1st rule above

∴ Its image is (3 - 4, 4)

∴ Its image is (-1, 4)

∵ Its is reflected across the x-axis

→ By using the 3rd rule above change the sign of its y-coordinate

∴ The new image is (-1, -4)

∵ It is translated 2 units down

∴ k = 2

→ By using the 2nd rule above

∴ The final image is (-1, -4 - 2)

∴ The final image is (-1, -6)

∴ The coordinates of the image of point A are (-1, -6).

6 0

3 years ago

Brian wants to build a ramp that leads to a storeroom 5 meters above the ground he wants a ramp to be 10 meters long what should

sveticcg [70]

The angle of elevation is 26.565 (3dp)
let h be the end height of the ramp above
the ground , l be the length of the ramp and
the angle of elevation is (30)
i'm not sure, sorry

6 0

3 years ago

Read 2 more answers

Evaluate the expression when m= -2.8 and n=-6.3.<br> 4n - 6m

Alex73 [517]

Answer is 42, hope this helps

5 0

2 years ago