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anastassius [24]

3 years ago

11

A slot machine has 3 slots. For each slot, the possible outcomes are an apple, orange, lemon, banana, melon, and a joker. When t

he player puts a coin in the machine, a wheel spins in each of the three slots and stops randomly on one of the possible outcomes. There are different ways to win for each coin played--All 3 jokers are visible, any 3 of a kind that isn't a joker, any 2 jokers, or any 1 joker.
1. How many ways could you win with 2 jokers?2. How many ways could you win with 1 joker?

1 answer:

PolarNik [594]3 years ago

6 0

Answer:

1. 15

2. 75

Step-by-step explanation:

The possible outcomes are an apple (A), orange (O), lemon (L), banana (B), melon (M), and a joker (J), 6 outcomes in total.

1. You could win with 2 jokers in

$5+5+5=15$ different ways.

You can list all these ways:

JJA JAJ AJJ

JJO JOJ OJJ

JJL JLJ LJJ

JJB JBJ BJJ

JJM JMJ MJJ

2. You could win with 1 joker in

$5\cdot 5+5\cdot 5+5\cdot 5=75$ different ways

You can list all these ways:

JAA JAO JAL JAB JAM

JOA JOO JOL JOB JOM

JLA JLO JLL JLB JLM

JBA JBO JBL JBB JBM

JMA JMO JML JMB JMM

AJA AJO AJL AJB AJM

OJA OJO OJL OJB OJM

LJA LJO LJL LJB LJM

BJA BJO BJL BJB BJM

MJA MJO MJL MJB MJM

AAJ AOJ ALJ ABJ AMJ

OAJ OOJ OLJ OBJ OMJ

LAJ LOJ LLJ LBJ LMJ

BAJ BOJ BLJ BBJ BMJ

MAJ MOJ MLJ MBJ MMJ

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If m∠a=47°, what is m∠b, m∠c, and m∠d? Explain how you know the measures are correct.

avanturin [10]

m ∠b = 133°, m ∠c = 47°, and m ∠d = 133°.

<h3>Further explanation</h3>

Follow the attached picture. I sincerely hope that's precisely a correct illustration.

We will use a graph of two intersecting straight lines.

Note that m ∠a and m ∠c are vertical angles. Since vertical angles share the same measures, in other words always congruent, we see $\boxed{ \ m \ \angle{c} = m \ \angle{a} \ } \rightarrow \boxed{\boxed{ \ m \ \angle{c} = 47^0 \ }}$

We continue to determine m ∠b and m ∠d.

Note that m ∠b and m ∠d represent supplementary angles. Recall that supplementary angles add up to 180°.

Let us see the following steps.

$\boxed{ \ m \ \angle{a} + m \ \angle{b} = 180^0. \ }$

$\boxed{ \ m \ 47^0 + m \ \angle{b} = 180^0. \ }$

Both sides subtracted by 47°.

$\boxed{ \ m \ \angle{b} = 180^0 - 47^0. \ }$

Thus $\boxed{\boxed{ \ m \ \angle{b} = 133^0. \ }}$

Finally, note that m ∠b and m ∠d are vertical angles. Accordingly, $\boxed{ \ m \ \angle{d} = m \ \angle{b} \ } \rightarrow \boxed{\boxed{ \ m \ \angle{d} = 133^0 \ }}$

<u>Conclusion:</u>

m ∠a = 47°
m ∠b = 133°
m ∠c = 47°
m ∠d = 133°

<u>Notes:</u>

Supplementary angles are two angles when they add up to 180°. $\boxed{ \ example: \angle{a} + \angle{b} = 180^0 \ }$
Vertical angles are the angles opposite each other when two lines cross. Note that vertical angles are always congruent, or of equal measure. $\boxed{ \ example: \angle{a} = \angle{c} \ }$

<h3>Learn more</h3>

About the measure of the central angle brainly.com/question/2115496
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Find out the measures of the two angles in a right triangle brainly.com/question/4302397

Keywords: m∠a = 47°, m∠b, m∠c, and m∠d, 133°, vertical angles, supplementary, 180°, congruent

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Answer:

Step-by-step explanation:

∠E = ∠B

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A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first the

Svetlanka [38]

Answer:

The hotel charge in each city before tax was <u>$5125</u> of the first city and <u>$3625</u> of the second city.

Step-by-step explanation:

Given:

A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first.

The tax of the first city was 6% and the tax of the second city was 10%.

Total hotel tax paid for two cities with $670.

Now, to find the hotel charge in each city before tax.

Let the hotel charge in first city before tax be $x.$

And the hotel charge in second city before tax be $y.$

<em>So, as the hotel charge of the second city was 1500 higher than the first.</em>

<em>Thus</em>,

$y=x-1500$ ........(1)

<em>And as given, the tax of the first city was 6% and the tax of the second city was 10%, total hotel tax paid for two cities with $670.</em>

6% of $x$ + 10% of $y$ = $670.

$\frac{6x}{100} +\frac{10y}{100} =670$

$0.06x+0.10y=670$

Substituting the value of $y$ from equation (1) we get:

$0.06x+0.10(x-1500)=670$

$0.06x+0.10x-150=670$

$0.16x-150=670$

<em>Adding both sides by 150 we get:</em>

$0.16x=820$

<em>Dividing both sides by 0.16 we get:</em>

$x=5125.$

<em>The hotel charge in first city before tax = $5125.</em>

Now, substituting the value of $x$ in equation (1) we get:

$y=x-1500$

$y=5125-1500$

$y=3625.$

<em>The hotel charge in second city before tax = $3625.</em>

Therefore, the hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.

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3 years ago