in how many ways can 4different prizes be givn to any 4 of 10 people if no person receives more than 1 prize?

The following are the measures of angles and sides using the sine and cosine rules:

1). QR = 15, m∠P = 52°, m∠Q = 43°

2). BC = 21, DC = 10.4, m∠C = 22°

3). VX = 10.7, WX = 10.2, m∠V = 39°

4). HF = 18.4, m∠H = 28.7, m∠F = 15.3

The sine rule is a relationship between the size of an angle in a triangle and the opposing side. While the cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

1). Using the sine rule:

19/sin85 = 13/sunQ

Q = sin⁻¹[(13 × sin85)/19] {cross multiplication}

Q = 43

m∠P = 180° - (85 + 43) = 52°

QR = sin⁻¹[(19 × sin52)/sin85]

QR = 15.

2). m∠C = 180 + (19 + 139) = 22°

Using the sine rule:

BC = (12 × sin139)/sin22

BC = 21.

DC = (12 × sin19)/sin22

DC = 10.4

3). m∠V = 180 - (41 + 100) = 39°

Using the sine rule:

VX = (16 × sin41)/sin100

VX = 10.7

WX = (16 × sin39)/sin100

WX = 10.2

4). Using the cosine rule:

HF² = 7² + 13² - 2(7)(13)cos136°

HF = √338.8491

HF = 18.4

applying sine rule;

F = sin⁻¹[(7 × sin136)/18.4]

F = 15.3

m∠H = 180 - (15.3 + 136) = 28.7

Therefore, the measures of angles and sides using the sine and cosine rules are:

1). QR = 15, m∠P = 52°, m∠Q = 43°

2). BC = 21, DC = 10.4, m∠C = 22°

3). VX = 10.7, WX = 10.2, m∠V = 39°

4). HF = 18.4, m∠H = 28.7, m∠F = 15.3

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Answer:

(-5,1)

Step-by-step explanation:

The vertex of a parabola is either the top most point or the bottom most, depending on which parabola is being talked about.

Step-by-step explanation:

look in thr comments and have a great day

The total surface area of the square based prism using the net is 119 square meters

From the question, we have the following parameters that can be used in our computation:

The net of a square based prism

The surface area of the square based prism from the net is calculated as

Surface area = sum of areas of individual shapes that make up the net of the triangular prism

Using the above as a guide, we have the following:

Area = Square + 4 * triangle

So, we have

Area = 7 * 7 + 4 * 1/2 * 5 * 7

Evaluate

Area = 119

Hence, the surface area is 119 square meters

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We distribute -3 to 2x and -8, and then we calculate the two multiplications.

We calculate -6x + 4x = -x(6 - 4) = -2x

[tex] \bf - 3(2x - 8) + 4x = \\ \\ \bf = - 3 \cdot 2x - 3 \cdot ( - 8) + 4x = \\ \\ \bf = - 6x + 24 + 4x = \\ \\ \bf = - 6x + 4x + 24 = \\ \\ \bf = - 2x + 24[/tex]

The answer is B -2x + 24

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Since 3-SAT is NP-complete and we have a polynomial-time reduction from 3-SAT to SAT', it follows that SAT' is NP-hard. Thus, SAT' is NP-complete, as required.

To prove that SAT' is NP-complete, we need to show that it is in NP and that it is NP-hard.

First, we show that SAT' is in NP. Given a CNF formula, we can verify in polynomial time whether a proposed assignment to the variables satisfies exactly m-2 clauses. Specifically, we can evaluate each clause in the formula under the proposed assignment, count the number of clauses that are satisfied, and compare it to m-2. If the count is exactly m-2, then the assignment satisfies exactly m-2 clauses, and we can verify this in polynomial time. Therefore, SAT' is in NP.

Next, we show that SAT' is NP-hard. We do this by reducing an NP-complete problem to SAT'. We choose 3-SAT, which is known to be NP-complete.

Given an instance of 3-SAT with m clauses and n variables, we construct an instance of SAT' as follows. We add two new variables, y and z, and construct the following CNF formula:

(a1 ∨ b1 ∨ y) ∧ (a2 ∨ b2 ∨ ¬y) ∧ (a3 ∨ b3 ∨ ¬z) ∧ (a4 ∨ b4 ∨ z) ∧ C1 ∧ C2 ∧ ... ∧ Cm,

where C1, C2, ..., Cm are the m clauses of the 3-SAT instance, and each clause in the 3-SAT instance has exactly three literals.

We claim that this construction is a polynomial-time reduction from 3-SAT to SAT'. First, note that the CNF formula has n+2 variables and m+4 clauses, which can be constructed in polynomial time. Second, note that any assignment that satisfies exactly m-2 clauses in the CNF formula must assign y to true and z to false. This is because the first two clauses require y to be true and false, respectively, and the last two clauses require z to be false and true, respectively. Thus, the assignment to the original n variables satisfies exactly m-2 clauses in the 3-SAT instance. Conversely, any assignment to the original n variables that satisfies exactly m-2 clauses in the 3-SAT instance can be extended to an assignment that satisfies exactly m-2 clauses in the CNF formula by setting y to true and z to false. Therefore, there is a 1-1 correspondence between solutions to the 3-SAT instance and solutions to the SAT' instance.

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Answer:

Rounded percent error = 38% So, Michael's percent error was 38%.

Step-by-step explanation:

Rounded percent error = 38% So, Michael's percent error was 38%.

The height of the football when it was kicked is 0.776 meter.

The maximum height of the ball is 29 meters, at a time of 2.4 seconds.

The height of the football after 2 seconds is 28.87 meter.

No, the ball was not in the air after 5 seconds.

In Mathematics and Geometry, the vertex form of a quadratic equation is modeled by this formula:

f(x) = a(x - h)² + k

Where:

The football was kicked when t = 0, so the height is given by;

h(0) = -4.9(0 - 2.4)² + 29

h(0) = 0.776 meter.

For the maximum height of the ball, we have:

Vertex (h, k) = (2.4, 29).

Maximum height, k = 29 meters.

After 2 seconds, the height of the ball is given by;

h(2) = -4.9(2 - 2.4)² + 29

h(2) = 28.87 meter.

After 5 seconds, the height of the ball is given by;

h(5) = -4.9(5 - 2.4)² + 29

h(5) = -4.124 meter.

In conclusion, the ball would not be in the air after 5 seconds because because it would land after 4.124 seconds.

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a. Models featuring a linear function are not appropriate for representing London's population data due to its steadily growing exponent over time, as opposed to a fixed rate.

b. Computing the parameters a, b, and c of the logistic growth equation necessitates employing an application, however the language of this model does not offer this capability.

The logistic growth equation P(t) = 1 / [1 + e^(-b(t-c))] has an S-shaped curve, indicative of a population commencing with a slow growth, then rapidly propagating towards its carrying capacity (represented by parameter a), before ultimately hitting an equilibrium near the maximum size.

Parameters a, b, and c in the equation respectively symbolize the highest sustainable populous, rate of growth, and peak point at which the increase is most pronounced. Variations of value among these three determine the graph of P; higher figures of a result in more spacious upper limit, larger values of b indicate a higher rise pace, whilst bigger results of c cause the inflection juncture to appear later.

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Answer:  Private ownership provides land or goods for all citizens to use. Private ownership can make it possible for a business to earn money. Private ownership might help a person move to another economic class. Private ownership allows a person to own goods that may increase in value.

Step-by-step explanation:

Answer:

Area of a triangle = 126.5 cm²

Step-by-step explanation:

Area of a triangle = (base * height) / 2

Area of a triangle = (23 in * 11 in) / 2

Area of a triangle = 253 in² / 2

Area of a triangle = 126.5 in²

Answer:

Step-by-step explanation:

The surface area of the hexagonal pyramid is 54√3 + 18√6 square units.

The base of the pyramid is a regular hexagon, so we can use the formula for the area of a regular hexagon:

Area of hexagon = (3√3/2)a^2, where a is the length of one side of the hexagon

Since the apothem of the hexagon is 3√2, we can use the relationship between the apothem and the side length:

apothem = (1/2)√3a

Solving for a,

a = 2√6

Substitute the value of a = 2√6 into the formula,

Area of hexagon = (3√3/2)(2√6)^2

= 54√3

Each face is a triangle with a base equal to one side of the hexagon and a height equal to the height of the pyramid, which is given as 3.

Using the formula for the area of a triangle,

Area of one face = (1/2)bh

= (1/2)(2√6)(3)

= 3√6

There are six identical faces, so the total area of the lateral faces is:

Total lateral area = 6(3√6)

= 18√6

Finally, we add the area of the base and the lateral faces to get the total surface area of the pyramid:

= 54√3 + 18√6

Therefore, the surface area of the hexagonal pyramid is 54√3 + 18√6 square units.

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The number of miles Celia drove than Rhonda is 4 miles. The correct option is C. 4 miles

From the question, we are to determine how much more Celia drove that Rhonda.

From the given information,

The total distance covered by Celia is

6 miles + 8 miles

= 14 miles

In the given diagram, we have right triangle

We can calculate the distance Rhonda covered using the Pythagorean theorem.

Let the distance Rhonda covered be R

Then,

R² = 6² + 8²

R² = 36 + 64

R² = 100

R = √100

R = 10 miles

Thus,

The distance Rhonda covered is 10 miles

Now,

The number of miles Celia drove more than Rhonda is

14 miles - 10 miles

= 4 miles

Hence, Celia drove 4 miles more than Rhonda

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The length of the hypotenuse is 10 inches.

What is a right triangle?

A given triangle is said to be a right triangle if the measure of only one of its internal angles is equal to 90^o. So that the sum of the internal angles of the triangle is 180^o.

Applying the Pythagorean theorem to the given right triangle, we have;

/Hyp/^2 = /Adj/^2 + /Opp/^2

             = 8^2 + 6^2

             = 64 + 36

             = 100

Hyp = (100)^1/2

      = 10

Therefore, the length of the hypotenuse of the right triangle is 10 inches.

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Answer:

y = 3x + 1

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick points (0,1) (1,4)

We see the y increase by 3 and the x increase by 1, so the slope is

m = 3

Y-intercept is located at (0,1)

So, the equation of the line is y = 3x + 1

The original statement simply makes a conditional assumption and does not specifically declare that all of the music play by a radio station was Elvis music.

The declaration "If a station of radio plays music, then that radio station are playing the Elvis song" has the contrapositive "If it's a radio station refuses to play a Elvis song, then this radio station is without playing music."

A conditional statement's contrapositive reverses the premise and conclusion and rejects both. The original assertion and the contrapositive are logically equal, thus if the former is true, the latter is likewise true, but vice versa.

In this instance, the contrapositive argument claims that a radio station can't be playing music if it isn't playing an Elvis song. This could be taken to mean that whenever the radio station plays music, it must be an Elvis song.

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In order to cut the standard error of the mean in half (to 12.5), you must select a sample size of 612.

To find the new sample size required to cut the standard error of the mean in half, you can use the following formula:

New Standard Error = (Old Standard Error) / √(New Sample Size / Old Sample Size)

We know the old standard error (25) and want to find the new standard error (12.5). So, we can rewrite the formula as:

12.5 = 25 / √(New Sample Size / 153)

First, divide both sides of the equation by 25:

0.5 = 1 / √(New Sample Size / 153)

Next, square both sides of the equation:

0.25 = 1 / (New Sample Size / 153)

Now, take the reciprocal of both sides:

4 = New Sample Size / 153

Finally, multiply both sides by 153 to find the new sample size:

New Sample Size = 4 * 153

New Sample Size = 612
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Answer:

Step-by-step explanation:

-.222 repeated

Answer:

The inequality 7x < 50 can be used to answer questions that involve finding the maximum value of x that satisfies the inequality. Specifically, we can solve this inequality to find the largest value of x such that 7x is less than 50.

For example, if x represents the number of hours you can work in a week and you are paid $7 per hour, then 7x represents your weekly earnings. If you want to earn less than $50 per week, the inequality 7x < 50 would be relevant. Solving this inequality would tell you the maximum number of hours you can work per week to earn less than $50.

Another example could be finding the maximum number of items you can purchase if each item costs $7 or less and you have $50 to spend. In this case, x would represent the number of items you can purchase, and 7x represents the total cost of the items. Solving the inequality 7x < 50 would give you the maximum number of items you can purchase while spending less than $50.

So, the question that can be answered by solving the inequality 7x < 50 depends on the context in which it is being used.

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Answer:  median of a: 40

                                 b: 54

Restaurant B is more likely to serve a grater number of meals it it has the grater median

[use median to compare two lets]

Step-by-step explanation:

Answer:

A: sum

Step-by-step explanation:

For adding or subtracting fractions, the denominators of the concerned fractions need to be equal.

The probability of the independent events are solved and P ( B ) = 0.7

Given data ,

Let the probability of the independent events be

P ( A ) = 0.04

P ( A ∩ B ) = 0.028

Now , If events A and B are independent, then we know that:

P(A ∩ B) = P(A) × P(B)

We are given that P(A) = 0.04 and P(A ∩ B) = 0.028

P(A ∩ B) = P(A) × P(B)

0.028 = 0.04 × P(B)

P(B) = 0.028 / 0.04

P(B) = 0.7

Hence , the probability of event B, P(B), is 0.7

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The polar coordinates of this same point is (-8, -2π).

The point (-10, 2π) can be plotted on a graph with polar coordinates by beginning at the origin (0,0) and moving -10 units along the θ axis and then 2π units along the r axis.

To find other polar coordinates (r, θ) of this same point for which r > 0 and -2π ≤ θ < 0, we can move the point along the θ axis and then along the r axis in the opposite direction. This will result in a new point (r, θ) where r > 0 and -2π ≤ θ < 0.

For example, we can move the point along the θ axis to (-10, -2π), and then move it along the r axis to (-8, -2π).

This would result in the new point (r = -8, θ = -2π), which satisfies the given conditions.

Therefore, the polar coordinates of this same point is (-8, -2π).

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The true statement regarding the diagram is this: m∠WXY = m∠YXZ.

In the diagram, we find that angles WXY and angle YXZ are supplementary. The meaning of this is that the two angles add up to give 180 degrees. First, we have the angle that is at 90 degrees while the second angle is also at 90 degrees.

When we add these two together, we arrive at 180 degrees. So, the two angles are supplementary and equal thus, we can arrive at the conclusion that m∠WXY = m∠YXZ.

Complete Question:

The image is a straight line with points W, X, Z, and an angle with axis Y, appended at 45°.

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Answer:

25%

Step-by-step explanation:

$112 × X =$84

X= 84/112

X=0.75

Converting to a percent is to multiply by 100

75%

$112-$84 = $28

25%

Answer: 25%

Step-by-step explanation:  $112 × X =$84                                   X= 84/112             X=0.75            Converting to a percent is to multiply by 100              75%            $112-$84 = $28                 25%

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The apple will be at the same height as the worker at 0.75 seconds and 1.25 seconds

Given that

So, the function is

h = -16t² + 32t +5

The worker's height is 20

So, we have

h = 20

This gives

-16t² + 32t +5 = 20

Evaluate the like terms

-16t² + 32t - 15 = 0

When solved on a graph, we have

t = 0.75 and 1.25

Hence, the times are 0.75 seconds and 1.25 seconds

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Therefore, there are 156 numbers consisting of 1, 2, or 3 digits that can be formed using the digits 1, 2, 3, 4, 5, 6 without repetitions.

We need to find the number of numbers consisting of 1, 2, or 3 digits that can be formed using the digits 1, 2, 3, 4, 5, 6 without repetitions.

1-digit numbers: There are 6 choices for the first digit.

2-digit numbers: There are 6 choices for the first digit, and 5 choices for the second digit (since we cannot repeat the first digit).

3-digit numbers: There are 6 choices for the first digit, 5 choices for the second digit (since we cannot repeat the first digit), and 4 choices for the third digit (since we cannot repeat the first or second digit).

Therefore, the total number of numbers that can be formed is:

1-digit numbers: 6

2-digit numbers: 6 x 5 = 30

3-digit numbers: 6 x 5 x 4 = 120

The total number of numbers is the sum of these:

6 + 30 + 120 = 156

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Angle ∠B = 35 degrees then Intercepted arc AC  is 70 degrees

∠B = 31 degrees then Intercepted arc AC  is 62 degrees

∠B = 28 degrees then Intercepted arc AC  is 56 degrees

∠B = 17 degrees then Intercepted arc AC  is 34 degrees

∠B = 42 degrees then Intercepted arc AC  is 84 degrees

Using the inscribed angle theorem, we have

∠B=1/2AC

When ∠B is 35 degrees

Intercepted arc AC = 2×35 =70 degrees

When ∠B is 31 degrees

Intercepted arc AC = 2×31 =62 degrees

When ∠B is 28 degrees

Intercepted arc AC = 2×28 =56 degrees

When ∠B is 17 degrees

Intercepted arc AC = 2×17 =34 degrees

When ∠B is 42 degrees

Intercepted arc AC = 2×42 =84 degrees

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The point estimate for the proportion of preschool children in Hillsborough County who are not vaccinated is 0.6 or 60%.

The point estimate for the true proportion of preschool children in Hillsborough County who are not vaccinated can be calculated by dividing the number of unvaccinated children in the sample by the total number of children in the sample

Point estimate = Number of unvaccinated children / Total number of children in sample

Since the sample size is 150 and the number of vaccinated children is 60, the number of unvaccinated children can be found by subtracting the number of vaccinated children from the total sample size

Number of unvaccinated children = Sample size - Number of vaccinated children

Number of unvaccinated children = 150 - 60 = 90

Therefore, the point estimate for the proportion of preschool children in Hillsborough County who are not vaccinated is

Point estimate = 90/150 = 0.6 or 60%

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The given question is incomplete, the complete question is:

A research team conducted a survey to check what proportion of preschool children in the hillsborough county who are not vaccinated. a random sample of 150 preschool children in hillsborough county revealed that only 60 had been vaccinated. what is the point estimate for the true proportion?

Answer:

1250 milligrams

Step-by-step explanation:

He adds an extra 15 grams, or 15000 milligrams, of sugar. The small spoon can scoop up 15000 milligrams in 12 spoonfuls. So it scoops up (15000/12) or 1250 milligrams per scoop.