20 adults and 15 children are going to attend a musical evening. The organizers have arranged the tables in such a way that there is equal number of adults and children on each table and no one is left over. What is the GREATEST number of tables that the organizer can set up ?

Answer:

A) where any seats empty? How do u know?

Yes, there were empty seats.

B) if ur answer to part a is yes find the number of empty seats

440 empty seats

Step-by-step explanation:

A) where any seats empty? How do u know?

Yes there were empty sits

B) if ur answer to part a is yes find the number of empty seats

We are told that the theater had the theartre has 49 rows with 48 seats in each row

This means the total number of seats in the theater =

49 × 48 = 2352 seats

The total number of people in the theater

= Number of teacher + Number of Students

= 1854 + 58 = 1912 people

This means 1912 seats were occupied

The number of empty seats = 2352 - 1912

= 440 seats

════════ ∘◦❁◦∘ ════════

════════════════════

x1 = (-4)

y1 = (-3)

x2 = (-5)

y2 = (-6)

════════════════════

slope = gradient (m)

════════════════════

\(m = \frac{y2 - y1}{x2 - x1} = \frac{( - 6) - ( - 4)}{( - 5) - ( - 3)} = \frac{( - 2)}{( - 2)} = 1 \)

════════════════════

To find the recursive formula of an arithmetic sequence, we need to identify the common difference between consecutive terms.

In this sequence, each term is decreasing by 7, so the common difference is -7.

Therefore, the recursive formula for this sequence is:

c(1) = 13 (the first term of the sequence)

c(n) = c(n-1) - 7 (the nth term is the previous term minus 7)

So we can use this formula to find any term in the sequence by recursively subtracting 7 from the previous term, starting with c(1) = 13.

For example:

c(2) = c(1) - 7 = 13 - 7 = 6

c(3) = c(2) - 7 = 6 - 7 = -1

c(4) = c(3) - 7 = -1 - 7 = -8

and so on.

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Answer:

0.6820

Step-by-step explanation:

Given data

Angle= 47°

Hence we want to find

cos 47°

From calculator

cos 47°=0.681998

to 4 dp

0.6820

Answer: 0.6820

Step-by-step explanation: I did the quiz

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

(a)The population of interest is the entire university community at Botho University. (b)The sample is the random sample of 200 members. (c)The average time spent in the library, which is 30 minutes, is a statistic because it is computed from the sample and represents a characteristic of the sample, not the entire population.

a) The population of interest in this case would be the entire university community at Botho University. It includes all members of the university community who could potentially spend time in the library.

b) The sample in this case is the random sample of 200 members that was taken from the university community. It represents a subset of the population of interest and is used to make inferences about the larger population.

c) In this case, 30 minutes is a statistic, not a parameter.

A statistic is a value calculated from a sample that describes some characteristic of the sample. In this case, the average time spent in the library, which is 30 minutes, was computed from the sample of 200 members. It represents the average time spent in the library by the sampled members.

On the other hand, a parameter is a value that describes a characteristic of the population. Since the average time spent in the library is based on the sample and not the entire population, it cannot be considered a parameter.

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Answer:

The answer is going to be 4r (2r + 3)

Answer:

L = -0.5x + 34

Step-by-step explanation:

When finding m in the formula y = mx + b. Find a word that means multiplication, in this case 0.5 feet per day.

Answer:

A

Step-by-step explanation:

The parentheses are switched around, making the answer still the same. However, for Answer choice C, it is Commutative Property because the factors are switched around.

=====================================================

Explanation:

The equation shown for choice A is in the form p*(q*r) = (p*q)*r which is the general format for the associative property of multiplication.

In this case, p = 2.5, q = 1/5 and r = 2/3.

The order of p,q,r stays the same while the parenthesis shift around. The stuff in the parenthesis is done first before anything else. Though with multiplication, the order doesn't matter which is why we can freely shift the parenthesis like this.

Addition has a similar rule which says p+(q+r) = (p+q)+r.

Answer:

your equation is false

the answer should be 12.1

The interval of convergence for the given power series is (2, 8).

To find the interval of convergence for the given power series. We have the power series:

∑(n=2 to ∞) ((x-5)ⁿ)/(3ⁿ)

To find the interval of convergence, we'll use the Ratio Test. For the Ratio Test, we need to compute the limit:

L = lim (n → ∞) |(a_(n+1)/a_n)|

For our series, a_n = ((x-5)ⁿ)/(3ⁿ). Therefore, a_(n+1) = ((x-5)(n+1))/(3(n+1)). Now, let's compute the ratio:

|(a_(n+1)/a_n)| = |(((x-5)(n+1))/(3(n+1))) / (((x-5)ⁿ)/(3ⁿ))|

Simplify the expression:

|(a_(n+1)/a_n)| = |(x-5)/3|

The series converges if L < 1. So we have:

|(x-5)/3| < 1

Now, we'll solve for x to find the interval of convergence:

-1 < (x-5)/3 < 1

Multiply each term by 3:

-3 < x-5 < 3

Add 5 to each term:

2 < x < 8

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(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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There are a total of $15^5 = 759,375$ distinct possibilities for the values in the diagonal going from top left to the bottom right of a BINGO card, in order.

To find the number of distinct possibilities for the values in the diagonal going from top left to the bottom right of a BINGO card, we need to consider the range of numbers that can be placed in the diagonal.

In the given BINGO card, the diagonal starts with the number 5 in the top left corner and ends with the number 71 in the bottom right corner. We can see that the numbers in the diagonal follow a pattern:

5, 17, 32, 49, 71

We can analyze this pattern to find the number of distinct possibilities.

- The first number, 5, can be any number from the set $1-15$.
- The second number, 17, can be any number from the set $16-30$.
- The third number, 32, can be any number from the set $31-45$.
- The fourth number, 49, can be any number from the set $46-60$.
- The fifth number, 71, can be any number from the set $61-75$.

To find the number of distinct possibilities, we multiply the number of choices for each position:

15 choices for the first number × 15 choices for the second number × 15 choices for the third number × 15 choices for the fourth number × 15 choices for the fifth number

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Answer: the answer is C

If the triangle is dilated by a scale factor of 2, the coordinates of Y' are: (12, 6).

Dilation simply refers to a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor that is being used.

A scale factor can be defined as the ratio of two (2) corresponding length of sides or diameter in two (2) similar geometric figures such as triangles.

For the given coordinates of triangle XYZ, the dilation with a scale factor of 2 about the origin (0, 0) or a center of dilation would produce an image with this Y' coordinates:

Coordinate Y (6, 3) → Coordinate Y' (6 × 2, 3 × 2) = Coordinate Y' (12, 6).

In conclusion, the coordinates of Y' in the image of triangle XYZ are (12, 6).

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Answer:

y = 1/2x - 7/2

Slope: 1/2

Y-intercept: (0, -7/2)

Step-by-step explanation:

We know the slope-intercept form of an equation of a line is y = mx + c where slope is m and y-intercept is c.

So, -4y = (-2)x + 14 [divide both sides by -4]

-4/-4 = -2/-4 + 14/-4

y = 1/2 -7/2

Hence the slope =  1/2 and y-intercept = -7/2.

Answer:

5

Step-by-step explanation:

\( \sqrt{29 - 4} \\ = \sqrt{25} \\ = 5\)

Answer:

85

Step-by-step explanation:

Consecutive numbers are numbers that follow each other in order. The two consecutive numbers are 42 and 43.

42+43=85

Answer:

42 & 43

Step-by-step explanation:

Let the two consecutive numbers be x and x+1 .

Here it is given that the sum of two consecutive numbers is 85.

So we get the equation,

x + (x+1) = 85

We get,

x + x + 1 = 85

2x + 1 = 85

Transposing +1 to RHS,

2x = 85 - 1

2x = 84

Transposing 2 to RHS,

x = 84 ÷ 2

Therefore, we get x = 42

Therefore, the two numbers are x and x+1, so they are: 42 and 43.

I hope this helped you! Pls mark me brainliest! Have a great day! <3

Answer:

Step-by-step explanation:

V = w h l

V = 7.5 * 7.5 * 6

V = 337.5cubic feet * 0.05

V = 16.875Lbs

V = 17Lbs (Rounded to nearest pound)

Answer:

slope: -3/4    y-intercept: 3   equation: y=(-3/4)x+3

Answer:

B

Step-by-step explanation:

a. The linear equation for the number of immigrants is y = 16,033.444t - 16,764,061.4.

b. The predicted number of immigrants admitted to the country in 2014 is approximately 1,825,753.

c. The validity of using this equation to model the number of immigrants throughout the entire 20th century is questionable due to the negative y-intercept, which implies negative immigrants in the year 1900.

a. Assuming a linear change in immigration, we can write the equation expressing the number of immigrants, y, in terms of t, the number of years after 1900, as:

y = mt + b

where m represents the rate of change (slope) and b represents the initial value (y-intercept).

To find the values of m and b, we can use the given data points (1950, 241,832) and (2004, 1,107,638).

Let's calculate the slope (m):

m = (change in y) / (change in t)

m = (1,107,638 - 241,832) / (2004 - 1950)

m = 865,806 / 54

m ≈ 16,033.444

Now, let's substitute one of the data points (1950, 241,832) into the equation to find the value of b:

241,832 = (16,033.444)(1950) + b

b = 241,832 - (16,033.444)(1950)

b ≈ -16,764,061.4

Therefore, the linear equation for the number of immigrants is:

y = 16,033.444t - 16,764,061.4

b. To predict the number of immigrants admitted to the country in 2014, we need to find the value of y when t = 2014 - 1900 = 114:

y = 16,033.444(114) - 16,764,061.4

Calculating the expression:

y ≈ 1,825,753.216

Therefore, the predicted number of immigrants admitted to the country in 2014 is approximately 1,825,753.

c. Considering the value of the y-intercept in the equation (-16,764,061.4), it suggests that in the year 1900 (t = 0), there were already negative immigrants, which does not make sense in the context of immigration. Therefore, using this linear equation to model the number of immigrants throughout the entire 20th century may not be valid. It is important to consider the limitations of the linear model and the historical context of immigration patterns.

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Complete Question:

In 1950, there were 241,832 immigrants admitted to a country. In 2004, the number was 1,107,638

a. Assuming that the change in immigration is linear, write an equation expressing the number of immigrants, y, in terms of t, the number of years after 1900

b. Use your result in part a to predict the number of immigrants admitted to the country in 2014

c. Considering the value of the y-intercept in your answer to part a, discuss the validity of using this equation to model the number of immigrants throughout the entire 20th century.

The equation that represents the relationship between the radius, r, and arc length, s is s = Θ * r

See attachment for the complete question

From the complete question, we have:

The angle is given in radians.

So, the arc length is calculated using

Arc length = Angle * Radius

Substitute known values

s = Θ * r

Hence, the equation that represents the relationship between the radius, r, and arc length, s is s = Θ * r

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Answer:

A

Step-by-step explanation:

On Edge

Answer:

Step-by-step explanation:

The line passes through the points:

Since all x- coordinates are same, the line is vertical and its equation is:

Answer:

133.3m³

Step-by-step explanation:

Volume of pyramid=lwh/3

=10×8×5/3

=400/3

=133.3m³

Hopefully this helped :D

Answer:

3n - 5

Step-by-step explanation:

f(n) = 3n - 5. Works for all of them

Answer:

Negative

Step-by-step explanation:

To solve this problem, we'll use the concept of permutations.

First, we need to choose a woman for the position of president, then another woman for the position of vice president, and finally, a man for the treasurer position.

1. President: Since there are 20 women, we have 20 options for the president position.
2. Vice President: We're left with 19 women (since we already chose one for the president), so we have 19 options for the vice president position.
3. Treasurer: Since there are 17 men, we have 17 options for the treasurer position.

Now, multiply the number of options for each position together to find the total number of ways to form the committee:

20 (president) × 19 (vice president) × 17 (treasurer) = 6,460 ways.

So, there are 6,460 possible ways to choose three different members with women as president and vice president and a man as treasurer.

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