A car travels 80 km. It travels the first half of the journey on motorways and the second half through towns.

What is the average speed of the car in the first half of the journey

The limit lim f(x) as x approaches 2 does not exist, as the function approaches different values from the left and right sides of x=2.

The limit of a function at a particular point is the value that the function approaches as the input approaches that point. To find the limit lim f(x) as x approaches 2, we look at the behavior of the function as x gets closer and closer to 2.

From the graph of the function f, we can see that as x approaches 2 from the left side, the function approaches a value close to 1. However, as x approaches 2 from the right side, the function approaches a value close to 3. Since the function approaches different values from the left and right sides of x=2, the limit does not exist.

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Answer:

$546

Step-by-step explanation:

726 is 1/3. 3/3 is 2178. - 1632= 546.

what are the sentences? but 2/4, could also be 1/2 or a half

Answer:

x²-8x-1=0

comparing above equation with ax²+bx+c=0

a=1

b=-8

c=-1

x=

\(x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a} \)

=(--8+-√(64-4×1×-1)/2×1

=8+-√(64+4)/2

taking positive

x=(8+√68)/2=2(4+√17)/2=4+√17

taking negative

x=(8-√68)/2=2(4-√17)/2=4-√17

The correct expression can be used to calculate 15% of 3500 is,

⇒ 15/100 × 3500

Given that;

The expression is,

⇒ 15% of 3500

Now, We can simplify as;

⇒ 15% of 3500

⇒ 15/100 × 3500

⇒ 15 × 35

⇒ 525

Thus, The correct expression can be used to calculate 15% of 3500 is,

⇒ 15/100 × 3500

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Answer:

A. They can be searched using keywords.

The Lotka-Volterra predation model shows There is no equilibrium in which one species has a non-zero population and the other does not. This is because there is no such equilibrium as the equations N and P are depended on each other. In the non-trivial equilibrium, a stable coexistence of both species exist. When N and P are zero, then value of N = 0 and P = r/a.

Without doing algebra, we can see that there is no equilibrium in which one species has a non-zero population and the other does not because both equations depend on both N and P. This means that the populations of both species affect each other, and there is no way for one species to exist without the other.

To find the equilibrium, we set N' and P' to zero and solve for N and P simultaneously:

N' = rN - aNP = 0

P' = caNP - 5P = 0

From the first equation, we can solve for N:

rN - aNP = 0

N(r - aP) = 0

N = 0 or r - aP = 0

N = 0 or P = r/a

If N = 0, then from the second equation, we get P = 0 as well. This represents the trivial equilibrium where both populations are extinct.

If P = r/a, then substituting into the first equation, we get:

N' = rN - aN(r/a) = 0

N(1 - r/a) = 0

N = 0 or a - r = 0

N = 0 or N = c(r/a-5)/a

So the non-trivial equilibrium is:

N = c(r/a-5)/a

P = r/a

where c is any non-zero constant. This equilibrium represents a coexistence of both species, with the predator population depending on the prey population and vice versa.

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Answer:

Hey there!

The question is basically asking for you to solve a fraction subtraction problem, and fill in the missing values as you solve.

The given problem is 2/3 - 1/2. However, we can't subtract right now, since the denominators are different.

2/3 can be expressed as 4/6, and 1/2 can be expressed as 3/6.

Thus, the missing denominator in line one is 6 and the missing numerator in line one is 3.

4/6-3/6=1/6.

Thus, the numerator in line two should be 1.

From top to bottom, the numbers in the three boxes should be 6, 3, and 1.

This can be a confusing topic, especially if you're just learning it. Let me know if you need additional help :)

Step-by-step explanation:

Expanding and simplifying 2(x + 7) + 3(x + 1):

2(x + 7) = 2x + 14

3(x + 1) = 3x + 3

Adding the two expressions:

2x + 14 + 3x + 3 = 5x + 17

So 2(x + 7) + 3(x + 1) = 5x + 17.

\( \sf2(x + 7) + 3(x + 1) \\ \sf2x + 14 + 3x + 3 \\ \sf5x + 17\)

a) The bias in a single measurement is 1.5 g and the uncertainty is 3 g.
b) The bias in the average of four independent measurements is 1.5 g and the uncertainty in the average is 2 g.
c) The bias in the average of four hundred independent measurements is 1.5 g and the uncertainty in the average is 0.6 g.

The bias of a measurement is a constant which does not change regardless of the number of measurements taken. Thus, the bias in each of the scenarios remains at 1.5 g. The uncertainty, however, is proportional to the square root of the number of measurements taken. This means that when four independent measurements are made, the uncertainty in the average decreases to 2 g (3/√4). When four hundred independent measurements are made, the uncertainty decreases further to 0.6 g (3/√400). The reduction in uncertainty is due to the fact that more measurements means the average value of the measurements is closer to the true value.

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The equation of the vertical line passing through the point (-7,2) is x = -7, while the equation of the horizontal line passing through the point (-7,2) is y = 2.

The equation of the vertical line passing through the point (-7,2) is x = -7.

The equation of the horizontal line passing through the point (-7,2) is y = 2.

To find the equation of a vertical line passing through a given point, we use the equation x = a, where 'a' is the x-coordinate of the point. In this case, the x-coordinate of the given point (-7,2) is -7, so the equation of the vertical line is x = -7.

To find the equation of a horizontal line passing through a given point, we use the equation y = b, where 'b' is the y-coordinate of the point. In this case, the y-coordinate of the given point (-7,2) is 2, so the equation of the horizontal line is y = 2.

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Yes, the result is a binomial probability distribution.

Therefore, the answer is D

An experiment is said to follow a binomial distribution if the following conditions are adequately met.

i. The experiment should consist of a definite number of independent and identical trials.

ii. Each trial should generate two outcomes- one success, and the other failure.

iii. The likelihood of success should be determined by a value that should remain constant throughout the experiment.

In the given experiment, we see that the 500 voters were selected randomly from the population of registered voters. This implies that n = 500 trials are independent and identical. Each trial generated into two outcomes- Political party A (success) and B (failure). The probability of success is 0.5, and it remains constant throughout the experiment. Thus the experiment is a binomial probability distribution.

The answer is D.

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Answer:

x=9

y=6

Step-by-step explanation:

x+y=15 .............(i)

x-y=3...........(ii)

Subtracting equation (ii) from equation (i)

or,  x+y -(x-y)=15-3

or,  x+y-x+y=12

or,  2y=12

or,  y=12/2

∴y=6

Now,

       Putting the value of y on equation (i),

or,  x+6=15

or,  x=15-6

∴x=9

polygon -- a closed figure made up of line segments

regular polygon -- a polygon whose sides are all the same length & whose angles are all the same measure

octagon -- a polygon with eight side

pentagon -- a polygon with five sides

quadrilateral -- a polygon with four sides

The exponential function that is equivalent to the given geometric equation is g(n) = 4^(log_4(g(n)/28) + 1)

To convert the given geometric equation to an exponential function, we need to rearrange the equation to isolate the exponential term on one side of the equation. This can be done by dividing both sides of the equation by 28.

g(n) = 28⋅4^(n−1)

g(n)/28 = 4^(n−1)

Next, we can use the property of logarithms to convert the exponential equation to a logarithmic equation. The property of logarithms states that log_b(a) = c is equivalent to a = b^c. Using this property, we can write the equation as:

log_4(g(n)/28) = n - 1

Finally, we can isolate n on one side of the equation by adding 1 to both sides of the equation:

n = log_4(g(n)/28) + 1

Therefore, the exponential function that is equivalent to the given geometric equation is:

g(n) = 4^(log_4(g(n)/28) + 1)

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Answer:

Any equation that has the same slope

Step-by-step explanation:

If two li es have the same slope that means they will never intercept

Answer:  -w

Step-by-step explanation:

21 – 8(w + 3) + 3 + 7 w

Answer:

27

Step-by-step explanation:

I broke the figure up into 3 rectangles.

5x2 = 10

2x3 = 6

4x5 = 20

This adds to 36.  Then subtract out the green square of 9

36 - 9 = 27

Answer:

Yes because 9 + 12 = 15

Step-by-step explanation:

Answer:

The resulting line would be x=10, which looks like a vertical line at the x-value of 10

Step-by-step explanation:

-7x=-70

You are trying to isolate the x, which means you must divide both sides by -7

Fortunately, this results in the right side being 10, so x=10.

Richard gets an average of 17 calls during his 8 hour work day. in order to find the probability that richard will get at most 5 calls in a 2 hour portion of his work day using the poisson distribution,The probability that Richard will receive at most 5 calls in a 2-hour portion of his work day is approximately 0.092.

In this scenario, the random variable X represents the number of calls that Richard receives during a 2-hour portion of his 8-hour work day.

The Poisson distribution is commonly used to model the probability of a certain number of rare events occurring in a fixed interval of time or space. In this case, we can use the Poisson distribution to model the number of calls that Richard receives in a 2-hour period, given that we know the average number of calls he receives in an 8-hour work day.

The Poisson distribution has a single parameter, λ, which represents the average rate at which the rare events occur. In this case, λ = 17/8 = 2.125, since Richard receives an average of 17 calls in an 8-hour work day.

To find the probability that Richard will receive at most 5 calls in a 2-hour portion of his work day, we can use the Poisson probability mass function (PMF), which gives the probability of observing k events in a given time interval, given the average rate λ. The PMF is given by:

P(X = k) = (e^(-λ) * λ^k) / k!

where k is the number of events, λ is the average rate, and e is the mathematical constant approximately equal to 2.71828.

So in this case, we want to find the probability that X ≤ 5, i.e., the probability that Richard will receive 0, 1, 2, 3, 4, or 5 calls in a 2-hour portion of his work day. We can use the cumulative distribution function (CDF) of the Poisson distribution to find this probability:

P(X ≤ 5) = Σ(k=0 to 5) P(X = k)

where Σ is the summation symbol.

Plugging in the values, we get:

P(X ≤ 5) = Σ(k=0 to 5) (e^(-λ) * λ^k) / k! = (e^(-2.125) * 2.125^0 / 0!) + (e^(-2.125) * 2.125^1 / 1!) + (e^(-2.125) * 2.125^2 / 2!) + (e^(-2.125) * 2.125^3 / 3!) + (e^(-2.125) * 2.125^4 / 4!) + (e^(-2.125) * 2.125^5 / 5!) ≈ 0.092

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Rounding to the nearest tenth, the area of the sector is approximately 3.4 square meters.

The area of a sector of a circle can be found using the formula:
Area = (θ/2π) * πr²
where θ is the central angle and r is the radius of the circle.
In this case, the radius is given as 3.2 m and the central angle is 2π/3.
Substituting these values into the formula, we get:
Area = (2π/3 * 1/2π) * π(3.2)²
Simplifying further, we have:
Area = (1/3) * 3.2²
Calculating the value, we get:
Area ≈ 3.4133 square meters
Rounding to the nearest tenth, the area of the sector is approximately 3.4 square meters.

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Hello!

total = 3 + 1 = 4

1/4 = 1*9/4*9 = 9/36

3/4 = 3*9/4*9 = 27/36

The test statistic is calculated to be \(t_0 = 0.59\). The p-value is found to be 0.278. The sample mean of 531 is not statistically significantly higher than the population mean of 524.

a) For the test statistic,

\(t_0 = \frac {(sample mean - population mean)}{\frac {(sample standard deviation)}{ \sqrt {n}}}\).
Plugging in the values, we get \(t_0 = \frac {(531 - 524)}{\frac {(119)}{ \sqrt {2200}}} \approx 0.59\).

b) The p-value represents the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true. To find the p-value, we compare the calculated test statistic with the appropriate t-distribution table or use statistical software. In this case, the P-value is found to be 0.278.
c) Since the P-value (0.278) is greater than the common significance level of 0.05, we fail to reject the null hypothesis. This means that the sample mean of 531 is not statistically significantly higher than the population mean of 524. Therefore, based on the available evidence, there is no convincing statistical support to claim that the review course developed by the math teacher has a significant impact on increasing the math scores of students.
d) While the increase in score from 524 to 531 may not have statistical significance, it is important to consider practical significance as well. Practical significance refers to the real-world impact or meaningfulness of the observed difference. In this case, a difference of 7 points may not have practical significance for a school admissions administrator since it falls within the natural variability of the test scores and may not significantly impact the admissions decision-making process. Other factors such as overall academic performance, extracurricular activities, and letters of recommendation may have a greater influence on the decision.

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Answer:

13) First blank: 2 Second blank: 5

14) First blank: 7 Second blank: 5

15) First blank: -11 Second blank: -2

16) First blank: 4 Second blank: 3

17) First blank: -3 Second blank: -8

18) First blank: -2 Second blank:6

Answer:

The number is 4/9

Step-by-step explanation:

3(6*(4/9))=3*(2+(2/3))=8

In order to move a the constant terms to the right hand side, we need to subtract 0.4 from both sides of the equation.

In an equation, the constant terms are those terms that do not have any alphabet attached to them. In this case, 4 and 0.4 are constant terms.

In order to move a the constant terms to the right hand side, we need to subtract 0.4 from both sides of the equation thus;

-9x + 0.4 - 0.4 = 4 - 0.4

-9x = 3.6

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Answer:

4 days

Step-by-step explanation:

to find this our you must add 78 and 25 before doing anything as they are both part of the daily pass rates

78 + 25 = 103

now you must divide 350 by 103

350/103 = 3.39805825

because you want to find when the season pass is less expensive than the daily pass you must round up

4 is your answer