What is the domain of the function y=3\sqrt(6x+42)

Answer: 6 m

This statement:

"Jared has run two-thirds of an 18-kilometer race" can be written as an equation:

[tex]18km.\frac{2}{3}=12km[/tex]

This means two-thirds of 18 km is equivalent to 12 km

If we substract this value to the total, we have the values of the kilometers left to run:

[tex]18km-12km=6km[/tex]

Therefore the correct option is D

The probability of selecting a male calculus student is approximately 57.14%, a female calculus student is approximately 42.86%, a business major calculus student is approximately 28.57%, a biology major calculus student is approximately 21.43%, a computer science major calculus student is approximately 10.71%, and a mathematics major calculus student is approximately 3.57%.

To find the probabilities, we will use the formula:

Probability of an event = (Number of favorable outcomes) / (Total number of possible outcomes)

Probability of selecting a male calculus student:

There are 80 male students in calculus, so the probability of choosing a male student is:

Probability (Male) = 80 / (80 + 60) = 80 / 140 ≈ 0.5714 or 57.14%

Probability of selecting a female calculus student:

There are 60 female students in calculus, so the probability of choosing a female student is:

Probability (Female) = 60 / (80 + 60) = 60 / 140 ≈ 0.4286 or 42.86%

Probability of selecting a business major calculus student:

There are 40 business majors in calculus, so the probability of choosing a business major student is:

Probability (Business Major) = 40 / 140 ≈ 0.2857 or 28.57%

Probability of selecting a biology major calculus student:

There are 30 biology majors in calculus, so the probability of choosing a biology major student is:

Probability (Biology Major) = 30 / 140 ≈ 0.2143 or 21.43%

Probability of selecting a computer science major calculus student:

There are 15 computer science majors in calculus, so the probability of choosing a computer science major student is:

Probability (Computer Science Major) = 15 / 140 ≈ 0.1071 or 10.71%

Probability of selecting a mathematics major calculus student:

There are 5 mathematics majors in calculus, so the probability of choosing a mathematics major student is:

Probability (Mathematics Major) = 5 / 140 ≈ 0.0357 or 3.57%

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Answer:

7.31 times.

Step-by-step explanation:

We have been given that Grand Canyon is approximately 29 kilometers long. Mariner Valley is a canyon on Mars that is approximately 212 kilometers long.

To find the number of times Mariner Valley is longer than the Grand Canyon, we will divide 212 by 29.

[tex]\frac{212}{29}=7.3103448\approx 7.31[/tex]

Therefore, the Mariner Valley is 7.31 times longer than the Grand Canyon.

Answer:

B. More members prefer a beach vacation and a ski vacation than a cruise vacation.

Roger does 600 joules of work on the box when he applies a force of 60 newtons and displaces the box 10 meters along a 30° incline.

When Roger pushes a box on a 30° incline with a force of 60 newtons and displaces the box 10 meters along the incline, the work done on the box can be calculated.

Work is given by the equation W = F  imes d imes cos(heta), where W is the work, F is the force applied, d is the displacement, and heta is the angle between the force and the direction of displacement. In this case, because the force is applied parallel to the incline and displacement is along the incline, the angle heta is 0°, making cos( heta) equal to 1.

To find the work done by Roger, we calculate it as:
W = 60 N imes 10 m imes cos(0°)
W = 60 N imes 10 m imes 1
W = 600 joules.

Hence, Roger will do 600 joules of work on the box.

Final answer:

To calculate the amount due at the end of 5 years with continuous compound interest, use the formula A = P*e^(rt), where A is the amount due, P is the principal, e is Euler's number, r is the interest rate, and t is the time. In this case, the amount due is approximately $10,021.66.

Explanation:

To calculate the amount due at the end of 5 years with continuous compound interest, we can use the formula A = P*e^(rt), where A is the amount due, P is the principal (initial amount borrowed), e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years.

In this case, the principal is $5,500, the interest rate is 12% or 0.12, and the time is 5 years.

So, A = $5,500 * e^(0.12 * 5) = $5,500 * e^0.6 ≈ $5,500 * 1.82212 ≈ $10,021.66.

Therefore, the amount due at the end of 5 years with continuous compound interest is approximately $10,021.66.

The number of gallons of gasoline in the tank before Javier added some is 2 3/4 gallons.

1. Subtract 10.3 gallons (the amount he added) from 12 3/4 gallons (the total capacity of the tank).

2. Calculate 12 3/4 - 10.3 to find the remaining amount of gasoline in the tank.

To subtract mixed numbers, we first convert them into improper fractions:

[tex]\[ 12 \frac{3}{4} - 10 \frac{3}{10} \][/tex]

[tex]\[ = \frac{(12 \times 4) + 3}{4} - \frac{(10 \times 10) + 3}{10} \][/tex]

[tex]\[ = \frac{48 + 3}{4} - \frac{100 + 3}{10} \][/tex]

[tex]\[ = \frac{51}{4} - \frac{103}{10} \][/tex]

To subtract fractions, we need a common denominator. Here, the least common denominator (LCD) is 20.

[tex]\[ = \frac{51 \times 5}{4 \times 5} - \frac{103 \times 2}{10 \times 2} \][/tex]

[tex]\[ = \frac{255}{20} - \frac{206}{20} \][/tex]

[tex]\[ = \frac{255 - 206}{20} \][/tex]

[tex]\[ = \frac{49}{20} \][/tex]

Now, we convert the improper fraction back to a mixed number:

[tex]\[ = 2 \frac{9}{20} \][/tex]

Therefore, Javier had 2 9/20 gallons of gasoline in the tank before adding more.

Javier had 2.45 gallons of gasoline in his tank before he added 10.3 gallons to fill it to its full capacity of 12.75 gallons.

To find how many gallons of gasoline were in Javier's tank before he added some, we need to subtract the amount he added from the total capacity of the tank. Javier's fuel tank can hold 12 3/4 gallons when full, which is equal to 12.75 gallons. He added 10.3 gallons to fill it up. Therefore, the amount of gas in the tank before he added more can be calculated as follows:

Amount of gasoline initially in the tank = Total capacity - Amount added

Amount of gasoline initially in the tank = 12.75 gallons - 10.3 gallons

Amount of gasoline initially in the tank = 2.45 gallons

Thus, Javier had 2.45 gallons of gasoline in the tank before he added the 10.3 gallons.

We know that the probability of a certain hockey player making a goal after hitting a slap shot is [tex]\frac{1}{5}[/tex].

We need to figure out the number of successful slap shots if she makes 120 attempts?

Since the player is able to make a goal once out of 5 attempts. Therefore, in order to find the number of goals that we can expect the player to make successfully if she attempts 120 slap shots we will multiply the probability with 120.

Number of successful goals = (Probability of making one goal)x(Number of attempts)

Number of successful goals = [tex]\frac{1}{5}\times 120 = 24[/tex].

Therefore, player will be able to make 24 goals out of 120 attempts.

Answer:

80%

Step-by-step explanation:

To convert a fraction to percent, we need to multiply the fraction with 100.

Multiply 100 and [tex]\frac{4}{5}[/tex], we get,

[tex]\frac{4}{5} (100)[/tex] = 4 × 20

= 80%

Hence, the correct option is (C) 80%.

The decimal equivalent of the fraction 5/33 is option A. o.15....

Fractions are type of numbers which are written in the form p/q, which implies that p parts in a whole of q.

Here p, called the numerator and q, called the denominator, are real numbers.

The given fraction is 5/33.

We have to find the decimal corresponding to the given fraction.

For that divide 5 by 33.

5 is not divisible by 33.

So add 0 and it become 50.

50 = (33 × 1) + 17

And the quotient is 0.1 with remainder 17.

Now 17 is not divisible by 33.

Add 0 and it becomes 170.

170 = (33 × 5) + 5

Quotient becomes 0.15 with remainder 5.

Again the remainder is 5 and add 0 and becomes 50.

It continues.

So the quotient is 0.1515....

Hence the decimal form is 0.(15) repeating.

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In an hour, the minute hand, which is 1.5 units long, travels a full revolution or approximately 9.4 units, while the hour hand, 1 unit long, covers one-twelfth, or about 0.5 units. Therefore, the minute hand travels approximately 7.9 units more than the hour hand.

This question can be solved by first examining the distance each hand travels. In an hour, the minute hand completes a full revolution around the clock face, moving a distance equal to the clock's circumference. If we call the length of the minute hand 1.5 units, then its distance traveled is 2π(1.5).

In contrast, the hour hand moves onto the next hour, covering on-twelfth of the clock's face, or 2π(1/12) using a length of 1 unit for the hour hand. Substract the second measure from the first to find the difference. Thus, the minute hand travels about 7.9 units farther than the hour hand.

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