Max puts a stopper in the bathtub and turns on the faucet at t = 0.
After 5 minutes, there are 11 gallons of water in the tub and after 10 minutes, there are 22 gallons in the tub.
Write an equation that relates the number of gallons, g, to the time, t.
Does the relationship represent a linear function? Justify your response.

C.) right and isosceles, but not equilateral

Answer:

C.) right and isosceles, but not equilateral

Step-by-step explanation:

The correct statements are given below.

Exponential growth and decay apply to quantities which change rapidly. Exponential growth and decay have been derived from the concept of geometric progression. Quantities that do not change as constant but change in an exponential manner can be termed as having an exponential growth or exponential decay.

Given here:

Now we know  For exponential growth, the value of b is greater than 1 (b > 1), and for exponential decay, the value of b is lesser than 1 (b < 1), where b is the growth factor and Exponential Growth f(x) = abˣ and Exponential Decay f(x) = ab⁻ˣ

1) f(x)=3×4ˣ

  Clearly b=4>1

Thus the function represents exponential growth.

2) f(x)=4×(1/4)ˣ

  Here b=1/4<1

∴ The function represents exponential decay.

3) f(x)=2×(1/2)ˣ

Again here the growth factor is b=1/2<1 , thus the function represents exponential decay.  

Similarly for equation 4 we have b=12>1 and thus the function represents  

exponential growth.

Hence, equation 1 and 4 represent exponential growth and equations 2 &3 represent exponential decay.

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A recent college graduate is looking to begin saving for retirement. Option A is a savings account with 3.5% annual simple interest. Option B is a savings account with 3.5% annual interest compounded monthly. If the principal investment is the same for both options, the account which would have a larger balance after 10 years is  Option B because compound interest generates earnings from both principal and interest which is denoted as option C.

This is referred to as the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

Compound interest makes a sum of money grow at a faster rate than simple interest, because in addition to earning returns on the money you invest, you also earn returns on those returns or interest accrued at the end of every compounding period.

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Answer:

Option B will have the larger balance after 10 years because compound interest generates earnings from both principal and interest.

The Real Zeros of the polynomial can be found by equating the given polynomial to zero(0) .

The polynomial function is  a function that involves only non negative integer exponents of a variable in the equation .

For example :  3x+6 is a polynomial which has the exponent equal to 1.

The process to find the real zeros of a polynomial is :

(i) we write the polynomial expression based on what is  given.

(ii) Equate the polynomial equal to zero.

(iii) Solve for the variable(s) by using the polynomial factorization.

The degree of the polynomial tells us about the maximum number of distinct zeros that the polynomial can Have . For example, x - 4 has a degree of 1 . Therefore , it has only one real zero .

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The sinusiodal function created from 2 given points is y = 3 sin (πx + 90) + 3

From the case, we have:

Minimum point = (-3,0)

Maximum point = (-9,6)

The sinusoidal fuction would be in the form of:

y = A sin (Bx - C) + D

where:

A = amplitudo

B = 2π / Period

C = Phase shift

D = Midline

First, we need to find the amplitudo:

A = (Y max - Y min) / 2

A = (6 - 0) / 2

A = 3

Periode = (X max - X min) x 2

Periode = (-9 - (-3) x 2

Periode = -6

B = 2π / Periode

B = 2π / 6

B = 1/3 π

D = (Y max + Y min) / 2

D = (6 + 0) / 2

D = 3

We can use one point to find the value of C:

0 = 3 sin (π/3 (-3) - C) + 3

0 = 3 sin (π - C) + 3

-3 = 3 sin (π - C)

sin (π - C) = -1

(π - C) = 270

C = -1/2 π

C = - 90

Then the sinusiodal function would be:

y = 3 sin (πx + 90) + 3

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Answer:

Step-by-step explanation:

Given two complementary angles labeled (4x)° and (x-5)°, you want an equation for finding x, and the measures of the two angles.

The equation will reflect the fact that the angles have a sum of 90°:

  4x +(x -5) = 90

The equation simplifies to ...

  5x -5 = 90

  5x = 95

  x = 19

  ∠1 = 4x° = 76° . . . . . . measure of larger angle

  ∠2 = (x -5)° = 14° . . . . . measure of smaller angle

__

Additional comment

The little square at the vertex of the angles means that is a right-angle corner. Its measure is 90°. The two angles 1 and 2 together make up that right angle. That is the relation you use to form the equation.

Rewriting (simplifying) the sum ...

  4x +(x -5) = 5x -5

tells you nothing about the value of x. Any value for x will satisfy this equation. In order to find x, you need to relate this sum to something other than itself. (There is a reason why the angle is marked as a right angle.)

In the equation for acceleration, a, equals final velocity - original velocity/time, acceleration would be negative if the numerator is negative.

The object is slowed down by the acceleration, which is acting against the motion. In this situation, your acceleration is negative. Positive value will be returned if your end velocity is lower than your initial velocity. The equation for acceleration can be related as:

Acceleration, a = [tex]v_{f}[/tex] - [tex]v_{i}[/tex] × [tex]\frac{1}{t}[/tex]

The general equation a = v/t denotes acceleration (a), which determines the change in velocity (v) over the change in time (t). This enables you to calculate the change in velocity in meters per second squared ([tex]m/s^{2}[/tex]). Since acceleration has both its magnitude and direvtion, it is a vector quantity.

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A right triangle is a triangle with one right angle (90 degrees). The hypotenuse of a right triangle is the side opposite the right angle and is usually the longest side of the triangle.

To find the area of the triangle, you will need to use the base and the height of the triangle. In this case, the base of the triangle is 48cm and the height is the length of the side opposite to the right angle.

To find the length of the side opposite to the right angle, you can use the Pythagorean Theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. The theorem can be written as:

c^2 = a^2 + b^2

where c is the hypotenuse, and a and b are the other two sides.

So, substituting the values we have:

50^2 = a^2 + 48^2

2500 = a^2 + 2304

a^2 = 2500 - 2304

a^2 = 196

a = 14

Area of the triangle = (1/2) * base * height

= (1/2) * 48 * 14

= 336 cm^2

So, the area of the triangle is 336 cm^2

The area of the triangle is 336 cm²

The area of a triangle can be found using the formula:

Area = (1/2) × base × height

In this case, we know the base is 48cm and the hypotenuse is 50cm. To find the height, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (a) is equal to the sum of the squares of the lengths of the other two sides (a and b) in the right triangle.

c² = a² + b²

So in this case, we have:

50² = 48²  + b²

Solving for b, we get:

b =√ 50² - 48²

b = √2500 - 2304

b = √196

b = 14 cm

So the height of the triangle is 14cm.

Now we can use this information to find the area:

area = (1/2) ×48 ×14 = 336 cm²

Hence, we can say the area of the triangle is 336 cm²

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An average and standard deviation in R is straightforward. The mean() function calculates the average and the sd() function calculates the standard deviation.

In information, the standard deviation is a degree of the quantity of variation or dispersion of a fixed of values. A low standard deviation indicates that the values tend to be near the implied (additionally called the predicted price) of the set, whilst an excessive preferred deviation suggests that the values are spread out over a wider variety.

Popular deviation can be abbreviated SD, and is maximum commonly represented in mathematical texts and equations by means of the decrease case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample general deviation.

The standard deviation of a random variable, pattern, statistical population, statistics set, or possibility distribution is the square root of its variance. it's miles algebraically easier, even though in exercise less sturdy, than the common absolute deviation.

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Answer:

To find the equation of the line passing through the point (3,2) and parallel to line x + 2y = 5, we need to use the point-slope form of a linear equation. The point-slope form of a linear equation is: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

We know that two lines are parallel if they have the same slope. Since the given line x + 2y = 5 has a slope of -1/2, the equation of the line passing through (3,2) and parallel to x + 2y = 5 is y - 2 = -1/2 (x - 3), or simplifying y = -1/2x + 7/2

To find the equation of the line passing through the point (2,5) and parallel to the line x + 3y - 8, we need to use the point-slope form of a linear equation. The point-slope form of a linear equation is: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

We know that two lines are parallel if they have the same slope. Since the given line x + 3y - 8 has a slope of 1/3, the equation of the line passing through (2,5) and parallel to x + 3y - 8 is y - 5 = 1/3 (x - 2), or simplifying y = 1/3x + 1/3

It's important to note that the lines are parallel because they have the same slope and different y-intercept, which means that they will never intersect.

Step-by-step explanation:

The graph of f(x) translated 3 units down.

correct option is D.

What is a graph of a function?

The graph of a function is a visual representation of the function that shows the relationship between the input (x) and output (y) values. It is typically plotted on a coordinate plane, with the x-axis representing the input values and the y-axis representing the output values. Each point on the graph corresponds to an (x, y) pair that satisfies the equation of the function.

The given options are:
A. It is the graph of f(x) translated 3 units up.

B. It is the graph of f(x) translated 3 units to the right.

C. It is the graph of f(x) where the slope is decreased by 3.

D. It is the graph of f(x) translated 3 units down.

Let y = f(x) then f(x)-3 means y-3. Subtracting 3 from the y coordinate of each point will move the entire curve down 3 units.

Thus, the graph of f(x) translated 3 units down.

correct option is D.

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1) y intercept in the given equation is 6

The graph's intersection with the y-axis is known as the y-intercept. Finding the intercepts for any function with the formula y = f(x) is crucial when graphing the function. An intercept can be one of two different forms for a function-t he x-intercept and the y-intercept. A function's intercept is the location on the axis where the function's graph crosses it.

An equation of a straight line is written in the form: y=mx+c

where y is the y-coordinate,

m is the slope of the line,

x is the x-coordinate

and c is the y-intercept

Thus, from the question, y=3/4x+6, we can say

m=3/4 and c=6

Thus, y intercept for this equation is 6

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4 is not a perfect number because the sum of its factors (besides 4 itself), 1+2, is less than 4. Numbers like 4 are known as deficient numbers.

In number theory, a natural number is called deficient if it is greater than the sum of its divisors, excluding itself. For example, the number 8 is deficient because its divisors are 1, 2, and 4, and 1 + 2 + 4 = 7, which is less than 8. A number that is not deficient is called abundant.

The concept of deficient numbers was first studied by the ancient Greek mathematician Nicomachus of Gerasa in his work "Introduction to Arithmetic". He classified numbers into three categories: abundant, perfect, and deficient numbers. He defined a perfect number as a number whose divisors (excluding the number itself) sum up to the number and abundant if the sum of divisors (excluding the number itself) is greater than the number.

The study of deficient numbers is closely related to the study of divisors of numbers, which is a fundamental area of number theory. The study of deficient numbers also has connections to other areas of mathematics such as algebraic number theory and the theory of quadratic forms. In addition, the study of deficient numbers has applications in computer science and cryptography.

It is important to note that only a small percentage of numbers are deficient, and the study of deficient numbers is not as widely studied as the study of prime numbers or perfect numbers, but it is still an interesting area of research in number theory.

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(h x $6.25) - $20 is a equation to figure how how many hair products she needs to sell to generate a profit of $120.

Profit is just the money left over after costs are paid. A loss is deemed to have occurred if the expenses exceeded the income.

A gain is a positive figure, whereas a loss is a negative one.

To determine whether a contract is lucrative or not, the phrases profit and loss are utilized. These words are frequently used in ordinary conversation. If the selling price exceeds the cost price, the difference between the two amounts is known as the profit.

The equation to determine how many hair products Jackie must sell to make a profit of $120 would be:

$120 (profit) = (h x $6.25) - $20 (cost of online membership)

where h is the number of hair products sold.

To solve for h, we can first add $20 to both sides of the equation:

$120 + $20 = h x $6.25

Next, we can divide both sides of the equation by $6.25 to find the value of h:

h = ( $120 + $20 ) / $6.25

h = 20

So Jackie must sell 20 hair products to make a profit of $120.

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(h x $6.25) - $20 is an equation to figure how many hair products she needs to sell to generate a profit of $120.

Profit is just the money that remains after expenses are covered. A loss is deemed to have occurred if the expenses exceeded the income.

A gain is a positive figure, whereas a loss is a negative one.

The terms profit and loss are used to assess how valuable a transaction is. In everyday discourse, these terms are often employed. The difference between the two sums is referred to as the profit if the selling price is higher than the cost price.

The equation to determine how many hair products Jackie must sell to make a profit of $120 would be:

$120 (profit) = (h x $6.25) - $20 (cost of online membership)

where h is the number of hair products sold.

To solve for h, we can first add $20 to both sides of the equation:

$120 + $20 = h x $6.25

Next, we can divide both sides of the equation by $6.25 to find the value of h:

h = ( $120 + $20 ) / $6.25

h = 20

So Jackie must sell 20 hair products to make a profit of $120.

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The graphing method is used to solve a system of linear equations by multiplying and adding.

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Answer:

blab blah??

Step-by-step explanation:

thats not a good question tbh

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{9a + 3 + 4 + (3a + 1)}\\\mathsf{= 9a + 3 + 4 + 3a + 1}}\\\text{COMBINE the LIKE TERMS}\\\mathsf{= (9a + 3a) + (3 + 4 + 1)}\\\mathsf{= 9a + 3a + 3 + 4 + 1}\\\mathsf{= 12a + 7 + 1}\\\mathsf{= 12a + 8}\\\\\\\huge\text{Therefore, your answer should be: } \\\huge\boxed{\mathsf{12a + 8}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

When we have a right triangle, Cos = a / h, according to the cosine law. In this situation, the letter "a" stands for adjacent.

The hypotenuse, denoted by the letter "h," can be calculated using the Pythagorean Theorem. All you need to get cosine is the hypotenuse and the neighboring side.

The ratio of the length of the side next to the angle divided by the length of the triangle's hypotenuse is known as the cosine of an angle.

The triangle's sides, a, b, and c, are determined using the cosine formula, which is given as

c = [a2 + b2 - 2ab cos C]

According to the Cosine Rule in trigonometry, the square of the length of any side of a given triangle equals the sum of the squares of the other sides minus twice the product of the other two sides multiplied by the cosine of the angle that separates them.

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Answer:

66

Step-by-step explanation:

2m = 11

m = 11/2

m = 5.5

m² - 1 = 29.25

m² + 1 = 31.25

The perimeter = 29.25+31.25+5.5 = 66

Answer:

30%

Step-by-step explanation:

Represent 15 out of 50 in fractions:

15/50

Simplify the fraction if you can and multiply by 100:

15/50 = 3/10

3/10 × 100 = 30%

The Sun transfer its energy to areas A and B by radiation.

The statement compares how much heat is absorbed

by areas A and B : Area A absorbs more heat.

The statement compares the temperatures of areas A

and B : Area A is warmer than area B.

Energy transfer by radiation is a way that energy travels through space without anything touching it. Just like the Sun sends energy to Earth without touching it. The Sun sends energy to Earth in the form of light and heat. This energy travels through the empty space between the Sun and Earth and reaches our planet. When this energy reaches the Earth, it helps plants grow, warms the air and water, and helps create the weather.

Heat absorption is the process by which an object or material takes in or absorbs heat energy from its surroundings. This can happen in a variety of ways, including conduction, convection, and radiation.

The temperature in different areas is determined by a complex interplay of factors, including latitude, altitude, proximity to bodies of water, and local weather patterns. Understanding these factors can help us make predictions about future temperatures and prepare for potential climate change.

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Answer: 3/11

Step-by-step explanation:

first add all the flowers, 3 roses, 4 daisies, and 4 lilies. 3 + 4 + 4 = 11. if only one flower is pink, and there are 3 roses, then there is a 3/11 chance its a rose.

Running a mile in five minutes is similar to moving at 12 mph (19.4 kph) on a treadmill.

the statutory mile, which has a length of 5,280 feet, is one example of a mile (1.609 km). Its original unit of measurement was the 5,000-foot-long Roman mile passus, often known as the "thousand paces."

Discover the distance formula, a Pythagorean theorem application, to determine the separation between two places. To get the separation between any two points, we can rewrite the Pythagorean theorem as d=((x 2-x 1)2+(y 2-y 1)2).

The formula for the distance between the points (a,b) and (c,d) is square root of (a,c)2 + (b,d)2. The distance in three dimensions between points (a, b, c) and (d, e, f) is equal to the square root of (a, d), (b, e), and (c, f)2.

We have,

Car speed = 0.4 miles per minute

We need to find the distance traveled in 30 minutes with a speed of 0.4 miles per minutes.

Speed is given by:

Speed = Distance / Time

Distance = Speed x Time

Distance = 0.4  x  30

Distance = 12 miles

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equation of circle : (x - h)² + (y - k)² = r²

h = x coordinate of center

k = y coordinate of center

hence h = 10, k = 8

center - (10 , 8)

The solution of RR(A) is (-3, -4).

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Three points can define a plane in a three-dimensional space.

Because a plane can be defined as a flat surface that extends infinitely in all directions, three points in space are sufficient to specify a plane. A plane can be determined by any three non-collinear points, i.e., points that are not on the same straight line, as long as they are not on the same line. Imagine three points in space, A, B, and C. We draw straight lines from A to C to create a plane. The triangle formed by these lines is a flat surface. A plane can be made by endlessly extending the flat surface in all directions.

The triangle formed by the three points A, B, and C, which are not collinear, extends in all directions to form a plane. A plane is therefore defined by three points. It's crucial to remember that any new point that lies on the same plane as A, B, and C will also be connected to the three defining points by the same straight line.

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Answer:

$807.39

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the compound interest formula and solve for A:

[tex]\implies A=500\left(1+\dfrac{0.04}{12}\right)^{12 \cdot 12}[/tex]

[tex]\implies A=500\left(1.00333333...\right)^{144}[/tex]

[tex]\implies A=500\left(1.61478492...\right)[/tex]

[tex]\implies A=807.392461...[/tex]

Therefore, Alyson will have $807.39 (nearest cent) in her account at the end of 12 years.

According to the model, the systolic blood pressure increases by 1 unit (e.g. mmHg) for each year of age.

What is scatter ?

A scatter plot, also known as a scatter diagram or scatter graph, is a type of graph used to display the relationship between two quantitative variables. It is a useful tool for visualizing and analyzing data.

A scatter plot consists of a set of points, each representing a pair of (x, y) values. The x-axis represents one variable and the y-axis represents the other variable. The points on the plot are placed based on the values of the two variables.

The equation given is Y = x + 95, where Y represents the systolic blood pressure and x represents the age.

The slope of the linear equation represents the rate of change of the dependent variable (systolic blood pressure) with respect to the independent variable (age). In this case, the slope of the equation is 1.

Therefore, according to the model, the systolic blood pressure increases by 1 unit (e.g. mmHg) for each year of age.

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the value x in this equation will be ±√1/3.

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally, the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

The given equation x² - 1/3 =0

x² = 1/3

taking square root both side

x = ±√1/3

Hence the value x in this equation will be ±√1/3.

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The variable restrictions on the rational equation 2x/5 = x+6/4 are 0,-6/4

Usually, simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.

Given;

2x/5 = x+6/4

Now, to find out the restrictions of the variable;

2x/5=0

2x=0

x=0

x+6/4=0

x=-6/4

Therefore, by simplification the restrictions will be 0 and -6/4

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