Each week Danny eats 540 grams of cereal over 8 weeks. He finishes a total of 12 boxes of cereal. Each box contains the same amount of cereal. How many grams of cereal are in each box?

Answer: F(x) = 2*sin(x/10  +(3/2)*pi) + 5

Step-by-step explanation:

The information that we have is that:

We have a minimum at (0, 3)

the midline is at (5*pi, 5)

This is a sinusoidal function, so we can write one generic one as:

F(x) = A*sin(c*x + p) + B.

where A and B are constants, c is the frequency and p is a phase

First, the minimum of the sine function is when sin(x) = -1, and this happens at (3/2)*pi

We know that this minimum is at x = 0.

sin(c*0 + p) = -1

Then p = 3/2*pi.

So our function is:

F(x) = A*sin(c*x  +(3/2)*pi) + B.

Now, we know that F(0) = 3, so:

3 = A*sin(c*0 +(3/2)*pi) + B = -A + B.

now we can use the other hint, the midpoint of the sine function is when sin(x) = 0, and this happens at x = 0 and x = pi, particularlly as we here have a phase of 3/2*pi, we should find x = 2*pi.

then:

c*5*pi + (3/2)*pi = 2*pi

c*5 + 3/2 = 2

c*5 = 2 - 3/2 = 1/2

C = 1/2*5 = 1/10

So our function is

F(x) = A*sin(x/10  +(3/2)*pi) + B

and we know that when x = 5*pi, F(5*pi) = 5, so:

5 = F(x) = A*sin(5*pi/10  +(3/2)*pi) + B

5 = B

and we aready knew that:

- A + B = 3

-A + 5 = 3

A = 5 - 3 = 2

So our equation is:

F(x) = 2*sin(x/10  +(3/2)*pi) + 5

Answer:

the correct answer is

[tex]f(x) = - 2 \cos( \frac{1}{10}x ) + 5[/tex]

Answer:

Step-by-step explanation:

that is 55/22 = 2.5 hrs

Answer: .two and a half hours.

Step-by-step explanation:

22/1 = 55/x

22x=55

X=2.5

Answer:

quotient  x² - 2x + 5

remainder  (-12x+5)

Step-by-step explanation:

                    x²      -2x       +5

x² + 2x - 1  | x^4   + 0*x³  + 0*x² + 0x + 0

                 |-(x^4  +  2x³   -   x²)

                            - 2x³    +x²     + 0x

                          -(-2x³   - 4x²   + 2x)

                                         5x²   - 2x + 0

                                     -(  5x²  +10x -5)

                                                  -12x + 5

x² - 2x + 5 + (-12x + 5)/(x² + 2x - 1)

The Quotient  is [tex]x^{2} -2x+5[/tex] and The remainder is  -12x +5

How to Solve this Problem?

This problem can be solved by following steps

Learn More about Quotient and remainder here

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Answer:hello

Because negative can't go under the radical 2

For example we can't find two number that multiplication of them be negative. 2×2=4,-2×-2=4.

I'll hope that l explane for you weel

Step-by-step explanation:

Answer:

(x - 4)^2 + 4

Step-by-step explanation:

  x^2 - 8x + 20

= x^2 - 2*4*x + 16 + 4

= x^2 - 2*4*x + 4^2 + 4

= (x - 4)^2 + 4

= (x - a)^2 + a, with a = 4

Hope this helps!

Answer:

x - y = 0

Step-by-step explanation:

The given line is y = x.

We could re-write this as x - y = 0, which is in general form.

Answer:

The question is asking to complete the passage about the sum of angle of the exterior angles of an n-gon, one at each vertex, and i would say that it should be 360 degree.

Step-by-step explanation:

Answer:[tex]c=60+0.05d[/tex]

Step-by-step explanation:

Given

Company charges [tex]\$60[/tex]  for  [tex]1\ GB[/tex] data

and charges [tex]\$0.05/MB[/tex]

If c is the total cost and d represent no of additional megabyte then

Cost is given by the sum of fixed price + additional data charge

[tex]c=60+0.05\times d[/tex]

Therefore final charge is given by

[tex]c=60+0.05d[/tex]

Answer:

The probability that a customer buys a taco, a drink, or both is 45%.

Step-by-step explanation:

apeeex

P(A or B) = 0.45 mean in terms of this problem will be the probability that a customer buys a taco, a drink, or both is 45%. Then the correct option is A.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

The value of the probability of an event must lie between the interval of [0, 1].

A food truck sells tacos, burritos, and drinks.

Let event A = A customer buys a taco.

Let event B = A customer buys a drink

P(A or B) = 0.45 mean in terms of this problem will be the probability that a customer buys a taco, a drink, or both is 45%. Then the correct option is A.

More about the probability link is given below.

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Answer:

Multiply 20 x 0.75 = 15

Step-by-step explanation:

Answer:

1. Subtract 2 from both sides.

2. Multiply both sides by 2.

3. Take the square root of both sides.

4. Subtract 5 from both sides.

Answer:

Subtract 2 from both sides

Multiply both sides by 2

Take the square root of both sides

Subtract 5 from both sides

Step-by-step explanation:

Please refer to the picture attached.

Answer:

26 ft

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

10^2+24^2 = c^2

100 +576 = c^2

676 = c^2

Take the square root of each side

sqrt(676) = sqrt(c^2)

26 = c

Answer:

26 ft

Step-by-step explanation:

Pythagoras theorem

a^2+b^2=c^2

10^2+24^2=676

square root of 676= 26

Answer:

About 0.66 or in fraction form 2/3

Step-by-step explanation:

You divide 3.9 by 5.9

Answer:

39/59

Step-by-step explanation:

3.9 / 5.9

Multiply the top and bottom by 10 to clear the decimals

3.9*10 / 5.9 * 10

39/59

Since 59 is prime, this is the simplest form

Answer:

3 x 3 =9

Step-by-step explanation:

9

Answer: x

Step-by-step explanation: When dividing 3x by 3, the 3's will cancel each other out simply leaving us with our variable, x.

Answer:

1. sin P = 20/29

cos P = 21/29

tan P = 20/21

sin Q = 21/29

cos Q = 20/29

tan Q = 21/20

2. We can notice that the sin and cos of P vs Q are switched and the tan's are a reciprocal of each other

Step-by-step explanation:

For Part 1

With knowledge of SOH CAH TOA

Sin = Opp/Hyp

Cos = Adj/Hyp

Tan = Opp/Adj

So:

sin P = 20/29

cos P = 21/29

tan P = 20/21

sin Q = 21/29

cos Q = 20/29

tan Q = 21/20

For Part 2

We can notice that the sin and cos of P vs Q are switched and the tan's are a reciprocal of each other

Answer:

Step-by-step explanation:

1,5,11,19,29

the series of numbers :

A 2-A 1 = 5–1=4

A 3-A 2 = 11–5=6

A 4-A 3 =19–11=8   the third term is 8

A 5-A 4= 29-19= 10  the forth term is 10  

nth term  is 4+(n-1)2.

Answer:

The last one is the answer

Step-by-step explanation:

Answer:

1)The probability that the ball drawn is not red is 6 /14

2)Probability of getting either a prime or a multiple of 3 is 7/10

3)Probability of  drawing three balls without replacement such that all three are Same colour  is 0.0747

Probability of drawing three balls without replacement such that all three are different colour is 0.5

Step-by-step explanation:

1) A ball is drawn randomly from a bag containing 8 red, 4 blue and 2 green identical balls. Find the probability that the ball drawn is not red.

No. of red balls = 8

No. of blue balls = 4

No. of green balls = 2

Total no. of balls = 8+4+2=14

P(Getting red bal)=[tex]\frac{8}{14}[/tex]

P( ball drawn is not red) = [tex]1 - \frac{8}{14}=\frac{6}{14}[/tex]

So,the probability that the ball drawn is not red is 6 /14

2)What is the probability that a number chosen at random from the integers between 1 and 10 inclusive is either a prime or a multiple of 3?

Numbers : 1 ,2,3,4,5,6,7,8,9,10

Prime numbers: 2,3,5,7 = 4

Multiple of 3 = 3,6,9 =3

So, Probability of getting prime number =[tex]\frac{4}{10}[/tex]

Probability of getting multiple of 3 =[tex]\frac{3}{10}[/tex]

So, Probability of getting either a prime or a multiple of 3=[tex]\frac{4}{10}+\frac{3}{10}=\frac{7}{10}[/tex]

Hence  Probability of getting either a prime or a multiple of 3 is 7/10

3)A bag contains four red balls, five blue balls and six green balls. Three balls are drawn from the bag at random without replacement. What is the probability that all three are:

The same colour

Different colour

No. of red balls = 4

No. of blue balls = 5

No. of green balls = 6

Total balls = 15

Case 1 :all three are Same colour

So, probability of  drawing three balls without replacement such that all three are Same colour = [tex]\frac{4}{15} \times \frac{3}{14} \times \frac{2}{13}+\frac{5}{15} \times \frac{4}{14} \times \frac{3}{13}+\frac{6}{15} \times \frac{5}{14} \times \frac{4}{13}=0.0747[/tex]

So, probability of drawing three balls without replacement such that all three are different colour =[tex]\frac{4}{10} \times \frac{5}{9} \times \frac{6}{8}+\frac{5}{10} \times \frac{4}{9} \times \frac{6}{8}+\frac{6}{10} \times \frac{5}{9} \times \frac{4}{8}=0.5[/tex]

So,probability of  drawing three balls without replacement such that all three are Same colour  is 0.0747

So,probability of drawing three balls without replacement such that all three are different colour is 0.5

Answer:

hundreth's place

Step-by-step explanation:

see attached for explanation

Answer: b = -52/7 - 4a/7

Answer: A

Step-by-step explanation:

it intercepts y at -3 and you can find slope using rise/run

Answer:

n = -1

Step-by-step explanation:

→The fraction [tex]\frac{n}{5}[/tex] is really just [tex]\frac{1}{5}n[/tex]:

[tex]\frac{1}{5}n = \frac{-1}{5}[/tex]

→To get n by itself, you must multiply both sides by the reciprocal of [tex]\frac{1}{5}[/tex], which is 5:

5 · [tex]\frac{1}{5}n = \frac{-1}{5}[/tex] · 5

n = -1

Answer:

$22.5

Step-by-step explanation:

Jim gets 9*2.5= $22.5

$50/20=2.5

2.5*4=10

2.5*7=17.5

2.5*9=22.5

Jim gets $22.50

Answer:

The total budget for their student film is $600

Step-by-step explanation:

Here, we want to calculate the total budget of a group of students on a movie given the amount the spent on props.

Since we do not know this amount, we can call it x

Now, 45% of this x was the amount spent on props and it is equal to $270

Mathematically;

45/100 * x = 270

45x = 100 * 270

x = (100 * 270)/45

x = 600

Answer:

113 moteis

Step-by-step explanation:

A = 7 x 4 = 28 yards^2

1 yard - 0,9 m

1 yard^2 - 0,81 m^2

28 yards^2 - A

A = 28 x 0,81 = 22,68m^2

22,68 x 5 = 113,4

113 moteis

Answer:

140

Step-by-step explanation:

because it is

Answer:

The total length of the fox is 30 3/5 inches

Step-by-step explanation:

Here, we are interested in calculating the total length of a fox, given the length of its head and body and also the length of its tail.

Mathematically, the total length of the fox = length of its head and body + length of its tail

length of the head and body = 19 4/5

length of its tail = 10 4/5

Plugging these values into the equation, we have;

19 4/5 + 10 4/5

99/5 + 54/5 = (99 + 54)/5 = 153/5 = 30 3/5 inches

Answer:

[tex]x=-3,4[/tex]

Step-by-step explanation:

Factorise in order to reveal factors.

[tex]x^2-x-12=0\\(x-4)(x+3)=0[/tex]

Answer:

336

Step-by-step explanation:

To define whether we use permutations or combinations we must define whether or not the order in which we arrange the results matters. If the order matters we use permutations and if the order doesn't matter we use combinations.

In this case, since we are talking about the first places in a competition, order definitely does matter, so we use permutations. Also in permutations it must be indicated if repetition is allowed, in this case not because the same person cannot be in more than one place.

We use the following formula:

[tex]P=\frac{n!}{(n-r)!}[/tex]

where in this case n is the numer of swimmers and r is the number of places we are considering (1st 2nd and 3rd), which is 3 places.

n = 8

and

r = 3

thus the number of permutations is given bt:

[tex]P=\frac{8!}{(8-3)!}\\ \\P=\frac{8!}{5!} \\\\P=\frac{8*7*6*5*4*3*2*1}{5*4*3*2*1}\\ \\P=8*7*6\\P=336[/tex]

the answer is that there are 336 ways in which the swimmers can finish in first second and third place