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3 years ago

Which pitcher had speeds that were the most consistent?

Mathematics

2 answers:

Ann [662]3 years ago

7 1

Answer:

Step-by-step explanation:

guajiro [1.7K]3 years ago

8 0

Answer:

C)Pitcher 1, because he has the lesser amount of variability in his pitches.

Step-by-step explanation:

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Help please

rusak2 [61]

Answer:

See below

Step-by-step explanation:

f(x) is quadratic function and g(x) is linear (since AP in the right column).

Find the equation of the function f(x), use the points on the graph:

f(x) = ax² + bx + c

c = 5 as the y-intercept is (0, 5)
a(-1)² + b(-1) + 5 = 0 ⇒ a + 5 = b
a(5²) + b(5) + 5 = 0 ⇒ 25a + 5b + 5 = 0 ⇒ 25a + 5a + 25 + 5= 0 ⇒ a = -1 ⇒ b= 4

The function is:

f(x) = -x² + 4x + 5

Find the equation of g(x)

Find the slope of g(x):

m = (1 - 7)/(-1 + 4) = -2

Use (-4, 7) to find its equation:

y - 7 = -2(x + 4)
y = -2x + 7 - 8
y = -2x - 1

<h3>See the required comparison below</h3>

The y-intercepts:

f(x) ⇒ 5,
g(x) ⇒ -1
-5 < - 1

Values at x = 3:

f(3) = -3² + 4(3) + 5 = 8
g(3) = -2(3) - 1 = - 7
8 > 7

Average rate of change in the interval [2,5]:

f(x) ⇒ (0 - 9)/(5 - 2) = -3
g(x) ⇒ (-11 + 5)/ (5 - 2) = -2
-3 < -2

Max of function in the interval [-5, 5];

f(x) ⇒ 9, vertex of the function
g(x) ⇒ g(-5) = -2(-5) - 1 = 9, taken the least point of x as it is a decreasing function
9 = 9

4 0

3 years ago

Read 2 more answers

The number of hours spent per week on household chores by all adults has a mean of 28 hours and a standard deviation of 7 hours.

Alchen [17]

Answer:

Probability that the mean hours spent per week on household chores by a sample of 49 adults will be more than 26.75 is 0.89435.

Step-by-step explanation:

We are given that the number of hours spent per week on household chores by all adults has a mean of 28 hours and a standard deviation of 7 hours.

Also, sample of 49 adults is given.

Let X = number of hours spent per week on household chores

So, assuming data follows normal distribution; X ~ N( $\mu=28,\sigma^{2}=7^{2}$ )

The z score probability distribution for sample mean is given by;

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

where, $\mu$ = mean hours = 28

$\sigma$ = standard deviation = 7 hours

n = sample of adults = 49

Let $\bar X$ = sample mean hours spent per week on household chores

So, probability that the mean hours spent per week on household chores by a sample of 49 adults will be more than 26.75 is given by =P( $\bar X$ > 26.75 hours)

P( $\bar X$ > 26.75 hours) = P( $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{26.75-28}{\frac{7}{\sqrt{49} } }$ ) = P(Z > -1.25) = P(Z < 1.25)