QUESTION 3
Elvis Louw has organized a hall for Mother's day celebration. He invited 150 guests and 2 motivational
3.2
Table
1,8 m
Walking space
Chair 45 cm
Chair 45 cm
NOTE:
Dimensions of the hall: 23 m x 18 m.
The venue includes round tables with a diameter of 1,8 m that can each seat 10 persons.
Use the information above to answer the questions that follow.
3.1
Define the term "Diameter" according to the given context.
Elvis Louw calculated that they need 9 m² per round table. He claims that 30 of the
(2)
(5)
round tables will fit into the space.
Verify Elvis Louw's claim that 30 tables will fit into the space.
You may use the following formula: Area of a rectangle length x breadth
3.3 Calculate the amount of walking space between two tables at the point where they are (5)
the closest, if the space allowed per chair is 45 cm.
(12)

Answer:

43.07

Step-by-step explanation:

remove the decimals and divide them as whole numbers then after the successful division return the decimal places according to the number of decimal places in each that is minus the number of decimal places in the divisor from the numbers of decimal places in the dividend

The arithmetic sequence is solved and the nth term is aₙ = 5n - 4

Given data ,

The formula for the nth term of an arithmetic sequence is:

aₙ = aₙ1 + (n - 1)d

where a₁ is the first term, d is the common difference, and n is the term number.

In this case, a₁ = 1 and d = 5, so the formula becomes:

aₙ = 1 + (n - 1)5

Simplifying, we get:

aₙ = 5n - 4

Hence ,  the formula for the nth term of the arithmetic sequence with first term 1 and common difference 5 is aₙ = 5n - 4

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The expression for the calculation is:

[tex]\sf 3+12\times(14+19)[/tex]

Let us focus on "product of... and the sum of..." first. Whenever you have procedures arranged in an order similar to this, always remember that the second keyword tells you to put a mathematical operation inside grouping symbols, while the first keyword tells you to keep an operation isolated on the outside. In this exercise, the product of 12 tells you that you will be distributing it amongst another individual or set inside grouping symbols, which in this case is a "set inside grouping symbols" because the sum of 14 and 19 tells you that in order to complete the produced expression, the additive expression must be placed inside grouping symbols. Now, all we have left is 3, which can be added on either side of the entire expression because according to the order of operations, in this case, multiplication is performed before addition.

Hence the expression for the calculation is

[tex]\sf 3+12\times(14+19)[/tex]

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The amount of fencing you will get is 5 feet.

Math operations include division as one of its types. This technique involves splitting the phrases or numbers into the same amount of components.

If $18 is the cost for every 3 feet of fencing, then as per the division operation the cost per 1 foot of fencing is,

$18/3 = $6.

So, if it costs $30, then the amount of fencing you will get is $30/$6 = 5 feet.

Therefore, the required amount of fencing is 5 feet.

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The zeros of the polynomial p(x) = x³ + x² + 8x - 60 will be (- 2 + √4 i), (- 2 - √4 i) and 3.

Given that:

Polynomial, p(x) = x³ + x² + 8x - 60

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

At x = 3, then we have

p(3) = 3³ + 3² + 8(3) - 60

p(3) = 60 - 60

p(3) = 0

The one zeros are 3. Then the other two zeros are given as,

(x³ + x² + 8x - 60) / (x - 3) = 0

[(x - 3)(x² + 4x + 20)] / (x - 3) = 0

x² + 4x + 20 = 0

x = [-4 ± √(4² - 4 × 1 × 20)] / (2 × 1)

x = - 2 ± √4 i

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The fair price for the smaller box should be $1.00.

From the question, we have that the larger box of popcorn sells for $3.00 and the two boxes have congruent openings and equal heights, we then can make the assumption  that the only difference between them is their volume.

The volume of a pyramid is found using the formula:

V = (1/3) B* h,

where 'B'=  base area

'h' = height of the pyramid

In conclusion, we can say that The fair price for the smaller box should be $1.00 because a pyramid is 1/3 the volume of a prism.

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The complete question is attached

Answer: To plot ratios and rates as ordered pairs on the coordinate plane, you can follow these steps:

Understand the ratio or rate: Make sure you understand the meaning and value of the ratio or rate you are working with. A ratio compares two quantities, while a rate compares two quantities with different units.

Choose a coordinate system: Set up a coordinate system on the plane with an x-axis and a y-axis. Determine the range of values you want to plot on each axis based on the given ratio or rate.

Determine the values for the axes: Assign the x-axis and y-axis values based on the given ratio or rate. For ratios, you can assign the values of the ratio to the x and y axes directly. For rates, you will need to convert the rate into a ratio by choosing a unit for one of the quantities.

Plot the points: Use the values obtained from step 3 as the x and y coordinates for each ordered pair. Plot the points on the coordinate plane.

Connect the points (if applicable): If you have multiple points, you can connect them with a line to show the relationship between the ratios or rates.

Label the axes and title the graph (if applicable): Add labels to the x and y axes to indicate the quantities being compared. You can also add a title to the graph to describe the relationship being represented.

Step-by-step explanation:

Answer:

[tex]\frac{13}{145}[/tex]

The decimal that represents the number of packs of loom bands that Natalie has is 7.57.

We can see that Natalie has 7 full packs of loom bands, which is a total of:

7*100= 700 loom bands

In addition, she has 57 other bands, making a total of:

700+57 =757 loom bands.

Now to find the decimal that represents the number of packs Natalie has, we need to divide the total number of loom bands by 100, since there are 100 bands in each pack. Thus, we have:

757 / 100 = 7.57

Therefore, the decimal that represents the number of packs of loom bands that Natalie has is 7.57.

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Answer:

Step-by-step explanation:

17

5 divided by 135

The seagull is approximately 47.86 feet above sea level, and the man's binoculars are approximately 46.25 feet away from the dolphin.

Let's denote the height of the seagull above sea level as "h" and the distance between the man's binoculars and the dolphin as "d."

For the seagull:

We have the angle of elevation as 27 degrees and the distance from the man's binoculars as 94 feet.

Using the tangent function, we can write:

tan(27 degrees) = h / 94

Solving for h, we have:

h = 94 × tan(27 degrees)

For the dolphin:

We have the angle of depression as 46 degrees and the distance from the man's binoculars as 44 feet (lenses level).

Using the tangent function, we can write:

tan(46 degrees) = h / d

Solving for d, we have:

d = h / tan(46 degrees)

Now, let's calculate the values:

h = 94 × tan(27 degrees) ≈ 47.86 feet

d = (47.86 feet) / tan(46 degrees) ≈ 46.25 feet

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The value of the product of expression is,

⇒ m⁶n² + 3m³n - 40

We have to given that;

Expression is,

⇒ (m³n + 8) (m³n - 5)

Now, We can product the expression is,

⇒ (m³n + 8) (m³n - 5)

⇒ m⁶n² - 5m³n + 8m³n - 40

⇒ m⁶n² + 3m³n - 40

Thus, The value of the product of expression is,

⇒ m⁶n² + 3m³n - 40

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A quadrilateral with double arrows going in the same direction for one pair of the opposite sides is a Parallelogram, and it is the shape that has two pairs of parallel sides.

The shape that has two pairs of parallel sides is the third option: a quadrilateral with double arrows going in the same direction for one pair of the opposite sides.

This shape is called a parallelogram, which is a type of quadrilateral where opposite sides are parallel and congruent. In a parallelogram, each pair of opposite sides has the same length and the same arrow direction, which is what is represented by the double arrows in the description.

The other options do not fit the definition of a parallelogram. The first option describes a shape with four right angles, but only two pairs of parallel sides, which would make it a trapezoid. The second option describes a shape with only one pair of parallel sides, which is not enough to be a parallelogram. The fourth option describes a shape with sides of different lengths and in the shape of an arrow, which does not fit the definition of a parallelogram.

Parallelograms have many interesting properties, such as opposite angles being congruent and diagonals bisecting each other. They are also the basis for other geometric shapes, such as rectangles and rhombuses, which have additional properties due to their specific angles and side lengths.

A quadrilateral with double arrows going in the same direction for one pair of the opposite sides is a parallelogram, and it is the shape that has two pairs of parallel sides.

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Answer:

W=26........

Step-by-step explanation:

26+9+10=45

Answer:

32.6

3.26

0.326

Step-by-step explanation:

You could use long division or a calculator to get these quotients (answers to division problems) but, probably you're supposed to see the pattern of how the decimal moves when you divide by 1, 10, 100 (these are powers of 10)

● Divide by 1, decimal does not move

● Divide by 10, the decimal moves left one place

● Divide by 100, the decimal moves left two places

mathworldwolfram

SOHCAHTOA

sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent

Quadrants

2 1

4 3

for a 1,2,√3 TRIANGLE

where a = 1 o = √3 h = 2

π = 180

tan 60 = 180/3 = π/3

tan 60 = π/3 in radians = √3/1 in degrees

tan 225 = (5*180)/4 = 5π/4 = -√2/2 in degrees

sin90 = π/2 in radians = soh = 1/2

sin150 = 5π/6 in radians = soh -√3/2

cos 90 = π/2 in radians = cah 1/2

tan 240 = 4π/3 in radians = toa = -√3/1

That value being n = 2

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

Explanation:

The only even prime number is n = 2. This leads to n^2+3 = 2^2+3 = 7 which is also prime. So far we found one such value of n that fits the criteria.

-----------

If n is odd, then n^2 is also odd.

The quick proof goes like this: let n = 2k+1 for some integer k. This guarantees n to be odd. Then n^2 = (2k+1)^2 = 4k^2+4k+1 = 2(2k^2+2k)+1 = 2*(some integer)+1 = some odd integer.

------------

If n is prime and n isn't equal to 2, then n must be odd.

If n was even and n > 2, then it would be a multiple of 2 by definition, and would rule out it being prime. Example: n = 16 is not prime since 2 is a factor.

So n must be odd if we want to find more numbers to fit the given criteria. That makes n^2 being odd as well from the previous section's proof.

But then we use the idea that:

odd + odd = even

I'll leave the proof of this to the reader.

The sum of any two odd numbers gives an even number. An example would be 3+5 = 8.

There are no odd values of n that are prime and n^2+3 is prime.

We therefore can conclude there's only one value of n that is prime and n^2+3 is also prime. That value being n = 2.

Answer:

p(3) = 16

Step-by-step explanation:

to evaluate p(3) substitute x = 3 into p(x)

p(3) = 0.5(3 - 5)² + 14

      = 0.5(- 2)² + 14

      = 0.5(4) + 14

      = 2 + 14

      = 16

Answer:

[tex]3 {x}^{2} - 15x - 18 = 0[/tex]

[tex] {x}^{2} - 5x - 6 = 0[/tex]

[tex](x + 1)(x - 6) = 0[/tex]

x = -1 or x = 6

The coordinates of the zeroes are (-1, 0) and (6, 0).

The area of the rectangle is 1632/3 square feet.

To calculate the area, we need to multiply the length and width of the given rectangle. The length is 51 feet, and the width is 10 2/3 feet, which can be expressed as an improper fraction as 32/3 feet.

Multiplying these values, we have:

Area = length × width

= 51 ft × (32/3) ft

= (51 × 32)/(3)

= 1632/3 square feet

So, the area of the rectangle is 1632/3 square feet.

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The value of P(B) is 0.7.

We are given that there are two events A and B which are independent of each other. It means that they are mutually exclusive. We are also given the value of P(A) = 0.26 and [tex]P(B|A)[/tex] = 0.7. We have to determine the value of P(B).

We will use the formula of conditional probability to solve this question.

The formula for conditional probability;

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

As we know that A and B are independent events, Therefore

P( A [tex]\cap[/tex] B ) = P(A). P(B)

Substituting the value of [tex]P(A \cap B)[/tex] in the formula of conditional probability,

Therefore,

[tex]P(B|A)[/tex] = [tex]\frac{P(A) P(B)}{P(A)}[/tex]

We are given that [tex]P(B|A)[/tex] is 0.7, we will substitute this value.

0.7 = P(B)

Therefore, the value of P(B) is 0.7 after rounding it to the nearest thousandth.

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The value of x when the Richter scale rating is 7.9, rounded to the nearest whole number, is approximately 79,432,823.

The formula relating the Richter scale rating (r) and the intensity ratio (x) is r = log(x). To find the value of x when r is 7.9, we can rearrange the formula and solve for x,

x = 10ʳ

Substituting r=7.9 into the formula, we get,

[tex]x = log((10)^{7.9} )[/tex]

Using a calculator, we get,

x ≈ 79432823.09

Rounding this to the nearest whole number, we get,

x ≈ 79432823

Therefore, the value of x when the Richter scale rating is 7.9, rounded to the nearest whole number, is approximately 79,432,823.

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Complete question - What is the value of x when the Richter scale rating is 7.9 round your answer to the nearest

r=log x

r=rating of the earthquakes size on the Richter scale

x=ratio of earthquake intensity to a minimum level of intensity

The area of the given figure is 12/25 cm²

According to the question, one grid represents 1/5 cm.

So, the dimensions of the shown rectangle are as follows:

Length of the rectangle = 4 grids = 4 × 1/5 cm = 4/5 cm

Width of the rectangle = 3 grids = 3 × 1/5 cm = 3/5 cm

As we know that the area of a rectangle is defined as the product of the length and width.

The area of the figure = Length of the rectangle × Width of the rectangle

The area of the figure = 4/5 cm × 3/5 cm

The area of the figure = 12/25 cm²

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The mean of the distribution in this problem is given as follows:

19.5625 pounds.

The mean of a data-set is given by the sum of all observations in the data-set divided by the cardinality of the data-set, which represents the number of observations in the data-set.

The dot plot shows the absolute frequency of each observation in the context of the problem.

Considering the dot plot, the sum of the observations in this problem is given as follows:

2 x 12 + 4 x 15 + 1 x 16 + 1 x 18 + 2 x 20 + 1 x 22 + 3 x 25 + 2 x 29 = 313.

The number of observations is given as follows:

2 + 4 + 1 + 1 + 2 + 1 + 3 + 2 = 16.

Hence the mean is given as follows:

313/16 = 19.5625 pounds.

The problem is given by the image presented at the end of the answer.

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Answer:

Let's denote the number of football games Tommy started as "f" and the number of baseball games he started as "b."

We're given two pieces of information:

Tommy has started a total of 109 RHS games:

f + b = 109 (Equation 1)

The number of baseball games he started was five less than twice the number of football games he started:

b = 2f - 5 (Equation 2)

We can solve this system of equations to find the value of "f," which represents the number of football games Tommy started.

Substitute Equation 2 into Equation 1:

f + (2f - 5) = 109

Combine like terms:

3f - 5 = 109

Add 5 to both sides:

3f = 114

Divide both sides by 3:

f = 38

Therefore, Tommy started 38 football games.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Tommy started with 71

The total surface area of the triangular prism is equal to 520 square centimeters. (Correct choice: D)

In this problem we find the case of a triangular prism, which has two triangular faces and three rectangular faces. We must determine the total surface area with the help of the following area formulas:

Rectangle

A = b · h

Triangle

A = 0.5 · b · h

Where:

Now we proceed to determine the total surface area of the prism:

A = 2 · 0.5 · (15 cm) · (8 cm) + (10 cm) · (8 cm) + (17 cm) · (10 cm) + (15 cm) · (10 cm)

A = 120 cm² + 80 cm² + 170 cm² + 150 cm²

A = 520 cm²

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The maximum amount Lauren should budget for housing is $445.50 per month.

Now, A good rule of thumb is that housing expenses should not exceed 30% of her income.

So, We get;

30% of Lauren's monthly income of $1485 would be:

= 30% x $1485

= $445.50

Therefore, the maximum amount Lauren should budget for housing is $445.50 per month.

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If the workers' union at a particular university is quite strong.  the probability that exactly 4 of the workers interviewed are union members is 0.1699.

You must count all conceivable outcomes as well as favourable outcomes in order to compute probability. The number of favourable outcomes divided by the total number of possible outcomes yields the chance that an event will occur.

Using this formula to the probability

P(X = k) = (n choose k) * [tex]p^{k}[/tex] * [tex](1-p)^{n-k}[/tex]

Where:

X = random variable

n = 5

p = 0.96

k = 4

Let plug in the formula

P(X = 4) = (5 choose 4) *[tex]0.96^{4}[/tex] *[tex](1-0.96)^{5-4}[/tex]

= 5 *[tex]0.96^{4}[/tex] * 0.04

= 0.1699

Therefore the probability is 0.1699.

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The molarity of the resulting solution is 0.42 M (rounded to two significant figures), which is option C.

To solve this problem, we can use the equation:

M₁V₁= M₂V₂

where M₁ is the initial molarity, V₁ is the initial volume, M₂ is the final molarity, and V₂ is the final volume.

We are given that the initial volume is 50.0 mL and the initial molarity is 1.25 M. We are also told that 100.0 mL of water is added to the solution, so the final volume is 50.0 mL + 100.0 mL = 150.0 mL.

Plugging these values into the equation, we get:

(1.25 M)(50.0 mL) = M2(150.0 mL)

Solving for M₂, we get:

M₂ = (1.25 M)(50.0 mL) / (150.0 mL) = 0.4167 M

Therefore, the molarity of the resulting solution is 0.42 M (rounded to two significant figures), which is option C.

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If a subset A of natural numbers (N) satisfies the conditions 0 ∈ A and if n ∈ A, then n+1 ∈ A, then A must be equal to the set of all natural numbers (N).

We will use a proof by contradiction to demonstrate this.

Assume that there exists a subset A of natural numbers that satisfies the given conditions, but A is not equal to N.

This means there exists a natural number k that is not in A.

Let B = N - A be the set of natural numbers that are not in A.

B is non-empty because it contains at least k.

Since 0 ∈ A, but k ∉ A, there must be a smallest natural number in B. Let's denote it as b.

Now, according to the given conditions, if n ∈ A, then n+1 ∈ A.

We can apply this repeatedly to obtain n+1, (n+1)+1, (n+1)+1+1, and so on.

Considering b-1, it is a natural number that is not in B because b is the smallest natural number in B. So, b-1 ∈ A.

Using the condition that if n ∈ A, then n+1 ∈ A, we can apply it repeatedly to b-1 to get (b-1)+1, (b-1)+1+1, and so on.

This implies that b, b+1, b+2, and so on, all belong to A.

However, this contradicts the fact that b is the smallest natural number in B, and A is defined such that it includes all natural numbers greater than or equal to 0.

Therefore, our assumption that A is not equal to N is false, and we can conclude that A = N.

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