A swimming pool has 500 gallons in it and is leaking. The change in the amount of water in the pool is -3 gallons per hour. How many gallons would the pool contain after 6 hours?

90, 000 will be the total number of different phone extensions.

A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.

Given, A company wants to have ​5-digit phone extensions with the first digit not being zero.

This problem is an application of the Basic Counting Rule which was discussed above. We want to compute the number of different 5-digit phone extensions.

there are 10 different digits, which are 0,1,2,3,4,5,6,7,8,9. The first digit can't be 0.

There are 9 choices for the first digit. For each choice of the first digit, there are 10 choices for the second digit. For each choice of the first and second digits, there are 10 choices for the third digit, and so on.

According to the Basic Counting Rule, we know that the total number of phone extensions is the product of the number of ways to choose each digit (the product of the 6 above numbers).

the total number of different phone extensions is = 9 *10 *10 *10 *10

therefore, the total number of different phone extensions is = 90,000.

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Therefore , the solution of the given problem of data plotting comes out to be Pre image is located in II quadrant.

Graphing the correlation between two additional variables is the most common way to use a chart to present data. It is also permitted to use hand-drawn or digitally generated diagrams. Go three pieces up and 2 types to the right starting at the origin. Displaying the numbers for rows 2, 3, and 4 on the standard system is crucial. Make sure to be very clear in what you say.

Here,

Given :

A figure having pre image and post image ,

We have to find in which quadrant the pre image is located,

So,

In order to find that,

We see the image are in quadrant II and quadrant III

Since ,

After II quadrant III quadrant comes,

Thus , Pre image is located in II quadrant.

Therefore , the solution of the given problem of data plotting comes out to be Pre image is located in II quadrant.

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Answer:

Step-by-step explanation:

divide $43.74 by 6 = 7.29 per pair

a) Strings of probability 0s and 1s, which reflect the results of the coin flips, make up the sample space, S.

In (b), I A wins equals (1, 01, 001, 0001), (ii) B wins equals (0, 10, 010, 0010), and (iii) (A U B) equals (1, 0, 01, 10, 001, 010, etc.).

(a) Strings of 0s and 1s, which reflect the results of the coin flips, make up the sample space, S. Each 0 denotes a tail, while each 1 denotes a head. Since there is no restriction on the number of coin flips that can take place, the sample space is unlimited. Due to the fact that every result can be expressed as a string of 0s and 1s, it is also a finite collection. (b) I A wins means that A flipped a head before B or C, and the results are 1, 01, 001, 0001, etc. (ii) B wins = 0 (zero), 10 (one), 010 (zero), 0010 (zero), etc., indicating that B flipped a head before A or C. (iii) (A U B) = 1, 0, 01, 10, 001, 010, etc., indicating that either A or B turned over a coin before C. Presumably, A flips first, followed by B, C, then A, and so on.

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The completion of the equation to find w, the number of weeks until Ashely and Tanner have the same amount in their savings accounts is 25w + 450 = 40w + 200.

An equation is a mathematical statement claiming that two or more mathematical expressions are equivalent or equal.

Equations are depicted with the equation symbol (=) to show equality of the expressions.

                                       Ashely  Tanner

Savings                            $450    $200

Planned weekly deposits $25      $40

Let the number of weeks to save equal amounts = w

Ashely's total savings in w weeks = 25w + 450 ... Equation 1

Tanner's total savings in w weeks = 40w + 200 ... Equation 2

For the two friends to have an equal amount, Equation 1 must equal Equation 2:

25w + 450 = 40w + 200

-15w = -250

w = 16.67

Thus, for Ashely's and Tanner's savings to become equal in amount, it would take 16.67 weeks.

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If a translation is applied to square ABCD,  the y-coordinate of B' = y_coordinate of B - 8 = -8.

What is the translation?

The translation is a term used in geometry to describe a function that moves an object a certain distance. The object is not altered in any other way. It is not rotated, reflected or re-sized. In a translation, every point of the object must be moved in the same direction and for the same distance.

When a translation of T-3, -8 is applied to square ABCD, it means that each point in the square is moved 3 units to the left and 8 units down.

The y-coordinate of B is found by moving 8 units down from the original y-coordinate of B.

Therefore, If a translation is applied to square ABCD,  the y-coordinate of B' = y_coordinate of B - 8 = -8.

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Both cash and credit sales for the period are reported on the income statement of a retail company. So the correct statement is option (b) Both cash and credit sales for the period.

An income statement shows the income, expenses, and profitability of a company for a specified period. It is also sometimes referred to as the Income Statement (P&L) or Income Statement. it shows you:

Revenue from sales of products or services. 

An income statement shows how much revenue a company has generated, what expenses it has spent, and what income it has allocated over a period of time. You can use it to understand your company's business model and understand how your company is competitive within your industry. 

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Two triangles having two pairs of congruent sides and a pair of congruent angles do not necessarily meet the SAS congruence criterion, therefore Angie is incorrect.

The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.

An included angle is found between two sides that are under consideration.

In the image, the triangles are congruent to each other by the Side-Angle-Side Congruence Theorem (SAS).

Thus, two triangles having two pairs of corresponding sides and one pair of corresponding angles that are congruent to each other is not enough justification for proving that the two triangles are congruent based on the SAS Congruence Theorem.

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The terms, when sorted into groups of " like terms " gives:

Like terms :

Unlike terms :

To sort a set of algebraic terms into groups of like terms, you must look for terms that have identical variables and exponents. These terms can be combined and simplified using the rules of addition and subtraction. in this scenario, they include: - 7 y ² and y ², 0. 5 kt and - 10 kt, 6 and 9.

Terms that have different variables or exponents are considered unlike terms and cannot be combined in this way. They include : - 4 p and p ², 5 x and 5, 3 ad and 2 bd .

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The line's equation is y = 3x - 3 with the z-intercept (-1, 0) and the y-intercept (0, -3).

What do intercepts mean? The x-intercept and y-intercept are the points at which a line crosses the x- and y-axes, respectively.

Put x = 0 and work out y to determine the y-intercept. The purpose will be (0, y). Set y = 0 and solve for x to determine the x-intercept. The purpose will be (x, 0).

It gives both a slope and an intercept, hence the name "slope intercept form." Thus, this is your slope. You can move by keeping in mind that slope is rise over run.

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Answer:

6000 bushels per hour.

Step-by-step explanation:

Let's assume that the rate at which the conveyor unloads wheat is proportional to its width.

If a 14-inch conveyor unloads 4000 bushels per hour, we can write this as:

Rate = 4000 bushels/hour * (Width of conveyor) / 14 inches

Now, if we want to find the rate at which an 21-inch conveyor would unload wheat, we can simply plug in the width into the equation:

Rate = 4000 bushels/hour * (21 inches) / 14 inches

Rate = 6000 bushels/hour

Therefore, an 21-inch-wide conveyor would unload 6000 bushels per hour.

The expression that represents the cube root of 1+i​ is ∛(1 + i)

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

The cube root of 1+i​

In mathematics and algebra, the cube root is represented as ∛

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

The cube root of 1+i​ is ∛(1 + i)

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The relative frequency or proportion of a given category is the number of sample items in that category divided by the total sample size.

The relative frequency or proportion of a given category is a measure of how often that category appears in a sample of categorical data. It is calculated by dividing the number of sample items in that category by the total sample size. For example, if a sample contains 10 items and three of them are in category A, then the relative frequency for category A is 3/10 or 0.3. This indicates that 30% of the sample items are in category A. Relative frequencies are used to compare categories within a sample, as well as to compare samples of different sizes. This allows us to draw conclusions about the frequency of occurrence of different categories within a population.

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by trigonometry the magnitude of the force P so that the resultant force exerted on the stake is vertical. The magnitude of the force is 196.6 N.

When a force system acts on an item, the difference between the forces is referred to as the Resultant force. When an item is under the influence of two or more forces, the combined force may be calculated by adding up the separate forces. The forces in all directions will be the same for all the forces if they are all acting in the same direction. The SI unit for resultant force is the Newton.

Given that,

α = 30°

Using the triangle rule, and the law of sines:

120 N / Sin 30° = P / Sin 25°

or, P =  (Sin 25° /  Sin 30°) × 120

or, P = 101.428 N

or, P = 101.4 N

and also, θ = 180 - 25 - 30

θ = 125°

the value of resultant is:

120 N / Sin 30° = R / Sin 25°

or, R = 196.6 N

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The proportion could be used to find the length of the actual wall, in feet is 2/5=13x/2, the correct option is B

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Given;

1 inch: 2 1/2 feet

One wall of the house was represented by a line 6 1/2 inches long on the floor plan.

Now,

6 1/2 inches= 13/2inch

1 inch: 2 1/2 feet=5/2feet

13/2inch=13/2 * 5/2

=65/4

b. 2/5=13x/2

Therefore, according to the given proportion the answer will be 2/5=13x/2.

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Answer: 1468.17

Step-by-step explanation:

The Surface area of Figure is  496 ft².

The Volume of Figure is 608 ft³.

A 3D object's surface area is the entire area that all of its faces cover. For instance, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it. It is consistently expressed in square units.

Given:

Surface Area of Pyramid

= Base area + 1/2 x P x l

= 64 + 1/2 x 32 x 3

= 64 + 16 x 3

= 112 ft²

and, Volume of Pyramid

= 1/2 x 64 x 3

= 96 ft³

So, total Surface Area

= 112 + 384

= 496 ft²

and, The total volume

= 96 + 512

= 608 ft³

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Step-by-step explanation:

(n+1)! = (n+1)n(n-1)(n-2)...×3×2

16n! = 16n(n-1)(n-2)...×3×2

16(n-1)! = 16(n-1)(n-2)...×3×2

we can now divide both sides by (n-1)! and get

(n+1)n = 16n + 16

n² + n = 16n + 16

n² - 15n - 16 = 0

1×n² - 15n - 16 = 0

we try to bring this into a form

(n + a)(n - b)

one factor has to contain "-", because we have "-16".

and because -15 = 1 - 16, we see that

a = 1

b = 16

n² - 15n - 16 = (n + 1)(n - 16)

and that is 0, when at least one of the factors is 0, because 0×... = 0.

so, the solutions are

n = -1

n = 16

n = -1 does not make any sense for n!

so, n = 16 is the solution.

Answer:

4. y = 3x

Step-by-step explanation:

A proportional relationship is one in which the ratio of two variables is always constant. This is also known as direct proportion.

Out of the given options, the equation that shows a proportional relationship is:

4. y = 3x

In this equation, the ratio of y to x (y/x) is always 3, so the relationship between y and x is proportional. As x increases, y also increases at a constant rate, and as x decreases, y decreases at a constant rate. This type of relationship is often represented by the equation y = kx, where k is the constant of proportionality.

hey, I checked on desmos, which is a calculator for this type of stuff, and got 1.8,5.2. So I think that's one solution. Sorry if wrong.

(AUB) will be equal to {2,4,6,7,6,10,11, .....even numbers). The empty set, or 0, is one of the most significant sets in mathematics.

A set that contains items from all related sets, without any repetition of elements, is known as a universal set (often symbolized by the letter U). If A and B are two sets, for example, A = 1, 2, 3 and B = 1, a, b, c, then U = 1, 2, 3, a, b, c is the universal set that these two sets belong to.

A set with no elements is referred to as a null set or empty set.  The null set is the intersection of two disjoint sets, or sets that have no elements in common.

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Dustin walk at the rate of 6 miles per hour.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Dustin can run 2 miles per hour faster than he can walk around the track. If Dustin walks around the track in 20 minutes and runs around the track in 15 minutes.

Let the speed of Dustin walking = x

We know that;

Speed = Distance / Time

For walking;

Speed = Distance / Time

x = Distance / (20/60)

x × 20/60 = Distance

Distance = x/3 miles

For run;

Speed = Distance / Time

⇒ x + 2 = (x/3) / (15/60)

⇒ 3 (x + 2) = 4x

⇒ 3x + 6 = 4x

⇒ 4x - 3x = 6

⇒ x = 6

Thus, Dustin walk at the rate of 6 miles per hour.

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A correct answer is option (B) 7.78%. so, the interest rate is  7.78% being charged in her lease.

What is the interest rate?

Interest rate is the amount charged over and above the principal amount by the lender from the borrower. In terms of the receiver, a person who deposits money to any bank or financial institution also earns additional income considering the time value of money, termed as interest received by the depositor.

The interest rate in a lease can be calculated using the money factor, which is essentially a type of interest rate used in auto leasing.

To calculate the interest rate from the money factor, multiply the money factor by 2400.

In this case, the money factor is 0.00324, so the interest rate would be:

0.00324 * 2400 = 7.776%

Therefore, the correct answer is option (B) 7.78%. so, the interest rate is  7.78% being charged in her lease.

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A correct answer is option (B) 7.78%. so, the interest rate is 7.78% being charged in her lease.

The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.

The money factor, which is essentially a sort of interest rate utilized in auto leasing, can be used to compute the interest rate in a lease.

By multiplying it by 2400, you can determine the interest rate from the money element.

Given that the money component in this situation is 0.00324, the interest rate would be:

The result of three consecutive conversions from an interest rate to a money factor is 2400 (1/2 × 1/12 × 1/100). 6/2400 = 0.0025 money factor, which can be multiplied by the entire amount borrowed to see how much the monthly interest would be roughly.

(1/2 × 1/12 × 1/100). 6/2400 = 0.0025

0.00324 × 2400 = 7.776%

Therefore, the correct answer is option (B) 7.78%. so, the interest rate is  7.78% being charged in her lease.

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It is not possible to make the statement true for one value of x, as the two linear functions have the same slope.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The number of solutions for a system of two linear functions is defined as follows:

The functions for this problem are defined as follows:

As the two functions have the same slope, there are two possible number of solutions.

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Answer:

$44.236.20

Step-by-step explanation:

First, we need to calculate the cost of purchasing new seats for all the buses. The company has 13 buses and each bus has 28 seats, so the total number of seats to be replaced is 13 * 28 = 364 seats. The cost of purchasing each seat is $89.40, so the total cost of purchasing new seats for all the buses is 364 * $89.40 = $32,610.40.

Next, we need to calculate the cost of installing new seats for all the buses. The cost of installing each seat is $31.70, so the total cost of installing new seats for all the buses is 364 * $31.70 = $11,625.80.

Finally, we need to add the cost of purchasing and installing new seats to get the total cost the company will pay. The total cost of purchasing new seats is $32,610.40 and the total cost of installing new seats is $11,625.80, so the total cost the company will pay is $32,610.40 + $11,625.80 = $44,236.20.

Step-by-step explanation:

The expression that is the factored form of 10x - 25 using the greatest common factor is option A: 5(2x - 5).

To factor the expression, we need to find the greatest common factor of the terms, which in this case is 5. We then write the expression as a product of 5 and a second expression with the remaining terms:

10x - 25 = 5 * (2x - 5)

So, option A is the correct answer.

Answer:

[tex]m^3+3m^2+3m+1[/tex]

Step-by-step explanation:

[tex](m^2+2m+1)(m+1)=(m^2)(m)+(m^2)(1)+(2m)(m)+(2m)(1)+(1)(m)+(1)(1)=m^3+m^2+2m^2+2m+1m+1=m^3+3m^2+3m+1[/tex]

You could also use the binomial theorem because the expression is equivalent to [tex](m+1)^3[/tex] but either method works.