3/4x + 1/2 = 2/3x + 2

I need the answer please work out this tough question for me

Crank

Answer:

56

Step-by-step explanation:

Let N be the total number of spins.

Probability of A on Red and B on Red = 0.5 x 0 .6 = 0.3 (top branch of tree)

Therefore with N spins, the estimated number of times spinner A and spinner B land on red is 0.3N and we are given this as 84

So 0.3N = 84
N = 84/0/3 = 280

The probability of spinner A on blue and spinner B on blue is 0.5 x 0.4 = 0.2 (lowest branch of tree)

For 280 spins, the estimated number of times that both spinners land on blue is given by 0.2 x 280 = 56

3 0

3 years ago

The U.S. Bureau of Economic Statistics reports that the average annual salary in the metropolitan Boston area is $50,542. Suppos

xenn [34]

Answer:

(a) P(X > $57,000) = 0.0643

(b) P(X < $46,000) = 0.1423

(c) P(X > $40,000) = 0.0066

(d) P($45,000 < X < $54,000) = 0.6959

Step-by-step explanation:

We are given that U.S. Bureau of Economic Statistics reports that the average annual salary in the metropolitan Boston area is $50,542.

Suppose annual salaries in the metropolitan Boston area are normally distributed with a standard deviation of $4,246.

Let X = annual salaries in the metropolitan Boston area

SO, X ~ Normal( $\mu=$50,542,\sigma^{2} = $4,246^{2}$ )

The z-score probability distribution for normal distribution is given by;

Z = $\frac{X-\mu}{\sigma }$ ~ N(0,1)

where, $\mu$ = average annual salary in the Boston area = $50,542

$\sigma$ = standard deviation = $4,246

(a) Probability that the worker’s annual salary is more than $57,000 is given by = P(X > $57,000)

P(X > $57,000) = P( $\frac{X-\mu}{\sigma }$ > $\frac{57,000-50,542}{4,246 }$ ) = P(Z > 1.52) = 1 - P(Z $\leq$ 1.52)

= 1 - 0.93574 = 0.0643

The above probability is calculated by looking at the value of x = 1.52 in the z table which gave an area of 0.93574.

(b) Probability that the worker’s annual salary is less than $46,000 is given by = P(X < $46,000)

P(X < $46,000) = P( $\frac{X-\mu}{\sigma }$ < $\frac{46,000-50,542}{4,246 }$ ) = P(Z < -1.07) = 1 - P(Z $\leq$ 1.07)

= 1 - 0.85769 = 0.1423

The above probability is calculated by looking at the value of x = 1.07 in the z table which gave an area of 0.85769.

(c) Probability that the worker’s annual salary is more than $40,000 is given by = P(X > $40,000)

P(X > $40,000) = P( $\frac{X-\mu}{\sigma }$ > $\frac{40,000-50,542}{4,246 }$ ) = P(Z > -2.48) = P(Z < 2.48)

= 1 - 0.99343 = 0.0066

The above probability is calculated by looking at the value of x = 2.48 in the z table which gave an area of 0.99343.

(d) Probability that the worker’s annual salary is between $45,000 and $54,000 is given by = P($45,000 < X < $54,000)

P($45,000 < X < $54,000) = P(X < $54,000) - P(X $\leq$ $45,000)

P(X < $54,000) = P( $\frac{X-\mu}{\sigma }$ < $\frac{54,000-50,542}{4,246 }$ ) = P(Z < 0.81) = 0.79103

P(X $\leq$ $45,000) = P( $\frac{X-\mu}{\sigma }$ $\leq$ $\frac{45,000-50,542}{4,246 }$ ) = P(Z $\leq$ -1.31) = 1 - P(Z < 1.31)

= 1 - 0.90490 = 0.0951

The above probability is calculated by looking at the value of x = 0.81 and x = 1.31 in the z table which gave an area of 0.79103 and 0.9049 respectively.

Therefore, P($45,000 < X < $54,000) = 0.79103 - 0.0951 = 0.6959

3 0

3 years ago

Write the equation in standard form for the circle with radius 9 centered at the origin.

amid [387]

The standard form of the equation of a circle of radius r, with (assuming centre h, k) is given as:

(X-h)^2 + (y-k)^2 = r^2

As we are required to write an equation in standard form for the circle with radius 9 centred at the origin.
Centre(h,k)=(0,0), r=9

Substituting these values into the standard form of the equation of a circle given above:

(X-0)^2 + (y-0)^2 = 9^2
X^2 + y^2 =81

The standard form is x^2 + y^2 =81

I’m pretty sure this is right

8 0

3 years ago

If f(x)=x-1/3 and g(x)=3x+1, what is (f o g)(x)?

BlackZzzverrR [31]

Answer:

$3x+\frac{2}{3}$