All categories

2 years ago

12. A, B and C are consecutive natural numbers. If 2/7 of the reciprocal of A is equal to ⅓ of the reciprocal of C, find B.

Mathematics

1 answer:

abruzzese [7]2 years ago

8 0

<h3>Answer: 13</h3>

===================================================

Explanation:

The set of natural numbers is {1,2,3,4,...} aka the set of positive whole numbers.

Consecutive natural numbers follow one right after another, like with that example above or something like 7,8,9,...

Since B follows right after A, this means B = A+1. Similarly, C = B+1 = (A+1)+1 = A+2 because C follows right after B.

So we have

A = some unknown natural number
B = A+1
C = A+2

In other words, we have the sequence A,A+1,A+2 to replace the sequence A,B,C in that order.

-----------------------

The reciprocal of A is 1/A. Taking 2/7 of this gets us 2/(7A). This result is equal to 1/3 of the reciprocal of C, so,

2/(7A) = 1/3 of 1/C

2/(7A) = 1/(3C)

2/(7A) = 1/(3(A+2))

2/(7A) = 1/(3A+6)

------------------------

Let's cross multiply and solve for A

2/(7A) = 1/(3A+6)

2(3A+6) = 7A*1

6A+12 = 7A

12 = 7A-6A

12 = A

A = 12

Therefore, B = A+1 = 12+1 = 13 and C = A+2 = 12+2 = 14

The sequence A,B,C updates to 12,13,14.

------------------------

Check:

A = 12

reciprocal of A = 1/A = 1/12

D = 2/7 of reciprocal of A = (2/7)*(1/12) = 2/84 = 1/42

C = 14

reciprocal of C = 1/C = 1/14

E = 1/3 of the reciprocal of C = (1/3)*(1/14) = 1/42

Items D and E are equal, so it confirms we have the correct answer.

You might be interested in

PLEASE HELP a three dight number has one more ten than it has hundreds, and it also has one more than twice as many units as ten

bija089 [108]

The reverse number of the three-digit number is 732

<h3>How to determine the reverse of the number?</h3>

Let the three-digit number be xyz.

So, the reverse is zyx

This means that

Number = 100x + 10y + z

Reverse = 100z + 10y + x

From the question, we have the following parameters:

y = x + 1

z = 1 + 2y

The sum is represented as:

100x + 10y + z + 100z + 10y + x = 10^3 - 31

100x + 10y + z + 100z + 10y + x = 969

Evaluate the like terms

101x + 101z + 20y = 969

Substitute y = x + 1

101x + 101z + 20(x + 1) = 969

101x + 101z + 20x + 20 = 969

Evaluate the like terms

101x + 101z + 20x = 949

121x + 101z = 949

Substitute y = x + 1 in z = 1 + 2y

z = 1 + 2(x + 1)

This gives

z = 2x + 3

So, we have:

121x + 101z = 949

121x + 101* (2x + 3) = 949

This gives

121x + 202x + 303 = 949

Evaluate the sum

323x = 646

Divide by 323

x = 2

Substitute x = 2 in z = 2x + 3 and y = x + 1

z = 2*2 + 3 = 7

y = 2 + 1 = 3

So, we have

x = 2

y = 3

z = 7

Recall that

Reverse = 100z + 10y + x

This gives

Reverse = 100*7 + 10*3 + 2

Evaluate

Reverse = 732

Hence, the reverse number of the three-digit number is 732

Read more about digits at:

brainly.com/question/731916

#SPJ1

8 0

1 year ago

Passing through (-6, -1) and parallel 2x+3y=3

RoseWind [281]

Answer:

the answer is -5

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

What is the circumference diameter of 12m

Evgesh-ka [11]

Answer:

C =37.68 m

Step-by-step explanation:

The formula for a circumference is given by

C = pi *d

C = 12 pi

Approximating pi = 3.14

C = 12*3.14

C =37.68 m

6 0

3 years ago

Six measurements were made of the magnesium ion concentration (in parts per million, or ppm) in a city's municipal water supply,

myrzilka [38]

Answer:

$163.83-4.03\frac{20.094}{\sqrt{6}}=130.77$

$163.83+4.03\frac{20.094}{\sqrt{6}}=196.89$

So on this case the 99% confidence interval would be given by (130.77;196.89)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Data: 175 177 175 180 138 138

We can calculate the mean and the deviation from these data with the following formulas:

$\bar X= \frac{\sum_{i=1}^n x_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}$

$\bar X=163.83$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=20.093 represent the sample standard deviation

n=6 represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=6-1=5$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,5)".And we see that $t_{\alpha/2}=4.03$

Now we have everything in order to replace into formula (1):

$163.83-4.03\frac{20.094}{\sqrt{6}}=130.77$

$163.83+4.03\frac{20.094}{\sqrt{6}}=196.89$

So on this case the 99% confidence interval would be given by (130.77;196.89)

7 0

3 years ago

Need answer to B!!! <br> With method

Amiraneli [1.4K]

Answer:

9.5 cm

Step-by-step explanation:

B ratio of angles ratio are 1:2:3

30-60-90 triangle (angles )

x-x√3 -2x triangle ( sides)

short side -long side- hypothenuse

2x = 19 so x= 19/2 = 9.5 cm

4 0

3 years ago

12. A, B and C are consecutive natural numbers. If 2/7 of the reciprocal of A is equal to ⅓ of the reciprocal of C, find B.​

12. A, B and C are consecutive natural numbers. If 2/7 of the reciprocal of A is equal to ⅓ of the reciprocal of C, find B.