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Stels [109]
3 years ago
8

Find the highest common factor and lowest common multiple of 60 and 150 using prime factors

Mathematics
1 answer:
mel-nik [20]3 years ago
7 0
Here, we know, 60 = 2 × 30
& 150 = 5 × 30

So, Highest Common Factor (HCF) would be 30

Now, Lowest common point = 60 × 5 = 300 or 150 × 2 = 300

In short, LCM would  be 300

Hope this helps!
You might be interested in
Problems 2.21, 2.22, 2.23
RoseWind [281]

Statements can be proved by contrapositive, contradiction or by induction.

  • <em>2.21 and 2.23 are proved by contrapositive</em>
  • <em>2.22 is proved by induction</em>

<u />

<u />

<u>2.21: If </u>n^3<u> is even, then n is even (By contrapositive)</u>

The contrapositive of the above statement is that:

<em>If n is odd, then  </em>n^3<em> is odd</em>

Represent the value of n as:

n = 2k + 1, where k \ge 0

Take the cube of both sides

n^3 = (2k + 1)^3

Expand

n^3 = 8k^3 + 6k^2 + 6k + 1

Group

n^3 =[ 8k^3 + 6k^2 + 6k] + 1

Factor out 2

n^3 =2[4k^3 + 3k^2 + 3k] + 1

Assume w is an integer; where:

w =4k^3 + 3k^2 + 3k

So, we have:

n^3 =2w + 1

The constant term (i.e. 1) means that n^3 is odd.

Hence, the statement has been proved by contrapositive.

<em>i.e. If n is odd, then  </em>n^3<em> is odd</em>

<u />

<u>2.22  </u>3n + 4<u> is even, if and only if n is even</u>

We have: 3n + 4<u />

<u />

Assume that: n = 2k + 2 for k \ge 0

So, we have:

3n + 4 = 3(2k + 2) + 4

Open bracket

3n + 4 = 6k + 6 + 4

3n + 4 = 6k + 10

Factorize

3n + 4 = 2(3k + 5)

The factor of 2 means that 3n + 4 is even.

<em>Hence, </em>3n + 4<em> is even, if and only if n is even </em>

<em />

<u />

<u>2.22: </u>s \ne -1<u> and </u>t \ne -1<u>, then </u>s + t + st \ne -1<u />

To do this, we prove by contrapositive.

The contrapositive of the above statement is:

If s = -1 and t=-1, then s + t + st = -1

We have:

s + t + st = -1

Substitute the values of s and t in: s + t + st = -1

-1 -1 -1 \times -1 = -1

-1 -1 + 1 = -1

-1 = -1

Hence, by contrapositive:

If s = -1 and t=-1, then s + t + st = -1

Read more about proofs  at:

brainly.com/question/19643658

7 0
3 years ago
The average cost of living for a family of four in twelve different cities was found to be $65,351 with a standard deviation of
Andrej [43]

Answer:

$65,351+/-$3,661.73

= ( $61,689.27, $69,012.73)

Therefore, the 90% confidence interval (a,b) = ( $61,689.27, $69,012.73)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $65,351

Standard deviation r = $7,711

Number of samples n = 12

Confidence interval = 90%

z(at 90% confidence) = 1.645

Substituting the values we have;

$65,351+/-1.645($7,711/√12)

$65,351+/-1.645($2,225.973962860)

$65,351+/-$3661.727168905

$65,351+/-$3,661.73

= ( $61,689.27, $69,012.73)

Therefore, the 90% confidence interval (a,b) = ( $61,689.27, $69,012.73)

6 0
3 years ago
According to the Complex Conjugate Root Theorem, if a+bi is a root of a quadratic equation, then __blank__ is also a root of the
Trava [24]

Answer:

a-bi


Step-by-step explanation:

If a quadratic equation lx^2+mx+n=0 has one imaginary root as a+bi then the other root is the conjugate of a+bi = a-bi

Because we have l, m and n are real numbers and they are the coefficients.

Sum of roots = a+bi + second root = -m/l

When -m/l is real because the ratio of two real numbers, left side also has to be real.

Since bi is one imaginary term already there other root should have -bi in it so that the sum becomes real.

i.e. other root will be of the form c-bi for some real c.

Now product of roots = (a+bi)(c-bi) = n/l

Since right side is real, left side also must be real.

i.e.imaginary part =0

bi(a-c) =0

Or a =c

i.e. other root c-bi = a-bi

Hence proved.


3 0
3 years ago
Can someone tell me this? I dont get it.
Harman [31]

Answer:

Step-by-step explanation:

Numbers 1 and 4 are perimeter questions so all you do is add up all the sides and the label is cm. For #2, this is an area problem and the area for a rectangle is length times width, so multiply the 2 together and the label is inches squared. For #3, the volume formula for a cube is side*side*side and the label for this is feet cubed. For #5, the area for a triangle is .5 times the base times the height, and the label is mm-squared. That should help you get all the answers on your wn. Very, very simple.

3 0
3 years ago
X.7=14 plz help me 4th grade work
OlgaM077 [116]

x*7=14

14/7=2

x=2

brainliest please

8 0
3 years ago
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