A survey is taken at a movie theater in Wayside. The first 200 people who entered the theater were asked about their favorite type of movie. What is true about this situation?

The population is the first 200 people at the theater, and the sample is the total number of people who go to the movie theater.
The population is the number of people who go to the movie theater, and the sample is the number of people in the town of Wayside.
The population is the total number of people who go to the movie theater, and the sample is the first 200 people at the theater.
The population is the number of people in the town of Wayside, and the sample is the number of people who go to the movie theater.

We have proven that the expression (36⁵ - 6⁹)(38⁹ - 38⁸) is divisible by both 30 and 37.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

To prove that the expression (36⁵- 6⁹)(38⁹ - 38⁸) is divisible by 30 and 37, we need to show that it can be written as the product of 30 and 37 with some integer coefficient.

First, let's look at the factorization of 30: 30 = 2 x 3 x 5.

We can see that 6 is a factor of 36, so we can rewrite 36^5 as (6²)⁵. Similarly, we can write 6⁹ as (6²)⁵ x 6³.

Now, let's factor out (6²)⁵ from the first factor in the expression:

(36⁵ - 6⁹) = (6²)⁵ (6⁵ - 6³)

We can factor out 38⁸ from the second factor in the expression:

(38⁹ - 38⁸) = 38⁸ (38 - 1)

So the original expression can be written as:

(36⁵ - 6⁹)(38⁹ - 38⁸) = (6²)⁵ (6⁵ - 6³) 38⁸ (38 - 1)

Now, let's look at the factorization of 37. We can see that 38 - 1 = 37, so we can rewrite the expression as:

(6²)⁵(6⁵ - 6³) 38⁸ (38 - 1) = (2⁵ x 3⁵) (6³) 38⁸ (37)

We can see that the expression contains a factor of 2⁵, a factor of 3⁵, and a factor of 37, so it is divisible by both 30 and 37.

Therefore, we have proven that the expression (36⁵ - 6⁹)(38⁹ - 38⁸) is divisible by both 30 and 37.

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The proof that the Quadrilateral WXYZ is a rectangle is shown below

To prove that Quadrilateral WXYZ is a rectangle, we need to show that it has four right angles.

First, we can find the slopes of each pair of opposite sides to determine if they are perpendicular.

The slope of WX is:

m(WX) = (y2 - y1)/(x2 - x1) = (-2 - 1)/(2 - (-1)) = -1

The slope of YZ is:

m(YZ) = (y2 - y1)/(x2 - x1) = (6 - 3)/(4 - 7) = -1

Since the slopes of WX and YZ are equal , we know that they are opposite sides.

Now we can use the distance formula to check if the sides of the quadrilateral are congruent. The length of WX is:

√((2 - (-1))^2 + (-2 - 1)^2) = √18

The length of YZ is:

√((7 - 4)^2 + (3 - 6)^2) = √18

The length of WY is:

√((7 - (-1))^2 + (3 - 1)^2) = √68

The length of XZ is:

√((4 - 2)^2 + (6 - (-2))^2) = √68

We can see that opposite sides WX and YZ have the same length, as do opposite sides WY and XZ.

So, the quadrilateral is a rectangle

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Okay, here are the steps to find the minimum value of P:

1) Given: |z|=|w|=1 (z and w are complex numbers with unit modulus)

|z+w|=sqrt(2)

Find z and w such that these conditions are satisfied.

Possible solutions:

z = 1, w = i (or vice versa)

z = i, w = 1 (or vice versa)

2) Substitute into P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|

For the cases:

z = 1, w = i: P = |-1-4+2(1+i)i| = |-5+2i| = sqrt(25+4) = 5

z = i, w = 1: P = |1-\frac{4}{i}+2(1+\frac{1}{i})i| = |-3+2i| = sqrt(9+4) = 5

3) The minimum value of P is 5.

So in summary, the minimum value of

P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|

is 5.

Let me know if you have any other questions!

In the given circle the formula for subtracting the length of AB is -3-(-14).

A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent.

A circle is also known as the location of points that are evenly spaced apart from the center.

The radius of a circle is measured from the center to the edge.

A car tire, a time-telling wall clock, and lollipops are a few objects in our immediate environment that have a circular form.

So, the measurement of an object's travel distance is the space between two spots.

We must calculate the distance between points A and B using the provided diagram.

The x-coordinate being equal, it follows that:

AB = y2 - y1

AB= -3 - (-14)

AB = 11 units

Therefore, in the given circle the formula for subtracting the length of AB is -3-(-14).

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Correct question:

A circle with center O(3,3)O(3,3) contains the point A(-1,14)A(−1,14).

Write a subtraction expression for each length OF AB and ABAB:

The leg measurement will make a right triangle is 21 cm.

The longest side of a right-angled triangle, i.e. the side opposite the right angle, is called the hypotenuse in geometry.

Pythagorean theorem :

If p be the length of the hypotenuse of a right-angled triangle, q and r be the lengths of the other two sides, then

p² = q² + r²

The lengths of the other two sides of the given right-angled triangle are 20 cm and 21 cm. Put these values in the above theorem to get the desired result.

Now, p² = (20)² + (21)²

= 400 + 441 = 841

i.e. p = √(841) = 29

Therefore the length of the hypotenuse is 29 cm. The right angle traingle is 21 cm.

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Thus, the Area of shaded region for the given sector of circle is found as:

1.14 sq. cm.

Two radii that meet at the centre to form a sector define a circle. The sector is the portion of the circle created by these two radii. Knowing a circle's central angle measurement and radius measurement are both crucial for solving circle-related difficulties.

Given:

Area of shaded region = area of sector - area of triangle

Area of shaded region = Ф/360° * (πr²) - 1/2*base*height

Area of shaded region = 90/360° * (3.14*2²) - 1/2*2*2

Area of shaded region = 1/4*3.14*4 - 2

Area of shaded region = 3.14 - 2

Area of shaded region = 1.14 sq. cm

Thus, the Area of shaded region for the given sector of circle is found as:

1.14 sq. cm.

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The value of the Central angle and Circumscribed angle are respectively: 97° and  83°

A circumscribed angle is the angle formed by the intersection of two tangent lines (lines that each touch the circle at exactly one point) to a circle.

The circumscribed angle theorem states that the measure of a circumscribed angle is the supplement of the central angle that intercepts the same arc (the supplement of an angle is the difference between 180° and the angle). Because a central angle has the same degree measure as its intercepted arc, it follows from the circumscribed angle theorem that the measure of a circumscribed angle is the supplement of the degree measure of the intercepted arc.

The formula for the circumscribed angle theorem is:

θ = 180° - C

Where:

θ is the circumscribed angle

C is the central angle

Thus:

3x + 11 = 180 - (5x - 23)

3x + 11 = 180 - 5x + 23

3x + 11 = 203 - 5x

8x = 203 - 11

8x = 192

x = 192/8

x = 24

Thus:

Central angle = 5(24) - 23

= 120 - 23

= 97°

Circumscribed angle = 180 - 97 = 83°

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the Princess Resort is the best deal with a total cost of $657 for a four-night stay.

What is Total fixed cost?

Total fixed cost refers to the cost of all fixed assets which incur a fixed cost irrespective of the level of production in a company.

The Contemporary Resort costs $239 per night, so the total cost for four nights would be:

$239 × 4 = $956.

The Fun Times Resort costs $189 per night, so the total cost for four nights would be:

$189 × 4 = $756.

The regular cost is $219 per night, so the total cost for three nights would be:

$219 × 3 = $657. But since they get the fourth night free, the total cost for four nights would be:

$657 + $0 = $657.

Comparing the three options, the Princess Resort is the best deal with a total cost of $657 for a four-night stay.

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Answer:

35° 21

Step-by-step explanation:

In an isosceles triangle, the angles opposite to the equal sides of an isosceles triangle are equal in measurement1. Therefore, if ∠A = 110° and ABC is an isosceles triangle, then ∠B = ∠C = (180° - ∠A)/2 = (180° - 110°)/2 = 35° 21.

I hope this helps!

Answer: False

Step-by-step explanation:

If the question is relating to equality, your answer currently is incorrect.
If we solve both sides of the ( + ) we have :

2(n + 6) = 2n + 12

2n + 12 + n + 6 = 3n + 18

Therefore, the  two that are equal are 2(n + 6) + (n + 6) and 3n + 18.

There is also another set of expressions that are equal:

2n + 2 + n + 4 = 3n + 6

The point (1,2) is the point of intersection of the two lines.

It should be noted that to verify if the point (1,2) is a solution to the system of linear equations, we need to substitute x=1 and y=2 into both equations and check if they are true.

The equation is true, so (1,2) is a solution to the first equation.

Substituting x=1 and y=2 into the second equation also makes the equation true.

Therefore, the point (1,2) is the point of intersection of the two lines.

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The correct answer from the following given to find the details regarding the bouquet is:

y > 0

x ≥ 2y

0.5x + 0.75y ≤ 50

From the problem, we know that Denae wants at least twice as many daisies as daffodils in each bouquet, and she has a total of $50 to spend. This means that the number of daisies (x) and daffodils (y) must satisfy certain constraints.

The correct inequality among the constraints for this situation are:

y > 0, since there must be at least one daffodil in each bouquet.

x ≥ 2y, since Denae wants at least twice as many daisies as daffodils in each bouquet.

0.5x + 0.75y ≤ 50, since Denae has a total of $50 to spend and daisies cost $0.50 each and daffodils cost $0.75 each.

Therefore, the correct answers are:

y > 0

x ≥ 2y

0.5x + 0.75y ≤ 50

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High Traffic, Large Database, Internet Connectivity are the reason for taking centuries for searches.

High Traffic: If there are many users accessing the site simultaneously, the servers might get overloaded, leading to slow searches.

Large Database: Brainly has a vast database of questions and answers, which could slow down searches if the search algorithm isn't optimized.

Internet Connectivity: Slow internet connection on your side could result in slow searches

If you're experiencing slow searches, you can try the following: Check your internet connection and make sure it's stable and fast. Try clearing your browser cache and cookies and restart your browser.

If you're using an outdated browser, try updating it to the latest version. Consider reaching out to Brainly's customer support team to report the issue and seek assistance.

Therefore, High Traffic, Large Database, Internet Connectivity are the reason for taking centuries for searches.

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The pair of vertical angles are;

<E and <F

<T and < U

Vertical angles are defined as a pair of non-adjacent angles formed when two lines intersect.

When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles.

A pair of vertically opposite angles are always equal to each other.

These angles are congruent and of the same measure.

From the diagram shown, we have the angles as;

Vertical pairs as;

<E and <F

<U and < T

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We must first convert the given information into an equivalent fraction. The answer is 56%.

Equivalent fractions have the same value or represent the same portion of a whole even though they may have different numerators and denominators.

To do this, we must multiply both the numerator (14) and denominator (25) by the same number so that the denominator equals 100.

To do this, we must multiply both 14 and 25 by 4.

This gives us 14*4/25*4 = 56/100.

To convert this fraction to a percent, we can simply divide the numerator by the denominator and multiply the result by 100.

Therefore, 56/100 * 100 = 56%.

This result can also be found by setting up a proportion. We can set up the proportion as follows:

14/25 = x/100.

To solve for x, we must multiply both sides by 100. This gives us 14*100/25 = x.

Hence, x = 56. Therefore, 56% of swimmers finished the race in less than 47 minutes.

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If a circle graph was constructed from the results, the lake activity has a central angle of 54° is Paddleboarding.

To find the lake activity with a central angle of 54° in the circle graph, we need to determine the percentage of campers who chose that activity.

The total number of campers surveyed is 100, and the number of campers who chose paddleboarding is 54. Therefore, the percentage of campers who chose paddleboarding is:

54/100 x 100% = 54%

To convert this percentage to a central angle in degrees, we can use the formula:

Central angle = Percentage * 360°

So, the central angle for paddleboarding is:

54% x 360° = 194.4°

Therefore, the correct option is d. Paddleboarding.

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Answer: 6 3/7

Step-by-step explanation:

9/1 x 5/7

If we multiply the numerators and denominators, we get 45/7 or 6 3/7 as a mixed number.

Answer:

[tex]\frac{45}{7}[/tex] or 6.4285

Step-by-step explanation:

First, multiply 9 and 5, which gives you 45.

9(5)=45

Then, divide 45 by 7.

45/7=6.4285

That gives  you  [tex]\frac{45}{7}[/tex] or 6.4285

Hope this helps!

Answer:

25:1

Step-by-step explanation:

To find the ratio of the areas of two figures, you need to divide the larger area by the smaller area. In this case, the larger area is 1125 square feet, and the smaller area is 45 square feet.

So the ratio of the larger area to the smaller area is:

1125 sq ft / 45 sq ft

To simplify the ratio, you can divide both numbers by their greatest common factor, which in this case is 45.

1125 sq ft / 45 sq ft = 25 / 1

Therefore, the ratio of the larger area to the smaller area is 25:1.

Hope this helps!

Answer:

y = -4

Step-by-step explanation:

13 - y = 17

y = 13 - 17 = -4

Answer:

y = -4

Step-by-step explanation:

Alright so you shift the y to the other side:
13 = 17 + y

Now you shift the 17 to the other side,
y = 13 - 17 = -4

Hence, y = -4

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(a) For the null hypothesis, we would use the claim that the average weight of a healthy 3-month-old colt is equal to 60 kg, that is,

H0 : μ = 60 kg.

(b) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is less than 60 kg, that is,

H1: μ < 60 kg.

(c) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is greater than 60 kg, that is, H1: μ > 60 kg.

(d) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is different from 60 kg, that is, H1: μ ≠ 60 kg.

(e) For the test in part (b), the area corresponding to the p-value would be on the left of the mean because the alternate hypothesis is one-tailed and represents a left-tailed test.

For the test in part (c), the area corresponding to the p-value would be on the right of the mean because the alternate hypothesis is one-tailed and represents a right-tailed test.

For the test in part (d), the area corresponding to the p-value would be on both sides of the mean because the alternate hypothesis is two-tailed and represents a two-tailed test.

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Overall, interpreting a two-way table requires careful attention to detail and the ability to think critically about the data. It is important to look beyond the numbers themselves and try to understand what they are telling you about the relationship between the variables.

What are the Two-way tables?

Two-way tables, also known as contingency tables, are a way to display the frequency distribution of two categorical variables. The variables are usually listed as rows and columns, with the frequency of each combination of values shown in the cells of the table.

Interpreting a two-way table involves looking at the relationships between the variables and identifying patterns in the data. Here are some steps you can follow to interpret a two-way table:

Look at the marginal frequencies: These are the totals for each row and column. They give you an idea of the distribution of each variable individually.

Look at the conditional frequencies: These are the frequencies of each combination of values, divided by the marginal frequency of one of the variables.

They tell you the proportion of one variable that has a certain value, given that the other variable has a certain value.

Look for patterns: Look for rows or columns with high or low frequencies, and try to identify any trends or patterns in the data.

Are there any combinations of values that are more or less common than others? Are there any values that seem to be associated with each other?

Draw conclusions: Based on the patterns you observe, draw conclusions about the relationship between the two variables. Do they appear to be independent, or is there evidence of a causal relationship?

hence, Overall, interpreting a two-way table requires careful attention to detail and the ability to think critically about the data. It is important to look beyond the numbers themselves and try to understand what they are telling you about the relationship between the variables.

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There are 10 ways to divide 5 people into two groups where the first group has 2 people, and the second group has 3 people.

There are two ways to divide 5 people into two groups where the first group has 2 people and the second has 3. The first way is to choose 2 people out of the 5 for the first group, which can be done in 5C2 ways, and then the remaining 3 people form the second group. The second way is to choose 3 people out of the 5 for the second group, which can be done in 5C3 ways, and then the remaining 2 people form the first group. Therefore, the total number of ways to divide 5 people into two groups with a group of 2 people and a group of 3 people is 5C2 + 5C3, which equals 10 + 10, or 20.
The formula for combinations is:

C(n, r) = n! / (r!(n-r)!)

where C(n, r) is the number of ways to choose r items from a set of n items, n! represents the factorial of n, and r! represents the factorial of r.

In this case, you want to choose 2 people from a set of 5. So, n = 5 and r = 2. Plug the values into the formula:

C(5, 2) = 5! / (2!(5-2)!)
C(5, 2) = 5! / (2!3!)
C(5, 2) = 120 / (2*6)
C(5, 2) = 120 / 12

So, there are 10 ways to divide 5 people into two groups where the first group has 2 people, and the second group has 3 people.

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Based on the definition of the tangent of a circle and the Pythagorean triple of a right triangle, AB is not tangent to circle C in both question 19 and 20.

In geometry, the tangent of a circle is a line that intersects the circle at exactly one point, which is called the point of tangency. This line is perpendicular to the radius of the circle at that point. This means that it forms a right angle at that point.

19. If AB is tangent to circle C, the lengths of the triangle ABC will form a Pythagorean triple. Let's check:

4.8² + 7.2² = 12²

74.88 = 144 [not true} Therefore, AB is not tangent to circle C.

20. Also, we will have the following:

15² + 11.2² = 6.8²

350.44 = 46.24 [not true].

AB is not tangent to circle C.

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Number of  exercise classes must you take in one month so that the cost of Forever Fitness is the ​same​ as Peachtree Gym is 8

Let's denote by x the number of exercise classes taken in one month.

For Forever Fitness, the total cost in one month would be:

50 + 15x

For Peachtree Gym, the total cost in one month would be:

75 + 10x

We want to find out when these two costs are equal, so we can set them equal to each other and solve for x

50 + 15x = 75 + 10x

Simplifying this equation by subtracting 10x from both sides gives:

40 = 5x

Dividing both sides by 5 gives

x = 8

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If the measure of angle RST is 60°, and RS=4 units, then the area of sector RST is 8.374 square units.

In geometry, a "Sector" of a circle is defined as the portion of circle enclosed by two radii and the arc between them. It can be thought of as a slice or a wedge cut out of a circle.

To find the area of the "sector-RST" in circle centered at "S", we use the formula for area of a sector of a circle, which is :

⇒ Area of sector = (θ/360) × π × r²,

where θ = central angle of sector in degrees, π = 3.14159, and r = radius of circle,

In this case, we are given that m∠RST = 60 degrees and RS = 4 units. Since RS is the radius of the circle centered at "S", we use RS = r,

Substituting the values, θ = 60 degrees, r = RS = 4 units,

We get,

⇒ Area of sector RST = (60/360) × 3.14 × (4)²,

= (1/6) × 3.14 × 16,

= 8.374 square units,

Therefore, the required area of sector is 8.374 square units.

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The given question is incomplete, the complete question is

In circle centered at "S", R and T are the points on the circumference with m∠RST = 60 and RS=4 units .Find area of sector RST.

The number of atoms in 8.500 moles of chlorine atoms can be calculated using Avogadro's number, which is approximately 6.022 × 10²³ atoms/mole.

So, the number of atoms in 8.500 moles of chlorine atoms would be:

8.500 moles × 6.022 × 10²³ atoms/mole = 5.12 × 10²⁴ atoms of chlorine.

The molar mass of oxygen is approximately 16.00 g/mol. Therefore, the mass of 15.50 moles of oxygen would be:

15.50 moles × 16.00 g/mol = 248 g of oxygen.

The molar mass of helium is approximately 4.00 g/mol. Therefore, the number of moles of helium in 1.953 x 10^8 g of helium would be:

1.953 x 10^8 g / 4.00 g/mol = 4.88 x 10⁷ moles of helium.

The molar mass of sulfur is approximately 32.06 g/mol. Therefore, the number of moles of sulfur in 147.82 g of sulfur would be:

147.82 g / 32.06 g/mol ≈ 4.61 moles of sulfur.

The molar mass of cobalt (Co) is approximately 58.93 g/mol.

The formula mass of Ca₃(PO₄)₂ can be calculated by adding the molar masses of all the individual atoms in the formula.

The molar mass of calcium (Ca) is approximately 40.08 g/mol, the molar mass of phosphorus (P) is approximately 30.97 g/mol, and the molar mass of oxygen (O) is approximately 16.00 g/mol.

Therefore, the formula mass of Ca₃(PO₄)₂ would be:

3 × 40.08 g/mol (for Ca) + 2 × (2 × 30.97 g/mol + 4 × 16.00 g/mol) (for P and O) = 310.17 g/mol.

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Answer: 144π

Step-by-step explanation:

The equation for the area of a circle is πr², with r being the radius given in the problem. The radius, as a reminder, is the distance between the middle of the circle and any point along its outer curve. Here, we know the radius is 12 because the line to the middle of the circle indicates we are finding the radius since it goes halfway and not all the way to the other side of the circle. We can plug into the equation and solve it.

A = πr²

A = π(12)²

A = 144π

I hope this helps!

Sampling is a statistical method of selecting a representative subset of a larger population, in order to make inferences about the population as a whole.

If you decide whether you want to see an entire movie based on a 90-second trailer, you are not using a sampling technique. In this case, you are making a personal decision based on a brief preview of the movie This decision is not based on a random or representative sample of the movie, nor is it part of a systematic or scientific sampling technique.

Therefore, it would not be accurate to describe this decision as a scientific sampling technique. However, movie studios may use sampling techniques to gather data on audience reactions to trailers and other promotional materials, in order to make informed decisions about marketing and distribution strategies.

For example, they may conduct surveys or focus groups to gather feedback on specific elements of the trailer, such as the plot, characters, or visual effects. This data can then be used to refine the marketing campaign and increase the likelihood of a successful release.

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Answer:

below

Step-by-step explanation:

26. yes because a straight line is formed

27. domain - -2 to 2

range -2 to 1

Answer:

Yes, the graph is a linear function.

Domain: x∈[-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5]

Range: y∈[-1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2]

Step-by-step explanation:

A linear function is an expression that will form a straight line when graphed (or a graph that forms a straight line). These points form a straight line, so the function is linear.

The domain of the function is everything that x can be equal to. We can see here that the ordered points are:

(-2, -1.5), (-1.5, -1), (-1, -0.5), (-0.5, 0), (0, 0.5), (0.5, 1), (1, 1.5), (1.5, 2)

So, the domain of the function is all of the x values of the ordered pairs, or:

x∈[-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5]

(the symbol next to the x means "belongs to.")

As for the range, it is everything that y can be equal to. Let us look once again at the ordered pairs. The range of the function is equal to the y coordinates of these ordered pairs, or:

Range: y∈[-1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2]

Keep in mind that if the function contains more than one value for x or y, it is listed ONLY ONCE in the domain/range.