All categories

4 years ago

Sum of natural number and it's reciprocal is 50/7.find the number by quadratic equations

Mathematics

1 answer:

Stells [14]4 years ago

3 0

Answer: 7

<u>Step-by-step explanation:</u>

The sum of a number and its reciprocal (n + $\dfrac{1}{n}$ ) is $\dfrac{50}{7}$ .

$n+\dfrac{1}{n}=\dfrac{50}{7}\\\\\text{multiply everything by 7n to clear the denominator:}\\\\(7n)n+(7n)\dfrac{1}{n}=(7n)\dfrac{50}{7}\quad \rightarrow \quad 7n^2+7=50n\\\\\text{subtract 50n from both sides:}\qquad 7n^2-50n+7=0\\\\\text{factor the quadratic equation:}\qquad (7n-1)(n-7)=0\\\\\text{apply the Zero Product Property:}\qquad 7n-1=0\quad and\quad n-7=0\\\\\text{solve each equation:}\qquad n=\dfrac{1}{7}\quad and\quad n=7$

Since n is a natural number, the fraction is not a valid solution.

You might be interested in

As an assistant in pet store, one of your responsibilities is to fill the aquariums with water. One 50-gallon aquarium is 36 inc

Fynjy0 [20]

Answer:

Eleven thousand five hundred and twenty

Step-by-step explanation:

E2021

6 0

3 years ago

A political action committee is interested in the proportion of all registered voters who will vote "Yes" on a measure to expand

kirza4 [7]

Answer: parameter: The proportion of registered voters who will vote Yes on the measure.

Sample: The 1000 registered voters who participated in the study.

Statistic: The proportion of the 1000 registered voters that were surveyed who will vote Yes on the measure.

Variable: Yes or No for each registered voter

Population: All registered voters in the US

Data: The list of Yes and No answers that were given by the 1000 participants in the study.

Step-by-step explanation:

Definitions of the given terms:

Population: Large groups of individuals having similar characteristics as per the researcher's point of view.

Sample: It is a subset of the population used to represent it.
Parameter: Measure of particular characteristics in the population.
Statistic: Measure of particular characteristics in the sample.
Variable: Characteristics that vary.
Data: A collected information facts and statistics.

Hence, by using the above definitions, we have

Parameter: The proportion of registered voters who will vote Yes on the measure.
Sample: The 1000 registered voters who participated in the study.
Statistic: The proportion of the 1000 registered voters that were surveyed who will vote Yes on the measure.
Variable: Yes or No for each registered voter.
Population: All registered voters in the US.
Data: The list of Yes and No answers that were given by the 1000 participants in the study.

4 0

3 years ago

You’re installing a new shower wall with square tiles that are one foot by one foot. The wall in your shower is a total of 7 fee

azamat

Answer:

A - It should be $2380.

Step-by-step explanation:

7 x 10 = 70 tiles needed total

70 x 34 = 2380

3 0

4 years ago

The true average diameter of ball bearings of a certain type is supposed to be 0.5 in. A one-sample t test will be carried out t

yulyashka [42]

Complete Question

The complete question is shown on the first uploaded image

Answer:

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 0.5 \ in$

Generally the Null hypothesis is $H_o : \mu = 0. 5 \ in$

The Alternative hypothesis is $H_a : \mu \ne 0.5 \ in$

Considering the parameter given for part a

The sample size is n = 15

The test statistics is t = 1.66

The level of significance $\alpha = 0.05$

The degree of freedom is evaluated as

$df = n- 1$

$df = 15- 1$

$df = 14$

Using the critical value calculator at (social science statistics web site )

$t_{\frac{\alpha}{2} ,df } = t_{\frac{0.05 }{2} ,14} = 2.145$

We are making use of this $t_{\frac{\alpha }{2} }$ because it is a one-tail test

Looking at the value of t and $t_{\frac{\alpha }{2} }$ the we see that $t < t_{\frac{\alpha }{2} }$ so the null hypothesis would not be rejected

Considering the parameter given for part b

The sample size is n = 15

The test statistics is t = -1.66

The level of significance $\alpha = 0.05$

The degree of freedom is evaluated as

$df = n- 1$

$df = 15- 1$

$df = 14$

Using the critical value calculator at (social science statistics web site )

$t_{\frac{\alpha}{2} ,df } = t_{\frac{0.05 }{2} ,14} = -2.145$

Looking at the value of t and $t_{\frac{\alpha}{2} ,df }$ the we see that t does not lie in the area covered by $t_{\frac{\alpha}{2} , df }$ (i.e the area from -2.145 downwards on the normal distribution curve ) hence we fail to reject the null hypothesis

Considering the parameter given for part c

The sample size is n = 26

The test statistics is t = -2.55

The level of significance $\alpha = 0.01$

The degree of freedom is evaluated as

$df = n- 1$

$df = 26- 1$

$df = 25$

Using the critical value calculator at (social science statistics web site )

$t_{\frac{\alpha}{2} ,df } = t_{\frac{0.01 }{2} ,25} = 2.787$

Looking at the value of t and $t_{\frac{\alpha }{2} }$ the we see that t does not lie in the area covered by $t_{\alpha , df }$ (i.e the area from -2.787 downwards on the normal distribution curve ) hence we fail to reject the null hypothesis

Considering the parameter given for part d

The sample size is n = 26

The test statistics is t = -3.95

The level of significance $\alpha = 0.01$

The degree of freedom is evaluated as

$df = n- 1$

$df = 26- 1$

$df = 25$

Using the critical value calculator at (social science statistics web site )

$t_{\frac{\alpha}{2} ,df } = t_{\frac{0.01 }{2} ,25} = -2.787$

Looking at the value of t and $t_{\frac{\alpha}{2} }$ the we see that t lies in the area covered by $t_{\alpha , df }$ (i.e the area from -2.787 downwards on the normal distribution curve ) hence we reject the null hypothesis

6 0

3 years ago

What is the measure of an exterior angle of a regular octagon? a. 360. b. 135. c. 60. d. 45

Darya [45]

An octagon has 12 sides;
The measure of an exterior angle is:
$\frac{360}{12} = 30^{0}$

5 0

4 years ago

Read 2 more answers