2. Blake interviewed 24 students to see whether they collected sports cards and whether they participated in sports. The table below shows his data Sports-Card Collecting and Sports Participation Collects Sports Cards Does Not Collect Sports Cards Participates in Sports 6 Does Not Participate in Sports 3 7 How many total students Blake interviewed, participate in sports?​

The dimensions of the rectangular field that maximize the enclosed area are 150 feet by 75 feet.

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

Let's call the length of the rectangle "l" and the width "w".

We can write two equations based on the given information -

Perimeter equation: 2l + 4w = 600 (since there are two sets of parallel sides, we have to add an extra "w" to the perimeter equation)

Area equation: A = 3lw (since the field is divided into 3 equal parts)

We want to maximize the enclosed area, which means we want to find the values of "l" and "w" that make the area as large as possible.

We can use the perimeter equation to solve for one of the variables in terms of the other -

2l + 4w = 600

2l = 600 - 4w

l = 300 - 2w

Now we can substitute this expression for "l" into the area equation -

A = 3lw

A = 3(300 - 2w)w

A = 900w - 6w²

To find the maximum area, we can take the derivative of this equation with respect to "w" and set it equal to zero -

dA/dw = 900 - 12w = 0

12w = 900

w = 75

So the width of each of the smaller rectangular plots is 75 feet.

We can use the perimeter equation to find the length -

2l + 4w = 600

2l + 4(75) = 600

2l = 300

l = 150

Therefore, the dimensions value are obtained as 150 feet by 75 feet.

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1. The equilibrium quantity = 60, the equilibrium price = 300

2. If the government imposes the tax of 24, the quantity supplies would fall to 56, and the price would rise to 308

At equilibrium we have P = Q

that is price is equal to quantity. Such that we would have:

420-2q = 60+ 4q

take the like terms

420 - 60 = 4q + 2q

360 = 6q

q = 360 / 6

q = 60

The equilibrium quantity = 60 then equilibrium price =

420-2q

420 - 2 * 60

300

The equilibrium price is 300

2. If the government imposes 24 dollar per unit

420-2q = 60+ 4q + 24

420 - 2q = 84 + 4q

420 - 84 = 4q + 2q

336 = 6q

56 = q

420-2 * 56

p = 308

If the government imposes the tax of 24, the quantity supplies would fall to 56, and the price would rise to 308

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Answer:

53.06 ft^2

Step-by-step explanation:

Calculate semi perimeter and use Scalence triangle area formula

Semi perimeter: a+b+c/2

Area of Scalence triangle: √s(s-a)(s-b)(s-c). {where s=semi perimeter}

Answer: I don't know

Answer:

Answer:

0.050

Rounded to the nearest 0.001 or

the Thousandths Place.

Step-by-step explanation:

Explanation

0.05__

You rounded to the nearest thousandths place. The _ in the thousandths place rounds down to 0 because the digit to the right in the ten thousandths place is _.

0.050

When the digit to the right is less than 5 we round toward 0.

0.05 was rounded down toward zero to 0.050

Answer:

Set the height equal to (1/2)gt^2 and solve for t.

h = (1/2)gt^2

t = (2h/g)^1/2

Plug in the numbers and get your answer in seconds:

h = 81 ft

g = 32 ft/s^2

Step-by-step explanation:

Answer:

The simplified expression is -13/12.  (are you sure you don't have a typo somewhere), double checked.

Step-by-step explanation:

First, let's simplify the expression inside the absolute value bars:

5/6 - 17/12 = 10/12 - 17/12 = -7/12

Next, we can simplify the expression outside the absolute value bars:

| -7/12 | - | 5/3 |

= 7/12 - 5/3 (since the absolute value of -7/12 is 7/12)

= 7/12 - 20/12

= -13/12

The simplified expression is -13/12.

_______________________

Simplify the following:

abs(5/6 - 17/12) - abs(5/3)

Put 5/6 - 17/12 over the common denominator 12. 5/6 - 17/12 = (2×5)/12 - 17/12:

abs(((2×5)/12 - 17/12)) - abs(5/3)

2×5 = 10:

abs(10/12 - 17/12) - abs(5/3)

10/12 - 17/12 = (10 - 17)/12:

abs(((10 - 17)/12)) - abs(5/3)

10 - 17 = -7:

abs((-7)/12) - abs(5/3)

Since 5/3 is a non-negative constant, abs(5/3) = 5/3:

abs(-7/12) - 5/3

Since -7/12 is a negative constant, abs(-7/12) = 7/12:

7/12 - 5/3

Put 7/12 - 5/3 over the common denominator 12. 7/12 - 5/3 = 7/12 + (4 (-5))/12:

7/12 - (5×4)/12

4 (-5) = -20:

7/12 + (-20)/12

7/12 - 20/12 = (7 - 20)/12:

(7 - 20)/12

7 - 20 = -13:

Answer: (-13)/12

The equivalent expression is (x -2)/(x+4)(x + 6)

It is important to note that algebraic expressions are defined as expressions composed of coefficients, terms, variables, constants and factors.

They are also made up of arithmetic operations.

Also, equivalent expressions are defined as expressions that have the same solution but differs in the arrangement of the terms.

From the information given, we have the expression;

(x - 2)/x² + 10x + 24

Now, let's factorize the denominator, we have;

x² + 10x + 24. Find the pair factors of 24 that add up to 10, we get;

x² + 4x + 6x + 24

Factorize in pairs

x(x + 4) + 6(x + 4)

Then, substitute the expressions;

(x -2)/(x+4)(x + 6)

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The sοlutiοn οf the given prοblem οf rectangle cοmes οut tο be E is the answer.

In the Euclidean plane, a rectangle is a square with fοur perpendicular edges. It is alsο referred tο as an equiangular parallelοgram οr a seemingly equal-sided rectangle. The trapezοid can alsο have a straight edge. Fοur οf the sides οf a square are equal in length. Rectangular quadrilaterals have fοur equal sides and fοur 90° edges. Its name is sοmetimes "rectangular trapezοid" as a cοnsequence.

Here,

Due tο the shared suits οf the adjacent sectiοns.

Therefοre,

Case 1: Triangles and circles must be arranged in a series fοr hοrizοntal fitting.

Therefοre,

A, C, and D are excellent οptiοns. Sο they can't be the sοlutiοns.

Again,

Case 2.

Tο accοmmοdate vertically,

Rectangle and Triangle need tο be in the same cοlumn. And B is where that is happening.

sο that,

The οnly exceptiοn is:

"E" is the answer.

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Complete question:

The longest flagopole that could fit in the box is 15.26 feet

The longest flagopole would have a length equal to the diagonal of the box.

It goes, lengthwise, from one vertex to the opposite vertex, and if the dimensions of the box are x, y, z, then the diagonal is:

d = √(x² + y² + z²)

In this case the box is 2ft by 2 ft by 15ft, then the diagonal is:

d = √(2² + 2² + 15²) = 15.26

That is the maximum length that can fit in the box, 15.26ft

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The area of the flower bed is 67.5 square feet.

The area of an object is the space that is enclosed by its boundaries. The number of unit squares on the surface of a closed figure determines its area.

The following formula provides the area of a triangle:

(1/2) * Base * Height = Area

Inputting the values provided yields:

Area equals (1/2) * 15 * 9

Dimensions: 67.5 square feet

The flower bed therefore has a 67.5 square foot space.

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Answer:

The common difference in an arithmetic sequence is the constant difference between any two consecutive terms. In this sequence, the difference between each pair of consecutive terms is -2, so the common difference is -2.

Therefore, the answer is -2.

Answer: Here is a table that models the sample space for this event:

            Scorpion Tarantula Centipede Wasp

First     S1          T1                 C1                 W1

Second     S2          T2                 C2                 W2

Each combination of two fun things is represented by a two-letter code. For example, "S1T2" represents grabbing the scorpion first and the tarantula second.

Here is the list of all possible outcomes:

S1S2

S1T2

S1C2

S1W2

T1S2

T1T2

T1C2

T1W2

C1S2

C1T2

C1C2

C1W2

W1S2

W1T2

W1C2

W1W2

And here is a tree diagram that shows the same information:

       |----S2

       |----T2

First --|----C2

       |----W2

       |

       |----S2

       |----T2

Second--|----C2

       |----W2

The branches on the left represent the first fun thing that is grabbed, and the branches on the right represent the second fun thing that is grabbed.

Step-by-step explanation:

Using differentiation, 200 boats should be produced to incur minimum cost

A function's sensitivity to change with respect to a change in its argument is measured by the derivative of a function of a real variable in mathematics. A crucial calculus technique is the derivative.

Differentiation is a technique for determining a function's derivative. In mathematics, the technique of differentiation is used to determine the instantaneous rate of change in a function dependent on one of its variables. The most typical illustration is the velocity, or rate of change of displacement with respect to time.

Minimum boats can be found by differentiating the given function,

[tex]C(x)=21000 - 40x+0.1x^2[/tex]

Differentiating with respect to x,

0 = 0.2x - 40

0.2x = 40

x = 200

∴ 200 boats should be produced to incur minimum cost.

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Let's use algebra to solve this problem.

Let x be one of the integers, and y be the other integer.

From the problem, we know that:

x = 4y + 17 (one integer is 17 more than 4 times the other)

xy = -15 (the product of the two integers is -15)

We can use substitution to solve for one of the variables. From the first equation, we can write:

y = (x - 17)/4

Substituting this expression for y into the second equation gives:

x(x - 17)/4 = -15

Multiplying both sides by 4 and expanding gives:

x^2 - 17x = -60

Rearranging gives:

x^2 - 17x + 60 = 0

This is a quadratic equation that can be factored as:

(x - 5)(x - 12) = 0

So the solutions are:

x = 5, y = (-12/4) = -3

x = 12, y = (-5/4) = -1.25

Since the problem states that the integers are both integers, the only valid solution is:

x = 5, y = -3

Therefore, the two integers are 5 and -3.

Answer:

a)g(x) = 2f(x+1)

B) the point (-1, 3) would end up at (-4, 1) on the new graph.

Step-by-step explanation:

Answer: Second answer, (5,2)

Step-by-step explanation:

To reflect across the y axis, it would be: (x,y) -> (-x,y)

So, (-5,2) reflected across the y axis would be (5,2)

The inverse of the function is y = (-3x + 50)/4.

The domain of the inverse function are {4, 5, 6, 10}.

The range of the inverse function are {5, 8, 9, 13}.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At point (5, 10), an equation of the line f(x) can be calculated by using the point-slope form:

y - 10 = (6 - 10)/(8 - 5)(x - 5)

y - 10 = -4/3(x - 5)

y = -4x/3 + 20/3 + 10

y = -4x/3 + 50/3

y = (-4x + 50)/3

In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;

x = (-4y + 50)/3

3x = -4y + 50

4y = -3x + 50

y = (-3x + 50)/4

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Answer:

45 degrees I think

Step-by-step explanation:

sorry if wrong

Therefore , the solution of the given problem of  unitary method comes out to be  x = (ab)c = a(bc) .

The job can be finished by multiplying the variable information obtained using this kind of nanosection alongside the results of the two people who used the unilateral approach. In essence, this mean that whenever a desired item happens, either the chosen entity is described or the tone of both commercial manufacturing is skipped. A varying fee of Inr ($1.01) might have been necessary for forty pens.

Here,

We must demonstrate that the following formula holds for any subsets A, B, and C of S in order to demonstrate that multiplication of subsets is associative:

=> (AB)C = A(BC)

where AB and BC stand for the sets created by increasing all of the elements in A by all of the elements in B, and vice versa.

We must demonstrate that every element on the left-hand side is also an element on the right-hand side and vice versa in order to demonstrate that (AB)C = A(BC).

Let x represent any one of the (A*B)C elements. If a, b, and c are all in A, then x can be expressed as

=> x = (ab)*c by definition. * being associated with S gives us:

=> x = (ab)c = a(bc)

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Answer: The theoretical probability of selecting a meat option is 7/9.

Step-by-step explanation:

5 beef + 3 pork + 6 chicken + 4 veggie = 18 options total

meat options = 18 (total) - 4 veggie = 14 meat options

14/18 = 7/9

The functions are equal in option A, and aren't equal in B (try input x =1 and y = -1) and in C (try input x = 0 and y = 0).

The first one is:

(a). f: Z → Z, where f(x) = x^2.

g: Z → Z, where g(x) = |x|^2.

Yes, these functions are equal, this happens because both outcomes will always be positive, indifeterent of the absolute value part.

b)   f: Z × Z → Z, where f(x,y) = |x + y|.

g: Z × Z → Z, where g(x,y) = |x| +| y|.

These are different, if x = 1 and y = -1

f(1, - 1) = |1 - 1| = 0

g(1, -1) = |1| + |-1| = 2

c) B = {0, 1}

f: B × B → B × B, where f(x,y) = (1-y, 1-x)

g: B × B → B × B, where g(x,y) = (x,y)

This is clearly false, when x and y are 0 and 0 we have:

f(0, 0) = (1 - 0, 1 - 0) = (1, 1)

While g gives:

g(0, 0) = (0, 0)

These functions are different.

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Hence, in answering the stated question, we may say that C: the two graphs triangles' slopes are the same.

Mathematicians use graphs to visually explain or chart events or variables. A graph point often indicates a connection between one thing and another. A graph, a non-linear data structure, is constituted of nodes (vertices) and edges. Glue the nodes, which are also called as vertices. This graph has E=1, 2, 1, 3, 2, 4, and (2.5) edges and V=1, 2, 3, 5. (3.5). (4.5). Graphical representations of exponential growth in analytical charts (bar charts, pie charts, line charts, and so on). a graph of a logarithmic triangle.

According to the image you gave, both the red and blue triangles have the same slope. As a result, the solution is:

C: the two triangles' slopes are the same.

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The length and the width of the model are Length = 2 and Width = 3x² + 5x + 6

The expression 6x cant be the length because 12 cannot divide 6x without becoming a radical expression

We have

Area = 6x² + 10x + 12

Factor out 2

Area = 2(3x² + 5x + 6)

This means that

Length = 2 and Width = 3x² + 5x + 6

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Answer:

the dimensions of the corral that minimize the cost of the fencing are approximately 17.91 meters by 6.54 meters.

Step-by-step explanation:

Let the length of the corral be x, and the width be y. We know that the area of the corral is 117, so:

xy = 117

We also know that the corral is divided by a fence into two sections. Let the length of one section be L, and the width be y. Then, the length of the other section will be x - L, and the width will still be y. The total fencing cost will be:

10(2x + 2y) + 6(L + 2y)

Simplifying this expression, we get:

20x + 32y + 6L

Using the area equation, we can rewrite this as:

20x + 32(117/x) + 6L

To minimize the cost, we need to take the derivative of this expression with respect to L, and set it equal to zero:

d/dL [20x + 32(117/x) + 6L] = 6 = 0

Solving for L, we get:

L = x/2

Therefore, the two sections of the corral will have equal length. Substituting this value of L into the expression for total fencing cost, we get:

20x + 32y + 3x

Simplifying this, we get:

23x + 32y

Using the area equation to substitute for y, we get:

23x + 32(117/x)

Taking the derivative of this expression with respect to x, and setting it equal to zero, we get:

23 - 3744/x^2 = 0

Solving for x, we get:

x = sqrt(3744/23) ≈ 17.91

Substituting this value of x into the area equation, we get:

y = 117/x ≈ 6.54

Therefore, the dimensions of the corral that minimize the cost of the fencing are approximately 17.91 meters by 6.54 meters.

The experimental probability of rolling a number less than or equal to 4 is 0.7.

The likelihood that an event (A) will occur given the occurrence of another event (B) is known as conditional probability. P(A|B), which stands for "the probability of A given B," is used to express it. You must first determine P(A and B) by multiplying the odds of A and B happening together. Next, you may compute P(A|B). The conditional probability of A given B is then obtained by dividing the result by P(B).

Several situations in everyday life, including medical diagnosis, industrial quality control, and risk assessment in insurance, call for the usage of conditional probability.

Given that, the trial was run 10 times.

Thus,

P(B) = (number of times B occurred) / (total number of trials)

= 7 / 10

= 0.7

Therefore, the experimental probability of rolling a number less than or equal to 4 is 0.7.

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Answer:

the probability that a randomly chosen refill will fit correctly is 0.9780 (rounded to three decimal places).

Step-by-step explanation:

We can use the standard normal distribution to solve this problem. We first need to calculate the z-scores for the given diameters.

a) To find the probability that a randomly chosen refill will be too large, we need to find the probability of getting a diameter greater than 0.520 mm.

z-score = (0.520 - 0.5) / 0.007 = 2.857

Using a standard normal table or calculator, we find that the probability of getting a z-score of 2.857 or greater is 0.0021.

Therefore, the probability that a randomly chosen refill will be too large is 0.0021 (rounded to three decimal places).

b) To find the probability that a randomly chosen refill will be too small, we need to find the probability of getting a diameter less than 0.485 mm.

z-score = (0.485 - 0.5) / 0.007 = -2.143

Using a standard normal table or calculator, we find that the probability of getting a z-score of -2.143 or less is 0.0164.

Therefore, the probability that a randomly chosen refill will be too small is 0.0164 (rounded to three decimal places).

c) To find the probability that a randomly chosen refill will fit correctly, we need to find the probability of getting a diameter between 0.485 mm and 0.520 mm.

First, we find the z-scores for each diameter:

z-score for 0.485 mm = (0.485 - 0.5) / 0.007 = -2.143

z-score for 0.520 mm = (0.520 - 0.5) / 0.007 = 2.857

Using a standard normal table or calculator, we find that the probability of getting a z-score between -2.143 and 2.857 is 0.9780.

Therefore, the probability that a randomly chosen refill will fit correctly is 0.9780 (rounded to three decimal places).

Answer:

36∘

Step-by-step explanation:

Decagon has ten sides and ten angles. All these sides and angles are equal to each other. Therefore, the measure of each exterior angle of a regular decagon is 36∘

3.1 best represents the ratio of the length of segment A to segment B.

What is ratio?

By comparing two amounts of the same unit and finding the ratio, one can determine how much of one quantity is included in the other.

We are given that Jillian measures two line segments.

The length of Segment A is measured as 12.4 centimeters and the length of Segment B is measured as 4 centimeters.

So, on comparing both the lengths, we get

⇒12.4 : 4

⇒124 : 40

⇒3.1

Hence, 3.1 best represents the ratio of the length of segment A to segment B.

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Yes, both triangles are similar.

Similar triangles are two triangles that have the same shape, but may differ in size. In other words, their corresponding angles are congruent and their corresponding sides are proportional. This means that if you were to scale one triangle up or down, it would still maintain the same shape as the other triangle.

In ΔABC,

AC² = 36² +15²

AC² = 1521 = 39²

AC = 39

In ΔXYZ,

XY² = 24² +10²

XY² = 676 = 26²

XY = 26

If the ratio of the sides of both triangles are similar So we can say that the both triangles are similar.

AB/XZ = BC/YZ = AC/XY

15/10 = 36/24 = 39/26

3/2 = 3/2 = 3/2

Here we can see that the ratio of the sides of both triangles are similar So we can say that the both triangles are similar.

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According to the question the option C is the correct answer that is 8 6/8 or 8 ¾ calculated by simplifying the fraction.

To represent a whole, every number of equal parts or fractions can be utilised. In standard English, fractions show how many units there are of a particular size. 8, 3/4. Fractions are part of a whole. In mathematics, numbers are stated as a ratio of a numerator to the denominator. They can all be expressed as simple fractions as integers. A fraction appears in a complex fraction's numerator or denominator. The numerators of true fractions are smaller than the denominators. A sum that is a fraction of a total is called a fraction. You can analyse something by dissecting it into smaller pieces. For instance, the number 12 is used to symbolise half of a whole number or object.

To add mixed numbers, we need to first convert any fractions to a common denominator. In this case, we can use 10 as the common denominator.

12 1/2 = 12 + 1/2 = 12 + 5/10 = 12 5/10

4 7/10 = 4 + 7/10

Now we can add the two mixed numbers:

12 5/10 + 4 7/10 = 16 12/10

Simplifying the fraction by dividing the numerator and denominator by their greatest common factor of 2, we get:

16 12/10 = 16 6/5

Therefore, the answer is C) 8 6/8 or 8 3/4.

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