I arrived home to discover that my 50-foot by 40-foot basement has 18 inches of water in it! There are about 7.5 gallons in 1 cubic foot of water. How much water is in the basement?
Calculate using the most appropriate units to describe the amount of water, and state your answer in a meaningful sentence.

The expression of angle in radian is -0.071.

Angles can be measured in two units: degrees and radians.

Radian is a unit of measurement for angles, and it is defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.

To be more precise, an angle of one radian is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.

The expression of angle in radian is calculated as follows;

θ = tan⁻¹ (-0.071)

θ = -0.071

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The interval that will have the highest frequency will be: C. 11 - 15.

The interval that will have the highest frequency will be 11 - 15. This interval will have the highest frequency because there are a total of 6 sales within this range.

The other intervals have sales that are 5 and below. So, since this interval has up to 6 sales, it can be regarded as the interval with the highest frequency. Frequency refers to how often something occurs. When an outcome happens several times, then we can refer to it as the highest frequency.

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Step-by-step explanation:

y=m(x-x1)+y1

y=-2(x-4)+0

y=2x-8+0

y=2x-8

The height of the larger cone is 71.13 meters

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

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

Scale factor = h1/h2

So, we have

h1/h2 = √(1883/7352)

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

36/h2 = √(1883/7352)

So, we have

h2 = 36 * √(7352/1883)

Evaluate

h2 = 71.13

Hence, teh height is 71.13

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snip, that's wrong nvm (not sure how to delete)

Sin A Cos A, and Tan A can be found respectively as follows:

1. 41.81°.

2. 44.19 degrees

2. 60 degrees

The angles can be found by following the rules for right-angled triangles. This can be achieved in the following ways:

1. sin A= opposite/hypotenuse

sin A = 6/9

Now we take the sine inverse:

sin^-1(6/9)

=  41.81°.

2. Cos 45° = Adjacent/hypotenuse

= cos 45° = x/4

x = cos 45° × 4

= 0.707 × 4

= 2.82

cos A = b2 + c2 – a2 ÷ 2bc

2.8² + 4² - a² ÷ 2×2.8×4

23.84 - 2.8² ÷ 22.4

23.84 - 7.84 ÷ 22.4

Cos A = 0.7142

= 44.19 degrees

3. tan A = Opposite/Adjacent

tan 60°  = 4/x

x = 4/tan 60°

x = 4/1.732

= 2.309

Tan A = 4/2.309

= 1.732

= 60 degrees

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The reduced form of the matrix is [tex]\begin{bmatrix}1 &-\frac{4}{7} &\frac{4}{7} \\0& 11& 79\end{bmatrix}[/tex]

A matrix is a rectangular array of numbers arranged in rows and columns. In linear algebra, matrices can be used to represent linear transformations and solve systems of linear equations.

In the given matrix, we need to perform a row operation to get a 1 in row 1, column 1. Row operations are operations performed on the rows of a matrix to transform it into another matrix that is equivalent in terms of solutions to a system of linear equations.

The three types of row operations are:

Swapping two rows.

Multiplying a row by a non-zero constant.

Adding a multiple of one row to another row.

To perform this row operation, we first multiply row 1 by 12 to get a multiple of 12 in the first column of row 1:

[tex]\begin{bmatrix}84 &-48 &96 \\-12& 7& -13\end{bmatrix}[/tex]

Next, we add row 1 to row 2 multiplied by 2 to get a 0 in column 1 of row 2:

[tex]\begin{bmatrix}84 &-48 &96 \\0& 11& 79\end{bmatrix}[/tex]

Finally, we can divide row 1 by 84 to get a 1 in row 1, column 1:

[tex]\begin{bmatrix}1 &-\frac{4}{7} &\frac{4}{7} \\0& 11& 79\end{bmatrix}[/tex]

Now we have a 1 in row 1, column 1, and the matrix is in row echelon form.

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A. Area of the rectangle, in standard form is: 14x² + 19x - 3

B. The degree of a polynomial is: 4. It has 4 terms (4x², 3y, -6x^4y, and 4.); C ALWAYS result in another polynomial.

A polynomial is a mathematical expression consisting of variables and coefficients that involves only the operations of addition, subtraction, and multiplication of non-negative integer exponents.

Part A:

Area of the rectangle = (7x - 1)(2x + 3) = 7x(2x + 3) -1(2x + 3)

= 14x² + 21x - 2x - 3

Combine like terms:

Area of the rectangle = 14x² + 19x - 3 (standard form)

Part B: Given the expression, 4x² + 3y - 6x^4y + 4,

The degree of a polynomial is the highest exponent of its variable.

Therefore, the degree is 4.

It has 4 terms, which are: 4x², 3y, -6x^4y, and 4.

Part C: When two polynomials are subtracted, multiplied, or added, it will ALWAYS result in another polynomial.

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The two equivalent expressions are 6(x − y) and 6x − 6y.

These expressions look different but their simplified forms are same expressions are called equivalent expressions.

The 1st expression shows subtracting the number of packages of cherry snacks from the number of packages of strawberry snacks in each box.

When we multiplying the difference by the number of boxes then, it will be: 6(x-y)

Now, total number of cherry snacks and subtracting it from the total number of strawberry snacks will be 6x - 6y. So, equivalent expressions means in terms of situation are 6(x − y) and 6x − 6y.

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Based the provided information, the t-value is approximately 1.824.

We shall work out the t-value by calculating the difference between the sample mean and the population mean, divided by the standard error of the mean.

We shall use the t-test formula to calculate the t-value:

t = (sample mean - population mean) / (sample standard deviation / [tex]\sqrt(sample size)[/tex])

where:

sample mean = 86.3

population mean = 83.5

sample standard deviation = 7.2

sample size = 22

Plugging in these values, we have:

t = (86.3 - 83.5) / (7.2 / √22)

t = 2.8 / (7.2 / 4.69)

t = 2.8 / 1.535

t ≈ 1.824

Therefore, the t-value is approximately 1.824.

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Answer:

FV = PV x (1 + r)^n

where:

FV = future value

PV = present value (the amount to be deposited today)

r = interest rate per period (in this case, per year)

n = number of periods (in this case, 8 years)

Plugging in the given values, we get:

$60,000 = PV x (1 + 0.09)^8

Simplifying this equation:

PV = $60,000 / (1 + 0.09)^8

PV = $60,000 / 1.999^8

PV = $60,000 / 3.058

PV = $19,602.68

Therefore, the amount that needs to be deposited in the bank today to accumulate $60,000 in 8 years with an interest rate of 9% is $19,602.68.

I hope this helps.

The conic section that is formed when a right, circular cone is intersected by a plane that is parallel to the base of the cone is a circle

The summary statement from the question is given as

A plane parallel to the base of a circular cone that intersects the cone.

By definition, a circle is the cross-section that is parallel to the base of a cone

This means that when a cone is cut through the base, the resulting shape is a circle

So, the conic section that is formed when a right, circular cone is intersected by a plane that is parallel to the base of the cone is a circle

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The surface area of the triangular prism is 1740cm²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of a prism is expressed as;

SA = 2B + ph

where B is the base area

p is the perimeter of the base

h is the height of the prism.

Base area = 1/2 bh

= 1/2 × 10 × 24

= 24×5

= 120 cm²

The perimeter of the base = 24+10+26

= 60cm

height = 25 cm

Therefore the surface area of the prism is

SA = 2 × 120 + 60 × 25

SA = 240+ 1500

SA = 1740 cm²

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The solution of the given inequality is x ≤ 13/4

Since Inequality can be defined as the relation which makes a non-equal comparison between two given functions.

We are given the Inequality  as;

4x + 45 ≤ 57

Solving;

4x + 45 ≤ 57

4x ≤ 57 - 45

4x  ≤ 13

x ≤ 13/4

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Hence, 8 and 14 are the two positive integers as Y must be 8 because we are seeking for positive integers.

All entire numbers (optimistic, negative, and zero) as well as their opposites are included in the category of integers. These can be visualised as evenly spaced-apart points with zero in the middle on a number line. The following numbers are part of the set of integers, which is represented by the symbol Z . The numbers of pupils in an educational setting, the weather in degrees Celsius, or the location of an object in relation to a reference point are all examples of quantities that can be represented by integers and are counted or measured in whole units. They adhere to specific arithmetic laws and can be added, deducted, multiplied, and divided.

given

Assume that x and y are the two positive integers, with x being the greater of the two. Finally, we may convert the provided data into equations:

In order to remove x, we can replace the first equation with the second equation as follows:

[tex](2y-2)^2 + y^2 = 260[/tex]

Adding and subtracting:

[tex]4y^2 - 8y + 4 + y^2 = 260[/tex]

combining comparable phrases

[tex]5y^2 - 8y - 256 = 0[/tex]

Using the quadratic formula, we can solve this quadratic equation:

y = [8 ± sqrt(8^2 - 45(-256))] / (2*5)

y = [8 ± sqrt(3368)] / 10

y ≈ 8.6 or y ≈ -9.4

Y must be 8 because we are seeking for positive integers. The first equation can then be used to determine x:

x = 2y - 2 = 2(8) - 2 = 14

Hence, 8 and 14 are the two positive integers as Y must be 8 because we are seeking for positive integers.

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The median number of eggs laid in a year is 231 from the given data, option A is correct.

The data table shows the numbers of eggs laid by individual chickens in a year.

Now, We can arrange it into ascending order as;

⇒ 222, 229, 229, 231, 234, 235, 262

Since, There are 7 terms

Hence, Median = (7 + 1)/2

= 4th term

= 231

Hence, the median number of eggs laid in a year is 231, option A is correct.

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The initial velocity of the car before the brake was pulled is 30m/s

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

A car pulls the emergency hand brake, accelerating at -4.0 m/s2 for 7.5 seconds

This means that

Acceleration = -4.0m/s^2

Time = 7.5 seconds

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

Initial velocity = -Acceleration  * Time

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

Initial velocity = 4  * 7.5

Evaluate

Initial velocity = 30

Hence, the initial velocity is 30

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Answer:

1 inch = 0.6 miles

= 9 inches = 0.6 miles*9

= 9 inches = 5.4 miles

Hence, the answer is 5.4 miles.

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The calculated value of the length RP is 107 units

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

The circles and the tangent lines

Start by calculating the segment PQ using the following Pythagoras theorem

PQ² = (50 + 11)² + 11²

Evaluate

PQ² = 3842

So, we have

PQ = 62

The value of the length RP is then calculated as

RP = PQ + TU

So, we hav

RP = 62 + 45

Evaluate

RP = 107

Hence, the value of the length RP is 107 units

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Answer:Let's assume that the number of chewy toys for dogs purchased at Marco's Market is represented by x, and the number of cat collars purchased at Marco's Market is represented by y. Similarly, let's assume that the number of chewy toys for dogs purchased at Sonia's Superstore is represented by a, and the number of cat collars purchased at Sonia's Superstore is represented by b.

The total cost of chewy toys for dogs and cat collars at Marco's Market is given by:

2x + 8y

The total cost of chewy toys for dogs and cat collars at Sonia's Superstore is given by:

4a + 4b

We want to find values of x, y, a, and b such that:

2x + 8y = 4a + 4b

Simplifying the equation, we get:

x + 4y = 2a + b

We also know that the total amount set aside for the purchases is $96. Therefore, we have:

2x + 8y + 4a + 4b = 96

Simplifying the equation, we get:

x + 4y + 2a + b = 48

Now, we can plot the graph of the equation:

x + 4y = 2a + b

To plot the graph, we can rearrange the equation as follows:

4y - b = 2a - x

y = (2a - x + b)/4

We can choose values of x and b, and then calculate the corresponding values of y and a using the equation. For example, let's choose x = 0 and b = 8. Then, we have:

y = (2a - 0 + 8)/4 = (2a + 8)/4 = 0.5a + 2

Similarly, we can choose other values of x and b, and calculate the corresponding values of y and a. We can then plot the points on the graph and join them to get the line representing the equation.

Here is the graph:

Graph

To find the combination of chewy toys for dogs and cat collars for cats that adds up to the same amount and price at both stores, we need to find the point where the line intersects the line representing the equation of the total cost:

x + 4y + 2a + b = 48

We can find this point by solving the two equations simultaneously. However, we can also use the graph to estimate the point. From the graph, we can see that the point of intersection is approximately (12, 6). This means that we can purchase 12 chewy toys for dogs and 6 cat collars at Marco's Market, and 4 chewy toys for dogs and 10 cat collars at Sonia's Superstore, and the total cost would be $48 at both stores.

Step-by-step explanation:

Answer:

Triangle A = scalene

Triangle B = scalene

Triangle C = equilateral

Step-by-step explanation:

scalene triangle = all lengths are different

isosceles triangle = 2 side lengths are the same

equilateral triangle = all 3 side lengths are the same

The solution to the equation 2,401 = 7⁶⁻²ˣ is x ≈ 1.4076.

In mathematics, a logarithm is the inverse operation to exponentiation. Given a base b and a positive number y, the logarithm of y with respect to the base b is the exponent to which b must be raised to yield y. In other words, if x is the logarithm of y with respect to base b, then bˣ = y.

We can begin solving this equation by isolating the exponential term on one side of the equation and taking the logarithm of both sides.

2,401 = 7⁶⁻²ˣ

Taking the logarithm base 7 of both sides:

log₇(2,401) = log₇(7⁶⁻²ˣ )

Using the property of logarithms that states that log base a (aᵇ) = b, we can simplify the right-hand side of the equation:

log₇(2,401) = (6-2x)log₇(7)

Since log₇(7) = 1, we can further simplify:

log₇(2,401) = 6-2x

-2x = log₇(2,401) - 6

x = (6 - log₇(2,401))/2

Using a calculator, we find:

x ≈ 1.4076

Therefore, the solution to the equation 2,401 = 7⁶⁻²ˣ  is x ≈ 1.4076.

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Answer:

711 L 936 mL

Step-by-step explanation:

3 L 456 ml times 206=711L 936mL

I hope this helps

The sculpture's base length = 9 cm and the height of sculpture is found as 6 cm.

The base and apex are joined to form a pyramid. To identify them from the base, the triangular sides are also also referred to as lateral faces. In a pyramid, the apex, which creates the triangle face, is connected to each base edge.

Put the values and find the length.

162 = 1/3 (x)² (x-3)

162 * (3) =  (x)² (x-3)

486 = x²(x-3)

486 = x³ - 3x²

x³ - 3x² - 486 = 0

(use a graphing tool or calculator equation mode).

x = 9

Thus,

side length of sculpture = 9 cm

height of sculpture = 9 - 3   = 6cm

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Correct question:

Nathan has a sculpture in the shape of a pyramid. The height of the sculpture is 3 centimeters less than the side length,x,of its square base. Nathan uses the formula for the volume of a pyramid to determine the dimesnsioms of the sculpture.

V=1/3 a^2h

Here, a is the side length of the pyramids square base and h is it’s height.

If 162 cubic centimeters of clay were used to make the sculpture, the equation x^3 + _x^2+ _ =0 can be used to find that the length of the sculptures.  base is _ centimeters.

The distance from town A that they will be,  when they will pass each other is  44 4/9 .

It should be noted that time traveled in each segment is constant, which implies that in this case the average speed can be regarded as the simple mean of speeds. An in the case whereby the distance traveled in each segment is constant, average speed can be described to be the reciprocal of simple mean .

This can be expressed mathematically as

Average speed = Reciprocal [ 1/40 & 1/50].

Average speed = Reciprocal of (1/40 + 1/50)/2

= Reciprocal of [(5+4)/400]

= 44 4/9 .

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