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s344n2d4d5 [400]
2 years ago
11

A card is randomly drawn from a standard $52$-card deck. An ace of hearts wins the grand prize; any other ace or heart wins a sm

all prize. What is the probability of winning a small prize? Express your answer as a common fraction. Assume that a grand prize winner does NOT also win a small prize.
Mathematics
1 answer:
gogolik [260]2 years ago
4 0

Answer:

3/52

Step-by-step explanation:

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Use the Law of Cosines to find the values of x and y. (PLEASE HELPPP!!!!)
vredina [299]

Answer:

x = 49.8^\circ\\y = 54.6^\circ

Step-by-step explanation:

Kindly refer to the image attached in the answer region for labeling of triangle.

<em>AB </em><em>= 16 </em>

<em>BC </em><em>= 19</em>

<em>AC </em><em>= 15 </em>

\angle ABC = x^\circ\\\angle ACB = y^\circ

We have to find the <em>angles </em><em>x</em> and <em>y</em> i.e. \angle B \text{ and }\angle C.

Formula for <em>cosine rule</em>:

cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}

Where  

<em>a</em> is the side opposite to \angle A,

<em>b</em> is the side opposite to \angle B  and

<em>c</em> is the side opposite to \angle C.

\Rightarrow cos x = \dfrac{19^{2}+16^{2}-15^{2}}{2 \times 19 \times 16}\\\Rightarrow cos x = \dfrac{392}{608} \\\Rightarrow x = 49.8^\circ

Similarly, for finding the value of <em>y:</em>

cos C = \dfrac{a^{2}+b^{2}-c^{2}}{2ab}\\\Rightarrow cos y = \dfrac{19^{2}+15^{2}-16^{2}}{2  \times 19 \times 15}\\\Rightarrow cos y = \dfrac{330}{570}\\\Rightarrow y = 54.6^\circ

Hence, the values are:

x = 49.8^\circ\\y = 54.6^\circ

7 0
3 years ago
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is
wel
X+y=24 so we can say

x=24-y making 3x+5y=100 become

3(24-y)+5y=100

72-3y+5y=100

72+2y=100

2y=28

y=14, since x=24-y

x=10

So there are 10 3-point questions and 14 5-point questions.
6 0
3 years ago
Read 2 more answers
Mary earns $6 per hour as a waitress. Last week she took home her regular earnings of $6 per hour plus $185 in tips for a total
Daniel [21]
Mary worked 22 hours.


To solve first you would subtract the amount she made in tips from her total earnings (317-185)
= 132
Then you divide that answer by her hourly salary of $6 (132/6)
=22
7 0
3 years ago
Austin purchase 2/3 of a pound of yum yum treats. If yum yum treats are $6.00 per pound how much does Austin pay
Oksi-84 [34.3K]
1. The information given in the problem above, is:

 - Austin purchases <span>2/3 of a pound of yum yum treats.
 - Y</span><span>um yum treats are $6.00 per pound (1 pound=$6.00).

 2. Keeping this on mind you have: If 1 pound of </span>yum yum treats is $6.00, how much is 2/3 of a pound?

 1 pound------------$6.00
 2/3 of a pound----x

 x=(2/3)(6.00)/1
 x=(2/3)(6.00)
 x=12/3
 x=$4.00
<span>
 Therefore: How much does Austin pay?
</span>
 The answer is: Austin pays $4.00.
5 0
3 years ago
The graph represents the balance on Harrison’s car loan in the months since purchasing the car.
dimulka [17.4K]

Answer:

Step-by-step explanation:

I think it's the loan balances decreases $500 per month because every month it starts decreasing down by 500

4 0
3 years ago
Read 2 more answers
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