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The Bellah's pool is leaking. The pool leaked 3/4
gallon in 20 minutes, or 1/3hour. How many
gallons is the pool leaking each hour?

Step-by-step explanation:

what is missing is the definition that QS is the height and therefore standing at a right angle (90°) at PR.

then this can be solved.

we use Pythagoras

c² = a² + b²

c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.

let's start with the triangle PQS.

21² = 15² + QS²

441 = 225 + QS²

QS² = 216

QS = sqrt(216) = sqrt(36×6) = 6×sqrt(6) = 14.69693846...

now for triangle QSR

(5x - 16)² = (3x - 4)² + QS²

25x² - 160x + 256 = 9x² - 24x + 16 + 216

16x² - 136x + 24 = 0

2x² - 17x + 3 = 0

the solution to a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (17 ± sqrt(17² - 4×2×3))/(2×2) =

= (17 ± sqrt(289 - 24))/4 = (17 ± sqrt(265))/4

x1 = (17 + 16.2788206...)/4 = 8.319705149...

x2 = (17 - 16.2788206...)/4 = 0.180294851...

but using x2 in side lengths 3x - 4 or 5x - 16 gives us negative side lengths. that does not make any sense for actual side lengths.

so, x1 is our solution :

x = 8.319705149...

Answer:

A solution of an equation is any value of the variable that satisfies the equality, that is, it makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation the same value. To solve an equation is to find the solution(s) for that equation.

Step-by-step explanation:

The probability of picking a second black marble is 4/13

Probability is the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Probability helps us know the chance an event has to occur. The closer it gets to zero(0) the less chance it has to occur. The closer it gets to one(1) the more chance it has to occur.

Therefore, The probability of picking a second black marble is 4/13

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The option are :

4/13

85/182

25/637

45/182

Answer:

B

Step-by-step explanation:

Trust

By Simplify  expression  -9y-10y -2z  this we get - 19y - 2z.

Examples :

-9y-10y -2z

Simplify

-9y - 10y - 2z : -19y - 2z

-9y - 10y - 2z

= - 19y - 2z.

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If f(x) = x⁴ + 2, g(x) = x-6 and h(x) = √x , then the simplified form of f(g(h(x))) is f(g(h(x))) = (√x - 6)⁴ + 2.

What is the polynomial expression?

Any expression which consists of variables, constants, and exponents, and is combined using mathematical operators like addition, subtraction, multiplication, and division is a polynomial expression.

We can simplify f(g(h(x))) by first evaluating h(x), then substituting the result into g(x), and finally substituting the result into f(x).

Starting with h(x) = √x, we can substitute this into g(x) to get:

g(h(x)) = g(√x) = √x - 6

Next, we can substitute g(h(x)) = √x - 6 into f(x) to get:

f(g(h(x))) = f(√x - 6) = (√x - 6)⁴ + 2

Simplifying this expression requires some algebraic manipulation, but we can expand (√x - 6)⁴ using the binomial theorem or by using the method of FOIL (first, outer, inner, last) repeatedly. Either way, we will end up with a polynomial expression in x with terms of various degrees.

Therefore, the simplified form of f(g(h(x))) is f(g(h(x))) = (√x - 6)⁴ + 2.

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We can see here that the people of ages 18-29 that have tried vaping or e-cigarettes is: 25,803,450.

Population refers to the number of individuals of a particular species living in a particular area or region. In the context of human populations, it refers to the number of people living in a particular geographic area or country.

To find out the number of people ages 18-29 who said they have tried vaping or e-cigarettes, you can use the following calculation:

30,357,000 (the number of people ages 18-29) x 0.85 (the percentage of people who have tried vaping or e-cigarettes) = 25,803,450.

So, approximately 25,743,950 people ages 18-29 said that they have tried vaping or e-cigarettes.

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The given relationship is such that 1 / z⁴ = z ⁻⁴.

When given 1 / z⁴, this can be rewritten in such a way that it becomes z ⁻⁴.

This is because when a denominator is raised to a exponent , it can be transformed to a numerator if the sign on the power is changed to the negative.

This means that when the fraction was 1 / z⁴, it can become the value of z ⁻⁴ because the negative in front of the 4 shows that it is a fraction.

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The correct answer is d.  The standard form of the equation of f(x) is −x2 + 6x + 16.

A downward opening parabola is a curve in the shape of a parabola that opens downward and is symmetrical about the x-axis. The equation of a downward opening parabola is y = ax^2 + bx + c, where a is a negative number, and b and c are constants.

The focus of a downward opening parabola is the point on the parabola where the curvature is greatest and is located at the vertex of the parabola.

The directrix of a downward opening parabola is a line parallel to the x-axis and the distance from the focus to the directrix is equal to the length of the latus rectum of the parabola. The equation of the directrix is y = -a(x - h)^2 + k, where h and k are constants.

Downward opening parabolas can be used to graphically represent any type of data that follows a parabolic shape. This includes physical phenomena such as the path of a projectile or the vibration of a string.

Downward opening parabolas can also be used to model economic or financial data, such as the demand for a product or the price of a commodity. They may also be used to describe relationships between two variables in a mathematical equation.

The standard form of a parabola equation is f(x) = ax2 + bx + c, where a, b, and c are real numbers. In this case, the vertex of the parabola is at (3, 25), so the equation is in the form f(x) = a(x - 3)2 + 25. Putting in the other points on the graph to solve for a, b, and c yields the equation f(x) = -x2 + 6x + 16.

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Simply multiply each value of the discrete random variable by the probability associated with that value to obtain the expected value, E(X), or mean. E(X)=xP is the formula's notation (x).

f(x) = 4x³,0 < x < 1

Domain of f(x) = 4x³,0 < x < 1 : Solution : 0 < x < 1

Interval notation : (0,1)

Range of 4x³ ,0 < x < 1;

Solution : 0 < f(x) < 4

Interval Notation : (0,4)

Axis interception points of 4x³,0 <x <1.

Asymptotes of 4x³. 0 < x < 1;

Extreme Points of 4x³ . 0<x < 1:

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Answer:

The slope of a line is represented by the coefficient of the x-term in the equation, which is also known as the "rise over run" or change in y over change in x.

In this equation y = 29/8x - 2/3

The coefficient of the x-term is 29/8, so the slope of the line is 29/8.

The constant of proportionality is equal to 6.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the relationship between correct answers and points on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 30/5 = 72/12 = 108/18 = 120/20

Constant of proportionality, k = 6

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Answer:

6

Step-by-step explanation:

120/20 = 6

108/18 = 6

72/12 = 6

30/5 = 6

See the pattern? :)

The coordinates of the fourth vertex is (1,-8).

As three of a parallelogram's vertices, we were given:

(3,-2), (-1,-4), (5,-6). (5,-6).

We see that (3,-2) and (-1,-4) form a diagonal after charting the points as in the attachment.

The midpoint formula determines what point on this diagonal is in the middle.

Keep in mind that both diagonals' midpoints are identical.

Specify the coordinates of the fourth point (x,y).

As a result of once more applying the midpoint formula to (3, -2), we get:

x=1 and y=-8

The fourth point's locational details are as follows:

(1,-8).

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The complete question is,

A good can be produced for a total cost of 600 or 850 when making 100 units and 150 units, respectively. Discover an equation for TC in terms of Q, the number of generated units, presuming that the total cost function is linear.

Answer:

= 7n − 3 emde n = 1, 2, 3, ...

Answer:

x = 1, y = - 5

Step-by-step explanation:

2x + 2y = - 8 → (1)

- 13x + 7y = - 48 → (2)

multiplying (1) by 7 and (2) by - 2 and adding will eliminate y

14x + 14y = - 56 → (3)

26x - 14y = 96 → (4)

add (3) and (4) term by term to eliminate y

40x + 0 = 40

40x = 40 ( divide both sides by 40 )

x = 1

substitute x = 1 into either of the 2 equations and solve for y

substituting into (1)

2(1) + 2y = - 8

2 + 2y = - 8 ( subtract 2 from both sides )

2y = - 10 ( divide both sides by 2 )

y = - 5

then solution is x = 1, y = - 5

Trapezoid PQRS having vertices P(0, 0), Q(0, 4), R(6, 4), and S(12, 0),

has the length of the midsegment as 11.07 units.

What is a trapezoid?

A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.

The length of the mid segment of trapezoid is half the sum of the lengths of the two parallel sides, PQ and RS.

The points for vertices are given as - P(0, 0), Q(0, 4), R(6, 4), and S(12, 0).

Length of sides PQ and RS is given as -

The line segment PQ = √(x2 - x1)² + (y2 - y1)²

PQ = √(0 - 0)² + (4 - 0)²

PQ = √0² + (4)²

PQ = √0 + 16

PQ = √16

PQ = 4 units

The line segment RS = √(x2 - x1)² + (y2 - y1)²

RS = √(12 - 6)² + (0 - 4)²

RS = √(6)² + (-4)²

RS = √36 + 16

RS = √50

RS = 5√2 units

To find the mid segment add the length of PQ and RS.

So, the equation will be -

Midsegment = PQ + RS

Midsegment = 4 + 5√2

Midsegment = 11.07 units

Therefore, the length of midsegment is 11.07 units.

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Answer: 9

Step-by-step explanation: (6+12) / 2 = 9

Average rate of change for the first 10 minutes after the soup was placed in the bowl is 200 .

220 +180/2 = 200

average rate of change for the first 10 minutes after the soup was placed in the bowl 200.

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The shingles are in the 6th row is 110 using arithmetic process.

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The study of numbers and the operations on those numbers, which are relevant to all other branches of mathematics, is the focus of a branch of mathematics known as arithmetic operations. It includes addition, subtraction, multiplication, and division as its fundamental operations.

Given that A = 75 and d = 7, n = 6

A₆ = A + (n-1)d

A₆ = 75 + (6-1)7

A₆ = 75 + 5 * 7

A₆ = 75 + 35

A₆ = 110

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Answer:

33

Step-by-step explanation:

it starts with 75 and decreases by 7 for each row. on the 6th row youll be at 33!

STARTS AT 75

row one: 68

row two: 61

row three:54

row four: 47

row five: 40

row six: 33

When two pairs of corresponding angles and the included pair of sides are likewise congruent, a triangle is said to be congruent.

When two triangles can be superimposed, have identical side lengths, and equal angles, they are said to be congruent.

Triangles with the same angle measurements and side lengths are said to be congruent. SSS (Side-Side-Side) SAS are the triangle congruence criteria (Side-Angle-Side). When they have, triangles are congruent. There are precisely the same three sides and three angles.

Triangles are said to be congruent if two pairs of corresponding angles and the included pair of sides are also congruent. The triangles are congruent if a pair of sides that are not included and two pairs of comparable angles are congruent.

When the coordinates of XYZ are converted to produce its congruent image, X'Y'Z.

The triangle XYZ's translated picture is X'Y'Z'.

The triangle XYZ's reflected image becomes X'Y'Z'.

The triangle XYZ does not turn into its rotated counterpart, X'Y'Z'.

Therefore, Option I and II are true statements. so D is the correct answer.

The complete question is:

XYZ is transformed on a coordinate plane to obtain its congruent image X'Y'Z. Which of the following statements could be true?

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The terms mean median, mode, and range describe properties of statistical distributions.

The statistical distributions' characteristics are described by the terms mean, median, mode, and range. The set of all potential values for terms that indicate predetermined events is known as a distribution in statistics. A term's value stated as a variable is referred to as a random variable.

The two main categories of statistical distributions are as follows. There are discrete random variables in the first category. This indicates that each phrase has a distinct, precise numerical value. A continuous random variable is present in the distribution of the second major kind. An unlimited number of possible values can be represented by a continuous random variable. A term is said to have a probability density function when any value can be assigned to it within an uninterrupted interval or span.

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Answer:

To add or subtract fractions, they must have a common denominator. In this case, the denominators of the fractions are 2 and 8, which are not the same. To find the least common multiple of 2 and 8, we can list the multiples of each number and find the smallest one that is common to both:

2: 2, 4, 6, 8, 10, 12, 14, ...

8: 8, 16, 24, 32, ...

The least common multiple of 2 and 8 is 8. Therefore, to add or subtract the fractions, we must convert them to have a denominator of 8.

-3/2 = -12/8 and 3/8 = 3/8

So, -3/2 - 3/8 = -12/8 - 3/8

Now we can subtract the fractions directly:

-12/8 - 3/8 = -12 - 3 / 8

= -15/8

Therefore, the simplified form of -3/2 - 3/8 is -15/8

Answer:

y ≥ -x -7

Step-by-step explanation:

The inequality is greater than or equal to because it is above the line and it is a solid line.

The slope is -1.  If you select a point on the line, you go down one unit and one unit to the right to get back on the line.  The slope is the rise over the run.  -1/1 = -1

The y intercept is where the graph crosses the y axis (0,-7) So the y intercept is -7

Answer: 7

Step-by-step explanation:

First, we need to prime factorize the number 189,

189 = 3 × 3 × 3 × 7 × m

From the factors we can see that there is no pair of same numbers for 7, so if we replace m with 7, we can get a perfect square.

Hence the answer is 7

Answer: Net (of a shape)

Step-by-step explanation:

Answer:

Step-by-step explanation:

no need for step by step its called a net

The given initial value problem y(0)=8, solution is [tex]y=\sqrt{64e^x-3x}[/tex]

Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation. Assuming that a function's rate of change with regard to x is inversely proportional to y, we may write it down as dy/dx = k/y. An equation involving the derivative (derivatives) of the dependent variable with respect to the independent variable is referred to as a differential equation in calculus (variables). The differential equation assists us in presenting a relationship between the changing quantity with respect to the change in another variable. The derivative represents nothing more than a rate of change. If y is a dependent variable, f is an unknown function, and x is an independent variable, then y=f(x) is a function.

The given differential equation is,

[tex]2yy'+3=y^2+3x\\\\2y\frac{dy}{dx}=y^2+3x-3\\\\(3-y^2-3x)dx+2ydy=0\\\\compare, Mdx+Ndy=0\\\\M=3-y^2-3x\\\\N=2y[/tex]

The given equation is not exact but if we multiplied by [tex]e^{-x}[/tex]

[tex]The D.E.\\(3-y^2-3x)e^{-x}dx+2ye^{-x}dy=0\\\\then M_y=-2ye^{-x}=N_x\\The G.S,=y^2e^{-x}+3xe^{-x}=c\\\\y(0)=8\\c=64\\hence,\\y=\sqrt{64e^x-3x}[/tex]

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The probabilities of adults who drinks only coffee , both/ coffee ,soda and doesn't drink any are 5% , 65% and 35%.

Let A be the event that an adult consumes coffee.

Let B be the event that an adult consumes carbonated soda.

Given probabilities of the events.

P (A) = 0.4

P (B) = 0.6

P(A∩B) = 0.35

(a). P(A)  - P(A∩B) = 0.4 - 0.35

                             = 0.05 OR 5 %

(b). P(AUB) = P (A) + P (B) - P(A∩B)

                   = 0.4 + 0.6 - 0.35

                   = 0.65 OR 65%

(c). The given case represents compliment of the event when the adult consumes at least one of the drink. According to probability axiom, the probability is given by:

P ((AUB)') = 1 - P (AUB) = 1-0.65 = 0.35

Therefore,

P ((AUB)') = 0.35 or 35 %.

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Answer:

there's ur answer ...........