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Step-by-step explanation:

Given the following expression;

Math Game: M(d)=x^2-9x-10

Reading Game: R(d)=2x+10

x is the number of days since the games went on sale

In order to determine after how many days the revenue for each game wil be the same, we will equate M(d) to R(d)

M(d) = R(d)

x^2-9x-10  = 2x+10

x^2-9x-10 -2x-10 = 0

x^2-11x-20 = 0

factorize

x = 11±√121-4(-20)/2

x = 11±√121+80/2

x = 11±√201/2

x = 11±37.16/2

x = 11+37.16/2

x = 48.16/2

x = 24.06

Hence the revenue for each game will be the same after 24 days

It takes about 13 days for the revenue for each game the same.

Revenue is the amount of money made from selling a particular amount of products.

Given that the revenue is given by:

Math Game: M(d)=x²-9x-10

Reading Game: R(d)=2x+10

For both games to have the same revenue, hence:

M(d) = R(d)

x² - 9x - 10 = 2x + 10

x² - 11x - 20 = 0

x = -1.6 or x = 12.6

Since the number of days cannot be negative, hence it takes about 13 days for the revenue for each game the same.

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The conditional probability, in a single roll of two fair 6 sided dice, that the sum is greater than 6, given that neither die is a two : 17/25

We know that the conditional probability is given by,

P(B | A) = probability of occurrence of event B, given that event A has

               occurred

           = P(A ∩ B) / P(A)

Here, P(A ∩ B)  means the probability of happening two events A and B at the same time.

We also know that  if  P (B | A ) = P(B)   i.e.,   P(A ∩ B) = P(A) × P(B)  the two events A and B are independent of each other.

For this question, let the dice D1 and D2 are rolled once.  

Let the numbers displayed on the dice be d1 and d2 respectively.  

The dice D1 and D2 are independent.

We need to find the conditional probability that the sum is greater than 6, given that neither die is a two.

Let S represents the sum of the numbers displayed on the dice.

S = d1 + d2

The sum is even, if d1 = d2 is odd OR  if d1 = d2 is even

P(d1 = even) = 3/6

                    =1/2

P(d2=even) = 1/2

P(d1 = odd) = 1/2

P(d2 = odd) = 1/2

So, P(S = even) = [P(d1=even) × P(d2 = even)] + [P(d1= odd) × P(d2=odd)]

                          = [1/2 × 1/2] + [1/2 × 1/2]

                          = 1/2

So, we can say that, the sum is either even or odd which are equally likely and hence its probability is 1/2.

First we find the probability for the sum is greater than 6 i.e., P(S > 6)

The possible combination of d1 and d2 for the sum greater than 6 would be,

{(1,6), (2,5), (2, 6), (3, 4), (3, 5), (3, 6), (4,3), (4,4), (4,5), (4,6), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

⇒ n(S > 6) = 21

The number of all possible outcomes = 36

So, P(S > 6) = 21/36

                   = 7/12

Now we find the probability that neither die is a two

⇒ P(neither die is a two) = [P(1) ∪ P(3 ≤ d1 ≤ 6)]  AND  [P(1) ∪ P(3 ≤ d1 ≤ 6)]

⇒ P(neither die is a two) = 5/6 × 5/6

⇒ P(neither die is a two) = 25/36

Now, we find the probability that the sum S > 6 AND  neither die is a two.

The possible combination for  the sum S > 6 AND  neither die is a two would be,

{(1,6), (3, 4), (3, 5), (3, 6), (4,3), (4,4), (4,5), (4,6), (5,3), (5,4), (5,5), (5,6), (6,1), (6,3), (6,4), (6,5), (6,6)}

⇒ n(S > 6 AND neither die is a two) = 17

So, P(S > 6 AND neither die is a two) = 17/36

Now we find the conditional probability P(S > 6 | neither die is a two)

⇒ P(S > 6 | neither die is a two) = P(S > 6 AND neither die is a two) ÷

                                                           (neither die is a two)

⇒ P(S > 6 | neither die is a two) = (17/36) / (25/36)

⇒ P(S > 6 | neither die is a two) = 17/25

Therefore, the conditional probability, in a single roll of two fair 6 sided dice, that the sum is greater than 6, given that neither die is a two : 17/25

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The motion of the object which is described by the quadratic equation is a projectile motion, and the horizontal distance the object travels is 20 feet .

Projectile motion is the motion of an object which is thrust into the air and moves under the effect of gravitational force alone.

The equation in the question is; y = -x² + 16·x + 80

Where;

y = The vertical distance above the ground

x = The horizontal distance of the object

y = -x² + 16·x + 80

From which we get;

When the object hits the ground, y = 0, which indicates;

y = 0 = -x² + 16·x + 80

The value of x that is a solution to the above equation represents the distance the object travels before it reaches the ground.

-x² + 16·x + 80 = 0

x² - 16·x - 80 = 0

(x - 20)·(x + 4) = 0

x = 20 or x = -4

The distances at which the object reaches the ground are x = -4 feet or x = 20 feet

The possible distance the object will travel in the horizontal direction is 20 feet.

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Answer:

75+3x=180

Step-by-step explanation:

Answer:

75 + 3x = 180

Step-by-step explanation:

The sum of the measures of the angles of a triangle is 180°.

45 + 30 + 3x = 180

75 + 3x = 180

Answer:

Part A: \(\frac{3}{5}\)

Part B: \(\frac{1}{2}\)

Step-by-step explanation:

We know that Alinn flipped a coin 20 times, and that 12 of those times resulted in heads. The other 8 times resulted in tails.

Part A wants us to find the experimental probability of the coin landing on heads. Experimental probability is the probability determined based on the experiments performed.

Part B wants us to find the theoretical probability of the coin landing on heads. Theoretical probability is determined based on the number of favorable outcomes over the number of possible outcomes.

Experimental probability is determined as # of times something occurred experimentally / total number of times.  

Since 12 of the 20 times that Alinn flipped the coin resulted in heads, this means that the experimental probability of Alinn flipping heads is \(\frac{12}{20}\), which simplifies down to \(\frac{3}{5}\).

Theoretical probability, as stated above, is the number of favorable outcomes / possible outcomes.

Our favorable outcome is flipping heads, and on a coin, there are two sides that a coin can land on: heads and tails. This means that there are two possible outcomes, and only one of them is favorable.

This means that our theoretical probability is \(\frac{1}{2}\).

The maximum of a graph is found on the y axis. Considering the given interval, the point on the y axis is 4. Thus, the maximum of the graph over the interval is 4.

Answer:

D.) (-2 1/2, -2)

Step-by-step explanation:

The solution is where the two lines intersect.  The two lines intersect at x = -2.5 and y = -2

The distance covered by the rover is the perimeter of the trapezoid, and it is 40 meters.

See attachment for the path followed by the rover.

From the attached graph, we have the following lengths

\(AD = 9m\)

\(AB = 2m\)

\(DC = 14m\)

Next, we calculate the distance BC using the following Pythagoras theorem

\(BC^2 = AD^2 + x^2\)

Where:

\(x = 12\)

So, we have:

\(BC^2 = 9^2 + 12^2\)

\(BC^2 = 225\)

Take positive square root of both sides

\(BC = 15\)

The distance covered is the sum of the side lengths of the trapezoid.

So, we have:

\(Distance =AD + AB +DC + BC\)

This gives

\(Distance =9m+ 2m +14m + 15m\)

Add the lengths

\(Distance =40m\)

Hence, the distance covered by the rover is 40 meters

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We have the following:

The patient can consume approximately 2 cans of 12 oz Coca Cola without exceeding the advised sugar limit.

To determine the number of 12 oz cans of Coca Cola the patient can consume, we need to convert the sugar limit provided by the doctor into grams and then calculate the amount of sugar in a 12 oz can of Coca Cola.

Provided:

Sugar limit: 8.5 × 10^(-2) kg

Coca Cola sugar content: 110 g/L

Volume of a 12 oz can: 12 oz (which is approximately 355 mL)

First, let's convert the sugar limit from kilograms to grams:

Sugar limit = 8.5 × 10^(-2) kg = 8.5 × 10^(-2) kg × 1000 g/kg = 85 g

Next, we need to calculate the amount of sugar in a 12 oz can of Coca Cola:

Volume of a 12 oz can = 355 mL = 355/1000 L = 0.355 L

Amount of sugar in a 12 oz can of Coca Cola = 110 g/L × 0.355 L = 39.05 g

Now, we can determine the number of cans the patient can consume by dividing the sugar limit by the amount of sugar in a can:

Number of cans = Sugar limit / Amount of sugar in a can

Number of cans = 85 g / 39.05 g ≈ 2.18

Since the number of cans cannot be fractional, the patient should limit their consumption to 2 cans of Coca Cola.

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Step-by-step explanation:

It is given that,

Volume of the cylindrical can 1 is 2 litres and that of cylindrical can 2 is 6.75 litres. The diameter of the smaller can is 16 cm. We need to find the diameter of the larger can.

The formula of the volume of a cylinder is given by :

\(V=\pi r^2h\)

So,

\(\dfrac{V_1}{V_2}=\dfrac{r_1^2}{r_2^2}\)

Diameter, d = 2r

\(\dfrac{V_1}{V_2}=\dfrac{(d_1/2)^2}{(d_2/2)^2}\\\\\dfrac{V_1}{V_2}=(\dfrac{d_1^2}{d_2^2})\)

V₁ = 2 L, V₂ = 6.75 L, d₁ = 16 cm, d₂ = ?

\(\dfrac{2}{6.75}=(\dfrac{16^2}{d_2^2})\\\\d_2=29.39\ cm\)

So, the diameter of the larger can is 29.39 cm.

Answer:

176

Step-by-step explanation:

Apply PEMDAS

Solve the parenthesis first

11 ( 7 + 9 )

11 ( 16 )

Now open the parenthesis and you will have your answer

11 times 16

176

Answer:

Yes, by AA, since angle DEF is congruent to HEJ (vertical angles are congruent), and angle DFE is congruent to HJE.

So triangle DEF is similar to triangle HEJ.

The expression that represents the area of the gray region, the area of the land remaining in the backyard is 3x²+10x-17 square yards. The correct option is B.

The area of the gray region is the area of the rectangular backyard minus the area of the circular pond.

The area of the rectangular backyard is given as 6x+14x-12 square yards, which simplifies to 20x-12 square yards.

The area of the circular pond is given as 3x²-4x+5 square yards.

So, the area of the gray region is:

(20x-12) - (3x²-4x+5)

= 20x-12 - 3x²+4x-5

= 3x²+10x-17

Therefore, the expression that represents the area of the gray region, the area of the land remaining in the backyard is 3x²+10x-17 square yards.

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you can perform the calculations for both the surface and triple integrals to verify the Divergence Theorem for the given vector fields and regions.

To verify the Divergence Theorem for the given vector fields and regions, we need to evaluate both the surface integral and the triple integral over the region E and confirm that they are equal.

(a) For the vector field F(x, y, z) = y^2z^3i + 2yzj + 4z^2k and the solid E enclosed by the paraboloid z = x^2 + y^2 and the plane z = 9:

According to the Divergence Theorem, the surface integral of F over the closed surface S bounding E is equal to the triple integral of the divergence of F over the region E.

Surface Integral:

∫∫S F · dS

Triple Integral:

∫∫∫E ∇ · F dV

To calculate the divergence of F, ∇ · F, we need to find the partial derivatives of each component and then take their sum:

∇ · F = ∂(y^2z^3)/∂x + ∂(2yz)/∂y + ∂(4z^2)/∂z

= 0 + 2z + 8z

= 10z

Now, we can proceed with the calculations of the surface and triple integrals.

(b) For the vector field F(x, y, z) = <x^2, -y, z> and the solid cylinder E where y^2 + z^2 ≤ 9 and 0 ≤ x ≤ 2:

Similarly, we need to evaluate the surface integral and the triple integral to verify the Divergence Theorem.

Surface Integral:

∫∫S F · dS

Triple Integral:

∫∫∫E ∇ · F dV

To find the divergence of F, ∇ · F, we take the sum of the partial derivatives of each component:

∇ · F = ∂(x^2)/∂x + ∂(-y)/∂y + ∂z/∂z

= 2x - 1 + 1

= 2x

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the complete question is;

Verify that the Divergence Theorem is true for the vector field F on the region E.

(a). F(x,y,z)=y2z3i+2yzj+4z2k, E is the solid enclosed by the paraboloid z=x2+y2 and the plane z=9.

(b). F(x,y,z)=<x2,-y,z>, E is the solid cylinder y2+z2\leq9, 0\leqx\leq2

The measure of ∠O is 56°. The solution has been obtained by using properties of circles.

What is a circle?

A circle is a round-shaped figure that has no sides or edges. A circle is a closed shape, a two-dimensional shape, and a curved shape in geometry.

We are given that m∠R = 28°.

Now, we take a point P on the circumference of the circle.

We know that in a circle, the angles that the same arc subtends on the circumference have equal measurements.

So, both the angles i.e. ∠P and ∠R are same as they are subtended by the same arc.

Therefore, we get

m∠P = m∠R = 28°

Moreover, an arc's angle at the circle's centre is twice as large as its angle at the circle's edge.

So, from this we get

⇒ m∠O = 2 * m∠P

⇒ m∠O = 2 * 28°

⇒ m∠O = 56°

Hence, the measure of ∠O is 56°.

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The complete question has been attached below

Answer:

138°

Step-by-step explanation:

x+115°=6x° [ being vertically opposite angle]

or, 115=6x - x

or, 115=5x

or, 115/5 =x

or, x=23

Then,

x+115°

= 23+115°

=138°

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The surface area of the pyramid is 41. 29 In²

The formula for determining surface area of a square pyramid is expressed as;

Surface area = a² + 2a \(\sqrt{\frac{a^2}{4 } + h^2\)

Where;

Substitute the values

Surface area = \(4^2 + 2(4) \sqrt{\frac{4^2}{4} } + 6\)

Find the squares

Surface area = \(16 + 8 \sqrt{\frac{16}{4} + 6 }\)

Divide the values

Surface area = 16 + 8√10

Surface area = 16 + 8(31.16)

expand the bracket

Surface area = 16 + 25. 29

Surface area = 41. 29 In²

Hence, the value is 41. 29 In²

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The given expression ((y-b)²/(y-b+1)+(y-b)/(y-b+1) after being reduced to a polynomial, can be represented as y-b.

In order to reduce the given equation to a polynomial, we are required to simplify and combine like terms. First, we can simplify the expression in the numerator by expanding the square:

((y-b)²/(y-b+1) = (y-b)(y-b)/(y-b+1) = (y-b)²/(y-b+1)

Now, we can combine the two terms in the equation by finding a common denominator:

(y-b)²/(y-b+1) + (y-b)/(y-b+1) = [(y-b)² + (y-b)]/(y-b+1)

Next, we can combine the terms in the numerator by factoring out (y-b):

[(y-b)² + (y-b)]/(y-b+1) = (y-b)(y-b+1)/(y-b+1)

Finally, we can cancel out the common factor of (y-b+1) in the numerator and denominator to get the polynomial:

(y-b)(y-b+1)/(y-b+1) = y-b

Therefore, the equation ((y-b)²)/(y-b+1)+(y-b)/(y-b+1)  after being simplified, is equivalent to the polynomial y-b.

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The value of the unknown number x is 8.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

The given numbers include:

The sum of the given numbers is calculated as follows:

\(2 + 4 + \text{x} + 6 = 12 + \text{x}\)

The mean of the given 4 numbers is calculated as follows:

\(\dfrac{12+\text{x}}{4} =5\)

\(12+\text{x}=20\)

\(\text{x}=20-12\)

\(\text{x}=8\)

Thus, the value of the unknown number x is 8.

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The length of each piece of wire is 2.5 inches.

Fractions are used to depict the components of a whole or group of items. Two components make up a fraction. The numerator is the number that appears at the top of the line. It specifies how many identically sized pieces of the entire event or collection were collected. The denominator is the quantity listed below the line. The total number of identical objects in a collection or the total number of equal sections that the whole is divided into are both displayed. A fraction can be expressed in one of three different ways: as a fraction, a percentage, or a decimal. The first and most popular way to express a fraction is in the form of the letter ab. Here, a and b are referred to as the numerator and denominator, respectively.

Let the number of pieces = x

The length of the wire = 5/8 inches

The length of one piece of wire = 1/4 inch

According to the question,

1/4 x = 5/8

So, x = 5/8 × 4

x = 20/ 8

x = 5/2

x = 2.5 inch

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The volume of the cone is approximately 58.107 ft³.

Given:

Radius, r = 3.4 ft

Height, h = 4.8 ft

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the base of the cone and h is the height of the cone.

Using the given values in the formula, we can calculate the volume of the cone:

V = (1/3)π(3.4²)(4.8)

= (1/3)π(11.56)(4.8)

= (1/3)(3.1416)(55.4688)

≈ 58.107 ft³

Therefore, the volume of the cone is approximately 58.107 ft³.

The correct answer is A) 58.107 ft³.

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To begin solving this problem, we need to determine the dimensions of the rectangular region that the farmer will fence in. Let's say the length of thr uses, is given by the equation:
e rectangle is L and the width is W. The perimeter of the rectangle, which will be the length of fencing the farme
2L + W = 350

Solving for W, we get:

W = 350 - 2L

Next, we need to divide the rectangular region into three smaller rectangles by placing two parallel fences. Let's say the two fences are placed along the length of the rectangle, dividing it into three sections with widths of x, y, and z. Therefore, we have:

L = x + y + z

Now, we can determine the area of the entire fenced-in region by summing the areas of the three smaller rectangles. The area of a rectangle is given by the equation:

Area = Length x Width

Therefore, the total area of the fenced-in region is:

Area = (xW) + (yW) + (zW)

Substituting W = 350 - 2L and L = x + y + z, we get:

Area = (x(350-2(x+y+z))) + (y(350-2(x+y+z))) + (z(350-2(x+y+z)))

Simplifying this equation, we get:

Area = 350(x+y+z) - 2(x^2 + y^2 + z^2)

To maximize the area, we need to take the derivative of this equation with respect to one of the variables (x, y, or z), set it equal to zero, and solve for the variable. This process is too complicated to do by hand, so we will use a calculator or computer program to find the maximum area.

After finding the maximum area, we can determine the dimensions of the region that give us this maximum area. We do this by using the equations we derived earlier:

W = 350 - 2L

L = x + y + z

With the maximum area and these equations, we can solve for the dimensions of the region that give us the maximum area.

In summary, the farmer should fence in a rectangular region with dimensions that maximize the total area of three smaller rectangles created by placing two parallel fences. The maximum area can be found by taking the derivative of the area equation and setting it equal to zero. The dimensions of the region that give us the maximum area can be found by using the equations we derived earlier.

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a) nearest integer = -7

Step-by-step explanation:

hope it helps you

For this case we have a graph given with x representing the oranges in pounds and the y axis representing the cost in $

We want to find the cost of 1 pound of orange and for this case we need to look the intersection of the x axis at x=1 with the line provided.

We can find the unitary space of the y axis using this:

The reason is because we have 4 spaces between 0 and 1 in the y axis.

So then the answer for this case would be:

The cost of 1 pound of oranges is $5/4

Answer:

(-3,-5)

Step-by-step explanation:

The solution to the system of equation is where the two graphs intersect.

They intersect at x=-3 y=-5

Answer:

there are 120 slices of orange.

Step-by-step explanation:

The reason for this is because if theres 10 slices per orange, and there is 12 oranges, you multiply 10x12 and you get 120 slices.

Answer:  The correct answer is 0.70 total

Step-by-step explanation:

Use the expression 0.10d + 0.05n where

d = number of dimes (4)

n = number of nickels (6)

= 0.10 (4) + 0.05 (6)

= 0.40 + 0.30

total = 0.70