To satisfy your curiosity about whether frogs from a pond on one side of town jump farther than frogs from a pond on the other side of town, you measure jumping distance for a random sample of frogs from each pond

The solution to each of the arithmetic sequence are:

1) a₁₀ = 56

2) a₁₀ = 87

3) missing term is 13

4) missing term is 14

The formula for the nth term of an arithmetic sequence is:

aₙ = a + (n - 1)d

where:

a is first term

n is nth term

d is common difference

1) a = 2

d = 6

a₁₀ = 2 + (10 - 1)6

a₁₀ = 2 + 54

a₁₀ = 56

2) a = 15

d = 8

a₁₀ = 15 + (10 - 1)8

a₁₀ = 87

3) The missing term will be gotten by finding the common difference.

d = (22 - 4)/2

d = 18/2

d = 9

missing term = 4 + 9 = 13

4) The missing term will be gotten by finding the common difference.

d = (53 - 25)/2

d = 28/2

d = 14

missing term = 4 + 9 = 14

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The left whisker is from 1 to 4, the 50% is 4 to 7 and the right whisker is between 7 to 10.

Given that a whiskers plot, we need to determine the left whisker, 50% and the right whisker of the plot,

We know that,

The plot divides the data into 4 equal parts. The left whisker represents the bottom 25% of the data, the left half of the box represents the second 25%, the right half of the box represents the third 25%, and the right whisker represents the top 25%.

Hence, the left whisker is from 1 to 4, the 50% is 4 to 7 and the right whisker is between 7 to 10.

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The period of the function is 30 seconds.

The distance between the repetition of any function is called the period of the function. For a trigonometric function, the length of one complete cycle is called a period.

The period of a function is the length of one complete cycle or oscillation. In this case, the function represents the height of a weight on a spring as a function of time. To determine the period, we need to identify the time it takes for the function to repeat.

Looking at the given table, we can observe that the values of t repeat after 30 seconds. From t = 0 to t = 30, the function completes one full cycle.

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The gradient of the stream is 1 meter per kilometre, which means that the stream drops 1 meter for every kilometre travelled. This is a relatively gentle slope and suggests that the stream is not flowing rapidly or eroding its bed very quickly.

The gradient of a stream is a measure of its steepness and is calculated by dividing the change in elevation by the distance travelled. In this case, the stream drops 15 meters in 15 kilometres, which means that the gradient can be calculated as follows:
Gradient = Change in elevation ÷ Distance travelled
Gradient = 15 meters ÷ 15 kilometers
Since we need to express the gradient in terms of meters per kilometre, we can simplify the above equation as follows:
Gradient = (15 meters ÷ 15,000 meters) × 1,000
Gradient = 1 meter per kilometer
Therefore,  understanding the gradient of a stream is important for a range of activities, including flood control, erosion management, and habitat restoration. By monitoring changes in the gradient over time, scientists and engineers can gain insights into the health and behaviour of streams and develop strategies to protect them.

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The reason why x ≥ 0 and y ≥ 0 is simply because the number of DVDs and the number of CDs cannot not be less than zero and the shop cannot have zero products.

A graph which shows the region that satisfies all three inequalities is shown below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of DVDs and the number of CDs, and then translate the word problem into an algebraic equation (linear inequalities) as follows:

Since the cost of a DVD is $10 and the cost of a CD is $8 and Andrew goes into the shop with $40 to spend, a system of linear inequalities that models the situation and constraints is given by;

x ≥ 0

y ≥ 0

10x + 8y ≤ 40

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Answer: The answer is D

Step-by-step explanation:

Brainliest Please! Good luck to your sis!

Answer: 9 inches is correct

Step-by-step explanation: 1 and half times 6 = 9 so your answer was correct.

Hope this helps!

Answer: There are different ways to approach this problem, but one possible method is:

First, we need to know how many minutes there are in a year. Since a year has 365 days (or 366 days in a leap year), we can multiply this by the number of minutes per day:

365 days/year × 24 hours/day × 60 minutes/hour = 525,600 minutes/year (non-leap year)

Next, we can use the given average heart rate of 1 × 10^2 beats per minute to calculate the total number of heart beats in a year:

1 × 10^2 beats/minute × 525,600 minutes/year = 52,560,000 beats/year

Therefore, Kenny's heart beats about 52,560,000 times in a non-leap year if his average heart rate is 1 × 10^2 beats per minute.

The probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 4 percentage points of the actual proportion is  98.6%.

We are given that the population proportion, p, is 0.6, and we want to find the probability that a sample of 1000 voters would yield a sample proportion within 0.04 of p. Let's first find the standard error of the sample proportion:

SE = √(p*(1-p) / n)

where p is the population proportion, 1-p is the proportion of voters who do not support the candidate, and n is the sample size.

Substituting the given values, we get:

SE = √(0.6 * 0.4 / 1000) = 0.01549193338

To find the probability that the sample proportion is within 0.04 of p, we can use the normal distribution and the z-score formula:

z = (sample proportion - p) / SE

where the sample proportion follows a normal distribution with mean p and standard deviation SE.

Substituting the values, we get:

z = (0.64 - 0.6) / 0.01549193338 = 2.590020246

z = (0.56 - 0.6) / 0.01549193338 = -2.590020246

Using a standard normal distribution table or calculator, we can find the area under the curve between z = -2.590020246 and z = 2.590020246 to be approximately 0.986.

Therefore, the probability that a sample of 1000 voters would yield a sample proportion within 0.04 of the actual proportion is approximately 0.986 or 98.6%.

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The requried,  quantities that can be represented by 0 have been mentioned below.

The quantities that can be represented by 0 are:

A. The elevation at sea level (since sea level is defined as 0 elevations)

D. The amount of money in an account in which a person owes money (since a negative balance is represented by 0)

Therefore, the correct options are A and D.

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There are 60 different possible outcomes if Brody spins all three spinners.

To determine the total number of different possible outcomes when spinning three spinners, we need to multiply the number of outcomes on each spinner. The first spinner has 4 equal-sized sections, the second spinner has 3 equal-sized sections, and the third spinner has 5 equal-sized sections.

Therefore, the total number of possible outcomes is:

4 x 3 x 5 = 60

So there are 60 different possible outcomes if Brody spins all three spinners.

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Answer:

to know how much grain the cylinder can contain/hold you calculate the volume of the cylinder.

Step-by-step explanation:

volume= πr^2h

=π×9^2×11

=891π inches cube/2799.16 inches cube

The given statement "A Bernoulli experiment has three possible outcomes." is False because a Bernoulli experiment only has two possible outcomes, which are often denoted as success or failure.

For example, flipping a coin is a Bernoulli experiment since the outcome can either be heads or tails. Rolling a die is not a Bernoulli experiment since it has more than two possible outcomes.

The outcome of a Bernoulli experiment is usually modeled by a random variable that takes on the value 1 if the experiment is a success and 0 if the experiment is a failure. The probability of success in a Bernoulli experiment is often denoted by p, while the probability of failure is denoted by q = 1 - p.

Bernoulli experiments are the building blocks for many other probability distributions and are often used to model real-world situations, such as whether a person will respond to a survey question with a "yes" or "no" answer, or whether a machine will produce a defective item during a manufacturing process.

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The volume of the right circular cylinder in terms of height "h" is (9π/16)h^3.

A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base.

To find the volume of a right circular cylinder, we use the formula:

V = πr^2h

Given that r = 3/4h, we can substitute this value into the formula:

V = π(3/4h)^2h

Simplifying the expression inside the parentheses:

V = π(9/16h^2)h

Expanding further:

V = (9π/16)h^3

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The value of x is 5 and value of y is 9 in the given equations.

[tex]\frac{8^x }{ 2^y} = 64[/tex]

[tex]3^4^x \times \frac{1}{9^(^y^ -^1^)} = 81[/tex]

From the first equation

[tex]\frac{2^3^x}{2^y } = 2^6[/tex]

[tex]2^(^3^x^-^y^) = 2^6[/tex]

As bases are equal then the powers will be added

So 3x - y = 6  ..........(1)

From the second equation:

[tex]3^4^x \times 9^(^-^(^y^-^1^)^) = 3^4[/tex]

[tex]3^4^x \times 3^2^(^-^(^y^-^1^)^) = 3^4[/tex]

So 4x + 2(1 - y) = 4

4x - 2y = 2

2x - y = 1   .............(2)

Subtract: (1) - (2):

value x = 5.

and  2(5) - y = 1

so y = 9.

Hence, the value of x is 5 and value of y is 9 in the given equations.

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The 95% confidence interval for Xavier's average distance traveled is (8.527, 8.673) miles, which means that we are 95% confident that the true population mean of Xavier's daily distance traveled is between 8.527 and 8.673 miles.

To create a 95% confidence interval for Xavier's average distance traveled, we can use the following formula:

[tex]CI = \bar{X} \pm z\times (\sigma /\sqrt{n } )[/tex]

Where:

[tex]\bar{X}[/tex] is the sample mean (8.6 miles)

σ is the population standard deviation (0.2 miles)

n is the sample size (30)

z is the z-score corresponding to the desired confidence level (95% confidence level corresponds to a z-score of 1.96)

Plugging in the values, we get:

CI = 8.6 ± 1.96*(0.2/√30)

CI = 8.6 ± 0.073

Therefore, the 95% confidence interval for Xavier's average distance traveled is (8.527, 8.673) miles.

Interpretation: We are 95% confident that the true population mean of Xavier's daily distance traveled is between 8.527 and 8.673 miles.

This means that if we were to repeat this study many times, we would expect the true population mean to be within this range 95% of the time.

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The two sets of possible dimensions for the rectangular plot are 12 m by 20 m, and 10 m by 24 m

A three-sided fence and the fourth side is the river, the perimeter will be:

P = 2L + W = 44 - L

where L is the length of the rectangular plot and W is the width.

We can simplify this equation by solving for W:

W = 44 - 2L - W

W = 44 - 2L

Next, we can use the area of the land to set up another equation:

A = LW = 192

Substituting the expression for W from the first equation into the second equation gives:

L(44 - 2L) = 192

-2L² + 44L - 192 = 0

Dividing both sides by -2 gives:

L² - 22L + 96 = 0

We can now use the quadratic formula to solve for L:

L = 12 or 10

So the possible dimension lengths of the rectangular plot are 12 m or 10 m.

We can use the first equation to find the corresponding widths:

W = 44 - 2L

For L = 12:

W = 44 - 2(12) = 20

So one set of possible dimensions is 12 m by 20 m.

For L = 10:

W = 44 - 2(10) = 24

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The value of x is 34.9cm( 1d.p)

A diagonal is the line segment that join two opposite vertices.A diagonal of a rectangle divides it into two congruent right triangles. The diagonals of a rectangle are the same length.

angle C = angle D

therefore 52+C +D = 180

2C = 180-52

C = 64°

To find BD

sin64/OD = sin52/17

OD = sin64 × 17/sin52

= 15.3/0.788

= 19.4

BD = 2 × 19.4 = 38.8

x = √ 38.8²-17²

x = √1505.44 - 289

x = √1216.44

x = 34.9 cm( 1 d.p)

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The number 320.5492492492... is rational and can be expressed as the fraction 1829/333.

To show that the number 320.5492492492... is rational, we can follow the same approach as before and express it as a sum of rational numbers.

Let x = 320.5492492492...

We can separate the integer part of x and the repeating decimal part:

x = 320 + 0.5492492492...

To express the repeating decimal part as a fraction, we can subtract a portion of it from the original number, like this:

1000x - 320000 = 549.2492492...

100000x - 32000000 = 549249.2492492...

Now we can subtract the first equation from the second equation:

99900x = 549249.2492492... - 549.2492492...

This simplifies to:

99900x = 548700

x = 548700/99900

Simplifying the fraction by dividing both numerator and denominator by their greatest common factor, we get:

x = 1829/333

Therefore, the number 320.5492492492... is rational and can be expressed as the fraction 1829/333.

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Many children develop the ability to do simple arithmetic problems during their early childhood years, typically between the ages of 4 and 6. Correct option is a).

During this time, children start to understand basic mathematical concepts such as counting, addition, and subtraction. They may also begin to recognize and name numbers and use basic math vocabulary. However, it's important to note that every child develops at their own pace and some may show these skills earlier or later than others. It's also important for parents and caregivers to provide opportunities for children to practice and reinforce these skills through activities such as counting objects, playing number games, and solving simple math problems.

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The equation that represents the data in the table is y = -0.5x^2 + 3.5x + 4.

To determine which equations represent the data in the table, we can plot the points given in the table and see which equations pass through all of them.

Plotting the points, we get:

(-2, 6)

(0, 3.5)

(2, 1)

(4, -1.5)

From this, we can see that the data does not lie on a straight line, so we can eliminate any linear equations.

However, we can use the method of finite differences to determine if a quadratic equation fits the data. Taking the first finite differences of the y values, we get:

(-2, 6)

(0, 3.5)

(2, 1)

(4, -1.5)

(3.5 - 6) = -2.5

(1 - 3.5) = -2.5

(-1.5 - 1) = -2.5

Since the first finite differences are constant, we know that the data can be represented by a quadratic equation.

Using the quadratic equation y = ax^2 + bx + c, we can plug in the given points to solve for a, b, and c.

Solving for a, b, and c, we get:

a = -0.5

b = 3.5

c = 4

Therefore, the equation that represents the data in the table is:

y = -0.5x^2 + 3.5x + 4

So the correct answer is:

y = -0.5x^2 + 3.5x + 4.

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True. In a test of hypothesis, if alpha (α) increases, beta (β) decreases. Alpha represents the probability of committing a Type I error, which occurs when the null hypothesis is rejected even though it is actually true.

Beta represents the probability of committing a Type II error, which occurs when the null hypothesis is not rejected even though it is false.

When alpha increases, it means we are more willing to reject the null hypothesis, thus making Type I errors more likely. As a result, the probability of making a Type II error (beta) decreases since we are less likely to accept the null hypothesis when it is false.  The relationship between alpha and beta in a test of hypothesis is complex and depends on several factors. It is not accurate to simply state that if alpha increases, beta decreases (or vice versa) without considering the context of the specific hypothesis test being performed.

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Answer:

it’s D

Have a Nice Best Day : )

So, the quartiles are Q1 = 59, Q2 = 62, and Q3 = 65.

IQR = Q3 - Q1 = 65 - 59 = 6.

The data set does have one outlier, The value 77.

It is above the upper outlier limit of 74.

a)To find the quartiles, we first need to arrange the data in order:

55 56 57 59 60 60 61 62 62 62 63 64 65 65 77

The median is the middle value of the data set, which is:

Median = 62

To find the first quartile (Q1), we take the median of the lower half of the data:

Q1 = Median of {55, 56, 57, 59, 60, 60, 61} = 58

To find the third quartile (Q3), we take the median of the upper half of the data:

Q3 = Median of {63, 64, 65, 65, 77} = 65

b)The interquartile range (IQR) is the difference between the third and first quartiles:

IQR = Q3 - Q1 = 65 - 58 = 7

c) To identify any outliers, we can use the rule that considers any value that falls below Q1 - 1.5 IQR or above Q3 + 1.5 IQR to be an outlier.

Lower outlier bound: Q1 - 1.5 IQR = 58 - 1.5(7) = 47.5

Upper outlier bound: Q3 + 1.5 IQR = 65 + 1.5(7) = 76.5

Since one value (77) that falls above the upper outlier bound, this value is considered an outlier.

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Sarah's final position would be negative. Therefore, option B is the correct answer.

Given that, Sarah starts at a positive position along the x-axis. She then undergoes a negative displacement.

A negative displacement means that Sarah has moved backward along the x-axis, so her final position would be negative.

Therefore, option B is the correct answer.

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The percentage of adults who have an IQ score between 92 and 112 points using the z score is 33.59%.

Given that,

Assume the distribution of IQ scores for adults can be modeled with a normal distribution with a mean score of 100 points and a standard deviation of 10 points.

μ = 100 and σ = 10

We have, z score, z = (x - μ) / σ

For x = 92,

z = (92 - 100) / 10 = -0.8

For x = 112,

z = (112 - 100) / 10 = 0.12

Percent corresponds to the left of z = -0.8 is 0.2119.

Percent corresponds to the left of z = 0.12 is 0.5478.

Required percent = 0.5478 - 0.2119 = 0.3359 = 33.59%

Hence the required percentage is 33.59%.

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With Audra climbing a mountain at a constant rate and her height at various times given as 11:13- 5211 1:33-5651 1:48-5981, she is climbing at the unit rate of D. 22 feet per minute.

The unit rate is the ratio that compares two values or quantities.

The unit rate is also described as the slope, which is calculated as the quotient between the Rise and the Run or the speed (the quotient between the total distance and the total time).

Time    Height

11:13-     5211

1:33-     5651

1:48-     5981

Unit rate (Slope) = Rise/Run

5,981 - 5,651 = 330 feet

1:48 - 1:33 = 15 minutes

330 ÷ 15 = 22 feet per minute

Thus, we can conclude that Audra is climbing the mountain at a rate or speed of Option D. 22 feet per minute.

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The equation of circle D is (x + 2)2 + y² = 32 then the points (-6,-4) and (-4,6) lie on circle D

The equation of a circle with center (h,k) and radius r is (x - h)² + (y - k)² = r².

This is called the standard form of the equation of a circle.

In the given equation, (x + 2)² + y² = 32, we can see that the center of the circle is (-2, 0) and the radius is √32 = 4√2.

To determine which points lie on the circle, we substitute the x and y coordinates of each point into the equation and check if the equation is true.

If it is true, then the point lies on the circle.

Let us check if (-6, -4) lies on the circle, we substitute x = -6 and y = -4 into the equation:

(-6 + 2)² + (-4)² = 32

(-4)² + (-4)² = 32

16 + 16 = 32

32 = 32

Since the equation is true, (-6, -4) lies on the circle.

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Answer:

-19d-4p+2

Step-by-step explanation:

This is very simple, we can rearrange this expression to make it easier to do the properties:

-9d-10d-4p-6+8

Next, we can subtract:

-19d-4p+2

This is the final expression, hope this helped :)

Answer:

Step-by-step explanation:

whats the meaning of life...

This value is approximate.

============================================

Explanation:

We need to determine mu.

We'll use the fact x = 662.5 pairs up with z = 1.5

z = (x - mu)/sigma

1.5 = (662.5 - mu)/75

1.5*75 = 662.5 - mu

112.5 = 662.5 - mu

112.5 + mu = 662.5

mu = 662.5 - 112.5

mu = 550

----------

Then compute the z score when x = 475

z = (x - mu)/sigma

z = (x - 550)/75

z = (475 - 550)/75

z = -1

----------

Use a Z table to determine that

P(Z < -1) = 0.15866

which is approximate.

About 15.866% of the 300 students scored less than 475.

0.15866*300 = 47.598 which rounds to 48 and it is the final answer.