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igor_vitrenko [27]

3 years ago

5

A football player starts on the 20 yard line and gains 9 yards. On the next play, he loses 4 yards. The referee says there’s a p

enalty and takes away the 4-yard loss of yardage. Which expression represents the total number of yards gained?
a) 20 + 9 – 4 – (−4)
b)20 + 9 – 4 + (−4)
c) 20 + 9 – 4 – 4
d)20 + 9 + 4 – (−4)

2 answers:

satela [25.4K]3 years ago

7 0

I think the answer is 20+9-4-4

zavuch27 [327]3 years ago

4 0

C) 20+9-4-4
Hope this Helps!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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A stereo store is offering a special price on a complete set of components (receiver, compact disc player, speakers, turntable).

Juli2301 [7.4K]

Answer:

a) 240 ways

b) 12 ways

c) 108 ways

d) 132 ways

e) i) 0.55

ii) 0.4125

Step-by-step explanation:

Given the components:

Receiver, compound disk player, speakers, turntable.

Then a purcahser is offered a choice of manufacturer for each component:

Receiver: Kenwood, Onkyo, Pioneer, Sony, Sherwood => 5 offers

Compact disc player: Onkyo, Pioneer, Sony, Technics => 4 offers

Speakers: Boston, Infinity, Polk => 3 offers

Turntable: Onkyo, Sony, Teac, Technics => 4 offers

a) The number of ways one component of each type can be selected =

$\left(\begin{array}{ccc}5\\1\end{array}\right) \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}4\\1\end{array}\right)$

$= 5 * 4 * 3 * 4 = 240 ways$

b) If both the receiver and compact disk are to be sony.

In the receiver, the purchaser was offered 1 Sony, also in the CD(compact disk) player the purchaser was offered 1 Sony.

Thus, the number of ways components can be selected if both receiver and player are to be Sony is:

$\left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}4\\1\end{array}\right)$

$= 1 * 1 * 3 * 4 = 12 ways$

c) If none is to be Sony.

Let's exclude Sony from each component.

Receiver has 1 sony = 5 - 1 = 4

CD player has 1 Sony = 4 - 1 = 3

Speakers had 0 sony = 3 - 0 = 3

Turntable has 1 sony = 4 - 1 = 3

Therefore, the number of ways can be selected if none is to be sony:

$\left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right)$

$= 4 * 3 * 3 * 3 = 108 ways$

d) If at least one sony is to be included.

Number of ways can a selection be made if at least one Sony component is to be included =

Total possible selections - possible selections without Sony

= 240 - 108

= 132 ways

e) If someone flips switches on the selection in a completely random fashion.

i) Probability of selecting at least one Sony component=

Possible selections with at least one sony / Total number of possible selections

$\frac{132}{240} = 0.55$

ii) Probability of selecting exactly one sony component =

Possible selections with exactly one sony / Total number of possible selections.

$\frac{\left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) + \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) + \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}1\\1\end{array}\right)}{240}$

$= \frac{(1*3*3*3)+(4*1*3*3)+(4*3*3*1)}{240}$

$\frac{27 + 36 + 36}{240} = \frac{99}{240} = 0.4125$

5 0

3 years ago

Given f (g (x)) = x + 4 and f (x) = 3x + 5, find g (x).

JulijaS [17]

Answer:

g(x) = $\frac{1}{3}(x - 1) = \frac{x}{3} - \frac{1}{3}$

Step-by-step explanation:

f(x) = 3x + 5

f[g(x)] = 3[g(x)] + 5

⇒ 3[g(x)] + 5 = x + 4

⇒ 3[g(x)] = x + 4 - 5

⇒ 3[g(x)] = x - 1

⇒ g(x) = $\frac{1}{3}(x - 1) = \frac{x}{3} - \frac{1}{3}$

5 0

3 years ago

A film student wants to capture a shot of a satellite dish placed at the top of a building. The line of sight between the ground

Vlad1618 [11]

Answer:

34.78 feet

Step-by-step explanation:

1) using the cosine function, I did cos(43)=x/51

This is because cosine is equal to adjacent over hypotnuse

Once I found x, I used the pythagorean theorem to get 34.78 feet

3 0

3 years ago

Use vieta's theorem to solve the problems.

Mnenie [13.5K]

Using Vieta's Theorem, it is found that c = 72.

<h3>What is the Vieta Theorem?</h3>

Suppose we have a quadratic equation, in the following format:

$y = ax^2 + bx + c$

The roots are p and q.

The Theorem states that:

$p + q = -\frac{b}{a}$

$pq = \frac{c}{a}$

In this problem, the polynomial is:

$x^2 - 17x + c$

Hence the coefficients are $a = 1, b = -17$ .

Since the difference of the solutions is 1, we have that:

$p - q = 1$

$p = 1 + q$

Then, from the first equation of the Theorem:

$p + q = -\frac{b}{a}$

$1 + q + q = 17$

$2q = 16$

$q = 8$

$p = 1 + q = 9$

Now, from the second equation:

$pq = \frac{c}{a}$

$72 = c$

$c = 72$

To learn more about Vieta's Theorem, you can take a look at brainly.com/question/23509978

6 0

2 years ago

Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 4 inches, and the larger gear has a ra

pychu [463]

Draw a diagram to illustrate the problem as shown below.

When the smaller gear rotates through a revolution, it sweeps an arc length of
2π(4) = 8π inches.

Part 1
The same arc length is swept by the larger gear. The central angle of the larger gear, x, is
7x = 8π
x = (8π)/7 radians = (8π)/7 * (180/π) = 205.7°

Answer: 205.7° (nearest tenth)

Part 2
When the larger gear makes one rotation, it sweeps an arc length of
2π(7) = 14π inches.
If the central angle for the smaller gear is y radians, then
4y = 14π
y = 3.5π radians = (3.5π)/2π revolutions = 1.75 revolutions

Answer:
The smaller gear makes 1.75 rotations

7 0

4 years ago