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3 years ago

Use the vertical angles theorem to name a pair of congruent angles

1 answer:

5 0

If we have two parallel line cut by a transversal such that the number of the angles are ordered in this manner:
1 | 2
3 | 4
5 | 6
7 | 8
The following the pair of vertical angles
∠1 and ∠4
∠2 and ∠3
∠5 and ∠6
∠7 and ∠8

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my sister wants to watch 6 star wars movies ,if each movie. is 2 hours , how long will it take her to watch all of the movies?

poizon [28]

12 hours, 6 x 2 = 12.

4 0

3 years ago

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Find the area of the region shaded in green. Use 3.14 to approximate pi.

8090 [49]

Answer:

254 cm² (to 3 s.f.)

Step-by-step explanation:

Area of shaded region

= area of large circle -area of smaller circle

$\boxed{area \: of \: circle = \pi {r}^{2} }$

Radius of large circle= 15cm

Radius of smaller circle= 12cm

Area of shaded region

= π(15²) -π(12²)

= 225π -144π

= 81π

= 81(3.14)

= 254.34

= 254 cm² (3 s.f.)

3 0

3 years ago

Which shape could be thought of as being created by stacking congruent polygons?

Amiraneli [1.4K]

You would form a prism.

7 0

3 years ago

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Y is a random variable that is distributed N(-16, 1.21). Find k such that Prob(-15.043 < Y ≤ k) = 0.1546. (Round your answer

IgorLugansk [536]

Transform Y to Z, which is distributed N(0, 1), using the formula

Y = µ + σZ

where µ = -16 and σ = 1.21.

Pr[-15.043 < Y ≤ k] = 0.1546

Pr[(-15.043 + 16)/1.21 < (Y + 16)/1.21 ≤ (k + 16)/1.21] = 0.1546

Pr[0.791 < Z ≤ (k + 16)/1.21] ≈ 0.1546

Pr[Z ≤ (k + 16)/1.21] - Pr[Z < 0.791] = 0.1546

Pr[Z ≤ (k + 16)/1.21] = 0.1546 + Pr[Z < 0.791]

Pr[Z ≤ (k + 16)/1.21] ≈ 0.1546 + 0.786

Pr[Z ≤ (k + 16)/1.21] ≈ 0.940

Take the inverse CDF of both sides (Φ(x) denotes the CDF itself):

(k + 16)/1.21 ≈ Φ⁻¹ (0.940) ≈ 1.556

Solve for k :

k + 16 = 1.21 • 1.556

k ≈ -14.118

8 0

3 years ago

Someone please HELP!?

jeka94

A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side.

For example

$x^{-2}=\frac{1}{x^2}$

or

$( \frac{2}{5} )^{-4}=( \frac{5}{2} )^4$

***************************************
$(8r^{-5})^{-3}$

$(8* \frac{1}{r^5} )^{-3} \\\\( \frac{8}{r^5} )^{-3}
 \\ \\ ( \frac{r^5}{8} )^3
\\\\ \mathrm{Apply\:exponent\:rule}:\quad *\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c} \ \ \ \ \ \ \ \ \ \ \ \ *(a^b)^c=a^{bc}
 \\\\( \frac{r^{15}}{8^3} )
\\\\( \frac{r^{15}}{512} )$

The answer is "D"

7 0

2 years ago