3. If the distance between P(-2, 3a - 4) and Q(-2, 5a - 2) is 12 units, find the possible values of a.​

Exercise 35:

Direction of p1p2⇀: (3, 4, -5)

Midpoint of line segment p1p2⇀: (0.5, 3, 2.5)

Exercise 36:

Direction of p1p2⇀: (3, -6, 2)

Midpoint of line segment p1p2⇀: (2.5, 1.5, 3)

Exercise 37:

Direction of p1p2⇀: (1, 1, 1)

Midpoint of line segment p1p2⇀: (1.5, 3.5, 4.5)

Exercise 38:

Direction of p1p2⇀: (2, -2, -2)

Midpoint of line segment p1p2⇀: (1, -1, -1)

To find the direction of p1p2⇀, we can subtract the coordinates of p1 from the coordinates of p2. This will give us a vector that points from p1 to p2. The direction of this vector is the direction of p1p2⇀.

To find the midpoint of line segment p1p2⇀, we can average the coordinates of p1 and p2. This will give us a point that is exactly halfway between p1 and p2.

Here is a more mathematical explanation of how to find the direction and midpoint of a line segment:

Let p1 = (x1, y1, z1) and p2 = (x2, y2, z2) be two points in space. The direction of p1p2⇀ is given by the vector

(x2 - x1, y2 - y1, z2 - z1)

The midpoint of line segment p1p2⇀ is given by the point

(x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2

Here is a sequence that is not an arithmetic sequence:

1, 4, 5, 8, 10

The explicit formula for this sequence is 2^n - 1, where n is the term number. The recursive formula is a_n = 2a_{n-1} - a_{n-2}.

Here is an explanation of the explicit formula:

The first term of the sequence is 1, which is just 2^0 - 1. The second term is 4, which is 2^1 - 1. The third term is 5, which is 2^2 - 1. The fourth term is 8, which is 2^3 - 1. The fifth term is 10, which is 2^4 - 1.

Here is an explanation of the recursive formula:

The first two terms of the sequence are 1 and 4. The third term is 5, which is equal to 2 * 4 - 1. The fourth term is 8, which is equal to 2 * 5 - 4. The fifth term is 10, which is equal to 2 * 8 - 5.

As you can see, the recursive formula generates the terms of the sequence by multiplying the previous term by 2 and then subtracting the previous-previous term. This produces a sequence that is not an arithmetic sequence, because the difference between consecutive terms is not constant.

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HERE YOU GO!!!!!!!!!!

Answer:

D

Step-by-step im not Shure but I think its D

Inferential statistics involves using sample data to make inferences, predictions, or generalizations about a larger population, providing valuable insights and conclusions based on statistical analysis.

The term "inferential statistics" is associated with the task of making inferences or drawing conclusions about a population based on sample data.

In other words, it involves using sample data to make generalizations or predictions about a larger population.

Inferential statistics is concerned with analyzing and interpreting data in a way that allows us to make inferences about the population from which the data is collected.

It goes beyond simply describing the sample and aims to make broader statements or predictions about the population as a whole.

This branch of statistics utilizes various techniques and methodologies to draw conclusions from the sample data, such as hypothesis testing, confidence intervals, and regression analysis.

These techniques involve making assumptions about the underlying population and using statistical tools to estimate parameters, test hypotheses, or predict outcomes.

The goal of inferential statistics is to provide insights into the larger population based on a representative sample.

It allows researchers and analysts to generalize their findings beyond the specific sample and make informed decisions or predictions about the population as a whole.

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The probability that all the marbles are red = 0.0058

When drawing without replacement, the total number of marbles decreases after each draw.

So, for the first draw, we have 21 marbles to choose from, for the second draw, we have 20 marbles, for the third draw, we have 19 marbles, and for the fourth draw, we have 18 marbles.

Therefore, the total number of possible outcomes = 21 × 20 × 19 × 18

Total outcomes = 143,640

Number of favorable outcomes

To draw all red marbles, we need to select 4 red marbles from the 7 red marbles available.

Favorable outcomes = 7 × 6 × 5 × 4

Favorable outcomes = 840

Probability = Favorable outcomes / Total outcomes

Probability = 840 / 143,640

Probability = 0.0058

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Answer:

\(a_{21}\) = 16

Step-by-step explanation:

You add the numbers.  The two top left, two top right, 2 bottom left, 2 bottom right.

8    -6

16    -12

They are asking what number is in the second row, first column.

This looks like a quadratic equation!

Let's first rewrite the equation in the standard form (where the coefficients of x2 and x, as well as the constant term all have absolute values greater than 0)

ax^2 + bx + c = 0

And then use the Quadratic Formula to solve for x.

x = (-b ± √[b^2 - 4ac])/2a

Where a, b, and c are the coefficients of x^2, x, and 1, respectively.

Now, we just need to substitute the constants and solve for x!

-8x^2 + 10x + 15 = 0

a = -8

b = 10

c = 15

x = (-10 ± √[100 - 4(-8)(-15)])/2(-8)

x = (-10 ± √[100 - 240])/-16

x = (-10 ± √-140)/-16

x_1 = -7/16

x_2 = -7/16

Since x must be a real number, we can disregard x_2 and therefore the value of x is -7/16.

So the value of x is -7/16!

If -7/16 isn't the answer you were looking for, then try it in decimal form.

Answer: Let's first rewrite the equation in the standard form (where the coefficients of x2 and x, as well as the constant term all have absolute values greater than 0)

ax^2 + bx + c = 0

And then use the Quadratic Formula to solve for x.

x = (-b ± √[b^2 - 4ac])/2a

Where a, b, and c are the coefficients of x^2, x, and 1, respectively.

Now, we just need to substitute the constants and solve for x!

-8x^2 + 10x + 15 = 0

a = -8

b = 10

c = 15

x = (-10 ± √[100 - 4(-8)(-15)])/2(-8)

x = (-10 ± √[100 - 240])/-16

x = (-10 ± √-140)/-16

x_1 = -7/16

x_2 = -7/16

Since x must be a real number, we can disregard x_2 and therefore the value of x is -7/16.

So the value of x is -7/16!

If -7/16 isn't the answer you were looking for, then try it in decimal form.

wich is -0.4375

Step-by-step explanation:

the asymptotic bound on the algorithm's running time is Θ(n^log_b(a)), which in this case is Θ(n^0.793).

To prove rigorously that f(n) = n² - 47n + 18 can be factored as (n - 2)(n - 9), we can use the factoring method.

Starting with f(n) = n² - 47n + 18, we look for two numbers, let's call them a and b, such that their sum is -47 and their product is 18.

We can try different factor pairs of 18 to find the combination that satisfies the conditions. In this case, the factors 2 and 9 satisfy the conditions because 2 + 9 = 11 and 2 * 9 = 18.

Now, we rewrite f(n) using these factors:

f(n) = n² - 47n + 18

    = n² - 2n - 9n + 18

    = (n² - 2n) + (-9n + 18)

    = n(n - 2) - 9(n - 2)

    = (n - 2)(n - 9)

Therefore, we have proven rigorously that f(n) = n² - 47n + 18 can be factored as (n - 2)(n - 9).

Regarding the algorithm's running time, T(n) = 3T(n/4) + n, we can apply the Master Theorem to find the asymptotic bound.

The Master Theorem is typically applied to recurrence relations of the form T(n) = aT(n/b) + f(n), where a ≥ 1, b > 1, and f(n) is an asymptotically positive function.

In this case, we have a = 3, b = 4, and f(n) = n.

Comparing the value of n in f(n) with n^log_b(a), we have n^log_b(a) = n^log_4(3) ≈ n^0.793.

Since f(n) = n is of the same order as n^log_b(a), we are in Case 2 of the Master Theorem.

Case 2 states that if f(n) is Θ(n^c) where c < log_b(a), then the running time T(n) is Θ(n^log_b(a)).

In our case, c = 1 and log_b(a) ≈ 0.793, which satisfies the condition c < log_b(a).

Therefore, the asymptotic bound on the algorithm's running time is Θ(n^log_b(a)), which in this case is Θ(n^0.793).

Note: The value of n^log_4(3) was approximated for simplicity, but the actual value can be calculated using logarithmic properties if needed.

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Answer:

103°

Step-by-step explanation:

A supplementary angle is when two angles add up to be 180°. So, we can subtract to find its suplement.

180 - 77 = 103

Best of Luck!

B. No, because the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough.

The Central Limit Theorem (CLT) is a fundamental concept in statistics that states that as the sample size increases, the sampling distribution of the sample means will approach a normal distribution. However, this is only true if certain conditions are met, one of which is having a large enough sample size.
The CLT states that the sampling distribution of x will be approximately normally distributed if the sample size is large enough (usually greater than 30). If the sample size is small, the sampling distribution may not be normally distributed. In such cases, other statistical techniques like the t-distribution should be used.
Furthermore, the CLT assumes that the population being sampled is not necessarily normally distributed, but it does require that the population has a finite variance. This means that even if the population is not normally distributed, the sampling distribution of x will still be approximately normal if the sample size is large enough.
In conclusion, the answer is B, as the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough.

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Answer:

B

Step-by-step explanation:

the mean changes a lot, the median doesn't change

Answer:

B

Step-by-step explanation:

the mean is 599.5 and the median is 410

Answer:

C. 3k + 4

Step-by-step explanation:

combine like terms

-k + 4 + 4k

3k + 4

The question gives the relationship to be

We will interpolate to solve the question.

First Question: 147 mi

Cross multiplying,

In mathematics, the associative and commutative qualities were laws that are constantly used to add & multiply.

What is associative property?

The associative property indicates that can group number again the same response is obtained as well as the flipping property shows that you might switch numbers around and always reach the very same solution.

Associative rules say that this does not matter to arrange the integers. The legislation contains for adding & multiplying, and does not include subtraction and division.

          a + (b + c ) = (a + b ) + c  ⇒   Associative property of addition

          a + b = b + a  ⇒  commutative property of addition.

As we show above both the property used for the addition and no used for the subtraction, that is why before applying the property Juan applied reverse additives.

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Given:

In \(\Delta DE F,EM=12,FJ=60,MK=11\).

M is the centroid of the triangle DEF.

To find:

The lengths of MJ, DM and EL.

Solution:

We know that the centroid is the intersection points of medians of a triangle and centroid divides each median in 2:1.

M is the centroid of the triangle DEF. It means DK, EL, FJ are medians and M divides these segments in 2:1.

It is given that \(FJ=60\).

\(MJ=\dfrac{1}{2+1}FJ\)

\(MJ=\dfrac{1}{3}(60)\)

\(MJ=20\)

Therefore, the length of MJ is 20 units.

Let DM and MK are 2a and a. It is given that, \(MK=11\). Then

\(a=11\)

Now,

\(DM=2a\)

\(DM=2(11)\)

\(DM=22\)

So, the length of DM is 22 units.

Let EM and ML are 2a and a. It is given that, \(EM=12\). Then

\(2a=12\)

\(a=\dfrac{12}{2}\)

\(ML=6\)

Now,

\(EL=EM+ML\)

\(EL=12+6\)

\(EL=18\)

So, the length of EL is 18 units.

The plot of the parametric curves in the phase plane is illustrated below.

To eliminate time, we need to express one of the variables in terms of the other and then plot the resulting equation in the xy-plane. Let's start with the first curve, x = 3sin(2πt) and y = 4cos(2πt).

To eliminate time, we can use the trigonometric identity sin²(θ) + cos²(θ) = 1 to express sin(2πt) in terms of cos(2πt):

sin²(2πt) + cos²(2πt) = 1

sin(2πt) = ±√(1 - cos²(2πt))

We can then substitute this expression for sin(2πt) in the equation for x:

x = 3sin(2πt) = 3*±√(1 - cos²(2πt))

Squaring both sides and rearranging, we get:

(x/3)² + (y/4)² = 1

This is the equation of an ellipse centered at the origin with semi-axes of length 3 and 4. We can graph this ellipse in the xy-plane to get the phase portrait of the first curve.

For the second curve, x =  \(e^{-2t}\)  and y = -2 \(e^{-2t}\) , we can eliminate time by solving for  \(e^{-2t}\)  in terms of y and substituting into the equation for x:

\(e^{-2t}\)  = -y/2

x = \(e^{-2t}\) = -y/2

This is the equation of a line passing through the origin with slope -1/2. We can graph this line in the xy-plane to get the phase portrait of the second curve.

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A. The researcher needs to sample at least 78 additional adult Americans.

B.  The researcher needs to sample at least 106 additional adult Americans.

To determine how many more adult Americans the researcher needs to sample in order to have a sample proportion that is approximately normally distributed, we need to use the following formula:

n >= (z * sqrt(p * q)) / d

where:

n is the required sample size

z is the standard score corresponding to the desired level of confidence (e.g. for a 95% confidence interval, z = 1.96)

p is the estimated population proportion

q = 1 - p

d is the maximum allowable margin of error

(a) If 10% of all adult Americans support the proposed changes, then the estimated population proportion is p = 0.1 and the sample proportion is equal to the number of adults who support the changes divided by the total sample size. Let's assume that the researcher wants a maximum margin of error of 0.05 and a 95% confidence interval. Then, we have:

d = 0.05

z = 1.96

p = 0.1

q = 0.9

Substituting these values into the formula above, we get:

n >= (1.96 * sqrt(0.1 * 0.9)) / 0.05

n >= 77.96

Therefore, the researcher needs to sample at least 78 additional adult Americans.

(b) If 15% of all adult Americans support the proposed changes, then the estimated population proportion is p = 0.15. Using the same values for z and d as before, we get:

d = 0.05

z = 1.96

p = 0.15

q = 0.85

Substituting these values into the formula, we get:

n >= (1.96 * sqrt(0.15 * 0.85)) / 0.05

n >= 105.96

Therefore, the researcher needs to sample at least 106 additional adult Americans.

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The value of test statistic for test of independence is 62.5

The Chi-square test of independence checks that two variables are related or not. We have to count for two nominal variables. We also believe that the two variables are unrelated. The test allows us to determine whether or not our idea is plausible.

The sections that follow go over what we need for the test, how to perform it, understanding the results, statistical details, and p-values.

Given,

the table shows the beverage preferences for random samples of teens and adults.

For calculating the test statistics,

First wee need to calculate the expected values of every observed values.

Expected values for teens,

\(E(50)=\frac{250*400}{1000}=100\\\\E(100=)\frac{250*400}{1000}=100\\\\E(200)=\frac{400*400}{1000}=160\\\\E(50)=\frac{100*400}{1000}=40\)

Expected values for adults,

\(E(200)=250-100=150\\\\E(150)=250-100=150\\\\E(200)=400-160=240\\\\E(50)=100-40=60\)

Now, the test statistic is given by:

\(X^2=\frac{\sum\limits^n_{i=1}(O_i-E_i)^2}{E_i}\)

Where, Ei=expected value and Oi = observed value

\(X^2=\frac{(50-100)^2}{100}+\frac{(100-100)^2}{100}+...\frac{(200-240)^2}{240}+\frac{(50-60)^2}{60}=62.5\)

So, the value of test statistic for this test independence is 62.5.

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Your question is incomplete, here is the complete question

The table below gives beverage preferences for random samples of teens and adults.

                  teens adults total

coffee      50 200        250

tea              100 150        250

soft drink      200 200        400

other       50 50        100

                     400 600        1000

we are asked to test for independence between age (i.e., adult and teen) and drink preferences. the test statistic for this test of independence is ?

Answer:eu noa

Step-by-step explanation:falo inglês

Answer:

hiiiiiiiiiiiiiiiiiiiiiiiiiiiii

Step-by-step explanation:

Answer:

22.4

Step-by-step explanation:

a^2 + b^2 c^2

20^2 + b^2 = 30^2

400 + b^2 = 900

b^2 = 500

b = 22.4

Answer:

To solve the system below by substitution, replace y in the second equation with 7−6x.

==> False

This statement is false. To solve the system by substitution, replace x in the second equation with 7−6x.

==> False.

This statement is false. To solve the system by substitution, replace y in the first equation with 7−6x.

==> False

This statement is false. To solve the system by substitution, replace y in the second equation with 6x−7.

==> True.

From the first equation, 6x-y=7

y= 6x-7

Answer: This statement is false. To solve the system by​ substitution, replace y in the second equation with 6x−7.

Answer:

Length of the shadow = 6.25 foot

Step-by-step explanation:

Given: A lamp post is of 10 foot

To find: length of the shadow cast of a lamp post when the angle of elevation of the sun is 58°

Solution:

Trigonometric ratios explain the relationship between the angles and sides of the triangle.

For any angle \(\theta\),

\(tan\theta=\) side opposite to \(\theta\)/side adjacent to \(\theta\)

In ΔABC,

\(tanC=\frac{AB}{BC}\)

Put \(AB=10\,\,foot\,,\,\angle C=58^{\circ}\)

\(tan58^{\circ}=\frac{10}{BC}\\BC=\frac{10}{tan58^{\circ}}\\=\frac{10}{1.6}\\=6.25\,\,foot\)

So,

length of the shadow = 6.25 foot

Answer:

To expand (x + 4)², we can use the formula for squaring a binomial: (a + b)² = a² + 2ab + b². In this case, a = x and b = 4.

So,

(x + 4)² = x² + 2(x)(4) + 4²

= x² + 8x + 16

Thus, (x+4)² when expanded and simplified gives x² + 8x + 16.

Step-by-step explanation:

Answer:

x²n+ 8x + 16

Step-by-step explanation:

(x + 4)²

= (x + 4)(x + 4)

each term in the second factor is multiplied by each term in the first factor, that is

x(x + 4) + 4(x + 4) ← distribute parenthesis

= x² + 4x + 4x + 16 ← collect like terms

= x² + 8x + 16

One year on Venus is 225 days on Earth.

Multiply that by 9 1/2.
The answer you get is 2137.5

9 1/2 years on Venus years is equivalent to 2137.5 days on Earth.

There are  9 1/2 years on Venus years is equivalent to 2137.5 days on Earth, the answer would be 2137.5 days.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

Equivalent to 9 1/2 years on venus.

Let the number of days on earth is x:

One year on Venus is 225 days on Earth.

= (225)(9 1/2)

= (225x19)/2

= 2137.5 days

Thus, there are  9 1/2 years on Venus years is equivalent to 2137.5 days on Earth, the answer would be 2137.5 days.

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Answer:

£4500

Step-by-step explanation:

12500 ×9/100

=1125

4 years =1125×4

=£4500

Answer:

(-1,-2) is the correct one but they all are the same

There is no vertex in the graph and the transformations from the parent function are

The graph represents the given parameter

As a general rule, the maximum or the minimum of a graph is the vertex

In this case, there is no maximum or minimum in the graph

This means that that there is no vertex in the graph

Here, we have:

We can see that:

The graph is 4 units to the left of the origin and 2 units below the origin

This means that the function has been shifted down and shifted to the left

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If you pick 1-card from each set, then the total number of outcomes which are possible is 12 outcomes.

To determine the total number of possible outcomes when picking one card from each set, we use the multiplication principle, which states that if there are "x" ways to select one thing, and "y" ways to select another thing, then in total there are "xy" ways to select both things together.

So, when we pick one card from the first-set of {5, 6, 7, 8}, there are 4 possible outcomes.

When we pick one card from the second-set of {1, 2, 3}, there are 3 possible outcomes.

By using the multiplication-principle, the total number of possible outcomes when picking one card from each set is : 4 × 3 = 12

Therefore, there are 12 possible outcomes when picking one card from each set.

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The given question is incomplete, the complete question is

There are two sets of cards : The cards in the first set contains the numbers  {5,6,7,8} and the second set contains {1,2,3}.

You pick one card from each set. How many outcomes are possible?

{{{ THE BOLDED CHARACTERS SHOULD BE SMALL. }}}

A sequence can be generated by using an = a(n-1) - 5, where a1 = 100 and n is a whole number greater than 1.

a1 = 100 (given)

a2 = a1 - 5 = 100 - 5 = 95

a3 = a2 - 5 = 95 - 5 = 90

a4 = a3 - 5  = 90 - 5 = 85

a5 = a4 - 5 = 85 - 5 = 80

ANSWER for PART (a): 100, 95, 90, 85, 80

-----------------------------------------------------------------------------

an = a1 + d(n - 1)

an = 100 + -5(n - 1)

an = 100 + -5n + 5

an = 105 - 5n

ANSWER for PART (b): an = 105 - 5n

Answer:

I agree with the person above me and here give him brainliest

Step-by-step explanation:

Answer: the 90th percentile for recovery times is 8.77 days.

Step-by-step explanation:

Let x be the random variable representing the recovery time of patients from a particular surgical procedure. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 5.7 days

σ = 2.4 days

The probability for the 90th percentile is 90/100 = 0.9

The z score corresponding to the probability value on the normal distribution table is 1.28

Therefore,

1.28 = (x - 5.7)/2.4

Cross multiplying, it becomes

1.28 × 2.4 = x - 5.7

3.072 = x - 5.7

x = 3.072 + 5.7 = 8.77 days