Homework:Assignment 3 Question 20 Score: 0 of 1 point A vending machine dispenses coffee into ​-ounce cup. The amount of coffee dispensed into the cup is normally distributed with a standard deviation of ounce. You can allow the cup to overfill ​% of the time. What amount should you set as the mean amount of coffee to be​ dispensed?

Answer:

3 seconds

Step-by-step explanation:

First, let's calculate the approximate speed of light.

3 · 10^14 = 3 · 100,000,000,000,000

              = 300,000,000,000,000

Approximately, light travels 300,000,000,000,000 centimeters per second.

Now, let's simplify 9x10^14.

9 · 10^14 = 9 · 100,000,000,000,000

              = 900,000,000,000,000

To find out how many seconds light takes to travel 900,000,000,000,000 centimeters, we have to divide this number by 300,000,000,000,000, the approximate speed of light.

900,000,000,000,000/300,000,000,000,000 = 3

Therefore, it will take 3 seconds for light to travel 900,000,000,000,000 centimeters.

It will take 3 seconds to cover the distance of 9×10¹⁴ cm.

We use the scientific notation of numbers to write very large numbers in compact form.

In the scientific form, we write a number in the form of base×10ⁿ.

Where 0 ≤ base < 10 and n can be any rational number.

Given the speed of light s approximately 3×10¹⁴ cm/sec.

∴ It will take (9×10¹⁴/3×10¹⁴) = 3 seconds.

We know that exponents are added when the same base is multiplied and exponents are subtracted when the same base or integral multiple of the same base is divided.

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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:

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:

-9

Step-by-step explanation:

-2 3 + |7| - 4 · 2

I assume -2 3 means -2^3.

-2^3 + |7| - 4 · 2 =

= -8 + 7 - 8

= -1 - 8

= -9

Answer:

-9

Step-by-step explanation:

-2^ 3 + |7| - 4 · 2

Parentheses first and an absolute value is considered parentheses

-2 ^3 + 7 - 4 · 2

Then exponenets

Since the sign is outside of the exponent it is considered multiplication

-1 * (2^3)+ 7 - 4 · 2

-1 *8 + 7 - 4 · 2

Then multiply

-8 +7 -8

Then add and subtract from left to right

-1-8

-9

Answer:

No.

Step-by-step explanation:

3x+2y<11 doesn't have a y-intercept of 6 and doesn't have a x-intercept of 4.

2x-y<9 is not the same direction as 3x+2y<11.

Answer:

8 months 11 days 1 year

Answer:

The number of devices infected with the virus increases by 24% each day.

Step-by-step explanation:

Have a nice day! ♡

Answer:

$25.80

Step-by-step explanation:

First, let's find the cost of one bag of chip:

10.32/8 = 1.29

If one bag costs $1.29, simply multiply the number of bags (20) by 1.29

1.29 x 20 = 25.80

               = $25.80

Answer:

25.80

Step-by-step explanation:

We can use a ratio to solve

8 bags             20 bags

-------------   = ----------------

10.32               x dollars

Using cross products

8x = 10.32 * 20

8x =206.40

Divide each side by 8

8x/7 = 206.40/8

x =25.80

Answer:

the domain is ALL reals numbers except ZERO

- ∞ < x < 0    ∪   0 <  x < ∞

Step-by-step explanation:

Answer:

(-∞,0) ∪ (0,∞), {x|x≠0}

Step-by-step explanation:

I think this is it. Im not completely sure though

Answer:

8. 72% × 850

= 72/100 × 850

= 72 × 8,5

= 612 ( b )

9. Poin B = 4 ( b )

Answer:

8. B

9. B

10. C

Step-by-step explanation:

8. To find 72% of 850, you would multiply 0.72 x 850. When you do that, it gives you 612.

9. B is on the number 4.

10. The expression is asking, "What is the absolute value of 28?". Absolute value means that the number inside will always be positive. For example, if it was -28, the absolute value would turn to 28. Since the question has 28 already positive, there is no change, so the answer would be 28.

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:

=3/8×1 1/2×1 1/2

=3/8 ×3/2×3/2                                            ∴ 1 1/2 =2×1+1/2=3/2

=27/32                                                        ∴3×3×3=27   ∴8×2×2=32

Answer:

[tex]A" = (7,-2)[/tex]

[tex]B" = (10,0)[/tex]

[tex]C"= (12,-3)[/tex]

Step-by-step explanation:

Given

[tex]A = (4,2)[/tex]

[tex]B = (7,0)[/tex]

[tex]C =(9,3)[/tex]

a: Reflect over x-axis

The rule of this is:

[tex](x,y) \to (x,-y)[/tex]

So, we have:

[tex]A' = (4,-2)[/tex]

[tex]B' = (7,0)[/tex]

[tex]C' = (9,-3)[/tex]

b: Shift 3 units left

The rule of this is:

[tex](x,y) \to (x+3,y)[/tex]

So, we have:

[tex]A" = (4+3,-2)[/tex]

[tex]A" = (7,-2)[/tex]

[tex]B" = (7+3,0)[/tex]

[tex]B" = (10,0)[/tex]

[tex]C"= (9+3,-3)[/tex]

[tex]C"= (12,-3)[/tex]

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

5x - 2 = 4 + 2x

3x - 2 = 4

3x = 6

x = 2

Hope this helps!

Answer:

a. The number of pounds of the meat required is 3 pounds and the number of pounds of cheese required is 2 pounds.

b. $ 16.7

Step-by-step explanation:

a. How many pounds of each are needed in order to minimize the cost and still meet the minimum requirements?

Let c represent the carbohydrate units and p the protein units.

For the meat portion M, we have 2 units of carbohydrates and 2 units of protein per pound. So, M = 2c + 2p

For the cheese portion K, we have 3 units of carbohydrates and 1 units of protein per pound. So, K = 3c + p.

Let x be the number of pounds of meat required and y be the number of cheese pounds required. The total number of pounds required is T

So, we have xM + yK = x(2c + 2p) + y(3c + p)

= 2xc + 2xp + 3yc + yp

= 2xc + 3yc + 2xp + yp

= (2x + 3y)c + (2x + y)p

Since the required number of units, R is 12 units of carbohydrates and 8 units of protein, we have R = 12c + 8p

Since T = R, we have

(2x + 3y)c + (2x + y)p = 12c + 8p

Equating coefficients, we have

2x + 3y = 12 (1) and 2x + y = 8 (2)

Subtracting (2) from (1), we have

2x + 3y = 12 (1)

-

2x + y = 8 (2)

2y = 4

y = 4/2

y = 2

Substituting y = 2 into (2), we have

2x + y = 8

2x + 2 = 8

2x = 8 - 2

2x = 6

x = 6/2

x = 3

Since x = 3 and y = 2

The number of pounds of the meat required is 3 pounds and the number of pounds of cheese required is 2 pounds.

What is the minimum cost?​

Since meat costs $3.70 per pound and the cheese costs $2.60 per pound and we have 3 pounds of meat and 2 pounds of cheese, the total cost of meat is C = $3.70/pound × 3 pounds = $ 11.1.

The total cost of cheese is C' = $2.60/pound × 2 pounds = $ 5.2.

So, the minimum cost C" = C + C' = $ 11.1 + $ 5.2 = $ 16.7

Answer:

Step-by-step explanation:

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:

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:

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

A = 10,00,000

P = 10,000

T = 2

1000000 = 10000(1+r/100)^2

1000000 = 10000((100 + r)/100)^2

1000000 = 10000× 100 + r/100 × 100 + r/100

1000000 = 10000 + r^2

1000000 - 10000 = r^2

990000 = r^2

√99000 = r

Quadratic Equation

10000(1+r/100)^2

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

explainion:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

Use The (Pythagorean Theorem) to find the length of any side of a right triangle. Form it like its shown in picture above. Follow the instructions that also shown in the picture above.

Answer: 7 / 8 should be added

Step-by-step explanation:

Let x be the number that should be added

Write the equation

-3/2 + x = -5/8

Add -3/2 on both sides

-3/2 + x + 3/2 = -5/8 + 3/2

x = -5/8 + 3/2

Change the denominator of 3/2 to 8 in order to do addition

x = -5/8 + 12 / 8

x = 7 / 8

Hope this helps!! :)

Please let me know if you have any questions

Step-by-step explanation:

well, what does the word "constant" tell you ?

e.g. "this is a constant reminder of ..."

a constant is steady and unchanging. always the same.

so, what could be the constant part/term in the expression ?

-3xy ? is that always the same value ? no matter what values you assign to x, y (and whatever other variables there might be in the system)?

or

10 ? is that always the same value, no matter what values are assigned to x, y, ... ?

there are no other parts/terms I can see here.

so, please use your common sense and pick the right one. you can do that !

this is so simple. to outright write the answer to this feels like an offense. also against your own intelligence.

Answer:

a first degree equation

Answer:

C

Step-by-step explanation:

Just trust

Answer:

C

Step-by-step explanation:

I did the assignment in edge and got it right.

Proof:

dy/dx = 4 + √(y - 4x + 6)

Make a substitution of v(x) = y(x) - 4x + 6, so that dv/dx = dy/dx - 4. Then the DE becomes

dv/dx + 4 = 4 + √v

dv/dx = √v

which is separable as

dv/√v = dx

Integrating both sides gives

2√v = x + C

Get the solution back in terms of y :

2√(y - 4x + 6) = x + C

You can go on to solve for y explicitly if you want.

√(y - 4x + 6) = x/2 + C

y - 4x + 6 = (x/2 + C )²

y = 4x - 6 + (x/2 + C )²

Answer:

it should be letter c

Step-by-step explanation:

I hope this help

Answer:

Step-by-step explanation:

One way of solution is to plot the lines and points and confirm the answer visually.

See attached.

Another way is to substitute the coordinates and verify if they satisfy both of the inequalities.

Each of the methods gives us the correct answer choice of D.

Answer:

2(1)+y =1 for × intercept

2x+(1)=1 for y intercept