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Sergio [31]
2 years ago
9

3.2.PS-33 Liam has 63 CDs​, Alex has 49 CDs​, and Michael has 77 CDs. Use the GCF and the Distributive Property to find the tota

l number of CDs Liam​, Alex​, and Michael have.
Mathematics
1 answer:
labwork [276]2 years ago
8 0

Answer:

The total number of CDs Liam​, Alex​, and Michael have is <u>189</u>.

Step-by-step explanation:

Given:

Liam has 63 CDs​, Alex has 49 CDs​, and Michael has 77 CDs.

Now, to find the total number of CDs using the GCF and the Distributive Property.

So, the CDs are :

Liam = 63.

Alex = 49.

Michael = 77.

Now, we factorize all the Number of CDs of Liam, Alex and Michael to get the GCF:

The factors of 63 are: 1, 3, 7, 9, 21, 63

The factors of 49 are: 1, 7, 49

The factors of 77 are: 1, 7, 11, 77

Thus, 7 is the GCF.

Now, we use the distributive property to get the total number of CDs Liam​, Alex​, and Michael have:

7(9+7+11)

=63+49+77

=189.

Therefore, the total number of CDs Liam​, Alex​, and Michael have is 189.

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Answer:

The measure of each sides of isosceles triangle is 16.67 inches , 16.67 inches , 11.25 inches

Step-by-step explanation:

Given as for a Isosceles triangle :

The base of Triangle = 11.25 inches

The sides of triangle meets at 56°

Let the unknown side measure = x inches

From <u>The property of isosceles triangle</u>

The angle opposite to the same side are equal

I.e \Theta _1 =  \Theta _2 = 56°

So, The third angle = 180° - ( \Theta _1 +  \Theta _2 )

Or, The third angle = 180° - ( 56° + 56° )

∴   The third angle = 180° - 112° = 68°

Now, From isosceles triangle

Tan 56° = \frac{perpendicular}{base}

Or, Tan 56° = \frac{x}{11.25}

∴   x = 11.25 × Tan 56°

Or, x = 11.25 × 1.482 = 16.672 inches

Hence The measure of each sides of isosceles triangle is 16.67 inches , 16.67 inches , 11.25 inches   Answer

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2 years ago
Kayla has decided to paint the ceiling in the living room. She has 1/30 gallon of paint left. The living room ceiling will take
ella [17]
So the ceiling takes 5/6 gallon to paint. We know that you already have 1/30 gallon and another gallon in addition to that. We must convert the 5/6 into ?/30 so we can see how much we need to use. So if we convert 5/6 to out of 30, we get 25/30. So the first can has 1/30 gallon so we subtract that amount from the total paint needed. So now we only need 24/30 gallon to paint the ceiling. If we subtract that amount needed from the full (30/30) can we have left, that will give us the remaining amount of paint we have left. 30/30-24/30= 6/30. This reduces to 1/5. So there is 1/5 gallon of paint left over after painting the ceiling.
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Answer:

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b) P(X \leq 190) = 0.165

Step-by-step explanation:

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P(X \ge x) = e^{- \lambda x}

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Answer:

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Step-by-step explanation:

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Now we want to find the 10 successive points of event B. Since the events are independent we can find this as

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