Hannah's suitcase has the following dimensions.

length: 27 inches
width: 21 inches
depth: 14 inches

What is the volume of Hannah's suitcase in cubic inches?

Answer:

5√3 / 2

Step-by-step explanation:

tan 30 = ( 5 / 2 ) / y

1 / √3 = 5 / 2y

2y = 5√3

y = 5√3 / 2

Answer: No, there isn't equal opportunity

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

Explanation:

Let's define the two events

From the table, we see that

P(B) = 340/500 = 0.68

meaning that there's a 68% chance of picking someone who got the class they wanted (i.e. 68% of the people got the class they wanted)

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

Now let's assume that the person is on the honor roll. This means we only focus on the "honor roll" column. There are 125 people here that got the class they wanted out of 205 honor roll students total.

So,

P(B given A) = 125/205 = 0.609756

which rounds to 0.61

This says that if a person is on the honor roll, then they have roughly a 61% chance of getting the class they want.

The chances have gone down from 68% to 61% roughly.

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

It appears that being on the honor roll does affect your chances of getting into the class you want.

Therefore, all students do not have the same equal opportunity.

We would need to have P(B) and P(A given B) to be the same exact value for true equal opportunity to happen.

All students do not have equal opportunity.

From the table, we have the following parameters:

The above means that:

The probability that a person is on honor roll call is:

p1 = 205/500

p1 = 0.41

The probability that a person got the math class requested

p2 = 340/500

p2 = 0.68

Both probabilities are not equal.

Hence, it is true that all students do not have equal opportunity.

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Answer: A & C

Step-by-step explanation:

[tex]i=\sqrt{-1}[/tex]

[tex]\sqrt{-1} *\sqrt{4} =\sqrt{-4}[/tex]

You can also simplify the above by taking the -4 out of the radical

It becomes 2 x [tex]\sqrt{-1}[/tex], which can be simplifed to C

Answer:

68%

Step-by-step explanation:

6,753/100=67.53 which rounds up to 68%

Answer:

87.5

Step-by-step explanation:

Let the missing side be x.

28 / 35 = x / 50

4 / 7 = x / 50

4 ( x ) = 7 ( 50 )

4x = 350

x = 350 / 4

x = 87.5

Answer:

D) Exponential decay

Step-by-step explanation:

The correct function is:

[tex]f(x) = 25(1/2)^x[/tex]

Required

What type of rate is it

An exponential function is represented as:

[tex]f(x) = ab^x[/tex]

If

[tex]b > 0[/tex], then it represents growth

[tex]b < 0[/tex], then it represents decay

By comparison:

[tex]b = 1/2[/tex]

[tex]1/2 < 0[/tex]

Hence, the rate is exponential decay

Answer:

Step-by-step explanation:

Answer:

4/27

Step-by-step explanation:

total number of marbles=9

probability of red=4/9

since you returned the first marble, the total number of marbles remains the same

prob(Blue)=(3/9)=1/3

P(red then blue)=(4/9)*(1/3)

=4/27

Answer: B. p = 3n-600

Step-by-step explanation:

Profit(p) = Earned - Cost

p = 5n - (2n + 600) = 5n - 2n - 600 = 3n - 600

The equation representing the profit function of the newsstand is

p = 3n - 600

Option B is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The revenue generated by selling n magazines is 5n dollars.

The cost of selling n magazines is the sum of the cost of purchasing n magazines and the fixed cost of rent and electricity, which is $2n + $600.

Now,

The profit function can be represented by:

p = revenue - cost

= 5n - (2n + 600)

= 3n - 600

Thus,

The equation representing the profit function of the newsstand is

p = 3n - 600

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Answer:

Add 81/4 to both sides.

Step-by-step explanation:

x^2 − 9x − 8 = 0

x^2 - 9x = 8

Take the coefficient of the x term: -9

Divide by 2: -9/2

Square it: 81/4

Add 81/4 to both sides.

Answer:

f(-4) = -1

f(-1) = -4

f(1) = 4

Step-by-step explanation:

We need to find the y value for the x values

f(-4) means find the y value for x= -4

f(-4) = -1

f(-1) = -4

f(1) = 4

Answer:

13

Step-by-step explanation:

since n is 4 substitute it where there's n in the equation

3(4)+1

12+1

13

I hope this helps

Answer:

13

Step-by-step explanation:

so you start with the equation 3n+1

since you know n=4 then u put it in place of n making the equation 3*4+1

then you multiply and it's 12+1 which equals 13

Answer:

y = -3 (you have to draw an horizontal line that passes for the point (0,-3)

Step-by-step explanation:

We have to find the middle points of the segments that unite the corrispettive points.

We are lucky because the images of the points have the same x coordinate of the original ones, so we have just to find the y coordinates.

Segment CC‘

(y1 + y2)/2 = (-1-5)/2 = -3

Segment AA’

(0-6)/2 = -3

Segmet BB’

(1-7)/2 = -3

Segment DD’

(1-7)/2 = -3

In conclusion we can say that the points of the reflection have all the y coordinate equal to -3.

the line is horizontal and its equation is : y = -3

Answer:

c

Step-by-step explanation:

hope it helps!!!!!!!!!!!!!!

Answer:

C) SQRT(65)

Step-by-step explanation:

the magnitude of 1-8i is given by the following:

sqrt(a^2+b^2)  

sqrt(1^2+8^2)

=sqrt(1+64)

=sqrt(65)

It is to be noted that the magnitude of   |1 − 8i| is √(65) (Option C)

To find the magnitude (or absolute value) of a complex number, we use the formula |a + bi| = √(a² + b²). In this case, the complex number is 1 - 8i.

Using the formula, we have  -

|1 - 8i| = √(1² + (-8)²)

= √(1 + 64)

= √65

Hence, the magnitude of 1 - 8i is √65.

So the correct answer is C) √65.

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Answer:

150 Newtons

Step-by-step explanation:

Given

[tex]t = \sqrt{\frac{4\pi^2mr}{F}}[/tex]

[tex]t = 12[/tex]

[tex]r =6.5[/tex]

[tex]\pi = 3.14[/tex]

[tex]m = 84.4[/tex]

See attachment

Required

Find F

We have:

[tex]t = \sqrt{\frac{4\pi^2mr}{F}}[/tex]

Square both sides

[tex]t^2 = \frac{4\pi^2mr}{F}[/tex]

Multiply both sides by F

[tex]Ft^2 = 4\pi^2mr[/tex]

Divide both sides by [tex]t^2[/tex]

[tex]F = \frac{4\pi^2mr}{t^2}[/tex]

Substitute known values

[tex]F = \frac{4*3.14^2*84.4*6.5}{12^2}[/tex]

[tex]F = \frac{21635.90624}{144}[/tex]

[tex]F = 150.249348889[/tex]

[tex]F = 150N[/tex]

Answer:

t- shirt cost £7, hat cost £3

Step-by-step explanation:

let t represent cost of t- shirt and h represent cost of hat , then

4t + h = 31  → (1)

2t + h = 17 → (2)

Subtract (2) from (1) term by term to eliminate h

(4t - 2t) + (h - h) = 31 - 17 , that is

2t = 14 ( divide both sides by 2 )

t = 7

Substitute t = 7 into either of the 2 equations and solve for h

Substituting into (1)

4(7) + h = 31

28 + h = 31 ( subtract 28 from both sides )

h = 3

t- shirt cost £7 and hat cost £3

Answer:

x = 9.8

Step-by-step explanation:

Please see attached photo for diagram.

We'll begin by calculating the value of y. This can be obtained as follow:

Angle θ = 45

Opposite = 6

Hypothenus = y

Sine θ = Opposite /Hypothenus

Sine 45 = 6/y

0.7071 = 6/y

Cross multiply

y × 0.7071 = 6

Divide both side by 0.7071

y = 6 / 0.7071

y = 8.5

Finally, we shall determine the value of x. This can be obtained as follow:

Angle θ = 60

Opposite = 8.5

Hypothenus = x

Sine θ = Opposite /Hypothenus

Sine 60 = 8.5 / x

Cross multiply

x Sine 60 = 8.5

Divide both side by sine 60

x = 8.5 / sine 60

x = 8.5 / 0.8660

x = 9.8

Answer:

send me again I can't understand question

5x - 2 = 4 + 2x

3x - 2 = 4

3x = 6

x = 2

Hope this helps!

Answer:

False

Step-by-step explanation:

The point that is equidistant from the vertices of a triangle is called the circumcenter.

9514 1404 393

Answer:

  False

Step-by-step explanation:

The incenter is the center of the inscribed circle, which is tangent to all of the sides of the triangle. The incenter is equidistant from the sides, not the vertices.

_____

Additional comment

The circumcenter is the center of the circumscribing circle. Each of the vertices of the triangle is on the circumcircle, so the circumcenter is equidistant from the vertices.

The incenter is located at the intersection point of the angle bisectors. The circumcenter is located at the intersection point of the perpendicular bisectors of the sides.

Answer:

x=6

Step-by-step explanation:

sqrt (2x-3) = sqrt (3x-9)

Square each side

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

2x-3 = 3x-9

Subtract 2x from each side

2x-3-2x = 3x-2x-9

-3 = x-9

Add 9 to each side

-3+9 = x-9+9

6 =x

Check solution

sqrt (2*6-3) = sqrt (3*6-9)

sqrt (9) = sqrt (9)

3=3

Solution is valid

sqrt (2x-3) = sqrt (3x-9)

Square each side

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

2x-3 = 3x-9

Subtract 2x from each side

2x-3-2x = 3x-2x-9

-3 = x-9

Add 9 to each side

-3+9 = x-9+9

6 =x

sqrt (2*6-3) = sqrt (3*6-9)

sqrt (9) = sqrt (9)

3=3

Therefore ans x = 6

Answered by Gauthmath must click thanks and mark brainliest

Answer:

the expected number of pairs of people who have the same birthday is 14

Step-by-step explanation:

The computation of the expected number of pairs of people who have the same birthday is as follows:

= 100 (100 - 1) ÷ 2 × 365

= 100 × 99 ÷ 730

= 9900 ÷ 730

= 13.5616

= 14

Therefore, the expected number of pairs of people who have the same birthday is 14

Answer:

0.9703 = 97.03% probability that 15 or more of them would agree with the claim.

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they agree with the claim, or they do not. The probability of an adult agreeing with the claim is independent of any other adult, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

75% of adults believe that an unattractive smile hurts career success.

This means that [tex]p = 0.75[/tex]

Suppose that 25 adults are randomly selected.

This means that [tex]n = 25[/tex]

What is the probability that 15 or more of them would agree with the claim?

This is:

[tex]P(X \geq 15) = 1 - P(X < 15)[/tex]

In which:

[tex]P(X < 15) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 13) + P(X = 14)[/tex]

14 is below the mean, so we start below and go until the probability is 0. Then

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 14) = C_{25,14}.(0.75)^{14}.(0.25)^{11} = 0.0189[/tex]

[tex]P(X = 13) = C_{25,13}.(0.75)^{13}.(0.25)^{12} = 0.0074[/tex]

[tex]P(X = 12) = C_{25,12}.(0.75)^{12}.(0.25)^{13} = 0.0025[/tex]

[tex]P(X = 11) = C_{25,11}.(0.75)^{11}.(0.25)^{14} = 0.0007[/tex]

[tex]P(X = 10) = C_{25,10}.(0.75)^{10}.(0.25)^{15} = 0.0002[/tex]

[tex]P(X = 9) = C_{25,9}.(0.75)^{9}.(0.25)^{16} \approx 0[/tex]

Then

[tex]P(X < 15) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) = 0.0002 + 0.0007 + 0.0025 + 0.0074 + 0.0189 = 0.0297[/tex]

And

[tex]P(X \geq 15) = 1 - P(X < 15) = 1 - 0.0297 = 0.9703[/tex]

0.9703 = 97.03% probability that 15 or more of them would agree with the claim.

Answer:

y= 1/2x-3/2

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

y = 1/2x+b

Using the point for x and y we can find b

-3 = 1/2(-3)+b

-3 = -3/2 +b

-6/2 = -3/2+b

Add 3/2 to each side

-6/2 +3/2 = b

-3/2 = b

y= 1/2x-3/2

Answer:

Step-by-step explanation:

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

y + 3 = 1/2x + 3/2

y + 6/2 = 1/2x + 3/2

y = 1/2x - 3/2

Answer:

y=-2x-7

Step-by-step explanation:

after putting the choices with the question in a graph I found that that ones stays in a line with the question

Brainliest please!!

Answer:

12 and 36

Step-by-step explanation:

Call the age of both Bill and his father is a and b, respectively

we have:

b=3a

b-3=4(a-3) ->b=4a-12 -> 3a=4a-12 ->a =12 -> b=36

Answer:

A. 24

Step-by-step explanation:

Five and above rounds up

so 25,26,27,28,29 rounds up to 30

We leave it alone when 4 or less

34,33,32,31,30 remains at 30

24 would not round to 30