Frank lost 5 points for not completing his homework, 3 points for talking, and 2 points for chewing gum. This happened 4 days in a row. Which expression represents the number of points Frank lost.

Answer:

The total amount of pollution discharged during the first 7 years of operation is 1.955 tons

Step-by-step explanation:

Given

[tex]r(t) = \frac{t}{t^2 + 1}[/tex]

Required

The total amount in the first 7 years

This implies that:

[tex]r(t) = \frac{t}{t^2 + 1}; [0,7][/tex]

The total amount is calculated by integrating r(t) i.e.

[tex]v = \int\limits^a_b {r(t)} \, dt[/tex]

So:

[tex]v = \int\limits^7_0 {\frac{t}{t^2 + 1}} \, dt[/tex]

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

We have:

[tex]t^2 + 1[/tex]

Differentiate

[tex]d(t^2 + 1) = 2t[/tex]

Rewrite as:

[tex]2t = d(t^2 + 1)[/tex]

Solve for t

[tex]t = \frac{1}{2}d(t^2 + 1)[/tex]

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

So:

Make t the subject

[tex]v = \int\limits^7_0 {\frac{t}{t^2 + 1}} \, dt[/tex]

[tex]v = \int\limits^7_0\frac{1}{2}* {\frac{d(t^2 + 1)}{t^2 + 1}} \, dt[/tex]

[tex]v = \frac{1}{2}\int\limits^7_0 {\frac{d(t^2 + 1)}{t^2 + 1}} \, dt[/tex]

Integrate

[tex]v = \frac{1}{2}\ln(t^2 +1)|\limits^7_0[/tex]

Expand

[tex]v = \frac{1}{2}[\ln(7^2 +1) - \ln(0^2 +1)][/tex]

[tex]v = \frac{1}{2}[\ln(50) - \ln(1)][/tex]

[tex]v = \frac{1}{2}[3.91 - 0][/tex]

[tex]v = \frac{1}{2}[3.91][/tex]

[tex]v = 1.955[/tex]

Answer:

C. 22

Step-by-step explanation:

The team played 75 games and 45 remaining.

75+45=120

60% of 120 = 0.6×120= 72

The team must win 72 games and they already won 50 games so the team has to win 72-50=22 games more.

Answer:

When the ticket price is $70, the weekly profit to the airline on flights from Boston to Washington is $1500.

Step-by-step explanation:

The function has the following format:

f(p)

That is, f is a function of p.

The derivative, f'(p), is the variation of f for the given value of p.

f'(70) = 1.5

p = 70, thus, ticket price of $70.

f'(70) = 1.5 means that the weekly profit to the airline on flights from Boston to Washington is 1.5 thousand dollars, that is, $1500.

Thus the correct answer is:

When the ticket price is $70, the weekly profit to the airline on flights from Boston to Washington is $1500.

Answer:

$54

Step-by-step explanation:

first find 1/4 of $80 and then take that answer and find 10% of that to get your answer

mEDF = 124°

Steps

360 = 146 + 90 + x

360 = 236 + x

-236 -236

124 = x

Answer:

m(EDF) = 214°

Step-by-step explanation:

GIVEN :-

TO FIND :-

FACTS TO KNOW BEFORE SOLVING :-

SOLUTION :-

According to the figure given in question ; in the orange circle ,

m(minor FE) + m(minor DE) + m(minor FD) = 360°

⇒ 146° + 90° + m(minor FD) = 360°

⇒ m(minor FD) = 360° - 236° = 124°

∴ m(major FE) [or] m(EDF) = m(minor DE) + m(minor FD) = 90° + 124° = 214°

Answer:

180⁰ 8. 20⁰ 3. rays and angle

Step-by-step explanation:

need ko po ang sagot

Answer:

18o rotational symetry  

Step-by-step explanation:

Answer:

a

Step-by-satep explanation:

just took it

Answer:

the aswer is 0.40 hope this helps

Step-by-step explanation:

Answer:

[tex]21^{\circ}[/tex]

Step-by-step explanation:

The Law of Sines is given by [tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex] and works for every triangle.

Substituting given values, we have the following equation:

[tex]\frac{\sin 68^{\circ}}{18}=\frac{\sin C}{7}, \\\\\sin C=\frac{7\sin 68^{\circ}}{18},\\\\C=\sin^{-1}(0.36057149899),\\\\C\approx \boxed{21^{\circ}}[/tex]

*Note that because [tex]\sin \theta=\sin(180-\theta)[/tex], when solving for an angle with the Law of Sines, there may be two answers. However, since the problem designates angle C as an acute angle, the other angle is negligible.

Answer:

a)  P (COO)  = 0,135

b) P ( SISI) = 0,00015

Step-by-step explanation:

a) the probability of an ion channel in open position is 50 %   0,5

   the probability of an ion channel in close position is 50 %   0,5

probability for the following sequence of states COO

to be closed   0,5    (C)

from (C) to pass to open  0,3  (O)

and to stay O  is 0,9

Then the probability of the sequence of states COO is

P (COO)  = 0,5 * 0,3 * 0,9  

P (COO)  = 0,135

b) If people are either infected or susceptible, then

Probability of an individual infected is  0,5

Probability of an individual susceptible  is 0,5

to pass from susceptible to infected is 0,05

to pass from infected to susceptible is 0,12

then

P ( SISI) = 0,5 * 0,05*0,12*0,05

P ( SISI) = 0,00015

probability for the following sequence of states COO

Answer:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100......

Step-by-step explanation:

This is a list of perfect squares.

1 is the square of 1. ( 1 x 1 = 2)

4 is the square of 2. (2 x 2 = 4)

9 is the square of 3. (3 x 3 = 9)

So, the next number would be the square of 4 which is 16 ( 4 x 4)

And so on.

Answer:

10.5

Step-by-step explanation:

65% of 70 is 45.5

So gold is 45.5 and silver is 54.5

so but45.5 + 54.5 = 100% but divide by 2

which is 50% but now we find 10% and 5%

10% = 7

5% = 3.5

now add 7 and 3.5 together

7+3.5 = 10.5

Answer:

592 cm

Step-by-step explanation:

16*10/2=80

16*10/2=80

16*12=192

10*12=120

10*12=120

Add all the sum, which would equal 592.

Hope this helps.

Answer:

a) 42

b) 42/120

Step-by-step explanation:

Oof, I was just about done with answering this question but I deleted it all by accident so I had to rewrite it.

Anyways, the first part of it is correct.

The second part of it is a bit harder. See, this is conditional probability, which uses the equation that I've attached below.

For Event A, you'll need the total boys / total students:

0.44166

For Event B, you'll need the total counters / total students:

0.83333

Now, plug these values into the equation. The weird U thingy is called "Union". It basically means "and".

P(A and B) / P(B)

P(0.44166 * 0.8333) / P(0.8333)

0.36803 / 0.8333

This is about 0.44165, or 53/120

Answer:

28 meters²

Step-by-step explanation:

Area of triangle = 1/2(base x height).

It is given that:

base = 4 meters

height = 14 meters

Plug in the corresponding numbers to the corresponding terms:

Area of the triangle = 1/2(4 * 14)

Area of the triangle = (4 * 14)/2

Area of the triangle = 56/2

Area of the triangle = 28 meters²

Answer:

The answer is 28 meters^2.

Step-by-step explanation:

To solve for the area of the triangle, start by using the area of a triangle formula, which is A= [tex]\frac{1}{2}[/tex] bh.

Next, plug in the information from the question into the formula. The formula will look like A= [tex]\frac{1}{2}[/tex](4)(14).

Then, solve the equation, and the final answer will be 28 meters^2.

Sn = a(1-r^n)/(1-r)

Sn= 8(1-1/4096)/3= 2.67

Answer:

1/2

Step-by-step explanation:

Given the equation

6/12 = x/8

We are to find the proportion

Cross multiply

12 * x  = 8 * 6

12x = 48

x = 48/12

x = 4

Hencethe value of x is 4

Substitute into the expression to get the proportion

6/12 = 4/8

In its lowest term;

6/12 = 4/8 = 1/2

Hence the required proportion is 1/2

Answer: Volume is 4308.1 in³

Step-by-step explanation: Volume is  pii· r²·h = 3.14 · (14 in)²·7 in

Answer:

D.  36 ft

Step-by-step explanation:

5 feet added to each of 4 sides is 20 feet

56 - 20 = 36

Answer:

Equation: y = (1/2)x - 1

Step-by-step explanation:

Answer:

There are 12 stools in the room

Answer:

Step-by-step explanation:

1*1*1/3*2*4=V

1/24=V

multiply all numerator and all denominator.

Answer:

(5 · x) + (8 · y) + (2 · 1)

Answer:

5x + 2 ( 4y + 1 )

Step-by-step explanation:

i just factorised 8y + 2

Answer:

b = 5√6

c = 10√5

Step-by-step explanation:

This is a 30-60-90 triangle

the hypotenuse is always twice the short leg

c = 2(5√2)

c = 10√5

The long leg is alway √3 times the short leg

b = √3(5√2)

b = 5√6

Between the 4 and the 7 is it a multiplication or an X?

If the multiplication sign, this is the solution

[tex] - 3x + 6v + 7 \times 14 \\ = 6v - 3x + 98[/tex]

Answer:

Step-by-step explanation:

2