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3 years ago

BRAINLIEST ASAP! PLEASE HELP ME :)

Mathematics

1 answer:

aleksandrvk [35]3 years ago

5 0

Answer:

Two

Step-by-step explanation:

The table is saying that, if Sandra swam enough races, she should expect to get 20 firsts, 12 seconds, 6 thirds, and two no placements.

Her expected value of points will be the average (mean) of all the points awarded for each race.

The average is the total number of points divided by the number of races.

$\begin{array}{cccl}\textbf{Points} & & \textbf{Total}\\\textbf{Awarded} & \textbf{Frequency} & \textbf{Points}\\3 & 20 & 60\\2 & 12 & 24\\1 & 6 & 6\\0 & 2 & 0\\\textbf{TOTAL} & \mathbf{40} & \mathbf{90}\\\end{array}$

The simulation says that, if she swam 40 races, she should expect to earn a total of 90 points.

$\text{Average} = \dfrac{\text{Total points}}{\text{Number of races }} = \dfrac{\text{90}}{\text{40}} =\textbf{2.25 points/race}$

She can't win a fraction of a point, so she can expect to win two points in her first race.

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A football is thrown from the top of the stands, 50 feet above the ground at an initial velocity of 62 ft/sec and at an angle of

Anvisha [2.4K]

a. i. The parametric equation for the horizontal movement is x = 43.84t

ii. The parametric equation for the vertical movement is y = 50 + 43.84t

b. the location of the football at its maximum height relative to the starting point is (60.1 ft, 60.1 ft)

<h2>a. Parametric equations</h2>

A parametric equation is an equation that defines a set of quantities a functions of one or more independent variables called parameters.

<h3>i. Parametric equation for the horizontal movement</h3>

The parametric equation for the horizontal movement is x = 43.84t

Since

the angle of elevation is Ф = 45° and
the initial velocity, v = 62 ft/s,

the horizontal component of the velocity is v' = vcosФ.

So, the horizontal distance the football moves in time, t is x = vcosФt

= vtcosФ

= 62tcos45°

= 62t × 0.7071

= 43.84t

So, the parametric equation for the horizontal movement is x = 43.84t

<h3>ii Parametric equation for the vertical movement</h3>

The parametric equation for the vertical movement is y = 50 + 43.84t

Also, since

the angle of elevation is Ф = 45° and
the initial velocity, v = 62 ft/s,

the vertical component of the velocity is v" = vsinФ.

Since the football is initially at a height of h = 50 feet, the vertical distance the football moves in time, t relative to the ground is y = 50 + vsinФt

= 50 + vtcosФ

= 50 + 62tsin45°

= 50 + 62t × 0.7071

= 50 + 43.84t

<h3>b. Location of football at maximum height relative to starting point</h3>

The location of the football at its maximum height relative to the starting point is (60.1 ft, 60.1 ft)

Since the football reaches maximum height at t = 1.37 s

The x coordinate of its location at maximum height is gotten by substituting t = 1.37 into x = 48.84t

So, x = 43.84t

x = 43.84 × 1.37

x = 60.0608

x ≅ 60.1 ft