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1 year ago

A rectangular tank measuring 35 cm by 28 cm by 16 cm is 2/5 filled with

Mathematics

1 answer:

Alina [70]1 year ago

7 0

Answer:

Amount of water left in tank = 440 cm³

Step-by-step explanation:

Given:

Sides of tank respectively = 35 cm , 28 cm , 16 cm

Water level in tank = 2/5

Side of a cubic tank = 18 cm

Find:

Amount of water left in tank

Computation:

Volume level in rectangular tank = [2/5][35 x 28 x 16]

Volume level in rectangular tank = [2/5][15,680]

Volume level in rectangular tank = [31,360/5]

Volume level in rectangular tank = 6,272 cm³

Volume of cube = side³

Volume of cube = 18³

Volume of cube = 5,832 cm³

Amount of water left in tank = Volume level in rectangular tank - Volume of cube

Amount of water left in tank = 6,272 - 5,832

Amount of water left in tank = 440 cm³

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Three years ago Tom was twice as old as Jean, and in two years the sum of their ages will be 28 years. Find their present ages.

lubasha [3.4K]

Answer:

Jean is 9 and Tom is 15.

Step-by-step explanation:

3 years ago, Tom was 12 and Jean was 6, hence Tom was twice as old as Jean.

Since that was their age 3 years ago, they are currently 15 (Tom) and 9 (Jean).

Add 2 years to each of these ages, you get 17 and 11.

17 + 11 = 28

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2 years ago

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FOR 14 POINTS Thalia, a quiz show contestant, answered 20 questions. She was awarded 2 points for every correct answer that she

Svetradugi [14.3K]

Answer:

The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28. Instead modifications should have been made before applying the equation.

Step-by-step explanation:

Given

Total Questions = 20

Total Points = 28

Correct Answers = +2 points

Incorrect Answers = -1 point

Required

Spot the error in the viewer's calculation

The viewer represents the correct answers with x and the incorrect ones with y.

This implies that

$x + y = 20$

Also, for every correct answers, she gets 2 points;

This can be represented by 2x

and for every incorrect answers, she gets -1 point

This can be represented by -y

This implies that

$2x - y = 28$

This is where the viewer made a mistake

The viewer's mistake is that; instead of subtracting total incorrect points from the correct points, the viewer added them together;

Solving further

$2x - y = 28$

$x + y = 20$

Add both equations together

$2x + x + y - y = 28 + 20$

$3x = 48$

Divide both sides by 3

$\frac{3x}{3} = \frac{48}{3}$

$x = \frac{48}{3}$

$x = 16$

Substitute $x = 16$ in $x + y = 20$

$16 + y = 20$

Subtract 16 from both sides

$16 - 16 + y = 20 - 16$

$y = 20 - 16$

$y = 4$

This implies that the contestant answered 16 questions correctly and 4 questions incorrectly

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1 year ago

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Mario is setting up a new tent during a camping trip. The tent came with 7 feet of rope. The instructions are to use 34.5 inches

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Answer: There are 6 sections of $8\frac{1}{4}\ inches$ of rope Mario can cut from the rope .

Step-by-step explanation:

Since we have given that

Length of the rope for the tent = 7 feet

As we know that

$1\ feet=12\ inches\\\\7\ feet=12\times 7=84\ inches$

Length of rope is used to tie a tarp on top of the tent = 34.5 inches

Remaining length of rope is given by

$84-34.5=49.5\ inches$

According to question, the remaining rope should be cut into

$8\frac{1}{4}\ inches\\\\=\frac{33}{4}\ inches$

So, Number of $8\frac{1}{4}\ inches$ sections of rope Mario can cut from the rope is given by

$\frac{49.5}{8\frac{1}{4}}\\\\=\frac{49.5}{\frac{33}{4}}\\\\=\frac{49.5\times 4}{33}\\\\=6$

Hence, there are 6 sections of $8\frac{1}{4}\ inches$ rope Mario can cut from the rope .

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1 year ago

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A random sample of 64 students at a university showed an average age of 25 years and a sample standard deviation of 2 years. The

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Answer:

The correct option is;

d. 24.2 to 25.6

Step-by-step explanation:

Here we have a sample with unknown population standard deviation, we therefore apply the student t distribution at 64 - 1 degrees of freedom

Therefore, we have

$CI=\bar{x}\pm t\frac{s}{\sqrt{n}}$

Where:

$\bar x$ = Mean = 25

σ = Standard deviation = 2

n = Sample size = 64

t = T value at 98% = $\pm 2.387$

Which gives

$CI=25\pm t_{63}\frac{2}{\sqrt{64}}$

That is the value is from

24.40325 to 25.59675 which gives,by rounding to one decimal place, is

24.4 to 25.6.

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1 year ago

In estimating the mean score on a fitness exam, we use an original sample of size n = 30 and a bootstrap distribution containing

ioda

Answer:

C. 67.5 to 72.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.