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3 years ago

A store sells two kinds of candles, scented and unscented. The scented candles burn one eighth inch

Mathematics

1 answer:

sineoko [7]3 years ago

7 0

Answer:

Scented candle, 1/2 inch per hour

Unscented 1/3 inch per hour

Step-by-step explanation:

The scented candle burns 1/8 inch in every 15 minutes. The unscented candle burns 1/9 inch in every 20 minutes.

We simply first convert the time taken in fraction to minutes for convenience using the conversion 60 minutes are in an hour.

Now let’s calculate unit rate per hour I.e every 60 minutes.

For the scented candle:

1/8 inch burns in 15 minutes

x inch will burn in 60 minutes

To get x, we cross multiply.

1/8 * 60 = 15 * x

15x = 7.5, x = 7.5/15 = 1/2 = 0.5

This means that half of the scented candle will have been burnt in 1 hour.

Now, for the unscented candle, if 1/9 inch burns in 20 minutes, x inch will burn in 60 minutes.

1/9 * 60 = 20x

180x = 60

x = 1/3 or 0.33

This means one-third will be burnt in an hour

The scented one burns more.

The unit rate is the rate of burning per hour. It is the fraction of the candles that will burn per hour. It enables us find the time it will take for either candles to burn up.

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Examine the system of equations. y = 4x + 8, y = 4x – 1 Which statements best describe the two expressions? Check all that apply

Lerok [7]

Answer:

The correct statements are as follows;

1. They have different y-intercepts

2. The substitution method results in false statement 8 = -1

3. There is no solution

Step-by-step explanation:

Here, we want to select the statement that best describes the equations

The equation for a straight line is generally;

y = mx + b

m is slope and b is the y-intercept

slope of both is same ; 4

So first assertion is wrong

they have different y-intercepts

First y-intercept is 8, second is -1

This is correct

The third statement is correct too

if we equated both y;

4x + 8 = 4x -1

We shall have 4x canceled out and left with 8 = -1

(8,-1) is not a solution

There is no solution is correct because after substituting, we have 8 = -1 which is not correct and also impossible

7 0

3 years ago

A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work pro

olchik [2.2K]

Answer:

0.756

Step-by-step explanation:

It is given that a machine has four components, A, B, C, and D.

$P(A)=P(B)=0.93, P(C)=0.95,P(D)=0.92$

If these components set up in such a manner that all four parts must work for the machine to work properly.

We need to find the probability that the machine works properly. It means we have to find the value of $P(A\cap B\cap C\cap D)$ .

If two events X and Y are independent, then

$P(X\cap Y)=P(X)\times P(Y)$

Assume the probability of one part working does not depend on the functionality of any of the other parts.

$P(A\cap B\cap C\cap D)=P(A)\times P(B)\times P(C)\times P(D)$

Substitute the given values.

$P(A\cap B\cap C\cap D)=0.93\times 0.93\times 0.95\times 0.92$

$P(A\cap B\cap C\cap D)=0.7559226$

$P(A\cap B\cap C\cap D)\approx 0.756$

Therefore, the probability that the machine works properly is 0.756.

7 0

3 years ago

If AD is the altitude of BC, what is the slope of AD?

koban [17]

Answer:

Step-by-step explanation:

First, find the slope of BC :

⇒ m (BC) = -1 - 5 / -3 - 5

⇒ m (BC) = -6/-8

⇒ m (BC) = <u>3/4</u>

Now, since AD is the altitude of BC, we can say the altitude is perpendicular to BC.

Hence, the slope of a perpendicular line is equal to the negative reciprocal of the original line.

⇒ m (AD) = - (1/m(BC))

⇒ m (AD) = - (1/(3/4))

⇒ m (AD) = -4/3

4 0

2 years ago

There are 10 boys and 20 girls in Mrs Brook's class.

notsponge [240]

Answer:

Step-by-step explanation:

First let us consider how we calculate the mean test mark in the first place, we add up the individual test marks of the entire class to give the total test mark then we divide by the number of students. This means we need two pieces of information to calculate the boys' mean mark, the total boys' mark and the number of boys. We already know the number of boys but how do we work out the total boys' test mark? If we can work out the total class mark and total girls' mark we can find the total boys' mark by subtracting the total girls' mark from the total class mark. To do this we can work backwards to find the total mark for the whole class by taking the mean mark and multiplying it by the number of students, this gives us Total Class Mark = Mean Class Mark x Number of Students = 60 x 30 = 1800. We can do the same for the girls' mark giving us Total Girls' Mark = Mean Girls' Mark x Number of Girls = 54 x 20 = 1080. This then gives us the total boys mark as Total Boys' Mark = Total Class Mark - Total Girls' Mark = 1800 - 1080 = 720. Now we have everything we need to work out the boys' mean mark and we get Boys' Mean Mark = Total Boys' Mark/Number of Boys = 720/10 = 72.

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3 years ago

An athlete runs 8 miles in 50 minutes on a treadmill. At this rate, how long will it take the athlete to run 9 miles?

Snowcat [4.5K]

I think it’s 56.25 mins

5 0

3 years ago

A store sells two kinds of​ candles, scented and unscented. The scented candles burn one eighth inch

A store sells two kinds of candles, scented and unscented. The scented candles burn one eighth inch