1 /4 of the schoolyard is used by the fifth graders for recess, as shown by the shaded part of the diagram. Teachers have 3 different activities planned for recess that will take up the same amount of space.

Answer:

(2P + G) feet/min

Step-by-step explanation:

Speed of the panda = P

Speed of the giraffe = P + G

Thus,

Speed of Panda + Speed of Giraffe = approaching time

= P + P + G

= 2P + G

Thus, The panda and the giraffe are approaching each other at a rate

of (2P + G) ft/min

Hope it helps :)

Answer:2p+g

Step-by-step explanation:

2+p+g=

2p+g

Answer:

The Median is 75

Step-by-step explanation:

median is the middle number in a set of given numbers

arranging in order will be

30,64,70,80,90,110

the middle numbers are 70 and 80

Median=80+70/2

=150/2

Median=75

ANSWER

14 days

EXPLANATION

The mean of a data set is the sum of all data, divided by the number of data,

In this case, the number of data is 6, so the mean is,

Hence, the mean number of days taken for medical leave each month is 14.

The angle that corresponds to point P on the polar curve r with y-coordinate 1 is given by arccos(x/sqrt(x^2 + 1)).

To find the angle that corresponds to point P on the polar curve r with y-coordinate 1, we need to determine the value of theta at point P.

The y-coordinate of point P is given as 1, which means that the point lies on the line y = 1. Since the polar curve is given in terms of r and theta, we need to eliminate r and express theta in terms of x and y coordinates.

We know that r^2 = x^2 + y^2, and substituting y = 1, we get r^2 = x^2 + 1. Hence, r = sqrt(x^2 + 1).

Now, we can express theta in terms of x and y as theta = arctan(y/x) = arctan(1/x). Substituting r in terms of x, we get theta = arctan(1/x) = arccos(x/sqrt(x^2 + 1)).

Therefore, the angle that corresponds to point P on the polar curve r with y-coordinate 1 is given by arccos(x/sqrt(x^2 + 1))

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Answer:

JL = √38.

a = 1 and b = 38.

Step-by-step explanation:

Using Pythagoras:

(JL)^2 = (√8)^2 + (√30)^2

(JL)^2 = 8 + 30 = 38.

JL = √38.

The value of the discriminant when a quadratic equation has exactly one real number solution is zero.

If a quadratic equation has exactly one real number solution, it means that the discriminant of the quadratic equation is equal to zero. The discriminant is a value calculated from the coefficients of the quadratic equation and determines the nature of its solutions.

For a quadratic equation of the form ax^2 + bx + c = 0, the discriminant (D) is given by the formula:

D = b^2 - 4ac

When a quadratic equation has exactly one real number solution, it means that the discriminant is equal to zero:

D = 0

Setting the discriminant to zero, we can solve for the value of the discriminant:

b^2 - 4ac = 0

Therefore, the value of the discriminant when a quadratic equation has exactly one real number solution is zero.

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Answer:

It should be multiplied by 100.

Poppy's sister used approximately 3.14 inches more wire per wall hanging than Poppy.

To find the amount of wire used by both Poppy and her sister, we'll calculate the circumference of their respective wall hangings using the formula:

C = 2πr

Since the diameter is twice the radius, we can find her sister's radius as follows:

Poppy's radius = 6.25 inches

Poppy's diameter = 2 * 6.25 = 12.5 inches

Sister's diameter = Poppy's diameter + 1 = 12.5 + 1 = 13.5 inches

Sister's radius = 13.5 / 2 = 6.75 inches

Now, we'll calculate the circumferences using the given value for π:

Poppy's circumference = 2 x 3.14 x 6.25 ≈ 39.25 inches

Sister's circumference = 2 x 3.14 x 6.75 ≈ 42.39 inches

Difference = Sister's circumference - Poppy's circumference

Difference = 42.39 - 39.25 = 3.14 inches

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The legal context and definitions are (a) Negligence - Establishes the link between the defendant's actions and the plaintiff's harm. (b) Negligence defenses - Plaintiff voluntarily accepts known risks, relieving the defendant of liability. (c) Invasion of privacy - Unjustified intrusion into private affairs that would offend a reasonable person. (d) Negligence - Accident itself suggests defendant's negligence without direct evidence (e) Defamation - False spoken statements harming someone's reputation (f) Monetary awards to punish and deter egregious behavior. (g) Defamation defenses - Immunity for certain statements made in specific contexts.

(a) Cause-in-fact

Legal context: Negligence.

Definition: Cause-in-fact refers to the actual cause or link between the defendant's conduct and the plaintiff's harm, establishing that the harm would not have occurred without the defendant's actions.

(b) Assumption of risk

Legal context: Negligence defenses.

Definition: Assumption of risk is a defense in negligence cases where the plaintiff voluntarily and knowingly accepts the risks associated with a certain activity, relieving the defendant of liability for any resulting harm.

(c) Seclusion

Legal context: Invasion of privacy.

Definition: Seclusion refers to the intentional and unjustified intrusion into an individual's private affairs or seclusion, which would highly offend a reasonable person.

(d) Res ipsa loquitur

Legal context: Negligence.

Definition: Res ipsa loquitur is a doctrine where the occurrence of an accident or injury itself suggests that the defendant was negligent, allowing the plaintiff to establish a prima facie case without direct evidence of negligence.

(e) Slander

Legal context: Defamation.

Definition: Slander is a form of defamation that involves making false spoken statements about someone that harm their reputation.

(f) Punitive damages

Legal context: Various tort subject areas.

Definition: Punitive damages are monetary awards beyond compensatory damages, awarded in certain cases to punish the defendant for particularly egregious behavior and to deter others from similar conduct.

(g) Absolute privilege

Legal context: Defamation defenses.

Definition: Absolute privilege is a defense in defamation cases that grants immunity from liability for statements made in certain contexts, such as during legislative or judicial proceedings, regardless of their truth or intent.

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--The given question is incomplete, the complete question is given below " For each term (1) identify the legal context in which it arises; and (2) define the term.

For the legal context part of your answer for each term, indicate which tort subject area the term relates to (e.g., "fraud," “false imprisonment,” “defamation,” “defamation defenses,” “invasion of privacy,” “interference with contract,” “interference with prospective economic advantage,” “negligence,” “negligence defenses,” “strict liability,” or, if and where appropriate, “intentional torts” generally).

In addition, the definition portions of your answers need not be more than one sentence for each term. Your answer for each term is worth a maximum of 2 points.

(a) cause-in-fact

(b) assumption of risk

(c) seclusion

(d) res ipsa loquitur

(e) slander

(f) punitive damages

(g) absolute privilege"--

Answer:

-11.5

Step-by-step explanation:

I just did it on the calculator :)

Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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The polynomial function \(\(f(x) = 2(x^2+3)(x+1)^2\)\) has zeros at -3 with multiplicity 1, and -1 with multiplicity 2. The graph of the function crosses the x-axis at -3 and -1.

To find the zeros and their multiplicities, we set \(\(f(x)\)\) equal to zero and solve for \(\(x\).\)

Setting \(\(f(x) = 0\),\) we have:

\(\[2(x^2+3)(x+1)^2 = 0\]\)

Since the product of two factors is zero, at least one of the factors must be zero. Thus, we solve for \(\(x\)\) in each factor separately:

1. \(\(x^2 + 3 = 0\):\)

  This equation does not have real solutions since the square of a real number is always non-negative. Therefore, this factor does not contribute any real zeros.

2. \(\(x + 1 = 0\):\)

  Solving for \(\(x\), we find \(x = -1\).\) This gives us a zero at -1 with multiplicity 1.

Since the factor \(\((x+1)^2\)\) is squared, the zero -1 has a multiplicity of 2.

Therefore, the zeros for the polynomial function are -3 with multiplicity 1 and -1 with multiplicity 2. The graph of the function crosses the x-axis at both zeros.

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To multiply mixed numbers, convert to improper fractions, cancel factors, multiply the remaining factors, and simplify if possible.

Increasing blended numbers can be tedious, yet there is an easy route that can work on the interaction. To duplicate blended numbers, convert them to ill-advised portions, then drop any elements that show up in both the numerator and denominator of the divisions. At long last, duplicate the leftover elements in the numerator and denominator and work on the subsequent division if conceivable. For instance, to duplicate 2 1/2 by 3 2/3, first proselyte them to inappropriate divisions, which are 5/2 and 11/3. Then, drop the variable of 2 in the numerator of the principal portion and the denominator of the subsequent division. The outcome is 55/3, which can be improved to 18 1/3. This alternate way can save time and assist understudies with taking care of augmentation issues all the more proficiently.

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Answer:

Step-by-step explanation:

d i think

Answer:

d I am pretty sure from what is looks like

Answer:170

Step-by-step explanation:

If 25% is 85 then multiply 25% by 2 to get 50% and 85 by 2 to get 179

Answer:

187

Step-by-step explanation:

Answer:

neutrons and protons

Step-by-step explanation:

Answer:

The turkey has to be put in the oven at 7:10 AM.

Step-by-step explanation:

We have:

Turkey stuffed with 16 pounds

Since the time of cooking is 15 minutes per pound with an addition of 5 minutes per pound when the turkey is stuffed, hence we have:

\(T = 16 pounds*15 \frac{min}{pound} + 5 \frac{min}{pound}*16 pounds = 320 min = 5 h + 20 min\)

Therefore, the total time of cooking is 320 minutes or 5 hours plus 20 minutes.

If they plan to eat at 1:00 PM with 30 minutes for cooling and carving, then:

\(t_{o} = 13 h - 5.33 h - \frac{1}{2} h = 7 h + 10 min\)

Hence, the turkey has to be put in the oven at 7:10 AM.

I hope it helps you!        

Answer:

7 years

Step-by-step explanation:

Let W = number of years they both have to work to make the same amount :

Amount made by Jaylon = 57000

Annual raise = 2500

Titak made after W years :

57000 + 2500w - - - (1)

Amount made by Anita = 64000

Annual raise = 1500

Total made after w years :

64000 + 1500w - - - (2)

Equate (1) and (2)

57000 + 2500w = 64000 + 1500w

2500w - 1500w = 64000 - 57000

1000w = 7000

w = 7000/ 1000

w = 7

Hemce, they'll both earn the same amount after 7 years

Answer:

Step-by-step explanation:each friend will get 9 beads.

Answer:

31

Step-by-step explanation:

Answer:

10^3×10^3

is 100000000 which is 10^7 in index form.

Answer:

5:46pm

Step-by-step explanation:

6:32 - :46 =

6:00 = :46 - :32 = :14

6:00 = 5:60

5:60 - :14 = :60 - :14 = :46

5:46

Answer:

Distancia restante = 1,3 kilómetroslp

Step-by-step explanation:

Dados los siguientes datos;

Distancia total = 4,5 km

Distancia recorrida = 3200 metros a kilómetros = 3200/1000 = 3,2 km

Para encontrar la distancia restante para cubrir la longitud requerida;

Distancia total = distancia recorrida + distancia a la izquierda

4.5 = 3.2 + distancia a la izquierda

Distancia a la izquierda = 4.5 - 3.2 Distancia restante = 1,3 kilómetros

The volume of the composite figure is solved to be

The volume of the composite figure is calculated by dividing the figure into simpler figure and solve each volume. The volumes calculated is the added to give the volume of the composite figure

formula for volume = length x width x depth

First simpler part

volume = 10.5 ft x 3 ft x 6 ft

volume = 189 cubic ft

second simpler figure

volume = (9 - 3) ft x 4 1/2 ft x 6 ft

volume = 162 cubic ft

volume of the composite figure

= 189 + 162

= 351 cubic ft

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Answer:

12 + 1x = 236 maybe that

Step-by-step explanation:

The half-life of a radioactive substance refers to the time it takes for half of the substance to decay. In this case, the substance decayed to 95% of its original amount after one year.

To find the half-life, we need to determine how much of the substance is left after one half-life. Since the substance decayed to 95% of its original amount, it means that 5% has decayed.

Now, let's set up an equation to solve for the half-life. We know that after one half-life, only 50% of the substance will remain. So, we can set up the following equation:
100% - 5% = 50%

Simplifying the equation, we get:
95% = 50%
To find the half-life, we need to determine how many times 5% can be halved to reach 50%.
Let's divide 95% by 5%:
95% ÷ 5% = 19
Therefore, it takes 19 half-lives for the substance to decay to 50% of its original amount.

Since we know that the substance decays to 50% of its original amount after one year, we can divide one year by 19 to find the half-life.
1 year ÷ 19 = 0.0526 years
Rounding to two decimal places, the half-life of the substance is approximately 0.05 years.

In summary, the half-life of the radioactive substance is approximately 0.05 years.

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The calculate value of the firm is the  growth rate of the firm's profit is 5 percent, the interest rate is 6 percent, and the current profits of the firm are $80 million = 8480 million

(1+r/r -p) * P

This can be substituted in the equation

1.06/ ( 0.06 - 0.05) * 80 million = 8480 million

Hence the value of the firm is given as  8,480 million dollars. The correct answer is C.

Suppose the growth rate of the firm's profit is 5 percent, the interest rate is 6 percent, and the current profits of the firm are $80 million, the value of the firm is 8480 million

Complete question

Suppose the growth rate of the firm's profit is 5 percent, the interest rate is 6 percent, and the current profits of the firm are $80 million. What is the value of the firm?

A. $89.2 million

B. $1,413.3 million

C. $8,480 million

D. None of the statements associated with this question are correct.

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The difference in the account balances at the end of the loan terms is given as follows:

$1,686.87.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

The parameters for the offer 2 are given as follows:

P = 75000, r = 0.035, n = 12, t = 62/12.

Hence the balance of the offer 2 is given as follows:

B = 75000 x (1 + 0.035/12)^(12 x 62/12)

B = $89,842.51.

The balance of Offer 1 is of $91,529.38, hence the difference in the balances is given as follows:

91529.38 - 89842.51 = $1,686.87.

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Answer:

\(x=20\)

Step-by-step explanation:

Solve the following equation for x:

\(1500=1/3(15)^{2} x\)