For how many different pairs of positive integers (a,b) with greatest common factor 1, and with a>b, does ab=30!

Answers

Answer 1

Answer:

4 pairs

Step-by-step explanation:

Given

ab = 30

Where

a > b

Required

Determine number of pairs (a,b)

To do this, we simply test values for a and b that satisfy the required condition.

First,

Take a = 30

Substitute 30 for a in ab = 30

30 * b = 30

b = 30/30

b = 1

The pair is (30,1)

Take a = 15

Substitute 15 for a in ab = 30

15 * b = 30

b = 30/15

b = 2

The pair is (15,2)

Take a = 10

Substitute 10 for a in ab = 30

10 * b = 30

b = 30/10

b = 3

The pair is (10,3)

Take a = 6

Substitute 6 for a in ab = 30

6 * b = 30

b = 30/6

b = 5

The pair is (6,5)

There exist no other pair that satisfy the given condition.

Counting the above pairs, there are just 4 pairs.


Related Questions

h-z=3
-3h + 3z = 6
I’ll give brainliest.

Answers

Answer:

-3h+3z =6

multiply by-1

3h-3z=-6

3(h-z)=-6

3(3)=-6

9=-6

9+6

15

If you deposit $850 into an account which earns 6% yearly interest compounded monthly, how much will be in the account after 4 years, assuming you never withdraw money from the account? Round your answer to the nearest cent if necessary and do not include the dollar sign.

Answers

Answer:

1079.9

Step-by-step explanation:

A = P(1 + [tex]\frac{r}{n}[/tex])^nt

A: ending amount

P: principal (850)

r: interest rate in decimal form (.06)

n: compounding periods, 12 months in a year.

t: time in years (4)

   = 850(1 + .06/12)^12(4)

    = 850(1.005)⁴⁸

    = 850(1.2704891)

    = 1079.9157

Answer:

1079.92

Step-by-step explanation:

Elliot spent 3/5 of his money on stereo equipment and 1/6 of the money he had left on lunch. He left the house with $24. How much money did Elliot return with?

Answers

$24/5 = $4.8 x 3 = $14.4
$24/6 = $4 x 1 = $4
$14.4 + $4 = $18.4
$24 - $18.4 = $5.6

Consider the function f(x) = -2x+15 . What is the value of y when x = 3?

Answers

Answer:

f(3) = 9

Step-by-step explanation:

Step 1: Define

f(x) = -2x + 15

x = 3

Step 2: Substitute and Evaluate

f(3) = -2(3) + 15

f(3) = -6 + 15

f(3) = 9

What is the following figure?
8 m
5 m
5 m
8 m
rhombus
rectangle
trapezoid
parallelogram

Answers

Answer:

rhombus

Step-by-step explanation:

you can't see what shape that is but Im doing this assignment right now I know what it looks like

Some of the other shades of paint are more yellow than others. Which mixture(s) are the most yellow? chiesta haces of this paint are more yellow Explain your reasoning.​

Answers

9514 1404 393

Answer:

  2, 5, 6

Step-by-step explanation:

If we number the mixes 1-6 from top to bottom, then the fraction of the total that is yellow is ...

  1. 1/(3+1+2) = 1/6

  2. 2/(5+2+3) = 2/10 = 1/5

  3. 2/(6+2+4) = 2/12 = 1/6

  4. 4/(12+4+8) = 4/24 = 1/6

  5. 6/(15+6+9) = 6/30 = 1/5

  6. 8/(20+8+12) = 8/40 = 1/5

Mixes 2, 5, and 6 are the most yellow.   (1/5 > 1/6)

3 + |-7| I would like some help

Answers

Answer: The answer will be -4

Two part-time instructors are hired by the Department of Statistics and each is assigned at random to teach a single course in probability, inference, or statistical computing. Assume that more than one section of each course is offered. List the outcomes in the sample space [Hint: each element consists of a pair of assignments]. Find the probability that they will teach different courses. Note: carefully define your notation (e.g. any events) in words before solving the problem.

Answers

Answer:

The probability that they will teach different courses is [tex]\frac{2}{3}[/tex].

Step-by-step explanation:

Sample space is a set of all possible outcomes of an experiment.

In this case we will write the sample space in the form (x, y).

Here x represents the course taught by the first part-time instructor and y represents the course taught by the second part-time instructor.

Denote every course by their first letter.

The sample space is as follows:

S = {(P, P), (P, I), (P, S), (I, P), (I, I), (I, S), (S, P), (S, I) and (S, S)}

The outcomes where the the instructors will teach different courses are:

s = {(P, I), (P, S), (I, P),(I, S), (S, P) and (S, I)}

The probability of an events E is the ratio of the number of favorable outcomes to the total number of outcomes.

[tex]P(E)=\frac{n(E)}{N}[/tex]

Compute the probability that they will teach different courses as follows:

[tex]P(\text{Different courses})=\frac{n(s)}{n(S)}=\frac{6}{9}=\frac{2}{3}[/tex]

Thus, the probability that they will teach different courses is [tex]\frac{2}{3}[/tex].

Wright the number 972,274 in words​

Answers

Nine hundred seventy two thousand two hundred seventy four

Answer:

Nine hundred seventy two thousand two hundred seventy four. Hope this helps

Construct a 2x2 matrix A= aij. whose elements are given by

a = |-3i + j| plz give step by step answer​

Answers

Hope it will help you


what is d divided by equals

Answers

Answer: X and Y

Step-by-step explanation: IF I REMEMBER dont get mad if you don’t get it right

PLEASE HELP


| y-x| + y-1


evaluate the absolute value expression for x= -3 and y= -6

Answers

Answer:

-4

Step-by-step explanation:

So we are given the expression: | y - x | + y - 1, and we have our values for (x,y): (-3,-6).

So, we can just start plugging things in and simplifying, so:

| -6 + 3 | - 6 - 1 = | -3 | -7

                       = 3 - 7

                       = -4

2 pay raises in 3 years unit rate

Answers

Answer:

1:1.5

Step-by-step explanation:

cut the 3 in half and cut the 2 in half

Which statements are true 25 (0)=25, 25(1)=25, 25+0=25, 25+1=25

Answers

25(1)=25
25+0=25
Those are the only ones that are true
25(1)=25 and 25+0=25 are correct

Fill in the missing num W + 2 7 9 2​

Answers

Answer:

What are you asking? What does it equal? W+2792=??

Answer:

there is no number that could fit, it actually could be anything, I think that there is a part of the problem not there that is a expression to solve that you need a equation

Step-by-step explanation:

I really need the answer. will give brainliest!
If we are driving to California. We are staring at a map. The map says for every inch in a half on the map it comes out to be 5 miles. There are 137 miles from Houston to Hufflepuffsberg. How many inches is it from Houston to Hufflepuffsberg.

Answers

Answer:

The answer is 27.4 I'm bad at math and I tried so hope is correct

can a line and a point lie on the same plane.

Answers

Answer:

yes

Step-by-step explanation:

3 - +4 - = ?
4 4
OA.
3
7 -
4
OB.
4
3
8
OC.
8
OD. 7

Answers

The answer to this question is 8.


You just simplify it

Xis all of the following except
a term
a variable
a constant
a an expression
Help I’ll give brainliest to the best answer

Answers

Answer:

a variable

Step-by-step explanation:

a variable.

x is not an expression unless it has signs. so x by itself would not be an expression without different numbers and sign between

0.42 - 4) = 0.24 + 7)

Answers

Answer:

im sorry if not but i think its 7.24

Step-by-step explanation:

Mr. Nell is painting his coffee table. The micture that he adds to the paint is made of 5/6 cup
baking soda for every 5 tablespoons of water.
What is the rate in cups of baking soda per tablespoon of water?

Answers

Answer:

1/6 cups

Step-by-step explanation:

5/6 /5 = 5/6 divided by 5

= 5/6 x 1/5

= 1/6

so your answer is 1/6 cups of baking soda per tablespoon of water

yw ;)

The rate for cups of baking soda per tablespoon of water is 1/6.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The mixture that he adds to the paint is made of 5/6 cup baking soda for every 5 tablespoons of water.

Hence, The rate for cups of baking soda per tablespoon of water is,

⇒ 5/6 ÷ 5

⇒ 5/6 × 1/5

⇒ 1/6

Learn more about the divide visit:

https://brainly.com/question/28119824

#SPJ2

Write in slope intercept form:
(-5,-11) and (-2,1)

Answers

Answer:

y = 4x + 9

Step-by-step explanation:

First, find the slope of the line, which is the change in y/the change in x:

(-11-1)/(-5-(-2)) = -12/-3 = 4

That leaves you with the equation:

y = 4x

But notice, when x = -2 in the equation, y = -8, but we want it to be 1, so we add 9 to the end of the equation:

y = 4x + 9

I hope this helped.

Answer:

Step-by-step explanation: -15/9 my teacher told me

?
Which expression is equivalent to 9x5 +3x(4x4–3x2)

Answers

Answer:

[tex]30x^2+45x[/tex]

Step-by-step explanation:

The answer is

[tex]48^{9} - 72x^{7} +36x^{5}[/tex]

How many millimeters are in 90 ounces?

Answers

Answer:2661615

Step-by-step explanation:

29573.5 is how many millimeters are in an ounce multiply that by 90 and you get 2661615

hope this helps

Answer:

you used two different types of things ounces measure mass and millimeters measure length

but I used google and it said 2.662e+6

if someone can anwser this ​

Answers

Answer:

944

Step-by-step explanation:

Answer:

944

Step-by-step explanation:

L*W*H then add them

is 78 closer to 77.54 or 77.6 closer to 77.54

Answers

77.6 closer to 77.54

a) Work out the value of 5^2-1^5 x 2^4

Answers

Answer: 9

Step-by-step explanation

Rewrite as a square or a cube:

0.001

Answers

Answer:

10^-3*1/3 = 10^-1=0.1

I can't find the right answer

Answers

Answer:

[tex]x<-10\quad \mathrm{or}\quad \:x>10[/tex]

Step-by-step explanation:

[tex]x^2 > 100\\\\\mathrm{For\:}u^n\:>\:a\\\mathrm{,\:if\:}n\:\mathrm{is\:even}\mathrm{\:then\:}u\:<\:-\sqrt[n]{a}\:or\:u\:>\:\sqrt[n]{a}\\\\x<-\sqrt{100}\quad \mathrm{or}\quad \:x>\sqrt{100}\\\\\sqrt{100}=10\\\\x<-10\quad \mathrm{or}\quad \:x>10[/tex]

use the distribution property to write the problem without parenthesis, 4 (2x+11) - 8x+36

Answers

Answer:

80

Step-by-step explanation:

8x+44-8x+36

8x-8x+44+36

44+36

80

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