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The table shows the number of badges earned, based on the number of boxes of cards sold. What does b(20) = 3 mean in terms of the problem

Answers

Answer 1

Answer:

Answer:

Someone who sells 20 boxes of cards earn 3 badges.

Step-by-step explanation:

Answer 2

Answer:

Answer:

b(20) = 3 means that for 20 boxes of cards sold, 3 badges were earned.

Step-by-step explanation:

The number of badges earned based on the number of boxes of cards sold means that badges earned are a function of the number of boxes of cards sold.

b(20) means the number of badges earned for selling 20 boxes of cards.

b(20) = 3 means that for 20 boxes of cards sold, 3 badges were earned.

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if equal amounts of a 50% alcohol solution and a 20% alcohom somution are mixed, what percentage of the mixture is alcohol

Answers

Answer: 60%

Is NOT RIGHT

Step-by-step explanation:

I don’t know

Final answer:

To calculate the percentage of alcohol in the mixture, multiply the percentage alcohol by the volume of each solution, add the alcohol content of both solutions, and divide by the total volume of the mixture.

Explanation:

When equal amounts of a 50% alcohol solution and a 20% alcohol solution are mixed, the resulting percentage of alcohol in the mixture can be calculated using the following steps:

Calculate the alcohol content of each solution by multiplying the percentage alcohol by the volume in liters. The 50% alcohol solution has a content of 0.5 x volume, and the 20% alcohol solution has a content of 0.2 x volume.
Add the alcohol content of both solutions together to get the total amount of alcohol in the mixture.
Divide the total amount of alcohol by the total volume of the mixture to get the percentage of alcohol in the mixture.

For example, if we mix 1 liter of the 50% solution with 1 liter of the 20% solution, we would have a total volume of 2 liters. The alcohol content of the 50% solution would be 0.5 x 1 liter = 0.5 liters, and the alcohol content of the 20% solution would be 0.2 x 1 liter = 0.2 liters. Adding these together, we have a total alcohol content of 0.5 + 0.2 = 0.7 liters. Dividing this by the total volume of 2 liters gives us a percentage of 0.7/2 = 0.35, or 35% alcohol in the mixture.

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A three-digit number has two properties. The tens-digit and the ones-digit add up to 5. If the number is written with the digits in the reverse order, and then subtracted from the original number, the result is 792. Use a system of equations to nd all of the three-digit numbers with these properties

Answers

Answer:

The three-digit numbers with these properties are 850 or 941.

Step-by-step explanation:

Let x be the hundreds digit, y the tens digit, and z the ones digit. The first condition says that $y+z=5$ . The second condition is:

the original number is $(100x+10y+z)$ while the reversed number is $(100z+10y+x)$ so

$(100x+10y+z)-(100z+10y+x)=792\n99x-99z=792$

Now we have the system

$y+z=5\n 99x-99z=792$

You can divide by 99 to simplify the second equation.

$y+z=5\n x-z=8$

Note that x, y, z must be digits between 0 and 9 and $x\neq 0$ . If $z>1$ , then the second equation forces $x>9$ , for example z=2 so x-2=8, x=10 which is impossible. If z=0, you get x=8, y=5 and the number is 850. If z=1, you get x=9,y=4 and the number is 941.

Find the length of side
x in simplest radical form with a rational denominator.

Answers

The length of sides x in the simplest radical form is 2√2

Properties of a right angled triangle:

One of the angle is equals to 90 degree.
The sides can be found using Pythagoras theorem
Trigonometric ratios can be used to find the angles.

Let's find x using trigonometric ratios

sin ∅ = opposite / hypotenuse

Therefore,

sin 30° = √2 / x

x sin 30° = √2

x = √2 / sin 30°

x = $(√(2) )/((1)/(2) )$

x = $√(2)$ × 2

x = 2√2

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In a right triangle, Angle A and B are acute. If tan B= 2, what is cos B? Round to three decimal places.Show work plzzz!!!

Answers

The value of cosB ≅ 0.447 to three decimal places.

Since angle A and angle B are acute and tanB = 2, we find cosB from the trigonometric identity

tan²B + 1 = sec²B

Find SecB

So, substituting the value of tanB into the equation, we have

tan²B + 1 = sec²B

2² + 1 = sec²B

4 + 1 = sec²B

5 = sec²B

Taking square root of both sides, we have

√sec²B = ±√5

secB = ±√5

Find CosB

Since secB = 1/cosB, we have that

1/cosB = ±√5

⇒cosB = ±1/√5

Since B is acute, cosB will be positive.

So, cosB = 1/√5

cosB = 1/2.2361

cosB = 0.4472

cosB ≅ 0.447 to three decimal places.

So, the value of cosB ≅ 0.447 to three decimal places.

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A vehicle designed to operate on a drag strip accelerates from zero to 30m/s while undergoing a straight line path displacement of 45m. What is the vehicle's acceleration if its value may b assumed to be constant? A.2.0m/s
B.5.0m/s
C.10m/s
D.15m/s

Answers

The vehicle's acceleration if its value may b assumed to be constant is 10 m/s. Therefore, option C is the correct answer.

Given that, a vehicle designed to operate on a drag strip accelerates from zero to 30m/s while undergoing a straight line path displacement of 45m.

What is an acceleration?

Acceleration is the name we give to any process where the velocity changes. Since velocity is a speed and a direction, there are only two ways for you to accelerate: change your speed or change your direction-or change both.

Here, Δx = 45 m, v₀ = 0 m/s and v = 30 m/s

Using the formula v² = v₀² + 2aΔx

(30 m/s)² = (0 m/s)² + 2b (45 m)

b = 10 m/s

The vehicle's acceleration if its value may b assumed to be constant is 10 m/s. Therefore, option C is the correct answer.

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Answer:

C. 10 m/s²

Step-by-step explanation:

Given:

Δx = 45 m

v₀ = 0 m/s

v = 30 m/s

Find: a

v² = v₀² + 2aΔx

(30 m/s)² = (0 m/s)² + 2a (45 m)

a = 10 m/s²

Yearly travel expenses for a family of four are normally distributed with a mean expense equal to $3,000 and a standard deviation equal to $500. What is the probability of travel expenses being greater than $4,000?