You want to limit the amount of television you watch to an average of at most 1.5 hours per week during an 8-week period. How many hours x of television must you watch in the eighth week to meet your goal?


Television Viewing

Week....... Hours Watched

1 .......................1

2 .....................1.5

3 .....................0.5

4 .......................3

5 ......................1.5

6 ........................2

7 .......................0.5

If |q| = 5 at an angle of 45° and |r| = 16 at an angle of 300°. then the

|q – r| will be 18.0

To find |q - r|, we need to subtract the complex numbers q and r after which discover the magnitude (or absolute value) of the end result.

First, we want to express q and r in rectangular form, which means that finding their actual and imaginary additives:

For q, we've:

|q| = 5 at an perspective of 45°

Re(q) = |q| cos(45°) = five cos(45°) = 5/√2

Im(q) = |q| sin(45°) = 5 sin(45°) = 5/√2

So q = (5/√2) + (5/√2)i

For r, we have:

|r| = 16 at an angle of 300°

Re(r) = |r| cos(300°) = 16 cos(300°) = sixteen(-√3/2) = -8√three

Im(r) = |r| sin(300°) = 16 sin(300°) = -8

So r = -8√three - 8i

Now we are able to discover q - r by using subtracting the actual and imaginary additives:

q - r = (5/√2) + (5/√2)i - (-8√3 - 8i)

= (5/√2) + 8√3 + (5/√2 + 8)i

To discover |q - r|, we want to take the importance of this complex number:

|q - r| = √[(5/√2 + 8√3)² + (5/√2 + 8)²]

= √[25/2 + 80√3 + 192 + 50/2 + 40 + 64]

= √[125/2 + 80√3 + 256]

= √[625/4 + 320√3 + 1024]

= √[(25/2 + 16√3)²]

= 25/2 + 16√3

≈ 18.0

Hence, |q - r| is about equal to 18.0.

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We are given a function y = -4x^3 - 9x^11, and we need to find its first and second derivatives.

To find the first derivative, we apply the power rule and the constant multiple rule. The power rule states that the derivative of x^n is nx^(n-1), and the constant multiple rule states that the derivative of kf(x) is k*f'(x), where k is a constant. Applying these rules, we can find the first derivative of y = -4x^3 - 9x^11.

Taking the derivative term by term, the first derivative of -4x^3 is -43x^(3-1) = -12x^2, and the first derivative of -9x^11 is -911x^(11-1) = -99x^10. So, the first derivative of y is dy/dx = -12x^2 - 99x^10.

To find the second derivative, we apply the same rules to the first derivative. Taking the derivative of -12x^2, we get -122x^(2-1) = -24x, and the derivative of -99x^10 is -9910x^(10-1) = -990x^9. Therefore, the second derivative of y is d^2y/dx^2 = -24x - 990x^9.

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Answer:

Step-by-step explanation:

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Answer:

The voltage is 110 V

Step-by-step explanation:

Given;

current in the circuit, I = 20 A

resistance in the circuit, R = 5.5 Ω

voltage in the circuit, V = ?

Voltage is given as = current x resistance

V = IR

V = 20 x 5.5

V = 110 V

Therefore, the voltage necessary to generate 20 amps of current in a circuit that has 5.5 ohms of resistance is 110 volts.

Answer:

1/1

Step-by-step explanation:

i hate math do you hate math?

Assuming that we are starting with a pool of 8 people, we can form the committee in 8 different ways. This is because the committee must contain exactly 3 Ravenclaws, 1 Gryffindor, and 4 people from other houses.

First, we will choose 3 Ravenclaws from the 8 people. This can be done in 8 combinations. Then, we will choose 1 Gryffindor from the remaining 5 people. This can be done in 5 combinations. Lastly, we will choose 4 people from the remaining 4 people, which can be done in 4 combinations.

By multiplying the number of combinations, we get for each step, we can conclude that the total number of ways to form an 8-person committee with the requirement is 8 x 5 x 4 = 160. However, since the order of the people in the committee does not matter, this total number is reduced to 8. In conclusion, we can form the 8 person committee with the given requirement in 8 different ways.

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The probability that joe and jane end up in the same class is 0.3258 .

In the question ,

it is given that

90 students is to be split into 3 equal size classes , so ,

the three classes  will have 30 students each .

let these classes be Class A , Class B and Class C .

Let Joe and Jane be in Class A .

the total number of ways of selecting 30 students for class A from 90 students is C(90,30) .

Since , we have fixed Joe and Jane in Class A , the remaining 28 spots of class A can be filled by remaining 88 students  in C(88,28) ways ,

So , the probability that Joe and Jane end up in the same class is

= C(88,28)/C(90,30) .

Since there are three  classes ,

the required probability is 3*C(88,28)/C(90,30) .

= 3×\(\frac{88!}{28!*60!}\)×\(\frac{60!*30!}{90!}\)

= 29/89

= 0.3258

Therefore , the probability that joe and jane end up in the same class is 0.3258   .

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Answer:

2198 cm²

Step-by-step explanation:

Total surface area of a cylinder = 2πrh + 2πr²

Radius, r = diameter/2

= 20cm/2

= 10 cm

Height, h = 25 cm

Total surface area of a cylinder = 2πrh + 2πr²

= 2*3.14*10*25 + 2*3.14*10²

= 1,570 + 6.28*100

= 1,570 + 628

= 2198 cm²

Total surface area of a cylinder = 2,198 cm²

Using a system of equations, it is found that the original number of students in Group B was of 120.

A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable.

In the context of this problem, the variables are described as follows:

There are 270 total students, hence:

x + y = 270.

x = 270 - y. (as we want to find y).

If 30 students move to Group B from Group A, then there will be twice as many students in Group A as in Group B, hence:

x + 30 = 2(y - 30).

Replacing the relation of the first equation on the second, it is found that:

270 - y + 30 = 2y - 60

3y = 360

y = 360/3

y = 120.

The original number of students in Group B is of 120.

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Answer:

Quarters=7

Dime=8

Nickel=2

Step-by-step explanation: 8*.10=.80, 2*.05=.10, 7*.25=1.75 If you add them up you get 2.65.

Answer: The table is shown in the attached image

The commas are not to be entered in any of the boxes. Just the numbers only.

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

Explanation:

"47 seventh graders were surveyed" means that 47 goes in the last value of the first row. This is the total of the 7th graders. Of this total, 19 pack their lunches (ie bring them from home). That indicates 47-19 = 28 seventh graders buy their lunch.

For row one, we have the values: 19, 28, 47 in that exact order when going from left to right.

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

We use the same idea for the 8th graders.

52 total eighth graders, 33 buy their lunch

52-33 = 19 pack their lunch

For row two, the values from left to right are: 19, 33, 52 in that exact order.

To get the values in row 3, we add up everything that's over top of it.

Meaning for column 1, we have 19+19 = 38 total students who pack their lunch. In column 2, there are 28+33 = 61 people who buy their lunch. Lastly, column 3 we have 47+52 = 99 students overall.

For row three, the values from left to right are: 38, 61, 99

Note that adding the first two items of row three gets us 38+61 = 99

It's not a coincidence that this is happening. This is just another way to get the grand total of 99. You could also add up the four values that are not in the total column or total row to get 19+28+19+33 = 99. Again, this is not a coincidence we end up with 99.

Refer to the table below to see a summary.

Answer: See explanation

Step-by-step explanation:

Your question isn't complete as you didn't tell us the total amount of liters of water that we have. Let's assume that the total amount of liters of water is 50 liters a d we are told to divide it into 4 containers.

The amount of liters that each container will get will be:

= 50 liters / 4

= 12 1/2 liters each

Answer:

18.4

Step-by-step explanation:

9.2 + 9.2 = 18.4

Answer:

6

Step-by-step explanation:

If you were scaling it by 1/6 it would be smaller.

To accumulate $3887 by investing $3078 at an annual interest rate of 4.4% compounded monthly, it will take Andrew a certain amount of time.

To find out how long it will take Andrew to accumulate $3887, we can use the formula for compound interest:

A = P\((1 + r/n)^{nt}\)

Where:

A = the final amount (in this case, $3887)

P = the principal amount (in this case, $3078)

r = annual interest rate (4.4% or 0.044)

n = number of times the interest is compounded per year (12 for monthly compounding)

t = number of years

We need to solve for t. Rearranging the formula, we have:

t = (1/n) * log(A/P) / log(1 + r/n)

Substituting the given values, we get:

t = (1/12) * log(3887/3078) / log(1 + 0.044/12)

Evaluating this expression, we find that t ≈ 0.57 years. Therefore, it will take Andrew approximately 3.42 years to accumulate the required amount of $3887 by investing $3078 at a 4.4% annual interest rate compounded monthly.

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The derivative of y = cos^3(e^5x) is dy/dx = -15e^5x sin(e^5x)cos^2(e^5x).

To compute the derivative of the function y = cos^3(e^5x), we will use the chain rule and the power rule of differentiation.

Let's denote u = e^5x. Applying the chain rule, the derivative of the outer function cos^3(u) with respect to u is -3sin(u)cos^2(u).

Now, we need to differentiate the inner function u = e^5x. The derivative of e^5x with respect to x is 5e^5x.

Multiplying these two derivatives together, we get:

dy/dx = -3sin(u)cos^2(u) * 5e^5x

Replacing u with e^5x, we have:

dy/dx = -3sin(e^5x)cos^2(e^5x) * 5e^5x

Therefore, the derivative of y = cos^3(e^5x) is dy/dx = -15e^5x sin(e^5x)cos^2(e^5x).

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The standard error of the sample mean of a given sample of 43 observations with standard deviation 8.85 is equal to 1.35 ( round to 2 decimal places).

As given in the question,

Population mean of the random variable 'μ' = 141

Standard deviation 'σ' = 8.85

Sample size 'N' = 43 observations

Standard error of the sample mean

= σ / √N

= 8.85 / √43

= 8.85 / 6.56

= 1.349

= 1.35 (round to 2 decimal places )

Therefore, for the given standard deviation and sample size the standard error of the sample mean is equal to 1.35.

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Answer:

y= -4x-24

Step-by-step explanation:

change in y/change in x = 0- -24/-6-0 = 24/-6 = -4

gradient is -4

then you put a set of coradinates into the formular y-y=m(x-x)

y - 0= -4 (x+6)

y-0=-4x-24

y=-4x-24

Answer:

  4x +y = -24

Step-by-step explanation:

The given points are the x- and y-intercepts. It is convenient to write the equation in intercept form:

  x/a +y/b = 1 . . . . . . x-intercept 'a', y-intercept 'b'

  x/-6 +y/-24 = 1 . . . . . equation in intercept form

  4x +y = -24 . . . . . . . equation in standard form (multiply by -24)

Answer:

955.0 ft^3 remains in A

Step-by-step explanation:

Volume of a cylnder = V = pi r^2 h

A:   pi (9)^2 *9   =  729 pi    (Note:  You are given DIAMETER...need RADIUS)

B:   pi  (5)^2 *17  = 425 pi

A - B =  pi ( 729 - 425) = 955.0 ft^3 remains

Step-by-step explanation:

y = kx, where k is a real constant.

When x = 12, y = 60.

=> (60) = (12)k, k = 5.

Therefore when x = 20,

y = kx = (5)(20) = 100.

James deposited $12,500 into a savings account that earns 4.5% annual simple interest. James can expect to earn $562.50 in interest at the end of the year.

Assuming he doesn't make any additional deposits or withdrawals, he can expect to earn $562.50 in interest at the end of the year. Simple interest is calculated by multiplying the principal amount by the interest rate and the time period. In this case, the principal amount is $12,500, the interest rate is 4.5%, and the time period is one year. Therefore, the interest earned is calculated as follows:
Interest = Principal x Rate x Time
Interest = $12,500 x 4.5% x 1
Interest = $562.50

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The sum of the measures of the interior angles of a polygon with n sides can be found using the formula (n-2) * 180 degrees.

For a 10-sided figure, we have (10-2) * 180 = 8 * 180 = 1,440 degrees.

Therefore, the sum of the measures of the interior angles of a 10-sided figure is 1,440°.

The answer is A.

Answer:

Hey man I have the same Problem too for my class but I don’t know what the answer is eather so I’m going with b

Step-by-step explanation:

There are 87 possible outcomes that contain at least three heads when a coin is flipped 9 times.

When a coin is flipped nine times, there are 512 possible outcomes, or 29. Using the equation:

P (At least one head) = 1 - 0.5n,

where n is the total number of flips, we can determine the number of outcomes that contain at least three heads.

Therefore, P (At least three heads) = 1 - P (No heads) - P (One head) - P (Two heads)

= 1 - (0.5)⁹ - 9(0.5)⁹ + 36(0.5)⁹

= 0.1718751.

The formula used to calculate the number of possible outcomes that contain at least three heads is C(9,3) + C(9,4) + C(9,5) + C(9,6) + C(9,7) + C(9,8) + C(9,9),

where C(n,r) denotes the variety of options for selecting item(s) r from a set of item(s) n.

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The molar mass of the unknown gas in the steel container is 31.3637 g/mol.

Given that:

Pressure, P = 9.99 atm

The volume of the container, V = 20 L

R = 0.0821 atm L / mol.K

Temperature, T = 25°C

                          = 25 + 273.16

                          = 298.16 K

Number of moles, n = n(C0₂) + n(N₂) + n(unknown gas)

Now, molar mass = Mass / Number of moles.

The molar mass of CO₂ = 12.01 + 2(16) = 44.01 g/mol

So, n(C0₂) = 77.7 / 44.01 = 1.7655

The molar mass of N₂ = 2 (14.01) = 28.02 g/mol

So, n(N₂) = 99.9 / 28.02 = 3.5653

So, n = 1.7655 + 3.5653 + n(x), where x represents the unknown gas.

Substitute the values in the gas equation.

PV = n RT

9.99 × 20 = (1.7655 + 3.5653 + n(x)) × 0.0821 × 298.16

199.8 = 24.478936(5.3308 + n(x))

5.3308 + n(x) = 8.162

n(x) = 2.8313 moles

So, the molar mass of the unknown gas is:

m = 88.8 / 2.8313

   = 31.3637 g/mol

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Hey there!

-2<3x+1

= 3x + 1 < -2

SUBTRACT 1 to BOTH SIDES

3x + 1 - 1 < -2 + 1

CANCEL out: 1 - 1 because that gives you 0

KEEP: -2 + 1 because that helps you solve for x

-2 + 1 = -3

New EQUATION: 3x > -3

DIVIDE 3 to BOTH SIDES

3x/3 > -3/3

CANCEL out: 3/3 because that gives you 1

KEE3 -3/3 because that helps us compare for x

-3/3 = -1

Answer to the equation: x > -1

OVERALL Answer: x > -1; It is an OPENED circle shaded to the right starting at -1 (Option A.)

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

5, 3

Step-by-step explanation:

correct on edge2020

Answer:

(5, 3)

Step-by-step explanation:

late but still lol

In both the U.S.A. and England, there are only two days of the year that share the same symbol: May 2 (5/2) and February 5 (5/2).

In the United States, the symbol 5/2 is interpreted as the 5th month and 2nd day, representing May 2. On the other hand, in England, 5/2 denotes the 5th day and 2nd month, indicating February 5. To determine how many days of the year have the same symbol in both countries, we need to find the dates that match.

In the U.S., there are 12 months, so there are 12 possible combinations with 5 as the month. However, only May 2 (5/2) coincides with the English interpretation.

In England, there are 31 days in January, so there is no match with the American format. However, in February, there are 28 days (or 29 in a leap year), and February 5 (5/2) aligns with the American interpretation.

Hence, there are only two days of the year that share the same symbol in both the U.S. and England: May 2 (5/2) and February 5 (5/2).

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Answer:

Hi,

Step-by-step explanation:

x>=0

y>=0

x+y-5<=0 line passing through (0,5)  and (5,0) with (0,0) in minus region

2x-y-8<=0 line passing trough (0,-8) and (4,0) with (0,0) in minus region

Answer C

La razón de cambio de la longitud de la sombra es \(\dot x = \frac{15}{7} \,\frac{ft}{s}\).

Sabemos que la longitud de la sombra (\(x\)), en pies, aumenta a medida que la niña se aleja del poste. Se puede derivar una expresión para la longitud de la sombra a partir de la semejanza entre dos triángulos rectángulos:

\(\frac{x}{5} = \frac{x+y}{12}\)

\(\frac{12\cdot x}{5} = x+y\)

\(y = \frac{7\cdot x}{5}\) (1)

Donde \(y\) es la distancia entre la niña y el poste, en pies.

Luego, obtenemos la expresión de razón de cambio por cálculo diferencial:

\(\dot x = \frac{5\cdot \dot y}{7}\) (2)

Donde:

Si sabemos que \(\dot y = 3\,\frac{ft}{s}\), entonces por (2) tenemos que la razón de cambio de la longitud de la sombra es \(\dot x = \frac{15}{7} \,\frac{ft}{s}\). \(\blacksquare\)

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