You visit an aquarium. One of the tanks at the aquarium holds 450 gallons of water. What should the third dimension be so that the diagram shows one possible set of dimensions of the tank?
(1 gal =
231 in.3
)



With a width of 21 inches and a height of 33 inches, the length needs to be
inches.

Answer:

This is a right angle

Step-by-step explanation:

There is a square inside of the triangle.

The correct answer is B) |x| > 6 for the given statement

What is meant by the statement?

A statement is a declarative sentence that can be either true or false. It is a proposition that can be proven using logical reasoning or evidence. Statements are the building blocks of mathematical proofs and are used to establish the truth of mathematical theories and concepts.

According to the given information

The statement “the absolute value of x is greater than 6” can be expressed as an inequality in the following way:

|x| > 6

This means that the distance between x and 0 on the number line is greater than 6 units. In other words, x can be any number that is either less than -6 or greater than 6.

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The changes that Jason should make are:

1. Plan a trip not during the tourist season.

2. In place of renting car, use transportation services of the country.

3. He should go to other places to find a nice hotel.

The solution has been obtained by using cost planning.

What is cost planning?

Estimating expenses, establishing an agreed-upon budget, and managing actual and projected expenditures in relation to that budget are all parts of cost planning and control.

The changes that Jason should make are:

1. Plan a trip not during the tourist season. This is because during the tourist season prices are high.

2. In place of renting car, use transportation services of the country. This is because the local transport will cost him less that the rental.

3. He should go to other places to find a nice hotel. This is because central Turkey is costly and he might find a nice hotel in other areas in less price.

Hence, the required solution has been obtained.

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The value -5°C represents the temperature outside as measured by the digital thermometer in Olivia's car.

In this context, the value -5 represents the temperature outside in Celsius degrees.

The minus sign indicates that the temperature is below freezing point. The Celsius scale is a temperature scale that uses the freezing point of water (0°C) and the boiling point of water (100°C) at standard atmospheric pressure as its reference points.

Thus, a temperature of -5°C means that it is five degrees Celsius below the freezing point of water.

The negative sign indicates that the temperature is below zero degrees Celsius, which is the freezing point of water.

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Area of the patio is -6x² + x + 2 square yards and perimeter of the patio is 6 - 2x yards.

A yard is a unit of measurement used to measure length or distance in both the US customary system and the British imperial system. One yard is equal to 3 feet or 36 inches. In the US customary system, a yard is equal to 0.9144 meters, while in the British imperial system, it is equal to 0.9144 meters or 3 feet. Yards are commonly used for measuring larger distances, such as in construction or landscaping, as well as in some sports like American football and cricket.

The area of the rectangular patio is given by multiplying its length by its width, so the area is:

A = (1 + 2x)(2 - 3x)

Now using distributive property we get,

A = 2 - 3x + 4x - 6x²

Simplifying further, we get:

A = -6x² + x + 2

Therefore, the area of the patio is described by the quadratic equation -6x² + x + 2.

To find the perimeter of the patio, we add up the lengths of all four sides. The length and width are given as (1 + 2x) and (2 - 3x), respectively, so the perimeter is:

P = 2(1 + 2x) + 2(2 - 3x)

Simplifying this expression, we get:

P = 2 + 4x + 4 - 6x

P = 6 - 2x

Therefore, the perimeter of the patio is described by the linear equation 6 - 2x.

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The given exponents 9⁻³/9¹² in the form 9ⁿ is 9⁻¹⁵ respectively.

A number's power or exponent, in other words, tells how many times it must be multiplied by itself.

Any integer, fraction, or decimal can serve as the basis in this situation.

Additionally, the exponent might have either a positive or negative value.

Subtract the exponents to divide exponents (or powers) with the same base.

Given that division is the inverse operation of multiplication, it stands to reason that, just as exponents are added when multiplying numbers with the same base, exponents are subtracted when dividing numbers with the same base.

So, we have the exponents as;
9⁻³/9¹²

Then, solve as follows:

9⁻³/9¹²

9⁻³⁻¹²

9⁻¹⁵

Therefore, the given exponents 9⁻³/9¹² in the form 9ⁿ is 9⁻¹⁵ respectively.

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The length of the rectangle is 15.9 inches. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

The four fundamental operations, often known as "arithmetic operations," can be used to explain any real number. Operations like quotient, product, sum, and difference come after operations like division, multiplication, addition, and subtraction in mathematics.

We are given that the perimeter of a rectangle is 42.4 inches and the length is three times its width.

Let the width be 'x'.

So, length will be 3x.

From this, we get

⇒ Perimeter = 2 (length + width)

⇒ 42.4 = 2 (3x + x)

⇒ 42.4 = 2 (4x)                             (Using addition operation)

⇒ 42.4 = 8x                                  (Using multiplication operation)                

⇒ x = 5.3                                      (Using division operation)

So,

⇒ Length = 3 * 5.3

⇒ Length = 15.9 inches

Hence, the length of the rectangle is 15.9 inches.

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Answer:

2

Step-by-step explanation:

Option 3. x+y≤6 , 32x + 20y ≥ 150. The inequality 32x + 20y ≥ 150 ensures that they bake enough cookies to meet the requirement of making at least 150 cookies.

The right disparity that addresses what is happening is:

32x + 20y ≥ 150

To see the reason why, we want to consider the quantity of treats Luka and Dana can heat in every hour and the all out number of hours they need to prepare. We should expect they have H hours to prepare, where H = 6 for this situation.

Luka and Dana can prepare 32 chocolate chip treats in 60 minutes, so they can heat a sum of 32x treats in x hours. Likewise, they can prepare a sum of 20y snickerdoodle treats in y hours. To make no less than 150 treats, they need to prepare a mix of chocolate chip and snickerdoodle treats in every hour, with the end goal that the complete number of treats they make in H hours is something like 150.

Thus, the imbalance 32x + 20y ≥ 150 guarantees that they heat an adequate number of treats to meet the necessity of making somewhere around 150 treats.

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The maximum value of the sequence is [tex]1/6[/tex], the minimum value is 0, the supremum is [tex]1/2[/tex], and the infimum is 1/6.

The given sequence is: [tex]{1/(2 ^ n) + ((- 1) ^ n)/(n + 1) / n * N}[/tex]

When [tex]n = 1,[/tex] the sequence evaluates to: [tex]1/2 + (-1)^1 / 2 * 2 = 0[/tex]

When [tex]n = 2,[/tex] the sequence evaluates to: [tex]1/4 + (-1)^2 / 3 * 2 = 1/6[/tex]

When [tex]n = 3,[/tex] the sequence evaluates to: [tex]1/8 + (-1)^3 / 4 * 2 = 7/96[/tex]

When [tex]n = 4,[/tex] the sequence evaluates to: [tex]1/16 + (-1)^4 / 5 * 2 = 17/240[/tex]

It appears that the sequence oscillates between positive and negative values, with the negative values getting smaller as n increases.

Therefore, the minimum value of the sequence is at n = 1, where it evaluates to 0.

The maximum value occurs at n = 2, where it evaluates to 1/6.

The term [tex]1/(2 ^ n)[/tex] has a lower bound of 0 and an upper bound of 1.

The term [tex]((- 1) ^ n)/(n + 1) / n * N[/tex] has a lower bound of [tex]-1/4[/tex] and an upper bound of [tex]1/4[/tex].

Therefore, the supremum of the sequence occurs when [tex]n = 1[/tex], where the sequence evaluates to [tex]1/2[/tex].

The infimum of the sequence occurs when [tex]n = 2[/tex], where the sequence evaluates to [tex]1/6.[/tex]

In summary, the maximum value of the sequence is [tex]1/6[/tex], the minimum value is 0, the supremum is [tex]1/2[/tex], and the infimum is [tex]1/6.[/tex]

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The solid displayed in the image is a trapezoidal prism.

A trapezoidal prism is a three-dimensional solid with two parallel trapezoids as its bases, and rectangular or parallelogram sides connecting them. The top and bottom faces are identical, and the side faces are parallelograms.

To classify the solid, look at its properties. The solid has two parallel trapezoids as its bases, and the side faces are parallelograms. Therefore, it is a prism.

Since the bases are not identical rectangles or squares, it is not a rectangular or square prism. However, since the bases are trapezoids, it is a trapezoidal prism.

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The attendance at the movie theatre is;

Children = 142

Students = 44

Adults = 71

What is arithmetic?

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.

Here, we have

Given:

Seating capacity = 257

Charges: Children = $5.00; Students = $7.00; Adults = $12.00

Total sales of ticket = $1870

A number of children, students, and adults were present in the theatre.

Let A, C, and S represent adults, children, and students respectively.

There are half as many adults as there are children; this means that

A = ½C

If the total seat capacity is 257, then

A + C + S = 257

Also, if the total sales of tickets are $1870, then

12A + 7S + 5C = 1870

So, we have two equations to be solved simultaneously.

A + C + S = 257 --- (1)

12A + 7S + 5C = 1860 --- (2)

Substitute ½C for A in (1) and (2)

½C + C + S = 257

Multiply both sides by 2

2(½C + C + S) = 2 * 257

C + 2C + 2S = 514

3C + 2S = 514 ----- (3)

12(½C) + 7S + 5C = 1870

6C + 7S + 5C ,= 1870

6C + 5C + 7S = 1870

11C + 7S = 1870 --- (4)

Make S the subject of the formula in (3)

2S = 514 - 3C

S = ½(514 - 3C)

S = 257 - 1.5C

Substituton 257 - 1.5C for S in (4)

11C + 7(257- 1.5C) = 1870

11C + 1799 - 10.5C = 1870

Collect like terms

11C - 10.5C = 1870 - 1799

0.5C = 71

Multiply both sides by 2

2 * 0.5C = 2 * 71

C = 142

Recall that

S = 257 - 1.5C

S = 257 - 1.5(142)

S = 257 - 213

S = 44

Also, recall that

A = ½C

A = ½ * 142

A = 71

Hence, the attendance at the movie theatre is;

Children = 142

Students = 44

Adults = 71

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Answer:

38 stduentstudents

Step-by-step explanation:

2(100)=$200, if 100 students attend.

38(2)=$76

Breaking even means getting back the same amount you spent. The exact answer would be 37.5, but you can't have half a student.

The proof that f(2x)=3f(x)+1/f(x)+3 is shown below.

To show that f(2x) = 3f(x) + 1/f(x) + 3, we substitute 2x for x in the expression for f(x):

f(x) = x - 1 / x + 1

f(2x) = 2x - 1 / 2x + 1

Next, we substitute x into the expression for f(x) and add the result to itself twice:

f(x) = x - 1 / x + 1

f(x) + f(x) + f(x) = (x - 1 / x + 1) + (x - 1 / x + 1) + (x - 1 / x + 1)

= 3x - 3 / 3x + 3

We can simplify the expression by dividing both the numerator and denominator by 3:

f(x) + f(x) + f(x) = x - 1 / x + 1

= (1/3) (3x - 3) / (1/3) (3x + 3)

= (x - 1) / (x + 1)

= f(x)

Now, we substitute f(x) and f(2x) back into the original equation:

f(2x) = 2x - 1 / 2x + 1

3f(x) + 1/f(x) + 3 = 3(x - 1 / x + 1) + 1/(x - 1 / x + 1) + 3

= (3x - 3 / x + 1) + (1 / (x - 1 / x + 1)) + 3

= (3x - 3 + (x + 1) / (x - 1)) / (x + 1)

= (2x + 2) / (x + 1)

= 2(x + 1) / (x + 1)

= 2

Thus, we have shown that f(2x) = 3f(x) + 1/f(x) + 3.

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An equivalent expression to 18sin^2(x)cos^2(x) that does not contain powers of trigonometric functions greater than 1 is 9 - 9cos(4x)/8.

The power-reducing formulas state that:

sin^2(x) = (1 - cos(2x))/2

cos^2(x) = (1 + cos(2x))/2

Using these formulas, we can rewrite the expression 18sin^2(x)cos^2(x) as:

18sin^2(x)cos^2(x) = 18[(1 - cos(2x))/2][(1 + cos(2x))/2]

Expanding the right-hand side of the equation, we get:

18[(1 - cos^2(2x))/4]

Using the identity cos^2(2x) = (1 + cos(4x))/2, we can simplify further:

18[(1 - (1 + cos(4x))/2)/4] = 9 - 9cos(4x)/8

Therefore, an equivalent expression to 18sin^2(x)cos^2(x) that does not contain powers of trigonometric functions greater than 1 is 9 - 9cos(4x)/8.

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The first bag has a better unit price, at $7.01 per pound compared to $7.13 per pound for the second bag. Based on the unit price, the first bag is a better buy.

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It involves the use of variables, which are represented by letters or other symbols, to represent unknown quantities and to formulate and solve equations and inequalities.

The fundamental operations of algebra include addition, subtraction, multiplication, and division, which are used to manipulate the variables and simplify expressions. Algebra also involves the use of exponents, which are used to represent repeated multiplication, and logarithms, which are used to represent the inverse of exponents.

Algebra is used in a wide range of applications, including science, engineering, economics, and statistics, to model and analyze various phenomena. It is also used as a tool for problem-solving and decision-making, and it provides a powerful framework for reasoning and abstraction in many areas of mathematics and beyond.

To find the unit price, we divide the total price of each bag by its weight:

For the first bag:

Unit price = Total price / Weight = 13.88 / 1.98 = 7.01 dollars per pound

For the second bag:

Unit price = Total price / Weight = 38.99 / 5.46 = 7.13 dollars per pound

Therefore, the first bag has a better unit price, at $7.01 per pound compared to $7.13 per pound for the second bag.

Thus, based on the unit price, the first bag is a better buy.

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The complete question is:

Chau paid 13.88 for a 1.98- pound bag of shrimp at one store. The following week, he paid 38.99 for a 5.46 -pound bag at another store.

Find the unit price for each bag. Then state which bag is better buy based on the unit price.

Answer:

Linear

Step-by-step explanation:

The table represents a consistent function and is therefore linear.

To find the value of a6, we need to first determine the value of a2, a3, a4, and a5 using the given recurrence relation:

a1 = 6

a2 = 5a1 = 5(6) = 30

a3 = 5a2 = 5(30) = 150

a4 = 5a3 = 5(150) = 750

a5 = 5a4 = 5(750) = 3750

Now, we can find a6 using the recurrence relation:

a6 = 5a5 = 5(3750) = 18750

Therefore, the value of a6 is 18750.

Francine can type 38 words per minute at this rate.

To find out how many words Francine can type per minute, we need to convert the time she took to type the words into minutes. Since there are 60 minutes in 1 hour, 1 hour and 30 minutes is equivalent to 1 × 60 + 30 = 90 minutes.

Next, we can use the formula:

words per minute = total words / total minutes

where "total words" is the number of words Francine typed (3,420) and "total minutes" is the time she took in minutes (90).

Substituting these values into the formula, we get:

words per minute = 3,420 / 90 = 38

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The probability statement is written below:

The middle 40% of heights fall between the 10th and 90th percentiles of the standard normal distribution.

The z-scores of the 10th and 90th percentiles are -1.28 and 1.28 respectively.

The heights in the given normal distribution are found using the formula:

where

The height of the 10th percentile is:

X = 66 + (-1.28)(2.5)

X = 62.8 inches

The height of the 90th percentile is:

X = 66 + (1.28)(2.5)

X = 69.2 inches

Therefore, the middle 40% of heights fall between 62.8 inches and 69.2 inches and the probability statement will be P(62.8 ≤ X ≤ 69.2) = 0.4

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The shape resulting from a horizontal cross section, a vertical cross section, and an angled cross section of the cube are:

horizontal cross section: square.

vertical cross section: square.

angled cross section: rectangle.

In this exercise, you are required to use a graphing tool to investigate and determine the cross-sections of the given three-dimensional geometric object (cube), by passing different planes through them.

By critically observing the cross-sections of the three-dimensional geometric object (cube) I used, we can reasonably infer and logically deduce the following types of quadrilateral based on the cross-sections;

A horizontal cross section would produce a square.

A vertical cross section would produce a square.

An angled cross section would produce a rectangle.

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The mean of the given set of numbers is 21.8. and median is 25.

In mathematics and statistics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by adding up all the numbers in the set and then dividing by the total number of values. The mean is also known as the arithmetic mean or average.

To find the mean and median of the given set of numbers, we can follow these steps:

Arrange the numbers in order from smallest to largest: 2, 5, 25, 35, 42.

To find the mean, add up all the numbers and divide by the total number of numbers:

Mean = (2 + 5 + 25 + 35 + 42) / 5

= 109 / 5

= 21.8

Therefore, the mean of the given set of numbers is 21.8.

To find the median, we need to find the middle number in the ordered list. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.

In this case, there are 5 numbers, so the median is the middle number, which is 25.

Therefore, the median of the given set of numbers is 25.

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As per the question of trigonometry the another equation that describes the given graph is

y = -cos5x. And after verifying the equation given in the question as well as the new equation we conclude that both equations are equal.

The sine and cosine function graphs' main characteristics are:  

a. We can use trigonometric identities to simplify the given equation in order to describe the graph using a different equation.

b. We can simplify the following equation and compare it with  [tex]y = -cos(5x)[/tex]to see if the two equations are equivalent.

We obtain this by applying the same trigonometric identity as before.

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(2+3)²=25, base=2+3, exponente=2, (-8)²=64, 3/5 expressed as a percent is 60%, a=7, 20 0/3 = 60/3 = 20/1.

What is percentage?

Percentage is a way of expressing a fraction or decimal as a portion of 100. It is often used to describe proportions or rates in various fields, such as finance, economics, and statistics.

What is exponent?

An exponent is a mathematical operation that involves raising a number to a power. The exponent represents the number of times the base is multiplied by itself. For example, in 2^3, 2 is the base and 3 is the exponent, and it means 2 multiplied by itself three times, resulting in 8.

According to the given information:

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The given parallelogram is not a rectangle.

One of the tests for a rectangle is if a right angled triangle can be created by diagonally dividing the rectangle .

The test for a right - angled triangle is the Pythagorean Theorem which is :

Side ² + Side ² = Hypotenuse ²

Using, the dimensions, check to see if there is a right triangle :

7. 2 ² + 9. 1 ² = 12 ²

134. 65 ≠ 144

There is no right angled triangle so this is a parallelogram that is not a rectangle .

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The senior math contest ended at 10:40 pm on Sunday

If the senior math contest began at 6:00 am on a Sunday and ended 1000 minutes later, we can add 1000 minutes to the starting time to find the ending time.

To do this, we can first convert the starting time of 6:00 am into minutes. There are 60 minutes in one hour, so 6:00 am is equivalent to:

6 hours × 60 minutes/hour = 360 minutes

Now, we can add 1000 minutes to this starting time:

360 minutes + 1000 minutes = 1360 minutes

Finally, we can convert this total number of minutes back into hours and minutes.

Since there are 60 minutes in one hour, we can divide 1360 minutes by 60 to get:

1360 minutes ÷ 60 = 22 hours and 40 minutes

Therefore, the senior math contest ended at 10:40 pm on the day (Sunday).

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a) The probability that an American chosen at random died as a passenger car occupant last year is 0.0042.

b) The probability that you died as a passenger car occupant last year is 0.0042

c) The probability that you will die as a passenger car occupant next year P(C) is 0.0042.

d) The probability that an American chosen at random will die as the result of a tornado next year is 0.0000018

e) The probability that you will die as the result of a tornado next year is 0.0000018

The given probabilities are determined as follows:

The probability that an American chosen at random died as a passenger car occupant last year is:

P(A) = 13,100 / 312,000,000

P(A) = 0.0042

b) The probability that you died as a passenger car occupant last year is:

P(B) = 13,100 / 312,000,000

P(B) = 0.0042

c) The probability that you will die as a passenger car occupant next year P(C) would be 0.0042 since the values do not change.

d) The probability that an American chosen at random will die as the result of a tornado next year is:

P(D) = 553  / 312,000,000

P(D) = 0.0000018

e) The probability that you will die as the result of a tornado next year, P(E) = 0.0000018

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Answer: 11 Cookies

Step-by-step explanation:

let C be cookies

17($3.25) + 1.60C = $72.85

$55.25 + 1.60C = $72.85

1.60C = $17.60

C=11

She sells 11 cookies

Answer:

11

Step-by-step explanation:

To be able solve, you need to do 17 x 3.25, which would give you 55.25. Then you need to subtract 72.85 by 55.25, which is 17.60. Now divide 17.60 by 1.60. This should give you 11. Therefore, she sold 11 cookies.

I AM SO SORRY IF THIS DIDN'T MAKE SENSE!

a) Jill receives £45

b) Jack receives £20 the following Christmas

c) Jack will be 5/4 years old, which is equivalent to 1 year and 3 months when he receives £25 from Uncle Fred.

Explain the term years

Years are a unit of time measurement used to quantify the duration of one complete orbit of the Earth around the sun. A year consists of 365 days, except in a leap year when an extra day is added. The concept of a year is used in various fields, including astronomy, geology, and history.

According to the given information

(a) Let's first find the total ratio of their ages:

1 + 3 = 4

So Jack's share will be:

1/4 x £60 = £15

And Jill's share will be:

3/4 x £60 = £45

Therefore, Jill receives £45.

(b) The next Christmas, Jack will be 2 and Jill will be 4. We can use the same ratio to find Jack's share:

2/6 x £60 = £20

So Jack receives £20.

(c) Let x be the age of Jack when he receives £25 from Uncle Fred. We know that:

1/4 x £60 = £25

Multiplying both sides by 4/60, we get:x = 5/4

So Jack will be 5/4 years old, which is equivalent to 1 year and 3 months, when he receives £25 from Uncle Fred.

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Answer:

a. 31 total trees

b. Least common range is 85-90

Step-by-step explanation:

A. On the side of the chart it is labeled frequency. That is where you will find the number of tree per height range. The tops of the bars indicate the number is directly across.
B. Looking at the lowest bar or the smallest amount of trees indicate the lowest range or the least common range.