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2 years ago

Can you predict the outcome of multiplying 750 by 0.1 without calculating

Mathematics

1 answer:

9966 [12]2 years ago

8 0

Answer:

750 × 1/10 = 750/10 = 75

Step-by-step explanation:

The best way to really predict the outcome of multiplying 750 by 0.1 without calculator is firstly, converting the decimal to a fraction to easily do the multiplication in your head.

Since one of the multiplicand is a decimal the products will be much complicated therefore, to convert the decimal number 0.1 to a fraction number we shift the point to the right hand side which simply translate to 1/10. The trick here is the number of times we shift the point will determine the number of zeros the denominator will possess. Assuming we have 0.12 as the decimal, it is required we shift the point twice and the resulting value we become 12/100. If the decimal is 0.123 it is required we shift the point 3 times , the resulting value will be 123/1000. Not the number of times we shift the point will determine the number of zero's of the denominator.

Finally, the 2 multiplicands are now 750 and 1/10 which is more easier to manipulate in our head.

750 × 1/10 = 750/10 = 75( you just cancel the zeros)

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Exercise 2.4.2: Proving statements about rational numbers with direct proofs. About Prove each of the following statements using

IgorLugansk [536]

Answer:

See Explanation

Step-by-step explanation:

(a) Proof: Product of two rational numbers

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

$A = \frac{1}{2}$

$B = \frac{2}{3}$

The product:

$A * B = \frac{1}{2} * \frac{2}{3}$

$A * B = \frac{1}{1} * \frac{1}{3}$

$A * B = 1 * \frac{1}{3}$

$A * B = \frac{1}{3}$

Proved, because 1/3 is rational

(b) Proof: Quotient of a rational number and a non-zero rational number

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

$A = \frac{1}{2}$

$B = \frac{2}{3}$

The quotient:

$A / B = \frac{1}{2} / \frac{2}{3}$

Express as product

$A / B = \frac{1}{2} / \frac{3}{2}$

$A / B = \frac{1*3}{2*2}$

$A / B = \frac{3}{4}$

Proved, because 3/4 is rational

(c) x + y is rational (missing from the question)

Using direct proofs.

Let x and y be

Such that:

$x = \frac{1}{2}$

$y = \frac{2}{3}$

The sum:

$x + y = \frac{1}{2} + \frac{2}{3}$

Take LCM

$x + y = \frac{3+4}{6}$

$x + y = \frac{7}{6}$

Proved, because 7/6 is rational

The above proof works for all values of A, B, x and y; as long as they are rational values

8 0

3 years ago

If 7x+3=24, find the value of -5 - 6x. a)-23 b)-7 c)1 d)17

OlgaM077 [116]

A. -23

If 7x plus 3 equals 24, X equals 3. -5 minus 6 time X(3) equals -23.

6 0

3 years ago

I REALLY NEED HELP ON 40 and 41, 50 POINTS

photoshop1234 [79]

Question 40 is D because from looking at the graph, its is symmetrical and the mean is the average, which usually the middle of the graph, so is the median. The median and mean would be within the 2.1-3 category because its the middle of the graph.

Question 41 is B because every pound is 16 ounces. If you multiply 16 and 12.5, you'll get 200.

3 0

3 years ago

A investor obtained a loan of $600,000 to buy a car wash business. The monthly mortgage payment was based on 30 years at 5.5%. F

Lisa [10]

Answer:

The monthly mortgage payment is $ 8306.58

Step-by-step explanation:

Given as :

The loan taken as $ 600,000

The rate of interest = 5.5 %

The time period = 30 Years

So, from compounded method

Amount = principal × $(1 +\frac{Rate}{100})^{Time}$

or, Amount = $ 600,000 × $(1 +\frac{5.5}{100})^{30}$

Or, Amount = $ 600,000 × $(1.055)^{30}$

∴ Amount = $ 2990370.77

Now for The monthly mortgage payment

∵ Time period is 30 years

So , 30 years = 12 × 30 = 360 months

∴ Amount payment in monthly =$ $\frac{2990370.77}{360}$

Or, Amount payment in monthly =$ 8306.58

Hence The monthly mortgage payment is $ 8306.58 Answer

4 0

3 years ago

The sum of three numbers is 100. The second number is 2 times the third. The third number is 8 less than the first. What are the

8_murik_8 [283]

Answer:

Step-by-step explanation:x+y+z=100(let x ,y,z represent the first second and third numbers respectively)

Therefore,y=2z

z=x-8

y=2x-16

substituting the values of x,y and z into the question,we have

x+(2x-16)+(x-8)=100

Simplifying,we have

4x-24=100

adding 24 to both sides of the equation,

4x=100+24

4x=124

dividing both sides of the equation by the co-efficient of x,we have

4x/4=124/4

4.31=124

therefore,x=31.

6 0

6 months ago