All categories

2 years ago

Is the quotient of √10 and 5 a rational number? Explain.

Mathematics

1 answer:

zhuklara [117]2 years ago

7 0

Answer:

No, it is irrational.

Step-by-step explanation:

The quotient of √10 and 5 is equal to $\frac{\sqrt{10}}{5} }$ which equals 0.6245553...

The number goes on and on forever with no determinable pattern (i.e. the decimal 0.234234234... although the decimal goes on forever, the 234 repeats over and over).

If you're still confused, check out https://www.mathsisfun.com/irrational-numbers.html I find it to be a really helpful website!

You might be interested in

Two brands of AAA batteries are tested in order to compare their voltage. The data summary can be found below. Find the 93% conf

kobusy [5.1K]

Answer:

$(\bar X_1 -\bar X_2) \pm z_{\alpha/2} \sqrt{\frac{s^2_1}{n_1}+\frac{s^2_}{n_2}}$

And replacing we got:

$(9.2 -8.8) - 1.811 \sqrt{\frac{0.3^2}{27}+\frac{0.1^2}{30}}= 0.2903$

$(9.2 -8.8) + 1.811 \sqrt{\frac{0.3^2}{27}+\frac{0.1^2}{30}}= 0.5097$

And the confidence interval for the difference of means would be given by:

$0.2903 \leq \mu_1 -\mu_2 \leq 0.5097$

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".

We have the following data given:

$\bar X_1 = 9.2 , \bar X_2 = 8.8, \sigma_1= 0.3, n_1 = 27, \sigma_2 = 0.1, n_2 = 30$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 93% of confidence, our significance level would be given by $\alpha=1-0.93=0.07$ and $\alpha/2 =0.035$ . And the critical value would be given by:

$z_{\alpha/2}=-1.811, z_{1-\alpha/2}=1.811$

The confidence interval is given by:

$(\bar X_1 -\bar X_2) \pm z_{\alpha/2} \sqrt{\frac{s^2_1}{n_1}+\frac{s^2_}{n_2}}$

And replacing we got:

$(9.2 -8.8) - 1.811 \sqrt{\frac{0.3^2}{27}+\frac{0.1^2}{30}}= 0.2903$

$(9.2 -8.8) + 1.811 \sqrt{\frac{0.3^2}{27}+\frac{0.1^2}{30}}= 0.5097$

And the confidence interval for the difference of means would be given by:

$0.2903 \leq \mu_1 -\mu_2 \leq 0.5097$

4 0

2 years ago

Find the missing value for the exponential function represented by the table below x -2 -1 0 1 2 y 29 20.3 14.21 6.9629

andre [41]

Answer:

y=4.8710 is the missing value

Step-by-step explanation:

The first step in approaching this question is determining the exponential equation that models the set of data. This can easily be done in Ms.Excel application. We first enter the data into any two adjacent columns of an excel workbook. The next step is to highlight the data, click on the insert tab and select the x,y scatter-plot feature. This creates a scatter-plot for the data.

The next step is to click the Add chart element feature and insert an exponential trend line to the scatter plot ensuring the display equation on chart is checked.

The exponential regression equation for the data set is given as;

$y=12.321e^{-0.464x}$

To find the missing y value, we simply substitute x with 2 in the regression equation obtained;

$y=12.321e^{-0.464(2)}\\\\y=4.8710$

5 0

1 year ago

(10 points) Person A leaves a $16 tip for a meal that costs $123. Person B leaves a tip of $12 for a meal that costs $89. Who is

miskamm [114]

Answer:

person b because the person has $89 so the person can get any meal

Step-by-step explanation:

3 0

1 year ago

Evan went to the park and saw for animals each animal was either a duck or dog if he saw a total of 14 legs how many of each ani

beks73 [17]

Answer:

Two dogs and three ducks

Step-by-step explanation:

Dogs have four legs and ducks have two, to find the answer, you add the number to get your answer.

In this case, two dogs would make a total of 8 legs and three ducks would make a total of 6 legs. Adding 8 and 6 together, you get 14.

7 0

2 years ago

AC ≅ AE; ∠ACD ≅ ∠AED

pshichka [43]

Answers:

A) △ACF ≅ △AEB because of ASA.

D) ∠CFA ≅ ∠EBA

E) FC ≅ BE

Solution:

AC ≅ AE; ∠ACD ≅ ∠AED Given

The angle ∠CAF ≅ ∠EAB, because is the same angle in Vertex A

Then △ACF ≅ △AEB because of ASA (Angle Side Angle): They have a congruent side (AC ≅ AE) and the two adjacent angles to this side are congruent too (∠ACD ≅ ∠AED and ∠CAF ≅ ∠EAB), then option A) is true: △ACF ≅ △AEB because of ASA.

If the two triangles are congruent, the ∠CFA ≅ ∠EBA; and FC ≅ BE, by CPCTC (Corresponding Parts of Congruent Triangles are Congruent), then Options D) ∠CFA ≅ ∠EBA and E) FC ≅ BE are true

4 0

2 years ago

Read 2 more answers