Joel is planning to pack 5 shirts and 2 pairs of pants for a weekend trip. If he has 11 shirts and 6 pairs of pants to choose from,
in how many different ways can this be done.

Answer:

I believe the answer is c) 3

Step-by-step explanation:

f(x) = (x + 3)(x - 1)(2x + 2)

x(x) + x(-1) + 3(x) + 3(-1)

f(x) = (x^2 - x + 3x - 3)(2x + 2)

f(x) = (x^2 + 2x - 3)(2x + 2)

2x(x^2) + 2x(2x) + 2x(-3) + 2(x^2) + 2(2x) + 2(-3)

f(x) = (2x^3 + 4x^2 - 6x + 2x^2 - 6)

f(x) = (2x^3 + 6x^2 - 6x - 6)

(a) w(x) = 5u(x) + 8v(x)

Differentiating with the sum rule gives

w'(x) = 5u'(x) + 8v'(x)

so that

w' (-5) = 5u' (-5) + 8v' (-5)

… = 5×2 + 8×4 = 42

(b) w(x) = u(x) v(x)

Differentiate using the product rule:

w'(x) = u'(x) v(x) + u(x) v'(x)

Then

w' (-5) = u' (-5) v (-5) + u (-5) v' (-5)

… = 2×6 + (-5)×4 = -8

(c) w(x) = u(x) / v(x)

Quotient rule:

w'(x) = (u'(x) v(x) - u(x) v'(x) ) / v(x) ²

Then

w' (-5) = (u' (-5) v (-5) - u (-5) v' (-5) ) / v (-5)²

… = (2×6 - (-5)×4) / 6² = 32/36 = 8/9

(d) w(x) = u(x) / (u(x) + v(x) )

Chain and quotient rule:

w'(x) = (u'(x) (u(x) + v(x)) - u(x) (u(x) + v(x))' ) / (u(x) + v(x) )²

… = (u'(x) (u(x) + v(x)) - u(x) (u'(x) + v'(x))) / (u(x) + v(x) )²

Then

w' (-5) = (u' (-5) (u (-5) + v (-5)) - u (-5) (u' (-5) + v' (-5))) / (u (-5) + v (-5) )²

… = (2×((-5) + 6) - (-5)×(2 + 4)) / ((-5) + 6)²

… = (2×1 + 5×6) / 1² = 32

Answer:

a.) 0.5

b.) 0.66

c.) 0.83

Step-by-step explanation:

As given,

Total Number of Batteries in the drawer = 10

Total Number of defective Batteries in the drawer = 4

⇒Total Number of non - defective Batteries in the drawer = 10 - 4 = 6

Now,

As, a sample of 3 is taken at random without replacement.

a.)

Getting exactly one defective battery means -

1 - from defective battery

2 - from non-defective battery

So,

Getting exactly 1 defective battery = ⁴C₁ × ⁶C₂ =  [tex]\frac{4!}{1! (4 - 1 )!}[/tex] × [tex]\frac{6!}{2! (6 - 2 )!}[/tex]

                                                                            = [tex]\frac{4!}{(3)!}[/tex] × [tex]\frac{6!}{2! (4)!}[/tex]

                                                                            = [tex]\frac{4.3!}{(3)!}[/tex] × [tex]\frac{6.5.4!}{2! (4)!}[/tex]

                                                                            = [tex]4[/tex] × [tex]\frac{6.5}{2.1! }[/tex]

                                                                            = [tex]4[/tex] × [tex]15[/tex] = 60

Total Number of possibility = ¹⁰C₃ = [tex]\frac{10!}{3! (10-3)!}[/tex]

                                                        = [tex]\frac{10!}{3! (7)!}[/tex]

                                                        = [tex]\frac{10.9.8.7!}{3! (7)!}[/tex]

                                                        = [tex]\frac{10.9.8}{3.2.1!}[/tex]

                                                        = 120

So, probability = [tex]\frac{60}{120} = \frac{1}{2} = 0.5[/tex]

b.)

at most one defective battery :

⇒either the defective battery is 1 or 0

If the defective battery is 1 , then 2 non defective

Possibility  = ⁴C₁ × ⁶C₂ = 60

If the defective battery is 0 , then 3 non defective

Possibility   = ⁴C₀ × ⁶C₃

                   =  [tex]\frac{4!}{0! (4 - 0)!}[/tex] × [tex]\frac{6!}{3! (6 - 3)!}[/tex]

                   = [tex]\frac{4!}{(4)!}[/tex] × [tex]\frac{6!}{3! (3)!}[/tex]

                   = 1 × [tex]\frac{6.5.4.3!}{3.2.1! (3)!}[/tex]

                   = 1× [tex]\frac{6.5.4}{3.2.1! }[/tex]

                   = 1 × 20 = 20

getting at most 1 defective battery = 60 + 20 = 80

Probability = [tex]\frac{80}{120} = \frac{8}{12} = 0.66[/tex]

c.)

at least one defective battery :

⇒either the defective battery is 1 or 2 or 3

If the defective battery is 1 , then 2 non defective

Possibility  = ⁴C₁ × ⁶C₂ = 60

If the defective battery is 2 , then 1 non defective

Possibility   = ⁴C₂ × ⁶C₁

                   =  [tex]\frac{4!}{2! (4 - 2)!}[/tex] × [tex]\frac{6!}{1! (6 - 1)!}[/tex]

                   = [tex]\frac{4!}{2! (2)!}[/tex] × [tex]\frac{6!}{1! (5)!}[/tex]

                   = [tex]\frac{4.3.2!}{2! (2)!}[/tex] × [tex]\frac{6.5!}{1! (5)!}[/tex]

                   = [tex]\frac{4.3}{2.1!}[/tex] × [tex]\frac{6}{1}[/tex]

                   = 6 × 6 = 36

If the defective battery is 3 , then 0 non defective

Possibility   = ⁴C₃ × ⁶C₀

                   =  [tex]\frac{4!}{3! (4 - 3)!}[/tex] × [tex]\frac{6!}{0! (6 - 0)!}[/tex]

                   = [tex]\frac{4!}{3! (1)!}[/tex] × [tex]\frac{6!}{(6)!}[/tex]

                   = [tex]\frac{4.3!}{3!}[/tex] × 1

                   = 4×1 = 4

getting at most 1 defective battery = 60 + 36 + 4 = 100

Probability = [tex]\frac{100}{120} = \frac{10}{12} = 0.83[/tex]

Answer: He would have 16590 but if we want to know in total

it would be, 11060 (just from the percent) if you want to know in total add 16590 and 79,000 which would be (95,590 for Landon) and (Elijah would be 90060) in total

Step-by-step explanation:So in total Landon would have:

Landon-(95,590)

Elijah-(90,060)

So Landon would have 5,530 more dollars in 7 years than Elijah.

Answer: 140

Step-by-step explanation:

6(8) = 48

4(23) = 92

48 + 92 = 140

Because of this, 6(8) + 4(23) = 140.

Answer: 41 i think

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

[tex]F \alpha \frac{1}{d^{2} }[/tex]

[tex]F = \frac{K}{d^{2} }[/tex]

When F = 18; d = 2

[tex]18 = \frac{K}{2^{2} }[/tex]

[tex]18 = \frac{K}{4}[/tex]

Cross multiply;

18 x 4 = K

72 = K

There the equation connecting F and [tex]d^{2}[/tex] is

[tex]F = \frac{72}{d}[/tex]

Now, Find F when d = 6

All you do is to substitute d = 6 in to [tex]F = \frac{72}{d}[/tex]

[tex]F = \frac{72}{6}[/tex]

Therefore;

F = 12

Please mark me brainiest if correct.

Answer:

x= 2y - 3/2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

x=2y - 3/2

Step-by-step explanation:

Answer:

640

Step-by-step explanation:

Using the Central Limit Theorem, it is found that the researcher should use a sample size of 640.

Hence, for the standard deviation to be cut be half, the sample size has to be multiplied by 4, which means that it should be of 4 x 160 = 640.

To learn more about the Central Limit Theorem, you can take a look at https://brainly.com/question/25581475

Hi there! Your answer to this question would be 90%..

Step By Step Explanation:

So we know that 100% is the average grade for an correct for an entire test.

But how can we find 90%?

Let think like this. 10=100%.

Well if 10 is 100% then 9 would be 90% since every 1 of 10 is 10%.

Final Result: 90%

Answer:

x = 84

Step-by-step explanation:

1. Solve for m<R

The sum of angles in a triangle is 180 degrees, regardless of each individual angle measure in the triangle. One can apply that to triangle QRS by stating that;

m<SQR + m<R + m<QSR = 180

Substitute

68 + 3x + m<R = 180

Inverse operations,

m<R = 112 - 3x

2. Solve or m<PSR

Verticle angles theorem states that when two lines intersect, four angles are formed. The angles that are opposite each other are congruent. Using this, one can concluce that;

m<TSU = m<PSR = 4x

3. Solving for x

Now all one has to do is apply the sum of angles in a triangle theorem for triangle PSR

m<P + m<R + m<PSR = 180

Substitute,

x + 112 - 3x + 4x = 180

Simplify

2x + 112 = 180

Inverse operations

2x + 112 = 180

     -112      -112

2x = 168

/5       /5

x = 84

Answer:

237 = m + 137

this is the equation showing the relationship

Answer:

ANSWER IS D

Step-by-step explanation:

forgive me if is wrong

Answer:

121 feet

Step-by-step explanation:

Equation:

484 / 4 = 121

Word Explanation:

If there are 4 sides in a square and the total of all 4 sides is 484, We have to divide 484 by 4 and get 121 feet.

The perimeter of the square fence is P = 88 feet and Tyrone needs 22 feet of fence on each side

The perimeter of a square is given by four times the length of its each side

The equation for the perimeter of the square with the side 'a' is given by

Perimeter of Square = 4a

Given data ,

Let the perimeter of the square be represented as P

Now , the equation will be

Let the side length of the square be a²

The area of the square is A = 484 feet²

Taking square roots on both sides of the equation , we get

A = a²

a² = 484

a = 22 feet

Now , perimeter of the square P = 4a

Substituting the values in the equation , we get

Perimeter of the square P = 4 x 22

Perimeter of the square P = 88 feet

Hence , the perimeter of the square is 88 feet

To learn more about perimeter of square click :

https://brainly.com/question/11495285

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Answer:

z = 4/5

Step-by-step explanation:

Answer:

is c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

x/4=21

multiply 4 on both sides

4*(x/4)=21*4

21*4=84

4*(x/4)=x

x=84

Answer:

this is an example

Step-by-step explanation:

There are a few different ways to approach this problem, including the following two methods.

1) Find 20% of the original price, then subtract that amount from the original price. 

    To find a percentage of a number, you multiply the number by the percentage.  (You are finding a part of a whole.)

                   20% = 20/100 = 1/5    or   20% = 0.20

    Original Price: $24   Find 20% of $24.                         (Note: "of" is taking part of a whole, so you multiply.)

                    0.20 x 24 = 4.80            This is the mark down, or the amount you subtract from original price.

    Sale Price = Original Price - Mark Down   

                   =   24.00 - 4.80

                   =   19.20

2) If you save 20%, you are still paying 80%. (100-20 = 80) Therefore the sale price is 80% of the original price.

                    80% = 80/100 = 4/5     or    80% = 0.80

     Sale Price = 80% of Original Price

                    = 0.80 x 24

                    = 19.20

Given:

[tex]\{(x,y)|5x-7y<0, x\in I, y\in I\}[/tex]

To find:

The test point is in the solution set for the linear inequality.

Solution:

The inequality is

[tex]5x-7y<0[/tex]

Here, [tex]x\in I, y\in I[/tex]. It means, both x and y both are integers. So, the option D is incorrect because 1.5 and 3.5 are not integers.

For option A, the point is (-2,-1).

Putting x=-2 and y=-1 in the given inequality, we get

[tex]5(-2)-7(-1)<0[/tex]

[tex]-10+7<0[/tex]

[tex]-3<0[/tex]

This statement is true. So, the point (-2,-1) is in the solution set.

For option B, the point is (-4,-3).

Putting x=-4 and y=-3 in the given inequality, we get

[tex]5(-4)-7(-3)<0[/tex]

[tex]-20+21<0[/tex]

[tex]1<0[/tex]

This statement is false. So, the point (-4,-3) is not in the solution set.

For option C, the point is (-2,-4).

Putting x=-2 and y=-4 in the given inequality, we get

[tex]5(-2)-7(-4)<0[/tex]

[tex]-10+28<0[/tex]

[tex]18<0[/tex]

This statement is false. So, the point (-2,-4) is not in the solution set.

Therefore, the correct option is A.

Answer:

The average speed at which Nimes drove his car was 50 miles per hour.

Step-by-step explanation:

Given that Nimes was driving to the hotel at 1:30 p.m., being 65 miles away from it, and finally arriving at its destination at 2:48 p.m., to determine the average speed at which the circle should be made. following calculation:

14:48 - 13:30 = 1:18

60 = 100

18 = X

(18 x 100) / 60 = X

1,800 / 60 = X

30 = X

65 / 1.30 = X

50 = X

Therefore, the average speed at which Nimes drove his car was 50 miles per hour.

Answer:

B, I think that's the answer

Answer:

When x = 2.4, we have y = 10.8

Step-by-step explanation:

A direct variation of two variables, x, and y, can be written as:

y = k*x

Where k is a constant, called the constant of variation.

We know that y = 7.2, when x = 1.6

Then we can replace these two in the above equation to get:

7.2 = k*1.6

Now we can solve this for k:

7.2/1.6 = k = 4.5

Then our relation is:

y = 4.5*x

Now we want to find the value of y, when x = 2.4

Then we just need to replace x by 2.4 in the above equation:

y = 4.5*(2.4) = 10.8

y = 10.8

Answer:

D. -12x + 18

Step-by-step explanation:

f(x) = -6x +5; g(x) = 2x + 8

[g o f](x) = g(f(x))

this means that in g(x), everywhere there's an x, f(x) replaces it. [g o f](x) is represented at the following: (f(x) is in bold)

g(f(x)) = 2(-6x +5) + 8                  distribute the 2 to (-6x + 5)

g(f(x)) = -12x + 10 + 8                   combine like terms

g(f(x)) = -12x + 18

Answer:

8 is not in the solution set

Step-by-step explanation:

Given, -y + 7 < -4

To find out if 8 is in the solution set, substitute y = 8 in the inequality and solve to see if the statement would be true.

Thus:

-8 + 7 < -4

-1 < -4

This -1 is less than -4. This is actually not TRUE. -1 is rather greater than -4.

Therefore, 8 is not in the solution set.

Answer:

The further compounding cycles in a given year, the greater the effect on the valuation of potential investment. Therefore, the more interest-posting dates, irrespective of the interest rate, the more compounding raises the account balance.

Step-by-step explanation:

Answer:

C

the computed value gets larger

Step-by-step explanation:

Answer:

The third one

Step-by-step explanation:

mP is not correct

Answer:

The answer is 20.

X = -20

Answer: -20

Step by step explanation:

-10=x÷2

•2 •2

-20=x

Answer: (-8,0) (0,4)

Step-by-step explanation: graphing it would be for coordinate one (-8,0) and for the second coordinate it would be (0,4.) and for the x y chart it goes for x's it goes -8 and then next is 0 and for the y's, it's 0 then next is 4. give me brainliest thankssss

Answer:

B

Step-by-step explanation:

If you look at 3 on the X-axis and go down 4 then you will get point B as your answer.

Answer:

E is the correct answer because A is (-4,-3), B is (-4,3), C is (5,1), D is (4,-3), E is (3,-4), and F is (-2,-4)

Answer:

14

Explanation: 2/9x 63= 2x 63/9= 2x7

Answer:

14

Step-by-step explanation:

i believe so....