Jeremy has a fish tank that has a 30 cm by 90 cm rectangular base. The water is 25 cm deep. When he drops rocks in
the tank, the water goes up by 2 cm. What is the volume in liters of the rocks?
The volume of the rocks is ____ L

The area of the regular hexagon with apothem 3√3 mm is approximately 125 mm². (option d)

The area of a regular hexagon can be found using the formula:

Area = (3√3 × s²) ÷ 2

Where s is the length of one side of the hexagon, and 3√3 is the apothem.

To solve for the area, we need to find the value of s. We can do this by using the fact that a regular hexagon can be divided into six equilateral triangles, and each of these triangles has sides equal to s.

The height of each equilateral triangle is equal to the apothem, which is 3√3 mm in our case. Using the Pythagorean theorem, we can find the length of one side of the hexagon:

s = 2 × (3√3) ÷ √3

s = 6

Now that we know the value of s, we can substitute it into the formula for the area of a regular hexagon:

Area = (3√3 × 6²) ÷ 2 = 125

Hence the correct option is (d).

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Answer:

Step-by-step explanation:

50%

Answer:

5 1/3

Step-by-step explanation:

2/3 x 6 + 2/3 x 2

2/3 x 6 = 12/3

2/3 x 2 = 4/3

12/3 + 4/3 = 16/3

16/3 = 5 1/3

Answer:

Find the mean and variance of 2,2,3,3,3,4,4,4, and 4

O 4.21, 0.58

O 6.53, 0.74

O 7.69, 0,69

Step-by-step explanation:

You're welcome.

Answer: The first one

Average x = 3.2222222222222

Count n = 9

Sum Sum = 29

Step-by-step explanation: Mean means the usual set of numbers found by adding all the numbers together and then dividing that by the number of the numbers.

Hope it helped

In order to find the height of 2 different 3-D shapes, we must identify which dimension represents the height for each individual shape and then add them together.

The first thing is that we must identify which dimension represents the height for each individual shape, for instance, if one shape is a rectangular prism, its height would be the length of one of its sides.

After we identified the height for each shape, you can add them together to get the total height of the composite figure, but, we must understand that this method assumes that the two shapes are stacked vertically on top of each other with their bases aligned.

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Note that the probability - P(X ≤25 or X ≥ 45) = 0.0784

P(X ≤25 or X ≥ 45)  = 1- P(X ≤25.5 or X ≥ 44.5)

= 1 - p [ (25.5 - 10(3.5)/ √(35/12) √10)   ≤ (X-10(3.5)/√(35/12) √10) ≤ (44.5 - 10(3.5)/√(35/12) √10)]

≈ 1 - (2Ф (1.76) - 1)

≈ 2(1-0.9608)

≈ 0.0784

Thus, P(X ≤25 or X ≥ 45) = 0.0784

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Full Question:

You roll a 6-sided die 10 times. Let X be the total value of all 10 dice = X1 + X2 + ...... + X10.
You win the game if  X ≤ 25 or X ≥ 45. Use the central limit theorem to calculate the probablity that you win.

Note that E[Xi] = 3.5 and Var (Xi) = 35/12

well, let's read the Set Builder

the variable "x", where "x" is greater than or equals to 2

Oh by the way "x" is also less than or equals to 2

hmmm what the heck?  how can "x" be greater than 2 and at the same time be less than 2?  well, that's kinda like a logical collision, so we can conclude that "x" is neither less than or greater than 2, but another condition is that it could be equal to 2, since the other two collided, the only conclusion is that "x" must be equal to 2.

The area of the triangle MNO is 14.7 sq cm and the shortest altitude is 2.1 cm

From the question, we have the following parameters that can be used in our computation:

MN = 5 cm, NO = 6 cm and MO = 7 cm

So, we have

s = 1/2 * (5 + 6 + 7)

Evaluate

s = 9

The area is then calculated as

Area = √[s(s - MN)(s - NO)(s - MO)]

Substitute the known values in the above equation, so, we have the following representation

Area = √[9 * (9 - 5)(9 - 6)(9 - 7)]

Evaluate

Area = 14.7

Also, we have

Shortest altitude = 14.7/7

Shortest altitude = 2.1

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Asked equations are written below with the explanation.

Here are three equations that involve adding negative numbers:

-5 + (-3) = -8

This equation involves adding the negative numbers -5 and -3.

-10 + (-2) + (-3) = -15

This equation involves adding the negative numbers -10, -2, and -3.

-7 + (-1) + (-4) + (-2) = -14

This equation involves adding the negative numbers -7, -1, -4, and -2.

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The correct equation to find that can be used to find the width of the feed  trough is (b) 4620 = 8w×w×6, and the width of the "feed-trough"  is 9.8 inches wide.

The "Volume" of "rectangular-prism" can be found using formula V = l×w×h, where V is = volume, l is = length, w is = width, and h is = height.

We know that the volume of the "feed-trough" is 4,620 cubic inches, and

The height is = 6 inches. Let us denote the width as "w" and the length as "8w" (because trough's length is 8 times the width),

So, the equation for the volume of the feed trough is:

⇒ 4620 = (8w) × (w) × (6),

So, the correct equation to find the width is Option (b) 4620 = (8w) × (w) × (6).

Simplifying further,

We get,

⇒ w² = 96.25,

⇒ w ≈ 9.8 inches (rounded to the nearest tenth)

Therefore, the width of the feed trough will be approximately 9.8 inches.

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The correct statements regarding the solutions of the quadratic function is given as follows:

Two complex solutions.

A quadratic equation is modeled by the general equation presented as follows:

y = ax² + bx + c

The discriminant of the quadratic function is given by the equation as follows:

Δ = b² - 4ac.

The numeric value of the coefficient and the number of solutions of the quadratic equation are related as follows:

The function for this problem is given as follows:

y = 2x² - 8x + 10.

The coefficients are given as follows:

a = 2, b = -8 and c = 10.

Hence the discriminant is given as follows:

Δ = (-8)² - 4 x 2 x 10

Δ = 64 - 80

Δ = -16.

Negative discriminant, hence the equation has two complex solutions.

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The size of skis is 160 cm.

Given that, Tavon wants to buy new skis that are the same as his height he is 1.6 meters tall. skis are sold in cm. we need to find the height of skis,

Using the concept of unit conversion,

1 m = 100 cm

Therefore,

1.6 m = 100 × 1.6 = 160 cm

Since, the length of the skis and the height of Tavon are same so the skis are of 160 cm.

Hence, the size of skis is 160 cm.

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Answer:

416.16

Step-by-step explanation:

First, solve the parenthetical expression (23-12) which equals 11. Next, use the order of operations to perform the multiplication and division from left to right: 48 ÷ 11 = 4.36 and 4.36 x 81 = 353.16. Finally, add this result to 63 to get the final answer: 63 + 353.16 = 416.16. Therefore, the solution is 416.16.

all

Gina wants to go to the water park with her friends. They have a total of www dollars to buy 555 tickets. Each ticket costs 151515 dollars.

Select the equation that matches this situation.

Choose 1 answer:

Choose 1 answer:

(Choice A)   5 = 15 \times w5=15×w5, equals, 15, times, w

A

5 = 15 \times w5=15×w5, equals, 15, times, w

(Choice B)   w = 15 +5w=15+5w, equals, 15, plus, 5

B

w = 15 +5w=15+5w, equals, 15, plus, 5

(Choice C)   w = 5 \times 15w=5×15w, equals, 5, times, 15

C

w = 5 \times 15w=5×15

About 49.87% of buyers paid between $150,000 and $156,000 for the new homes.

According to the 68-95-99.7 rule, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean in a normal distribution.

In this case, the mean price of a certain model of new homes is $150,000, and the standard deviation is $2000. Thus, we can calculate the price range of one standard deviation above and below the mean as:

Lower Bound = Mean - 1 × Standard Deviation = $150,000 - $2,000 = $148,000

Upper Bound = Mean + 1 × Standard Deviation = $150,000 + $2,000 = $152,000

Therefore, approximately 68% of buyers paid between $148,000 and $152,000 for the new homes.

To find the percentage of buyers who paid between $150,000 and $156,000, we need to calculate the z-scores for these values using the formula:

z-score = (value - mean) / standard deviation

For $150,000:

z-score = ($150,000 - $150,000) / $2,000 = 0

For $156,000:

z-score = ($156,000 - $150,000) / $2,000 = 3

Looking at the z-score table, we can see that the area under the normal curve between z = 0 and z = 3 is approximately 49.87%.

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Answer:

648ft

Step-by-step explanation:

18 multiplied by 36 is 648

Answer:

648 ft ^2

Step-by-step explanation:

A = L * W A = 18 ft * 36 ft A = 648 ft^2

The resulting number is the area of the rectangle, which is expressed in square units. So the area of the figure is 648 square feet

The distance between the points (1, 2) and (10,-10) is 15 units.

In Mathematics and Geometry, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given points into the distance formula, we have the following;

Distance = √[(10 - 1)² + (-10 - 2)²]

Distance = √[(9)² + (-12)²]

Distance = √[81 + 144]

Distance = √225

Distance = 15 units.

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The length of the rectangle is 43 inches.

The width of the rectangle is 18 inches.

Given that,

The length of a rectangle is seven more than double the width.

Let width = x

Length = 7 + 2x

Perimeter of the rectangle = 122 inches

The formula to find the perimeter of a rectangle is,

Perimeter = 2 (length + width)

Substituting,

122 = 2 (7 + 2x + x)

61 = 7 + 3x

3x = 54

x = 18

Width = 18 inches

Length = 7 + 2x = 7 + 36 = 43 inches

Hence the length and width are 43 inches and 18 inches respectively.

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Triangle A and Triangle C are congruent to each other because a series of rigid transformations, a translation and a reflection, were applied to A to form C. Therefore, the correct answer is "A Is congruent to B and B Is congruent to C". So, the correct answer is A).

Identify the coordinates of the vertices of Triangle A and Triangle C

Triangle A: (1, -2), (3, -2), (3, -5)

Triangle C: (4, 0), (6, 0), (6, 3)

Apply the first transformation that was used to transform Triangle A to Triangle C, which is a translation of 3 units right and 2 units up. To do this, add 3 to the x-coordinates and add 2 to the y-coordinates of each vertex of Triangle A to get

Triangle A': (4, 0), (6, 0), (6, -3)

Triangle A' is not congruent to Triangle A because the translation changes the position of the vertices, but it does not change the size or shape of the triangle.

Apply the second transformation that was used to transform Triangle A' to Triangle C, which is a reflection over the x-axis. To do this, negate the y-coordinates of each vertex of Triangle A' to get

Triangle C': (4, 0), (6, 0), (6, 3)

Triangle C' is congruent to Triangle C because the reflection over the x-axis preserves the size and shape of the triangle, and negating the y-coordinates of the vertices only changes their position, not their size or shape.

Compare Triangle A with Triangle C'

Triangle A: (1, -2), (3, -2), (3, -5)

Triangle C': (4, 0), (6, 0), (6, 3)

We can see that Triangle A is congruent to Triangle C' because they have the same shape and size, and the corresponding angles and sides are equal.

Therefore, since Triangle A is congruent to Triangle C', and Triangle C' is congruent to Triangle C, we can conclude that Triangle A is congruent to Triangle C.

Therefore, the correct answer is "A Is congruent to B and B Is congruent to C" and option is A).

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--The given question is incomplete, the complete question is given

" Figure A is translated 3 units right and 2 units up. The translated figure is labeled figure B. Figure B is reflected over the x-axis. The reflected figure is labeled figure C. On a coordinate plane, triangle A has points (1, negative 2), (3, negative 2), (3, negative 5). Triangle B has points (4, 0), (6, 0), (6, negative 3). Triangle C has points (4, 0), (6, 0), (6, 3). Which best explains why figure A is congruent to figure C?A Is congruent to B and B Is congruent to C A Is congruent to A, B Is congruent to B, C Is congruent to C Each triangle is a right triangle. Each triangle is an isosceles triangle."--

Answer:Need answer choices to answer

Step-by-step explanation:

The approximate amount to be deposited each month at a guaranteed APR of 6.5% that will accrue to $15,000 in 9 years is $97.57.

In order to find out how much you should deposit each month to end up with $15,000 in 9 years, we can use the future value formula for an annuity:

FV = PMT * [(1 + r)^n - 1] / r

where:

The total number of deposits, n,  is the number of months in 9 years:

n = 9 * 12 = 108

The monthly interest rate from the annual percentage rate (APR):

r = (1 + 0.065/12) - 1 = 0.0054166667

Let's substitute the values and solve for PMT:

Therefore, you should deposit approximately $97.57 each month to end up with $15,000 in 9 years, assuming a guaranteed APR of 6.5%.

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Answer:

86.60254

Step-by-step explanation:

30-60-90 triangle, which means that the base is 10. 1/2(10)(10 rt 3). Simplify answer as needed :)

Answer: D

Step-by-step explanation:

2x-36=0                                                

+36     +36

___________

2x=36

x=18

Even if one equation, -18 was not solved, you can easily cross out the ones without 18 and get the answer.

Answer:

The width of the garage is 22 feet

Step-by-step explanation:

64 = 20 + 2w

44 = 2w

22 = w

The width of the garage is 22 feet

Answer:

This (1.) unlikely

now, taking a peek at the picture above, let's notice, the pyramid is really just 4 triangles, three standing up and one lying down.

[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{triangles standing up} }{3\left[\cfrac{1}{2}(\underset{b}{5})(\underset{h}{7}) \right]}~~ + ~~\stackrel{ \textit{triangle lying down} }{\cfrac{1}{2}(\underset{b}{5})(\underset{h}{4.3})}}\implies 52.5+10.75\implies \text{\LARGE 63.25}~yd^2[/tex]

The correct expression for the company use to approximate the percent increase in revenue through a certain number of months, m is,

⇒ [tex]A = P (1 .0465 )^m[/tex]

We have to given that;

A company's revenue increased by 4.65% over the previous year.

We know that;

Formula is,

[tex]A = P (1 + \frac{r}{100} )^m[/tex]

Where, A = final amount

P = principal amount

r = rate

m = time in months

So, The correct expression for the company use to approximate the percent increase in revenue through a certain number of months, m is,

⇒ [tex]A = P (1 + \frac{r}{100} )^m[/tex]

⇒ [tex]A = P (1 + \frac{4.65}{100} )^m[/tex]

⇒ [tex]A = P (1 + 0.0465 )^m[/tex]

⇒ [tex]A = P (1 .0465 )^m[/tex]

Thus, the correct expression for the company use to approximate the percent increase in revenue through a certain number of months, m is,

⇒ [tex]A = P (1 .0465 )^m[/tex]

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Answer:

1.1 percent of her monthly income is spent on

Step-by-step explanation:

The expressions that are equivalent to 24a - 6 are 1/2(48a - 12) and -3(2a + 2) + 18a

Let's start with the first expression,

=> 12(48a - 12).

We can distribute the 12 to get

=> 576a - 144.

This expression is not equivalent to 24a - 6 since 576a - 144 cannot be simplified to 24a - 6.

Moving on to the second expression,

=> 1/2(48a - 12) = 24a - 6.

This expression is equivalent to 24a - 6 since it simplifies to the same expression.

The fourth expression,

=> -3(2a + 2) + 18a

can be simplified by distributing the -3 to get

=> -6a - 6 + 18a.

Combining like terms, we get

=> 12a - 6.

This expression is equivalent to 24a - 6 since it simplifies to the same expression.

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