−3(x+1)(x−3) in standard form

Does a population have to be normally distributed in order to use the chi-square distribution? Choose the correct answer below B. No, the population can have any distribution to use the chi-square distribution.

The chi-square distribution is commonly used to test the goodness-of-fit between an observed distribution and an expected distribution (which can be any theoretical distribution). It is not necessary for the population to be normally distributed or follow any specific distribution to use the chi-square test.

The chi-square distribution can be used with any population distribution, not just the normal distribution or any other specific distribution.

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The velocity with which the apple strikes the ground​ is 2 m/s.

In every case, we add the speed of the object (relative to the reference point) to the speed of the reference point (relative to the ground) to find the speed of the object relative to the ground. (We choose to use + to mean "up" or "forward".)

The hot air balloon is descending with a constant velocity of 3 ms. when somebody inside the balloon throws an apple downward with a velocity of 5 m.s¹ so the velocity with which the apple strikes the ground​

... (3m/s) + (-5m/s) = -2m/s

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The value of the angles m∠A is 95 degrees, m∠BOT is 195 degrees, m∠ATO is 40 degrees and m∠PBQ is 40 degrees.

First, let's find the measure of angle m∠A. Since PT is tangent to circle O, we know that angle m∠T is a right angle (90 degrees). Since arc AB and arc BT add up to the whole circle (360 degrees), we can find their measures as follows:

m(arc AB) = m(arc OB) - m(arc OA)

= 360 - m(arc OA)

= 360 - 2m∠P (since m∠P = m(arc OA)/2)

= 360 - 2(40) = 280

m(arc BT) = 180 - m∠T (since arc BT is a minor arc and m(arc BT) = 180 - m∠T)

= 180 - 90 = 90

Therefore, m∠A = (m(arc AB) - m(arc BT))/2 = (280 - 90)/2 = 95 degrees.

Next, let's find the measure of angle m∠BOT. Since PT is tangent to circle O, we know that angle m∠T is a right angle (90 degrees).

This gives us:

m∠BOT = 1/2 (m(arc BA) - m(arc BT))

= 1/2 (m(arc OA) + m(arc AB) - m(arc BT))

= 1/2 (2m∠P + 280 - 90) (using the same arc measures as before)

= 1/2 (2(40) + 190)

= 135 degrees.

Next, let's find the measure of angle m∠ATO. This is the angle between the secant PBOA and the tangent PT, on the opposite side of point T from angle m∠BOT.

We can use the alternate segment theorem, which states that the angle between a tangent and a chord at the point of contact is equal to the angle in the alternate segment. In this case, angle m∠ATO is equal to angle m∠P.

Therefore, m∠ATO = 40 degrees.

Finally, let's find the measure of angle m∠PBQ. In this case, angle m∠PBQ is congruent to angle m∠P, which we have already found to be 40 degrees. Therefore, m∠PBQ = 40 degrees.

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Answer:

Step-by-step explanation:

near 9000

The absolute value function that matches the graph is given as follows:

y = |x|

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

The vertex of the function in this problem is at the origin, hence:

(h,k) = (0,0).

The leading coefficient is of a = 1, as when x = 1, y = 1.

Hence the absolute value function that matches the graph is given as follows:

y = |x|

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The value of y is given as follows:

y = 12.

The value of x is obtained applying the angle bisection theorem, which divides an angle into two angles of equal measure, hence the opposite segments also have equal length.

The segments for this problem, along with their lengths, are given as follows:

Hence the value of y is obtained as follows:

5y - 18 = 3y + 6

2y = 24

y = 12.

(due to the angle bisection theorem, both segments have equal length, hence we equal their lengths to obtain the variable y).

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Answer:

The probability is 2/10 or 0.2

Step-by-step explanation:

Probability of student getting grade A=number of students who will get grade A/Total number of students grade

T(s)=28+35+56+14+7=140

P=28/140

P=2/10 or 0.2

a) The actual distance between towns K and L is: 100 km

b) As shown in the attached file

c) The bearing of town L from town K is 117 degrees.

The scale of the map is given as:

1 cm to represent 50 km

Now, when we measure the distance between K and L on the map, we see that it gives us a distance of 2 cm.

Using the scale of 1 cm: 50 km, we can say that:

Actual distance between towns K and L = (2 * 50)/1 = 100 km

b) Using a compass and it’s 3cm aiming down {South} as seen in the attached photo. Then a line was drawn aiming {South} with a ruler. On the end of the line the (x) point was put there to get the mark.

c) Measuring the angle gives the bearing of town L from town K which is 117 degrees.

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There is an 86.06% chance that the sample mean fill volume for a random sample of 45 bottles will fall between 1.98 and 2.02 liters.

The sampling distribution of the sample mean fill volume for a random sample of 45 bottles is approximately normal by the Central Limit Theorem, provided that the sample size is sufficiently large. The mean of the sample mean fill volume is equal to the target mean fill volume, μ=2.0 liters.

The standard deviation of the sample mean fill volume is equal to the standard error of the mean, which is σ/√n = 0.05/√45 ≈ 0.0075 liters.

To find the probability that the sample mean of 45 bottles is between 1.98 and 2.02 liters, we need to standardize the values using the formula z = (x - μ) / (σ / √n), where x is the sample mean, μ is the target mean, σ is the standard deviation of the population, and n is the sample size.

Thus, we have z1 = (1.98 - 2.0) / (0.05 / √45) ≈ -1.79 and z2 = (2.02 - 2.0) / (0.05 / √45) ≈ 1.79.

Using a standard normal distribution table or calculator, we find that the probability is approximately 0.8606. Therefore, there is an 86.06% chance that the sample mean fill volume for a random sample of 45 bottles will fall between 1.98 and 2.02 liters.

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The probability that the sample mean of 45 bottles is between 1.98 and 2.02 liters is approximately 0.9934 or 99.34%.

(a) The sampling distribution of the sample mean fill volume for a random sample of 45 bottles is approximately normal due to the Central Limit Theorem. The mean of the sampling distribution is equal to the target mean fill volume, which is μ = 2.0 liters. The standard deviation of the sampling distribution, also known as the standard error of the mean, is σ/√n, where σ is the standard deviation of the population and n is the sample size. Therefore, the standard error of the mean is:

SE = σ/√n = 0.05/√45 = 0.00746

So the mean and standard deviation of the sampling distribution are:

Mean = μ = 2.0 liters

Standard deviation = SE = 0.00746 liters

(b) We want to find the probability that the sample mean of 45 bottles is between 1.98 and 2.02 liters. We can standardize the values using the formula:

z = (x - μ) / SE

where x is the sample mean, μ is the population mean, and SE is the standard error of the mean. Thus:

z1 = (1.98 - 2.0) / 0.00746 = -2.68

z2 = (2.02 - 2.0) / 0.00746 = 2.68

Using a standard normal distribution table or calculator, we can find the probability that z is between -2.68 and 2.68:

P(-2.68 < z < 2.68) = 0.9967 - 0.0033 = 0.9934

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The opportunity cost of leisure can be measured by calculating the cost of the next-best alternative that could have been pursued instead of leisure.

To measure the opportunity cost of leisure, follow these steps:

Step 1: Identify the alternatives to leisure time. These can include activities like working, studying, or doing household chores.

Step 2: Determine the value of these alternative activities. For example, if you choose to work instead of enjoying leisure time, the value can be the income you would earn during that time.

Step 3: Compare the values of the alternative activities to the value of leisure. The opportunity cost of leisure is the highest value among these alternatives that you give up by choosing leisure. For example, if someone decides to spend an hour watching TV instead of working on a freelance project that could earn them $50, the opportunity cost of leisure in this case would be $50.

In summary, the opportunity cost of leisure is the value of the best alternative activity you forgo when choosing to spend time on leisure activities.

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Answer:

The value of x is 10cm

Step-by-step explanation:

The triangle given is a right angled triangle.

so two angles of the triangle is known,

let it be a=45

b= 90

and c=45, since its a right angled triangle.

to find out the sides of the triangle, we use the formula

tan45= opposite side/ adjacent side= 10/x; value of tan 90 is 1

so, 1= 10/x

x= 10cm

This is basically using SOH CAH TOA method, that is, sine theeta cosine theeta and tangent theeta.

We cannot determine the p-value for the test of whether or not there is a difference between the post- and pre-tests from the given information.

The confidence interval indicates the range of values that the true population mean difference is likely to fall within with 95% confidence. If the interval contains zero, then we cannot reject the null hypothesis that there is no difference between the post- and pre-tests. However, we don't know the exact p-value for this test based on the confidence interval alone.

To determine the p-value, we would need to know the sample mean difference, the standard error of the mean difference, and the sample size. With these values, we could calculate the test statistic and look it up in a t-distribution table or use software to find the p-value.

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(a) The ratio of the areas, A2/A1, is (4π[tex]r^{2}[/tex])/π[tex]r^{2}[/tex] = 16.
(b) The ratio of the volumes, V2/V1, is (4/3)π[tex]4r^{3}[/tex] / (4/3)π[tex]r^{3}[/tex] = 64.

(a) Given that the radius of sphere 2 is four times the radius of sphere 1, let's denote their radii as r1 and r2 = 4r1. The surface areas A1 and A2 can be calculated as follows:

A1 = 4πr1^2
A2 = 4π(4r1)^2 = 4π(16r1^2) = 64πr1^2

To find the ratio A2/A1:

A2/A1 = (64πr1^2) / (4πr1^2) = 64/4 = 16

So, the ratio of the areas is 16:1.

(b) Similarly, let's calculate the volumes V1 and V2:

V1 = (4/3)πr1^3
V2 = (4/3)π(4r1)^3 = (4/3)π(64r1^3) = 64(4/3)πr1^3

To find the ratio V2/V1:

V2/V1 = (64(4/3)πr1^3) / ((4/3)πr1^3) = 64

So, the ratio of the volumes is 64:1.

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The "v" shape of the concrete canal in Land Town is a smart design choice that helps to improve the efficiency and durability of the canal.

Canals are man-made waterways that are used for transportation, irrigation, drainage, and other purposes. The concrete canal in Land Town is shaped like a "v" at the bottom, which is a common design for canals. The "v" shape helps to improve the flow of water and reduce erosion. When water flows through a canal, it creates friction with the bottom and sides of the canal. This friction slows down the water and can cause erosion over time.

By shaping the bottom of the canal like a "v", the water can flow more smoothly and quickly, reducing friction and erosion. The "v" shape also helps to prevent debris from accumulating in the canal. Debris such as leaves, branches, and other debris can collect in the corners of a canal, obstructing the flow of water. With a "v" shape, the debris is more likely to be swept away by the flowing water.

In addition, the "v" shape can help to improve the capacity of the canal. By creating a deeper channel, more water can be transported through the canal, which can be especially important during times of heavy rainfall or flooding. Overall, the "v" shape of the concrete canal in Land Town is a smart design choice that helps to improve the efficiency and durability of the canal.

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Answer:

a) 15

b) 10

Step-by-step explanation:

a) [tex]3\sqrt{25}[/tex]

[tex]\sqrt{25}=5\\ 5(3)\\=15[/tex]

b) [tex]\sqrt{(2(50))}\\\sqrt{100}\\ =10[/tex]

Hope this helps!  Let me know if you need clarification.

To see the internal details of plant cells with a very high power of resolution, Zelda should choose a Scanning Electron Microscope (SEM).

A Scanning Electron Microscope uses a beam of electrons to produce high-resolution images of the surface of an object.

It provides a much higher resolution than a compound light microscope or a dissecting microscope, allowing for detailed observations of the internal structures of plant cells at a subcellular level.

A compound light microscope and a dissecting microscope are both optical microscopes that use visible light to produce an image.

While they can be used to observe plant cells, they have a much lower resolution than an SEM and may not provide the level of detail required for Zelda's research.

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You had $24.50 before your aunt gave you $50  to help buy the reflector telescope

If your aunt gave you $50 and you now have $25.50 left after buying the reflector telescope, then you spent:

$50 - $25.50

Fifty minus twenty five point five

We get twenty four point five

= $24.50

Therefore, you had $24.50 before your aunt gave you $50  to help buy the reflector telescope

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The length of YM in triangle XYZ, where XY = 8.3 cm and YZ = 11.9 cm, is approximately 2.77 cm.

To construct triangle XYZ with XY = 8.3 cm and YZ = 11.9 cm:

i. Start by drawing a line segment XY with a length of 8.3 cm.

ii. From point X, draw a line segment in the direction of YZ, measuring 11.9 cm. Label the endpoint as Z.

iii. Connect points Y and Z to complete the triangle XYZ.

To construct the midpoint M of XZ with angle YXZ = 60 degrees:

i. Draw a ray from point Y, forming an angle of 60 degrees with line segment YZ. Label the point where the ray intersects XY as M.

ii. Construct a line segment from point M perpendicular to line segment XY. This line segment will intersect line segment XZ at the midpoint M.

The length of YM can be calculated using the Pythagorean theorem.

If we let XZ = a, then XZ/2 = XM = MZ = a/2.

Using the angle YXZ = 60 degrees, we can write the length of YM as:

YM = [tex]\sqrt{(XM^2 + YX^2)} = \sqrt{((a/2)^2 + (8.3-a)^2)[/tex]

We can solve for a by setting the derivative of YM with respect to a to zero and solving for a, which yields a value of a = 4.85 cm.

Therefore, the length of YM is:

YM = [tex]\sqrt{((4.85/2)^2 + (8.3-4.85)^2)[/tex] = [tex]\sqrt{(7.686)[/tex] ≈ 2.77 cm.

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A fact is a statement that is considered to be true based on evidence or experience. It starts with a relationship, which expresses a connection or correlation between two or more entities, and is followed by a list of arguments.

The arguments of a fact can be variables, which represent unknown values, or simple values, such as numbers or strings. In some cases, a fact can have a structure similar to that of a rule, which defines a set of conditions that must be satisfied for the fact to be true. However, unlike a rule, a fact is not conditional and is considered to be true at all times.

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The given expression is (4x + 3) + (-2x + 4). To simplify the expression, we first combine like terms.

(4x + 3) + (-2x + 4) = 4x - 2x + 3 + 4 = 2x + 7

Therefore, the expression equivalent to (4x + 3) + (-2x + 4) is 2x + 7.

When adding or subtracting two expressions, we combine like terms by adding or subtracting the coefficients of the same variables. In the given expression, we have two terms, (4x + 3) and (-2x + 4).

We can first rearrange the terms by adding the coefficients of x and constants separately. By doing so, we obtain 4x - 2x and 3 + 4, which simplify to 2x and 7, respectively. Thus, we have the expression 2x + 7 as the simplified form of the given expression.

This is a useful technique when simplifying algebraic expressions and can be used to simplify more complex expressions involving multiple variables and terms.

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The given differential equation is of the form dy/dx = x^(9/2 + 1). To solve this, we can integrate both sides with respect to x to obtain the general solution:

y = (2/11)x^(11/2) + C

where C is a constant of integration.

Using the initial condition y(1) = 3, we can solve for C:

3 = (2/11)1^(11/2) + C

C = 3 - 2/11

Substituting this value of C in the general solution, we obtain the particular solution:

y = (2/11)x^(11/2) + 3 - 2/11

y = (2/11)x^(11/2) + 31/11

However, none of the given answer choices match this form exactly. Answer choice A can be simplified to:

y = (2/3)(x^(9/2 + 1))^(3/2) + 7/3

y = (2/3)(x^11)^(3/2) + 7/3

y = (2/3)x^(33/2) + 7/3

This is not equivalent to the given particular solution. Answer choice B can be simplified to:

y = (2/27)x^8(x^(9/2 + 1))^(3/2) + (81 - 4sqrt(2))/27

y = (2/27)x^8(x^11)^(3/2) + (81 - 4sqrt(2))/27

y = (2/27)x^8x^(33/2) + (81 - 4sqrt(2))/27

y = (2/27)x^(49/2) + (81 - 4sqrt(2))/27

This is also not equivalent to the given particular solution. Answer choice C is an integral that does not evaluate to the given particular solution. Answer choice D is similar to the given general solution, but the lower limit of integration should be 1 instead of 0.

Therefore, none of the given answer choices are correct. The particular solution to the given differential equation with initial condition y(1) = 3 is:

y = (2/11)x^(11/2) + 31/11.

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The numbers that form a fact family are as follows:

The numbers that do not form a fact family are:

A fact family is a group of mathematical facts that relate the same set of numbers together. It is also known as a number family and often employs three numbers.

Fact families are typically depicted as triangles. The three numbers that make up the fact family are written in the three corners of the triangle close to the vertices.

An example of a fact family is 9, 7, 16

9 + 7 = 16

7 + 9 = 16

16 - 9 = 7

16 - 7 = 9

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The confidence interval 0.333 < p < 0.777 can be expressed in the form p +- E as 0.555 +- 0.222.

The confidence interval 0.333 < p < 0.777 gives a range of possible values for the true population proportion, p, with a certain level of confidence. To express this interval in the form p +- E, we need to find the midpoint of the interval, which is (0.333 + 0.777)/2 = 0.555. This midpoint represents the best estimate of the true population proportion based on the sample data.

To find the margin of error, E, we need to calculate half of the width of the confidence interval, which is (0.777 - 0.333)/2 = 0.222. The margin of error represents the maximum amount by which the sample proportion may differ from the true population proportion.

Therefore, the confidence interval 0.333 < p < 0.777 can be expressed in the form p +- E as 0.555 +- 0.222.

A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. In this case, the confidence interval 0.333 < p < 0.777 gives a range of possible values for the true population proportion, p, with 95% confidence. This means that if we were to repeat the sampling process many times and construct a confidence interval each time, about 95% of the intervals would contain the true population proportion.

To express the confidence interval in the form p +- E, we need to find the midpoint of the interval, which is (0.333 + 0.777)/2 = 0.555. This midpoint represents the best estimate of the true population proportion based on the sample data.

The margin of error, E, represents the maximum amount by which the sample proportion may differ from the true population proportion. To find the margin of error, we need to calculate half of the width of the confidence interval, which is (0.777 - 0.333)/2 = 0.222. This means that the sample proportion could vary by up to 0.222 in either direction from the midpoint of the interval.

Therefore, the confidence interval 0.333 < p < 0.777 can be expressed in the form p +- E as 0.555 +- 0.222. This means that we are 95% confident that the true population proportion falls within the range of 0.333 to 0.777, with the best estimate of the true population proportion being 0.555 and a margin of error of 0.222.

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The number of people sharing the video doubles each hour.

From the question, we have the following parameters that can be used in our computation:

f(x) = 4(2)ˣ

The above function is an exponential function

Where

x represents the number of hours after the first time it appears

An exponential function is represented as

f(x) = a(b)ˣ

Where

a = initial value = 4

b = rate = 2

This means that the number of the video doubles each hour i.e. b is correct

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The given expressions are a+12, 7+a, a+7, & 5a.

The given values 1, 3 & 4 are substituted in the given expressions as follows

For value 1 the expressions will be given as follows

1+12=13, 7+1=8, 1+7=8 & 5*1=5

For value 3 the expressions will be given as follows

3+12=15, 7+3=10,3+7=10 & 5*3=15

For value 4 the expressions will be given as follows

4+12=16, 7+4=11,4+7=11 & 5*4=20

From the obtained results above it is clear that expressions a+7 & 7+a are equal for all possible values as the result obtained from them is same irrespective of the value substituted.

Similarly, the expressions a+12 & 5a are equivalent for a = 3 as the result obtained is same on substituting a=3 but it is not true for all other values.

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Answer:

54 et 60 sont les multiples de 6 entre 50 et 70

In case of one-way anova where x are treatments and y are observations, the degrees of freedom for the f statistic are three and 20.

A one way analysis of variance refers to the technique that is used in knowing if there's significant difference between two samples means. ANOVA uses F-tests to statistically test the equality of means.

Now, if x and y are represented the number of treatments and observations then degree of freedom for f statistic is either 3 or 20. Because two separate samples are used to compute a F-score and the samples with different size, so, there are two separate degrees of freedom one for each sample, either it is three or twenty. Hence, required value either 3 or 20.

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