2.8 repeating as a fraction

Perimeter of the rectangle is 64.5 m

To solve the above questions, we need to recall some of the formulas as follows:

Area of Rectangle = Length × Width

Perimeter of Rectangle = 2 × ( Length + Width )

Let us now tackle the problem !

Given:

Area of Rectangle = A = 256.5 m²

Length of Rectangle = L = 18 m

Unknown:

Perimeter of Rectangle = P = ?

Solution:

This problem is about Area and Perimeter of Rectangle.

Let's find the width of Rectangle.

[tex]\texttt{Area of Rectangle} = \texttt{Length} \times \texttt{Width}[/tex]

[tex]256.5 = 18 \times \texttt{Width}[/tex]

[tex]\texttt{Width} = 256.5 \div 18[/tex]

[tex]\texttt{Width} = \boxed {14.25 ~ \texttt{m}}[/tex]

Let's find the perimeter of Rectangle.

[tex]\texttt{Perimeter of Rectangle} = 2 (\texttt{Length} + \texttt{Width})[/tex]

[tex]P = 2 ( L + W )[/tex]

[tex]P = 2 ( 18 + 14.25 )[/tex]

[tex]P = 2 ( 32.25 )[/tex]

[tex]P = \boxed {64.5 ~ \texttt{m}}[/tex]

Grade: College

Subject: Mathematics

Chapter: Two Dimensional Figures

Keywords: Perimeter, Area , Square , Rectangle , Side , Length , Width

Final answer:

The area of the base is increasing at a rate of 200π m²/min after 5 minutes.

Explanation:

To find how fast the area of the base is increasing, we first need to calculate the rate at which the height and radius of the cone are changing. Given that the height of the pile is always twice the length of the base diameter, we can write the equation h = 2r, where h is the height and r is the radius of the cone. Differentiating both sides with respect to time, we get dh/dt = 2dr/dt. Since the height is changing at a constant rate of 20 m³/min, dh/dt = 20 m³/min. Using this information, we can find the rate at which the radius is changing, dr/dt. Since the base diameter is equal to 2r, the base radius changes at a rate of dr/dt = 10 m/min. Now, we can find the rate of change of the area A of the base using the formula A = πr². Differentiating both sides with respect to time, we get dA/dt = 2πr(dr/dt). Plugging in the values, we have dA/dt = 2π(10)(10) = 200π m²/min. Therefore, the area of the base is increasing at a rate of 200π m²/min after 5 minutes.

To determine the time it takes to ride around the neighborhood, equations are set up from the given scenarios and solved algebraically, resulting in 10 minutes for one neighborhood lap.

To solve the problem, we need to set up equations based on the information provided. Let's let N represent the time it takes to ride around the neighborhood once and B represent the time it takes to ride around the block twice. The first scenario gives us:

B + N = 15 minutes

In the second scenario, the only difference is the number of neighborhood laps, so:

B + 5N = 55 minutes

Subtracting the first equation from the second gives us:

4N = 40 minutes

Dividing both sides by 4, we find:

N = 10 minutes

Therefore, it takes 10 minutes to ride around the neighborhood once.

Final answer:

The percentage decrease in the price of the notebook from $3.90 to $3.40 is 12.8% when rounded to the nearest tenth of a percent.

Explanation:

To find the percentage decrease in the price of a notebook from $3.90 to $3.40, we use the formula for percentage change:

Percentage Change = [(Old Price - New Price) / Old Price] × 100%

Plugging in our values we get:

Percentage Decrease = [($3.90 - $3.40) / $3.90] × 100%

Percentage Decrease = [$0.50 / $3.90] × 100%

Percentage Decrease = 0.1282 × 100%

Percentage Decrease = 12.82%

When rounded to the nearest tenth, the percentage decrease is 12.8%.

Final answer:

If a chi-square test produces a chi-square statistic near zero, it implies that there is minimal deviation between the observed and expected values, suggesting independence or a good fit. However, interpretation should consider the specific test and hypotheses.

Explanation:

If a chi-square test produces a chi-square statistic near zero, it implies that there is minimal deviation between the observed and expected values. This suggests that the variables being tested are independent of each other or that the data fits the assumed distribution very well.

For example, in a chi-square test of independence, if the chi-square statistic is close to zero, it indicates that there is no significant relationship between the two factors being tested.

However, it is important to interpret the results in the context of the specific test being conducted, considering the null and alternative hypotheses as well as the significance level.

Answer

Find out the how much hardener should be added to 19 containers of resin .

To prove

Let us assume that the hardener should be added to 19 containers of resin be x .

As given

The formula for glue says to add 60 ml of hardener to each container of resin.

than the equation become

x = 19 × 60

x =  1140 ml

Therefore the  1140 ml hardener should be added to 19 containers of resin .

Hence proved

After rounding off the given number 0.125 to the nearest tenth it becomes 0.1.

We know that,

When you round a number to a certain digit, you have to check the value of the digit before the place you want to round off to.

1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

The given number is:

0.125

To round off this digit nearest tenth,

See the number at the hundredth place, which is 2.

And 2 < 5  

Therefore,

0.125 is rounded down to 0.1

So after rounding 0.125 number becomes 0.1.

Hence,

The rounded-off number nearest tenth is 0.1.

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The number of pennies, nickels, and dimes will be 227, 49, and 49, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

In a pack, a kid has 325 coins worth $19.50. There were three kinds of coins: pennies, nickels, and dimes. In the event that the pack contained a similar number of nickels as dimes.

Let 'x' be the number of dimes and nickels and 'y' be the number of pennies. Then the equations are given as,

x + x + y = 325

2x + y = 325           ....1

0.1x + 0.25x + 0.01y = 19.50

0.35x + 0.01y = 19.50        ...2

From equations 1 and 2, then we have

0.35x + 0.01(325 - 2x) = 19.50

0.35x + 3.25 - 0.02x = 19.50

0.33x = 16.25

x = 49

Then the value of 'y' will be given as,

2(49.24) + y = 325

y = 227

The number of pennies, nickels, and dimes will be 227, 49, and 49, respectively.

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Answer:

She left a 15% tip.

Step-by-step explanation:

Just do $10.99 (The original price, I believe.) and then the tip she gave. ($2.00)

And turn it into a percentage.

I know the other person already answered, 50% credits to them, because they only gave the "Answer:" part. (No offense if you're reading this.)

Hope this helped, and enjoy the little pun!

"The other person already answered 50%"

The probability of rolling a sum greater than 9 (Event A) on two fair dice is 1/6, and the probability of rolling a sum divisible by 5 or 6 (Event B) is 1/3.

To compute the probability of Event A, where the sum is greater than 9, we first identify the possible combinations that yield a sum greater than 9: (4,6), (5,5), (5,6), (6,4), (6,5), and (6,6). Since there are 6 possible outcomes and 36 total possible outcomes when rolling two dice (6 for the first die × 6 for the second die), the probability is 6/36 or 1/6.

For Event B, we look for sums divisible by 5 or 6. These sums are 5, 6, 10, 12, 15, 18, and 20. The combinations yielding these sums are (1,4), (2,3), (2,6), (3,2), (3,6), (4,1), (4,6), (5,1), (5,5), (6,2), (6,3), (6,6). By counting these results, we have 12 outcomes that meet the Event B criteria out of 36, so the probability is 12/36 or 1/3.

The probability of Event A, the sum being greater than 9, is 1/6, and the probability of Event B, the sum being divisible by 5 or 6, is 1/3.

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