Miss Elder directs her class to find the area of the
Z in the sign for the City Zoo. A replica of the Z
is shown in the diagram. The work of two of
Miss Elder’s students is shown. Which student,
if either, is correct? Explain.

The only exponential growth equation is the third one:

y = 2*(4)^x

A general exponential equation is:

y = A*(b)^x

if 0 < b < 1, then it is a decay.

if 1 < b, then it is a growth.

So any equation where the base, b, is larger than 1, represents a growth.

Then the correct option is the third one:

y = 2*(4)^x

All the other options are decays.

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There are 16 possible move sequences for the frog.

The possible moves that the frog can make.

The frog can move to either the closest point with a greater integer coordinate that is a multiple of 3, or to the closest point with a greater integer coordinate that is a multiple of 13.
Let's consider the first type of move, where the frog moves to the closest point with a greater integer coordinate that is a multiple of 3.

If the frog is at the point [tex]$n$[/tex], then the closest point with a greater integer coordinate that is a multiple of 3 is either [tex]$n+3$ or $n+6$[/tex].

Similarly, if the frog is at the point [tex]$n$[/tex] and wants to move to a multiple of 13, then the closest point with a greater integer coordinate that is a multiple of 13 is either[tex]$n+13$[/tex] or [tex]$n+26$[/tex].
Constructing move sequences.

The sequence starts with 0 and ends with 39.

The frog has two choices for its first move: either move to 3 or move to 13.

Let's assume that the frog moves to 3.

From there, the frog has two choices again:

move to 6 or move to 13. If the frog moves to 6, then it has two choices again: move to 9 or move to 13.

If it moves to 13, then it has two choices: move to 26 or move to 16.

We can continue this process until we reach 39.
We can create a tree diagram to help us keep track of the possible move sequences:
                            0
                             |
                        3 or 13
                      /            \
                6 or 13       13 or 26
                  /       \       /        \
             9        13     16         26
            / \        / \    / \           / \
          ... ...     ... ... ... ...         ... ...
Each branch represents a different move sequence.

We can see that there are 16 possible move sequences in total.

We can also see that some sequences are longer than others.

The longest sequence has 7 moves, while the shortest sequence has only 2 moves.

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The value of both domain and range of this exponential function is (−∞,∞).

y = 2x-9

The domain of the function can be defined as all real numbers except the ones where the expression is undefined. In the case of 2x-9, there is no real number for which this expression is undefined. Therefore, a domain of this exponential function is (−∞,∞).

The range of the function is defined as the set of all valid y values. In this case, all real numbers are valid values of y. Therefore, the range of this exponential function is (−∞,∞).

Therefore, domain of y = 2x-9 is (−∞,∞) and range is also (−∞,∞).

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The total distance Brown family drove this morning at the speed of  65 miles per hour in 2.5 hours is equal to 162.5 miles.

Let 's' represents the speed of the moving object.

And 't' represents the time to cover distance.

The speed was 65 miles per hour.

And the time they drove was 2.5 hours.

The distance the Brown family drove this morning

=  Multiplying their speed by the time they drove.

This implies,

distance = speed x time

Substitute the values we have,

The distance they drove this morning is equal to,

⇒ distance = 65 miles per hour x 2.5 hours

⇒ distance = 162.5 miles

Therefore, the distance drove by Brown family this morning is 162.5 miles at the speed of 65 miles per hour.

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Answer:

see the images and explanation

Step-by-step explanation:

for the graph:

the domain 0 < x < 5

the range for each functions:

g(x) = 2x + 1

g(x) = y  ,   1 < y < 11

h(x) = 2x + 2 ,  2 < y < 12

The confidence interval in which you have the most confidence that it captures the population mean is the one with the highest level of confidence.

But keep in mind that this interval will be wider and less precise, so we must balance the level of confidence with the desired precision of your estimate.

The terms confidence interval, population mean, and level of confidence.
A confidence interval is a range of values that is likely to contain the population mean, which is the average value of a certain variable in the entire population.

The level of confidence, expressed as a percentage (e.g., 95%), represents the probability that the confidence interval captures the true population mean.
In general, the confidence interval with the highest level of confidence will give you the most certainty that it captures the population mean.

However, as the level of confidence increases, the width of the confidence interval also increases, making it less precise.

This means that while we have more confidence that the interval contains the population mean, you have less specific information about where the mean lies within that interval.

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Answer:

first answer is correct

y = -1/2 x^2 + x + 1

Step-by-step explanation:

based on the graph, you can find two points

(2,1) and (0,1)

I input (2, 1) to each equation to check

y = -1/2 x^2 + x + 1 is correct

Answer:

The answer is 7x(5-2y)

Step-by-step explanation:

35x-14xy

7x(5-2y)

the error made is the x in the bracket

Answer: i dont know if this is right but i put a^4+b^4=c^4

Step-by-step explanation:

I have no idea tho

The only possible elements that can appear in all the sets are 4 and 5. Since both 4 and 5 appear in each set, they must be in the intersection.

Based on the given set definition, we have:

A₁ = {4, 5}

A₂ = {4, 5, 6}

A₃ = {4, 5, 6, 7}

A₄ = {4, 5, 6, 7, 8}

and so on.

To find the union of all the sets, we need to find all the distinct elements that appear in at least one of the sets. We can do this by listing the elements in each set and removing duplicates:

⋃[infinity] =1 Aᵢ = {4, 5, 6, 7, 8, ...}

We can see that the union includes all the natural numbers greater than or equal to 4. We can prove this by showing that any natural number n greater than or equal to 4 is included in at least one of the sets. Indeed, for any such n, we can choose i = n - 3, which is a natural number since n is at least 4, and then we have n in Aᵢ.

To find the intersection of all the sets, we need to find the elements that appear in all the sets. We can do this by listing the elements in each set and finding the common elements:

⋂[infinity] =1 Aᵢ = {4, 5}

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Answer:

Perimeter:

[tex]2( \frac{2}{3} + \frac{1}{2} ) = 2( \frac{4}{6} + \frac{3}{6} ) = 2( \frac{7}{6} ) = \frac{7}{3} = 2 \frac{1}{3} [/tex]

The perimeter is 2 1/3 inches.

Area:

[tex] \frac{2}{3} \times \frac{1}{2} = \frac{1}{3} [/tex]

The area is 1/3 of a square inch.

The value of g(x) = x^2 + 4x depends on the value of x.

If, for example, x = 2, then:

g(2) = 2^2 + 4(2) = 4 + 8 = 12

If x = -3, then:

g(-3) = (-3)^2 + 4(-3) = 9 - 12 = -3

In general, we can evaluate g(x) for any value of x by substituting that value into the expression x^2 + 4x.

vehicle?

The average delay per vehicle would be 20 minutes. This is calculated by taking the total time the freeway was shut down (40 minutes) and dividing it by the total number of vehicles that would have been on the freeway during that time (2400 vehicles).

There are 23 quarters and 29 dimes in the bag.

Let's denote the number of quarters as "q" and the number of dimes as "d".

We can set up a system of two equations based on the given information:

The total number of coins is 52:

q + d = 52

The total value of the coins is $8.35, where each quarter is worth $0.25 and each dime is worth $0.10:

0.25q + 0.10d = 8.35

To solve this system of equations, we can use substitution, elimination, or any other appropriate method.

Let's use elimination to solve this system of equations.

0.10(q + d) = 0.10(52)

25q + 10d = 835

25q + 10d = 835

0.25q + 0.10d = 8.35 (multiply by 100)

Now, let's multiply both sides of the first equation by 2 and the second equation by 8 to make the coefficients of "q" the same:

50q + 20d = 1670

200q + 80d = 6680

Now, let's subtract the first equation from the second equation to eliminate "q":

200q + 80d - (50q + 20d) = 6680 - 1670

150q + 60d = 5010

Now, let's divide both sides of the resulting equation by 30 to solve for "q":

150q/30 + 60d/30 = 5010/30

5q + 2d = 167

After trying different values, we find that when "q" = 23 and "d" = 29, the equation is satisfied and the condition "q + d = 52" is also satisfied. Therefore, there are 23 quarters and 29 dimes in the bag.

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Equation that represents the total number of minutes y Emily studied for the math exam is y = 40 +x.

We can represent the total number of minutes Emily studied for the math exam using the equation,

y = 40 + x

Here, 'y' represents the total number of minutes Emily studied for the math exam, '40' represents the number of minutes she studied in the morning, and 'x' represents the number of minutes she studied later that evening.

By adding the number of minutes studied in the morning to the number of minutes studied later that evening, we can calculate the total number of minutes Emily studied for the math exam.

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In linear equation, 3f² + 8f + 16 feet is the length of the fourth side of the room.

What is  linear equation?

An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a linear equation.

                         The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.

= 5f² + 19f + 11 - 6f - 5f + 7 - 2f² - 2

= 3f² + 8f + 16 feet

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The expression that represent the length of the fourth side of the room is  [tex]3f^2 + 8f + 16[/tex].

What is  expression ?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here Total length of the room = [tex]5f^2+19f+11[/tex]

Three sides length of the room = 6f , 5f-8 and [tex]2f^2+2[/tex]

Fourth side = Total length - sum of length of three sides

=> [tex]5f^2+19f+11-(6f+5f-7+2f^2+2)[/tex]

=>  [tex]5f^2+ 19f + 11 - 6f - 5f + 7 - 2f^2 - 2[/tex]

=>  [tex]3f^2 + 8f + 16[/tex] .

The expression that represent the length of the fourth side of the room is  [tex]3f^2 + 8f + 16[/tex].

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Answer: Sarah bought 5 first class tickets and (13-5) = 8 coach tickets.

Step-by-step explanation: The taken a toll of one to begin with lesson ticket is $1200 and the fetched of one coach ticket is $380.

So, the full taken a toll of first class tickets would be 1200x and the entire cost of coach tickets would be 380(13-x) = 4940 - 380x.

The overall fetched of the tickets is given as $9040, so we will set up the taking after condition:

1200x + 4940 - 380x = 9040

Streamlining and tackling for x, we get:

820x = 4100

x = 5

If rosanne makes 112 liters of strawberry lemonade, she pours 14 of a liter of lemonade into a thermos to take to the park, rosanne's brother drink 25 liters of lemonade

To solve this problem, we can start by subtracting the 14 liters of lemonade that Rosanne poured into the thermos from the total 112 liters to get the amount of lemonade that remained:

112 - 14 = 98 liters

Next, we need to subtract the amount of lemonade that Rosanne's brother drank, which is 25 liters, from the remaining amount:

98 - 25 = 73 liters

Therefore, Rosanne's brother drank 25 liters of lemonade.

To check our answer, we can add the amount of lemonade in the thermos, the amount that Rosanne's brother drank, and the remaining amount to see if it adds up to the original 112 liters:

14 + 25 + 73 = 112

Since the sum is indeed equal to 112, we can be confident that our answer of 25 liters for the amount of lemonade that Rosanne's brother drank is correct.

In summary, to find the amount of lemonade that Rosanne's brother drank, we subtracted the amount that Rosanne poured into the thermos and the amount that her brother drank from the total amount of lemonade that Rosanne made. The answer is 25 liters.

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For a normal distribution ,a positive value of z simply means that the observation or sample mean is above the population mean this implies

none of the options provided is completely accurate.

All the observations must have had positive values,

It is not necessarily true for a positive value of z.

The value of z indicates how many standard deviations away from the mean a particular observation or sample mean is.

A positive value of z simply means that the observation or sample mean is above the population mean.

The area corresponding to the z is either positive or negative,

It is also not accurate.

The area under the normal curve corresponds to probabilities, not positive or negative values.

The area to the right of the mean corresponds to positive z-values, and the area to the left of the mean corresponds to negative z-values.

The sample mean is smaller than the population mean,

It is a possibility when the z-value is negative, indicating that the sample mean is below the population mean.

The sample mean is larger than the population mean,

It is a possibility when the z-value is positive, indicating that the sample mean is above the population mean.

Therefore, the sample mean can be either larger or smaller than the population mean depending on the direction of the z-value.

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The length of the given line AB is 6 units and the polygon ABCDEF has been created.

A graph is a mathematical structure made up of a collection of points called VERTICES and a set of lines connecting some pair of VERTICES that may or may not be empty.

There is a chance that the edges will be directed, or orientated.

If the lines are directed or undirected, respectively, they are referred to as ARCS or EDGES.

Make a sequence of bars on graph paper as an example of a graph.

So, in the given situation the polygon ABCDEF has been created:

(Refer to the graph attached below)

Now, the length of the side AB:

Count the units as follows which comes to 6 units.

Therefore, the length of the given line AB is 6 units and the polygon ABCDEF has been created.

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Correct question:

Help Here is your graph of the points on the previous screen.

Connect the points in order to create polygon `ABCDEF`.

1.2 Enter the length of the segment between A and B.

approximately 3.6 milliliters of medication would be needed for this prescription.

To calculate the total milliliters of medication needed for this prescription, we will use the formula dosage × frequency × day supply.

In this case, the dosage is 2 drops per ear, the frequency is twice a day, and the day supply is 9 days.

First, let's find out how many drops are needed per day:
2 drops/ear × 2 ears = 4 drops
Since the frequency is twice a day, multiply this number by 2:
4 drops × 2 = 8 drops per day

Now, multiply the number of drops per day by the day supply (9 days):
8 drops/day × 9 days = 72 drops

Typically, 1 drop is approximately 0.05 millilitres. To find out how many millilitres of medication are needed, multiply the total number of drops by the volume of one drop:

72 drops × 0.05 mL/drop = 3.6 mL

So, approximately 3.6 millilitres of medication would be needed for this prescription.

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Approximately 1.8 milliliters of medication would be needed for this prescription.

To calculate how many milliliters of medication would be needed for this prescription, we need to use the following formula:

dosage × frequency × day supply.
The dosage is 2 drops, the frequency is twice a day, and the day supply is 9 days.
First, we need to convert drops to milliliters.

One drop is equal to approximately 0.05 milliliters.

2 drops would be equal to 0.1 milliliters.
Next, we can plug in the values into the formula:
[tex]0.1 milliliters/drop \times 2 drops/twice a day \times 9 days = 1.8 milliliters. [/tex]

The patient will be using exactly 2 drops in each ear for each dose, and that there will be no waste or spillage of the medication.

To determine how many milliliters of medicine would be required for this prescription:

dose frequency day supply.

The recommended dosage is 2 drops, twice day, with a 9-day supply.

We must first convert droplets to milliliters.

A drop is around 0.05 milliliters in volume. As a result, 2 drops are equivalent to 0.1 milliliters.

The values may then be entered into the formula as follows:

0.1 milliliters each drop times twice daily for nine days equals 1.8 milliliters.

As a result, this prescription would require about 1.8 milliliters of medicine.

It's crucial to note that this estimate is predicated on the patient applying precisely 2 drops to each ear for each dose.

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The probability is approximately 0.446 or 44.6%.

Waiting time is exponentially distributed, we can use the cumulative distribution function (CDF) of the exponential distribution to solve this problem.

Let X be the waiting time in minutes.

X is exponentially distributed with a mean of 8 minutes.

The rate parameter λ is equal to 1/8.

The CDF of the exponential distribution is given by:

[tex]F(x) = 1 - e^(-\lambda x)[/tex]

The probability that a patient will see the doctor within eleven minutes of the scheduled time.

The value of F(11) - F(0).

[tex]F(11) = 1 - e^(-\lambda \times 11) = 1 - e^(-11/8)[/tex] ≈ 0.554

[tex]F(0) = 1 - e^(-\lambda \times 0) = 1 - e^0 = 1[/tex]

Therefore, the probability that a randomly selected patient will see the doctor within eleven minutes of the scheduled time is:

F(11) - F(0) ≈ 0.554 - 1 ≈ 0.446

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the probability that none of the outcomes is an even number is 1/8 or approximately 0.125

The probability of rolling an even number on a fair six-sided die is 3/6 or 1/2, and the probability of rolling an odd number is also 1/2.

To find the probability that none of the outcomes is an even number, we need to calculate the probability of rolling an odd number on all three dice. Since the dice are rolled independently, we can multiply the probabilities together to get the overall probability:

P(rolling odd on one die) = [tex]1/2[/tex]

P(rolling odd on two dice) = [tex](1/2)^2 = 1/4[/tex]

P(rolling odd on three dice) =[tex](1/2)^3 = 1/8[/tex]

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Answer:

Jaxon made 11 free throws over the season.

Step-by-step explanation:

If he made 5% of his free throws, we know that he will make 5% of the total number of free throws he took, which is 220:

We multiply 220 by 0.05, or 5% to find out how many free throws he made:

220*0.05 = 11

After that, we now know that Jaxon made 11 of his free throws out of 220 over the course of the season, or 5%.

The probability of seeing the word "math" in a 10-letter string typed by a monkey is 0.0024 (or 0.24%).

To calculate this probability, we first need to determine the total number of possible 10-letter strings that the monkey can type. Since the monkey never repeats letters, the number of possible 10-letter strings is given by the permutation formula:

10P10 = 10!/(10-10)! = 3,628,800

Next, we need to determine the number of 10-letter strings that contain the word "math". We can do this by fixing the position of the "m" and the "a", and then allowing the monkey to freely choose the remaining 6 letters. The number of ways to do this is given by:

8P6 = 8!/(8-6)! = 56

Finally, we divide the number of 10-letter strings containing "math" by the total number of possible 10-letter strings to obtain the probability:

56/3,628,800 = 0.000024 = 0.0024 (or 0.24%)

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Lee needs to score a total of 26 points in the next game to increase his mean score to 13 points.

Given that

Scores = 12,14,14,15,8,10,3,15

To increase his mean score to 13 points,

Lee needs to have a total of 13 x 9 = 117 points after the next game.

He has already scored a total of 12+14+14+15+8+10+3+15 = 91 points in the first 8 games.

Therefore, Lee needs to score a total of 117 - 91 = 26 points in the next game to increase his mean score to 13 points.

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The logical assumption used is: An arithmetic sequence is a set of discrete values, whereas a line is a continuous set of values.

An arithmetic sequence is a set of numbers where, with the exception of the first term, each term is obtained by adding a fixed constant to the term before it. Every pair of following terms in the sequence has the same fixed constant, which is known as the common difference. A1 stands for the first term in an arithmetic sequence, while an is used to represent the nth term.

A solid line symbolises continuous numbers, whereas the classmate's logical presumption is that an arithmetic series comprises of discrete values. This presumption is untrue, though, as a line can effectively represent an arithmetic series.

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Answer:

B

Step-by-step explanation:

The value of 0.6 is greater than the value of 0.39 because 0.6 represents a larger proportion or fraction of a whole than 0.39 does.

To compare these two values, we can think of them as parts of a whole. For example, we can consider 0.6 as 60% of a whole and 0.39 as 39% of the same whole. When we compare 60% and 39%, it is clear that 60% is greater than 39%.

Another way to compare these two values is to convert them to fractions. 0.6 can be written as 6/10 or 3/5, while 0.39 can be written as 39/100.

When we compare 6/10 and 39/100, we can see that 6/10 is greater than 39/100 because 6/10 represents 6 parts out of 10, while 39/100 represents 39 parts out of 100.

Therefore, we can conclude that the value of 0.6 is greater than the value of 0.39 because it represents a larger proportion or fraction of a whole.

A minimum sample size of 665 consumers that FiveThirtyEight should survey to guarantee a margin of error of 0.05 or less with a 99% confidence level.

Sample size refers to the number of observations or individuals included in a study or experiment. It is the number of subjects or units that are selected from a population to be studied. The sample size is an important consideration in statistical analysis, as it can affect the accuracy and generalizability of the results. A larger sample size generally leads to more precise estimates and stronger statistical power, but it can also be more costly and time-consuming to collect and analyze.

To calculate the minimum sample size required to maintain a margin of error of 0.05 or less with a 99% confidence level, we can use the formula:

n = (Z² * p * (1-p)) / E²

where n is the sample size, Z is the Z-score for the desired confidence level (2.576 for 99% confidence level), p is the estimated proportion of the population that has a certain characteristic (we can use 0.5 for maximum variability), and E is the margin of error.

Plugging in the values, we get:

n = (2.576² * 0.5 * (1-0.5)) / 0.05²

n = 664.3

Rounding up to the nearest whole number, we get a minimum sample size of 665 consumers that FiveThirtyEight should survey to guarantee a margin of error of 0.05 or less with a 99% confidence level.

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