HELP PSLSSSSSSSSSSSSSS

the difference of two squares, you will use the formula. answers are (x + y)(x - y), (x + 4)(x - 4), (a + 5)(a - 5), (x + 11)(x - 11), (15 + a)(15 - a), (20 + y)(20 - y), (30 + z)(30 - z), (2x + 7)(2x - 7), (4x + 5)(4x - 5), 8(3x + 4)(3x - 4), (8 + a)(8 - a),8(3x + 4)(3x - 4), (5a + 4)(5a - 4), 9(a + 9)(a - 9), (7a + 2)(7a - 2), (10x + 3)(10x - 3), (8x + 5)(8x - 5),4(6x + 5)(6x - 5), 25(x + y)(x - y)

what is formula ?

A formula is a mathematical equation or expression that is used to solve a specific problem or perform a specific calculation. Formulas are often used in mathematics, physics, chemistry, engineering, and other fields to express a relationship between different variables or quantities.

In the given question,

Sure! To solve by finding the difference of two squares, you will use the formula:

a² - b² = (a + b)(a - b)

Using this formula, we can simplify the expressions given:

x² - y² = (x + y)(x - y)

=>  (x + y)(x - y) =0

=>  (x + y)=0    , (x - y)=0

=> x = -y   ,x = y

x² - 16 = (x + 4)(x - 4)

=>  (x + 4)(x - 4) =0

=>  (x + 4)=0    , (x - 4)=0

=> x = -4   ,x = 4

a² - b² = (a + b)(a - b)

a² - 25 = (a + 5)(a - 5)

x² - 121 = (x + 11)(x - 11)

225 - a² = (15 + a)(15 - a)

400 - y² = (20 + y)(20 - y)

900 - z² = (30 + z)(30 - z)

4x² - 49 = (2x + 7)(2x - 7)

16x² - 25 = (4x + 5)(4x - 5)

36x² - 64 = (6x + 8)(6x - 8) = 8(3x + 4)(3x - 4)

64 - a² = (8 + a)(8 - a)

36x² - 64 = (6x + 8)(6x - 8) = 8(3x + 4)(3x - 4)

25a² - 16 = (5a + 4)(5a - 4)

9a² - 81 = 9(a + 9)(a - 9)

49a² - 4 = (7a + 2)(7a - 2)

100x² - 9 = (10x + 3)(10x - 3)

64x² - 25 = (8x + 5)(8x - 5)

144x² - 100 = 4(6x + 5)(6x - 5)

25x² - 25y² = 25(x + y)(x - y)

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Answer:

1. x^2 - y^2 = (x+y)(x-y)

2. x^2 - 16 = (x+4)(x-4)

3. a^2 - b^2 = (a+b)(a-b)

4. a^2 - 25 = (a+5)(a-5)

5. x^2 - 121 = (x+11)(x-11)

6. 225 - a^2 = (15+a)(15-a)

7. 400 - y^2 = (20+y)(20-y)

8. 900 - z^2 = (30+z)(30-z)

9. 4x^2 - 49 = (2x+7)(2x-7)

10. 16x^2 - 25 = (4x+5)(4x-5)

11. 36x^2 - 64 = 4(3x+4)(3x-4) or (6x+8)(6x-8)

12. 64 - a^2 = (8+a)(8-a)

13. 36x^2 - 64 = (6x+8)(6x-8) or 4(3x+4)(3x-4)

14. 25a^2 - 16 = (5a+4)(5a-4)

15. 9a^2 - 81 = 9(a+3)(a-3)

16. 49a^2 - 4 = (7a+2)(7a-2)

17. 100x^2 - 9 = (10x+3)(10x-3)

18. 64x^2 - 25 = (8x+5)(8x-5)

19. 144x^2 - 100 = 4(6x+5)(6x-5) or (12x+5)(12x-5)

20. 25x^2 - 25y^2 = 25(x+y)(x-y)

Step-by-step explanation:

:)

(a)the volume will reach 275000 shares in a week at two different times.

(b)the volume will reach 400,000 shares in a week at two different times.

(a) 275,000 shares in a week (V=2750),  solve the equation:

the part of the quadratic formula underneath the square root symbol.

[tex]250t - 5t^2 = 2750\\5t^2 - 250t + 2750 = 0[/tex]

by quadratic formula,

t = [250 ± ([tex]\sqrt{250^2 - 4(5)(2750))}[/tex]]/(2(5))

t = [250 ± [tex]\sqrt{187500}[/tex]]/10

t = [250 ± [tex]50\sqrt{3}[/tex]]/10

[tex]t = 25 ± 5\sqrt{3}[/tex]

Since both solutions are real, the volume will reach 275000 shares in a week at two different times.

(b)  400,000 shares in a week,  solve the equation:

[tex]250t - 5t^2 = 4000\\5t^2 - 250t + 4000 = 0[/tex]

by discriminant formula, we have:

[tex]b^2 - 4ac = (-250)^2 - 4(5)(4000) = 2500[/tex]

the discriminant is positive but not equal to zero, the quadratic equation has two real roots. Therefore, the volume will reach 400,000 shares in a week at two different times.

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Therefore, it takes the flare 2 seconds to hit the water.

In mathematics, a factor refers to a number or an algebraic expression that divides another number or expression without leaving any remainder. For example, the factors of 6 are 1, 2, 3, and 6, since these numbers divide 6 evenly with no remainder. Similarly, the factors of x^2 - 4 are (x-2) and (x+2), since when multiplied together, they produce x^2 - 4.

Factors are important in many areas of mathematics, including algebra, number theory, and geometry. They are used to simplify and solve equations, factorize polynomials, and find common factors and multiples. Factors are also used in prime factorization, where a number is expressed as a product of its prime factors.

To find the time it takes the flare to hit the water, we need to solve the equation -16t² + 140t + 56 = 0 for t. We can start by factoring out a common factor of -4:

[tex]-16t^{2} + 140t + 56 = 0[/tex]

[tex]-4(4t^{2} - 35t - 14) = 0[/tex]

Next, we need to factor the quadratic expression inside the parentheses. We can do this by finding two numbers whose product is -56 (the constant term) and whose sum is -35 (the coefficient of the t term). The numbers are -7 and 8:

[tex]-4(4t^{2} - 35t - 14) = 0[/tex]

-4(4t + 7) (t - 2) = 0

Now we have a product of three factors that equals zero. According to the zero-product property, this means that one of the factors must be zero:

[tex]4t + 7 = 0 or t - 2 = 0[/tex]

Solving for t in each equation, we get:

[tex]4t = -7 or t = 2[/tex]

[tex]t = -7/4 or t = 2[/tex]

Since time cannot be negative, the only solution that makes sense is t = 2. Therefore, it takes the flare 2 seconds to hit the water.

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Answer:

It is A. dont ask i did that on paper

The solution for the system of equation is (8, 1), Hence the correct option is c.

The given system of equations is:

–3x + 2y = –22

–5y = –4x + 27

We can solve for x and y using elimination method:

–3x + 2y = –22

⇒ -3x + 2y = -22

–5y = –4x + 27

⇒  –4x + –5y = - 27

Eliminate x,

-3x + 2y = -22

-4x  - 5y = -27

That is

-12x + 8y = -88

-12x - 15y = −81

0  −7y = −7

or

-7y = -7

y = 7/7

y = 1

Solve for x by substituting the value of y in –3x + 2y = –22

–3x + 2(1) = –22

–3x + 2 = –22

–3x  = –22 - 2

–3x  = −24

x = 24/3

x = 8

Thus, The solution for the system of equation is (8, 1), Hence the correct option is c.

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Complete question:

Select the statement that correctly describes the solution to this system of equations.

–3x + 2y = –22

–5y = –4x + 27

A

There is no solution.

B

There are infinitely many solutions.

C

There is exactly one solution at (8, 1).

D

There is exactly one solution at (1, 8)

The amount of water wasted in a year is 36,960 gallons and the additional cost on the water bill due to the leaky faucet is $381.31.

(a). We know that the faucet leaks 9 oz of water per minute. There are 60 minutes in an hour and 24 hours in a day, so the total number of minutes in a day is

60 x 24 = 1440

The number of ounces of water wasted in a day is

1440 x 9 = 12,960.

To find out how many ounces of water is wasted in a year, we multiply the number of ounces wasted in a day by the number of days in a year is

12,960 x 365 = 4,734,240 oz.

To convert the number of ounces wasted in a year to gallons, we divide by the number of ounces in a gallon is

4,734,240 ÷ 128 = 36,960

(b). Water costs ​$10.31 per 1000​ gal, so to find the cost per gallon

$10.31 ÷ 1000 = $0.01031 per gallon.

To calculate the additional cost on the water bill, we multiply the number of gallons wasted in a year by the cost per gallon is

36,960 x $0.01031 = $381.31.

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The length of the room on the blueprint is 12 inches.

what is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

To solve this problem, we first need to find the length of Jean's bedroom in real life.

Let L be the length of Jean's bedroom in real life. According to the problem, the width of the room is 9 feet, so we can write:

9 = 0.25x, where x is the width of the room on the blueprint.

Solving for x, we get:

x = 9/0.25 = 36

So the width of the room on the blueprint is 36 inches.

Since the width of the room on the blueprint is 75% of its length, we can write:

36 = 0.75L

Solving for L, we get:

L = 36/0.75 = 48

So the length of Jean's bedroom in real life is 48 feet.

To find the length of the room on the blueprint, we use the same scale of 0.25 inch = 1 foot. Therefore:

1 foot = 0.25 inch on the blueprint

48 feet = 48 x 0.25 = 12 inches on the blueprint

Therefore, the length of the room on the blueprint is 12 inches.

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The transformations that turn y = cos(x) into the graph of y = cos(5(x + 3)) - 2 is a horizontal translation of -3 units, followed by a horizontal compression by a factor of 5, and finally a vertical translation of -2 units.

To transform the graph of y = cos(x) into the graph of y = cos(5(x + 3)) - 2, we can use the following sequence of transformations:

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Answer: Since cos(theta) = 2/3 and theta is in quadrant IV, we know that sin(theta) is negative. We can use the Pythagorean identity to find the value of sin(theta):

sin^2(theta) + cos^2(theta) = 1

Substituting cos(theta) = 2/3, we get:

sin^2(theta) + (2/3)^2 = 1

Simplifying, we get:

sin^2(theta) = 1 - (2/3)^2 = 1 - 4/9 = 5/9

Since sin(theta) is negative in quadrant IV, we have:

sin(theta) = -sqrt(5/9) = -sqrt(5)/3

Therefore, sin(theta) = -sqrt(5)/3.

Step-by-step explanation:

Answer:

∠ B = 55°

Step-by-step explanation:

the sum of the 3 angles in triangle = 180° , that is

∠ B + 35° + 90° = 180°

∠ B + 125° = 180° ( subtract 125° from both sides )

∠ B = 55°

Answer:24x5^29

Step-by-step explanation:

(5^2 -1) x5^29

(25-1)x5^29

24x5^29

The probability that they will win the World Cup is 17.01%. This result is logical because when your team lost the first game, their chances of winning the World Cup decreased.

It is used to estimate the chance of winning, the chance of drawing a particular card, or the chance of rolling a particular number. It is a measure of the potential for a certain outcome to happen.

P(win WC| lost 1st game) = P (win WC ∩ lost 1st game) / P (lost 1st game)

P (win WC ∩ lost 1st game) = P (win WC) * P (lost 1st game| win WC)

= 0.63 * 0.27

= 0.1701

P (lost 1st game) = P (lost 1st game| win WC) + P (lost 1st game| lose WC)

= 0.27 + 0.73

= 1

Therefore, the probability that your team will win the World Cup is

0.1701 / 1 = 17.01%.

This result is logical because when your team lost the first game, their chances of winning the World Cup decreased.

This is because the team that wins the championship usually wins the first game of the series 67% of the time, so if your team did not win the first game, their chances of winning the championship decreased. Therefore, the probability that they will win the World Cup is 17.01%.

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Answer:

Step-by-step explanation:

Value of y can be found using the tan ratio of the angle.

tan 26.5 = opposite/adjacent

.49858161 = y/24

mulitply each side by 24

11.97 = y

Answer: The value of y=116.28ft

Step-by-step explanation:

tan x = opposite side/adjacent side

let x=26.5 degree

opposite side= y

adjacent side=24ft

Therefore,

 tan(26.5) = y/24

y = tan(26.5) * 24

tan(26.5) = 4.8450

y = 4.8450*24

y = 116.28ft

Answer:

4 cups=2 pint

3 cups=1.5 pint

5 cups=2.5 pints

Step-by-step explanation:

Because there are 2 cups in each pint, we can divide the number of cups by two to get the number of pints.

4/2=2

3/2=1.5

5/2=2.5

Let me know if you have any questions!

Answer:

it is 10 and 40 i think

Answer:

slope = -3

Step-by-step explanation:

The function f(x) = -3x + 125 is a linear function in slope-intercept form y = mx + b.  The slope, m, is -3.  This means that for every increase of 1°C, 3 less fish are caught.  

Let's start by simplifying both sides of the equation:

−4(3x + 2) = x + 2(x − 1)

−12x − 8 = x + 2x − 2 (distributing the negative 4)

−12x − 8 = 3x - 2 (combining like terms)

Now we can add 12x to both sides and add 2 to both sides:

−12x − 8 + 12x + 2 = 3x - 2 + 12x + 2

−6x = 0

Finally, we can divide both sides by -6 to isolate x:

x = 0

Now we can check which of the given equations is equivalent to this solution:

A. −12x + 2 = 3x − 1 (substituting x = 0 gives 2 = -1, which is false)

B. −12x − 8 = 2x − 2 (substituting x = 0 gives -8 = -2, which is false)

C. −8 = 15x − 2 (substituting x = 0 gives -8 = -2, which is false)

D. −15x = −10 (substituting x = 0 gives 0 = 0, which is true)

So the answer is D.

Answer:

Step-by-step explanation:

First, let's solve the equation -4(3x + 2) = x + 2(x − 1):-

→ [tex]\boxed{\bf {x=-\frac{2}{5}\;\;or\:\:x=-0.4}}[/tex]

________________________

A. -12x + 2 = 3x - 1

The sides are not equal therefore, this equation is false and not equivalent to −4(3x + 2) = x + 2(x − 1).

________________________

B. -12x - 8 = 2x - 2

Sides are not equal therefore, this equation is false and not equivalent to −4(3x + 2) = x + 2(x − 1).

________________________

C. −8 = 15x − 2

Sides are equal therefore, this equation is True and is equivalent to −4(3x + 2) = x + 2(x − 1).

________________________

D. -15x = -10

Sides are not equal therefore, this equation is false and not equivalent to −4(3x + 2) = x + 2(x − 1).

Hence, C. -8 = 15x - 2 is the only equation equivalent to -4(3x + 2) = x + 2(x - 1).

______________________

Hope this helps!

The degree of the polynomial is 9.

What is polynomial in maths?

In mathematics, a polynomial is an expression composed of variables (also called indeterminates) and coefficients, and involves only addition, subtraction, multiplication, and non-negative integer powers of the variables. An example of a single indefinite x-polynomial is x2 − 4x + 7.

                                     Polynomials can be classified by the number of terms with nonzero coefficients, so a 1st polynomial is called a monomial and a 2nd polynomial is called a monomial. Binomials, tripartite polynomials are called trinomials. The term "quaternomial" is sometimes used for a fourth-order polynomial.  

Determine the degree of  y = 10x⁹ - 18x⁸ + 12x⁶

                  Degree = 9

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Required area of the rhombus is 173 cm².

What is rhombus?

A rhombus is a parallelogram with four equal sides. It is also called a diamond or a lozenge. In a rhombus, opposite angles are equal, and the diagonals bisect each other at right angles. Since all sides of a rhombus are equal, its opposite sides are parallel, and its opposite angles are congruent. The area of a rhombus can be calculated by multiplying the length of one of its diagonals by the length of the other diagonal and dividing the result by 2.

Here given,the rhombus with a base of 20 centimeters and a height of 17.3 centimeters.

So, the area of the given rhombus is

[tex] \frac{1}{2} \times base \times \: height \\ = \frac{1}{2} \times 20 \times 17.3 \\ = 173[/tex]

So, Area = 173 cm²

Therefore, the area of the given rhombus is 173 cm².

Hence, the correct option is C.

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The probability that both marbles are red is approximately 0.245, rounded to 3 significant digits.

Probability is a branch of mathematics that deals with the study of uncertainty and randomness. It is used to describe the likelihood or chance of a particular event occurring. Probability is expressed as a number between 0 and 1, where 0 indicates an event is impossible, and 1 indicates that the event is certain to occur.

The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes. For example, if you roll a six-sided die, the probability of rolling a four is 1/6, because there is one way to roll a four out of six possible outcomes.

When the first marble is drawn, there are a total of 30 + 20 + 10 = 60 marbles in the box. If the first marble is red, then there are 29 red marbles left out of a total of 59. If the first marble is not red, then there are still 30 red marbles left out of a total of 59.

So, the probability that the first marble is red is:

P(Red on first draw) = 30/60 = 1/2

And the probability that the second marble is red, given that the first marble was red, is:

P(Red on second draw given first marble is red) = 29/59

The probability that the second marble is red, given that the first marble was not red, is:

P(Red on second draw given first marble is not red) = 30/59

To find the probability that both marbles are red, we need to multiply the probability of getting a red marble on the first draw by the probability of getting a red marble on the second draw given that the first marble was red:

P(Both marbles are red) = P(Red on first draw) × P(Red on second draw given first marble is red)

= (1/2) × (29/59)

= 0.245

Therefore, the probability that both marbles are red is approximately 0.245, rounded to 3 significant digits.

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Therefore , the solution of the given problem of unitary method comes out to be  -10 and 8 are the two numbers that sum up to -16 and multiply to -80.

This generally recognized ease, preexisting variables, and any crucial elements from the initial Diocesan customizable query may all be used to complete the task. If therefore, you might have another chance to interact with the item. Otherwise, major influences on algorithmic evidence will cease to exist.  

Here,

We can use the knowledge that if two numbers x and y multiply to a constant k and add to a constant z to solve this issue by writing:

=> xy=k and x+y=z

We have k = -80 and z = -16 in this instance. Thus, we can say:

=>  xy = -80

=>  x + y = -16

=>  (x + y)² = (x + y)² + (x + y)².

=>  (x + y)² = (-16)2 = 256 x, 2 + 2xy + y, 2 = (x + y), 2 - 4xy, which equals 256 - 4(-80) = 576.

Thus, we can say:

=>  x² + 2xy + y² = 576

=> [tex]x^{2} - 160x + y^{2} = 576[/tex]

=>[tex](-10) - 160(-10) + 8^{2} = 576[/tex]

Since x = -10 and y = 8 satisfy the equation, this is correct. Therefore, -10 and 8 are the two numbers that sum up to -16 and multiply to -80.

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If you earn a $65,000 salary, you would owe approximately $5,772.50 in FICA taxes.

As a self-employed individual on a $65,000 salary, you would owe $9,945.00 in FICA taxes.

Answer:

15/100

Step-by-step explanation:

8/10 is equal to 80/100

95/100 - 80/100 = 15/100

The final figure is congruent to the original figure because a reflection over the y-axis is an isometric transformation.

A translation is a rigid transformation that moves an object without rotating or reflecting it.

In a reflection transformation, all the points of an object are reflected or flipped on a line called the axis of reflection or line of reflection.

1) Given the original coordinates of A, B, and C:

A(7, 5), B(2, 9), C(1, 3)

To translate the triangle 4 units to the left and 8 units up, we add -4 to the x-coordinates and +8 to the y-coordinates:

New coordinates for A:

x-coordinate: 7 - 4 = 3

y-coordinate: 5 + 8 = 13

Therefore, A after translation is A(3, 13).

2) To reflect A over the y-axis, we use the rule for reflecting a point over the y-axis, which is to keep the y-coordinate unchanged and change the sign of the x-coordinate:

New coordinates for A after reflection:

x-coordinate: -3

y-coordinate: 13

Therefore, A after reflection is A(-3, 13).

3) The rule for reflecting a point (x,y) over the y-axis is:

(x, y) -> (-x, y)

This means that we take the original x-coordinate, change its sign, and keep the y-coordinate the same.

4) The coordinates for A after reflection are (-3, 13).

5) Yes, the final figure after translation and reflection is congruent to the original figure. This is because both translation and reflection are rigid transformations, which means they preserve distances and angles, and therefore, they preserve the shape and size of the original figure. Translation preserves the orientation of the figure, and reflection preserves the orientation and reverses the handedness. Therefore, the new figure is congruent to the original figure.

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The function that determines the number of triangles in any given level of the pyramid is given as n = n ×(n + 1) / 2 where 'n' represents the level of the pyramid.

It is a rule that assigns to each input value a unique output value, based on a specific set of operations or calculations. Functions are commonly represented using function notation, such as f(x) or g(y), where the input variable (x or y) is substituted into an expression to obtain the corresponding output value.

A pyramid is a geometric shape that has a polygonal base and triangular faces that meet at a common vertex. The polygonal base can be any shape, such as a square, rectangle, triangle, or polygon, and the number of triangular faces depends on the number of sides of the base. Pyramids are named according to the shape of their base, such as a square pyramid, rectangular pyramid, triangular pyramid, or pentagonal pyramid.

Args:

level (int): The level of the pyramid.

Returns:

int: The number of triangles in the given level.

if level ≤ 0:

return 0

else:

Each level of the pyramid has one large triangle at the top

and additional smaller triangles underneath it, forming a pattern

of 1 + 2 + 3 + ... triangles, where each term is the level number.

The number of triangles in a given level can be calculated as the

sum of the first 'level' numbers using the formula (n × (n + 1)) / 2.

num of triangles = (level × (level + 1)) // 2

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There is not enough Evidence to support the claim that more than 20% of users of the pain medication will develop nausea.

To test the claim that more than 20% of users of a pain medication will develop nausea, we can use a hypothesis test with a significance level of 0.05. The null hypothesis (H0) would be that the proportion of users who develop nausea is less than or equal to 0.20, while the alternative hypothesis (Ha) would be that the proportion is greater than 0.20.

To conduct the test, we can use the binomial distribution since we are looking at the number of successes (subjects who develop nausea) out of a fixed number of trials (total number of subjects). We can calculate the expected number of successes under the null hypothesis by multiplying the total number of subjects (239) by the assumed proportion (0.20). This gives an expected number of 47.8 subjects who would develop nausea.

We can then use a one-sample z-test to compare the observed proportion of subjects who developed nausea (52/239 = 0.218) to the expected proportion under the null hypothesis (0.20). The test statistic is calculated as (0.218 - 0.20) / sqrt(0.20 * 0.80 / 239), which is approximately 1.08.

With a significance level of 0.05 and one-sided test, the critical value for the z-statistic is 1.645. Since the calculated test statistic (1.08) is less than the critical value (1.645), we fail to reject the null hypothesis. Therefore, there is not enough evidence to support the claim that more than 20% of users of the pain medication will develop nausea.

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Answer:

1. 60 ft^2

2. 175 cm^2

3. 36 cm^2

4. ≈ 121 cm^2

Step-by-step explanation:

1.

First, let's find the area of the whole rectangle:

A (whole) = 7 × 12 = 84 ft^2

Then, we have to find the area of the smaller rectangle which is inside the whole rectangle:

A (smaller) = 3 × 8 = 24 ft^2

Finally, let's subtract the area of the smaller rectangle from the area of the whole rectangle and we'll get the answer:

A (shaded) = 84 - 24 = 60 ft^2

.

2.

The opposite side lengths of a rectangle are equal

First, we can find the shorter side's length of each shorter rectangle:

(16 - 9) / 2 = 3,5 cm

A shorter side of the larger rectangle would be:

16 - 9 = 7 cm

Now, we can find the area of two smaller rectangles that are on top of the larger one:

A (2 smaller rectangles) = 9 × 3,5 × 2 = 63 cm^2

Also, we have to find the area of the larger rectangle:

A (larger) = 16 × 7 = 112 cm^2

In order to find the area of the shaded region, we have to add both of these areas together:

A (shaded) = 63 + 112 = 175 cm^

.

3.

Given:

h = 12 cm

b (triangle's base) = 9 cm

a (rectangle's longer side) = 6 cm

c (rectangle's shorter side) = 3 cm

Find: A (shaded) - ?

First, let's find the area of the triangle:

[tex]a(triangle) = \frac{1}{2} \times b \times h[/tex]

[tex]a(triangle) = \frac{1}{2} \times 9 \times 12 = 54 \: {cm}^{2} [/tex]

Now, we have to find the area of the rectangle:

[tex]a(rectangle) = a \times c = 6 \times 3 = 18 \: {cm}^{2} [/tex]

In order to find the area of the shaded region, we have to subtract the rectangle's area from the triangle's area:

[tex]a(shaded) = 54 - 18 = 36 \: {cm}^{2} [/tex]

.

4.

Given:

r (radius) = 7 cm

a (rectangle's longer side) = 11 cm

b (rectangle's shorter side) = 3 cm

Find: A (shaded) - ?

First, let's find the area of the circle:

[tex]a(circle) = \pi {r}^{2} = \pi \times {7}^{2} = 49\pi \: {cm}^{2} [/tex]

Now, we have to find the area of the rectangle:

[tex]a(rectangle) = a \times b = 11 \times 3 = 33 \: {cm}^{2} [/tex]

In order to find the shaded area, we have to subtract the rectangle's area from the circle's area:

[tex]a(shaded) = 49\pi - 33 ≈ 121 \: {cm}^{2} [/tex]

the inn had the greatest number of guests in December 2023, with 1428 guests staying at the inn during that month.

To find the month with the greatest number of guests, we need to find the maximum value of N(x) over the range of x from 0 to 11 (representing January to December).

We can find the maximum value of N(x) by taking the derivative of N(x) with respect to x, setting it equal to zero, and solving for x. However, since N(x) is a quadratic function, we can also use the vertex formula to find the x-value of the vertex of the parabola.

The vertex formula states that the x-value of the vertex of the parabola   [tex]y = ax^2 + bx + c[/tex] is given by [tex]x = -b/2a[/tex] .

In this case, N(x) is a quadratic function with a = -10%, b = 120, and c = 120. Plugging these values into the vertex formula, we get:

[tex]x = -b/2a = -120/(2\times -10%) = 60[/tex]

Since x represents the number of months after January 2019, the month with the greatest number of guests is the 60th month after January 2019, which is December 2023.

To find the number of guests who stayed at the inn during that month, we can plug x = 11 (representing December) into the formula for N(x):

[tex]N(11) = -10%(11^2) + 120(11) + 120[/tex]

[tex]= -0.1(121) + 1320 + 120[/tex]

[tex]= -12.1 + 1440[/tex]

[tex]= 1427.9[/tex]

Since the number of guests must be a whole number, we round 1427.9 to the nearest integer, which is 1428.

Therefore, the inn had the greatest number of guests in December 2023, with  [tex]1428[/tex] guests staying at the inn during that month.

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16) The number of guests during that month was 720.

17) In the year 2003, there were 4,600 triplet and higher order births.

18) The greatest average viewership occurred in the year 2015, with 17.95 million viewers per game.

16) How to find the month during which the inn had the greatest number of guests?

To find the month during which the inn had the greatest number of guests, we need to find the maximum value of the quadratic function N(x) = -10x² + 120x + 120.

We can begin by finding the x-coordinate of the vertex of this quadratic function, which is given by x = -b/2a, where a = -10 and b = 120.

x = -b/2a = -120/(2×(-10)) = 6

So the vertex of the quadratic function is at x = 6.

To find the maximum value of the function, we can evaluate N(6):

N(6) = -10(6)² + 120(6) + 120 = 720

So the inn had the greatest number of guests during the 6th month, which represents June 2019. The number of guests during that month was 720.

17) How to find the year when the number of triplet and higher order births was greatest?

To find the year when the number of triplet and higher order births was greatest, we need to find the maximum value of the function N(t). The formula for the maximum value of a quadratic function is -b/2a, where a is the coefficient of the squared term, b is the coefficient of the linear term, and c is the constant term.

In this case, a = -0.266 and b = 6.974. So, the t-value for the maximum number of triplet and higher order births is t = -b/(2a) = -6.974/(2×(-0.266)) = 13.12

Rounding this value to the nearest whole number, we get t = 13.

Therefore, the year when the number of triplet and higher order births was greatest is 1990 + 13 = 2003

To find the maximum number of triplet and higher order births, we substitute t = 13 into the function N(t):

N(13) = -0.266(13)² + 6.974(13) + 27.056 = 45.7 (in hundreds)

Rounding this value to the nearest whole number, we get 46.

Therefore, in the year 2003, there were approximately 4,600 triplet and higher order births

18) How to find the vertex of the quadratic function A(x)?

We can start by finding the vertex of the quadratic function A(x) to determine the year in which the greatest average viewership occurred:

The x-coordinate of the vertex of the quadratic function A(x) is given by x = -b/2a, where a = -0.59 and b = 3.5. Substituting these values,

x = -3.5/(2*(-0.59)) = 2.966

This means that the vertex occurs approximately 2.966 years after 2012, which corresponds to the year 2015.

To find the maximum average viewership, we can simply plug in x = 2.966 into the function A(x):

A(2.966) = -0.59(2.966)² + 3.5(2.966) + 12.71 ≈ 17.95 million viewers per game

Therefore, the greatest average viewership occurred in the year 2015, with approximately 17.95 million viewers per game.

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1. First, we need to find the volume of the hemisphere bowl:

V_bowl = (2/3)πr^3

V_bowl = (2/3)π(6 cm)^3

V_bowl = 288π cm^3

Since water fills two-fifths of the volume, we can find the volume of water:

V_water = (2/5)V_bowl

V_water = (2/5)(288π cm^3)

V_water = 115.2π cm^3

2. Now, we need to find the radius and height of the cone to which the water is poured. Let's call the radius of the cone r and the height h. We know that the volume of the cone is equal to the volume of the water in the bowl:

V_cone = V_water

(1/3)πr^2h = 115.2π

r^2h = 345.6

We also know that the depth of the water in the cone is 12 cm, so h = 12 cm. Substituting this value into the equation above, we get:

r^2(12 cm) = 345.6

r^2 = 28.8

r ≈ 5.36 cm

So, the radius of the cone is approximately 5.36 cm, and the height is 12 cm.

Barbara Smith made $6,492 in total last month from her $42,800 in sales, 14% Commission, and her $500 monthly wage.

To calculate the total amount that Barbara Smith earns from A-1 Chemical Supply, we need to find her monthly salary, commission on sales, and then add them together.

1. Monthly Salary: Barbara receives a fixed monthly salary of $500.

2. Commission on Sales: To find her commission, we'll use the formula:
Commission = (Sales Amount) * (Commission Rate)

Barbara's sales for last month were $42,800, and she earns a 14% commission. To calculate the commission:
Commission = ($42,800) * (14/100)

3. Total Earnings: Add the monthly salary and commission to find Barbara's total earnings for the month.
Total Earnings = Monthly Salary + Commission

Now, let's calculate the commission and total earnings.

Commission = ($42,800) * (14/100) = $5,992

Total Earnings = $500 (Monthly Salary) + $5,992 (Commission) = $6,492

So, Barbara Smith earned a total of $6,492 last month, including her $500 monthly salary and 14% commission on her $42,800 in sales.

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