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expeople1 [14]
4 years ago
7

Austin collects rare Pokémon cards. He currently has 42 cards in his collection. His parents buy him 3 rare cards every year on

his birthday. How long will it take him to collect 78 Pokémon cards?
A: 3p+42=78
B: 78p-3=78
C: 42p+3=78
D: 3p-78=42
Mathematics
2 answers:
barxatty [35]4 years ago
8 0

Answer:

i believe the answer is A. hope this helped.

Step-by-step explanation:

Naya [18.7K]4 years ago
3 0

Answer: option A is the correct answer.

Step-by-step explanation:

Let p represent the number of years for which his parents bought him rare Pokémon cards.

His parents buy him 3 rare cards every year on his birthday. This means that in p years, he would be getting 3p rare cards from his parents.

He currently has 42 cards in his collection. This means that the number of cards that he would have in his collection in p years is

3p + 42

Therefore, the time it will take him to collect 78 Pokémon cards would be

3p + 42 = 78

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Alla [95]

18/15/12/9 = 0.0111111111111

Have a great evening. I hope this helped! :)

4 0
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A researcher is interested in the lengths of brook trout, which are known to be approximately Normally distributed with mean 80
aliya0001 [1]

Answer:

P(X

And we can find this probability with the normal standard distirbution or excel and we got:

P(z

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the lenghts of a population, and for this case we know the distribution for X is given by:

X \sim N(80,5)  

Where \mu=80 and \sigma=5

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X

And we can find this probability with the normal standard distirbution or excel and we got:

P(z

6 0
3 years ago
What is the measure of XYZ shown in the diagram below?
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Answer: A.                                                                                                          

Explenation: Apex                                

4 0
4 years ago
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Some rectangles are not parallelograms
VARVARA [1.3K]

Answer:

I'm not sure what your asking, but, no, all rectangles are parallelograms.

I found this over the internet, and I hope it helps you understand why a rectangle is always a parallelogram, but a parallelogram is not always a rectangle:

It is true that every rectangle is a parallelogram, but it is not true that every parallelogram is not a rectangle. For instance, take a square. It's a parallelogram — it is a quadrilateral with two pairs of parallel faces. But it is also a rectangle — it is a quadrilateral with four right angles.

5 0
4 years ago
2. Find the general relation of the equation cos3A+cos5A=0
mars1129 [50]
<h2>Answer:</h2>

A=\frac{\pi}{8}+\frac{n\pi}{4}or\ A=\frac{\pi}{2}+n\pi

<h2>Step-by-step explanation:</h2>

<h3>Find angles</h3>

cos3A+cos5A=0

________________________________________________________

<h3>Transform the expression using the sum-to-product formula</h3>

2cos(\frac{3A+5A}{2})cos(\frac{3A-5A}{2})=0

________________________________________________________

<h3>Combine like terms</h3>

2cos(\frac{8A}{2})cos(\frac{3A-5A}{2})=0\\\\  2cos(\frac{8A}{2})cos(\frac{-2A}{2})=0

________________________________________________________

<h3>Divide both sides of the equation by the coefficient of variable</h3>

cos(\frac{8A}{2})cos(\frac{-2A}{2})=0

________________________________________________________

<h3>Apply zero product property that at least one factor is zero</h3>

cos(\frac{8A}{2})=0\ or\ cos(\frac{-2A}{2})=0

________________________________________________________

<h2>Cos (8A/2) = 0:</h2>

<h3>Cross out the common factor</h3>

cos\ 4A=0

________________________________________________________

<h3>Solve the trigonometric equation to find a particular solution</h3>

4A=\frac{\pi}{2}or\ 4A=\frac{3\pi}{2}

________________________________________________________

<h3>Solve the trigonometric equation to find a general solution</h3>

4A=\frac{\pi}{2}+2n\pi \ or\\ \\ 4A=\frac{3 \pi}{2}+2n \pi\\ \\A=\frac{\pi}{8}+\frac{n \pi}{4\\}

________________________________________________________

<h2>cos(-2A/2) = 0</h2>

<h3>Reduce the fraction</h3>

cos(-A)=0

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<h3>Simplify the expression using the symmetry of trigonometric function</h3>

cosA=0

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<h3>Solve the trigonometric equation to find a particular solution</h3>

A=\frac{\pi }{2}\ or\ A=\frac{3 \pi}{2}

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<h3>Solve the trigonometric equation to find a general solution</h3>

A=\frac{\pi}{2}+2n\pi\ or\ A=\frac{3\pi}{2}+2n\pi,n\in\ Z

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<h3>Find the union of solution sets</h3>

A=\frac{\pi}{2}+n\pi

________________________________________________________

<h2>A = π/8 + nπ/4 or A = π/2 + nπ, n ∈ Z</h2>

<h3>Find the union of solution sets</h3>

A=\frac{\pi}{8}+\frac{n\pi}{4}\ or\ A=\frac{\pi}{2}+n\pi ,n\in Z

<em>I hope this helps you</em>

<em>:)</em>

5 0
3 years ago
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