What is x if cos(15%) = x/5?
A. cos(15%)/5
B. cos(75°)
C. 5cos(15%)
D. cos(3⁰)

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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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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The result of the operation 3a²-ab-2b² and 2a² +5ab "-3b² is

4a² + 7ab - b².

What is an algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.

Let's simplify the expressions and then perform the given operation:

3a² - ab - 2b² + 2a² + 5ab - 3b² - (a² - 3ab - 4b²)

Combining like terms within parentheses:

3a² - ab - 2b² + 2a² + 5ab - 3b² - a² + 3ab + 4b²

Combining like terms outside parentheses:

4a² + 7ab - b²

Therefore, the result of the operation is 4a² + 7ab - b².

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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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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!

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

Hope this helps and be sure to mark this as brainliest! :)

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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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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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!

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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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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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 correct option is (a) i.e. The translation direction is downward, and the number of units is 8.

What is translation?

In mathematics, translation refers to the process of moving a geometric object from one location to another, without changing its size, shape, or orientation.

To determine the translation direction and number of units, we need to find the vector between the original point Q(4,3) and the new point Q'(4,-5).

The vector between two points is found by subtracting the coordinates of the initial point from those of the final point. Therefore, we have:

Q'Q = (4,-5) - (4,3) = (0, -8)

This tells us that the new point Q' is 8 units down (in the negative y-direction) from the original point Q. Therefore, the translation direction is downward, and the number of units is 8.

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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

Answer:

Rows:

1: Add the exponents instead of subtracted.  Correct answer [tex]h^{2}[/tex]

2: 9/3 is 3 not 6.  Correct answer 3[tex]b^{5}[/tex]

3: This answer is correct.  You subtract the exponents when you divide.

[tex]n^{2-6}[/tex] is [tex]n^{-4}[/tex]

4: The 5 should be in the numerator.  Correct answer [tex]\frac{5}{c^{8} }[/tex]

5:  You add the exponents when you are multiplying the bases and subtract the exponents when you are dividing the bases.  Correct answer is  [tex]d^{4}[/tex]

6: [tex]2^{3}[/tex] = 8 Correct answer [tex]\frac{a^{4} }{8b^{24} }[/tex]

Step-by-step explanation:

Helping in the name of Jesus.

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 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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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!

(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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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:

Eleven below Zero

Step-by-step explanation:

Every number below zero (less than zero) is a negative number.

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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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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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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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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The probability that Sam catches a bluegill, then a carp is 1/40.

The probability of catching a bluegill on the first try is 3/16, since there are 3 bluegills in the pond out of a total of 16 fish. Once Sam releases the first fish, there are 15 fish left, and 2 of them are carp. Therefore, the probability of catching a carp on the second try is 2/15.

To find the probability of both events occurring together (catching a bluegill and then a carp), we need to multiply the probabilities of each event. So the probability of catching a bluegill, then a carp is

P(bluegill and then carp) = P(bluegill) x P(carp | bluegill not caught)

We use "bluegill not caught" in the second event to indicate that the pond has one less fish after the first event, and we can't assume that the first fish is still in the pond.

P(bluegill and then carp) = (3/16) x (2/15)

P(bluegill and then carp) = 1/40

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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:

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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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!

True. The Conditional statement is known as the inductive hypothesis.

In mathematical induction, we use this hypothesis to prove that a certain statement or equation is true for all positive integers.

The process involves proving a base case for the smallest possible value of k and then using the inductive hypothesis to prove that the statement is true for the next consecutive value of k.

This process can be repeated infinitely, proving that the statement is true for all positive integers.
Let's say we want to prove that the sum of the first n positive integers is [tex]n(n+1)/2[/tex] for all positive integers n.

We can start by proving the base case for n=1, which states that [tex]1(1+1)/2 = 1.[/tex]

Now, assuming that the statement is true for some positive integer k, we can use the inductive hypothesis to prove that it is also true for k+1.

This involves showing that[tex](k+1)(k+2)/2 = k(k+1)/2 + (k+1)[/tex] which simplifies to the original equation.

By using the inductive hypothesis, we can prove that the statement is true for all positive integers.
Statement "[tex]P(K) - P(k + 1)[/tex] is true for all positive integers k" is indeed the inductive hypothesis. [tex]1(1+1)/2 = 1[/tex]

It is an important concept in mathematical induction, allowing us to prove statements and equations for all positive integers.

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