(Theoretical Probability MC)

Joseph has a bag filled with 3 red, 3 green, 9 yellow, and 10 purple marbles. Determine P(not green) when choosing one marble from the bag.

92%
88%
24%
12%

we dunno, hmmm let's check for the slope for PQ

[tex]P(\stackrel{x_1}{-8}~,~\stackrel{y_1}{-10})\qquad Q(\stackrel{x_2}{-5}~,~\stackrel{y_2}{-12}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-12}-\stackrel{y1}{(-10)}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{(-8)}}} \implies \cfrac{-12 +10}{-5 +8} \implies \cfrac{ -2 }{ 3 } \implies - \cfrac{2 }{ 3 }[/tex]

keeping in mind that perpendicular lines have negative reciprocal slopes, then if both are truly perpendicular, then line RS will have a slope of

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-2}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-2} \implies \cfrac{3}{ 2 }}}[/tex]

let's see if that's true

[tex]R(\stackrel{x_1}{9}~,~\stackrel{y_1}{-6})\qquad S(\stackrel{x_2}{17}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-5}-\stackrel{y1}{(-6)}}}{\underset{\textit{\large run}} {\underset{x_2}{17}-\underset{x_1}{9}}} \implies \cfrac{-5 +6}{8} \implies \cfrac{ 1 }{ 8 } ~~ \bigotimes ~~ \textit{not perpendicular}[/tex]

Answer:

Step-by-step explanation:

No they are not perpendicular.

Perpendicular lines have slopes that are negative reciprocals of each other.

PQ slope = -12 - -10/-5 --8 = -2/3

RS slope = -5 - -6/17 -9 = 1/8

Slope are not negative reciprocals - the lines are not perpendicular.

Slope formula is m = y2 - y1/x2 - x1

Use this to determine slope.

For example if the the slope of RS was 3/2 - the lines would be perpendicular.

Answer:

yes

Step-by-step explanation:

working for 2 5/6 hours, she has 5/8 of the fence.

so per hour = 5/8 ÷ 2 5/6 =15/68 per hour

5 hours she'll do: 15/68*5 = 75/68

75 >68

so yes she will finish it

The boxplot which is reasonable to the summary of the data used to create the histogram is equals to boxplot A. So, correct answer is option (c).

Histogram is a graph which discribes the distribution of data by using of bars of different heights and same width. In this problem, we'll have a histogram and 3 box plots as box plot A, box plot B and box plot C, and we have to choose here which of these 3 box spots is a reasonable summary of the data. We can see that the histogram in above figure is skewed to left because it's maximum data present on the right end. The box plot C, is representing a normally distributed data, but are data is right side distributed so, it is wrong. Similarly, as we see box plot B shows distribution of data in left end, which is also not right choice. So, boxplot A is correct because it's showing the maximum data and the median where we have. We can see the median line over her median on the right hand. Thus, data is very highly negatively skewed hence boxplot A is appropriate.

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Complete question:

See the above figure, which box plot a, b, or c is a reasonable summary of the data used to create the histogram? there are 16 data points.

a) boxplot C

b) boxplot B

c) boxplot A

On solving the provided question, we can say that the inequality that will be formed is  [tex]1\leq x\leq 1.5 and 6\leq y\leq 8[/tex] and Two possible combinations are (1.25.7). (1.35.7.5)

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

the inequality that will be formed is

[tex]1\leq x\leq 1.5\\6\leq y\leq 8[/tex]

Two possible combinations are (1.25.7). (1.35.7.5)

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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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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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Answer:

20%

Step-by-step explanation:

45

22 bronze

14 silver

so 45- 22 -14 =9 gold

9/45 = 1/5 =20%

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 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 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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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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Answer:

The answer to the problem is c

When you graph it x+2y <-2

y-x<3 you will get c

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

Step-by-step explanation:

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 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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The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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Answer:

800

Step-by-step explanation:

1/4 =200

200+200 =2/4

200+200+200+200 =4/4 = all = 800

Answer:

Step-by-step explanation:

$800

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 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 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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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:

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

Yes, the equation 1/4y = 5x represents a direct proportion, and has a constant of proportionality of

A direct proportion is defined by the equation, y = kx, where k is the constant of proportionality.

To check if see the equation is a direct proportion, multiply both sides of the equation by 4:

1/4y * 4 = 4 * 5x

y = 20x

This shows that the ratio of y to x is equal to a constant value of 20, so y and x are directly proportional. The constant of proportionality is 20.

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The correct answer is e, none of the above, as a relatively flat, horizontal pattern indicates the absence of a trend or seasonality making it difficult to use any of the mentioned methods for forecasting.

This type of pattern is commonly referred to as a "stationary time series" and may require different forecasting techniques such as moving averages or ARIMA models.

A stationary time series means that the statistical properties of the series, such as the mean and variance remain constant over time. This type of series may still exhibit random fluctuations and noise that need to be accounted for in the forecasting process. Moving averages are commonly used to smooth out the noise and highlight any underlying patterns in the data.

This question should be provided with answer choices, which are;

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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

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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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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Answer:

C

Step-by-step explanation:

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