All categories

3 years ago

If you answer yo get 20 points

Mathematics

2 answers:

Elodia [21]3 years ago

6 0

Answer:

n = 2 + 2√3 and n = 2 - 2√3

Step-by-step explanation:

Let the number be n.

Then n² + 1 = 4n.

Rearranging this in proper quadratic format:

n² - 4n + 1

Here the coefficients are a = 1, b = -4 and c = 1.

Then the discriminant is b²-4ac, or (-4)²-4(1)(1) ), or 16 - 4, or 12.

By applying the quadratic formula, we find that the roots are:

- (-4) ± √12

n = ------------------

or n = 2 + 2√3 and n = 2 - 2√3

Ierofanga [76]3 years ago

5 0

Answer:

3.732 or 0.268 to the nearest thousandth.

Exact values are 2 + √12/2 or 2 - √12/2.

Step-by-step explanation:

Let the original number be x, then:

x^2 + 1 = 4x

x^2 - 4x + 1 = 0

x = [-(-4) +/- sqrt(16 - 4*1*1]) / 2

x = (4 + sqrt12)/ 2 , (4 - sqrt12) / 2

= 3.732, 0.268.

You might be interested in

Jacob Lee is a frequent traveler between Los Angeles and San Diego. For the past month, he wrote down the flight times in minute

valkas [14]

Solution :

We know that

$H_0: \mu_1 = \mu_2=\mu_3$

$H_1 :$ At least one mean is different form the others (claim)

We need to find the critical values.

We know k = 3 , N = 35, α = 0.05

d.f.N = k - 1

= 3 - 1 = 2

d.f.D = N - k

= 35 - 3 = 32

SO the critical value is 3.295

The mean and the variance of each sample :

Goust Jet red Cloudtran

$\overline X_1 =50.5$ $\overline X_2 =50.07143$ $\overline X_3 =55.71429$

$s_1^2=19.96154$ $s_2^2=14.68681$ $s_3^2=36.57143$

The grand mean or the overall mean is(GM) :

$\overline X_{GM}=\frac{\sum \overline X}{N}$

$=\frac{51+51+...+49+49}{35}$

= 52.1714

The variance between the groups

$s_B^2=\frac{\sum n_i\left( \overline X_i - \overline X_{GM}\right)^2}{k-1}$

$=\frac{\left[14(50.5-52.1714)^2+14(52.07143-52.1714)^2+7(55.71426-52.1714)^2\right]}{3-1}$

$=\frac{127.1143}{2}$

= 63.55714

The Variance within the groups

$s_W^2=\frac{\sum(n_i-1)s_i^2}{\sum(n_i-1)}$

$=\frac{(14-1)19.96154+(14-1)14.68681+(7-1)36.57143}{(14-1)+(14-1)+(7-1)}$

$=\frac{669.8571}{32}$

= 20.93304

The F-test statistics value is :

$F=\frac{s_B^2}{s_W^2}$

$=\frac{63.55714}{20.93304}$

= 3.036212

Now since the 3.036 < 3.295, we do not reject the null hypothesis.

So there is no sufficient evidence to support the claim that there is a difference among the means.

The ANOVA table is :

Source Sum of squares d.f Mean square F

Between 127.1143 2 63.55714 3.036212

Within 669.8571 32 20.93304

Total 796.9714 34

3 0

2 years ago

The teacher buys a pack of notebooks for give his students the ratio of the gold notebooks to red notebooks is represented in th

katovenus [111]

Answer-

~The answer is 40 gold notebooks~

(Thank me later~)

7 0

3 years ago

Read 2 more answers

Which of the following proves these two triangles congruent by AAS?

Nataly [62]

Answer:

b is correct

Step-by-step explanation:

hope this helps

3 0

2 years ago

the combined area of two squares is 45 square centimetres each side is twice as long as a side of the other square what length o

Ostrovityanka [42]

Answer:

Let the side of one square be x. Area = x*x = x²

Then the side of other square would be 2x , Area = 2x*2x = 4x²

Combined area = x² + 4x² = 5x²

This combined area = 45 cm²

you simplify

Therefore 5x² = 45 Divide both sides by 5

x² = 45/5

x² = 9 Take square root of both sides

x = √9

x = 3

Length of larger square is 2x = 2*3 = 6 cm

Length of larger square = 6cm

Step-by-step explanation:

4 0

2 years ago

How do you write (6)^-2 without exponents?

m_a_m_a [10]

(6)^-2 Is equivalent to 1/36

5 0

3 years ago

Read 2 more answers