vis

If sin =

2 and r, what are the values of cos O and tan O? (2 points)

1

cos o = 2 ; tan =

13

1

2 ; tan o = -1

COS O

V3

cos O = 4 ; tan = -2

O

1

2 : tan =

3

COS O =

There are 462 possible 5-player combinations that can be formed from a roster of 11 players.

The number of ways to choose a team of 5 from a roster of 11 players can be calculated using the formula for combinations:

C(11, 5) = (11!)/(5!(11-5)!) = (11x10x9x8x7)/(5x4x3x2x1) = 462

To understand the formula for calculating combinations, it's helpful to know what a combination is. A combination is a way of selecting objects from a larger set without regard to their order. In other words, if you have a set of n objects and you want to choose k of them, a combination gives you all the possible subsets of size k that can be chosen from the set of n objects.

In this case, we want to find the number of ways to choose a team of 5 players from a roster of 11 players. We can use the formula for combinations to solve this problem:

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

where "n" is the total number of objects in the set (in this case, 11 players), "k" is the number of objects we want to choose (5 players), and the exclamation mark ("!") denotes factorial notation. Factorial notation means that you multiply all the numbers from 1 up to the given number. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

So plugging in the values for n and k, we get:

C(11, 5) = 11! / (5!(11-5)!)

C(11, 5) = (11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / [(5 x 4 x 3 x 2 x 1) x (6 x 5 x 4 x 3 x 2 x 1)]

C(11, 5) = (11 x 10 x 9 x 8 x 7) / (5 x 4 x 3 x 2 x 1)

C(11, 5) = 462

Therefore, there are 462 possible 5-player combinations that can be formed from a roster of 11 players.

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The reciprocal of each of the following fractions:

i) 7/3 - improper fraction

ii) 8/5 - improper fraction

iii) 7/9 - proper fraction

iv) 5/6 - proper fraction

v) 7/12 - proper fraction

vi) 8 - whole number

vii) 11 - whole number

To find the reciprocal of a fraction, we simply invert the fraction by swapping the numerator and the denominator.

i) Reciprocal of 3/7: 7/3

  - Classification: Improper fraction

ii) Reciprocal of 5/8: 8/5

   - Classification: Improper fraction

iii) Reciprocal of 9/7: 7/9

    - Classification: Proper fraction

iv) Reciprocal of 6/5: 5/6

   - Classification: Proper fraction

v) Reciprocal of 12/7: 7/12

  - Classification: Proper fraction

vi) Reciprocal of 1/8: 8/1 or simply 8

   - Classification: Whole number

vii) Reciprocal of 1/11: 11/1 or simply 11

    - Classification: Whole number

So, to summarize the classifications:

- Proper fractions: 7/9, 5/6, 7/12

- Improper fractions: 7/3, 8/5

- Whole numbers: 8, 11.

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Fοr the equatiοn οf circle x² + y² - 2x - 8 = 0, the statements which are true is A, B and E.

A circle is a clοsed curve that extends οutward frοm a set pοint knοwn as the centre, with each pοint οn the curve being equally spaced frοm the centre. A circle with a (h, k) centre and a radius οf r has the equatiοn:

(x-h)² + (y-k)² = r²

Tο determine which statements are true, we can manipulate the given equatiοn tο standard fοrm, which is -

(x - h)² + (y - k)² = r²

where (h, k) is the center οf the circle and r is the radius.

Starting with the given equatiοn -

x² + y² - 2x - 8 = 0

Rearranging the terms -

x² - 2x + y² = 8

Cοmpleting the square fοr x -

(x - 1)² + y² = 9

Cοmparing with the standard fοrm, we see that -

Statement A is true because the radius οf the circle is sqrt(9) = 3 units.

Statement B is true because the center οf the circle is (1, 0), which lies οn the x-axis.

Statement C is false because the center οf the circle is (1, 0), which dοes nοt lie οn the y-axis.

Statement D is false because the standard fοrm οf the equatiοn is (x - 1)² + y² = 9, nοt (x - 1)² + y² = 3.

Statement E is true because the radius οf this circle is 3 units, which is the same as the radius οf the circle whοse equatiοn is x² + y² = 9.

Therefοre, the third and fοurth statement is false.

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Answer:

the car would use 49 gallons because you get a decimal of 49.49 so you would put got decimal to the nearest 1's place and that would be 49

In the given project, students are required to work in the same groups as in Project 1 to study and understand the workings of a 7-segment display counter.

The main task for each group is to design a number generator (RNG) using only electronic components. This RNG should be able to predictably display 3-digit numbers on the 7-segment display. The term "predictably display" implies that the generated numbers should follow a specific pattern or sequence, making it possible to anticipate the upcoming numbers.

This project helps students gain practical experience in designing electronic circuits and understanding the functionality of 7-segment displays.

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Answer:

77.25

Step-by-step explanation:

Fastest rapper comparison.

A student wants to know which of two rappers reps the fastest. The graph below represent the average number of words Rapper 1 could rap based on the number of words in his most popular song and the length of the song. Number of Words Rapped Answer 315 245 175 140 105 70 35 RAPPER 1 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (min) The equation y = 156x can be used to represent the average number of words, y, that Rapper 2 could rap in x minutes based on the number of words in her most popular song and the length of the song. How many more words per minute does the faster rapper rap than the slower rapper? words per minute

To find out how many more words per minute the faster rapper can rap than the slower rapper, we need to compare the slopes of their respective lines.

From the graph, we can see that Rapper 1 raps 315 words in 4 minutes, which means they have an average rate of:

315 words / 4 minutes = 78.75 words per minute

We can also see that Rapper 2 has an equation for their line: y = 156x, where y represents the average number of words and x represents the time in minutes. This means that Rapper 2 has an average rate of:

156 words / minute

Therefore, the difference in their rates is:

156 words/minute - 78.75 words/minute = 77.25 words/minute

So the faster rapper raps 77.25 more words per minute than the slower rapper.

Answer:

Step-by-step explanation:

The area of the 7 cm by 11 cm rectangle is ...

  A = bh

  A = (7 cm)(11 cm) = 77 cm^2

The area of the circle of radius 2 cm is ...

  A = πr^2 = π(2 cm)^2 = 4π cm^2

If the shaded area lies between the circle and the rectangle, its area is the difference of these:

  shaded area = 77 cm^2 -4π cm^2

Using π = 3.14, this area is ...

  (77 -4·3.14) cm^2 = 64.44 cm^2

Using π = 3.141592, this area is ...

  (77 -4·3.141592) cm^2 ≈ 64.43 cm^2

The shaded area is 64.43 cm^2, (64.44 if you use π=3.14).

_____

Comment on π

Often, you are required to use a specific valued for π, even if that is inappropriate for the number of significant digits required in the answer. In recognition of that, we have offered both the correct answer (64.43) and the one associated with the value of π you may be expected to use.

Answer:

64.43cm ^2

Step-by-step explanation:

First, calculate the area of the whole figure, including the unshaded area.

The area of a rectangle is the length times the width.

7cm x 11cm = 77c\(m^{2}\)

Next, calculate the area of the inner figure.

The area of a circle is \(\pi\)\(r^{2}\)

\(\pi\) x 2cm x 2cm = 4\(\pi\) c\(m^{2}\)

Finally, subtract the area of the inner circle from the area of the outer rectangle.

77 c\(m^{2}\) - 4\(\pi\) c\(m^{2}\) ≈ 64.43 c\(m^{2}\)

Answer: 6√3 i

............................

The correct answer is C. Set Only set 1 with n = 2, l = 0, and m_l = 0 correctly specifies an orbital.

In quantum mechanics, orbitals are described by a set of quantum numbers that specify their energy level, shape, and orientation. The four quantum numbers are n, l, m_l, and m_s.

In set 1, we have n = 2, l = 0, and m_l = 0. These values are consistent with the rules for assigning quantum numbers to orbitals. The principal quantum number (n) represents the energy level, and having n = 2 means the orbital is in the second energy level.

The angular momentum quantum number (l) represents the shape of the orbital, and having l = 0 indicates an s orbital.

The magnetic quantum number (m_l) represents the orientation of the orbital within a subshell, and having m_l = 0 means the orbital is oriented along one axis (no angular dependence).

On the other hand, sets 2, 3, and 4 have incorrect combinations of quantum numbers. In set 2, having l = 5 is not possible since l can only have integer values from 0 to n-1. In set 3, having l = -2 is not allowed since l must be a non-negative integer.

In set 4, having l = 2 and m_l = 1 is not consistent since m_l can have values from -l to +l, and in this case, it should range from -2 to +2.

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1) The transformations we have in this function y=-4(x+1)²-5 In comparison to its parent function y=x²

1.1) A horizontal shift to the left the +1 y=-4(x+1)²-5 inside the parentheses

1.2) A reflection marked by the minus y=-4(x+1)²-5

1.3) A Vertical Stretch: y=-4(x+1)²-5

1.4) A vertical shift down: y=-4(x+1)²-5

2) We can see that in a plotted graph.

Statement 1- No satyrs are goats.

Statement 2- All satyrs are animals.

A representation of logical or mathematical sets as closed curves or circles within a rectangle (the universal set), with the crossings of the circles denoting the elements that are shared by all the sets.  is called venn diagram.

As some animals are satyrs, and satyrs cannot be goats, this implies that not all animals are goats. Therefore, if statements 1 and 2 are accurate, then assertion 3 must also be accurate.

However, the mythological divinity known as the Satyr is really shown as a human with certain animal parts, making the premise false. However, phrase 1 and 2 logically imply sentence 3.

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Venn diagram attached below,

The bearing of point P from R is approximately 45 degrees.

To find the bearing of point P from point R, we can use trigonometry.

First, let's visualize the situation. Point R is 8 km due east of point P, and 8 km due south. This forms a right-angled triangle, with the hypotenuse being the straight line distance between R and P.

Using the Pythagorean theorem, we can calculate the length of the hypotenuse (distance between R and P):

hypotenuse = √((8 km)² + (8 km)²)

hypotenuse = √(64 km² + 64 km²)

hypotenuse = √(128 km²)

hypotenuse ≈ 11.31 km

Now, we can find the angle between the hypotenuse and the due east direction. This angle represents the bearing of point P from R.

cosine(angle) = adjacent side / hypotenuse

cosine(angle) = (8 km) / (11.31 km)

angle = arccos((8 km) / (11.31 km))

angle ≈ 45 degrees

Therefore, the bearing of point P from R is approximately 45 degrees.

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There are 2 tablespoons in 1 fluid ounce. This conversion is often used in cooking and baking recipes, where ingredients are measured in ounces or tablespoons.

Fluid ounces and tablespoons are both units of volume used to measure liquids in cooking and baking recipes. One fluid ounce is equal to 29.5735 milliliters or approximately 2 tablespoons, which is equivalent to 6 teaspoons. Therefore, there are 2 tablespoons in 1 fluid ounce.

This conversion is important to know when following recipes that call for ingredients in fluid ounces or tablespoons. It allows for accurate measurement of ingredients, which is crucial for successful cooking and baking. Other common units of volume used in the kitchen include teaspoons, cups, and quarts, among others.

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The probability that Bill does not serve an ace or a double fault is 0.6.Option E (0.6) is the correct answer.

The probability of bill serving an ace in tennis is 0.15, and the probability that he double faults is 0.25. The probability that Bill does not serve an ace or a double fault is 0.6.What is probability?Probability refers to the chance that an event or circumstance will happen. It's the likelihood of something happening. Probability is usually expressed as a fraction or percentage. In many everyday situations, probability is used to make informed decisions. A probability of 1 indicates that an event is guaranteed to happen, while a probability of 0 indicates that an event is impossible to occur. A probability of 0.5 or 50% implies that an event is equally likely to happen or not. Probabilities can range from 0 to 1.What is the probability that Bill does not serve an ace or a double fault?The probability of Bill serving an ace is 0.15. The probability that he double faults is 0.25. The probability that he serves neither an ace nor a double fault is therefore 1 - (0.15 + 0.25) = 0.6Therefore, the probability that Bill does not serve an ace or a double fault is 0.6.Option E (0.6) is the correct answer.

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Answer:

8 units

Step-by-step explanation:

distance= sqrt((x2-x1)^2+(y2-y1)^2))

sqrt((5-(-3))^2+(4-4)^2))

sqrt(5+3)^2+(4-4)^2)

sqrt(8^2+(4-4)^2)

sqrt(64+(4-4)^2)

sqrt(64+0^2)

sqrt(64+0)

sqrt(64)

sqrt(8^2)

8

Answer:

see below

Step-by-step explanation:

g(x) = (x) -5

Let x = -5

g(-5) = -5 -5 = -10

Let x= 0

g(0) = 0-5 = -5

Let x= 5

g(5) = 5-5 = 0

We assume that G is a connected planar graph with no vertex of degree <= 5. We will use e <= 3v - 6 to prove that G is not a planar graph. By handshaking lemma, we know that 2e = sum of degrees of all vertices. Let d be the maximum degree of G.

Qa. Contrapositive of an implication is a new implication formed by negating both the hypothesis and the conclusion.

The contrapositive of the implication "If G is a connected planar graph, then G has at least one vertex of degree <= 5" is "If G has no vertex of degree <= 5, then G is not a connected planar graph."

Qb. Proof: We assume that G is a connected planar graph with no vertex of degree <= 5.

We will use e <= 3v - 6 to prove that G is not a planar graph. By handshaking lemma, we know that 2e = sum of degrees of all vertices.

Let d be the maximum degree of G. Since G has no vertex of degree <= 5, then d >= 6.

Thus, the sum of degrees of all vertices in G is greater than or equal to 6v/2, which is equal to 3v.

Hence, 2e >= 3v.

Substituting this inequality in e <= 3v - 6, we get 2e >= 3e - 6, which implies that e >= 6.

Since e >= 6, it follows that G is not planar.

Qc. Proof: We use proof by induction on the number of vertices of G. For a graph with one vertex, the statement is trivially true.

For a graph with n > 1 vertices, assume that every planar graph with at most n - 1 vertices can be colored with 6 (or less) colors.

Let G be a planar graph with n vertices.

By part (a), there exists a vertex v of G with degree <= 5.

We remove v and all its edges from G to get a new graph G' with n - 1 vertices.

By the induction hypothesis, we can color G' with 6 (or less) colors.

We add back v and its edges to G.

Since v has degree <= 5, at most 5 colors are used on its adjacent vertices.

We use a new color for v.

Thus, G can be colored with 6 (or less) colors.

Therefore, by induction, the statement is true for all planar graphs.

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Answer: You can make 8 servings with 1 gallon.

Answer:

\(\frac{1}{6}\)

Step-by-step explanation:

Given: One serving of special sundae is made up of one third mint ice cream one third chocolate and one third vanilla.

To find: Ratio of vanilla ice cream is in a half serving

Solution:

Ratio of mint ice cream in one serving \(=\frac{1}{3}\)

Ratio of chocolate ice cream in one serving \(=\frac{1}{3}\)

Ratio of vanilla ice cream in one serving \(=\frac{1}{3}\)

Here, \(\frac{1}{3} +\frac{1}{3} +\frac{1}{3} =1\)

Therefore,

Ratio of vanilla ice cream is in a half serving \(=\frac{1}{3}(\frac{1}{2})=\frac{1}{6}\)

Answer:

7/15

Step-by-step explanation:

First, we have to make the bottom part the same:

2/3 - 1/5 = 10/15 - 3/15

10 - 3 = 7 = 7/15

Answer:

• =multiplication

question 7:

1/2•5•x=20

x=8cm

question 8:

answer:y=10cm.

Answer:

1. 25cm² x

2. 36cm² y

3. 18cm² z

Answer:

○ C. \(\displaystyle 0, 2, and\:4\)

Step-by-step explanation:

Wherever the graph intersects the x-axis is considered your zero [x-intercept], therefore you have your answer:

\(\displaystyle [0, 0], [2, 0], and\: [4, 0]\)

I am joyous to assist you at any time.

Answer:

the answer is 14 liters

Step-by-step explanation:

no of cans: 7

liters present in each can: 2

therefore, liters of juice= 7×2

=14

∠CFA ≅ ∠EDA (By Transitive Property of Congruence).

Given:

Three lines AD, CF, and BE are intersecting each other at the midpoint O.

To prove:

∠CFA ≅ ∠EDA

Proof:

Given that AD, CF, and BE intersect at the midpoint O.

By definition of a midpoint, OA ≅ OD, OB ≅ OE.

OA = OD and OB = OE.

Triangle OAD ≅ Triangle OBE (By Side-Side-Side congruence).

∠OAD ≅ ∠OBE (By Corresponding Parts of Congruent Triangles are Congruent).

∠CFA and ∠EDA are vertical angles.

∠OAD ≅ ∠CFA and ∠OBE ≅ ∠EDA (By Vertical Angles are Congruent).

Therefore, ∠CFA ≅ ∠EDA (By Transitive Property of Congruence).

Hence, it is proven that ∠CFA ≅ ∠EDA.

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Using the z-distribution, supposing a population standard deviation of 5, the minimum number of snapdragons you need for the new study is of 267.

The bounds of the confidence interval are presented as follows:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

In which the parameters are described as follows:

The margin of error of the interval is:

\(M = z\frac{\sigma}{\sqrt{n}}\)

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value of the interval is of z = 1.96.

The population standard deviation is given as follows:

\(\sigma = 5\)

The minimum number of dragons needed is n when M = 0.6, hence:

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(0.6 = 1.96\frac{5}{\sqrt{n}}\)

\(0.6\sqrt{n} = 1.96 \times 5\)

\(\sqrt{n} = \frac{1.96 \times 5}{0.6}\)

\((\sqrt{n})^2 = \left(\frac{1.96 \times 5}{0.6}\right)^2\)

n = 266.8 = 267 (rounded up, as 266 would have a margin of error slightly above the desired).

The population standard deviation is missing, and we suppose that it is of 5.

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Answer: $47

Step-by-step explanation: if he had $47 before and has $0 now, he used all of his money which is $47!

Answer: $47

Step-by-step explanation: