An object is launched directly in the air at a speed of 64 feet per second from a platform located 16 feet above the ground. The position of the object can be modeled using the function f(t)=−16t2+64t+16, where t is the time in seconds and f(t) is the height, in feet, of the object. What is the maximum height, in feet, that the object will reach?

The closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is 14

From the question, we have the following ordered pairs

x intercepts = (6,0) and (18, 0)

Vertex = (12, -36)

Points (21, 41.25)

The closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is the calculated using

m = [f(21) - f(18)]/[21 - 18]

This becomes

m = [f(21) - f(18)]/3

Substitute the known values in the above equation

m = [41.25 - 0]/3

Evaluate the difference

m = 41.25/3

Evaluate the quotient

m = 13.75

Approximate

m=14

Hence, the closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is 14

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Complete question

The graph below shows the value of Edna's profits f(t), in dollars, after t months:

What is the closest approximate average rate of change for Edna's profits from the 18th month to the 21st month?

See attachment for graph

Answer:

Side b is the longest because the longer side always lie opposite the bigger angle. Angle B is the biggest angle, and since side b is opposite angle B, side b is the longest.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

The side opposite to the largest angle is the longest side of a triangle.

[tex] \qquad \large \sf {Conclusion} : [/tex]

hence, we can conclude that the longest side is b

( since it's opposite angle is the largest, i.e 91° )

Answer:

16

Step-by-step explanation:

18,903

Answer:

d - 7

Step-by-step explanation:

The word "difference" tells us that we will be using subtraction. Also, subtraction is not the same if you reverse the terms like, x - 2 and 2 - x are not the same. In your question it say "d and 7" so that's the order we use in the algebraic expression.

The inverse equation of x = y is y = x

Inverse equations are the opposite of an original equation

The equation is given as

x = y

Swap the positions of x and y in the above equation

y = x

This means that the inverse equation of x = y is y = x

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The statements with their correct matches in relation to 0 are:

When a building is 37 feet tall, it means that if 0 feet was the ground level, the building would be 37 higher than 0. This is the same for the basement which will be -13.7 in relation to a ground level of 0.

Erica jumping 2.5 feet above the ground is 2.5 in relation to 0feet and the scuba driver is -37 by the same relation to 0 feet.

Oliver owes his sister $25 which means that in relation to a state of no debt or $0, Oliver is -25 deep in debt.

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Answer:

100, 25, 50

Step-by-step explanation:

[tex]700: \frac{700}{700} \times 100=100 \\ \\ 175: \frac{175}{700} \times 100=25 \\ \\ 350: \frac{350}{700} \times 100=50[/tex]

Solving a system of equations, we can see that:

Let's define the variables:

With the given information, we can write:

P*8h = D

C*7h = D

C = 2*P - 144mi/h

So we have a system of 3 equations, where D is the distance in the problem.

With the first and second equations we can write:

P*8h = D = C*7h

Isolating P, we get:

P = C*(7/8)

Now we can replace that in the last equation:

C = 2*P - 144mi/h

C = 2*C*(7/8) - 144mi/h

And now we can solve that for C.

C - 2*(7/8)*C = - 144mi/h

C*(1 - 14/8) = -144mi/h

C*(8/8 - 14/8) = - 144mi/h

C*(6/8) = 144mi/h

C = (8/6)*144mi/h = 192mi/h

Now that we know the speed of the commercial jet, we can find the speed of the private jet.

P = C*(7/8) = 192mi/h*(7/8) = 168 mi/h

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The service charge rate are: Help desks $50 per call, Network center $75 per device monitored, Electronic mail $10 per user or per e-mail account, Local voice support $14 per phone extension.

a. Service charge rate

Service charge rate=Budgeted cost/ Budgeted activity base quantity

Help desks:

Service charge rate=$160,000/3,200 calls

Service charge rate=$50 per call

Network center:

Service charge rate=$735,000/9,800 devices

Service charge rate=$75 per device monitored

Electronic mail:

Service charge rate=$100,000/10,000 accounts

Service charge rate=$10 per user or per e-mail account

Local voice support:

Service charge rate=$124,600/8,900 phone extensions

Service charge rate=$14 per phone extension

b.  Help desk charge

Help desk charge =(Number of employees times × Percentage of office employees× Percentage with a computer ×Number of calls)× Service charge rate

Help desk charge:

(5,200 employee×25%×96%×1.5)× $50 per call

=$93,600

Network center charge:

[(5,200 employee×25%×96%)+ 600]× $75 per device

=$138,600

Electronic mail:

(5,200 employee×25%×96%×100)×$10 per user or per e-mail account

=$12,480

Local voice support:

(5,200 employee×25%)× $14 per phone extension

=$18,200

Therefore the service charge rate are: Help desks $50 per call, Network center $75 per device monitored, Electronic mail $10 per user or per e-mail account, Local voice support $14 per phone extension.

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The probability that at least 11 of them graduated is 0.7739 if graduation rate is 92.5%.

Given that graduation rate is 95.2%.

We are required to find the probability that out of 12 selected candidates atleast 11 should be graduated.

Probability is basically the chance of happening an event among all the events possible. It cannot be negative. It lies between 0 and 1.

Probability=Number of items/ Total items.

Probability that atleast 11 will be graduated out of 12 selected candidates is as under:

It will be a binomial distribution.

So,

P(X>=11)=[tex]12C_{11}(0.925)^{11} (0.075)^{1} +12C_{12}(0.925)^{12} (0.075)^{0}[/tex]

=12*0.4241*0.075+1*0.3923

=0.3816+0.3923

=0.7739

Hence the probability that at least 11 of them graduated is 0.7739 if graduation rate is 92.5%.

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The expression, [tex](-243)^{-3/5}[/tex] on simplification using the laws of the exponent can be written as - (1/27).

Exponents are of the form aˣ, read as " a to the power x", function as a multiplied by itself x number of times, and are used in a numerical and algebraic expression.

To simplify these expressions, we use the following laws of the exponents:

[tex]1. a^m.a^n = a^{m + n}\\2.\frac{a^m}{a^n} = a^{m-n}\\ 3. (a^m)^n = a^{mn}\\4. a^{-m} = \frac{1}{a^m}\\5. a^0 = 1[/tex]

In the question, we are asked to simplify the expression, [tex](-243)^{-3/5}[/tex].

The expression can be solved using the laws of exponent as follows:

[tex](-243)^{-3/5}\\[/tex]

= [tex]((-3)^5)^{-3/5}[/tex]

= [tex](-3)^{-3}[/tex] {Using the law of exponent: [tex](a^m)^n = a^{mn}[/tex]}

= [tex]\frac{1}{-3^3}[/tex] {Using the law of exponent: [tex]a^{-m} = \frac{1}{a^m}[/tex]}

= 1/(-27)

= - (1/27).

Thus, the expression, [tex](-243)^{-3/5}[/tex] on simplification using the laws of exponent can be written as - (1/27).

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The events E1 and E2 are not independent events.

The two events are given as:

E1 and E2 such that

P(E1) = 0.27, P(E2) = 0.40 and P(E1 U E2) = 0.58.

The two events E1 and E2 are independent if the following equation is true

P(E1 and E2) = P(E1) * P(E2)

Where

P(E1 and E2) = P(E1) + P(E2) - P(E1 U E2)

Substitute the known values in the above equation

P(E1 and E2) = 0.27 + 0.40 - 0.58

Evaluate the sum in the above equation

P(E1 and E2) = 0.67 - 0.58

Evaluate the difference in the above equation

P(E1 and E2) = 0.09

Substitute P(E1 and E2) = 0.09 in P(E1 and E2) = P(E1) * P(E2)

P(E1) * P(E2) = 0.09

Substitute P(E1) = 0.27 and P(E2) = 0.40 in the above equation

0.27 * 0.40 = 0.09

Evaluate the product

0.108 = 0.09

The above is false because 0.108 and 0.09 are not equal

Hence, the events E1 and E2 are not independent events.

How to solve for x

We  have:

P(A) = x

P(B) = x + 0.2

P(A n B) = 0.15

For independent events, we have:

P(A) * P(B) = P(A n B)

So, we have:

x * (x + 0.2) = 0.15

Expand

x^2 + 0.2x - 0.15 = 0

Using  a graphing calculator, we have:

x = 0.3

Hence, the value of x is 0.3

The value of P(A U B)

This is calculated using

P(A U B) = P(A) + P(B) - P(A n B)

Substitute the known values in the above equation

P(A U B) = x + x + 0.2 - 0.15

Evaluate the like terms

P(A U B) = 2x + 0.05

Substitute 0.3 for x

P(A U B) = 2 * 0.3 + 0.05

Evaluate

P(A U B) = 0.65

Hence, the value of P(A U B) is 0.65

The value of P(A' U B')

This is calculated using

P(A' U B') = P(A') + P(B') - P(A' n B')

Where

P(A') = 1 - x

P(B') = 1 - x - 0.2 = 0.8 - x

P(A' n B') = P(A') * P(B')

P(A' n B') = (1 - x) * (0.8 - x)

Substitute the known values in the equation P(A' U B') = P(A') + P(B') - P(A' n B')

P(A' U B') = (1 - x) + (0.8 - x) - (1 - x) * (0.8 - x)

Substitute 0.3 for x

P(A' U B') = (1 - 0.3) + (0.8 - 0.3) - (1 - 0.3) * (0.8 - 0.3)

Evaluate

P(A' U B') = 0.85

Hence, the value of P(A' U B') is 0.85

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Answer:

d

Step-by-step explanation:

using the cosine ratio in the right triangle

cos B = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{2}{10}[/tex] , then

B = [tex]cos^{-1}[/tex] ( [tex]\frac{2}{10}[/tex] ) ≈ 78.46° ( to 2 dec. places )

Answer:

2y - 100

Step-by-step explanation:

Last year's income = y

2y-100

Answer:

[tex]52\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\frac{1}{2}(11+15)(4\sqrt{3})=52\sqrt{3}[/tex]

Using the binomial distribution, the probability that:

(a) Exactly 29 of them are spayed or neutered, that is, P(X = 29) = 0.1163.

(b)  At most 29 of them are spayed or neutered, that is, P(X ≤ 29) = 0.6648.

(c)  At least 28 of them are spayed or neutered, that is, P(X ≥ 28) = 0.5714.

(d) Between 28 and 32 (including 28 and 32) of them are spayed or neutered, that is, P(28 ≤ X ≤ 32) = 0.48345.

A binomial distribution, with a success rate of p on each trial, gives us the probability of x number of success in n number of trials, using the formula:

P(X = x) nCx.pˣ.qⁿ⁻ˣ, where q = 1 - p.

In the question, we are informed that 61% of owned dogs in the United States are spayed or neutered, and are given that 46 owned dogs are randomly selected.

This can be seen as a binomial probability distribution, with n = 46, and p = 61% = 0.61, q = 1 - p = 1 - 0.61 = 0.39.

(a) We are asked for the probability of exactly 29 of them being spayed or neutered.

Thus, x = 29, and we need to find P(X = 29).

Using the given calculator, P(X = 29) = 0.1163.

(b) We are asked for the probability of at most 29 of them being spayed or neutered.

Thus, we need to find P(X ≤ 29).

Using the given calculator, P(X ≤ 29) = 0.6648.

(c) We are asked for the probability of at least 28 of them being spayed or neutered.

Thus, we need to find P(X ≥ 28).

Using the given calculator, P(X ≥ 28) = 0.5714.

(d) We are asked for the probability between 28 and 32 of them are spayed or neutered.

Thus, we need to find P(28 ≤ X ≤ 32), which can be shown as;

P(28 ≤ X ≤ 32) = P(X ≤ 32) - P(X < 28).

Using the given calculator, P(X ≤ 32) = 0.91209.

Using the given calculator, P(X < 28) = 0.42864.

Thus, P(28 ≤ X ≤ 32) = P(X ≤ 32) - P(X < 28) = 0.91209 - 0.42864 = 0.48345.

Thus, using the binomial distribution, the probability that:

(a) Exactly 29 of them are spayed or neutered, that is, P(X = 29) = 0.1163.

(b)  At most 29 of them are spayed or neutered, that is, P(X ≤ 29) = 0.6648.

(c)  At least 28 of them are spayed or neutered, that is, P(X ≥ 28) = 0.5714.

(d) Between 28 and 32 (including 28 and 32) of them are spayed or neutered, that is, P(28 ≤ X ≤ 32) = 0.48345.

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Answer:

you better give me brainliest

Step-by-step explanation:

i think they are lying about being in jail

The speed ratio of the two trains is 4:3, that is, for every 4 hours that one train is delayed, the other is delayed 3.

To find the speed ratio of the trains we must do the following operation:

Note: This question is incomplete because there is some information missing. Here is the complete information in:

A train started from Howrah for Allahabad another train started from Allahabad for Howrah at the same time. The two trains reached their destinations in 9hours and 16 hours respectively after they meet each other. Find the ratio of speed of the two trains.​

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The number of three-digit positive integers that have three different digits and at least one prime digit are 7960.

The definition of a prime number is a natural number larger than 1 that is not the sum of two lesser natural numbers. A composite number is any natural number that is more than 1 but not a prime.

The only two components in prime numbers are 1 and the number itself.

Any whole number greater than one is a prime number.

It has exactly two factors—1 and the actual number.

There is just one 2-digit even prime number.

Every pair of prime numbers is always a co-prime.

The product of prime numbers can be used to represent any number.

Three-digit positive integers that have three different digits and at least one prime digit = 3!*4!*10*9 = 7960

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Answer:

328,233

Step-by-step explanation:

Use the algorithm method.

4 8 9 9

×     6 7

3 6 6 6

3 4 2 9 3

2 5 5 5  

2 9 3 9 4 0

1  1 1  

3 2 8 2 3 3

⇒ 328,233

Based on the fact that there is no country which had won more than 900 silver medals, set E using the roster method would be E = {  }.

Set E is meant to include the set of countries who have attained more than 900 silver medals in the Olympic games.

The highest number of silver medals attained is that of the United States which is 860 silver medals.

This means that no single country has attained more than 900 silver medals.

Set E would therefore be null. Using the roster method, the way to show set E would be:

E = {  }

In conclusion, set E is E = {  }.

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Answer:

Step-by-step explanation:

3/5 = x/10

5x = 30

x = 6

6/10

Hey there!

Original equation:

3/5 = ?/10

Convert to:

3/5 = x/10

Cross multiply the numbers:

3 * 10 = 5 * x

Simplify it:

3 * 10 = 5 * x

30 = 5x

5x = 30

Divide 5 to both sides:

5x/5 = 30/5

Simplify it:

x = 30/5

x = 6

Therefore, your mystery number should be: 6

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The statement that a linear equation is an equation whose graph is a straight line is True.

A  linear equation can be defined as an algebraic equation with each term having an exponent and the graphing of the equation results in a straight line.

From the definition, it can be deduced that the statement is True.

Thus, the statement that a linear equation is an equation whose graph is a straight line is True.

The complete question is:

True or false

A linear equation is an equation whose graph is a straight line.

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Answer:

$2.00 each day so $2.00 x 5 = $10

The set of natural numbers greater than or equal to 6 will be 6, 7, 8, 9, 10, ....

It should be noted that the first information is about the set of natural numbers greater than or equal to 6. Therefore, they will be 6 and above.

It should be noted that the descriptive form simply states in words the elements that are in a set. It is the verbal description of the elements in the set. It is the determination of the elements that belong to a set and those that doesn't.

Also, the way that a set is described is known as the roster form. In this case, the contents of a set can be described by listing the elements that are in the set which are separated by a comma inside the bracket.

Also, the roster form: (5, 7, 9, 11) indicates odd natural numbers. The numbers that are given are odd.

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Answer:

160

Step-by-step explanation:

22 + 18 = 25 percent

40 = 25 percent

100 / 25 = 4

40 x 4 = 160.

Using the probability concept, we have that:

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 35 people, out of which 17 are female and 5 are male that prefer mint chocolate chip, hence:

p = (17 + 5)/35 = 22/35 = 0.6286.

There is a 0.6286 = 62.86% probability that a randomly selected person is female or prefers mint chocolate chip.

Out of the same 35 people, 11 people prefer cookie and cream and 2 people prefer vanilla, hence:

p = (11 + 2)/35 = 13/35 = 0.3714

There is a 0.3714 = 37.14% probability that a randomly selected person prefers cookie and cream or vanilla.

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The answers to the service charge rate are:

This is the number of calls for the help desk

160000/3200 = 50per call

For the network center

735000/9800

= 75 per device that was monitored

For the Electronic mail

100000/10000 =

10 for the mail account

For local voice support

124600/8900

= 14 per phone extension

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The number of different groups of cookies he can choose from the 12 cookies is 220

The given parameters are:

Number of cookies, n = 12

Selected cookies, r = 3

The number of different groups of cookies he can choose from the 12 cookies is calculated as:

Numbers = 12C3

The combination formula is represented as:

nCr = n!/(n - r)!r!

Substitute the known values in the above equation

Numbers = 12!/(12 - 3)!3!

Evaluate the difference in the above equation

Numbers = 12!/9!3!

Expand the above equation

Numbers = 12*11*10*9!/9!3!

Evaluate the quotient

Numbers = 12*11*10/3!

Expand the above equation

Numbers = 12*11*10/3*2*1

Evaluate the products

Numbers = 1320/6

Evaluate the quotients

Numbers = 220

Hence, the number of different groups of cookies he can choose from the 12 cookies is 220

So, the complete parameters are:

Number of cookies, n = 12

Selected cookies, r = 3

Number of selection = 220

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