If we assume that all possible poker hands (comprised of 5 cards from a standard 52 card deck) are equally likely, what is the probability of being dealt: a. a flush? (A hand is said to be a flush if all 5 cards are of the same suit. Note that this definition means that straight flushes (five cards of the same suit in numeric sequence) are also considered flushes.) b. one pair? (This occurs when the cards have numeric values a, a, b, c, d, where a, b, c, and d are all distinct.) c. two pairs? (This occurs when the cards have numeric values a, a, b, b, c, where a, b and c are all distinct.) d. three of a kind? (This occurs when the cards have numeric values a, a, a, b, c, where a, b and c are all distinct.) e. four of a kind? (This occurs when the cards have numeric values a, a, a, a, b.)

Answer:

C. a paper clip

Step-by-step explanation:

An apple generally weighs more than 3 grams, and can go even into oz.

Depending on the type of material the backpack is made of, and also how big it is, the mass can vary, however, it is safe to say the backpack will be more than 3 grams.

A cat definitely weighs more than 3 grams. Any born cat that weighs only 3 grams will not survive.

~

For this case we have the following options:

An apple, it is known that the apple will never weigh 3 grams.

A backpack will not have that weight either.

A cat would never weigh 3 grams or be newborn.

To have an object of 3 grams, the object must be very light.

A paperclip is very likely to weigh 3 grams because it is a very small and extremely light object.

Answer:

Option C

Answer:

Step-by-step explanation:

1. The problem statement tells you the function applies for year values (x) 2009 and later. The domain is real numbers greater than or equal to 2009.

__

2. We can use the distributive property to eliminate parentheses:

  3.2(x -2009) +206 = 3.2x -6428.8 +206

  = 3.2x -6222.8

__

3. Put 2025 in the equation and do the arithmetic

  g(2025) = 3.2·2025 -6222.8 = 257.2 . . . . mm

__

4. Put this value of level rise in the equation and solve for x.

  g(x) = 3.2x -6222.8

  500 = 3.2x -6222.8 . . put 500 mm where g(x) is in the equation

  6722.8 = 3.2x . . . . . . . add 6222.8

  x = 6722.8/3.2 = 2100.875

The water rise will be equal to about half a meter late in the year 2100.

Answer:

rate of the plane in still air is 33 miles per hour and the rate of the wind is 11 miles per hour

Step-by-step explanation:

We will make a table of the trip there and back using the formula distance = rate x time

                 d              =            r       x       t

there

back

The distance there and back is 264 miles, so we can split that in half and put each half under d:

               d            =         r        x        t

there    132

back     132

It tells us that the trip there is with the wind and the trip back is against the wind:

              d           =        r         x        t

there     132        =    (r + w)

back      132       =     (r - w)

Finally, the trip there took 3 hours and the trip back took 6:

             d         =        r        *        t

there    132     =    (r + w)     *       3

back     132     =    (r - w)      *       6

There's the table.  Using the distance formula we have 2 equations that result from that info:

132 = 3(r + w)        and        132 = 6(r - w)

We are looking to solve for both r and w.  We have 2 equations with 2 unknowns, so we will solve the first equation for r, sub that value for r into the second equation to solve for w:

132 = 3r + 3w and

132 - 3w = 3r so

44 - w = r.  Subbing that into the second equation:

132 = 6(44 - w) - 6w and

132 = 264 - 6w - 6w and

-132 = -12w so

w = 11

Subbing w in to solve for r:

132 = 3r + 3(11) and

132 = 3r + 33 so

99 = 3r and

r = 33

I guess the function is [tex]f(x)=9-x^{2/3}[/tex]. Then [tex]f(-27)=0[/tex] and [tex]f(27)=0[/tex].

The derivative is [tex]f'(x)=-\dfrac23 x^{-1/3}[/tex], but there is no [tex]c[/tex] such that

[tex]-\dfrac23c^{-1/3}=0[/tex]

This doesn't contradict Rolle's theorem because [tex]f'(0)[/tex] does not exists. In other words, [tex]f[/tex] is not differentiable on (-27, 27), so the conditions of Rolle's theorem are not met. (Looks like that would be the last option, or the second to last option if the last one is "Nothing can be concluded")

The function f(x) = 9 - x²/3 is even, and its derivative f'(c) equals to zero at c=0, which lies within the interval (-27, 27). Therefore, it does not contradict Rolle's theorem.

The function in question is f(x) = 9 - x²/3. When we substitute x with -27 and 27, we get f(-27) = 9 - ((-27)²/3) = -243 and f(27) = 9 - (27²/3) = -243. This confirms that the function is even as f(-27) = f(27).

To find the critical values, we'll take the derivative of the function, which gives us f'(x) = -2x/3. We set f '(c) = 0, solving for c, and determine c = 0. Rolle's Theorem states that if a function is continuous on a closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one c in the interval (a, b) such that f '(c) = 0. With f(-27) = f(27) and the derivative proving to be zero at c=0 (which is inside the interval (-27,27)) this does not contradict Rolle's theorem.

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Subtract the smaller angle from the larger angle and divide by 2.

66 -14 = 52

52/2 = 26

x = 26

Answer:

B.   -1.5x − 3.5y = -31.5

Step-by-step explanation:

You forgot to provide the reference image which is essential to answer the question, but I managed to find it... and attach it to my answer.

In the given equation for AB, if we place the y term on the left and x term on the right, we see the slope of that line is 7/3 (y = (7x - 21.5)/3 ==> 7/3x).

We see on the image that the line PQ is perpendicular to AB.  That means that its slope is -3/7.

If we quickly check the slopes of each of the possible answers...

A. -3x + 4y = 3 ----> 4y = 3x - 3 ==> y = (3x-3)/4 => slope = 3/4

Not what we're looking for.

B. -1.5x - 3.5y = -31.5 ==> 3.5y = -1.5x + 31 ===> y = (-1.5x +31)/3.5

that gives us a slope of -1.5/3.5... We can simplify it... -3(0.5)/7(0.5) = -3/7

Exactly as predicted.

Since we have the point P (7,6), we can enter it in the equation to verify:

-1.5x - 3.5y = -31.5

-1.5 (7) - 3.5 (6) = -10.5 - 21 = -31.5  --- Verified

C. 2x + y = 20 ==> y = 20 - 2x ===> slope is -2, not what we want.

D. -2.25x + y = -9.75 ==> y = 2.25x - 9.75 ==> slop is 2.25 cannot be it.

Answer: B. -1.5x − 3.5y = -31.5

Step-by-step explanation:

Answer:

x=14

Step-by-step explanation:

4(x - 8)³ - 18 = 846

4(x - 8)³ = 864

(x - 8)³ =216

∛(x - 8)³ =∛216

x-8 = 6

x= 6+8

x=14

Answer:

x=14

Step-by-step explanation:

look this solution :

Answer:

6.7 cm

Step-by-step explanation:

To make use of the Law of Sines for finding b, you need to know the missing angle B. Since the sum of the angles of a triangle is 180°, you can find angle B as ...

B = 180° -82° -55° = 43°

Now, you put the numbers you know into the formula given and solve for b.

sin(A)/a = sin(B)/b

sin(55°)/(8 cm) = sin(43°)/b

Cross multiplying gives ...

b·sin(55°) = (8 cm)·sin(43°)

and dividing by the coefficient of b gives you ...

b = (8 cm)·sin(43°)/sin(55°) ≈ 6.7 cm

Answer:

6.7 cm

Step-by-step explanation:

Try this option, the answer is marked with red colour.

Answer:

m=13 b=17

Step-by-step explanation:

Answer:

m=13 b=17

hope this helps

Answer:

4

Step-by-step explanation:

[tex] 16a+32b+16c= 4*(4a+8b+4c)[/tex]

Answer:

If 4a+8b+4c=1, then 16a+16c+32b = 4

Step-by-step explanation:

To answer the question, a rule of three can be raised:

4a + 8b + 4c --------------- 1

16a + 16c + 32b --------- X

X = (16a + 16c + 32b) ÷ (4a + 8b + 4c)

This is equivalent to the division of the two polynomials, 16a + 16c + 32b by 4a + 8b + 4c.

Before dividing we organize the first polynomial,

16a + 16c + 32b = 16a + 32b + 16c

Dividing the two polynimials, we have

16a + 32b + 16c   | 4a + 8b + 4c  

-16a - 32b - 16c            4

       = 0 =

The exact quotient is 4, since the residue is 0

Hope this hepls!

Answer:

it is $30.00

Step-by-step explanation:

Answer:

B. (1,7)

Step-by-step explanation:

Answer is B. (1,7)

If x = 1 then

y > 1 + 5

7 > 6

Answer:

(1 , 7) is a solution of y > IxI + 5 ⇒ answer B

Step-by-step explanation:

* Lets revise the absolute value

- IxI = positive value

- IxI can not give negative value

- The value of x could be positive or negative

* Lets solve the problem

∵ y > IxI + 5

∴ y > x + 5 OR y > -x + 5

- Lets check the answers

∵ y > 0 + 5 ⇒ y > 5

- But y = 5, and 5 it is not greater than 5 and there is no difference

 between the two cases because zero has no sign

∴ (0 , 5) not a solution

∵ y > 1 + 5 ⇒ y > 6

- Its true y = 7 and 7 is greater than 6

∵ y > -1 + 5 ⇒ y > 4

- Its true y = 7 and 7 is greater than 4

∴ (1 , 7) is a solution

∵ y > 7 + 5 ⇒ y > 12

- But y = 1 and 1 is not greater than 12

∵ y > -7 + 5 ⇒ y > -2

- Its true y = 1 and 1 is greater than -2

* we can not take this point as a solution because it is wrong

 with one of the two cases

∴ (7 , 1) is not a solution

Answer:

21.1 percent

Step-by-step explanation:

Total balls after -1 red ball=7+5+4+3=19

Prob of purple ball= purple ball/total balls

= 4/19

=0.2105...

percentage:21.1%

The probability of selecting a red ball and then a purple one without replacement from a box containing 8 red, 5 brown, 4 purple, and 3 green balls is approximately 8.4%.

In probability, there are two events of interest here: selecting a red ball and then selecting a purple ball. Since the total number of balls changes after picking the red ball, these are dependent events. The probability of the first event (selecting a red ball) is 8 out of 20 (total balls). Then, with a red ball removed and not replaced, the probability of the second event (selecting a purple ball) is 4 out of 19. To find the overall probability, we multiply the probabilities of these two events.

To convert the probability to a percentage, multiply the result by 100. By doing this, the probability rounds to approximately 8.4%.

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2 * 10^2

Divide the first numbers, which are 6 and 3, to get 2. Then, subtract the powers of the exponents, which are 5 and 3, to get 2.

the two numbers are 18 and 3

Number 2,3,5 are true

Answer:

  •  x = -4, x = 0, x = 1

Step-by-step explanation:

x is a factor of all terms, so x=0 is a zero. (Eliminates choices 1 and 5.)

The sum of coefficients is 0, so x=1 is a zero. (Eliminates choices 3 and 4.)

Reversing the sign of the odd-degree terms gives signs of -++, so there is one sign change, hence one negative real root (by Descartes' rule of signs). This confirms choice 2 as the answer.

___

Of course, your graphing calculator can answer this almost as quickly.

Answer:

  A  404 mi

Step-by-step explanation:

If we designate the points of the triangle A, B, and C for the locations of the western station, eastern station, and balloon, respectively, we have the following:

  ∠CAB = 90° - 41° = 49°

  ∠CBA = 90° + 21° = 111°

  ∠ACB = 41° -21° = 20°

side "c" (opposite ∠ACB) is 148 miles

The distance we're asked to find is AC = b, the longest side of the triangle. The law of sines tells us ...

  b/sin(B) = c/sin(C)

  b = c·sin(B)/sin(C) = (148 mi)·sin(111°)/sin(20°) ≈ 403.98 mi ≈ 404 mi

Using trigonometry and the law of sines, the distance from the balloon to the western station is approximately 373 miles.

This is a problem involving trigonometry, particularly the use of the law of sines. The two tracking stations and the balloon form a triangle. The angle at the western station is 41°, the angle at the eastern station is (180 - 21 - 41) = 118°, and the distance between the two stations (the side opposite to the 41° angle) is 148 miles. According to the Law of Sines, the ratio of each side of the triangle to the sine of its opposite angle is constant. Thus, we can set up the equation sin(41°) / x = sin(118°) / 148 miles, where x represents the distance from the balloon to the western station. Solving for x gives us approximately 373 miles.

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10/10 it simplifies to 1

Answer: 10/10

Step-by-step explanation:

10 divided by 10 is 1.

Answer:

The result is the well-known quadratic formula: x = (-b±√(b²-4ac))/(2a)

Step-by-step explanation:

Start with the standard form quadratic equation:

ax² +bx +c = 0

1. Divide by a

x² +(b/a)x +(c/a) = 0

2. Subtract the constant

x² +(b/a)x = -(c/a)

3. Complete the square

x² +(b/a)x + (b/(2a))² = (b/(2a))²-(c/a)

(x +b/(2a))² = (b²-4ac)/(2a)²

4. Take the square root

x +b/(2a) = ±√(b²-4ac)/(2a)

5. Subtract the constant on the left to get x by itself

x = (-b±√(b²-4ac))/(2a)

Final answer:

The quadratic formula, which provides the solution to the standard quadratic equation ax² + bx + c = 0, is derived through a series of algebraic manipulations, including dividing by a, completing the square, taking the square root, and solving for x.

Explanation:

Derivation of the Quadratic Formula

The objective is to derive the quadratic formula from the standard quadratic equation (ax² + bx + c = 0). Following the given steps:

B. 16 Inches The original length was 12 inches but since you are cutting across the cheese it will be longer. Since you are cutting across that means the width of the cheese will come into the equation as well.

Just add 12 and 4.

Check the picture below.

Answer: The answer is C

Step-by-step explanation: If you think about it the spinner only spun 3 times and when that happens them you sum up X

(C) When the spinner is spun three times, X is the sum of the numbers the spinner lands on.

Therefore, the correct option is (C) When the spinner is spun three times, X is the sum of the numbers the spinner lands on.

Know more about binomial distribution here:

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Answer:

[tex]t=2.47\ s[/tex]  

Step-by-step explanation:

The equation that models the height of the ball in feet as a function of time is

[tex]h(t) = h_0 + s_0t -16t ^ 2[/tex]

Where [tex]h_0[/tex] is the initial height, [tex]s_0[/tex] is the initial velocity and t is the time in seconds.

We know that the initial height is:

[tex]h_0 = 4.5\ ft[/tex]

The initial speed is:

[tex]s_0 = 110sin(20\°)\\\\s_0 = 37.62\ ft/s[/tex]

So the equation is:

[tex]h (t) = 4.5 + 37.62t -16t ^ 2[/tex]

The ball hits the ground when when [tex]h(t) = 0[/tex]

So

[tex]4.5 + 37.62t -16t ^ 2 = 0[/tex]

We use the quadratic formula to solve the equation for t

For a quadratic equation of the form

[tex]at^2 +bt + c[/tex]

The quadratic formula is:

[tex]t=\frac{-b\±\sqrt{b^2 -4ac}}{2a}[/tex]

In this case

[tex]a= -16\\\\b=37.62\\\\c=4.5[/tex]

Therefore

[tex]t=\frac{-37.62\±\sqrt{(37.62)^2 -4(-16)(4.5)}}{2(-16)}[/tex]

[tex]t_1=-0.114\ s\\\\t_2=2.47\ s[/tex]  

We take the positive solution.

Finally the ball takes 2.47 seconds to touch the ground

Answer:

KJL = 40 degrees

Step-by-step explanation:

KJL = 1/2*( arc KP - arc IP)

arc IPK=360-120=240

KP=2(IP)

Kp=2x, IP = x

3x=240, x=80

KP=160

IP=80

KJL=(160-80) / 2 = 40 degrees

Answer:

40°

Step-by-step explanation:

Answer:

  x = −3

Step-by-step explanation:

A zero of a function is a value that makes one of the factors be zero.

To make x+3 = 0, x = -3.

To make x-7 = 0, x = 7.

To make x+5 = 0, x = -5.

Of these values that make the factors zero, only x = -3 is on your choices list.

Answer:  The correct option is

(B) x = - 3.

Step-by-step explanation:  We are given to select the correct zero of the following polynomial function :

[tex]f(x)=(x+3)(x-7)(x+5)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

The zeroes of the function f(x) are given by

[tex]f(x)=0\\\\\Rightarrow (x+3)(x-7)(x+5)=0\\\\\Rightarrow x+3=0,~~x-7=0,~~x+5=0\\\\\Rightarrow x=-3,7,-5.[/tex]

Therefore, the zeroes of the given function are

x = -3, x = 7 and x = -5.

Thus, the correct option is

(B) x = -3.

Answer:

62 degrees

Step-by-step explanation:

degrees in a triangle: 180

this triangle is isosceles, so remaining 2 angles must be congruent

2x+56=180

2x=124

x=62

C. 4

First, rearrange the equation into slope intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. You get y = -5x + 4. This means the y-intercept is 4.

For this case we have a function of the form [tex]y = f (x)[/tex]

Where:

[tex]f (x) = 4-5x[/tex]

To find the y-intercept of the function we must do x = 0.

Then, replacing:

[tex]f (0) = 4-5 (0)\\f (0) = 4-0\\f (0) = 4[/tex]

So, the y-intercep of the function is 4

ANswer:

4

Option C

Answer:D pie

Step-by-step explanation:

You get 2pie/2 cancel out you get pie

The period of y=cos(2x) is π, so the frequency is 1/π.

The key features of the graph are:

Amplitude: The amplitude of the graph is 1, which means the function oscillates between −1and 1.

Period: The period of the graph is π, which means the function completes one cycle every πunits on the x -axis. This is because the frequency of the function is 2, which means it completes two cycles for every 2π units on the x -axis.

Midline: The midline of the graph is y=0. This is because the function is neither shifted up nor down.

Extrema: The graph has maxima at x=2kπ​ for any integer k, and minima at x=2(2k+1)π​for any integer k.

The graph of the function y=cos(2x). The frequency of a trigonometric function is the reciprocal of its period. The period of y=cos(2x) is π, so the frequency is 1/π.

Answer:

18) a. h(x) = -16x² + vx + h(0) ⇒ h(x) = -16x² + 128x + 144

b. The maximum height = 400 feet

c. Attached graph

19) The rocket will reach the maximum height after 4 seconds

20) The rocket hits the ground after 9 seconds

Step-by-step explanation:

* Lets study the rule of motion for an object with constant acceleration

# The distance S = ut ± 1/2 at², where u is the initial velocity, t is the time

  and a is the acceleration of gravity

# The vertical distances h in x second is h(x) - h(0), where h(0)

   is the initial height of the object above the ground

∵ h(x) = vx + 1/2 ax², where h is the vrtical distance, v is the initial

  velocity, a is the acceleration of gravity (32 feet/second²) and x

  is the time

18)a.

∵ The value of a = -32 ft/sec² ⇒ negative because the direction

   of the motion

  is upward

∴ h(x) - h(0) = vx - (1/2)(32)(x²) ⇒ (1/2)(32) = 16

∴ h(x) = vx - 16x² + h(0)

∴ h(x) = -16x² + vx + h(0) ⇒ proved

* Find the height of the object after x seconds from the ground

∵ h(0) = 144 and v = 128 ft/sec

∴ h(x) = -16x² + 128x + 144

b.

* At the maximum height h'(x) = 0

∵ h'(x) = -32x + 128

∴ -32x + 128 = 0 ⇒ subtract 128 from both sides

∴ -32x = -128 ⇒ ÷ -32

∴ x = 4 seconds

- The time for the maximum height = 4 seconds

- Substitute this value of x in the equation of h(x)

∴ The maximum height = -16(4)² + 128(4) + 144 = 400 feet

c. Attached graph

19)

- The object will reach the maximum height after 4 seconds

20)

- When the rocket hits the ground h(x) = 0

∵ h(x) = -16x² + 128x + 144

∴ 0 = -16x² + 128x + 144 ⇒ divide the two sides by -16

∴ x² - 8x - 9 = 0 ⇒ use the factorization to find the value of x

∵ x² - 8x - 9 = 0

∴ (x - 9)( x + 1) = 0

∴ x - 9 = 0 OR x + 1 = 0

∴ x = 9 OR x = -1

- We will rejected -1 because there is no -ve value for the time

* The time for the object to hit the ground is 9 seconds