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3 years ago

Factor 54+27 using the GCF.

Mathematics

2 answers:

vlabodo [156]3 years ago

6 0

Answer: $54+27=27(2+1)\ or\ 27(3)$

Step-by-step explanation:

To factorize 54+27, we need to find the greatest common factors of 54 and 27.

First write the prime factorization of 54 and 27 as

$54=2\times3\times3\times3$

$27=3\times3\times3$

We can see the greatest common factor here= $3\times3\times3=27$

As 27 is the GCF of 54 and 27 then 54+27 can be written as

$54+27=27(2+1).....[\text{by taking 27 as GCF outside}]\\=27(3)$

e-lub [12.9K]3 years ago

3 0

So, we need the Greatest Common Factor of the two numbers, 54 and 27, right?

first, is one maybe a multiplication of the other?

yes, it is! in fact, 54 is 27*2; 53 is 27 multiplied by 2.

that means that 27 IS the Greatest Common Factor of the two!

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John has two jobs. For daytime work at a jewelry store he is paid

djyliett [7]

Given Information:

John's mean monthly commission = μ = $10,000

Standard deviation of monthly commission = σ = $2,000

Answer:

$P(9,000 < X < 11,000) = 0.383\\\\P(9,000 < X < 11,000) = 38.3 \%$

The probability that John's commission from the jewelry store is between $9,000 and $11,000 is 38.3%

Step-by-step explanation:

What is Normal Distribution?

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.

We want to find out the probability that John's commission from the jewelry store is between $9,000 and $11,000?

$P(9,000 < X < 11,000) = P( \frac{x - \mu}{\sigma} < Z < \frac{x - \mu}{\sigma} )\\\\P(9,000 < X < 11,000) = P( \frac{9,000 - 10,000}{2,000} < Z < \frac{11,000 - 10,000}{2,000} )\\\\P(9,000 < X < 11,000) = P( \frac{-1,000}{2,000} < Z < \frac{1,000}{2,000} )\\\\P(9,000 < X < 11,000) = P( -0.5 < Z < 0.5 )\\\\P(9,000 < X < 11,000) = P( Z < 0.5 ) - P( Z < -0.5 ) \\\\$

The z-score corresponding to 0.50 is 0.6915

The z-score corresponding to -0.50 is 0.3085

$P(9,000 < X < 11,000) = 0.6915 - 0.3085 \\\\P(9,000 < X < 11,000) = 0.383\\\\P(9,000 < X < 11,000) = 38.3 \%$

Therefore, the probability that John's commission from the jewelry store is between $9,000 and $11,000 is 38.3%

How to use z-table?

Step 1:

In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.4, 2.2, 0.5 etc.)

Step 2:

Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.50 then go for 0.00 column)

Step 3:

Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.

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4 years ago

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mel-nik [20]

Answer:

Step-by-step explanation:

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3 years ago

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In the complex plane, the rectangular coordinates (x, y) represent a complex number. Which statement explains why polar coordina

bonufazy [111]

Answer:

The correct option is;

r = √(x² + y²)

θ = tan⁻¹(y/x)

Step-by-step explanation:

The rectangular coordinate of a complex number on the complex plane is given as (x, y)

Given that the complex number is represented by a point on the plane, we have;

The distance, r, of the point from the origin, (0, 0) is r = √(x² + y²)

The direction, θ, by which we rotate to be in line with the point on the complex number is given by tan⁻¹(y/x)

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3 years ago

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Sarah is 6 years older than Amy.

Umnica [9.8K]

Answer:

Step-by-step explanation:

The problem has got to be addition.

The sentence "Sarah is 6 years older than Amy." does not include any hint of subtracting, or multiplying.

A hint of multiplying in a expression would be the word 'times', like "Brandon is 6 times the age of Emily" which eliminates D.

A hint of subtraction in an expression would be the word 'less', like "Brandon is 6 less the age of Emily." which eliminates A and C.

The word 'older' indicates addition, or adding, and if it would have been subtraction, the keyword would be 'younger' because you are subtracting their age, like 19 - 11. The same goes with B, but adding.

Finally, we now know that it is B because there is no other addition choice.

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3 years ago

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umka21 [38]

Answer:

(3, 0).

Step-by-step explanation:

dentifying the vertices of the feasible region. Graphing is often a good way to do it, or you can solve the equations pairwise to identify the x- and y-values that are at the limits of the region.

In the attached graph, the solution spaces of the last two constraints are shown in red and blue, and their overlap is shown in purple. Hence the vertices of the feasible region are the vertices of the purple area: (0, 0), (0, 1), (1.5, 1.5), and (3, 0).

The signs of the variables in the contraint function (+ for x, - for y) tell you that to maximize C, you want to make y as small as possible, while making x as large as possible at the same time.

Hence, The Answer is ( 3, 0)

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3 years ago

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