According to the general equation for conditional probability, if P(AuB)=3/7

Please help me with this !! I REALLY need to have good grades because...Back story I had my phone and I broke it and I can't get

nevsk [136]

Answer:

Transformation include reflecting and dilating of points

The scale factor from PQR to P'Q'R' is 1/4

The coordinates of P"Q"R" are P"=(-1,0) Q"=(0,-1) R"=(2,-1) .

PQR and P′'Q′'R′' are not congruent

The points are given as:

p=(4,0)

q=(0,-4)

r=(-8,-4)

p'=(1,0)

q'=(0-1)

r'=(-2,-1)

(a)The scale factor from PQR to P'Q'R

To do this, we make use of corresponding sides QR and Q'R

So, the scale factor (k) is:

k=q'r'/qr

k=2/8

k=1/4

(b) The coordinates of P"Q"R from reflecting P'Q'R' about the y-axis

The rule of this transformation is:

(x,y)--------(-x,y)

So, we have:

p"=(-1,0)

q"=(0,-1)

r"=(2,-1)

(c) Are triangle PQR and P"Q'R" congruent?

No they are not

This is so because

PQR was dilated by 1/4 to get P'Q'R

P'Q'R' and P"Q"R" are congruent

Hence, PQR and P′'Q′'R′' are not congruent

Step-by-step explanation:

4 0

2 years ago

If you can solve all parts I will give brainliest (also give strategy)

Alexxx [7]

The Halloween conical hat, with given height, circular base and brim

extension has the following calculated parameters;

Part a. The slant height is 18.2 inches

Part b. The volume of the cone is $37\frac{1}{2} \cdot \pi$ in.³

Part c. The area of the brim, A = 36·π in.²

Part d. The area of the brim is found by subtracting the area of the base of the cone from the area covered by the perimeter of the brim

Reasons:

Known parameters;

Height of the conical portion, h = 18 inches

Base circumference, C = 5·π inches

Part a. Slant height of the conical portion; Required

Solution:

The circumference of a circle, C = 2·π·r

Therefore;

$r = \dfrac{C}{2 \cdot \pi}$

Which gives;

$r = \dfrac{5 \cdot \pi}{2 \cdot \pi} = \dfrac{5}{2} = 2.5$

Radius, r = 2.5 inches

According to Pythagoras's theorem, we have; s² = r² + h²

Where;

s = The slant height of the cone

s² = 2.5² + 18² = 330.25

s = √(330.25) ≈ 18.2

The slant height, s ≈ 18.2 inches

Part b. The measure in cubic inches of candy that exactly fills the conical portion of the hat is the volume of the cone.

$Volume \ of \ a \ cone = \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h$

Therefore;

$V = \dfrac{1}{3} \times \pi \times 2.5^2 \times 18 = 37\frac{1}{2} \cdot \pi$

The volume of the cone, V = $37\frac{1}{2}$ ·π in.³

Part c. The extension of the brim from the base of the cone = 4 inches

The radius of the brim, R = Radius of the base of the cone + 4 inches

∴ R = 2.5 inches + 4 inches = 6.5 inches

Area of the brim, A = Area of the 6.5 inch circle - Area of the circular base of the cone

∴ A = π × 6.5² - π × 2.5² = 36·π

The area of the brim, A = 36·π in.²

Part d. The procedure for solving the question in part c, is described as follows;

The area of the brim can be found by finding the entire area of the circle formed by the perimeter of the brim, then subtracting the area of the base of the cone from that area.

Learn more here:

brainly.com/question/17023854

4 0

3 years ago

Write an expression to describe the situation. "Your cell phone costs $50 a month plus $0.25 for each text message (t). Do not i

sveticcg [70]

The expression is 50 + 0.25t.

<h3>How to compute the value?</h3>

It should be noted that from the information, the cell phone costs $50 a month plus $0.25 for each text message (t).

The expression will be:

= 50 + 0.25(t)

= 50 + 0.25t

Therefore, the expression is 50 + 0.25t.

Learn more about expressions on:

brainly.com/question/723406

#SPJ1

8 0

1 year ago

Consider two vectors A and B A=14i and B= -4i+8j

DaniilM [7]

Assuming $\mathbf a,\mathbf b\in\mathbb R^3$ , you have

$\mathbf a\cdot\mathbf b=(14)(-4)+(0)(8)=-56$

so

$((\mathbf a\cdot\mathbf b)\,\mathbf i)\cdot\mathbf a=(-56\,\mathbf i)\cdot(14\,\mathbf i)=(-56)(14)=-784$

Next,

$\mathbf a+\mathbf b=(14\,\mathbf i)+(-4\,\mathbf i+8\,\mathbf j)=10\,\mathbf i+8\,\mathbf j$

Then

$(\mathbf a+\mathbf b)\times\mathbf b=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\10&8&0\\-4&8&0\end{vmatrix}=112\,\mathbf k$

$((\mathbf a+\mathbf b)\times\mathbf b)\times\mathbf k=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\0&0&112\\0&0&1\end{vmatrix}=\mathbf 0$

4 0

3 years ago

The number 6 has exactly four different factors:1,2,3 and 6. How many different factors does the number 36 have?

Aliun [14]

36 has 1,2,3,4,6,and 9

3 0

3 years ago

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