Which function is a linear function?

In linear equation, 15% is percentage of students are faster than pat .

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.

                            The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.

             = (100 - 85 )%

             = 15%

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The joint probability mass function of (x, y) is given by P(Xi, Yj) = (1/i) * (1/5) for 1 ≤ j ≤ i ≤ 5 and 0 otherwise. x and y are not independent because their joint PMF does not factorize into the product of their individual PMFs.

(a) The joint probability mass function (PMF) of the pair (x, y) can be calculated by considering the probabilities of each possible outcome.

Let's denote the event "x = i" as Xi and the event "y = j" as Yj. We can calculate the joint PMF P(Xi, Yj) by considering the conditions for each pair (i, j).

P(Xi, Yj) = P(Yj | Xi) * P(Xi)

Since x is uniformly selected from the set {1, 2, 3, 4, 5}, the probability P(Xi) for each value of i is 1/5.

Now let's consider the conditional probability P(Yj | Xi). For a given value of x = i, the possible values of y are {1, 2, ..., i}, each with equal probability of 1/i. Therefore, P(Yj | Xi) = 1/i for j ≤ i and 0 for j > i.

Putting it all together, the joint PMF for (x, y) is:

P(Xi, Yj) = (1/i) * (1/5)   for 1 ≤ j ≤ i ≤ 5

P(Xi, Yj) = 0               otherwise

(b) x and y are not independent. To determine independence, we need to check if the joint PMF factorizes into the product of the individual PMFs for x and y.

In this case, the joint PMF does not factorize because P(Xi, Yj) ≠ P(Xi) * P(Yj) for all values of (i, j). Therefore, x and y are not independent.

The value of y depends on the value of x since the range of y is determined by x. If we know the value of x, it restricts the possibilities for y. Thus, the outcome of y is not independent of the outcome of x.

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Answer:

162 miles

Step-by-step explanation:

54(3) = 162

Answer:

162 miles?

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

3 * 2/4  =

3/1   * 1/2

(3*1) / (2*1) =  3/2 = 1  1/2

Answer:

13 egrets

Step-by-step explanation:

According to the Question,

Given That, Molly is birdwatching at the coast. She has seen 2 egrets and 4 other birds. Considering this data.

Therefore, The next 39 birds Molly sees would you expect to be egrets is

⇒ (39/6)×2 =  13 egrets.

The isosceles triangle of the maximum area is also an equilateral triangle.

Given, an isosceles triangle ABC is inscribed in a circle with center D and radius r.

We can obtain the side a in function of r and α by applying Law of Sines to triangle BCD,

a/sin(2α) = r/sin β

Since, 2α + β + β = 180°

2α + 2β = 180°

α + β = 90°

β = 90° - α

a = r(sin 2α/sin(90°-α))

a = r(2 sinα cosα)/cosα

a = 2r sinα

a = 4r sin(α/2) cos(α/2)

We can obtain the height h in function of r and α,

tan(α/2) = (a/2)/h

h = a/2tan(α/2)

Replacing with the value of a,

h = [4r sin(α/2) cos(α/2)/2][cos(α/2)/sin(α/2)]

h = 2r cos2(α/2)

Now, find the area of the triangle in function of a and r,

Area, A = (base)(height)/2

A = [4r sin(α/2) cos(α/2)][2r cos2(α/2)]/2

A = 4r2sin(α/2) cos3(α/2)

Now, take the derivative to find the maximum or minimum of the area of the triangle.

dA/dα = [4r2cos(α/2)(1/2)cos3(α/2)] + [4r2sin(α/2) 3cos2(α/2)(-sin(α/2))(1/2)]

On simplification,

= [2r2cos4(α/2)] - 6r2sin2(α/2) cos2(α/2)

Taking out common terms,

= 2r2cos2(α/2)[cos2(α/2) - 3sin2(α/2)]

Equating the derivative to zero, we get

2r2cos2(α/2)[cos2(α/2) - 3sin2(α/2)] = 0

2r2cos2(α/2) = 0

cos2(α/2) = 0

Thus, α/2 = 90°

α = 180°

Also, cos2(α/2) - 3sin2(α/2) = 0

cos2(α/2) = 3sin2(α/2)

[sin2(α/2)/cos2(α/2)] = 1/3

tan2(α/2) = 1/3

tan(α/2) = 1/√3

So, α/2 = 30°

α = 60°

This implies that ∠B = ∠C = 60°

Thus, the isosceles triangle of the maximum area that can be inscribed in a circle of radius r. is also an equilateral triangle.

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Answer:

The slope of a linear model can be calculated using the formula:

m = Δy / Δx

where:

Δy = change in y (the dependent variable, in this case, total cost)

Δx = change in x (the independent variable, in this case, number of candy bars)

This is essentially the "rise over run" concept from geometry, applied to data points on a graph.

In this case, we can take two points from the table (for instance, the first and last) and calculate the slope.

Let's take the first point (3 candy bars, $6.65) and the last point (25 candy bars, $48.45).

Δy = $48.45 - $6.65 = $41.8

Δx = 25 - 3 = 22

So the slope m would be:

m = Δy / Δx = $41.8 / 22 = $1.9 per candy bar

This suggests that the cost of each candy bar is $1.9 according to this linear model.

Please note that this assumes the relationship between the number of candy bars and the total cost is perfectly linear, which might not be the case in reality.

Answer:

Step-by-step explanation:

Let the number of free throws = x

And the number of regular field goals = y

Total shots made by the team = 31

Equation for the shots will be,

x + y = 31 ------(1)

If the team gets 1 point for free throws and 2 points for a regular field goal,

x + 2y = 49 --------(2)

[total points gained by the team = 49]

1). Option (2) is the correct option.

2). Subtracting equation (1) from equation (2),

  (x + 2y) - (x + y) = 49 - 31

  y = 18

  Therefore, number of  regular field goals made by the team = 18

Answer:

∠JTS≅∠RST

Step-by-step explanation:

ss already there, just needs the angle in the middle

Answer:

Step-by-step explanation:

One side is congruent, one side is common= congruent

Need to add the angle between them

Answer:

A. 2x

Step-by-step explanation:

x + 2x +? = 5x

1x + 2x + ? = 5x

-1x -2x          -1x-2x

? = 2x

The solution is all values of x greater than -9.

The correct graph for the given inequality "Negative 3x - 7 < 20" is:

From negative 10 to positive 10, a number line runs. An open circle shows up at negative 9. From negative 9 to positive 10, the number line is shaded.

To chart the arrangement, we initially confine the variable by adding 7 to the two sides of the imbalance:

Negative 3x - 7 + 7 < 20 + 7

Negative 3x < 27

Next, we divide both sides by -3, remembering to flip the inequality sign since we're dividing by a negative number:

Negative 3x/-3 > 27/-3

x > -9

Therefore, the arrangement is all upsides of x more prominent than - 9. Since these are the values that satisfy the inequality, we graph this by drawing an open circle at -9 on the number line and shading all values to the right of -9.

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The large division mathematical problem can be solved using partial

quotient;

The methods that could be used to find the quotient are;

B. Subtract (30 × 12) from 468to get 108. Subtract (9 × 12) from 108 to have

0 remainder.

C. Subtract (20 × 12) from 468 to get 228. Subtract (10 × 12) from 228 to get

108. Subtract (3 × 12) from 108 to get 72. Subtract 6 × 12 from 72 to get a 0

remainder.

Reason:

The division of 468 by 12 using partial quotient gives;

12|\(\overline{468}\)

  \({}\) -360  ← 30 × 12

\({}\)      108

  \({}\)   -108  ← 9 × 12

\({}\)           0

Therefore, the quotient = 30 + 9 = 39

Therefore, option B. can be used to find the quotient;

Option B: Subtract (30 × 12) from 468; 468 - 30 to get 108. Subtract (9 ×

12) from 108 to have 0 remainder.

The method in option C which is expressed as follows;

468 - 20 × 12 = 228

228 - 10 × 12 = 108

108 - 3 × 12 = 72

72 - 6 × 12 = 0

Therefore, option is C. could be used and the statement is expressed as follows;

Subtract (20 × 12) from 468 to get 228. 468 - (20 × 12) = 228

Subtract (10 × 12) from 228 to get 108. 228 - (10 × 12) = 128

Subtract (3 × 12) from 108 to get 72. 108 - (3 × 12) = 72

Subtract (6 × 12) from 72 to get a 0 remainder.

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Answer:

a)

\(12 {x}^{3} \)

Step-by-step explanation:

\(a {b}^{3} \)

\( \frac{12}{x {}^{ - 3} } \)

Answer:

Both packages are 3.5 lb.

The equation is 7 / 2

Step-by-step explanation:

All you have to do is divide 7 by 2.

7 / 2 = 3.5

3.5 * 2 = 7

So, the answer is 3.5

Hope this helps! :)

Answer:

Part A: 15.55

Part B: 0.45

Step-by-step explanation:

Part A:

The giraffe is already 14.29 so when you add the length of its tongue (equation 14.29 + 1.26) then that would equal 15.55

Part B:

The giraffe is trying to eat some leaves that are 16 feet above the ground so you would subtract 16 - 15.55 to see how much farther it needs to reach, so the answer is 0.45.

(This is what I got, I apologize if I get this wrong. If I messed up on something, someone please correct me, thank you and have a nice day!)

Answer:

Part A:   It can reach 15.55 feet.

Part B:   Need to reach 0.45 feet farther to get to the leaves of a 16 feet tree.

Step-by-step explanation:

giraffe + tongue = reach

      14.29 + 1.26 = 15.55

tree height - giraffe reach = extra distance

16 - 15.55 = 0.45 feet

The line y ≤ 4x will be a solid line and shaded below the graph while the line y < -3x + 7 will be a dashed line and also shaded below the graph.

Inequalities are expressions that are not separated by an equal sign. Given the following system of equations;

y ≤ 4x

y+3x < 7

The inequalities can also be written as;

y ≤ 4x

y < -3x + 7

From the linear inequalities, the slopes of the lines are 4 and -3 respectively. The line y ≤ 4x will be a solid line and shaded below the graph while the line y < -3x + 7 will be a dashed line and also shaded below the graph.

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By applying algebra, radical and power properties, we find that the simplified form of (√5 + √6) · (√7 - √5) is equal to √35 + √42 - 5 - √30.

How to simplify a product of two binomials with radical numbers

Herein we need to apply algebra and radical and power properties to simplify the expression described in the statement, whose procedure is shown below:

(√5 + √6) · (√7 - √5)     Given

(√5 + √6) · √7 + (√5 + √6) · (- √5)     Distributive property

√7 · √5 + √6 · √7 + √5 · (- √5) + √6 · (- √5)     Distributive property

√35 + √42 - 5 - √30     (- a) · b = - a · b/ √a · √b = √a · b/Result

By applying algebra, radical and power properties, we find that the simplified form of (√5 + √6) · (√7 - √5) is equal to √35 + √42 - 5 - √30.

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Answer:

140°

Step-by-step explanation:

The sum of angle of a triangle is equal to 180°.

Two of the angles measured 20°.

We need to find the measure of the third angle of Nora’s triangle. let the third angle is x. So,

20+20+x = 180

40+x = 180

x = 180-40

x = 140°

So, the third angle of the triangle is 140°.

The integral of e^(-cos(8)) can't be evaluated using elementary functions. However, it can be expressed in terms of the special function called the exponential integral function, denoted as Ei(x). The integral is equal to Ei(cos(8)) + C, where C is the constant of integration.

Unfortunately, there is no straightforward way to integrate e^(-cos(8)) using elementary functions. The function e^(-cos(x)) is known as the Fourier transform of the Bessel function of the first kind of order zero. This function does not have an elementary antiderivative, which means that we need to use alternative methods to evaluate the integral.

One possible way to express the solution is by using the special function Ei(x), known as the exponential integral function. This function is defined as:

Ei(x) = -∫(-x, ∞) e^(-t)/t dt

Using this function, we can write the integral of e^(-cos(8)) as:

∫ e^(-cos(8)) dx = Ei(cos(8)) + C

where C is the constant of integration. This result holds true for any value of x, not just x=8.

To understand this result better, note that Ei(x) is a well-studied function in mathematics and has many important applications in physics, engineering, and statistics. It is closely related to other special functions such as the logarithmic integral and the gamma function. The function Ei(x) can be expressed in terms of other elementary functions, but these expressions are usually more complicated than the original definition. In conclusion, the integral of e^(-cos(8)) can't be evaluated using elementary functions. However, we can express the solution in terms of the special function Ei(x). The result is Ei(cos(8)) + C, where C is the constant of integration. The function Ei(x) is an important special function in mathematics, with many applications in various fields of science.

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Answer:

5\(\sqrt{3}\)

Step-by-step explanation:

Using the rule of radicals

\(\sqrt{a}\) × \(\sqrt{b}\) ⇔ \(\sqrt{ab}\) , then

\(\sqrt{75}\)

= \(\sqrt{25(3)}\)

= \(\sqrt{25}\) × \(\sqrt{3}\) = 5\(\sqrt{3}\)

Answer:

the answer to your question is

5√3.

The area of an obtuse triangle can be found using the formula: Area = (1/2) * base * height.

To find the base and height of the triangle, we need to identify a right angle within the triangle. One way to do this is by drawing an altitude from one vertex to the opposite side.

Once we have the right angle, we can determine the base and height. The base is the length of the side to which the altitude is drawn, and the height is the length of the altitude itself.

Unfortunately, the given information does not provide any measurements or angles of the triangle. Therefore, we cannot calculate the area of the obtuse triangle accurately.  Hence, the answer cannot be determined with the given information.

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There are 40,320 ways to line up the 8 people in a row for the photograph.

To determine the number of ways to line up the 8 people in a row for a photograph, we can use the concept of permutations.

Since the order of the members matters (i.e., the arrangement is distinct based on the order), we can calculate the number of permutations using the formula for permutations of n objects, which is n!.

In this case, we have 8 members, so the number of ways to line them up is:

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320

Therefore, there are 40,320 ways to line up the 8 people in a row for the photograph.

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Answer:

-⅖ + ⁹/¹⁵ = 3/15

Step-by-step explanation:

-⅖ + ⁹/¹⁵ = 3/15

The correct answer for the given equation is  \(\frac{3}{15}\).

PEMDAS is the right standardized way of solving math problems if multiple operations are being used. The acronym stands for parentheses, then exponents, then multiplication and division, then addition and subtraction.

Given the equation, \(-\frac{2}{5} -(\frac{-9}{15} )\) if we follow the PEMDAS then we have to remove the bracket first, and after that negative sign before 9/15 will get positive as follow:

⇒  \(-\frac{2}{5} +(\frac{9}{15} )\)

⇒    \(-\frac{6}{15} +(\frac{9}{15} )\)

      \(\frac{3}{15}\) .

Hence, The equation which shows the value of the given Problem is D.

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Answer:

3000 ................,...

Answer:

(57.1 miles per hour. )

7.8 hours

Step-by-step explanation:

Answer:

Suppose that G(X) = F(x+ 9). Which statement best compares the graph of

G(X) with the graph of F(x)?

O A. The graph of G(X) is the graph of F(x) shifted 9 units try the left.

B. The graph of G(x) is the graph of F(X) shifted 9 units down.

C. The graph of G(x) is the graph of F(x) shifted 9 units up.

D. The graph of G(X) is the graph of F(x) shifted 9 units to the right.

Step-by-step explanation:

Suppose that G(X) = F(x+ 9). Which statement best compares the graph of

G(X) with the graph of F(x)?

O A. The graph of G(X) is the graph of F(x) shifted 9 units try the left.

B. The graph of G(x) is the graph of F(X) shifted 9 units down.

C. The graph of G(x) is the graph of F(x) shifted 9 units up.

D. The graph of G(X) is the graph of F(x) shifted 9 units to the right.

In shape (i), there are two electron domains around the central atom. This means that the electron-domain geometry is linear. However, there are two bonding pairs and no lone pairs of electrons around the central atom, resulting in the molecular geometry also being linear.

The concept of electron-domain geometry and molecular geometry is essential in understanding the properties of molecules. The electron-domain geometry is determined by the number of electron domains (bonding or lone pairs) around the central atom in a molecule. On the other hand, the molecular geometry is determined by the arrangement of atoms in the molecule, taking into account the presence of lone pairs.

Knowing the electron-domain geometry and molecular geometry of a molecule is crucial in predicting its polarity and reactivity. For instance, polar molecules have an asymmetric distribution of electron density, while nonpolar molecules have a symmetric distribution. This difference in polarity affects the physical and chemical properties of a molecule, such as boiling point, melting point, and solubility.

In summary, in shape (i), both the electron-domain geometry and molecular geometry are linear, which means that the central atom has two bonding pairs and no lone pairs. Understanding the electron-domain and molecular geometry of molecules is essential in predicting their properties and behavior.

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