All categories

3 years ago

Is 7.07106781 Rational Or Irrational?

Mathematics

2 answers:

elena-14-01-66 [18.8K]3 years ago

7 0

Answer:

It is irrational

Step-by-step explanation:

• 7.07106781 is equivalent to √50

$7.07106781 \equiv \sqrt{50}$

CaHeK987 [17]3 years ago

5 0

Answer:

It is rational

I have to add more characters so don't worry

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The manager of Petco, a nationwide chain of pet supply stores, wants to study characteristics of the customers, particularly the

shutvik [7]

Answer:

The 95% confidence interval would be given by (19.141;23.538)

Step-by-step explanation:

1) 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".

$\bar X=21.34$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=9.22 represent the sample standard deviation

n=70 represent the sample size

2) Confidence interval

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:

$df=n-1=70-1=69$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,69)".And we see that $t_{\alpha/2}=1.994$

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

$21.74-1.994\frac{9.22}{\sqrt{70}}=19.141$

$21.74+1.994\frac{9.22}{\sqrt{70}}=23.538$

So on this case the 95% confidence interval would be given by (19.141;23.538)

3 0

3 years ago

24.8 = t + 5.1 what is t?

monitta

Answer:

t = 19.7

Step-by-step explanation:

24.8 = t + 5.1

-5.1 -5.1

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

19.7 = t

4 0

3 years ago

Read 2 more answers

What are the zeros of the function f(x) = x4 − x2 − 2?

goblinko [34]

Answer:

x = ± $\sqrt{2}$ , x = ± i

Step-by-step explanation:

f(x) = $x^{4}$ - x² - 2

to find the zeros , equate f(x) to zero , that is

$x^{4}$ - x² - 2 = 0

using the substitution u = x² , then

u² - u - 2 = 0 ← in standard form

(u - 2)(u + 1) = 0 ← in factored form

equate each factor to zero and solve for u

u - 2 = 0 ⇒ u = 2

u + 1 = 0 ⇒ u = - 1

convert u back into terms of x

x² = 2 ( take square root of both sides )

x = ± $\sqrt{2}$

x² = - 1 ( take square root of both sides )

x = ± $\sqrt{-1}$ = ± i

8 0

2 years ago

For what value of k is there one solution to the given quadratic equation (k+1)x²+4kx+2=0.

andriy [413]

Answer:

If $k = 1$ or $k = -\frac{1}{2}$ , there is only one solution to the given quadratic equation.

Step-by-step explanation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = (x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

The signal of $\bigtriangleup$ determines how many real roots an equation has:

$\bigtriangleup > 0$ : Two real and different solutions

$\bigtriangleup = 0$ : One real solution

$\bigtriangleup < 0$ : No real solutions

In this problem, we have the following second order polynomial:

$(k+1)x^{2} + 4kx + 2 = 0$ .

This means that $a = k+1; b = 4k; c = 2$

It has one solution if

$\bigtriangleup = 0$

$b^{2} - 4ac = 0$

$16k^{2} -8(k+1) = 0$

$16k^{2} - 8k - 8 = 0$

We can simplify by 8

$2k^{2} - k - 1 = 0$

The solution is:

$k = 1$ or $k = -\frac{1}{2}$

So, if $k = 1$ or $k = -\frac{1}{2}$ , there is only one solution to the given quadratic equation.

4 0

4 years ago

(p²-pq + q²) ( 3p+ 3q)

RUDIKE [14]

Answer:

3p^3 + qp^2 - pq^2 + 3q^3

Step-by-step explanation:

(p²-pq + q²) ( 3p+ 3q)

3p^3 + 3qp^2 - 3qp^2 - 3pq^2 + 3pq^2 + 3q^3

3p^3 + qp^2 - pq^2 + 3q^3

3 0

3 years ago