Water comes out of a garden hose at a constant rate to fill a pool. After 3 minutes, the pool is filled with 30 gallons of water. After 6.5 minutes, the pool is filled with 65 gallons of water.

a. Write an equation that represents the number of gallons of water y in the pool after x minutes.
b. How long will it take to fill a pool that needs 10,000 gallons of water?

Linear relationships can be represented mathematically by equations of the form y = mx + b or visually by graphs.

A linear relation, also known as a simple relation, is a linear equation in linear algebra that contains the elements of a vector space or a module as its solution.

A statistical word used to express a straight-line relationship between two variables is a linear relationship (or linear association). Graphs and mathematical equations of the form y = mx + b can both be used to represent linear relationships.

If the slope is upward, there is a positive linear relationship, meaning that when one rises, the other rises as well. A negative slope indicates a negative linear relationship, whereby as one variable rises, the other falls. If the slope is 0, the two variables do not change as one rises.

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The Volume of the cell with an edge length of 10 Angstroms is 1×10⁻²¹cm³.

The volume of a cube with edge length of "L" is calculated as "L³" .

In order to find the volume of a cube with edge length = 10 angstroms (A) , we first need to convert the units to cm.

we know that 1 Angstrom = 1×10⁻⁸ cm,

So, 10 angstroms = 10×10⁻⁸ cm ;

The volume of a cell with an edge length of 10 Angstroms can be calculated as follows:

The volume of the cube in cm³ is =  (10×10⁻⁸ cm)³

⇒ 10³×10⁻²⁴ cm³

⇒ 1×10⁻²¹ cm³ .

Therefore , the volume of the cell is 1×10⁻²¹ cm³ .

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Answer:

x = 0

y = -2

Step-by-step explanation:

1. 6x+2y = -4

2. x - 2y = 4

in our second equation lets isolate x

x = 2y + 4

now lets plug this into our first equation

6(2y+4) + 2y = -4

12y + 24 + 2y =-4

14y +24 = -4

14y = -28

y = -2

lets plug in y into the second equation to find x

x = 2(-2)+4

x = -4+4

x = 0

The difference is that in an observational study, the researchers do not control treatment, and in an experiment, they do.

An experiment is a method used to verify or disprove a theory, as well as to determine something's effectiveness or likelihood.

An experiment vs an observational research differs fundamentally in that:

Members of a sample are measured or surveyed during an observational study without any attempt to manipulate them.

In an experiment, decisions are made under controlled conditions, subjects are divided into groups, and one group is given therapy while the other is left untreated. The main distinction between well-executed observational studies and experimental designs is that the replies of participants are unaffected, whereas in experiments, at least some participants are subjected to a treatment condition at random.

As a result, the researchers in an experiment control the therapy, but they do not in an observational study.

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Answer:

x = 15

Step-by-step explanation:

We take x as the variable that replicates the number

When we put it into a equation we get

x + 15 = 2x

x = 15

When we check

15 + 15 = 2(15)

30 = 30

Examples of categorical variables are race, sex, age group, and educational level.

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Technetium-99m has a half-life of 6 hours. After 21 hours, the remaining radioactive material  in the patient's blood stream is 0.053 mL.

The formula for half life is given by:

P(t) = Po (1/2)^(t/T)

Where:

P(t) = the remaining quantity of the substance at period t

Po = initial quantity

T = half life

Information available in the problem:

Po = 0.6 mL

T = 6 hours

t = 21 hours

Plug these parameters into the formula:

P(21) = 0.6 x (1/2)^(21/6)

P(21) =  0.6 x (1/2)^(3.5)

P(21) = 0.053

Hence, the remaining radioactive material  in the bloodstream is 0.053 mL

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The probability P that all the students with A’s and B’s are female and all the students with C’s and D’s are male is 0.0000907 or 0.00907%.

To determine the probability P, we can use the formula for combinations:

P = (number of ways to select A's and B's from the females) * (number of ways to select C's and D's from the males) / (number of ways to assign grades to all students)

Let's first find the number of ways to select A's and B's from the females:

There are 2 ways to select 2 A's from 7 females.

There are 7 choose 5 ways to select 5 B's from 7 females, which is 21.

So, there are 2 * 21 = 42 ways to select A's and B's from the females.

Next, let's find the number of ways to select C's and D's from the males:

There are 8 ways to select 8 C's from 11 males.

There are 11 choose 3 ways to select 3 D's from 11 males, which is 165.

So, there are 8 * 165 = 1320 ways to select C's and D's from the males.

Finally, let's find the number of ways to assign grades to all students:

There are 18 choose 2 ways to select 2 A's from 18 students, which is 153.

There are 18 choose 5 ways to select 5 B's from 18 students, which is 18564.

So, there are 153 * 18564 = 2827672 ways to assign grades to all students.

Putting it all together, the probability P is:

P = (42) * (1320) / (2827672) = 0.0000907

Therefore, the probability P that all the students with A’s and B’s are female and all the students with C’s and D’s are male is 0.0000907 or 0.00907%.

Complete Question:

An EEOC investigation into course grading encountered the following situation. In a course with eighteen students, 7 females and 11 males, grades were assigned as follows: 2 A’s, 5 B’s, 8 C’s, and 3 D’s. Determine the probability P that all the students with A’s and B’s are female and all the students with C’s and D’s are male.

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The Mustang is worth $24,320 after one year.

Compound interest is computed on the principal as well as the interest accumulated over the preceding period. It differs from simple interest in that interest is not added to the principal when computing interest for the next month.

Compound annual growth rate (CAGR) is the average yearly growth rate of an investment over a time period greater than one year. It is one of the most reliable methods for calculating and determining returns for individual assets, investment portfolios, and anything else whose value might grow or decline over time.

The formula to calculate the value of the Mustang after one year is:

value_after_one_year = value_initial * (1 - 0.24)

Plugging in the given values:

value_after_one_year = $32,000 * (1 - 0.24)

= $32,000 * 0.76

= $24,320

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Answer:

obtuse

Step-by-step explanation:

or acute triangle

is the answer

By using the tangent property of a circle, it has been proved that  ABC is isosceles

<BAY = 72°

< ABC = 54°

What is a circle's tangent?

First, it's crucial to understand circles.

Every point on a circle keeps a set distance from the center point in a two-dimensional, rounded form known as a circle. The circle's radius is the fixed separation.

The tangent to a circle is the straight line that intersects the circle at any point.

Then Now

<ACB = <BAY = 72° ( angles in alternate segments)

<ABC + <ACB + < CAB = 180° { being sum of angles of triangle }

54° + 72° + <CAB = 180°

<CAB = 180° - 126°

<CAB = 54°

Hence

ABC is an isosceles triangle

(being <CAB = <ABC)

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Answer:

The linear function for the first store is y = 2.5x + 10.75, where x is the number of comic books and y is the cost of the package. The linear function for the second store is y = 2.5x + 5.75. The second store has the better deal, as the cost of the package is lower for any given number of comic books.

Point (2, 1) is not the solution of the inequality y ≥ (1/2)x + 3.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

y ≥ (1/2)x + 3

Check whether point (2, 1) is the solution or not. Then we have

1 ≥ (1/2)(2) + 3

1 ≥ 1 + 3

Point (2, 1) is not the solution of the inequality y ≥ (1/2)x + 3.

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If A limousine service has 15 cars available for rides: then the number of different collections C of 5 limousines are possible is 3003 .

To find the number of different collections C of five limousines, we can use combinations. A combination is a way to choose a subset of items from a larger set, without regard to order.

Let the number of Cadillac models n.

Then, 15 - 8 = 7 cars are Cadillacs. So, n = 7.

The number of different collections of 5 limousines from the 15 cars is given by the number of combinations of 5 items taken from a set of 15 items:

⇒ ¹⁵C₅ = 15!/(5!×(15 - 5)!) = 15!/(5!×10!) = 3003.

Therefore , there are 3003 different collections C of five limousines that the event organizer can choose from the limousine service's fleet of 15 cars.

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On solving the linear equations 14x + 5y = 975 and 10x + 4y = 750, the price for small ad and full page ad is obtained as $25 and $125 respectively.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The two linear equations given are -

14x + 5y = 975 .... (1)

10x + 4y = 750 .... (2)

Here, x represents the price of small ad and y represents the price of a full-page ad.

To get the value of x and y solve the system of linear equations -

Multiply equation (1) by 4 and (2) by 5 -

4 (14x + 5y) = 4 × 975

56x + 20y = 3900 .... (3)

5 (10x + 4y) = 5 × 750

50x + 20y = 3750 .... (4)

Subtract equation (4) from (3) -

56x + 20y - (50x + 20y) = 3900 - 3750

56x + 20y - 50x - 20y = 3900 - 3750

6x = 150

x = 150/6

x = 25

Substitute the value of x in equation (1) -

14(25) + 5y = 975

350 + 5y = 975

5y = 975 - 350

5y = 625

y = 625/5

y = 125

So , the prices of small ad is $25 and prices of full-page ad is $125.

Therefore, the values for x and y are $25 and $125 respectively.

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20×3=60

the present age of shirsha

Answer:

Let Shrisha's present age be x

According to question ,

After 20 years ,

Shrisha's age will be 3 times her present age.

[tex]\therefore \: 20 + x = 3x \\ \longrightarrow \: 3x - x = 20 \\ \longrightarrow \: 2x = 20 \\ dividing \: both \: sides \: by \: 2 \\ \\ \longrightarrow \: \cancel \frac{2x}{2} = \cancel \frac{20}{2} \\ \\ \longrightarrow \:\boxed{ x = 10}[/tex]

hence , Shrisha's present age is 10 years.

hope helpful! :)

Answer:

Below

Step-by-step explanation:

I believe your equation is incorrect ( perhaps a typo)

probably it is   x^2 - 17x +16

  then you could choose factors 16 and 1

     to get this    (x-1)(x-16)

The correct response is D, all real numbers x can either be greater than or equal to 2 or less than 2.

solving a problem by either a method or action; communicating the answer. a range of values for something like a statistic that fulfill an equation, specifically The solution of just an equation is any variable of a variable that makes the Left Hand Side (Dataframe) and the Dominant Hand Side (RHS) of the equation equal. To solution an equation is to identify its solution or solutions. One manner to express the concentration of a solvent is as a percentages of the solute in the solvent. The ratio of something like the mass of the solute to the mass of something like the solution, and the fraction of the mass of the solute toward the mass of the solution, is one of two supplementary techniques for computing the percentage.

given

(x Ix<2}u [xlx ≥2]

x<2 or x>=2

The correct response is D, all real numbers x can either be greater than or equal to 2 or less than 2.

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The ratio of the volume of the cylinder to the volume of the prism is 4/π.

The volume of a cylinder is the number of unit cubes (cubes of unit length) that can be fit into it. It is the space occupied by the cylinder as the volume of any three-dimensional shape is the space occupied by it. The volume of a cylinder is measured in cubic units such as cm3, m3, in3, etc.

The volume of a square prism is referred to as the amount of space occupied by a 3-dimensional prism that has two congruent square bases and four rectangular faces are known as the volume of square prism. It is measured in cubic units. The volume of a prism is the product of the cross-sectional area and its length. The cross-sectional area is also known as the base area of the square prism.

We are given that a certain cylinder and square prism have equal lateral surface area.

Lateral surface area of cylinder = 2πrh

Lateral surface area of square prism = 4sH

So, 2πrh = 4sH

Also, the height of the cylinder is equal to the height of the prism.

So, h=H

Put in above equation:

2πrh = 4sh

⇒ πr = 2s

⇒ r/s = 2/π

The ratio of the volume of the cylinder to the volume of the prism

⇒ Volume of cylinder/ Volume of prism

⇒ πr²h/s²h

⇒ π(r/s)²

⇒ π(2/π)² ---- (From above)

⇒ 4/π

Thus, the ratio of the volume of the cylinder to the volume of the prism is 4/π.

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randomly choosing a male first and randomly choosing a male second are independent events.

Sample Space:

M1, M2, M3, M4, F1, F2, F3, F4, F5

Independent Events:

M1, M2, M3, M4, M1, M2, M3, M4

The sample space includes all of the possible outcomes of picking two contestants from the audience of 5 females and 4 males. Since the order of choosing does not affect the outcome, the sample space does not change regardless of which gender is chosen first. Therefore, randomly choosing a male first and randomly choosing a male second are independent events.

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No, the angles are not Complementary because the sum is not 90 degree.

Two angles are called complementary when their measures add to 90 degrees.

For example, 30 degrees and 60 degrees are complementary angles.

Given:

The pair of angles measure 38 degrees and 67 degrees.

Now, we know that if the sum of angles are 90 then they are said to be pair of Complementary Angle.

so, 67 + 38

= 105 > 90

Thus, the given pair is not pair of Complementary Angle.

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Answer: The correct option is, (B) SAS.

Step-by-step explanation: The SAS Postulate says that triangles are congruent if any pair of corresponding sides and their included angle are congruent.

Maximum or the upper limit of the amount of water leaked in 2 hours will be r(2) since t = 2 hrs.

The lower bound or limit will be zero if the leaked is fixed or the amount of water is zero.

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

The set of integers x for which a function has a valid definition is known as its domain. A closed interval is referred to as a function's domain if it is specified across the interval a≤ x ≤b.

A function's range can be used to describe one of two related ideas: The function's codomain a representation of the action A binary relation f between two sets X and Y is a function if there is precisely one y in Y such that f connects x to y for every x in X.

The tank is leaking in the function of time givenas

r(t), where t is measured in hours

Maximum or the upper limit of the amount of water leaked in 2 hours will be r(2) since t = 2 hrs.

The lower bound or limit will be zero if the leaked is fixed or the amount of water is zero.

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For the function f(x) = -5(4)x - 10, the end behaviour signifies that [x→∞,f(x)→-∞] and [x→-∞,f(x)→∞].

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The given function is f(x) = -5(4)x - 10

On solving the function it gives -

f(x) = -20x - 10

The graph for the function is plotted.

The end behavior of a function f(x) describes the behavior of the function as x approaches +∞ and as x approaches -∞.

Since the leading term of the polynomial (the term in the polynomial which contains the highest power of the variable) is -20x, the degree is 1, i.e. odd, and the leading coefficient is -20, i.e. negative.

This means that function f(x) approaches ∞ as x approaches -∞, and f(x) approaches -∞, as x approaches ∞.

Therefore, the end behaviour is [x→∞,f(x)→-∞] and [x→-∞,f(x)→∞].

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An increase in demand would result in a shift of line two to the right (option b).

The lines shown are known as demand and supply curves. The demand curve is a curve that shows the relationship between price and quantity demanded.

The demand curve has a negative slope.  This means that the higher the price, the lower the quantity demanded. This is in line with the law of demand.

When there is a change in demand, the demand curve would shift either to the left or to the right. If demand increases, the demand curve would shift to the right.

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Answer:

Q11: x = 3

Q12: x = -4

Step-by-step explanation:

Q11
We have the equation as
[tex]\:64^{2x\:+\:4}=16^{5x}[/tex]

Convert the bases in terms of the common base 4

64 = 16 x 4 = 4 x 4 x 4  = 4³

16 = 4 x 4 = 4²

Therefore the original equation becomes:
[tex]\mbox {\large 4^{3\left(2x+4\right)}=4^{2\cdot \:5x}}[/tex]

Since the bases are the same in this equation, the exponents must also be the same

Equation the two exponents we get

3(2x + 4) = 2·5x

==> 6x + 12 = 10x

Move 12 to the right side

6x = -12 + 10x

Move 10x to the left:

6x - 10x = -12

-4x = -12

x = -12/-4 = 3

Answer to Q11

-------------------------------------------------------------

Q12

We can solve this in a similar manner to Q12

27 = 3 x 3 x = 3³

9 = 3 x 3 = 3²

Plugging these in we get

[tex]\mbox {\large 27^x = 3^{3(x)} = 3^{3x}}[/tex]

[tex]\mbox {\large 9^ {(x - 2)} = 3^{2(x-2)} = 3^{2x -4} }\\\\[/tex]

Thus we get

[tex]\mbox {\large 3^{3x} = 3^{2x -4} }\\\\[/tex]

Equating the exponents we get

[tex]3x = 2x - 4\\\\3x - 2x = -4\\\\x = -4[/tex]

ANSWER to 12

The function g(x) = (3x + 5) + 8 is a translation of 8 units upwards of f(x).

For a general function f(x), we define a vertical translation of N units as:

g(x) = f(x) + N

if N > 0, then the translation is upwards.

if N < 0, then the translation is downwards.

For a general function f(x), we define a horizontal translation of N units as:

g(x) = f(x) + N

if N > 0, then the translation is to the left.

if N < 0, then the translation is to the right.

Here we start at:

f(x) = 3x + 5

Function g(x) is:

g(x) = (3x + 5) + 8

g(x) = f(x) + 8

So this is a translation of 8 units up.

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Answer:

the answer is 20

Step-by-step explanation:

formulate the given
2/10%
rewrite the fraction
2/0.1  (then multiply both the numerator and denominator with the same integer)

= 20/1 (then simplify)
= 20
FA: 20

Answer:

Step-by-step explanation:

y = C1e^(kx) is a valid solution to the equation.

To check that the given y is a solution to the equation, we must first substitute the given y into the given equation. We can do this by substituting the constants C1, C2, and k into the equation. We then move each side of the equation to the same side and simplify. This will result in an equation of 0 = 0, which confirms that the given y is a solution to the equation. In this case, the general solution to the second order differential equation dy dx + ky is yx) C1 cos(kx) + C2 sin(kx) or yx = D1 cosh(kx) + D2 sinh(kx). As such, the given y is a solution to the equation.

For the given equation, dy/dx = Py, with a constant k > 0, the given solution is y = C1e^(kx) or y = D1 cosh(kx) + D2 sinh(kx). To check that this is a valid solution, we can substitute the given solution into the equation and calculate dy/dx. If the result is equal to Py, then we can be sure that the given solution is a valid solution to the equation. For example, if we take the first solution y = C1e^(kx), then we can calculate dy/dx as dy/dx = C1ke^(kx) which is equal to Py = kC1e^(kx). We can see that the two sides are equal, so we can confirm that y = C1e^(kx) is a valid solution to the equation.

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The total number of bars which were sold Online = 14816

Multiplication is a mathematical operation that embodies the fundamental concept of repeated addition of the same integer.

The multiplied numbers are known as the factors, and the outcome of the multiplication of two or more numbers is known as the product of those numbers.

Multiplication is used to make repetitive adding of the same number easier.

The number of cases of Essence soap sold is one-third as many as the number of Zing soap,

So:

Essence soap = 72 cases / 3 = 24 cases

The total number of cases sold will be:

72 cases + 24 cases = 96 cases.

And the total number of bars sold is:

96 cases * 156 bars/case = 14816 bars.

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