Suppose that two cards are randomly selected from a standard​ 52-card deck.
​(a) What is the probability that the first card is a spade and the second card is a spade if the sampling is done without​ replacement?
​(b) What is the probability that the first card is a spade and the second card is a spade if the sampling is done with​ replacement?

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

Let's think of the boat and wind as vectors:

Boat Vector --> [tex]\langle28cos36^\circ,28sin36^\circ\rangle[/tex]

Wind Vector --> [tex]\langle10cos22^\circ,10sin22^\circ\rangle[/tex]

Now, let's add the vectors:

[tex]\langle28cos36^\circ+10cos22^\circ,28sin36^\circ+10sin22^\circ\rangle[/tex]

Find the magnitude (the true velocity):

[tex]\sqrt{(28cos36^\circ+10cos22^\circ)^2+(28sin36^\circ+10sin22^\circ)}\approx37.78\approx38[/tex]

Find the direction (angle):

[tex]\theta=tan^{-1}(\frac{28sin36^\circ+10sin22^\circ}{28cos36^\circ+10cos22^\circ})\approx32.32^\circ\approx32^\circ[/tex]

Thus, D is the best answer

Problem 2

Recall that the angle between two vectors is [tex]\theta=cos^{-1}(\frac{u\cdot v}{||u||*||v||})[/tex] where [tex]u\cdot v[/tex] is the dot product of the vectors and [tex]||u||*||v||[/tex] is the product of each vector's magnitude:

[tex]\theta=cos^{-1}(\frac{u\cdot v}{||u||*||v||})\\\\\theta=cos^{-1}(\frac{\langle-82,47\rangle\cdot\langle92,80\rangle}{\sqrt{(-82)^2+(47)^2}*\sqrt{(92)^2+(80)^2}})\\\\\theta=cos^{-1}(\frac{(-82)(92)+(47)(80)}{\sqrt{6724+2209}*\sqrt{8464+6400}})\\\\\theta=cos^{-1}(\frac{(-7544)+3760}{\sqrt{8933}*\sqrt{14864}})\\\\\theta=cos^{-1}(\frac{-3784}{\sqrt{132780112}})\\\\\theta\approx109.17^\circ\approx109^\circ[/tex]

Therefore, C is the best answer

Volume = length x width x height

Volume of large box = 4 x 3 x 5 = 60 cubic feet.

the volume of the smaller boxes is greater than the volume of the larger box so he cannot fit them all.

Answer: 832

Step-by-step explanation:

trust i got correct

Answer:

84°

Step-by-step explanation:

The central angle of a circle is twice any inscribed angle subtended by the same arc.

because AB is a diameter, we also know that the triangle angle at C is 90° (all the inscribed triangles with their baseline being a diameter are right-angled).

as always, the sum of all angles in a triangle is 180°.

so, we know the triangle angle at A is

180 - 90 - 48 = 42°.

this is also the inscribed angle of the arc BC.

the central angle for arc BC (that is what is requested here) is then twice that angle : 2×42 = 84°

Answer:

38.5 cm²

Find area of the full rectangle:

Length * Width

6 * 7

42 cm²

Find area of the missing triangle

1/2 * base * height

1/2 * 7 * 1

3.5 cm²

Area of the figure:

42 - 3.5

38.5 cm²

Answer:

the means to and reroof is 10

the distributions are somewhat similar

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\bf\:62}[/tex]

Step-by-step explanation:

[tex](9*7) + 7 - 8 = ?[/tex]

We can solve this by using the PEMDAS concept where,

So, to solve this, we need to solve the numbers in the parentheses by doing the requested operation (here it is, mutiplucation).

[tex](9*7) + 7 - 8\\= (63) + 7 - 8[/tex]

Now, by looking at the PEMDAS rule, we can see that the next step is addition (as, we don't have to divide in this question).

[tex](63) + 7 - 8\\= 63 + 7 - 8\\= 70 - 8[/tex]

Now, subtract 8 from 70 .

[tex]70 - 8\\= \boxed{\bf\:62}[/tex]

[tex]\rule{150pt}{2pt}[/tex]

Answer:

Bo Peep's lasso is 34ft long.

Step-by-step explanation:

Simply add 11 to 23.

Hope that helps!

Answer:

no peep lasso: 34ft

Step-by-step explanation:

11 + 23 = 34

Step-by-step explanation:

Using the combination formula, it is found that there are 3300 ways to choose the songs.

The order in which the musics are chosen is not important, hence the combination formula is used to solve this question.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

For the rock songs, we have three from a set of eleven, hence:

[tex]C_{11,3} = \frac{11!}{3!8!} = 165[/tex]

For the alternative songs, we have four from a set of five, hence:

[tex]C_{5,4} = \frac{5!}{4!1!} = 5[/tex]

For the rap songs, we have three from a set of four, hence:

[tex]C_{4,3} = \frac{4!}{3!1!} = 4[/tex]

Since the songs are independent, the total number of ways is given by:

[tex]T = 165 \times 5 \times 4 = 3300[/tex]

More can be learned about the combination formula at https://brainly.com/question/25821700

Hey there!

Basically for all of your equations/questions you have to COMBINE the LIKE TERMS (if they are any in the particular equation you have)

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\

QUESTION/EQUATION #1

x - 5 ÷ 3 + b

We pretty much CANNOT do anything to this equation because it doesn’t have that many like terms.

So, thus your answer will most likely be/

[b + x - 5 ÷ 3]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

QUESTION/EQUATION #2

6b + 15b ÷ 3

= 21b ÷ 3

= 7b

Thus, your answer is: [7b]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
QUESTION/EQUATION #3

c - 2c × 4

REWRITE

= 1c - 2c × 4

COMBINE the LIKE TERMS

= 1c - 7

= -7c
Thus, your answer is: [-7c]

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

12 cm

Explanation:

The formula or method to find the area of any shape is to go around the shape.

In this case, they are 3, 4 and 5.

p = 3 + 4 + 5

p = 12 cm

Answer:

47.82 grams of carbohydrates.

Step-by-step explanation:

3.5 bagels have 167.37 grams of carbohydrates.

1 bagle = ???

In order for 3.5 to be 1 (just as we are asked) we need to divide by 3.5 both the amount of bagles and the amount of carbohydrates.

3.5 / 3.5 = 167.37 / 3.5

1 bagle = 47.82 grams of carbohydrates.

Answer:

Choice A.  (10, -1)
Choice B.  (-8, 9)
Choice D.  (6, -3)

Step-by-step explanation:

If we plug the coordinates of point A into the inequality, then we get,
x+y > -2

10 + (-1) > -2
9 > -2
That last inequality is a true statement since 9 is to the right of -2 on the number line. That means (10,-1) is a solution. Choice A is one of the answers.
Choices B and D are also answers for similar reasons.
Something like choice C is not a solution because
x+y > -2
-1+(-9) > -2
-10 > -2
Which is false.
You should find that choice E is false as well.

If you graphed the inequality and all of the points mentioned (see below), then you can visually confirm the answers. Notice how points A, B and D are in the blue shaded region which is the solution set.
The point E on the boundary does not count as a solution. This is due to the lack of "or equal to" portion of the inequality sign. That visually shows point E is not a solution. Point C isn't a solution either as it's nowhere near the blue shaded region.

Answer:

£78

Step-by-step explanation:

65 divided by 5= £13

13+65=£78

Answer:

£78

Step-by-step explanation:

Let the total value be T.

Answer:

325/377×100= 116% it means they completed 116%of the trip

Check the picture below.

Answer:

13-10=3 hence, the Q of ans is 3

Answer:

Step-by-step explanation:

4t + 11 = 19

Subtract 11 from both sides

4t = 19 - 11

4t = 8

Divide both sides by 4

t = 8/4

t = 2

Answer:

your answer is correct

Step-by-step explanation:

Answer:

6.7

please give brainliest

Answer:

The second option, 1,008 cm²

Step-by-step explanation:

   This shape has 5 sides to solve for with reguards to surface area.

   Let us solve for them all.

[1 & 2 - the triangles]

12 * 9 = 108 cm²

-> I am not going to divide since we have 2 congruent triangles

[3 - the bottom side]

25 * 12 = 300 cm²

[4 - the side facing away]

25 * 9 = 225 cm²

[5 - the side facing up]

25 * 15 = 375 cm²

   Now we will add them together for the total.

108 + 300 + 225 + 375 = 1,008 cm²

             The surface area for the triangular prism shown is 1,008 cm².

Answer:

Your answer would be:
C.) 1,350 cm2

Volume = 0.5 x b x h x length

0.5 x (25 x 12) x 9 =
0.5 x 300 x 9 =
= 1,350 cm2

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

If 750 people go to this store each day, 75 people would be sampled and 60 people would be expected to use a coupon

Probability is the likelihood of occurrance of an event. It is given by:

Probability = number of occurrence / total number of possible occurence

A cashier samples the transaction of every 10th person who goes though the line at a craft store out of 40 people, 32 used a coupon.

Probability of using coupon = 32/40 = 0.8

Hence if 750 people go to this store each day, number of people sampled = 75.

Number of people expected to use the coupon = 75 * 0.8 = 60

If 750 people go to this store each day, 75 people would be sampled and 60 people would be expected to use a coupon

Find out more on probability at: https://brainly.com/question/24756209

Answer:

x=  -1/7

Step-by-step explanation:

2x + 5x + 1 = 0

7x = -1

x =  -1/7

By rewriting the weights in decimal form and applying them to the correspondent percentages, we will see that the final grade is 92.8%.

The final grade will be given by:

G = a₁*x₁ + a₂*x₂ + ...

Where the values "a" are the weights, and the values "x" are the averages of Jeorge.

We know that the weights are:

Then we can write the weights in decimal form:

a₁ = 0.3

a₂ = 0.1

a₃ = 0.4

a₄ = 0.2

And the scores are:

So the final math grade will be:

G = 0.3*92 + 0.1*98 + 0.4*91 + 0.2*95 = 92.8%

If you want to learn more about percentages, you can read:

https://brainly.com/question/843074

Answer:

the answer is 92.8%

Step-by-step explanation:

165,400 and 220,574

=================================================

Explanation:

The value in the hundred thousands digit of 165,400 is "1". Just to right of it is "6", which is five or more, meaning we bump that "1" up to "2". Everything else gets replaced with a zero.

The number 165,400 rounds to 200,000 when rounding to the nearest hundred thousand. The number 165,400 is closer to 200,000 than it is to 100,000.

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

In 220,574 we have the first "2" in the  hundred thousands digit with another "2" just to the right of it. Since that second "2" is not five or more, we replace everything with zeros to get 200,000. We won't bump that first "2" up by one.

220,574 is closer to 200,000 than it is to 300,000.

These two sections help show why choices C and D are the answers.

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

Something like 142,026 rounds to 100,000 for similar reasoning as the previous section. So we can rule out choice B.

Choice A rounds to 100,000 as well, so we can rule it out also.

Choice D rounds to 1,000,000 which means we cross it off the list.

Answer:

8

----

125

Step-by-step explanation:

(2/5)³

2      2     2          8

--- x --- x ---  =  ---------

5      5     5         125

I hope this helps!

Answer:

First one is 10x + 5 = 35

Second one is 5x + 10 = 35

Third one is 35x + 5 = 10

go into settings and click on subscription

Answer: Its 1,110

Step-by-step explanation: