The computed chi-square value is positive because the difference between the observed and expected frequencies is

There are 4 boys and 7 girls, how many four person group combinations are possible?

irina1246 [14]

There are 4 boys and 7 girls with a total of 11. Now, how many 4 persons group combinations are possible.
=> 1 boy and 3 girls
=> 2 boys and 2 girls
=> 3 boys and 1 girl
Thus, there are 3 possible combinations that might happen.

5 0

2 years ago

How to solve this pythagoras theorem

My name is Ann [436]

Answer:

see explanation

Step-by-step explanation:

The hypotenuse is the longest side thus is (4x + 1)

The legs are 2x and (4x - 1)

Using Pythagoras' theorem, then

(4x + 1)² = (2x)² + (4x - 1)² ← expanding factors

16x² + 8x + 1 = 4x² + 16x² - 8x + 1 , that is

16x² + 8x + 1 = 20x² - 8x + 1 ( subtract 20x² - 8x + 1 from both sides )

- 4x² + 16x = 0 ( multiply through by - 1 )

4x² - 16x = 0 ← factor out 4x from each term

4x(x - 4) = 0

Equate each factor to zero and solve for x

4x = 0 ⇒ x = 0

x - 4 = 0 ⇒ x = 4

Now x > 0, thus x = 4

2x = 2(4) = 8

4x - 1 = 4(4) - 1 = 16 - 1 = 15

4x + 1 = 4(4) + 1 = 16 + 1 = 17

Thus

perimeter = 8 + 15 + 17 = 40 cm

3 0

2 years ago

Dylan wants to buy both the tablet and

nignag [31]

Answer:

108$

Step-by-step explanation:

6 0

2 years ago

Evaluate the six trigonometric functions of the angle 0.

Arturiano [62]

Given:

Right triangle

To find:

The six trigonometric functions of θ

Solution:

Hypotenuse = 18

Adjacent side to θ = 10

Opposite side to θ = ?

Using Pythagoras theorem:

$\text {Hypotenuse}^2 = \text{adjacent}^2+\text{opposite}^2$

$18^2 =10^2+\text{opposite}^2$

$324=100+\text{opposite}^2$

Subtract 100 from both sides.

$224=\text{opposite}^2$

Taking square root on both sides.

$4\sqrt{14}=\text{opposite}$

Using trigonometric ratio formula:

$$\sin\theta =\frac{\text{opposite }}{\text{hypotenuse}}$

$$\sin\theta =\frac{4\sqrt{14} }{18}$

$$\csc\theta =\frac{\text{hypotenuse}}{\text{opposite }}$

$$\csc\theta =\frac{18}{4\sqrt{14} }$

$$\cos \theta=\frac{\text { adjacent side }}{\text { hypotenuse }}$

$$\cos \theta=\frac{10}{18}$

$$\sec \theta=\frac{\text { hypotenuse }}{\text { adjacent side }}$

$$\sec \theta=\frac{18 }{10}$

$$\tan \theta=\frac{\text { opposite side }}{\text { adjacent side }}$

$$\tan \theta=\frac{4\sqrt{14} }{10}$

$$\cot \theta=\frac{\text { adjacent side }}{\text { opposite side }}$

$$\cot \theta=\frac{10}{4\sqrt{14} }$

8 0

2 years ago

PLEASE HELP :'))

andreev551 [17]

Answer:

D) 54 cm

Step-by-step explanation:

We can use the Centroid Theorem to solve this problem, which states that the centroid of a triangle is $\frac{2}{3}$ of the distance from each of the triangle's vertices to the midpoint of the opposite side.

Therefore, $R$ is $\frac{2}{3}$ of the distance from $U$ to $V$ , since the latter is the midpoint of the side opposite to $U$ . We know this because $R$ belongs to $UV$ , so $R$ must be $QS$ 's midpoint due to the fact that by definition, the centroid of a triangle is the intersection of a triangle's three medians (segments which connect a vertex of a triangle to the midpoint of the side opposite to it).