Jerry is filling a 10 gallon aquarium with water at a constant rate. There are 5.6 gallons of water in the aquariafter filling it for 14 minutes. At what rate, in gallons per minute, is Jerry filling the bucket?

The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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Answer:

d i would think hope it helps

Answer:

rectangle 10 by 6 or something like that

Step-by-step explanation:

a) With regard to Edward, single deposit would he need to make now into an account that pays 4.3% interest, compounded daily, to meet his goal  is $32,526.67.

b) The total interest that he would pay on this loan is given as follows: $2,160.

c) The finance charge is $295.84

A) Let the Principle be P

amount here A= $50,000

time n= 10 years n= 10 x 36 5= 3650 days

rate of interest= 4.3% compounded daily= 4.3/365

let us use compound interest formula to calculate the principle

A = P (1 + (r/100)ⁿ

putting all the values we get

50000 = P (1 + (4.3/(100 x 365))⁽¹⁰ ˣ ³⁶⁵)

on solving we get P =  $32,526.67

therefore he need to deposit $32,526.67

B)

The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation shown as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are explained as follows:

P is the value of the initial deposit.

r is the interest rate, as a decimal.

Considering this equation, the interest accrued is given as follows:

I(t) = Prt.

In the context of this problem, the values of these parameters are given as follows:

P = 7500, r = 0.064, t = 4.5.

Hence the interest accrued on the payment is obtained as follows;

I(4.5) = 7500 x 0.064 x 4.5 = $2,160.


C)

We know that,

Finance charge = Total Amount Paid - Original cost

As the original cost of the drum is = $1972

She paid 20% as down payment. So the amount of down payment is,

1972 x 20/100 = $394.40

She has to pay 36 monthly payments of $52.04 each. So the amount to be paid is,

= 36 x 52.04 = $1873.44

So the total amount paid will be,

=  $1873.44 + 394.40 = $2267.84

Therefore, the finance charge is 226.84 - 1972 = $295.84

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The probability that Hannah's number is an even palindrome is 1/45.

There are 45 even palindrome numbers between 1000 and 9999, out of a total of 4500 possible 4-digit numbers.

So, the probability of Hannah writing an even palindrome number is 1/45.

A palindrome number is the same when read from left to right or right to left. There are 90 possible 2-digit palindrome numbers (11, 22, 33, etc.), and 9 possible 1-digit palindrome numbers (1, 2, 3, etc.), making a total of 99 palindrome numbers from 1 to 999. In a 4-digit number, the first and last digits must be the same for it to be a palindrome.

Therefore, the first digit has 9 choices (1-9), and the last digit also has 9 choices. The second digit can be any of the 10 digits (0-9), and the third digit can be any of the 5 remaining even digits (0, 2, 4, 6, 8).

Thus, there are 45 even palindrome numbers between 1000 and 9999.

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The sequence of transformations of rectangle A onto rectangle B is

B)  A dilation with a center of dilation at the origin, followed by a translation down and a translation to the left.

The graph's curve "moves to the left/right/up/down," "it expands or compresses," or "it reflects" when a function is transformed. For instance, simply advancing the graph of the function g(x) = x2 by 3 units will yield the graph of f(x) = x2 + 3. Function transformations are very useful for graphing the functions by simply moving, expanding, compressing, or reflecting the curve, as opposed to having to start from scratch with the graphing.

A function transformation "moves," "resizes," or "reflects" the parent function's graph, depending on the case. Function transformations can be broadly divided into three categories:

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An equation that matches the table include the following: y = x + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 5)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1.

At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 1(x - 0)

y - 5 = x

y = x + 5

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Anthony's "hiring process" or "recruitment period" was 30 days.

The blank can be filled with "hiring process" or "recruitment period" to indicate the duration between placing the advertisement for a new assistant on November 1 and hiring Marquis on December 1. This period represents the time it took Anthony to evaluate applicants, conduct interviews, and make the decision to hire Marquis.

The hiring process typically involves several steps, such as advertising the job opening, reviewing applications, conducting interviews, and finalizing the selection. The duration of this process can vary depending on various factors, including the number of applicants, the complexity of the position, and the efficiency of the hiring process.

In this case, the hiring process took 30 days, indicating the length of time it took for Anthony to complete the necessary steps and choose Marquis as the new assistant. This duration provides insight into the timeframe Anthony needed to assess candidates and make a hiring decision.

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Answer:

1 is m and b

2 is two order pars

3 is one set of ordered pars

Step-by-step explanation:

Answer:

Use the two ordered pairs to find the slope, m . Then substitute the slope, and one set of ordered pairs into y = mx + b to solve for b.

Step-by-step explanation:

Slope is m in the equation.

You need one set of ordered pairs to solve for the y-intercept.

The y-intercept is b in the equation.

Hope it helps!

Answer:

X = 208

Step-by-step explanation:

By applying probability concept, it can be concluded that the probabilities for the different time ranges are:
(a) No more than 10 seconds: 55%
(b) At least 6 seconds: 79%
(c) Between 6 and 20 seconds: 66%
(d) Between 1 and 15 seconds: 67%

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

It is usually expressed as a percentage with a range from 0% to 100%, where the greater the percentage, the greater the event occurs, and vice versa.

We have the following table about how long mobile phone users would wait for a page to load:

Time​ (Seconds)             Percentage

         <1                                 5%

        1-5                                16​%

       6–10                             34%

       11–15                             17%

      16–20                            15​%

        >20                              13​%

To find the probabilities for the different time ranges, we need to use the percentages from the table.

(a) No more than 10 seconds: This includes the percentages for <1, 1-5, and 6-10 seconds.

So, we add those percentages together:

5% + 16% + 34% = 55%.

The probability that a person would wait no more than 10 seconds is 55%.

(b) At least 6 seconds: This includes the percentages for 6-10, 11-15, 16-20, and >20 seconds.

So, we add those percentages together:

34% + 17% + 15% + 13% = 79%.

The probability that a person would wait at least 6 seconds is 79%.

(c) Between 6 and 20 seconds: This includes the percentages for 6-10, 11-15, and 16-20 seconds.

So, we add those percentages together:

34% + 17% + 15% = 66%.

The probability that a person would wait between 6 and 20 seconds is 66%.

(d) Between 1 and 15 seconds: This includes the percentages for 1-5, 6-10, and 11-15 seconds.

So, we add those percentages together: 16% + 34% + 17% = 67%.

The probability that a person would wait between 1 and 15 seconds is 67%.

So, the probabilities for the different time ranges are:
(a) No more than 10 seconds: 55%
(b) At least 6 seconds: 79%
(c) Between 6 and 20 seconds: 66%
(d) Between 1 and 15 seconds: 67%

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The bottleneck time is 18.18%. Therefore, option A is the correct answer.

In economics terms, the bottleneck is a chain of supply of resources that wants the most extended time in the supply chain operation for specific demand. It also evaluated to estimate the supply chain throughput.

Through put time = Sum of all times=1+2+3+4+5+6+7+8+9+10=55

Given,

Assembly line has 10 stations

Throughput time is 55

The formula for bottleneck time is:

Bottle neck time = Total stations/Throughput time ×100

= 10/55 ×100

= 18.18%

The bottleneck time is 18.18%. Therefore, option A is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

An assembly line has 10 stations with times of 1, 2, 3, 4,...,10, respectively. What is the bottleneck time?

a. 18.18% of the throughput time

b. 100% of the throughput time

c. 550% of the throughput time

d. 50% of the throughput time

e. 1.82% of the throughput time

Parrots are tropical birds. These parrots survive, while most others cannot, due to a variation that allows these parrots to live in colder climate.

Parrots are found on all tropical and subtropical continents and regions including Australia and Oceania, South Asia, Southeast Asia, Central America, South America, and Africa. There are some important facts of Parrots are they can live over 100 years and also speak in like human voice. Parrots weight around 7 pounds.

About the diet of parrot, but all species are vary too what are available in the environment in which they live. Parrots are mostly eating fruits, nuts, chilly, grasses, leafy vegetation and all types of food.

And it also for help us to convey any message and about any story teller.

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Answer:

73.50

Step-by-step explanation:

3.5 * 3.5=12.25

12.25 * 6 cube =73.50

The statement, "Events which occur in extremes of normal-curve have a very small-probability of occurrence" is True because the normal distribution is a bell-shaped curve that is symmetrical around mean.

The Events which occur in extremes of normal curve have a very small probability of occurring because normal-distribution is a bell-shaped curve that is symmetrical around mean, with most values falling close to mean and fewer values occurring further away from mean.

So, as one moves further from the mean, the probability of occurrence decreases exponentially.

So, events that occur in the tails (extremes) of the normal curve have a very small probability of occurring.

Therefore, the statement is True.

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Answer:

158 degrees

Step-by-step explanation:

Step 1:

Let Angle CDE =y

Since Angle BCD = 2 X angle CDE

Angle BCD = 2y

Step 2

Consider Figure 2 attached, each of the figure forms an isosceles trapezoid ABCF and DEFC.

By these properties of Isosceles Trapezoids

Therefore:

\(\angle ABC+\angle BCF=180^\circ\\\angle FCD+\angle CDE=180^\circ\\Therefore:\\\angle ABC+\angle BCF+\angle FCD+\angle CDE=360^\circ\\$But \angle BCF+\angle FCD=\angle BCD\\So:\\\angle ABC+\angle BCD+\angle CDE=360^\circ\)

123+2y+y=360

3y=360-123

3y=237

y=79 degrees

Therefore:

\(\angle BCD=2 X 79^\circ=158^\circ\\\angle BCD=\angle AFE=158^\circ\\\angle AFE=158^\circ\)

Answer:

x = 0

Step-by-step explanation:

AB + BC = AC

therefore

2x+8 + 2x+ 12 = 20

combine like terms

4x+ 20 = 20

Subtraction property of equality

4x + 20 - 20 = 20 - 20

4x = 0

Division property of equality

4x/4 = 0/4

x=0

The function f(x) is: neither old nor even

Trigonometric functions can be categorized as odd, even, or neither odd nor even based on their symmetry properties. Let's analyze each category:

Odd Functions: An odd function satisfies the condition f(-x) = -f(x) for all values of x. This means that if we reflect the graph of the function across the y-axis, it remains unchanged. In other words, the function is symmetric with respect to the origin (0,0).

Examples of odd trigonometric functions include sine (sin(x)) and tangent (tan(x)). When you plug in -x into these functions, you'll get the negation of the function's value at x.

Even Functions: An even function satisfies the condition f(-x) = f(x) for all values of x. This means that if we reflect the graph of the function across the y-axis, it remains unchanged. In other words, the function is symmetric with respect to the y-axis.

An example of an even trigonometric function is the cosine function (cos(x)). When you plug in -x into the cosine function, you'll get the same value as when you plug in x.

Neither Odd nor Even: Some trigonometric functions do not exhibit either odd or even symmetry. These functions do not satisfy the conditions for odd or even functions. Examples of trigonometric functions that are neither odd nor even include secant (sec(x)), cosecant (csc(x)), and cotangent (cot(x)). When you plug in -x into these functions, you won't get the negation or the same value as when you plug in x.

Therefore, the trigonometric functions can be categorized as odd, even, or neither odd nor even, depending on their symmetry properties.

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The probability that a test revealed that Jared is a carrier but Lucia is not is 1/4

Mendel discovered that genes are inherited as separate, paired units, one from each parent. Its application of mathematics to illuminate observations of natural phenomena.

Given that lucia and jared each have a sibling with cystic fibrosis, but neither lucia nor jared nor their parents have the disease

Mendel theory is a technique used to estimate the probability of getting specific characteristics.

Lucia and Jared have a probability of both carrier and non carrier

If both of them are non carrier then the children born to their family have no chances of getting disease.

If any one of them is carier, then there is a chance of getting one child as a carrier. That is ¼ or the ratio is 1:4

If both of them are carriers then the ratio will be 1:2:1

If Jared is carrier then the probability will be ¼

Therefore the probability if a test revealed that jared is a carrier but lucia is not is ¼

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To prove that AD ≅ DB, we can use the ASA (Angle-Side-Angle) congruence criterion.

Given:

∠CAD ≅ ∠CBD (Angle CAD is congruent to angle CBD)

∠CAB ≅ ∠CBA (Angle CAB is congruent to angle CBA)

To Prove:

AD ≅ DB (Segment AD is congruent to segment DB)

Proof:

Step 1: Draw segment AC and segment BC.

Step 2: By the given information, we have ∠CAD ≅ ∠CBD and ∠CAB ≅ ∠CBA.

Step 3: Draw segment CD to complete triangle ABC.

Step 4: Now, we have two pairs of congruent angles (∠CAD ≅ ∠CBD and ∠CAB ≅ ∠CBA).

Step 5: According to the ASA congruence criterion, if two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

Step 6: Apply the ASA congruence criterion to triangles CAD and CDB:

∠CAD ≅ ∠CBD (Given)

∠CAB ≅ ∠CBA (Given)

CD ≅ CD (Common side)

Step 7: By the ASA congruence criterion, triangles CAD and CDB are congruent.

Step 8: Since the triangles CAD and CDB are congruent, their corresponding sides are congruent.

Step 9: By the corresponding parts of congruent triangles (CPCTC), we can conclude that AD ≅ DB.

Therefore, we have proved that AD ≅ DB using the ASA congruence criterion.

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Answer:

Y= -x - 1

Step-by-step explanation:

Answer:

y= -x - 1

Step-by-step explanation:

i just got it right

If you are having either soup or salad, you have 7 choices in total (2 kinds of soup + 5 kinds of salad). If you are having both soup and salad, you have 10 choices in total (2 kinds of soup x 5 kinds of salad).

(a) If you are having either soup or salad, you have two choices of soup and five choices of salad. To find the total choices, add the two options together:
2 (soups) + 5 (salads) = 7 choices

(b) If you are having both soup and salad, you need to find the combinations of soup and salad. To do this, multiply the number of soups by the number of salads:
2 (soups) x 5 (salads) = 10 choices

So, you have 7 choices for either soup or salad, and 10 choices for both soup and salad.

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Train a total of 200 miles each week. 160 miles I bike, 32 miles I run, 8 miles I swim.

What do you mean by Simultaneous linear equations?

A system of simultaneous linear equations is any pair of linear equations or more that have the same unknown variables in common. To solve such a system, one must identify values for the unknown variables that simultaneously satisfy each of the equations. A system of simultaneous linear equations is any pair or group of linear equations where each equation has the same unknown variables. Finding values for the unknown variables that simultaneously satisfy each equation in such a system is the first step in its solution.

according to the question,

you bike five times as far as I run and you run four times as far as iswim. you train a total of 200 miles each week.

let, I swim x miles then I run 4x times and I bike 20x miles.

so, 4x+x+20x=200

by solving linear equations,

we get, x=8

hence,160 miles I bike.

32 miles I run.

8 miles I swim.

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There is an 8.08% chance that the average lifetime of the four printers will be more than 1568 hours, assuming that the lifetimes are normally distributed with a mean of 1500 hours and a standard deviation of 160 hours.

The mean lifetime of the four printers can be modeled as a normal distribution with a mean of 1500 hours and a standard deviation of 80 hours (since the standard deviation of the sample mean is the population standard deviation divided by the square root of the sample size). Therefore, we need to standardize the value of 1568 hours to find the corresponding z-score, and then find the probability of getting a z-score greater than that.

\(z = (1568 - 1500) / (160 / \sqrt{4}) = 1.4\)

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score greater than 1.4 is 0.0808. Therefore, the probability that the mean lifetime of the four printers is more than 1568 hours is 0.0808 or approximately 8.08%.

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Answer:

I pretty sure the answer is ASA, I hope it's right!

The equation that can be used to find the value of x is 120 = (x + 5) × (120/x - 1/3).

Carmen's first trip was 120 miles, and she traveled at an average of x miles per hour. We can use the formula:

distance = rate × time, which can be written as:
120 miles = x miles/hour × time

where, time is the time for outgoing.

For the return trip, Carmen traveled at a rate that was 5 miles per hour faster, so her speed was (x + 5) miles/hour. The time for the return trip was one-third of an hour less than the time for the outgoing trip, so we can represent the return trip time as (time - 1/3) hours. Using the distance formula again for the return trip:
120 miles = (x + 5) miles/hour × (time - 1/3) hours

Now, let's express both times in terms of x. From the first equation, we can find the time for the outgoing trip as:
time = 120 miles / x miles/hour

Substitute this expression for time in the return trip equation:
120 miles = (x + 5) miles/hour × (120/x - 1/3) hours

Now you have an equation that can be used to find the value of x:
120 = (x + 5) × (120/x - 1/3)

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Answer:

6.5 cm

Step-by-step explanation:

The computation of the length of the apothem is shown below:

Given that

The side length is 9.4 centimeters

And, the radius is 8 centimeters

Now based on the above information

As per the attached figure  

AB = 8 cm

BC = 9.4 ÷ 2 = 4.7 cm

Now apply the pythagoras theorem

AB^2 = BC^2 + AC^2

8^2 = 4.7^2 + AC^2

AC^2 = 41.91

AC = 6.47 cm

= 6.5 cm

Answer: D). 6.5 cm

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

So the perimeter of a square is 4 times the side length.

4 (x+3) = 32 is the equation we can make out with the given information.

Solve for x:

Distribute the 4 to the terms inside the parenthesis;  4x + 12 = 32

Subtract 12 from both sides;  4x = 20

Divide both sides by 4;  x = 5

By isolating x, we get 5 as the value of x.