james and bethany morrison are celebrating their 10th anniversary by having a reception at a local reception hall. they have budgeted $2.500 for their reception. if the reception hall charges a $100 cleanup fee plus $33 per person, find the greatest number of people that they may invite and still stay within their budget

Answer:

The answer is very clear is 2/3

Step-by-step explanation:

Answer:

10 and 6. The product is 60, 10*6. The difference is 4, 10–6.

Step-by-step explanation:

The expression for the statement "2 numbers that subtract to 4 and multiply to 60" is; (xy- 4)60

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that the statement is "2 numbers that subtract to 4 and multiply to 60"

Therefore,

let the number be x and y then;

(xy- 4)60

Hence, the expression for the statement "2 numbers that subtract to 4 and multiply to 60" is; (xy- 4)60

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The value of the missing ratio = 25. That is 5/25.

Ratio is an expression that shows the quantity of a variable that is found in another variable. It can be represented as a:b or can be written as a numerator all over a denominator. That is a/b.

To determine the missing part of the ratio, the following is carried out.

if 1 = 5, 2 = 10 then 5 = 25 = 1/5

Therefore the value of the missing part of the ratio is 5 and the complete ratio is written as 5/25.

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Answer: my answer for dat will be sin 16 degrees

Step-by-step explanation:

The equation of line B is y = -3x + 8.

To find the equation of line B, which is parallel to line A and passes through point P, we need to determine the slope of line A and use it to write the equation of line B.

Looking at line A, we can observe that it has a slope of -3. This is because line A has a rise of -3 (decreasing y-values) for every run of 1 (constant x-values).

Since line B is parallel to line A, it will have the same slope of -3.

Now, we have the slope (-3) and the point P(x, y) through which line B passes. Let's use the point-slope form of the linear equation to write the equation of line B:

y - y1 = m(x - x1)

Substituting the values, we have:

y - (-7) = -3(x - 5)

Simplifying:

y + 7 = -3x + 15

To write the equation in the form y = mx + c, we rearrange the equation:

y = -3x + 15 - 7

y = -3x + 8

Therefore, the equation of line B is y = -3x + 8.

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The trigonometric values for a right triangle can be obtained through the measurements of the different sides,

this can be found in a triangle like this,

then, identify the measurements in the given triangle

then,

If a divides b and a divides c, then a divides (bm + cn).

To prove that if a divides b and a divides c, then a divides (bm + cn), we can use the properties of divisibility.

Given:

a|b, which means b is divisible by a.

a|c, which means c is divisible by a.

We want to show that a|(bm + cn), which means (bm + cn) is divisible by a.

By definition, if a divides b, then there exists an integer k₁ such that b = ka. Similarly, if a divides c, there exists an integer k₂ such that c = ka.

Now, let's substitute these expressions into (bm + cn):

(bm + cn) = (ka)m + (ka)n

= kam + kan

= a(km + kn)

We can see that (bm + cn) can be written as a times the integer (km + kn). Since (km + kn) is an integer, this implies that (bm + cn) is divisible by a.

Therefore, if a divides b and a divides c, then a divides (bm + cn).

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Work Shown:

7(8+4k)+12

7*8+7*4k+12 ..... distributive property

56+28k+12

28k+56+12

28k+68

Answer:

28k + 68? I think

Step-by-step explanation:

expand by distributing terms

56+28k+12

collect lile terms

28k+(56+12)

Simplify

28k+ 68

Answer:

2:9 option b is the ans.

Answer: B and E

Step-by-step explanation:

Tip: 4:18 can be written in many ways, try dividing and multiplying 4 and 18 by different numbers so you can match the options

Divide 4 by 2 which gives you 2, do the same thing to 18 because in a ratio we do the same to both numbers

Doing so gives us 2:9, so this ratio is equal to 4:18

Now, multiply 4 by 2, do the same to 18 because we have to do the same thing to both sides of a ratio

Doing so gives us 8:36, this is equal to 4:18

So, the answer is 2:9 and 8:36 (B and E)

Answer:

rational

Step-by-step explanation:

cause it can be written as a fraction.

To find the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ), we need to first visualize the graph of the limaçon.

The equation r = 1 2 + cos(θ) represents a curve that resembles a snail shell or a heart shape with a loop inside another loop. To find the area inside the larger loop and outside the smaller loop, we need to set up the integral using the polar coordinates.

The formula for the area enclosed by a polar curve is given by:
A = 1/2 ∫(θ2-θ1) (r2-r1)² dθ, where r2 is the outer curve, r1 is the inner curve, and θ1 and θ2 are the angles where the curves intersect.

In this case, the inner curve is r = 1 - cos(θ), and the outer curve is r = 1/2 + cos(θ). The curves intersect when cos(θ) = 1/2 or θ = π/3 and θ = 5π/3.
So, we need to split the integral into two parts, one for θ = π/3 to θ = 5π/3, and another for θ = 5π/3 to θ = π/3.

This is because the outer curve becomes the inner curve and vice versa when we cross the angle θ = 5π/3. For the area inside the larger loop and outside the smaller loop, we need to subtract the area enclosed by the inner curve from the area enclosed by the outer curve.

Using the formula above and plugging in the values, we get:
A = 1/2 ∫(5π/3-π/3) [(1/2 + cos(θ))² - (1-cos(θ))²] dθ

Simplifying this integral, we get:
A = 1/2 ∫(5π/3-π/3) [5/4 + 2cos(θ)] dθ
A = 5/8 [θ + sin(θ)](5π/3-π/3)
A = 5/8 [4π/3 + sin(4π/3) - (π/3 + sin(π/3))]
A = 5/8 [4π/3 - √3/2]
A = 5π/6 - (5/16)√3
Therefore, the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ) is 5π/6 - (5/16)√3.

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To find the area inside the larger loop and outside the smaller loop of the limaçon r = 1 + 2cos(θ), use the formula for finding the area enclosed by a polar curve.

The general formula is A = (1/2)∫(r^2)dθ, where r is the equation of the curve. In this case, we need to find the area between two curves: the larger loop given by r = 1 + 2cos(θ) and the smaller loop given by r = 1. To find the limits of integration, we need to find the values of θ where the two curves intersect. After finding the values of θ where the curves intersect, we can integrate the difference between the two equations r = 1 + 2cos(θ) and r = 1 with respect to θ.

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Given the sequence:

Let's find the third term of the sequence.

To find the third term, a3, we have:

First find the second term, a2:

The second term is -5.

To find the third term, we have:

Therefore, the third term of the

Answer:

90

Step-by-step explanation:

210 divided by 7 is 30 and times 3 is 90

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{90 \: dollars}}}}}\)

Step-by-step explanation:

Total amount of money that Rob had = $ 210

Total amount of money that he spent = \( \sf{ \frac{4}{7} \times 210} = \: 120 \: dollars\)

Finding the amount of remaining money

\( \boxed{ \sf{total \: amount \: of \: money \: that \: he \: had \: - \: total \: amount \: of \: money \: that \: he \: spent}}\)

\( \dashrightarrow{ \sf{210 - 120}}\)

\( \dashrightarrow{ \sf{90 \: dollars}}\)

Hope I helped!

Best regards! :D

Answer:

$223.45

Step-by-step explanation:

premium fuel: 4.59 x 545

= 2501.55

regular fuel: 4.18 x 545

=2278.1

2501.55-2278.1 = 223.45

Answer:

\( \sqrt{34} = \sqrt{17 \times 2} =5.831\)

Answer:

5.831

Step-by-step explanation:

hope it hlp u

plz follow me

To test Vince's claim, we need to calculate the slope of the zip line between the starting tree and the ending tree for both Tree A and Tree B.

Let's start with Tree A. The horizontal distance between Tree A and the ending point is 80 feet, and the vertical change is 16 feet (from the starting point on the tree) to 9 feet (at the ending point).

Therefore, the slope of the zip line for Tree A is:

slope = (9 - 16) / 80 = -7/80

Now let's calculate the slope for Tree B. The horizontal distance between Tree B and the ending point is 60 feet, and the vertical change is also 7 feet (from the starting point on the tree) to 0 feet (at the ending point). Therefore, the slope of the zip line for Tree B is:

slope = 0 - 7 / 60 = -7/60

Since Vince's claim was that a vertical change of 7 feet would satisfy the slope constraint, we can compare the calculated slopes for each tree to see if they are equal to or less than -1/5.

For Tree A, the slope is -7/80, which is less than -1/5. Therefore, Vince's claim is true for Tree A.

For Tree B, the slope is -7/60, which is greater than -1/5. Therefore, Vince's claim is false for Tree B.

In conclusion, Vince's claim is true for Tree A but false for Tree B.

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The child advocate collects data by randomly selecting 4 out of the 25 state orphanages. In each of the four selected orphanages, the child advocate surveys every child.

This approach allows the child advocate to obtain information from a representative sample of children in state orphanages. By surveying every child in the selected orphanages, the child advocate ensures that no child is excluded from the data collection process. This method provides a comprehensive understanding of the experiences, needs, and concerns of the children in the four chosen orphanages.

By collecting data in this manner, the child advocate can gather valuable insights that can inform policies and interventions to improve the well-being and support for children in state orphanages.

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Answer: $47.30

Step-by-step explanation:

add the numbers and then divide by how many people there are

The result is 20.997 if 497 is Divided by 23.67 and tenth 2.099 and hundredth is 0.2099

A decimal is a number that has two parts one is whole number, and the remaining is fractional part. The two parts are separated by a point named decimal point.

Hundredth means the fraction that is equal to one is divided by 100

and tenth of a number means the number is divided by 10.

As example a hundredth of 4444 is 44.44 and tenth of 4444 is 444.4.

We are given two numbers 497 and 23.67

In the above, 497 is a whole number and 23.67 is a decimal number.

In order to divide these, we can multiply the two numbers by 100

and get 49700 and 2367

now 49700 is divided by 2367

and the result is 20.99

In the next, the tenth of 20.99 is 2.099 and hundredth of 20.99 is 0.2099

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The probability of selecting a human character randomly in the game is \(\frac{1}{3}\)

The probability that a human character will be chosen when the player selects a character randomly can be calculated by dividing the number of human characters by the total number of available characters.

There are 8 animal characters and 4 human characters, making a total of 12 characters to choose from. Therefore, the probability of selecting a human character randomly is:

P(Human) = Number of human characters / Total number of characters

P(Human) = 4 / 12

Simplifying this fraction, we find:

P(Human) = 1 / 3

Therefore, the probability of selecting a human character randomly is 1/3 or approximately 0.333.

In the given scenario, there are a total of 8 animal characters and 4 human characters, making a total of 12 characters to choose from. When a player selects a character randomly, each character has an equal chance of being chosen. Since there are 4 human characters, the probability of selecting one of them is determined by dividing the number of human characters (4) by the total number of characters (12).

When we simplify the fraction 4/12, we find that it is equal to 1/3.

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¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)

Proof:

1. ∃x(Fx & Gx) [Premise]

2. Fx & Gx [∃-Elimination, 1]

3. ∃xFx [∃-Introduction, 2]

4. ∃xGx [∃-Introduction, 2]

5. ∃xFx & ∃xGx [Conjunction Introduction, 3 and 4]

6. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx [1-5, Modus Ponens]

ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks)

Proof:

1. ¬ 3x(Px v Qx) [Premise]

2. ¬ Px v ¬ Qx [DeMorgan’s Law, 1]

3. Vx ¬ Px [∀-Introduction, 2]

4. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px [1-3, Modus Ponens]

iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)

Proof:

1. ¬ Vx(Fx → Gx) v 3xFx [Premise]

2. (¬ Vx(Fx → Gx) v 3xFx) → (¬ Vx(Fx → Gx) v Fx) [Implication Introduction]

3. ¬ Vx(Fx → Gx) v Fx [Resolution, 1, 2]

4. (¬ Vx(Fx → Gx) v Fx) → (Fx → Gx) [Implication Introduction]

5. Fx → Gx [Resolution, 3, 4]

6. ¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

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There is a 21.5% chance that a point in a square with nine congruent circles drawn there won't be within one if it is chosen at random.

It is given to us that :

Nine congruent circles are inscribed in a square

The square has a side length of 126

We have to find out the probability that the point is not in a circle, if a point in the square is chosen at random.

It is known that the square has a side length of 126.

=> Area of the square = \((Length)^{2}\)

=> Area of the square = \(126^{2}\)

=> Area of the square = 15876 ------ (1)

It is also known to us that nine congruent circles are inscribed in the square that has a side length of 126.

=> Diameter of each circle = 126/3

=> Diameter of each circle = 42

=> Radius of each circle = 21  ------ (2)

We know that the area of a circle is given as -

Area of circle = \(\pi r^{2}\)  ------ (3)

where,

r = radius of the circle

Substituting the value of r from equation (2) in equation (1), we have

Area of circle = \(\pi r^{2}\)

=> Area of circle = \(\pi (21)^{2}\)

=> Area of circle = 1385.44

=> Area of 9 circles = 12468.96    ----- (4)

Now, we can say that -

Area not in a circle = Area of square - Area of 9 circles

=> Area not in a circle = 15876 - 12468.96 [From equation (1) and (4)]

=> Area not in a circle = 3407.04    ------ (5)

We know that the probability of a outcome is given as -

Probability = Number of favorable outcomes/Total number of outcomes

So, the probability that the point is not in a circle can be calculated as -

Probability = Area not in a circle/Area of square

=> Probability = 3407.04/15876

=> Probability = 0.215

=> Probability = 21.5%

Thus, if there are nine congruent circles inscribed in a square and a point in the square is chosen at random, the probability that the point is not in a circle is 21.5%.

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Answer:

8x- y

Step-by-step explanation:

Answer:

Step-by-step explanation:

-5 = -3(h - 10) + (-8)

−5 = −3h + 22

−3h + 22 = −5

−3h = −27

h = 9

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

check

-5 = -3(9-10)+(-8)

-5 = -27 + 30 - 8

- 5 = -5

the answer is good

Answer:

1/48

Step-by-step explanation:

This is a case of joint probability, and the desired result is the product of P(spins a 5) and P(rolls a 6):  (1/8)(1/6) = 1/48.

Answer:

min: (-2;-6) & (1; 3/4); max: (0;2).

Step-by-step explanation:

1) f`(x)=3x³+3x²-6x;

2) f`(x)=0, ⇒ 3x³+3x²-6x=0;

3) 3x³+3x²-6x=0; ⇒ x(x²+x-2)=0; ⇒ x(x-1)(x+2)=0; ⇒ x₁=0; x₂=1; x₃=-2;

other steps are provided in the attachment.

The town's Population in 2025 is estimated to be approximately 5643.

The town's population in 2025, we need to calculate the population growth over the 20-year period from 2005 to 2025.

Given that the population in 2005 was 3800, and it grows at a rate of 2% every year, we can calculate the population for each year using the formula:

Population = Initial Population * (1 + Growth Rate)^Number of Years

Substituting the given values into the formula:

Population in 2025 = 3800 * (1 + 0.02)^20

Calculating this expression:

Population in 2025 = 3800 * (1.02)^20

Using a calculator or software, we can find the population in 2025:

Population in 2025 ≈ 3800 * 1.485947

Population in 2025 ≈ 5643.47

Therefore, the town's population in 2025 is estimated to be approximately 5643.

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It is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

In the given scenario, it is not completely true that based only on the r and p values listed above, you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

Let's first understand what is meant by the term "moderator.

"Moderator: A moderator variable is a variable that changes the strength of a connection between two variables. If there is a statistically significant bivariate relationship between the amount of texting during driving and the number of accidents, scientists investigate whether this bivariate relationship is moderated by age.

Therefore, based on the values of r and p, it is difficult to determine if age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

As we have to analyze other factors also to determine whether the age is a moderator or not, such as the sample size, the effect size, and other aspects to draw a meaningful conclusion.

So, it is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

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For the simple harmonic motion equation d=2 sin(pi/3t), the period is 6 seconds.

The period of a simple harmonic motion is the time taken for one complete cycle of the motion. In this equation, d represents the displacement or position of the object at time t. The equation is in the form of sin function with the argument (pi/3)t. The general form of the equation for simple harmonic motion is d=A sin(ωt+φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle. To determine the period of this motion, we can use the formula T=2π/ω, where T is the period and ω is the angular frequency. In this case, ω=pi/3, so the period is T=2π/(pi/3)=6 seconds (rounded to the nearest second). Therefore, the object completes one full cycle of motion every 6 seconds.

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