A small kitchen sink is 14in x 16in x 6in = 3584 cubic inches. If your water faucet in the kitchen is leaking 1 drop of water per second (volume of a typical drop is 0.05 ml ≈ 0.003 cubic inches), how long would it take for a clogged sink to fill and start overflowing. Write your answer in days.

The given graph is represented by the function ( x + 2 )(x - 1 )³(x - 3 ). The correct option is A.

The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.

Graphing functions involve drawing a curve on the coordinate plane that represents the function. Every point on a curve (graph) that represents a function satisfies the function equation.

The graph is represented by the function,

( x + 2 )(x - 1 )³(x - 3 )

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Solving the provided question, we can say that By, Pythagorean theorem PR = √277 and b = 11.31

The Pythagοrean Theorem, sometimes known as the Pythagοrean Theorem, is the basic Euclidean geοmetry relationship between a right triangle's three sides. Accοrding to this rule, the area of a square with the hypotenuse side equals the sum οf the areas of squares with the other twο sides. The Pythagοrean Theorem, often knοwn as the generic algebraic nοtation a² + b² = c², states that the square that crοsses the hypotenuse οf a right triangle οpposite the right angle equals the sum of the squares that span the sides of a right triangle.

By, Pythagοrean theorem

PR² = PQ² + QR²

PR² = 14² + 9²

PR² = 196 + 81

PR = √277

Again by Pythagorean theorem

c² - a² = b²

18² - 14² = b²

b² = 324 - 196

b = √128

b = 11.31

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The original price of the upright bike is $3,600.

Percentage is the fraction of an amount that is usually expressed as a number out of hundred. The sign that is used to represent percentages is %. Percentage is a measure of frequency.

Original price of the upright bike = sales price / percent discount

= $720 / (20/100)

$720 / 0.2

= $3,600

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The measure of the angles m∠BOX = 77.5° and  m∠AOX = 77.5°.

What is the angle bisector of an angle?

The angle bisector of an angle is a line or line segment that divides the angle into two equal parts, creating two smaller angles that are congruent (i.e., have the same measure). The angle bisector starts from the vertex of the angle and extends to the opposite side or ray of the angle, dividing the angle into two smaller angles that have the same number of degrees.

By the definition of the angle bisector of an angle, the angle bisector divides the angle in two equal measures.

As m∠AOB = 155°

m∠BOX = 1/2 * m∠AOB

m∠BOX = 1/2 * 155

m∠BOX = 77.5°

also m∠AOX = 77.5°

Hence, the measure of the angles m∠BOX = 77.5° and m∠AOX = 77.5°.

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Answer:

7.5dollars

Step-by-step explanation:

25%/100×$30

multiply the second equation by -1, you get

y=5x-10

-y=3x-14

add both of the equations together

0=8x-24

then

24=8x

x=3

to find y replace x in one of the original equations

y=5x-10

y=5(3)-10

y=15-10

y=5

(x,y)

(3,5)

The future value is 6,495,554.308.

What has compounded annually?

The interest charged on a loan or deposit is known as compound interest. It is the idea that we use the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The main distinction between compound and simple interest is this.

Compound interest can be calculated in math in a variety of ways depending on the circumstances. To make the calculations simpler, we can use the compound interest formula. We need to know the amount and the principal in order to calculate compound interest. The distinction is between the amount and the principal.

Given that  $12,000 is invested in a project at 7% for 9 years.

The formula of compound interest is

A = P(1+r/n)^nt

A = amount

P = principal

r = rate of interest

t = time

n =  number of compound interest per annum

For the given problem:

P =12,000, r = 7%, t = 9, n = 365:

The amount after 9 years will be:

A = 12,000(1+0.07/365)^(365×9)

A = 6,495,554.308

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The annual percentage rate is 19.59%.

An expression contains terms with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Repayment months =  48

Interest rate = 10%

The annual percentage rate.

=  (2 x repayment months x interest rate) ÷ (repayment months + 1)

= (2 x 48 x 10/100) / (48 + 1) x 100

= (2 x 48 x 0.10) / 49 x 100

= 9.6/49 x 100

= 0.1959 x 100

= 19.59%

Thus,

The annual percentage rate is 19.59%.

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The potential energy of the roller coaster car at the top of a hill is 661,068.8 J.

The correct answer choice is option D

Potential energy is a form of energy which is dependent on the relationship between different system components.

The gravitational constant, g = 9.8 m/s².

Mass, m = 1088 grams

Height, h = 62 meters

So, The amount of potential energy the car has;

PE = mgh.

PE = 1088 × 9.8 × 62

PE = 661,068.8J

Ultimately, the car has a potential energy of 661,068.8J.

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Note that the size of angle x = 115°. This is a problem relating to the sum of angles in a circle. See the computation below.

The sum of angles in a circle is always equal to 360 degrees or 2π radians.

This means that the sum of the measures of the angles formed by any number of rays or line segments that meet at a common point, or vertex, and whose endpoints lie on the circle, will always add up to 360 degrees or 2π radians. This property is often used in geometry and trigonometry to solve problems involving circles and angles.

With regard to the above problem,

We are given three angles in a circle named as follows:

a) 81°

b) 164°

c) x

The above rule state that

81 + 164 + x = 360°

thus, x = 360 - 81 - 164

x = 360 -245

x = 115°

Thus the value of ∠x is  115°

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Full Question:

See attached image.

If AD = 12 and BD = 36 in the right triangle ABC with altitude BD was drawn to hypotenuse AC, then the length of AC is 12√82.

What is the similarity law for triangles?

It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the complementary angles are congruent.

We can use the property of similar triangles to find the length of AC.

Since BD is an altitude of triangle ABC, we can write:

(AD)(DC) = (BD)²

Substituting the given values, we get:

12(DC) = 36²

Solving for DC, we get:

DC = (36)²/12 = 3 x 36 = 108

Now, using the Pythagorean theorem, we can write:

(AC)² = (AD)² + (DC)²

Substituting the given values, we get:

(AC)² = 12² + 108²

Simplifying and solving for AC, we get:

AC = √(12² + 108²) = √(12² x (1 + 9²)) = 12 x √(1 + 9²) = 12 x √(82)

Therefore,  If AD = 12 and BD = 36 in right triangle ABC with altitude

BD was drawn to hypotenuse AC, then the length of AC is 12√82.

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if the ratio of two sample variances exceeds the critical value of f at a defined confidence level, then the level of confidence also exceeds the critical level.

All tests that make use of the F-distribution are collectively referred to as "F Tests." The F-Test to Compare Two Variances is often what is meant when the term "F-Test" is used. However, a number of tests, including regression analysis, the Chow test, and the Scheffe test, use the f-statistic. If we are conducting an F-Test, we might employ a variety of technological tools. since doing an F-test manually while accounting for variations is a difficult and time-consuming operation.

if the ratio of two sample variances exceeds the critical value of f at a defined confidence level, then the level of confidence also exceeds the critical level.

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There are 2(3/16) cups of shredded cheese on each pizza.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Large pizza = 1(1/4) cups of sauce

Now,

1(3/4) of the sauce = shredded cheese

The amount of shredded cheese.

= 1(3/4) x 1(1/4)

= 7/4 x 5/4

= 35/16

= 2(3/16)

Thus,

The amount of shredded cheese is 2(3/16).

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If Erin were to lay the index cards in one long row, the row would be 35 inches long.

What is Multiplication?

Multiplication is an arithmetic operation that is used to find the result of combining equal groups of a given quantity. It involves repetitive addition of equal groups, where one factor represents the number of groups, and the other factor represents the number of items in each group.

Solution:

If Erin has 10 index cards, and each index card is 3 ½ inches long, then the total length of the row would be:

10 cards x 3 ½ inches per card = 35 inches

Therefore, if Erin were to lay the index cards in one long row, the row would be 35 inches long.

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Answer:

Step-by-step explanation:

sinX = 18/32

sinX = 0.5625

X = 34.23

The Formula will be in form of exponential function that is y=$3200(1.09)ˣ

where x= no. of years.

What exactly are exponential functions?

An exponential function is a mathematical function with the formula f (x) = aˣ, where "x" is a variable and "a" is a constant that is termed the function's base and must be greater than zero. The transcendental number e, which is approximately equal to 2.71828, is the most often used exponential function basis.

Growth that is exponential

The amount expands extremely slowly at first, then rapidly in Exponential Growth. The rate of change accelerates with time. As time passes, the pace of growth accelerates. The quick expansion is designed to represent a "exponential rise".

The exponential growth formula is: y = a (1+ r)ˣ, where r is the growth percentage.

Now,

Initial value=$3200

% increase=9%

then

Amount in x years will  be =3200(1+9/100)ˣ

=3200(109/100)ˣ

=3200(1.09)ˣ

Hence,

           The Formula will be in form of exponential function that is y=$3200(1.09)ˣ

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Answer:

D

Step-by-step explanation:

We can see that we are not increasing by the same amount.

[tex]\frac{1}{25}= \frac{2}{50} \neq \frac{3}{70} \neq \frac{5}{168}[/tex]

The coordinates of point H' will be: H'(3, 9)

We know that a translation is basically a transformation that occurs when an object is moved from one place to another place.

The original object's dimensions, orientation, or shape are unaffected by translation.

Translating a point P(x, y) 1 unit up means we need to add to use P'(x, y+1), that is adding 1 unit to the y-coordinate of the point P'(x, y).

Now we have to translate the triangle 1 unit up. So, use the formula

P(x, y) → P'(x, y + 1)

Thus, the coordinates of point H' will be:

H( 3, 8) → H'( 3, 8+1) → H'(3, 9)

Therefore, the coordinates of point H' will be: A'(3, 9).

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The triangles are congruent using: 1. LM = LO - segments of the same length as given. 2. LN = LN - common segment. 3. Angle MLN = Angle OLN - LN bisects the angle. 4. ΔMLN ≅ ΔOLN - SAS criteria.

A triangle is a closed polygon with three line segments that intersect at each of its three angles.

When the sides and angles of two triangles match, the triangles are said to be congruent. Thus, two triangles can be placed side by side and angle by angle on top of one another.

Given that the segments LM = LO, and LN bisects angle MLO.

Thus,

1. LM = LO - segments of the same length as given.

2. LN = LN - common segment

3. Angle MLN = Angle OLN - LN bisects the angle.

4. ΔMLN ≅ ΔOLN - SAS criteria.

Hence, the triangles are congruent using: 1. LM = LO - segments of the same length as given. 2. LN = LN - common segment. 3. Angle MLN = Angle OLN - LN bisects the angle. 4. ΔMLN ≅ ΔOLN - SAS criteria.

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The probability of drawing an orange marble and then a green marble without replacement  is (a) 1/15 .

The probability of drawing an orange marble on the first draw = 2/10 because there are 2 orange marbles out of total of 10 marbles .

After 1 orange marble is drawn, there are 9 marbles left in the box, of which 3 are green.

So, the probability of drawing a green marble on the second draw, given that an orange marble was drawn on the first draw, is 3/9.

⇒ P(orange, green) = P(orange) × P(green | orange was drawn)

⇒ P(orange, green) = (2/10) × (3/9) = 6/90 = 1/15  ;

Therefore , the value of P(Orange , Green) is = 1/15 .

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The given question is incomplete , the complete question is

A box contains 5 purple marbles, 3 green marbles and 2 orange marbles. Draws are made without replacement. P(orange ,green)

(a) 1/15

(b) 2/15

(c) 3/31

(d) 1/5

The measured value x = 13.

What is parallelogram?

A unique variety of quadrilateral made up of parallel lines is known as a parallelogram. A parallelogram can have any angle between its adjacent sides as long as its opposite sides are parallel. If two opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Consequently, a quadrilateral in which both pairs of opposite sides are parallel and equal is known as a parallelogram.

We can solve this easily using alternative interior angles. A parallelogram's interior is always 360 degrees, right?

In the given parallelogram the side vy = yx

VY = YX = 80 = 6x+2

6x = 80-2=78

x = 78/6= 13

Hence The measured value x = 13.

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Answer:

5,840,000

Step-by-step explanation:

Let P be the population after x years. The population after 24 years is 2P. So, we have:

P = 365,000 * 2^(x/24)

To find the population after 96 years, we plug in x = 96:

P = 365,000 * 2^(96/24) = 365,000 * 2^4 = 365,000 * 16 = 5,840,000

So, the population of the city will be 5,840,000 after 96 years.

Answer:

Step-by-step explanation:

The domain of f  * g is the set of all real numbers x such that x ≤ 6.

In interval notation, we can write:

Domain of f * g = (-∞, 6].

What is the domain of the function?

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The domain of the function f(x) = √(6-x) is the set of all real numbers x such that 6-x ≥ 0, which is x ≤ 6.

The domain of the function g(x) = x² - x is the set of all real numbers x, since there are no restrictions on the input.

To find the domain of the function f * g, we need to consider the values of x for which the expression f(x) * g(x) is defined.

We have:

f(x)g(x) = √(6-x)(x² - x)

The expression is defined only if both factors are defined.

For the first factor, √(6-x) to be defined, we need 6-x ≥ 0. This means that x ≤ 6.

For the second factor, x² - x to be defined, there are no restrictions on the input.

Therefore, the domain of f * g is the set of all real numbers x such that x ≤ 6.

In interval notation, we can write:

Domain of f * g = (-∞, 6].

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The value of the piecewise function f(-2) + 2f(-1) - f(3) is -14

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

The definition of a piecewise function

Given that

f(-2) + 2f(-1) - f(3)

Using the definition of the piecewise function and the domain values. we have

f(-2) + 2f(-1) - f(3) = -(-2)^2 + 3(-2) + 2(4(-1)^3) + [(3 + 5)/(3 - 1)]

Evaluate

f(-2) + 2f(-1) - f(3) = -14

Hence, the solution is -14

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The probability that a randomly selected cat has no treatment and no fleas is 43/87.

It is a branch of mathematics that deals with the occurrence of a random event.

Total number of cats = (cats sprayed with flea deterrent + cats with no treatment)

= (33+6 + 43+5)

=87

we need to find the number of cats with no treatment and no fleas, and divide it by the total number of cats.

Now we can see that the number of cats with no treatment and no fleas is 43.

Therefore, the probability that a randomly selected cat has no treatment and no fleas is:

P(no treatment and no fleas) = number of cats with no treatment and no fleas / total number of cats

= 43 / 87

Hence, the probability that a randomly selected cat has no treatment and no fleas is 43/87.

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The low Q₁ is 13 and the median Q₃ is 16.5, the high is 18 and the interquartile range is 3.5

The interquartile range is a measure of dispersion that tells us how spread out the middle 50% of a dataset is. To calculate the IQR, we first need to find the quartiles of the dataset. Quartiles divide a dataset into four equal parts, with the first quartile (Q₁) representing the 25th percentile, the second quartile (Q₂) representing the 50th percentile (also known as the median), and the third quartile (Q₃) representing the 75th percentile.

To find the quartiles of the dataset {10, 13, 13, 14, 15, 15, 16, 17, 18}, we first need to order the data in ascending order:

10, 13, 13, 14, 15, 15, 16, 17, 18

The low is the smallest value in the dataset, which is 10.

To find Q₁, we need to find the value that is 25% of the way through the dataset. Since we have 9 values in our dataset, 25% of 9 is 2.25. This means that Q₁ lies between the 2nd and 3rd values in the dataset, which are both 13. To find the exact value of Q₁, we can take the average of these two values:

Q₁ = (13 + 13) / 2 = 13

The median is the middle value in the dataset, which is 15.

To find Q₃, we need to find the value that is 75% of the way through the dataset. 75% of 9 is 6.75, which means that Q₃ lies between the 6th and 7th values in the dataset, which are 16 and 17, respectively. To find the exact value of Q₃, we can take the average of these two values:

Q3 = (16 + 17) / 2 = 16.5

The high is the largest value in the dataset, which is 18.

Now that we have found the quartiles, we can calculate the IQR by subtracting Q1 from Q₃:

IQR = Q₃ - Q₁ = 16.5 - 13 = 3.5

Therefore, the interquartile range of the dataset {10, 13, 13, 14, 15, 15, 16, 17, 18} is 3.5. This tells us that the middle 50% of the dataset is relatively tightly clustered around the median, with values ranging from 13 to 16.5.

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A sorting algorithm is defined as an algorithm that sorts the elements of a list. The most commonly used sequences are numerical sequence and lexicographical sequence, ascending or descending.

A sorting algorithm is used to reorder an array or list of elements according to an element comparison operator. Comparison operators are used to define a new order of elements in that data structure. Consider example, The above list of characters is sorted in ascending order by their value. That is, characters with lower values are placed before characters with higher values. It is important in real life because it supports the development of the scientific concept that things can be owned and organized into distinct groups (e.g. creatures, cars, weather types, etc.). We will now discuss some real-world examples of using sorting algorithms.

1) Your phone's contact list is sorted. This means that your data is organized in this way so you can easily access the contacts you want from your phone. That is, "I ordered."

2) Paper sorting : Imagine a teacher sorting students' work alphabetically by student name. This type of operation is similar to the functionality of sorting algorithms such as bucket sort. Sorting is more efficient process.

3) Traffic lights : Traffic lights are a good example of how algorithms are used in the real world around us. Next time you get stuck in a car at a red light, think about the algorithm that traffic lights run." Most traffic lights don't automatically switch between green, yellow, and red. This algorithm is a well-established turn-by-turn algorithm that directs traffic correctly. It's in order (it may not seem that way when you're sitting at a red light).

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The side length of the square with the same area as the circle is given as follows:

9.75 cm.

The area of a circle of radius r is given by π multiplied by the radius squared, as follows:

A = πr²

The radius for this problem is of 5.5 cm, hence the area of the circle is given as follows:

A = π x 5.5²

A = 95.03 cm².

For a square of side length s, the area is given by the side length squared, that is:

A = s².

Hence the desired side length is obtained as follows:

s² = 95.03

s = sqrt(95.03)

s = 9.75 cm.

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[tex]\cot\left(\frac{\pi}{2}-\theta\right)=\tan(\theta) \hspace{5em}\cos\left(\frac{\pi}{2}-\theta\right)=\sin(\theta) \\\\\\ \textit{Symmetry Identities} \\\\ \sin(-\theta )=-\sin(\theta) \hspace{5em}\cos(-\theta )=\cos(\theta )\hspace{4em} \tan(-\theta)=-\tan(\theta ) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cot\left(\frac{\pi}{2}-x\right)=-1.84\implies \tan(x)=-1.84 \\\\\\ \tan(-x)\implies -\tan(x)\implies -(-1.84)\implies \text{\LARGE 1.84} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\sin(\theta )=-0.57\implies \cos\left(\frac{\pi}{2}-\theta\right)=-0.57 \\\\\\ \boxed{\alpha = \frac{\pi}{2}-\theta} \hspace{5em}\cos(-\alpha)= \cos(\alpha) \\\\\\ \cos\left[ -\left(\frac{\pi}{2}-\theta\right) \right]\implies \cos\left(\theta -\frac{\pi}{2}\right)=\cos\left(\frac{\pi}{2}-\theta\right) \implies \cos\left(\theta -\frac{\pi}{2}\right)=\text{\LARGE -0.57}[/tex]