A bat and a ball cost one dollar and ten cents in total. The bat costs a dollar more than the ball. How much does the ball cost?

A market research team compiled the following discrete probability distribution, where X represents the number of automobiles ow

rodikova [14]

Answer:

The standard deviation of X is 0.7

Step-by-step explanation:

We are given the following distribution:

x: 0 1 2 3

P(x): 0.3 0.5 0.2 0.4

We have to find the standard deviation of X.

Formula:

$E(x) = \displaystyle\sum x_iP(x_i)\\\\E(x) =0(0.3) + 1(0.5) + 2(0.2) + 3(0.4)\\\\E(x) = 2.1\\\\E(x^2) = \displaystyle\sum x_i^2P(x_i)\\\\E(x^2) =0(0.3) + 1(0.5) + 4(0.2) + 9(0.4)\\\\E(x^2) = 4.9\\\\Var(x) = E(x^2) - (E(x))^2 = 4.9-(2.1)^2 = 0.49\\\\\sigma(x) = \sqrt{Var(x)} =\sqrt{0.49} = 0.7$

Thus, the standard deviation of X is 0.7

6 0

3 years ago

A running circuit is in the shape of a triangle with lengths of 6km, 6.5km and 7km. What are the sizes of the angles (in minutes

Rudik [331]

A triangle is an example of a class of figures referred to as plane shapes. It has three straight sides and three internal angles which sum up to $180^{o}$ . The measures of the internal angles of the triangle given in the question are A = $52.6^{o}$ , B = $59.4^{o}$ , and C = $68^{o}$ .

A triangle is an example of a class of figures referred to as plane shapes. It has three straight sides and three internal angles which sum up to $180^{o}$ .

Considering the given question, let the sides of the triangle be: a = 6 km, b = 6.5 km, and c = 7 km.

Apply the Cosine rule to have:

$c^{2}$ = $a^{2}$ + $b^{2}$ - 2ab Cos C

So that;

$7^{2}$ = $6^{2}$ + $(6.5)^{2}$ - 2(6 * 6.5) Cos C

49 = 36 + 42.25 - 78Cos C

78 Cos C = 78.25 - 49

= 29.25

Cos C = $\frac{29.25}{78}$

= 0.375

C = $Cos^{-1}$ 0.375

= 67.9757

C = $68^{o}$

Apply the Sine rule to determine the value of B,

$\frac{b}{Sin B}$ = $\frac{c}{Sin C}$

$\frac{6.5}{Sin B}$ = $\frac{7}{Sin 68}$

SIn B = $\frac{6.5 *Sin 68}{7}$

= 0.861

B = $Sin^{-1}$ 0.861

= 59.43

B = $59.4^{o}$

Thus to determine the value of A, we have;

A + B + C = $180^{o}$

A + $59.4^{o}$ + $68^{o}$ = $180^{o}$

A = $180^{o}$ - 127.4

= 52.6

A = $52.6^{o}$

Therefore the sizes of the internal angles of the triangle are: A = $52.6^{o}$ , B = $59.4^{o}$ , and C = $68^{o}$ .

For more clarifications on applications of the Sine and Cosine rules, visit: brainly.com/question/14660814

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8 0

1 year ago

Which of the following best describes a rational exponent

bija089 [108]

The answer I think is B

3 0

3 years ago

Triangle WXY has coordinates W(1, 5), X(1, 1), and Y(5, 1). Which of the following sets of points represents a dilation of trian

timofeeve [1]

The correct answer for the question shown above is the second option, the option B, which is: B. W'(2, 10), X'(2, 2), Y'(10, 2)
The explanation is shown below: As you can see, the original triangle has the following coordinates W(1, 5), X(1, 1), and Y(5, 1); the triangle must be dilated by a common scale factor, so if you analize the option B, you can notice that the triangle was dilated by a scale factor of 2.

3 0

3 years ago

I need help on all of number 2!!!!

erica [24]

9514 1404 393

Answer:

a: 0; b: 1; c: 1; d: ∞; e: 0; f: ∞

Step-by-step explanation:

Simplify the expressions to put the left and right in the same form. Then compare. If the x-coefficients are the same, there will be 0 or ∞ solutions. If they are different, there will be 1 solution.

If the x-coefficients are the same, look at the constants. If they are different, there will be 0 solutions. If they are the same, there will be ∞ solutions.

__

a) -2x -10 = -6x +4x -8 ⇒ -2x -10 = -2x -8 . . . . 0 solutions

b) 0.8x -4.8 = -0.5x +3.4 . . . . 1 solution

c) -1/4x -7/2 = -3x -4 . . . . 1 solution

d) 2x -8 +x = 3x -6 -2 ⇒ 3x -8 = 3x -8 . . . . ∞ solutions

e) 3 -2/5x -12/5 = 2 -2/5x ⇒ -2/5x +3/5 = -2/5x +2 . . . . 0 solutions

f) 6x -6 +21 = 6x +15 ⇒ 6x +15 = 6x +15 . . . . ∞ solutions

7 0

2 years ago

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