What percent of 18 is 36

If the function d(x) = 1375 − 110x represents the distance (in miles) a high-speed  train is from its destination after x hours:

a) The train is 495 miles from its destination after 8 hours

b) It will take the train 12.5 hours to travel before reaching its destination

The given function is:

d(x)  =  1375  -  110x

Where d(x) is the distance (in miles) a high-speed  train is from its destination after x hours.

a) How far is the train from its destination after 8 hours?

To find how far the train is from its destination after 8 hours, substitute x = 8 into d(x)  =  1375  -  110x

d(8)  =  1375  -  110(8)

d(8)  =  1375  -  880

d(8)  =  495

The train is 495 miles from its destination after 8 hours

b) How long does the train travel before reaching its destination?

Note that:

d(x)  =  1375  -  110x

From the equation above, the speed at which the train is traveling is 110 miles/hr

The distance of the destination = 1375

The time it will take to reach the destination will be calculated as:

Time = Distance / speed

Time = 1375 / 110

Time = 12.5

It will take the train 12.5 hours to travel before reaching its destination

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Priscilla and Herb can address 10,000 envelopes together in approximately 44.44 hours, when we combine their individual work rates of 100 and 125 envelopes per hour respectively.

Priscilla and Herb are addressing envelopes for a firm, and we need to determine how long it would take them to address 10,000 envelopes if they work together. Priscilla can address 10,000 envelopes in 100 hours, and Herb can do the same in 80 hours.

To solve this, we can calculate each person's work rate and then combine these work rates to get the rate at which they complete the task together.

First, we calculate their work rates:

Working together, their combined rate would be:

Combined rate = Priscilla's rate + Herb's rate

Combined rate = 100 envelopes/hour + 125 envelopes/hour

Combined rate = 225 envelopes per hour

To address 10,000 envelopes at this combined rate, we can divide the total number of envelopes by their combined rate:

Time to address 10,000 envelopes together = 10,000 envelopes / 225 envelopes/hour

Time to address 10,000 envelopes together = approximately 44.44 hours

divide 52.5o by 7

52.50 / 7 = 7.50 per hour

Final answer:

The probability of rolling a 12 with two six-sided dice is 1/36, since there is only one combination (6+6) that yields a sum of 12 out of 36 possible outcomes.

Explanation:

The question requires calculating the probability of getting a specific sum when rolling a pair of six-sided dice, which is a common problem in probability theory. To find the probability of getting a sum of 12, we first need to understand that each die has 6 faces, and therefore, there are a total of 6 x 6 = 36 possible outcomes when rolling two dice.

Now, only one combination yields a sum of 12: when both dice show a six (6 + 6). Therefore, there is only one favorable outcome that gives the sum of 12. The probability of this outcome is then 1 (favorable outcome) divided by 36 (total possible outcomes), which gives us a probability of 1/36.

To put it mathematically, we apply the fundamental principle of probability which states that the probability of an event is equal to the number of ways the event can happen divided by the total number of possible outcomes. Hence:

Probability of rolling a sum of 12 = Number of ways to get a sum of 12 / Total number of possible outcomes = 1/36.

Final answer:

Each student gets 1/4 of a pizza when 12 students share 3 pizzas equally. This is because 3 pizzas divided by 12 students results in each student receiving 1/4 of a pizza.

Explanation:

To determine the fraction of the pizza each student gets when 12 students share 3 pizzas equally, you'd divide the total number of pizzas by the number of students. Here's the step-by-step breakdown:

Understanding fractions can be similar to figuring out slices of pie or the number of quarters in a dollar.

y/9 +5 =0

 subtract 5 from each side

y/9 = -5

 multiply both sides by 9

y = -5 * 9

y = -45

Answer: s=-1

Explanation:

We can re-write the equation as follows:

[tex]\frac{1}{64}=(4^{2s-1})(16^{2s+2})[/tex]

Let's rewrite the terms on the left and on the right as follows:

[tex]2^{-6} = ((2^2)^{2s-1})((2^4)^{2s+2})[/tex]

So we have

[tex]2^{-6} = (2^{2(2s-1)})(2^{4(2s+2)})[/tex]

Now we can use the following rule:

[tex]x^{a+b}=x^a x^b[/tex]

to rewrite the term on the right:

[tex](2^{2(2s-1)})(2^{4(2s+2)})=2^{2(2s-1)+4(2s+2)}[/tex]

So now we have

[tex]2^{-6}=2^{2(2s-1)+4(2s+2)}[/tex]

and since the bases are the same, we can just equalize the exponents:

[tex]-6=2(2s-1)+4(2s+2)[/tex]

[tex]-6=4s-2+8s+8\\-12 = 12 s\\s=-1[/tex]

The equation of the circle passing through the point (−5, −2) and center at (−2, 3) is  [tex]\bold{( x +2 )^2 + ( y - 3 )^2 = 34}[/tex]

The general equation of the circle whose center at (h, k) and radius r is,

[tex]( x - h )^2 + ( y - k )^2 = r^2[/tex]

For given example,

the circle passing through the point (−5, −2) whose center is at (−2, 3).

The radius of the circle is the distance between point (-5, -2) and the center (-2, 3).

Using distance formula the radius of a circle would be,

⇒ [tex]r=\sqrt{(-2-3)^2 + (-5-(-2))^2}[/tex]

⇒ [tex]r=\sqrt{(-5)^2+(-3)^2}[/tex]

⇒ [tex]r=\sqrt{25+9}[/tex]

⇒ [tex]r=\sqrt{34}[/tex] units

Let center (h, k) = (-2, 3)

Using the general form of the circle,

⇒ [tex]( x - h )^2 + ( y - k )^2 = r^2[/tex]

⇒ [tex]( x - (-2) )^2 + ( y - 3 )^2 = (\sqrt{34})^2[/tex]

⇒ [tex]( x +2 )^2 + ( y - 3 )^2 = 34[/tex]

Therefore, the equation of the circle passing through the point (−5, −2) whose center is at (−2,3) would be [tex]\bold{( x +2 )^2 + ( y - 3 )^2 = 34}[/tex]

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Answer:

the answer is t = 20.625

Step-by-step explanation:

To begin, you would need to find the displacement of the first car and the equation to find that is d = 1/2at^2. So you would plug in what you have from the problem into the equation: d = (1/2)3(6)^2 and d is equal to 54 m. THIS IS YOUR DISPLACEMENT FOR THE FIRST CAR.

Next, you need to find the velocity of the car and the equation would be v = at. Plug in what you know from the problem: v = 3(6) which is 18. THIS IS YOUR INITIAL VELOCITY.

Next, we need to find out the distance of the 2nd car and we would use d = 1/2at^2. Plug in what you now from the problem: d = (1/2)5t^2 which would be d = 2.5t^2.

Next, you would equal these two equations together: 2.5t^2 = 1.5t^2 + 18t +54.  All these values are from when we solved them from above, and once you solve it you will get 20.625. (SOLVE FOR T)

Answer:

False; True; True.

Step-by-step explanation:

In this situation, the y-intercept would represent the amount of money in her account at x=0 weeks, or the beginning of the year.  This is not the x-intercept, so the first statement is false.

The slope is the rate of change.  This would describe how her account changes every week, so this represents the amount of money she deposits into her account each week.  This means the second statement is true.

The line goes through the point (4, 0).  Since x is the number of weeks, this would represent the amount in her account after 4 weeks.  Since the y-value is 0, this means she no longer has an overdraft balance after 4 weeks.  This means the second statement is true.

Following are the response to the given points:

Therefore, the final answer is "false, true, and true".

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The complete list of possible pairs of rodents from the choices woodchuck, prairie dog, beaver, and chipmunk includes six combinations, showcasing an application of combinatorics in mathematics to determine all possible selections.

The question involves determining the complete list of possible pairs of rodents that radio listeners could choose from four options: woodchuck, prairie dog, beaver, and chipmunk. This is a matter of combinatorics, a branch of mathematics focused on counting, arrangement, and combination of sets of elements. Since each listener picks two favorites and the order in which they pick them does not matter (choosing a beaver and a woodchuck is the same as choosing a woodchuck and a beaver), we use combinations to find the total number of possible pairs.

Mathematically, the number of ways to choose 2 favorites out of 4 is given by the combination formula C(n, r) = n! / r!(n-r)!, where n is the total number of options and r is the number being chosen. Here, n=4 and r=2, resulting in C(4, 2) = 4! / 2!(4-2)! = 6, which matches our list of 6 possible pairs.

It's important to understand and apply various mathematical concepts taught in high school, including basic algebra, arithmetic, and vector representation. Success also often comes from group work and discussions, which can provide new perspectives.

In mathematics, figuring for yourself and collaborative group activities are essential aspects of learning. When we talk about basic algebra and arithmetic, it means we are dealing with mathematical operations such as addition, subtraction, multiplication, division, and solving equations. The principles given in a chapter can be applied to various questions. For instance, if you understand the concept of 'solving for x', you can apply it in different scenarios and questions.

Similarly, when vectors are represented with an arrow above them, this is one of the common notations in mathematics, specifically in vector algebra. It is also important to note that working in groups and participating in discussions can bring another perspective and help understand the subject better.

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