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timama [110]
3 years ago
15

Please Help Me, Take Your Time.

Mathematics
1 answer:
Doss [256]3 years ago
7 0
<h3>Given</h3>

72 blue, 42 red beads

beads are used to make identical necklaces

<h3>Find</h3>

(a) the greatest number of necklaces that can be made

(b) the number of each color bead in each necklace

<h3>Solution</h3>

You can write and factor the equation

... necklaces = 72 blue + 42 red

... necklaces = 6(12 blue + 7 red)

where 6 is the greatest common factor (GCF) of 72 and 42.

(a) You can make up to 6 identical necklaces. 6 is the largest common factor of 72 and 42. If you were to try to make more, they could not be identical.

(b) Each necklace can consist of 12 blue and 7 red beads. These are the numbers obtained when the total bead count is divided into 6 equal groups.

_____

There are several ways you can find the GCF of two numbers. For small numbers, it is generally feasible to use your knowledge of multiplication tables and factors to choose the largest common factor of two numbers. You can also use Euclid's algorithm, which is to repeatedly compute

... (largest number) modulo (smallest number)

until the result is zero. The final "smallest number" is the GCF.

Here, that looks like

... 72 mod 42 = 30

... 42 mod 30 = 12

... 30 mod 12 = 6

... 12 mod 6 = 0 . . . . . . . so 6 is the GCF

___

Of course, you know that

... 72 = 2³×3²

... 42 = 2×3×7

so, the largest set of common factors is 2×3 = 6.

___

Your graphing calculator may have a function for computing the greatest common divisor (GCD), too. The TI-84 does, for example.

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andreev551 [17]
3 tan³ t(theta) = tan t(theta)
3 tan³ t - tan t = 0
tan t ( 3 tan² t - 1 ) = 0
tan t = 0
t 1 = k π ,  k ∈ Z
3 tan ² t - 1 = 0
3 tan ² t = 1
tan ² t = 1/3
tan t = +/- √3/3
t 2 = π / 6 + k π
t 3 = - π / 6 + k π ,  k ∈ Z
8 0
3 years ago
Which conic section does the equation below describe? x+2^2=4y-3
Dmitry [639]

Answer: Circle

Step-by-step explanation:

6 0
2 years ago
What is the image of (6,-4) after a reflection over the y-axis?
kirill115 [55]

Answer:

(-6,-4)

Step-by-step explanation:

Hope this helps! (:

3 0
3 years ago
1,236,840 in scientific notation.
Leni [432]
The answer is 123684 x 10^1. Hope i helped.(whatever comes after ^ is an exponent)
4 0
3 years ago
The proportion of American births that result in a birth defect is approximately 1/33 according to the Centers for Disease Contr
max2010maxim [7]

Answer:

The appropriate probability model for X is a Binomial distribution,

X \sim Bin (<em>n</em> = 5, <em>p</em> = 1/33).

Step-by-step explanation:

The random variable <em>X</em> can be defined as the number of American births resulting in a defect.

The proportion of American births that result in a birth defect is approximately <em>p</em> = 1/33.

A random sample of <em>n</em> = 5 American births are selected.

It is assumed that the births are independent, i.e. a birth can be defective or not is independent of the other births.

In this experiment the success is defined as a defective birth.

The random variable <em>X</em> satisfies all criteria of a Binomial distribution.

The criteria are:

  • Number of observations is constant
  • Independent trials
  • Each trial has only two outcomes: Success and Failure
  • Same probability of success for each trial

Thus, the appropriate probability model for X is a Binomial distribution, Bin (<em>n</em> = 5, <em>p</em> = 1/33).

7 0
3 years ago
Read 2 more answers
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