What are the values of x and y?
A) x = 18√3; y = 9√3
B) x = 9; y = 9√3
C) x = 9√3; y = 9
D) x = 9√2; y = 9

The probability that all four cards are clubs is approximately 0.0026. Option A.

To understand why, let's break down the calculation. In a well-shuffled deck, there are 13 clubs out of 52 cards.

When dealing the first card, there are 13 clubs out of the total 52 cards, so the probability of getting a club on the first draw is 13/52.

For the second card, after the first club has been removed from the deck, there are now 12 clubs left out of the remaining 51 cards. Therefore, the probability of getting a club on the second draw is 12/51.

Similarly, for the third card, after two clubs have been removed, there are 11 clubs left out of the remaining 50 cards. The probability of drawing a club on the third draw is 11/50.

Finally, for the fourth card, after three clubs have been removed, there are 10 clubs left out of the remaining 49 cards. The probability of drawing a club on the fourth draw is 10/49.

To find the probability of all four cards being clubs, we multiply the probabilities of each individual draw:

(13/52) * (12/51) * (11/50) * (10/49) ≈ 0.0026.

This calculation takes into account the fact that the deck is being dealt without replacement, meaning that the number of available clubs decreases with each draw.

The third option, 1/4, is incorrect because it assumes that each card dealt is independent and has an equal probability of being a club. However, as cards are drawn without replacement, the probability changes with each draw. So Option A is correct.

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Note the complete question is

A 52-card deck contains 13 cards from each of the four suits: clubs ♣, diamonds ♦, hearts ♥, and spades ♠. You deal four cards without replacement from a well-shuffled deck so that you are equally likely to deal any four cards.

What is the probability that all four cards are clubs?

A.) 13/52 ⋅ 12/51 ⋅ 11/50 ⋅ 10/49 ≈0.0026

B.) 13/52 ⋅ 12/52 ⋅ 11/52 ⋅ 10/52 ≈0.0023

C.) 1/4 because 1/4 of the cards are clubs

(a) The average cost in 2011 is  $2247.64.

(b) A graph of the function g for the period 2006 to 2015 is: C. graph C.

(c) Assuming that the graph remains accurate, its shape suggest that: A. the average cost increases at a slower rate as time goes on.

Based on the information provided, we can logically deduce that the average annual cost (in dollars) for health insurance in this country can be approximately represented by the following function:

g(x) = -1736.7 + 1661.6Inx

where:

x = 6 corresponds to the year 2006.

For the year 2011, the average cost (in dollars) is given by;

x = (2011 - 2006) + 6

x = 5 + 6

x = 11 years.

Next, we would substitute 11 for x in the function:

g(11) = -1736.7 + 1661.6In(11)

g(11) = $2247.64

Part b.

In order to plot the graph of this function, we would make use of an online graphing tool. Additionally, the years would be plotted on the x-axis while the average annual cost would be plotted on the x-axis of the cartesian coordinate as shown below.

Part c.

Assuming the graph remains accurate, the shape of the graph suggest that the average cost of health insurance increases at a slower rate as time goes on.

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Answer:

Yes, a sinusoidal function is a great way to model temperatures over a 24-hour period because the pattern of temperature changes tends to be cyclic.

A sinusoidal function can be written in the general form:

D(t) = A sin(B(t - C)) + D

where:

- A is the amplitude (half the range of the temperature changes)

- B is the frequency of the cycle (which would be `2π/24` in this case because the temperature completes a full cycle every 24 hours)

- C is the horizontal shift (which is determined by the fact that the minimum temperature occurs at 6 AM)

- D is the vertical shift (which is the average of the maximum and minimum temperature)

Given the information you've provided, let's fill in the specifics:

- The high temperature for the day is 95 degrees.

- The low temperature is 75 degrees at 6 AM.

The amplitude, A, is half the range of temperature changes. It's the difference between the high and the low temperature divided by 2:

A = (95 - 75) / 2 = 10

The frequency, B, is `2π/24` because the temperature completes a full cycle every 24 hours.

The horizontal shift, C, is determined by the fact that the minimum temperature occurs at 6 AM. The sine function hits its minimum halfway through its period, so we want to shift the function to the right by 6 hours to make this happen. In our case, this means C = 6.

The vertical shift, D, is the average of the maximum and minimum temperature:

D = (95 + 75) / 2 = 85

So the equation for the temperature, D, in terms of t (the number of hours since midnight) is:

D(t) = 10 sin((2π/24) * (t - 6)) + 85

This equation represents a sinusoidal function that models the temperature over a day given the information provided.

The lengths of the other two sides of the right triangle are 36 and 85, respectively.

To find the lengths of the other two sides of a right triangle when one leg has a length of 11, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's denote the lengths of the other leg and the hypotenuse as x and y, respectively.

According to the Pythagorean theorem, we have:

x² + 11² = y²

To find the values of x and y, we need to find a pair of whole numbers that satisfy this equation.

We can start by checking for perfect squares that differ by 121 (11^2). One such pair is 36 and 85.

If we substitute x = 36 and y = 85 into the equation, we have:

36² + 11² = 85²

1296 + 121 = 7225

This equation is true, so the lengths of the other two sides are:

The other leg = 36

The hypotenuse = 85

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To find the local and absolute maximum and minimum points of the function f(x) = (3/5)x^5 - 9x^3 + 2 on the closed interval [-4,5], we need to follow these steps:

a) Find all critical numbers (x-coordinates only):

To find the critical numbers, we need to identify where the derivative of the function is zero or undefined. Let's find the derivative of f(x) first:

f'(x) = 3x^4 - 27x^2

Now, set the derivative equal to zero and solve for x:

3x^4 - 27x^2 = 0

Factoring out a common factor of 3x^2, we get:

3x^2(x^2 - 9) = 0

This equation is satisfied when either 3x^2 = 0 or x^2 - 9 = 0.

For 3x^2 = 0, we have x = 0.

For x^2 - 9 = 0, we have x = -3 and x = 3.

Therefore, the critical numbers (x-coordinates) are 0, -3, and 3.

b) Find the intervals on which the graph is increasing (mark critical numbers):

To determine the intervals of increasing, we need to analyze the sign of the derivative on each side of the critical numbers. We create a sign chart for f'(x):

Interval (-∞, -3): Choose a test point x < -3, e.g., x = -4

f'(-4) = 3(-4)^4 - 27(-4)^2 = 768 > 0

The derivative is positive, indicating the graph is increasing.

Interval (-3, 0): Choose a test point x between -3 and 0, e.g., x = -1

f'(-1) = 3(-1)^4 - 27(-1)^2 = -24 < 0

The derivative is negative, indicating the graph is decreasing.

Interval (0, 3): Choose a test point x between 0 and 3, e.g., x = 1

f'(1) = 3(1)^4 - 27(1)^2 = -24 < 0

The derivative is negative, indicating the graph is decreasing.

Interval (3, ∞): Choose a test point x > 3, e.g., x = 4

f'(4) = 3(4)^4 - 27(4)^2 = 768 > 0

The derivative is positive, indicating the graph is increasing.

Therefore, the graph is increasing on the intervals (-∞, -3) and (3, ∞).

c) Find the intervals on which the graph is decreasing (mark critical numbers):

From the analysis above, we can see that the graph is decreasing on the intervals (-3, 0) and (0, 3).

d) Find all local maximum points:

To find the local maximum points, we need to examine the points where the graph changes from increasing to decreasing. By observing the sign changes in the derivative, we can identify potential local maximum points.

From our analysis in part b, we can see that the graph changes from increasing to decreasing at x = -3 and x = 0. Therefore, these are the local maximum points.

e) Find all local minimum points:

To find the local minimum points, we need to examine the points where the graph changes from decreasing to increasing. By observing the sign changes in the derivative, we can identify potential local minimum points.

From our analysis in part c, we can see that the graph changes.

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Answer:

It's A

Step-by-step explanation:

Use the following models to show the equivalence of the fractions 35 and 610 a) Set model

Use the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set model

Answer:

(a) The graph is entirely above the x-axis and rises from left to right, more steeply than the graph of y = 5^x.

(b) The second coordinate of the point with first coordinate 0 is 2.

The second coordinate of the point with first coordinate 1 is 10.

Answer:

[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[

Step-by-step explanation:

[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[

Answer:

[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[

Step-by-step explanation:

what this is?

The group of individuals fitting a description is called option D: Population, this is because, in statistics, a population is seen as am entire group of individuals, items, or elements that tends to have or share a common characteristics.

The term "population" describes the complete group of people or things that you are interested in investigating. It is the group of individuals or thing(s) about which you are attempting to draw conclusions.

There are infinite and finite populations. A population with a set quantity of people or things is said to be finite. An endless population is one that has an infinite amount of people or things.

Therefore, the correct option is D

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See full text below

A group of individuals fitting a description is the _____

Which of the term below fit the description above.

A.census

B.sample

C.parameter

D.population

The surface area of the cone is: 213.66 cm²

The volume of a cone is: 7.33 cm³

The formula for the surface area of a cone is:

T.S.A = πrl + πr²

where:

r is radius

l is slant length

From the diagram and using Pythagoras theorem,we have:

l = √(7² + 5²)

l = √74

Thus:

TSA =  (π * 5 * √74) + (π * 5²)

TSA = 213.66 cm²

Formula for the volume of a cone is:

V = ¹/₃πr²

V = ¹/₃π * 7

V = 7.33 cm³

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The cosine function repeats its pattern every 2π radians (or 360 degrees), we can say that the period of y = cos(x) is 2π.

The period of the function y = cos(x) is 2π.

To understand the period of the cosine function, we need to examine its graph. The cosine function is a periodic function that oscillates between -1 and 1 as x varies. It repeats its pattern over regular intervals.

The cosine function completes one full cycle from 0 to 2π radians (or 0 to 360 degrees). This means that within this interval, the cosine function goes through one complete oscillation, starting from its maximum value of 1, then going through its minimum value of -1, and returning back to 1.

Since the cosine function repeats its pattern every 2π radians (or 360 degrees), we can say that the period of y = cos(x) is 2π.

This means that for any value of x, the value of cos(x) will repeat after an interval of 2π.

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Answer:

p =1 0

Step-by-step explanation:

x³(x - y)⁹ - y³(x - y)⁹ = (x - y)⁹[x³ - y³]

= (x - y)⁹(x - y)(x² + y² + xy)

= (x - y)¹⁰(x² + y² + xy)

where p = 10 and q = 1

Answer:

p = 10

Step-by-step explanation:

Given expression:

[tex]x^3(x-y)^9 - y^3(x-y)^9[/tex]

Factor out the common term (x - y)⁹:

[tex](x-y)^9(x^3- y^3)[/tex]

[tex]\boxed{\begin{minipage}{5cm}\underline{Difference of two cubes}\\\\$x^3-y^3=(x-y)(x^2+y^2+xy)$\\\end{minipage}}[/tex]

Rewrite the second parentheses as the difference of two cubes.

[tex](x-y)^9(x-y)(x^2+y^2+xy)[/tex]

[tex]\textsf{Apply\:the\:exponent\:rule:} \quad a^b\cdot \:a^c=a^{b+c}[/tex]

[tex](x-y)^{9+1}(x^2+y^2+xy)[/tex]

[tex](x-y)^{10}(x^2+y^2+xy)[/tex]

Comparing the rewritten original expression with the given expression:

[tex](x-y)^{10}(x^2+y^2+xy)=(x-y)^p(x^2+y^2+qxy)[/tex]

We can see that [tex](x-y)^p[/tex] corresponds to [tex](x-y)^{10}[/tex] in the given expression.

Therefore, we can conclude that p = 10.

Answer:

Step-by-step explanation:

pic is not clear

The length of side BC is approximately 3.725 cm.

In triangle ABC, we are given that angle BAC is 40 degrees, angle ABC is 20 degrees, and side AB measures 7 cm. We need to find the length of side BC.

To solve this problem, we can use the law of sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides.

Applying the law of sines, we have:

sin(ABC) / BC = sin(BAC) / AB

Since sin(ABC) = sin(20 degrees) and sin(BAC) = sin(40 degrees), we can substitute these values into the equation:

sin(20 degrees) / BC = sin(40 degrees) / 7 cm

Now, we can rearrange the equation to solve for BC:

BC = (7 cm * sin(20 degrees)) / sin(40 degrees)

Using a calculator to evaluate the trigonometric functions, we find that sin(20 degrees) ≈ 0.3420 and sin(40 degrees) ≈ 0.6428. Substituting these values into the equation:

BC ≈ (7 cm * 0.3420) / 0.6428

BC ≈ 3.725 cm

Therefore, the length of side BC is approximately 3.725 cm.

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Reason:

If CD was parallel to AB, then triangles CDE and ABE would be similar. In turn it would mean that EA/EC = EB/ED is a true proportion.

Let's calculate each side separately.

Both decimal values are approximate.

The two values don't match up which makes EA/EC = EB/ED to be false.

Since EA/EC = EB/ED is false, we know that triangles CDE and ABE are not similar. Therefore, CD is not parallel to AB.

Answer:

CD is not parallel to AB

Step-by-step explanation:

According to the Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

Therefore, if CD is parallel to AB, then EA : AC = EB : BD.

Substitute the values of the line segments into the equation:

[tex]\begin{aligned}EA : AC &= EB : BD\\\\28:20&=16:10\\\\\dfrac{28}{20}&=\dfrac{16}{10}\\\\1.4 &\neq 1.6\end{aligned}[/tex]

As 1.4 does not equal 1.6, then CD is not parallel to AB.

Answer:

measure of arc JL = 55°

measure of angle PKJ = 27.5°

Answer:

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

Area is the product of two dimensions hence the ratio of areas of similar figures is the square of the scale factor.

Let the area of the enlarged shape be A, and the scale factor be k = 6.

Then we have the area of the larger shape:

The limit of f(x) as x approaches 10 is 315 and The value of k is 250.

The function f(x) is a piecewise function, so we need to evaluate it separately for x < 10 and x >= 10.

[tex]f(x)= { \frac{(0.1x(2)+20x+15,x < 10)}{(0.25x(3)+k,x > 10)}[/tex]

For x < 10, the function is equal to 0.1x^2 + 20x + 15. So the left-hand limit of f(x) as x approaches 10 is equal to 0.1(10)^2 + 20(10) + 15 = 315.

For x >= 10, the function is equal to 0.25x^3 + k. So the right-hand limit of f(x) as x approaches 10 is equal to 0.25(10)^3 + k = 250 + k.

Since the left-hand limit and the right-hand limit are equal, the limit of f(x) as x approaches 10 is also equal to 315, and the value of k is equal to 250.

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Answer:

The sixth angle is 115°.

Step-by-step explanation:

Number of sides in a hexagon = n =6

Sum of interior angles = (n−2)180°

= (6−2)180 ∘

= 720

∴ Let the six angle of hexagon be x.

⇒ x + 123 + 124 + 118 + 130 + 110 = 720°

⇒ x + 605 = 720°

⇒ x = 720 - 605

⇒ x = 115

Answer:

D. 48

Step-by-step explanation:

When a tangent and a secant, two secants, or two tangents intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

56 = 1/2(160 - ?)

112 = 160 - ?

? = 160 - 112 = 48

Answer:

To evaluate -15 + 7 - (-8), we can simplify the expression by first removing the double negative.

-15 + 7 + 8 = 0

Therefore, the answer is 0.

Step-by-step explanation:

The answer is:

Work/explanation:

Remember the integer rule,

[tex]\bullet\phantom{4444}\sf{a-(-b)=a+b}[/tex]

Similarly

[tex]\sf{-15+7-(-8)}[/tex]

[tex]\sf{-15+15}[/tex]

Simplify fully.

[tex]\sf{0}[/tex]

Answer:

8cm

Step-by-step explanation:

perimiter A = 11+11+4+4=30

perimiter B = 4+4+8+8=24

24+30=54

perimeter c =4+8+8+4+11+7+4=46

so perimiter of c is 8cm shorter than A and B total

hope this helps

The property that is illustrated by the statements is Transitive. Option C

Using the principle of transitivity, if two objects are equal to a third, they are also equal to one another.

From the information given, we have that;

< ABC = <DEF

< DEF = < XYZ

This simply proves that < ABC and < XYZ are both equivalent to < DEF in this situation.

By using the transitive property, we can determine that A ABC and A XYZ are also equal. This attribute enables us to construct relationships between many elements based on their equality to a shared third element and to connect logically equalities.

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Sure! Here’s the solution:

F(x)=k9−kx2​​

First, let’s square both sides to get rid of the square root:

F(x)2=k9−kx2​

Now, let’s multiply both sides by k to isolate the term with x^2:

kF(x)2=9−kx2

Next, let’s move all terms to one side of the equation:

kF(x)2+kx2=9

Finally, let’s factor out x^2:

x2(k+kF(x)2)=9

And solve for x^2:

x2=k+kF(x)29​

Answer:

Step-by-step explanation:

To show the work for evaluating the function f(x) = √(9 - kx^2) / k, we can follow these steps:

9 - kx^2

(9 - kx^2) / k

√((9 - kx^2) / k)

Answer:

x = 4

Step-by-step explanation:

By property, if two tangents are drawn from an external point , then they are equal

⇒ 2x + 3 = 11

⇒ 2x = 11 - 3

⇒ 2x = 8

⇒ x = 8/2

⇒ x = 4

Answer:

x = 4

Step-by-step explanation:

To find the value of x, we can use the Two-Tangent Theorem.

The Two-Tangent Theorem states that if two tangent segments are drawn to a circle from the same external point, the lengths of the two tangent segments are equal.

Therefore:

[tex]\begin{aligned}AD &= AB\\\\2x+3&=11\\\\2x+3-3&=11-3\\\\2x&=8\\\\\dfrac{2x}{2}&=\dfrac{8}{2}\\\\x&=4\end{aligned}[/tex]

Therefore, the value of x is 4.

Answer:

m∠BEC + m∠CED = m∠BED; Angle Addition Postulate

Step-by-step explanation:

You need to show that <BED is made up of angles BEC and CED by the Angle Addition Postulate.

m∠BEC + m∠CED = m∠BED; Angle Addition Postulate