A rectangular aquarium measures 21 inches long by 11 inches wide by 18 inches tall. If the aquarium is filled to the 15 inch mark, what is the volume of the water in the aquarium?

The width of the brochure is 3/2 inches and the height is 10 inches.

Let's assume that the width of the brochure is x and the height is y.

The area of the brochure is given as 30 square inches:

xy = 30

The perimeter of the brochure is given as 23 inches:

2x + 2y = 23

We can use the second equation to solve for one variable in terms of the other.

2x + 2y = 23

2x = 23 - 2y

x = (23 - 2y)/2

Now we can substitute this expression for x into the equation for the area:

xy = 30

[(23 - 2y)/2]y = 30

23y/2 - y^2 = 60/2

y^2 - 23y/2 + 30 = 0

We can solve for y using the quadratic formula:

y = [23/2 ± sqrt((23/2)^2 - 4(1)(30))]/(2)

y = [23/2 ± sqrt(529/4 - 120)]/2

y = [23/2 ± sqrt(289/4)]/2

y = [23/2 ± 17/2]/2

y = 10 or y = 3/2

Since the height must be greater than the width, we can eliminate y = 3/2 as a solution.

So, y = 10 and

x = (23 - 2y)/2 = (23 - 20)/2 = 3/2

Therefore, the width of the brochure is 3/2 inches and the height is 10 inches.

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Answer:

B)  6

Step-by-step explanation:

Calculate the value of c by substituting point (0, 15) into the quadratic equation formula:

[tex]f(x)=ax^2+bx+c[/tex]

[tex]\begin{aligned}f(0)=a(0)^2+b(0)+c&=15\\0+0+c&=15\\c&=15\end{aligned}[/tex]

Therefore:

[tex]f(x)=ax^2+bx+15[/tex]

Substitute the point (1, 22) into the formula and create an equation for a in terms of b:

[tex]\begin{aligned}f(1)=a(1)^2+b(1)+15&=22\\a+b+15&=22\\a+b&=7\\a&=7-b\end{aligned}[/tex]

Therefore:

[tex]f(x)=(7-b)x^2+bx+15[/tex]

Finally, substitute another point from the table (-3, 6) and solve for b:

[tex]\begin{aligned}f(-3)=(7-b)(-3)^2+b(-3)+15&=6\\(7-b)9-3b+15&=6\\63-9b-3b+15&=6\\78-12b&=6\\-12b&=-72\\b&=6\end{aligned}[/tex]

Therefore, the value of b is 6.

Answer:

6

Step-by-step explanation:

The average rate of change of the height of the rocket is 11.25/(a - 1)

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

h(1) = 23 meters and h(a) = 34.25 meters.

The average rate of change of the height of the rocket is

Rate = Change in height /Time

So, we have

Rate = (34.25 - 23)/(a - 1)

Evaluate

Rate = 11.25/(a - 1)

Hence, the rate = 11.25/(a - 1)

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Complete question

Melissa launches a rocket from a 3-meter-tall platform. The height, h, of the rocket, in meters, can be modeled by the given graph.

Melissa knows that h(1) = 23 meters and h(a) = 34.25 meters.

What is a reasonable estimate of the average rate of change of the height of the rocket, in meters per second

Check the picture below.

The answer to the expression is  (x+3)/(x-1)

You should recall that a quadratic expression is an algebraic expression of the form ax2 + bx + c = 0, where a ≠ 0

The given expressions are

(x² - 3x - 18) / (x²- 7x +6

(x²-6x +3x +19) / (x²-x -6x +6)

This implies that {(x²-6x)+(3x-18)} / {(x²-x) -(6x+6)}

⇒[x(x-6)+3(x-6)] / [x(x-1) - 6(x-1)]

This means that [(x+3)(x-6)] / [(x-6)(x-1)]

Dividing by (x-6) to have

Therefore the value of the expression is (x+3)/(x-1)

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The line of reflection of the graph is y = -3

The given graph is added as an attachment

From the graph, we can see that the shapes are symmetrical about the line y = -3

When shapes are symmetrical about a point or a line, then the point or the line is the point of reflection

This means that the line of reflection is y = -3

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Answer:

The calculated line of reflection of the graph is y = -3

Step-by-step explanation:

The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.

Given that:

Endpoints of diameter, (13, -1) and (15, 9)

The equation of the circle when endpoints of diameter are given is written as,

(x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0

The equation of the circle is calculated as,

(x - 13)(x - 15) + (y + 1)(y - 9) = 0

x² - 28x + 195 + y² - 8y - 9 = 0

x² + y² - 28x - 8y + 186 = 0

The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.

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Answer:

0

Step-by-step explanation:

The measure of the obtuse angle with vertex P is 30 degrees.

We have,

If there is an acute angle with vertex Q measuring 60 degrees, then there must be a corresponding obtuse angle with vertex P that shares the same side as angle Q.

Let's call the measure of this obtuse angle x.

By the angle sum property of triangles, the sum of the measures of the three angles in any triangle is always 180 degrees.

Therefore, we can write the equation:

60 degrees + 90 degrees + x = 180 degrees

Simplifying this equation, we get:

x = 180 degrees - 60 degrees - 90 degrees = 30 degrees

Therefore,

The measure of the obtuse angle with vertex P is 30 degrees.

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The number of players  who included red and purple as their favorite colors is 0.

option A.

The number of people who included red and purple as their favorite colors are calculated as follows;

We are going to determine this number based on the given Venn diagram.

Check the intersection of red and purple, you will notice it is empty, so there is volleyball team member who included red and purple as their favorite colors.

So the answer is zero (0) since the intersection or connection point between red and purple is empty.

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From the given figure, we have the following:

In Mathematics and Geometry, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

Based on the cartesian coordinate (grid) above, the coordinates points and quadrants should be identified as follows;

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Complete Question:

From the given figure, write

a) The coordinates of the points B and F. b) The point identified by the coordinates (1,1)

c) The abscissa of the points D and H.

d) The ordinates of the points A and C.

e) The quadrant in which points B and I lie.

f) The perpendicular distance of the point G from the x-axis.

g) The perpendicular distance of the point I from the y-axis.

h) The point whose perpendicular distance from y- axis is 2 units​

(a) Volume of the cylinder is 153 cm³

(b) Volume of the cone is 51 cm³

(c) Volume of the cone = 1/3 × Volume of the cylinder

From the question, we are to determine the volume of the cylinder and the volume of the cone

The volume of a cylinder can be calculated by using the formula,

V = πr²h

Where V is the volume

r is the radius

and h is the height

From the given information,

A = πr² = 17 cm²

A is the area of the base

h = 9 cm

Thus,

V = 17 cm² × 9 cm

V = 153 cm³

Therefore,

Volume of the cylinder is 153 cm³

(b)

For the volume of the cone

V = 1/3 πr²h

Substitute the given parameters

V = 1/3 × 17 cm² × 9 cm

V = 17 cm² × 3 cm

V = 51 cm³

Hence,

Volume of the cone is 51 cm³

(c)

Volume of the cone = 1/3 × Volume of the cylinder

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The distance between Alberto and the base of the building is  93.4ft

We can view this as a right triangle, such that one cathetus (opposite to the known angle) measures:

40ft - 6ft = 34ft

And the known angle is 70°, we want to get the other leg of the right triangle, so we can use the tangent trigonometric relation which is:

tan(angle) = (opposite cathetus)/(adjacent cathetus)

Replacing the things that we know we get:

tan(70) = x/34ft

tan(70)*34ft = x = 93.4ft

That is the distance.

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According to the information, the distance from your starting point to the library is 4 miles.

To calculate how far do you live from the library we have to assume that the distance from the starting point to the library is "x" miles.

According to the problem, when you are 75% of the way there, you realize you forgot a book. It means you have traveled 75% of the distance, which is 0.75x miles.

Now, you turn around and bike back. When you are 1/3 of the way back, you realize you don't need the book, so you turn around again and bike 3.2 miles to the library.

From the starting point, you have traveled 0.75x miles to the point where you forgot the book, and then you traveled back 1/3 of 0.75x miles, which is (1/3)*0.75x = 0.25x miles.

Now you turn around again and bike 3.2 miles to the library. It means that the distance between the point where you realized you don't need the book and the library is 3.2 miles.

Therefore, the total distance from your starting point to the library is:

Simplifying the equation:

Thus, the distance from your starting point to the library is 4 miles.

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Answer:

The Correct answer is D and F

Answer:

3. 504,875 shares

4. $10,829,568.75

5. $30,383,377.5

Step-by-step explanation:

1. For the first one, you just need to find 70% of 721,250, which we can do several ways:

If Allen owns 70% of Bull Corp, he owns 0.7 x 721,250 = 504,875 shares.

Therefore, Allen owns 504,875 shares of Bull Corp.

you can use cross-multiplication to solve this problem as well. Here's how:

Let X be the number of shares that Allen owns.

According to the problem, Allen owns 70% of the total number of shares, which is 721,250.
So we can write:

X/721,250 = 70/100

To solve for X, we can cross-multiply:

100X = 70 * 721,250

Simplifying the right-hand side:

100X = 50,487,500

Dividing both sides by 100:

X = 504,875

Therefore, Allen owns 504,875 shares of Bull Corp, which is the same answer we got earlier.

I added a picture below.

2. If Allen paid $21.45 PER share we just multiply that by he amount of shares, which is 504,875:

If Allen owns 504,875 shares of Bull Corp, and he paid $21.45 per share, his initial total investment would be:

Total investment = Number of shares * Price per share

Total investment = 504,875 * $21.45

Total investment = $10,829,568.75

Therefore, Allen's initial total investment was $10,830,093.75.
i added a picture for this too.

3. Just replace the 21.45 with 60.18:

If the shares are now worth $60.18, the total value of Allen's shares would be:

Total value = Number of shares * Current price per share

Total value = 504,875 * $60.18

Total value = $30,383,377.5

Therefore, the total value of Allen's shares now is $30,382,078.50.

Added a picture.

The summation of the given expression is as follows:

17.) = 5

18.) = 1

19.) = 1/2

For question 17.)

The summation of 2k+3 when K= 1

= 2(1)+3

= 2+3

= 5

For question 18.)

The summation of (3/2)^k where k = 0 would be = 1

For question 19.)

The summation of 1/2^k+1 where k = 0

= 1/2^0+1

=1/2^1

=1/2

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The pattern that the scatterplot would suggest, given that they have an exponential relationship is :

A function expressed as y = ab^x or y = a × e^(kx), where a, b, and k are constants represents an exponential relationship between two variables. Exponential functions demonstrate continuous increase or decrease throughout their entire domain; they do not alter direction.

In the event that the base 'b' is greater than 1, or if 'k' is positive, the function increases its output, otherwise, it will decrease when either or both conditions apply ('b' being between zero and one, or 'k' being negative). The concavity of a function is determined by the second derivative which takes on the form of an exponential function for all exponential functions, producing unchanged concavity throughout its entire domain.

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The probability that fewer than 30% of the rolls result in a two is given as follows:

0.3085 = 30.85%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

2 out of the six faces are two, and there will be 50 trials, thus the parameters n and p are given as follows:

n = 50, p = 2/6 = 1/3 = 0.3333.

The mean and the standard error are given as follows:

The probability that fewer than 30% of the rolls result in a two is the p-value of Z when X = 0.3, hence:

Z = (0.3 - 0.3333)/0.0667

Z = -0.5

Z = -0.5 has a p-value of 0.3085.

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The equation for the translated function is the one in option D:

G(x) = (x - 6)² - 4

We start with the parent quadratic function:

F(x) = x²

We apply two translations, one of 6 units to the right which can be written as:

G(x) = F(x - 6)

And a translation of 4 units down, which is written as:

G(x) = F(x - 6) - 4

Replacing F(x) we will get:

G(x) = (x - 6)² - 4

The correct option is D.

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The record long jump is 8 inches short of 10 yards.

First, we need to convert 10 yards to inches. Since 1 yard = 3 feet and 1 foot = 12 inches, we have:

10 yards = 30 feet

= 30 x 12 inches

= 360 inches

To find how many inches short of 10 yards the long jump is, we can subtract the length of the long jump from 360 inches:

360 inches - 29 feet 4 inches

= 360 inches - (29 x 12 + 4) inches

= 360 inches - 352 inches

= 8 inches

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The water cooler tank has to be filled 18 times to quench the thirst of 1200 students.

We have

Number of students= 1200

Water consumption per student= 750 ml

So, Total water consumption

= Number of students × Water consumption per student

= 1200 × 750 ml

= 900000 ml

= 900 Liter

Now, the time cooler tank has to be filled to quench the thirst

= 900 / 50

= 18 times

Thus, the water cooler tank has to be filled 18 times to quench the thirst of 1200 students.

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The equation 2 (p+ 7) = 4 - 8p has only one solution that is; -9.

We know that solution of an equation refers usually to the values of the variables involved in that equation that if substituted in place of that variable would give a true mathematical statement.

We need to determine the solutions does the equation 2 (p+ 7) = 4 - 8p have;

Now solving for p,

2 (p+ 7) = 4 - 8

Open the bracket,

2p+ 14 = 4 - 8

Combine the like terms,

2p = -4 - 14

2p = -18

p = -18/2 = -9

Therefore, the equation has only one solution which is -9.

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The graph is a function, the domain is (-∝, ∝), the range is (-∝, 4] and the graph is symmetrical with the y-axis

Given that we have the graph

As a general rule of the vertical line test

For a graph to represent a function, a line drawn from the x-axis must intersect with the graph at most once

Using the above as a guide, we have the following:

The graph would not intersect with a line from the x-axis more than once

Hence, the graph is a function

The domain is the set of input values

In this case, we have

Domain = (-∝, ∝) i.e. all set of real values

The range is the set of output values

In this case, we have

Range = (-∝, 4]

When the graph is rotated across the y-axis, the graph maintains it orientation

This means that the graph is symmetrical with the y-axis

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The concepts of percentage, rate, and base can be defined as follows:

In our daily lives, we utilize these three concepts in many different ways, some examples of which are outlined below:

When we go shopping, we frequently come across discounts or sale prices offered as percentages off the original price. For example, if an item was initially $40 but is now available at a discount of 20%, it will be priced at $32.

Rates enable us to measure speed when we are driving or running with unit-based measurements. In addition, rates allow us to compare prices during grocery shopping, where we might need to know the cost per pound of apples and/or calculate interests on investments or loans.

Bases have utility while dealing with ratios or proportions. For instance, if we wish to prepare food for eight people instead of four, one can take the existing recipe as a base and adjust ingredient quantities proportionally.

The formulas P = B × R, B = P / R, and R = P / B are basic calculations that correspond to different values based on the given percentage, rate, or base. For instance, P = B × R allows us to obtain the value of P given the input of B and R.

Meanwhile, B = P / R enables us to get the value of B by punching in P and R much like calculating interest paid out each month in compound-interest cases.

Finally, R = P / B yields the value of R using inputs for P and B. These formulas find rampant use in fields like finance, economics, and mathematics.

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The word problem is given thus: Given this gridlock, which child between Matt and Riley still had more proportionate remaining sandwich contents provided they both possess a shared 4/8 numerator?

Four sandwiches were prepared by Mrs. Ericson, each identical in size, for her offspring: Matt, Elisa, Carl, and Riley.

The children consumed varying portions of their respective sandwiches during the shared midday meal.

Post-lunch investigations denoted different fractions residual from each child's original sandwich quantity.

Matt kept 7/8 of his portion while Elisa held on to 3/4 of hers. Meanwhile, two halves (2/4) constitute what remained of Carl's sandwich with Riley retaining 4/8 for himself.

Given this gridlock, which child between Matt and Riley still had more proportionate remaining sandwich contents provided they both possess a shared 4/8 numerator?

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The question in English is:

Mrs. Ericson made sandwiches for her 4 children. All the sandwiches had

The same size. After lunch, each child had a fraction left.

different from your sandwich. Matt had, Elisa had

7

3, Carl was 2, and Riley was 8

8

4

Use this information to write a problem comparing two fractions

with the same numerator.

The circles are similar because you can translate Circle 1 using the transformation rule (0, -7) and then dilate it using a scale factor of 3/5.

Translation involves moving an object in a straight line without changing its size or shape. In this case, we can translate Circle 1 7 units down to match the y-coordinate of Circle 2. The transformation rule for this translation is (0, -7), since we are not changing the x-coordinate.

Dilation involves uniformly scaling an object, either making it larger or smaller. We can dilate Circle 1 by a scale factor of 3/5 to make it have the same radius as Circle 2. The scale factor is determined by taking the ratio of the radii:

scale factor = radius of Circle 2 / radius of Circle 1

scale factor = 9 / 15

scale factor = 3/5

The center of dilation is the center of Circle 1, since we want to preserve its position.

Therefore, we can transform Circle 1 into Circle 2 by translating it 7 units down and dilating it by a scale factor of 3/5. The transformation rule is:

(0, -7) followed by dilation with a scale factor of 3/5

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Answer:

8.604 in.

Step-by-step explanation:

We can use the formula for compound interest to find the height of domino #9:

A = P(1 + r)^n

where A is the final amount, P is the initial amount, r is the growth rate, and n is the number of compounding periods. In this case, P is the height of domino #0, r is 15% or 0.15, and n is 9 (since we want to find the height of domino #9).

Substituting the given values:

A = 3.00 in * (1 + 0.15)^9

Simplifying:

A = 3.00 in * 2.86797199

A ≈ 8.604 in

Therefore, the height of domino #9 is approximately 8.604 inches.

The transformation that maps the pre-image (red) onto the image (blue) is reflection

Given that

the pre-image (red) and the image (blue)

From the figure, we can see that

Both triangles are mirrors of one another

As a general rule

When two shapes with the same orientation and properties mirror one another, then the transformation between the shapes is the reflection transformation

This means that the transformation of the two triangles is a reflection transformation

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