Complete the chart please :)

(a). The above context-free grammar (CFG) generates the language that has at least five "a's" and any combination of "b's".

(b). The above CFG generates the language {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}.

(c).  it is ambiguous.

(a). Context-free grammar for L₁ = {w = {a, b}*w contains at least five as}:

S → aaaaaA | aaaaS | bS | aA | bA | ε

A → aA | bAb → bB | ε

B → bB | aB | ε

The above CFG generates the language that has at least five "a's" and any combination of "b's".

(b). Context-free grammar for L₂ = {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}:

S → AbC | AcB | BCa | CBa

A → aA | ε

B → bBb

B → bBbBbBb

C → cC | ε

C → cC | ε

The above CFG generates the language {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}.

(c). Yes, the language for b) is inherently ambiguous. It is because there are two variables A and B in the grammar, so the string can be generated in two ways. Thus, it is ambiguous.

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Answer:

The top right graph

Step-by-step explanation:

For the given vectors u = -i + 2j + k and v = -2i - 5j - 8k, the solution is:

u = (-1, 2, 1)

v = (-2, -5, -8)

u · v, = -16

Write the vectors in component form:
u = (-1, 2, 1)
v = (-2, -5, -8)

Compute the dot product (u · v) using the formula:
u · v = (u1 * v1) + (u2 * v2) + (u3 * v3)

Substitute the components of u and v into the formula:
u · v = (-1 * -2) + (2 * -5) + (1 * -8)
u · v = 2 - 10 - 8
u · v = -16

So, the given vectors are:
u = -i + 2j + k or (-1, 2, 1)
v = -2i - 5j - 8k or (-2, -5, -8)
and their dot product, u · v, is -16.

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Answer:

umm i think it is 6.8 but i dontknow for sure

Answer:

Step-by-step explanation:

GIVEN that,

AC = BC

Therefore, Angle A = Angle B

so, angle B = 32°

(Angles Opposite to equal sides are equal)

Using, Sum of all angles in a triangle = 180°

Angle A + Angle B + Angle C = 180°

34° + 34° + 4y = 180°

68° + 4y = 180°

4y = 180° - 68°

4y = 112°

y = 112/4

y = 28°

Answer:

Step-by-step explanation:

The scenario represented by the given scatter plot is the score of one observation is high, we expect the score of the other observation to be low, and vice versa.

A scatter plot is a set of points plotted on a horizontal and vertical axes. Scatter plots are important in statistics because they can show the extent of correlation, if any, between the values of observed quantities or phenomena called variables.

When the points on a scatterplot graph produce a upper-left-to-lower-right pattern, we say that there is a negative correlation between the two variables. This pattern means that when the score of one observation is high, we expect the score of the other observation to be low, and vice versa.

Hence, the scenario represented by the given scatter plot is the score of one observation is high, we expect the score of the other observation to be low, and vice versa.

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To calculate Pearson's correlation coefficient between variables X and Y, the following need to be calculated:

- The means of X and Y variables: Yes, the means of X and Y variables are needed to calculate Pearson's correlation coefficient.

- Z-scores of X and Y variables: No, calculating Z-scores is not necessary for calculating Pearson's correlation coefficient.

- The standard deviations of X and Y variables: Yes, the standard deviations of X and Y variables are needed to calculate Pearson's correlation coefficient.

- The medians of X and Y variables: No, calculating medians is not necessary for calculating Pearson's correlation coefficient.

So, the correct options are:

- The means of X and Y variables

- The standard deviations of X and Y variables

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Answer:

x = 1

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The required system that can be obtained by substituting is

2 (1 - 2c) + 3c = 5, because a = 1 - 2c.

Given the system of equation;

2a + 3c = 5

a +2c=1

This system can be solved using the substitution method.

From equation 2:

Substitute equation 3 into 1 will give:

Hence the required system that can be obtained by substituting is

2 (1 - 2c) + 3c = 5, because a = 1 - 2c.

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Answer:

Answer:1296π

Step-by-step explanation:

As we know,

Area of cicle=πr^2

= π(36)^2

=1296π

Answer:

y=-2x+6

Step-by-step explanation:

For this question, you need the slope-intercept form which is y=mx+b, where m is the slope and b is the y-intercept. We should first find the slope of the equation. The slope is the rise-over-run; this means that the slope is equal to the difference in y over x. One way to find the slope is to count the difference between the two coordinates or you can use the formula. Either way, the y decreases by 2, and the x increases by 1. Therefore, the slope is -2.

Then, find the intercept. One way to do this by plugging in one of the coordinates into the equation we have so far, y=-2x+b. So, plug 4 in for y and 1 in for x; 4=-2(1)+b. Next, solve for b. This equals b=6.

Finally, plug in the slope and intercept for the final answer, y=-2+6.

Answer:

Yes,

\(y^{6} x\)

Step-by-step explanation:

\(y^{5} xy = y^{5} *y*x = y^{6} x\)

Answer:

13√(2) = x

Step-by-step explanation:

The given is an isosceles triangle so the two side lenghts are same (13 units)

in right triangles the square lenght of the hypotenus is equal to sum of two side's square lenght

13^2 + 13^2 = x^2

169 + 169 = x^2

338 = x^2

13√(2) = x

Answer:

9x^3/y^3

Step-by-step explanation:

Hope this helps!

The scatter plot can provide insights into whether the variables are positively or negatively related, if there is a linear or non-linear relationship, or if there are any outliers or clusters present in the data.

By creating a scatter plot of the length and width variables, you would be exploring the relationship between these two variables. A scatter plot is a graphical representation that displays the values of two continuous variables as individual data points. It allows you to visualize the pattern or trend between the two variables and identify any potential correlation or association between them. The scatter plot can provide insights into whether the variables are positively or negatively related, if there is a linear or non-linear relationship, or if there are any outliers or clusters present in the data.

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Answer:

\(-\frac{5}{2} x^{3} +\frac{17}{8} x^{2} -15\)

Step-by-step explanation:

First combine like terms so for numbers with x^3 you have one:

-\(\frac{5}{2} x^{3}\)

Then x^ 2

\(\frac{9}{8}x^{2} +x^{2}\)

(4/4x^2 is just x^2 because 4/4 is 1)

So

\(\frac{17}{8} x^{2}\)

Then all numbers with x cancel out because

2x+3x-5x is 0.

Then you just have -15.

So put them back together to get what I wrote in the answer.

Hope that helps lmk if I calculated that wrong!

Answer:

1. Reflection across the x-axis:

  1) (-2,-2)

  2) (-1,-4)

  3) (3,-4)

2. Reflect across the y-acis:

  1) (-1,-3)

  2) (-2,1)

  3) (-4,1)

Brainiest PLZZZ

Answer: It would be D. 22.5°

Have a nice day!

Answer: 5/8

\(m=\frac{-1-4}{-8-0}=\frac{-5}{-8}=\frac{5}{8}\)

Step-by-step explanation:

Answer:5/8

Step-by-step explanation:

Answer:

X = 3.6

Step-by-step explanation:

tan x = O/A

tan 20° = x/10

x = tan 20°(10)

x = 3.6

Answer:

x = 3.6 cm

Step-by-step explanation:

Using trigonometric ratios :

        \(sin \theta = \frac{ opposite} {hypotenuse} \\\\cos \theta = \frac{adjacent }{hypotenuse}\\\\tan \theta = \frac{opposite}{adjacent}\\\\\)

\(where \ \theta = 20, \ opposite = x \ , hypotenuse = y \ , \ adjacent = 10cm\)

\(we \ will \ take \ tan \ 20 , \ because\ we \ have \ to \ find \ opposite \ and \ adjacent \ is\ given.\\\\tan 20 = \frac{x}{10}\\\\x = 10 \times tan 20\\\\x = 10 \times 0.36397\\\\x = 3.6397\\\\x = 3.6 \ cm\)

Using the inclusion-exclusion principle for Venn diagram to expand the intersection of two events we conclude that 2p + 2q + 2r = 4/5.

In the area of mathematical logic known as set theory, we study sets and their characteristics. A set is a grouping or collection of items. These things are frequently referred to as elements or set members. A set is, for instance, a team of cricket players. We may claim that this set is finite since a cricket team can only have 11 players at a time.

P[(A ∪ B) ∩ (B' ∪ A')] = 8/25

Using the inclusion-exclusion principle to expand the intersection of two sets:

P[(A ∪ B) ∩ (B' ∪ A')] = P[(A ∪ B) - (A ∩ B')] + P[(B' ∪ A') - (A ∩ B')]

P[(A ∪ B) ∩ (B' ∪ A')] = [P(A) + P(B) - P(A ∩ B')] + [P(B') + P(A') - P(A ∩ B')]

Substituting the given probabilities and simplifying, we get:

P[(A ∪ B) ∩ (B' ∪ A')] = [(7/25) + (1/5) - x] + [(4/5) - (7/25) - x] = 8/25

Solving for x, we get:

x = 1/25

Now we can use the given probabilities to solve for 2p + 2q + 2r:

2p = P(A) = 7/25

2r = P(B') = 1 - P(B) = 4/5

2q = P[(A ∩ B') ∪ (A' ∩ B)] - P(A ∩ B') - P(A' ∩ B) = (8/25) - (1/25) - (q)

2q = 7/25

Simplifying, we get:

2p + 2q + 2r = (7/25) + (7/25) + (4/5) = 28/25 + 20/25 = 48/25

Dividing by 2, we get:

p + q + r = 24/25

Finally, multiplying by 2 again, we get:

2p + 2q + 2r = 48/25

So we have shown that 2p + 2q + 2r = 4/5.

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Answer:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex:

(

−

1

,

−

6

)

(

-

1

,

-

6

)

Focus:

(

−

1

,

−

49

8

)

(

-

1

,

-

49

8

)

Axis of Symmetry:

x

=

−

1

x

=

-

1

Directrix:

y

=

−

47

8

y

=

-

47

8

x

y

−

3

−

14

−

2

−

8

−

1

−

6

0

−

8

1

−

14

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex:

(

−

1

,

−

6

)

(

-

1

,

-

6

)

Focus:

(

−

1

,

−

49

8

)

(

-

1

,

-

49

8

)

Axis of Symmetry:

x

=

−

1

x

=

-

1

Directrix:

y

=

−

47

8

y

=

-

47

8

x

y

−

3

−

14

−

2

−

8

−

1

−

6

0

−

8

1

−

14

Step-by-step explanation:

Therefore ,the heart beat the time per beat in units of seconds is 0.5s/beat.

A well-formed equation in algebra unites two variables with the equals sign to indicate the equality of the two terms. An equation, for instance, is any well-formed formula that consists of two expressions joined by the equals sign in English. An équation, on the other hand, is described as consisting of one or more variables in French.

Here,

Given: your heart rate is 120 beats per minute during strenuous exercise

Thus to calculate time per beat in units of seconds

We,

time  per second per beat =  total second in a minute /heart rate

time  per second per beat =60/120

time  per second per beat =1/2

time  per second per beat = 0.5 s/beat

Therefore ,the heart beat the time per beat in units of seconds is 0.5s/beat.

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Answer: 0.88 should be the answer

The length of the curve defined by the polar equation r = 8a cos(theta) over the interval [-π/16, π/16] is πa units.

To find the length of the curve defined by the polar equation r = 8a cos(theta) over the interval [-π/16, π/16], we can use the arc length formula for polar curves.

The arc length formula for a polar curve is given by:

L = ∫[a, b] √(r^2 + (dr/dθ)^2) dθ

In this case, we have:

r = 8a cos(theta)

dr/dθ = -8a sin(theta)

Substituting these values into the arc length formula and simplifying, we get:

L = ∫[-π/16, π/16] √(64a^2 cos^2(theta) + 64a^2 sin^2(theta)) dθ

L = ∫[-π/16, π/16] √(64a^2) dθ

L = 8a ∫[-π/16, π/16] dθ

Integrating the constant term, we have:

L = 8a [θ] from -π/16 to π/16

L = 8a (π/16 - (-π/16))

L = 8a (2π/16)

L = 8a (π/8)

L = πa

Therefore, the length of the curve defined by the polar equation r = 8a cos(theta) over the interval [-π/16, π/16] is πa units.

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\(answer \\ = 10 {x}^{5} y \sqrt{6xy} \\ please \: see \: the \: attached \: picture \: for \\ full \: solution \\ hope \: it \: helps\)

The product of the given expression is;

B: 10x^(5) • y√(6xy)

We are given the expression;

√(5x^(8) • y²) × √(10x³) × √(12y)

Now, according to laws of exponents, we know that; √(a⁴) × √(b³) = √(a⁴ × b³)

Thus, our given expression will be;

√(5x^(8) • y²) × √(10x³) × √(12y) = √[(5x^(8) • y²) × (10x³) × (12y)]

√[(5x^(8) × 10x³) × (y² × 12y)]

√(50x¹¹ × 12y³)

>> √(600x¹¹y³)

Now, further break down of this gives;

10x^(5) • y√(6xy)

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For a normal distribution with mean 0 and standard deviation 1 the python line will be 0.627409464153

What is mean?

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. It is known as the "average" and is the most widely used central tendency measure.

What is standard Deviation?

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Appropriate function and output are given below

import scipy.stats as st

print(st.norm.cdf(0.325,0,1)

0.627409464153

The python line will be 0.627409464153 for a normal distribution with a mean of 0 and a standard deviation of 1.

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Answer:

{-1,7}

Step-by-step explanation:

1/2 | 5x-15| = 10

Multiply each side by 2

1/2 *2 | 5x-15| = 10*2

| 5x-15| = 20

Absolute value equations have two solutions, one positive and one negative

5x-15 = 20     5x-15 = -20

Add 15 to all sides

5x-15+15 = 20+15          5x-15 +15 = -20+15

5x= 35                                   5x=-5

Divide by 5

5x/5 = 35/5                              5x/5 = -5/5

x=7                                                   x=-1

The seller receives x+3 dollars for each gallon of cider sold in the fundraiser.

Use the concept of fraction defined s:

A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p/q.

Given that,

Apple cider is being sold for a fundraiser.

The company that makes the cider receives $x$ dollars for each gallon sold.

The seller receives the remaining amount of money after the company's share.

A total of 15 gallons of cider were sold.

The total amount of money from selling the cider is $15x + 45$ dollars.

To find out how much money you receive for each gallon of cider sold, Set up an equation based on the given information.

Assume that you receive y dollars for each gallon of cider sold.

Since you sold 15 gallons of cider for 15x + 45 dollars,

Then write the equation:

15y = 15x + 45

To find the value of y,

Divide both sides of the equation by 15:

\(y = \frac{15x + 45}{15}\)

Simplifying the equation further, we get:

y = x + 3

Therefore,

You receive x + 3 dollars for each gallon of cider that you sell.

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