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3 years ago

What is the probability that the card is either a black cardblack card or aa 99?

1 answer:

6 0

It sounds like your book is asking "what is the probability that the card is either a black card or a 9"

If so, there are 26 black cards (13 spades and 13 clubs) and four cards that have "9" on them (one in each suit). We have 26+4 = 30 cards that are either one or the other. There is overlap though. Namely the 2 black cards that have "9" on them (we count them twice), so we should subtract to get 30-2 = 28

There are 28 cards that either have a '9' on them, they are black, or both

This is out of 52 cards total

Divide the two values: 28/52 = 14/26 = 7/13 = 0.53846

Answer as a fraction: 7/13
Answer in decimal form: 0.53846
Answer as a percentage: 53.846%
Side note: the decimal form and percentage form are approximate

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What is the value of y? Please show work of how you solved! Thankyou

kap26 [50]

$log_4(y+2)=3$
raise each side to base 4
$4^{log_4(y+2)}=4^3$
simplify
$(y+2)}=64$ using the law of logarithms $a^{log_ab}=b$
=>
y=62

6 0

3 years ago

Give the appropriate theorem or postulate that can

Ratling [72]

Answer:

Step-by-step explanation:

<ACB = <ECD

These 2 angles are vertically opposite and are equal.

<B = <D

They are both right angles are therefore equal.

The answer is the AA postulate.

Note

ASA is a congruence postualate. If S is between two angles that can be shown to be corresponding and equal, then you will have 2 congruent triangles.

SSS if three sides of 1 triangle = 3 sides of a second triangle, then the 2 triangles are congruent. If the the three sides of one triangle are in a ratio with 3 sides of the other triangle, then the triangles could be similar, but that is not the case here.

SAS this is the terminology for congruence as well. We don't know enough to use it for similarity. Some sort of ratio would have to be mentioned to do that.

You are intended to use AA as your answer.

8 0

2 years ago

What is the equation of a circle with center (9,-7) and radius 2?

kirza4 [7]

Answer:

B. (x-9)^2 + (y + 7)^2 = 4

Step-by-step explanation:

The standard form of a circle is (x-h)^2 + (y-k)^2 = r^2. Hopefully you can memorize that, because it's very helpful in these problems!

(h,k) is our center, and r is our radius, so plug those values into the standard form:

(x - 9)^2 + (y + 7)2 = 2^2

2^2 = 4, so

B. (x - 9)^2 + (y + 7)2 = 4 is our answer!

3 0

3 years ago

Semicircles and quarter circles are types of arc lengths. Recall that an arc is simply part of a circle. We learned about the de

attashe74 [19]

The question is incomplete. Here is the complete question.

Semicircles and quarter circles are types of arc lengths. Recall that an arc is simply part of a circle. we learned about the degree measure of an ac, but they also have physical lengths.

a) Determine the arc length to the nearest tenth of an inch.

b) Explain why the following proportion would solve for the length of AC below: $\frac{x}{12\pi } = \frac{130}{360}$

c) Solve the proportion in (b) to find the length of AC to the nearest tenth of an inch.

Note: The image in the attachment shows the arc to solve this question.

Answer: a) 9.4 in

c) x = 13.6 in

Step-by-step explanation:

a) $\frac{arclength}{2\pi.r } = \frac{mAB}{360}$ , where:

r is the radius of the circumference

mAB is the angle of the arc

arc length = $\frac{mAB.2.\pi.r }{360}$

arc length = $\frac{90.2.3.14.6}{360}$

arc length = 9.4

The arc lenght for the image is 9.4 inches.

b) An arc length is a fraction of the circumference of a circle. To determine the arc length, the ratio of the length of an arc to the circumference is equal to the ratio of the measure of the arc to 360°. So, suppose the arc length is x, for the arc in (b):

$\frac{x}{2.6.\pi } = \frac{130}{360}$