, –1, –3, –9, –27, ____, _______…

The probability of rolling a 6 and then rolling a 4 is 1/36.

This is because the probability of rolling a 6 is 1/6 and the probability of rolling a 4 is also 1/6. To calculate the probability of rolling a 6 and then rolling a 4, we need to multiply the two probabilities together. This gives us

To understand this further we can use a tree diagram. The branching nodes in the tree diagram represent the two dice rolls, with the leaves representing the outcomes of each roll. The probability of rolling a 6 and then rolling a 4 is the probability of taking the path from the root node to the leaf node representing 6 and then 4. This probability is 1/36 because there is only one path through the tree diagram that leads to this outcome.

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The perimeter and area of a parallelogram can be determined if the length and width are known.

The perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.

Without additional information, it is not possible to determine the exact perimeter and area of each cookie. Assuming the length and width are given, we can use the formula for the perimeter of a parallelogram (2 times the sum of the length and width) and the formula for the area of a parallelogram (length times width) to find the desired quantities.

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Answer:

Step-by-step explanation:

x+y-ax-ay

by grouping the like terms,

x-ax+y-ay

since x and y are common in all the terms,

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

= (1-a) ( x+y)

hope this helps

plz mark it as brainliest!!!!!!!!!

The factorized expressions of (x + y)² is

x² + y² + 2xy

The factorized expressions of (-ax - ay)² is

a²x² + ay² + 2a²xy

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Using middle-term factorization.

1)

(x + y)²

x² + y² + 2xy

2)

(-ax - ay)²

(-ax)² + (-ay)² + 2 x (-ax)(-ay)

a²x² + ay² + 2a²xy

Thus,

The factorized expressions are:

x² + y² + 2xy

a²x² + ay² + 2a²xy

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can't be solve sa foil method Yung ganyan equation

Answer:

100.

Step-by-step explanation:

The 2 smaller triangles are similar, so:

48 / (x - 64) = 64 / 48

64(x - 64) = 48^2

x - 64 = 48^2/64

x = 48^2/64 + 64

= 100.

Answer:

The African Elephant is 2.27 times heavier than a African Lion.

Step-by-step explanation:

9 × 103 pounds = 927E.

4 × 102 pounds = 408L.

Answer:

for people who use time4learning:

the answer is (a) 22.5 x 10^1

Step-by-step explanation:

9 x 10^3 / 4 x 10^2 = 22.5

2.25 x 10^1 = 22.5

The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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Answer:

D) 100% Positve

Step-by-step explanation:

You would choose the second option (y=1/3x) because the slope would be 1/3. Think of the slope as your directions, you go up 1 over to the right 3 times. Since the y-intercept is 0, you don't have to add anything at the end.

Hope this answer makes sense.

For the given f(x) =  \(\frac{9-x^2}{x^2-4}\), function f(x) is positive in intervals (-3,-2) and (2,3).

To check if function f(x) is positive in the interval, we put a value of x lying in the interval and note the sign of f(x).

f(x) = \(\frac{9-x^2}{x^2-4}\)

In the interval (-∞,-3), we take x = -5

f(x) = \(\frac{9-25}{25-4} = -\frac{16}{21} < 0\)

Hence f(x) < 0

In the interval (-3,-2), we take x = -2.5

f(x) = \(\frac{9-6.25}{6.25-4} = \frac{2.75}{2.25} > 0\)

Hence f(x) > 0

In the interval (-2,2), we take x = 1

f(x) = \(\frac{9-1}{1-4} = -\frac{8}{3} < 0\)

Hence f(x) < 0

In the interval (2,3), we take x = 2.5

f(x) = \(\frac{9-6.25}{6.25-4} = \frac{2.75}{2.25} > 0\)

Hence f(x) > 0

In the interval (3,∞), we take 5

f(x) = \(\frac{9-25}{25-4} = -\frac{16}{21} < 0\)

Hence f(x) < 0

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To use a normal distribution to approximate binomial probabilities, we require that both n and p be at least 5. To use a normal distribution to approximate binomial probabilities, we require that both n and p be at least 5.

The binomial distribution can only be approximated by a normal distribution when the sample size is sufficiently large. According to the central limit theorem, the distribution of a large number of samples from any population with a finite mean and finite variance will be approximately normal.

Here are some of the reasons why we need to follow this condition:

Accuracy of approximation of binomial probabilities: The normal approximation of the binomial distribution is more accurate when n and p are both greater than 5.

The greater the values of n and p, the closer the normal distribution will be to the actual binomial distribution.

Normal distribution properties: In a normal distribution, the mean and variance are well-defined.

As a result, we require that n and p be at least 5 to ensure that the mean and variance of the binomial distribution are well-defined. Appropriateness of the normal distribution: The normal distribution is suitable when both the mean and variance are known. The mean and variance are well defined when n and p are both greater than 5.

Therefore, we require that n and p are both greater than 5 to ensure that the normal distribution is appropriate.

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Angle 1 is 35°, angle 2 is 65°, angle 3 is 29°, angle 4 is 115°, angle 5 is 65°, angle 6 is 36° and finally angle 7 is 144° considering the shape triangle whenever possible.

A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.

Considering the triangle that is containing angle 3 along with the angles 90° and 61° and as we know the sum of angles in a triangle = 180° so the angle 3 is 29°

As we know that opposite angles are equal we can say that angle 4 is 115°

Now considering the triangle that contain angle 3 which is 29° and angle 4 which is 115°  we can say that angle 6 is 36° by applying sum of angles in a triangle.

Considering the triangle that consists of angles 1 , 6 and 80°+ angle 3 we can say that angle 1 is 35°

now considering the trinaglewith angles 1, 2 and 80° we can say that angle 2 is  65°

As we know that opposite angles are equal we can that angle 5 is same as angle 2 which is 65°.

Finally as angle 6 + angle 7 sum = 180° as they are on the straight line

we can say that angle 7 is 144°

Angle 1 is 35°, angle 2 is 65°, angle 3 is 29°, angle 4 is 115°, angle 5 is 65°, angle 6 is 36° and finally angle 7 is 144° considering the shape triangle whenever possible.

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Answer:

54=n  u=25  G=50  O=31  D=42

B=58  R=30 F=60

Step-by-step explanation:

hopefully, it's right

Since Y = 1/X, then X = 1/Y. The PDF of Y, g(y) is 4/y⁵, where 0 < y ≤ 1. If Y < 0 or y > 1, the PDF of Y is equal to z of Y, g(y) is 4/y⁵, where 0 < y ≤ 1. If Y < 0 or y > 1, the PDF of Y is equal to zero.

The PDF of X is given by fx(x) = { 4x³, 0 < x ≤ 1}When 0 < Y ≤ 1, the values of X would be 1/Y < x ≤ ∞ .Thus, the PDF of Y, g(y) would be g(y) = fx(1/y) × |dy/dx| where;dy/dx = -1/y², y < 0 (since X ≤ 1, then 1/X > 1). The absolute value is used since the derivative of Y with respect to X is negative. Note that;g(y) = 4[(1/y)³] |-(1/y²)|g(y) = 4/y⁵ , 0 < y ≤ 1. The PDF of Y is 4/y⁵, where 0 < y ≤ 1. When Y < 0 or y > 1, the PDF of Y is equal to zero. The above can be verified by integrating the PDF of Y from 0 to 1.

∫ g(y) dy  = ∫ 4/y⁵ dy, from 0 to 1∫ g(y) dy  = (-4/y⁴) / 4, from 0 to 1∫ g(y) dy  = -1/[(1/y⁴) - 1], from 0 to 1∫ g(y) dy  = -1/[(1/1⁴) - 1] - (-1/[(1/0⁴) - 1])∫ g(y) dy  = -1/[1 - 1] - (-1/[(1/0) - 1])∫ g(y) dy  = 1 + 1 = 2. From the above, it can be observed that the integral of g(y) is equal to 2, which confirms that the PDF of Y is valid. The PDF of Y, g(y) is 4/y⁵, where 0 < y ≤ 1. If Y < 0 or y > 1, the PDF of Y is equal to zero.

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Answer: 18.6

Step-by-step explanation: 9.3 is one side of the diagonal and the other side will be 9.3 as well, so you add 9.3+9.3=18.6

Answer:

-4,0 and 6.

Step-by-step explanation:

f(x) = 0 is when y = 0.

If you look at the graph, there are 3 instances when y = 0

and it happens when x = -4, x = 0 and x = 6.

Therefore, the solutions of f(x) when y =0 are -4,0 and 6.

The time Sonto spent doing housework to the time she spent visiting friends to the time she spent watching television can be expressed as 2 : 3 : 4 : 6 .

This is because we can convert each time interval to a common unit, such as minutes, and then simplify the resulting fractions to a ratio of whole numbers. Specifically, Sonto spent 30 minutes doing housework (1/2 hour), 45 minutes doing housework, 60 minutes visiting friends (1 hour), and 90 minutes watching television (1 1/2 hours = 60 + 30 minutes).

Simplifying these fractions gives us the ratio

30 : 45 : 60 : 90

Dividing by GCF 15

2 : 3 : 4 : 6

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The final answer is 82.33.

To arrive at the final answer of 82.33, the following steps were taken:

Step 1: The initial calculation or data gathering process involved various numerical values and computations. However, specific details regarding the question or problem were not provided in the initial prompt.

Step 2: The available information may have included numerical data, mathematical operations, or formulas that were used to arrive at an intermediate result.

Step 3: The intermediate result was further processed or manipulated using additional mathematical operations, leading to the final answer of 82.33. This answer is expressed with two decimal places, as specified in the question prompt.

It's important to note that without the specific context or details of the question, it is challenging to provide a more detailed explanation of the calculations leading to the final answer. The accuracy and correctness of the answer heavily depend on the information and data provided in the original question.

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(a) shows that every pair of opposite sides in the hexagon a′b′c′d′e′f′ are parallel and equal in length. On the other hand, (b) demonstrates that the triangles a′c′e′ and b′d′f′ have equal areas.

(a) To show that every pair of opposite sides in hexagon a'b'c'd'e'f' are parallel and equal in length, we can use the fact that the centroids of triangles divide the medians into segments of equal length.

Let's consider a'b' and d'e'. The centroid of triangle fab, a', divides the median fb into two segments, a'f and a'b', such that a'f = 2/3 * fb. Similarly, the centroid of triangle def, e', divides the median de into two segments, e'd and e'f', such that e'd = 2/3 * de.

Since fb = de (opposite sides of hexagon abcdef), we have a'f = e'd. Now, we can consider the triangles a'f'd' and e'df'. By the properties of triangles, we know that if two sides of a triangle are equal, and the included angles are equal, then the triangles are congruent.

In this case, a'f' = e'd' (as shown above) and angle a'f'd' = angle e'df' (corresponding angles). Therefore, triangle a'f'd' is congruent to triangle e'df'.

By congruence, the corresponding sides a'd' and e'f' are equal in length.

By similar reasoning, we can show that b'c' and e'f', as well as c'd' and f'a', are parallel and equal in length.

(b) To show that triangles a'c'e' and b'd'f' have equal areas, we can use the fact that the area of a triangle is one-half the product of its base and height.

In triangle a'c'e', the base is c'e' and the height is the perpendicular distance from a' to c'e'. Similarly, in triangle b'd'f', the base is d'f' and the height is the perpendicular distance from b' to d'f'.

Since opposite sides in hexagon a'b'c'd'e'f' are parallel (as shown in part (a)), the perpendicular distance from a' to c'e' is equal to the perpendicular distance from b' to d'f'.

Therefore, the heights of triangles a'c'e' and b'd'f' are equal. Additionally, the bases c'e' and d'f' are equal (as shown in part (a)).

Using the area formula, area = 1/2 * base * height, we can see that the areas of triangles a'c'e' and b'd'f' are equal.

Hence, we have shown that triangles a'c'e' and b'd'f' have equal areas.

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The area of the rectangle can be expressed as a fraction by multiplying 3/4 and 5/12. The answer is 5/16, which represents the area of the rectangle.

1. Multiply the length and width of the rectangle: 3/4 x 5/12 = 15/48

2. Reduce the fraction to its simplest form: 15/48 = 5/16

3. The answer is 5/16, which represents the area of the rectangle.

To find the area of a rectangle, you need to multiply the length and width of the rectangle together. In this case, the rectangle is 3/4 of a foot long and 5/12 of a foot wide. To express the area as a fraction, you need to multiply the two fractions together. 3/4 x 5/12 = 15/48. Since 15 and 48 have a common factor of 3, the fraction can be reduced to its simplest form, 5/16. Therefore, the area of the rectangle can be expressed as 5/16. This fraction represents the area of the rectangle.

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The complete question is

A rectangle is 3/4 of a feet long and 5/12 of a feet wide. What fraction represents the area of the rectangle of a feet wide.

Answer:

10.

Step-by-step explanation:

Write 2% as 2/100. Since finding the fraction of a number is same as multiplying the fraction with the number, we have 2/100 of 500 = 2/100 × 500? Therefore, the answer is 10? If you are using a calculator, simply enter 2÷100×500 which will give you 10 as the answer.

y= a(x - 5)^2 - 2.This equation represents a parabola with its vertex at the point (5, -2) and opens upward if a > 0 or downward if a < 0.

To translate the vertex of a quadratic function right 5 units and down 2 units, we can use the vertex form of the quadratic equation:

y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola and a is the coefficient of the quadratic term.

To translate the vertex right 5 units, we need to replace x with (x - 5). This will shift the entire parabola 5 units to the right.

To translate the vertex down 2 units, we need to subtract 2 from the value of k. This will shift the entire parabola 2 units downward.

Therefore, the equation that translates the vertex right 5 units and down 2 units is:

y= a(x - 5)^2 - 2

where a is the coefficient of the quadratic term. This equation represents a parabola with its vertex at the point (5, -2) and opens upward if a > 0 or downward if a < 0.

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If Aaron is designing a party game in which he needs exactly 24 possible outcomes, then he can use the following sets of actions to have a statistically fair game from the Statistics point  of view,

Toss a coin twice, and then then roll a 6-sided number cube.

How can he play a statistically fair game to get exactly 24 outcomes?

The game has 24 alternative outcomes, as far as we know. The next step is to identify a series of activities that produces 24 distinct outcomes with equal probabilities.

The first of the alternatives is the only one with a sample space of 24 elements.

Flip two coins, then roll a D6.

The results of each coin toss are 2:  (tails and heads).

There are 6 outcomes for the D6: (1, 2, 3, 4, 5, 6)

The combined outcomes of the two throws and rolling the number are then given by the product between the numbers of outcomes for each individual part, as solved below:

C = 2 × 2 × 6

C = 24

Thus, by tossing a coin twice, and then then rolling a 6-sided number cube, Aron can play a statistically fair game if h needs exactly 24 outcomes.

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Answer:

FE = 9 , DE = 15

Step-by-step explanation:

Δ FDE and Δ HGE are similar , then the ratios of corresponding sides are in proportion , that is

\(\frac{FE}{HE}\) = \(\frac{FD}{HG}\) ( substitute values )

\(\frac{FE}{6}\) = \(\frac{12}{8}\) ( cross- multiply )

8 × FE = 6 × 12 = 72 ( divide both sides by 8 )

FE = 9

and

\(\frac{DE}{GE}\) = \(\frac{FD}{HG}\)

\(\frac{DE}{10}\) = \(\frac{12}{8}\) ( cross- multiply )

8 × DE = 10 × 12 = 120 ( divide both sides by 8 )

DE = 15

9514 1404 393

Answer:

  a = 169 ft, b = 363 ft, B = 65°

Step-by-step explanation:

The mnemonic SOH CAH TOA can help you remember the necessary trig relations. For side 'a', opposite the given angle A, the appropriate relation is ...

   Sin = Opposite/Hypotenuse

  a = (400 ft)sin(25°) ≈ 169 ft

For side 'b', adjacent to the given angle, the appropriate relation is ...

  Cos = Adjacent/Hypotenuse

  b = (400 ft)cos(25°) ≈ 363 ft

Of course angle B is the complement of angle A:

  B = 90° -25° = 65°

__

In summary, ...

  (a, b, A) = (169 ft, 363 ft, 65°)

The interval of convergence of the series ∑a_n x^n is given by |x|∞} |a_{n+1} nx^n| / |a_n x^(n-1)|.We can write L as L = lim_{n->∞} |a_{n+1}| / |a_n| x, where x is the same in the numerator and denominator. Since the series ∑a_n x^n converges for |x|<2, we have lim_{n->∞} |a_{n+1}| / |a_n| = L' < 2. Thus, L = L' x.

For the series to converge, we need L < 1, which gives |x| < 1 / L'. Thus, the radius of convergence of the series ∑a_n nx^(n-1) is 1 / L'.Since the radius of convergence is the same as that of the series ∑a_n x^n, we get L' = 2. Thus, the radius of convergence of the series ∑a_n nx^(n-1) is 1 / L' = 1/2. Thus, the interval of convergence of the series ∑a_n nx^(n-1) is |x| < 1/2. However, since the interval of convergence of the series ∑a_n x^n is |x| < 2, we have |nx^(n-1)| = n|x^(n-1)| <= 2n for |x|<=1. Thus, we have |a_n nx^(n-1)| <= |a_n| 2n for |x|<=1, which shows that the series converges for x=-1, and thus for -1<=x<=1. Also, we have |a_n nx^(n-1)| <= |a_n| 2^n for |x|<=2, which shows that the series converges for x=2, and thus for -2<=x<=2. Thus, the possible interval of convergence of the series ∑a_n nx^(n-1) is [-2, 2].

The possible interval of convergence of the series ∑a_n nx^(n-1) is [-2, 2].

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Answer:

\( (x + 3)^{2} - 2\)

Step-by-step explanation:

\(h(x)= x^2 + 6x + 7 \\ = x^2 + 2.3.x + {3}^{2} - {3}^{2} + 7 \\ = (x + 3)^{2} - 9 + 7 \\ \purple { \bold{h(x)= (x + 3)^{2} - 2 }}\)

Answer:

6×6

=36

Step-by-step explanation: Negative multiplied by negative is positive.

Answer:

36

Step-by-step explanation:

6 times -2 = -12

-12 times -3 = 36