A standard deck of playing cards contains 52 cards, equally divided among four suits (hearts, diamonds, clubs, and spades). Each suit has the cards 2 through 10, as well as a jack, a queen, a king, and an ace. If the 3 of spades is drawn from a standard deck and is not replaced, what is the probability that the next card drawn is a spade OR a king?

A. 1/17

B. 16/51

C. 4/17

D. 5/17

comparing with:

Then a = 1 and b=3

To find the y-intercept, substitute x=0

The y-intercept is 1

Comparing with

The value of a =-1 and the value of b is 3

To find the y-intercept, substitute x=0 into the equation

y=-1

The y-intercept is -1

Step-by-step explanation:

4² = 16

5² = 25

16+25 = 41

41 is the answer.

Hope it helps! :)

Answer:

\(( {4}^{2} + {5}^{2} ) \\ (16 + 25) \\ = 41\)

The probability that no two of them celebrate their birthday in the same month is very low.

There are 12 months in a year, so the probability that the first person has a birthday in a particular month is 1/12. The probability that the second person does not have a birthday in the same month is 11/12, since there are 11 months left that the second person's birthday can fall in. The probability that the third person does not have a birthday in any of the two previously chosen months is 10/12, and so on.

Therefore, the probability that none of the 12 people have a birthday in the same month is:

P = (1/12) x (11/12) x (10/12) x ... x (2/12) x (1/12)

which is approximately 0.00010578, or about 0.01%.

So the probability that no two of them celebrate their birthday in the same month is very low.

To learn more about probability please click on below link        

https://brainly.com/question/16484393

#SPJ4

Answer:

Step-by-step explanation: well the  anwser is 48

Using Stokes' Theorem and the given vector, we have approximated the line integral ∫C(ydx+zdy+xdz) to be equal to the area of the region R, which is 2.

To approximate the line integral ∫C(ydx+zdy+xdz) using a computer algebraic system (CAS) and Stokes' Theorem, we first need to find the intersection of the plane x+y=2 and the curve C.

1. Find the parametric equations for the curve C:
  Let x = t, then y = 2 - t, and z = 0.
  So, the parametric equations for C are:
  x = t, y = 2 - t, and z = 0.

2. Calculate the cross product of the tangent vector and the given vector:
  The tangent vector to the curve C is given by dr = (dx, dy, dz) = (1, -1, 0).
  The given vector is V = (y, z, x) = (2 - t, 0, t).

  Taking the cross product of dr and V, we get:
  dr x V = (dy * dz - dz * dy, dz * dx - dx * dz, dx * dy - dy * dx)
         = (0 - 0, 0 - 0, 1 - (-1))
         = (0, 0, 2).

3. Evaluate the line integral using Stokes' Theorem:
  The surface S enclosed by the curve C is the projection of the region R in the xy-plane bounded by the curve C.

  Applying Stokes' Theorem, we have:
  ∫C(ydx+zdy+xdz) = ∬S(curl(F) · dS),

  where curl(F) = (curl(F1), curl(F2), curl(F3)) and dS is the surface area vector.

4. Determine the curl of F:
  Since F = (y, z, x), we have:
  curl(F) = (0, 0, 1).

5. Calculate the surface area vector dS:
  The surface area vector dS is given by dS = (dSx, dSy, dSz).

  Since the surface S is in the xy-plane, dSx = 0, dSy = 0, and dSz = 1.

  Therefore, dS = (0, 0, 1).

6. Evaluate the surface integral:
  ∫C(ydx+zdy+xdz) = ∬S(curl(F) · dS)
                   = ∬S(0 * 0 + 0 * 0 + 1 * 1) dS
                   = ∬S dS.

  Since the surface S is a region in the xy-plane, the double integral of dS over S is simply the area of S.

7. Find the area of the region R:
  The region R is the projection of the plane x+y=2 onto the xy-plane.

  To find the area of R, we can solve the equation x+y=2 for y:
  y = 2 - x.

  The region R is bounded by the lines x = 0, x = 2, and the curve C.

  Integrate the expression 2 - x with respect to x over the interval [0, 2] to find the area A:
  A = ∫[0, 2] (2 - x) dx.

  Solving this integral, we get:
  A = [2x - (x^2)/2] evaluated from 0 to 2
    = [4 - 2] - [0 - 0]
    = 2.


Using Stokes' Theorem and the given vector, we have approximated the line integral ∫C(ydx+zdy+xdz) to be equal to the area of the region R, which is 2.

To know more about Stokes' Theorem visit:

https://brainly.com/question/33850552

#SPJ11

We get the perimeter of the circle as 87.92 m and area of the circle as 615.44 m².

We are given the radius of the circle as:

Radius = r = 14 m

We are also given the value of π as:

π = 3.14

We need to find the perimeter and area of the circle.

Perimeter of the circle is given by:

Perimeter = 2 π r

Substituting the values in the formula, we get that:

P = 2 × (3.14) × (14) m

P = 87.92 m.

Area of the circle is given by:

Area = π r²

Substituting the values in the formula, we get that:

Area = (3.14) × (14)²

A = 615.44 m²

Therefore, we get the perimeter of the circle as 87.92 m and area of the circle as 615.44 m².

Learn more about perimeter and area here:

https://brainly.com/question/24571594

#SPJ9

Answer:

21

Step-by-step explanation:

1+6=7

7+4=11

11+11=21

Answer:

m=7

Step-by-step explanation:

it's in the picture

the left got cut out but there's a bracket at the end of the first line

The distance between the planes after 20 minutes = 15496.8

What is Distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

1st planes = 570mph at a bearing of s 62e plane

2nd planes = 525 mph at a bearing of n 18e plane

Coverting 20 minutes into hour = 0.3333 hours

speed of 1st plane = 570mph

Distance travelled by plane after 0.3333 hours= 570*0.3333 hours

= 189.981

speed of 2st plane = 525mph

Distance travelled by plane after 0.3333 hours= 525*0.3333 hours

= 174.982

Angle made by both plane between their is 62 + 18 = 80° ≅ 90°

Distance between both the planes

= \(\sqrt{(189.981)^{2} + (174.982)^{2} }\)

= \(\sqrt{36092.78 + 30618.700}\)

= \(\sqrt{66711.48}\)

= 258.28 hours

Converting hours into minutes

=15496.8

The distance between the planes after 20 minutes = 15496.8

To learn more about Distance visit:

brainly.com/question/15172156

#SPJ4

i have now attached the picture but it can be wrong!

Triangle ABC is indeed similar to Triangle CDE by the SAS (Side-Angle-Side) Congruence Postulate.

Assume that we have the following to prove congruence:

AB/DC = AC/CE (proportional sides)

AB || CD (parallel lines)

This means that angle ABC is congruent to angle CDE.

Looking at this, we can infer that Side AB is proportional to side DC. We also see that Angle ABC is the same as Angle CDE.

Going by the SAS Congruence theorem, Triangle ABC is indeed similar to Triangle CDE because two sides of the triangle are similar and one angle is congruent.

Find out more on congruence at https://brainly.com/question/18922904

#SPJ1

The points are (7, 13/3).

Lets simplify the equation,

The equation of first line: y = 1/3 x + 2

the equation of second line: y= 4/3x - 5

Solve the system of equations by elimination,

Multiply equation A by -4 both sides

-4y = -4(1/3x +2)

-4y = -4/3x-8

After eliminating the equation we get,

y = 13/3

So now have to find x

13/3 = 1/3x + 2

Lets multiply above by 3
x = 13-6

x = 7.

Hence the points are (7, 13/3)

Learn more about Quadratic Equation on:

brainly.com/question/1214333

#SPJ4

Answer:

B

Step-by-step explanation:

What is the solution to the system of equations?

(7, 4)

(7, StartFraction 13 over 3 EndFraction)

(8, StartFraction 14 over 3 EndFraction)

(9, 7)

SSS postulate of congruence, to prove ∠ L N M ≅ ∠ L N P.

What do you mean by congruent?

In triangles MLN and PLN,

MN ≅ PN,

LM ≅ LP

To prove :

Δ MLN ≅ Δ PLN

  Statement                                              Reason

1. LN ≅ LN                                           1. Common segment

2. MN ≅ PN;                                        2. Given

LM ≅ LP

3. Δ MLN ≅ Δ PLN                              3. SSS  postulate of congruence,

Learn more about congruence

brainly.com/question/12413243

#SPJ4

Answer:

14.4 Fahrenheit

Step-by-step explanation:

1.6 times 9= 14.4 Fahrenheit

Answer: K’ (0, -1), L’ (-2, 3), M’ (-5, -1)

Step-by-step explanation:

In order to get the coordinates that are reflected across the y-axis, you need to make all x coordinates negative (-x, y)

(0, -1) — (0, -1)

(2, 3) — (-2, 3)

(5, -1) — (-5, -1)

(a) p(2), that is, P(X = 2)The cdf is given by: F(x) = 0 x < 00.06 0 ≤ x < 10.16 1 ≤ x < 20.33 2 ≤ x < 30.69 3 ≤ x < 40.92 4 ≤ x < 50.99 5 ≤ x < 61 6 ≤ x

The probability mass function p(x) can be derived from the cdf by taking differences:

p(x) = F(x) − F(x-1)Thus the probability mass function p(x) is as follows: p(x) = 0.06  x = 10.1  x = 20.17 x = 30.36  x = 40.23 x = 50.07 x = 60.01 x = 6The probability P(X = 2) can be found as follows: P(X = 2) = p(2) = 0.17(b) P(X > 3)The probability can be found as follows: P(X > 3) = P(4 ≤ X) = 1 - P(X < 4) = 1 - F(3) = 1 - 0.33 = 0.67(c) P(2 ≤ X ≤ 5)The probability can be found as follows: P(2 ≤ X ≤ 5) = F(5) - F(1) = 0.99 - 0.1 = 0.89(d) P(2 < X < 5)

The probability can be found as follows: P(2 < X < 5) = F(4) - F(2) = 0.92 - 0.17 = 0.75.

To learn more about this visit -m A branch of a certain bank has six ATMs : https://brainly.com/question/31026593

#SPJ11

Vertical angles : 8 and 10

Linear pair : 9 and 10

Adjacent angles : 7 and 10

Answer:

Step-by-step explanation:

LCM×HCF= Product

LCM×3=180

LCM=180/3=60

The probability that x is between 40 and 50 will be 0.5.

From the information, the continuous random variable x is uniformly distributed on the interval [35, 45].

The probability that x is between 40 and 50 will be:

(45 - 40)/(45 - 35)

= 5/10

= 0.5

Learn more about probability on:

brainly.com/question/24756209

#SPJ4

Answer:

C)

Step-by-step explanation:

The correct answer is C: Tony did not use the property correctly because he did not multiply every term on both sides of the equals sign by 1/4.

To solve the equation 4x = 12x + 20, Tony used the multiplicative property of equality but made an error in the application. The correct approach would be to multiply every term on both sides of the equals sign by the reciprocal of the coefficient of x, which is 1/4 in this case.

However, Tony only multiplied one term on each side by 1/4, resulting in equation x = 3x + 20. This action is incorrect because it does not apply the property to every term containing x. To solve the equation correctly, Tony should have multiplied both sides by 1/4, resulting in x/4 = (3x + 20)/4.

With regards to the probabilities of getting each color in the game played by Larry and Jessica, the correct answer is B. No, the probabilities are NOT equally likely.

In the game being played by Larry and Jessica, the colors that can be picked by either person include:

The probability of picking blue is:

= Number of blue sections / Total sections

= 3 / 8

The probability of picking red is :

= 3 / 8

The probability of picking green is:

= 2 / 8

= 1 / 4

The probabilities are therefore not equally likely.

Find out more on probabilities at https://brainly.com/question/28109373

#SPJ1

Using the conversion factors, we find that 3 cubic miles is approximately equal to 1.2504543 × 10^10 cubic meters. 5 cubic feet per second is equal to 2244.156 gallons per minute. 9.50 centimeters is equal to 9.50 * 10^7 nanometers per second squared.

1.1. One mile is equal to 1609.34 meters. Since we're dealing with cubic units, we cube the conversion factor.

1 mile = 1609.34 meters

1 mile³ = (1609.34 meters)³ = 4.168181 × 10^9 cubic meters

Therefore, 3 cubic miles is equal to 3 * 4.168181 × 10^9 cubic meters, which is approximately 1.2504543 × 10^10 cubic meters.

1.2. To convert from cubic feet per second (ft³/s) to gallons per minute (gal/min), we use the appropriate conversion factors.

Here are the conversion factors:

1 cubic foot = 7.48052 gallons

1 minute = 60 seconds

So, we set up the conversion as follows:

5 ft³/s * 7.48052 gal/ft³ * 60 s/min = 2244.156 gal/min

Therefore, 5 cubic feet per second is equal to 2244.156 gallons per minute.

1.3. To convert centimeters (cm) to nanometers per second squared (nm/sec²), we use the appropriate conversion factors. Here are the conversion factors:

1 centimeter = 10^7 nanometers

1 second = 1 second

So, we set up the conversion as follows:

9.50 cm * (10^7 nm/cm) / (1 sec)² = 9.50 * 10^7 nm/sec²

Therefore, 9.50 centimeters is equal to 9.50 * 10^7 nanometers per second squared.

To know more about conversion factors, refer to the link :

https://brainly.com/question/30567263#

#SPJ11

Answer:

Although this (attached) would be the correct answer always; A would be the most logical one since only one piece is shaded the opposite color.

:)

Answer:

1/8 and 2/16

Step-by-step explanation:

The summation for the given information is 860.

Given set of data is: \(\( 4,5,5,6,7,8 \)\)

Perform the summation using the given set of data:

\(\[ \sum\left(4 x^{2}-5\right) \]\)

Let's replace each value of x in the set of data into the given equation.

\(\[ \begin{aligned}4 x^{2}-5 &=4 \cdot 4^{2}-5 \\&=61 \\4 x^{2}-5 &=4 \cdot 5^{2}-5 \\&=75 \\4 x^{2}-5 &=4 \cdot 5^{2}-5 \\&=75 \\4 x^{2}-5 &=4 \cdot 6^{2}-5 \\&=139 \\4 x^{2}-5 &=4 \cdot 7^{2}-5 \\&=195 \\4 x^{2}-5 &=4 \cdot 8^{2}-5 \\&=315\end{aligned}\]\)

Sum of these values would be:

\(\sum\left(4 x^{2}-5\right) = 61+75+75+139+195+315\)

= 860

Hence, the answer is 860.

To know more about summation visit

https://brainly.com/question/9879549

#SPJ11

The given summation is:

$$\sum (4x^2 - 5) $$

The set of data is:

{4, 5, 5, 6, 7, 8}

For evaluating the given summation using the provided set of data, we need to plug in all the data points in the given expression and then sum them up.

$$ \begin{aligned}\sum\left(4 x^{2}-5\right) &= (4(4)^2 - 5) + (4(5)^2 - 5) \\&\quad+ (4(5)^2 - 5) + (4(6)^2 - 5) \\&\quad+ (4(7)^2 - 5) + (4(8)^2 - 5)\end{aligned} $$

Simplifying the above expression, we get:

$$ \begin{aligned}\sum\left(4 x^{2}-5\right) &= (4(16) - 5) + (4(25) - 5) \\&\quad+ (4(25) - 5) + (4(36) - 5) \\&\quad+ (4(49) - 5) + (4(64) - 5) \\ &= 56 + 95 + 95 + 143 + 191 + 251 \\ &= 831\end{aligned} $$

Hence, the summation is equal to 831 using the provided set of data.

To know more about expression, visit:

https://brainly.com/question/1859113

#SPJ11

Answer:

give me my mf points

Step-by-step explanation:

Answer:

Sure, let's break down each part step by step.

Part A:

To calculate how much fabric is needed to make 3 aprons, we need to multiply the amount of fabric needed for one apron by 3.1 apron requires

1 1/2 yards of fabric for the front and 1/8 yards of fabric for the tie.1 1/2 yards + 1/8 yards = 15/8 yards (Adding fractions with a common denominator)

Now we can multiply the total fabric needed for one apron by 3 to get the fabric needed for 3 aprons:

3 * 15/8 yards = 45/8 yards (Multiplying by a whole number)

So, the total fabric needed to make 3 aprons is 45/8 yards.

Part B:

If Susan originally has 7 yards of fabric and she uses 45/8 yards to make 3 aprons, we can subtract the amount used from the original amount to find out how much fabric is left over.

7 yards - 45/8 yards = 56/8 yards - 45/8 yards (Subtracting fractions with a common denominator)

= 11/8 yards (Subtracting fractions)

So, after making the aprons, Susan will have 11/8 yards of fabric left over.

Part C:

To determine if Susan has enough fabric left to make another apron, we need to compare the amount of fabric left (11/8 yards) with the amount of fabric needed for one apron (1 1/2 yards + 1/8 yards = 15/8 yards).

Since 15/8 yards is greater than 11/8 yards, Susan does not have enough fabric left to make another apron. She is short by 4/8 yards (or 1/2 yard) of fabric.

Hope this helps! Let me know if you have any further questions.

Step-by-step explanation:

Answer:

\(\frac{5\pi }{3} = 0.5\)

Step-by-step explanation:

5π/3 radians = 5π/3 × (180°/π) = 300°

⇒ cos 5π/3 = cos 5π/3 = cos(300°) = 1/2 or 0.5

Answer:

see explanation

Step-by-step explanation:

Given

4x³ + x² - 8x - 2 ( factor the first/second and third/fourth terms )

= x²(4x + 1) - 2(4x + 1) ← first option on list

Finishing the factoring by factoring out (4x + 1) from each term

= (4x + 1)(x² - 2)

Answer:

x2(4x + 1) – 2(4x + 1)

Step-by-step explanation:

it's A on edg

The area bounded by y=x and y=x³ is 1/4. So, the correct option is option 4.

We need to integrate the difference of these two functions with respect to x over the given interval:

A = ∫[0,1] (x - x³) dx

Using the power rule of integration, we can simplify this expression:

A = [x²/2- x⁴/4)] evaluated from x = 0 to x = 1

A = [x²(2 - x²)/4] = 1/4

A = 1/4

Therefore, the area bounded by y=x and y=x³ is 1/4.

Learn more about area here:

brainly.com/question/31315232

#SPJ4