Which mixed number correctly describes the shaded area of the fraction bars when each bar represents 1 whole?

A friend who works in a big city owns two cars, one small and one large. One-quarter of the time he drives the small car to work

lubasha [3.4K]

Answer:

The probability that he drove the small car is 0.318.

Step-by-step explanation:

We are given that a friend who works in a big city owns two cars, one small and one large. One-quarter of the time he drives the small car to work, and three-quarters of the time he takes the large car.

If he takes the small car, he usually has little trouble parking and so is at work on time with probability 0.7. If he takes the large car, he is on time to work with probability 0.5.

Let the Probability that he drives the small car = P(S) = $\frac{1}{4}$ = 0.25

Probability that he drives the large car = P(L) = $\frac{3}{4}$ = 0.75

Also, let WT = event that he is at work on time

So, Probability that he is at work on time given that he takes the small car = P(WT / S) = 0.7

Probability that he is at work on time given that he takes the large car = P(WT / L) = 0.5

Now, given that he was at work on time on a particular morning, the probability that he drove the small car is given by = P(S / WT)

We will use the concept of Bayes' Theorem for calculating above probability;

So, P(S / WT) = $\frac{P(S) \times P(WT/S)}{P(S) \times P(WT/S)+P(L) \times P(WT/L)}$

= $\frac{0.25 \times 0.7}{0.25 \times 0.7+0.75 \times 0.5}$

= $\frac{0.175}{0.55}$

= 0.318

Hence, the required probability is 0.318.

8 0

3 years ago

Write the slope-intercept form of the equation of the line described.

Genrish500 [490]

Answer:

The slope-intercept form is y = 7x + 3

Step-by-step explanation:

Remember: Perpendicular lines slope are negative reciprocals of each other.

y = -1/7x + 4.

Now you know the slope of the given line is -1/7.

So the slope of the perp line is 7/1 = 7 .

Use the given point (-1, -4) and the perp slope = 7 into y =mx + b and solve for "b".

y = mx + b

-4 = 7(-1) + b

-4 = -7 + b

-4 + 7 = b

3 = b

The slope-intercept form is y = 7x + 3

4 0

3 years ago

Evaluate each function following the specification.

telo118 [61]

Answer:

#3 a. g(-1) = 2, g(0) = 3, and g(1) = 2

b. No restrictions for all real numbers

$\#4 \ a. \ h(-1) = \dfrac{1}{3}, \ h(0) =0, \ h(2) = \infty$

b. Yes, x ≠ 2

Step-by-step explanation:

#3 The function is given as g(x) = -x² + 3

a. From the given function, by plugging in the value of 'x' in the bracket, we have;

g(-1) = -(-1)² + 3 = -1 + 3 = 2

g(-1) = 2

g(0) = -0² + 3 = 3

g(0) = 3

g(1) = -1² + 3 = -1 + 3 = 2

g(1) = 2

g(-1) = 2, g(0) = 3, and g(1) = 2

b. The given function g(x) = -x² + 3 for finding the value of g can take any value of x which is a real number

Therefore, therefore, there are no restrictions

#4 a. The given function is given as follows;

$h(x) = \dfrac{x}{x - 2}$

By substitution, we get;

$h(-1) = \dfrac{-1}{(-1) - 2} = \dfrac{-1}{-3} = \dfrac{1}{3}$

$\therefore h(-1) = \dfrac{1}{3}$

$h(0) = \dfrac{0}{0 - 2} = \dfrac{0}{-2} =0$

$\therefore h(0) =0$

$h(2) = \dfrac{2}{2 - 2} = \dfrac{2}{0} = \infty$

$\therefore h(2) = \infty$

$h(-1) = \dfrac{1}{3}, \ h(0) =0, \ h(2) = \infty$

b. From the values of the function, we have that h(x) is not defined at x = 2

Therefore, there is a restriction for x in the function, which is x ≠ 2

3 0

3 years ago

Given line y-1/6x+9,find a perpendicular line to the given line passes through points (6,-3)?

DerKrebs [107]

Answer:

y + 3 = (6)(x - 6)

Step-by-step explanation:

The proper format for this equation y-1/6x+9 is y = (-1/6)x+9.

Any line perpendicular to y = (-1/6)x+9 has the slope which is the negative reciprocal of that of y = (-1/6)x+9, or the negative reciprocal of -1/6. That is +6.

Thus, the desired line, which passes through (6, -3), is found using the point-slope formula for the equation of a straight line:

y + 3 = (6)(x - 6)

7 0

3 years ago

ANOTHER 20 POINTS

Mnenie [13.5K]

Answer:

$960

Step-by-step explanation:

1/5= .2

1-0.2= 0.8

1200×0.8= 960

7 0

3 years ago

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