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enyata [817]
3 years ago
10

Please help me answer this geometry question!

Mathematics
1 answer:
mihalych1998 [28]3 years ago
6 0
It either equals 12 OR 21... the problem isn't entirely clear...
so it IS
12 < x < 21
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The amount of time it takes Isabella to wait for the bus is continuous and uniformly distributed between 3 minutes and 17 minute
Arturiano [62]

Answer:

P(X>5) = 0.857

Step-by-step explanation:

Let X \sim uniform(3.17)

f(x) = \dfrac{1}{17-3}   ; \ \ \ 3 \le x \le 17

The required probability that it will take Isabella more than 5 minutes to wait for the bus can be computed as:

P(X > 5) =  \int ^{17}_{5} f(x) \ dx

P(X > 5) =  \int ^{17}_{5} \dfrac{1}{17-3} \ dx

P(X > 5) =\dfrac{1}{14}  \Big [x \Big ] ^{17}_{5}

P(X > 5) =\dfrac{1}{14} [17-5]

P(X > 5) =\dfrac{12}{14}

P(X>5) = 0.857

6 0
3 years ago
SOMEONE PLZ HELP ME!!!! I WILL GIVE BRAINLIEST!!!
MAXImum [283]

Answer:

Step-by-step explanation:

Let the quadratic equation of the function by the points in the given equation is,

f(x) = ax² + bx + c

If the points lying on the graph are (-3, -10), (-4, -8) and (0, 8),

For (0, 8),

f(0) = a(0)² + b(0) + c

8 = c

For a point (-3, -10),

f(-3) = a(-3)² + b(-3) + 8

-10 = 9a - 3b + 8

9a - 3b = -18

3a - b = -6 --------(1)

For (-4, -8),

f(-4) = a(-4)² + b(-4) + 8

-8 = 16a - 4b + 8

-16 = 16a - 4b

4a - b = -4 ------(2)

Subtract equation (1) from equation (2)

(4a - b) - (3a - b) = -4 + 6

a = 2

From equation (1),

6 - b = -6

b = 12

Function will be,

f(x) = 2x² + 12x + 8

     = 2(x² + 6x) + 8

     = 2(x² + 6x + 9 - 9) + 8

     = 2(x² + 6x + 9) - 18 + 8

     = 2(x + 3)² - 10

By comparing this function with the vertex form of the function,

y = a(x - h)² + k

where (h, k) is the vertex.

Vertex of the function 'f' will be (-3, -10)

And axis of symmetry will be,

x = -3

From the given graph, axis of the symmetry of the function 'g' is; x = -3

Therefore, both the functions will have the same axis of symmetry.

y-intercept of the function 'f' → y = 8 Or (0, 8)

y-intercept of the function 'g' → y = -2 Or (0, -2)

Therefore, y-intercept of 'f' is greater than 'g'

Average rate of change of function 'f' = \frac{f(b)-f(a)}{b-a} in the interval [a, b]

                                                               = \frac{f(-3)-f(-6)}{-3+6}

                                                               = \frac{-10-8}{3}

                                                               = -6

Average rate of change of function 'g' = \frac{g(b)-g(a)}{b-a}

                                                                = \frac{g(-3)-g(-6)}{-3+6}

                                                                = \frac{7+2}{-3+6}

                                                                = 3

Therefore, Average rate of change of function 'f' is less than 'g'.

6 0
3 years ago
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