A type of Dark Chocolate is made by mixing cocoa and cocoa butter in the ratio 5 to 2. Let C be an unspecified number of grams of cocoa, which vary, and let B be the corresponding number of grams needed to make that type of dark chocolate. Reason about quantities and use math drawings to explain three different equations that relate C and B (and do not include any other variables)

By definition of trigonometric functions, the exact value of sine trigonometric function of angle S is equal to 2 / 9.

In this problem we find the case of a right triangle, of which two of its three sides are known, the hypotenuse (r) and the leg opposite to angle S (y). The exact value of sine trigonometric function is defined below:

sin S = y / r

sin S = QR / QS

sin S = 2 / 9

The sine trigonometric function of angle S is equal to 2 / 9.

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Yes, there is a statistically significant association between the variables when a p-value of 0.0000005 is obtained after running a chi-square test.

The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming that the null hypothesis is true.

In most cases, if the p-value is less than 0.05 (5%), it is considered statistically significant. This means that there is less than a 5% chance that the results observed in the chi-square test are due to random chance, and that there is likely a real association between the variables being tested.

In the case of a p-value of 0.0000005, this is much less than 0.05 and therefore, it can be concluded that there is a statistically significant association between the variables.

This means that the observed differences between the actual values and expected values are not due to chance, but rather, there is a strong relationship between the two variables being tested.

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Price values, p, of new mountain bikes that Maddie can afford is 375 + 215 ≥ p

Inequality is a relationship between two expressions or values that are not equal to each other.

The inequality that can be used to find the possible price values, p, of new mountain bikes that Maddie can afford is:

375 + 215 ≥ p

This inequality represents the total amount of money Maddie has saved and the amount her grandmother will give her being greater than or equal to the cost of the bike. If the left side of the inequality is greater than or equal to the right side, Maddie can afford the bike at that price.

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In linear equation,  30 is the depth of the two dives by first rounding to the nearest ten.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

= 75-43 feet,

= 32 feet.

Round 32 to the nearest ten, and you get 30 feet.

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The complete question is -

A scuba diver plans to go on two dives in one day. In the first, she will descend to 75 feet, and in the second she plans to descend to 43 feet. Estimate the difference between the depth of the two dives by first rounding to the nearest ten.

A) 30 feet

B) 40 feet

C) 120 feet

D) 32 feet

The probability of the family having at most one right-handed child is [tex](2/3)^3 + 3 * (2/3)^2 * (1/3) = 0.593[/tex].

The probability of event A can be calculated using the formula P(A) = 1 - P(not A). Since the left-handed:right-handed ratio is 1:2, the probability of a child being right-handed is 2/3 and the probability of a child being left-handed is 1/3. Thus, the probability of the family having children of both handedness is[tex]1 - P(not A) = 1 - (2/3)^3 = 0.741[/tex].

The probability of event B can be calculated using the formula P(B) = P(not A) + P(A and B). Since the left-handed:right-handed ratio is 1:2, the probability of a child being right-handed is 2/3 and the probability of a child being left-handed is 1/3. Thus, the probability of the family having at most one right-handed child is[tex](2/3)^3 + 3 * (2/3)^2 * (1/3) = 0.593.[/tex]

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The probability that three cards chosen at random from a standard 52-card deck that are not all the same color is 3/4.

Total number of combinations of three cards: There are 52 choose 3 = 22,100 ways to choose three cards from a standard deck of 52 cards.

Number of combinations that are not all the same color: There are two possibilities for the colors of the three cards:

a. Two red cards and one black card: There are 26 choose 2 ways to choose two red cards and 26 choose 1 ways to choose one black card, for a total of (26 choose 2) * (26 choose 1) = 325 * 26 = 8,450 combinations.

b. Two black cards and one red card: There are 26 choose 2 ways to choose two black cards and 26 choose 1 ways to choose one red card, for a total of (26 choose 2) * (26 choose 1) = 325 * 26 = 8,450 combinations.

The total number of combinations that are not all the same color is 8,450 + 8,450 = 16,900.

The probability that three cards chosen at random are not all the same color is:

P(not all the same color) = (number of combinations that are not all the same color) / (total number of combinations of three cards) = 16,900 / 22,100 = 3/4.

Therefore, the probability that three cards chosen at random from a standard 52-card deck are not all the same color is 3/4.

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the probability that he found his dog. alive is 15%.

What is probability?

The chance of an event can be calculated using the probability formula by simply dividing the favourable number of possibilities by the total number of outcomes. The likelihood of an event occurring can be anything between 0 and 1, as the favourable number of outcomes can never exceed the total number of outcomes. Probability theory is a branch of mathematics that focuses on calculating the likelihood that an event will occur. Probability measures how likely something is to happen.

if he searched in a for two days and b for two days

P(A) = 0.4

P(B) = 0.6

P(Dn D-1 F-1)= n n+2

P(FnA, Sn, F-1) = 0.25

P(FB, S, F-1) = 0.15

Hence the probability that he found his dog. alive is 15%.

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The equation is correct and the point (5,-2) is on the line.

The point slope equation of a line with slope 0.25 and a point (5,-2) would be y-(-2) = 0.25(x-5). This equation can be rearranged to y = 0.25x - 1.5.

Calculation:

y = 0.25x - 1.5

Plugging in x = 5

y = 0.25(5) - 1.5

y = -2

The point (5,-2) is on the line.

The point slope equation of a line with slope 0.25 and a point (5,-2) can be written as y-(-2) = 0.25(x-5) which can further be rearranged to y = 0.25x - 1.5. This equation can be further tested by plugging in the x value of the point (5) into the equation and the y value of the point (-2) should be obtained. This proves that the equation is correct and the point (5,-2) is on the line.

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The standard form of the quadratic function with the given vertex is f(x) = 9x² + 6x + 10.

Quadratic functions are polynomial functions where the highest degree of the variable is 2..

The general form of a quadratic function is f(x) = ax² + b x + c.

We know that, graph of a quadratic function is parabola.

General equation of a parabola is a(x - h)² + k.

Here (h, k) is the vertex.

Given vertex = (-1/3, -1)

Substituting,

a(x - h)² + k = a(x + 1/3)² - 1

Also we have a point (x, y) = ((0, -10/9)

a(0 + 1/3)² - 1 = -10/9

a/9 - 1 = -10/9

a/9 = -1/9

a = -1

General form is -1(x + 1/3)² - 1 = -1(x² + 2/3 x + 1/9) - 1

                                                = -x² - 2/3 x -10/9

                                                = 9x² + 6x + 10

Hence the standard form of the function is f(x) = 9x² + 6x + 10

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Answer:

5.3

Step-by-step explanation:

so, to round this up we need to look at the number beside 2

5 is always rounded up

so, 5.3

Answer:

2:1

Step-by-step explanation:

We know

To get from F to G, we have to go from -2 to 2, for which the length is 4.

To get from F' to G', we have to go from -2 to 0, for which the length is 2.

What is the ratio of the sides from the big to the small rectangle?

The ratio is 4:2 = 2:1

The range of g(x) is all real numbers less than 0.

An easy definition of a function?

As a set of inputs with one output for each, a function is defined as a relationship between them.

                    A function, expressed simply, is an association between inputs where each input is connected to one and only one output.

 The given function is

    f(x) = 1/2(2.5)ˣ

If a graph reflected across x axis, then

     (x,y) ⇒ (x, -y )

The function f(x) reflected across x-axis, so

        g(X) = -f(x)

         g(X) = -1/2(2.5)ˣ

It is an exponential function.

    g(x) ⇒ -∞ as x⇒ ∞

   g(X) ⇒ 0 as x ⇒ - ∞

Since the value of g(x) lies between ∞ and 0, therefore the range of g(x) is all real numbers less than 0.

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Answer:

20%

Step-by-step explanation:

45

22 bronze

14 silver

so 45- 22 -14 =9 gold

9/45 = 1/5 =20%

Answer: The discount is $13.75, which is found by multiplying the original price by the discount percentage, 0.25.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Average ROC is [tex]Change=\frac{f(b)-f(a)}{b-a} \\[/tex] so we need to look at the points (0,20) at 0 our y is 6 and at 20 its 12 so we have (0,6) and (20,12) we now use our formula so we have Change=[tex]\frac{12-6}{20-0} =\frac{6}{20} =\frac{3}{10}[/tex] so our answer is 3/10

Answer:

C

Step-by-step explanation:

add each of them all up and you'll see only C 4y = the sum

The area of the rhombus is 384 cm²

The diagonals of a rhombus are the lines that connect the opposite vertices (corners) in the center of the shape. The diagonals of a rhombus are perpendicular and form four right triangles through their intersection

Area of Rhombus = d₁ x d₂

Area of Rhombus = base x height

Given data ,

Let the area of the Rhombus be represented as A

Now , the value of A is

Let the base of the rhombus be B = 20 cm

Let the height of the rhombus be H = 19.2 cm

Now , the area of the rhombus = base x height

Substituting the values in the equation , we get

Area of Rhombus A = 19.2 x 20

Area of Rhombus A = 384 cm²

Hence , the area of the rhombus is 384 cm²

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The suitable inequality is 8x + 12y < 240

Inequalities are the relationship two expressions which states that the two expressions are not equal. It is denoted by the symbols like < , >, ≤, ≥.

Given that x equal small rugs and y equals medium rugs.

A company needs 8 hours for dyeing small rugs then, 8x.

And it needs 12 hours for dyeing medium rugs then, 12y.

The company must do 22 rugs less than 240 hours.

So the inequality is 8x + 12y < 240, it is paired with x + y ≥ 22.

Hence the suitable inequality is 8x + 12y < 240.

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The solution is, the value of lengths are x & 4.

Area of a rectangle (A) is the product of its length (l) and width (w).

A= l. w

here, we have,

from the given figure we get,

area = 5x+20

where, two rectangles are with areas 5x & 20

now, from the diagram we have,

the area as product = 5 ( x+ 4)

so, we get,

1st rectangle , length = 5,

area = 5x

so, width = x ,

again. 2nd rectangle, length = 5

area = 20

so. width = 4

Hence, The solution is, the value of lengths are x & 4.

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The graph shows the  inequality x² ≤ 16

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4.

Inequalities are often used to describe conditions or constraints in real-world problems.

You will notice that the values represented in the graph ranges from -4 to 4. Thus, solving x² ≤ 16 will produce these values. That is:

x² ≤ 16

x ≤ ±√16

x ≤ ±4

x ≤ -4 or x ≤ 4

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Answer:

The answer to the problem is c

When you graph it x+2y <-2

y-x<3 you will get c

Based on the information provided, 2 is not a solution of x>5 because a possible solution requires a number greater than 5.

Inequalities include symbols such as >, ≤, ≥, among others that should be interpreted correctly to solve the inequality. In this case, the symbol in the inequality is >, which means greater than. Based on this, the value of x should be greater than 5, for example, 7, 19, 2948, etc.

Therefore, 2 is not a solution to the inequality x>5 because a number greater than 5 rather than less than 5 is required to solve this expression.

Note: This question is incorrect and incomplete; here is the complete question:

Explain why 2 is NOT a solution of x>5

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The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given line equations are y=3x-6 and y=-2x+8.

Here, 3x - 6 = -2x + 8

Add 2x to both sides of the equation.

5x - 6 = 8

Add 6 to both sides of the equation.

5x = 14

Divide both sides of the equation by 5.

x = 14/5  

Find the y-value where these points intersect by plugging this x-value back into either equation.

y = 3(14/5) - 6

Multiply and simplify.

y = 42/5 - 6

Multiply 6 by (5/5) to get common denominators.

y = 42/5 - 30/5  

Subtract and simplify.

y = 12/5

These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.

Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.

Set both equations equal to 0.

(I) 0 = 3x - 6  

Add 6 both sides of the equation.

6 = 3x

Divide both sides of the equation by 3.

x = 2  

Set the second equation equal to 0.

(II) 0 = -2x + 8

Add 2x to both sides of the equation.

2x = 8

Divide both sides of the equation by 2.

x = 4

The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.

The height of the triangle is 12/5 units.

Formula for the Area of a triangle:

A = 1/2bh

Substitute 2 for b and 14/5 for h.

A = 1/2 ×2 × 12/5

Multiply and simplify.

A = 12/5

Therefore, the area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.

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Answer:

Step-by-step explanation:

The closest solution to this total among the available possibilities is 0.68, indicating that the portfolio is likely to surpass its benchmark in three or fewer quarters over the course of a year.

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms.

Here,

The probability that the portfolio outperforms its benchmark in three or fewer quarters over the course of a year is the sum of the probabilities of outperforming the benchmark in exactly 0 quarters, 1 quarter, 2 quarters, and 3 quarters.

Since the probability of outperforming the benchmark in any quarter is 0.75, the probability of not outperforming the benchmark in a quarter is 1 - 0.75 = 0.25.

The probability of not outperforming the benchmark in exactly 0 quarters is 0.25⁰ = 1

The probability of not outperforming the benchmark in exactly 1 quarter is 0.25¹= 0.25

The probability of not outperforming the benchmark in exactly 2 quarters is 0.25² = 0.0625

The probability of not outperforming the benchmark in exactly 3 quarters is 0.25³ = 0.015625

So, the probability of outperforming the benchmark in exactly 0 quarters, 1 quarter, 2 quarters, and 3 quarters is 1 - 0.25⁰, 1 - 0.25¹, 1 - 0.25², and 1 - 0.25³, respectively.

The sum of these probabilities is the probability of outperforming the benchmark in three or fewer quarters over the course of a year:

P(outperform in three or fewer quarters) = 1 - 0.25⁰ + 1 - 0.25¹ + 1 - 0.25² + 1 - 0.25³

This expression can be calculated to get an exact answer, but to get the closest answer to the options given, we can round off the intermediate results to 2 decimal places:

P(outperform in three or fewer quarters) = 1 + 0.75 + 0.94 + 0.98

The closest answer to this sum among the options given is 0.68, so the probability that the portfolio outperforms its benchmark in three or fewer quarters over the course of a year is closest to 0.68.

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The probabilities are given as follows:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

Each dice has six outcomes, hence the total number of outcomes when two dice are rolled is given as follows:

6² = 36.

The possible outcomes for the pair of dice are given as follows:

We can see a pattern of the sum, even-odd-even-odd and so on, hence the probability of an odd sum is given as follows:

p = 18/36 = 1/2.

For a sum greater than 6, the number of outcomes is given as follows

1 + 2 + 3 + 4 + 5 + 6 = 21.

Hence the probability is of:

p = 21/36

p = 7/12.

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The equation that represents the transformation is y = (1/4)f(x-3) + 7

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

This equation applies the following transformations to the graph of y = f(x):

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Enola needs to ride 3.2 miles a day

In the given question enola wants to ride her bicycle 23.8 miles this week and she has already ridden 11 miles and if she rides for 4 more days the we have to write and solve an equation which can be used to determine xx, the average number of miles she would have to ride each day to meet her goal.

The target distance of 23.8 miles can be reached in 4 days if the average rate is x and 11 miles are travelled.

This can be expressed as equation:

4x + 11 = 23.8

Solve it for x:

4x = 23.8 - 11

4x = 12.8

x = 12.8/4

x = 3.2

The value of x is 3.2

So, Enola needs to ride 3.2km

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