Hi guys, how to calculate this in system? {2a+3b=14 {5b+4a=20 Thanks,

In a game of rolling a die. If the number showing is even, you win $3, if the number showing is 1 you win $3 and if the number s

IceJOKER [234]

Answer:

(a)

$\left|\begin{array}{c|c|c}---&---&---\\x&\$0&\$3\\---&---&---\\P(x)&\dfrac13&\dfrac23\\---&---&---\\\end{array}\right|$

(b)$2

Step-by-step explanation:

In the given game of rolling a die. these are the possible winnings.

If the number showing is even(2, 4, or 6) or 1, you win $3.
If the number showing is either 3 or 5 you win $0.

There are 6 sides in the die.

$P($obtaining a 1,2,4 or 6)=\dfrac46=\dfrac23\\P($obtaining a 3 or 5)=\dfrac26=\dfrac13$

(i)The probability distribution of x.

Let x be the amount won

Therefore:

Probability distribution of x.

$\left|\begin{array}{c|c|c}---&---&---\\x&\$0&\$3\\---&---&---\\P(x)&\dfrac13&\dfrac23\\---&---&---\\\end{array}\right|$

(ii) Expected amount of dollar won

Expected Amount

$=\sum x_iP(x_i)\\=(0*\dfrac13)+(3*\dfrac23)\\=\$2\\$

You would expect to win $2.

7 0

3 years ago

Question 10 The hypotenuse of a right triangle is I m longer than the longer leg. The other leg is 7 m shorter than the longer l

bonufazy [111]

Answer:

5, 12, 13

Step-by-step explanation:

let x be the longer leg then x + 1 is the hypotenuse and x - 7 the shorter leg

Using Pythagoras' identity in the right triangle

x² + (x - 7)² = (x + 1)² ← expand using FOIL

x² + x² - 14x + 49 = x² + 2x + 1

2x² - 14x + 49 = x² + 2x + 1 ( subtract x² + 2x + 1 from both sides )

x² - 16x + 48 = 0 ← in standard form

(x - 4)(x - 12) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x - 12 = 0 ⇒ x = 12

x = 4 , then x - 7 = 4 - 7 = - 3 ← not possible

x = 12, then x - 7 = 12 - 7 = 5 and x + 1 = 12 + 1 = 13

The lengths of the 3 sides are

longer leg = 12 m , shorter leg = 5 m and hypotenuse = 13 m

5 0

3 years ago

there are 22 roses, 12 daisies, and 16 carnations in a bouquet. what is the ratio of roses to the total number of flowers in the

Temka [501]

Given:
Roses: 22
Daisies: 12
Carnation: 16

22 + 12 + 16 = 50 flowers in one bouquet

The ratio of the roses to the total number of flowers in the bouquet is 22/50 or simplified to 11/25

Ratio of daisies to carnations is 12:16 or 3:4.

Number of carnations to add to make the ratio into 1:3

12:x = 1:3
12*3 = x
36 = x

36 - 16 = 20 additional carnations.

There must be an additional 20 carnations to make the ratio of daisies to carnation 1:3.

12:36 = 1:3

4 0

3 years ago

During battling practice, two pop flies are hit from the same location, 2s apart the paths are modeled by the equations h equal

Oliga [24]

Answer:

Step-by-step explanation:

To find the time at which both balls are at the same height, set the equations equal to each other then solve for t.

h = -16t^2 + 56t

h = -16t^2 + 156t - 248

-16t^2 + 56t = -16t^2 + 156t - 248

You can cancel out the -16t^2's to get

56t = 156t - 248

=> 0 = 100t - 248

=> 248 = 100t

=> 2.48 = t

Using this time value, plug into either equation to find the height.

h = 16(2.48)^2 + 56(2.48)

Final answer:

h = 40.4736

3 0

3 years ago

Which of the following options represents a characteristic of an exponential equation?

Dmitry [639]

Answer: The answer is (b) A constant with an exponent on it.

Step-by-step explanation: We are to select the correct statement from the given options that represents a characteristic of an exponential function.

We know that an exponential function is a function of the form

$f(x)=b^x,$ where b ≠ 0.

Here 'b' is a constant and the variable 'x' is called an exponent. Also, if b > 0, then the function shows an exponential growth and if b < 0, then the function shows an exponential decay.

Thus, an exponential function involves a constant with an exponent on it.

Thus, (b) is the correct option.

4 0

3 years ago

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