Find m and n if the remainder when 8x^3+mx^2-6x+n if divided by (x-1) and (2x-3) are 2 and 8 respectively

The final conclusion should be based on the test statistic and p-value obtained from the hypothesis test. If the p-value is less than the chosen level of significance, you would reject the null hypothesis, you would fail to reject the null hypothesis.

To conduct a formal hypothesis test for the claim that the wait times at the Space Mountain ride in Walt Disney World have a mean equal to 39 minutes, you can follow these steps:
(a) State the null hypothesis (H0) and the alternative hypothesis (Ha):
H0: The mean wait time at Space Mountain is equal to 39 minutes.
Ha: The mean wait time at Space Mountain is not equal to 39 minutes.
(b) Choose the level of significance (α) for the test, which represents the probability of rejecting the null hypothesis when it is true.

Common choices are 0.05 or 0.01.
(c) Collect a sample of wait times from Space Mountain and calculate the sample mean and sample standard deviation.
(d) Conduct the hypothesis test using a suitable statistical test, such as a t-test.

This test will allow you to compare the sample mean to the hypothesized mean of 39 minutes.

If the test statistic falls in the rejection region (determined by the level of significance), you can reject the null hypothesis.
Remember, the final conclusion should be based on the test statistic and p-value obtained from the hypothesis test.

If the p-value is less than the chosen level of significance, you would reject the null hypothesis.

Otherwise, you would fail to reject the null hypothesis.

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The answer is (A) (11, 4).

Step-by-step explanation:  Given that two vertices of a right-angled triangle are A(5, 12) and B(11, 12).

We can plot the given points on the co-ordinate plane as shown in the attached figure.

We will then see that only the point C(11, 4) will lie exactly below the point B(11, 12). Also, the segment AB and BC are the legs of the triangle, AC is the hypotenuse.

The lengths of the three sides are

\(AB = 11 - 5 = 6\\\\BC = 12 - 4 = 8\\\\AC = \sqrt{AB^{2} +BC^{2} } = \sqrt{6x^{2}+8^{2} } = \sqrt{100} = 10\)

Thus, the correct option is (A).

Answer:

x= 2.2

Step-by-step explanation:

10/11 = 2/x

cross multiply to get

10x=22

x=2.2

Answer:

Step-by-step explanation:

We need to set up a proportion where the triangle with side x is proportional to the triangle with a side measure of 2.

So, 10/2 = 11/x

We cross multiply to get 10x = 22

Dividing gives us x = 2.2

We can check our answer by substituting our answer in for x.

10/2 = 11/2.2

22 = 22 ✅

Answer:

so sorry

Step-by-step explanation:

I'm sorry I need points.

...

The smallest possible value of nullity(A) is 0, and the largest possible value of nullity(A) is 8.

The nullity of a matrix is the dimension of its null space, which represents the set of vectors that satisfy the equation A * x = 0, where A is the matrix and x is a vector.

The nullity of a matrix can range from 0 to the number of columns in the matrix. In this case, since A is a 3 x 8 matrix, the minimum possible value of nullity(A) is 0, indicating that the null space is trivial and contains only the zero vector. This occurs when the matrix is full rank, meaning that its columns are linearly independent.

On the other hand, the maximum possible value of nullity(A) is 8, which would occur if the matrix has rank 0. In this case, all the columns of the matrix are linearly dependent, and the null space spans the entire vector space of size 8.

Therefore, the smallest possible value of nullity(A) is 0, and the largest possible value of nullity(A) is 8.

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Answer:

-13/4, -3, 16/5, 5

Step-by-step explanation:

-13÷4= -3.25

-3=-3

16÷5=3.2

5=5

For -13/4, you can just take away the negative symbol and do 13÷4, then add it on for 3.25. That does not work for every problem like this though.

Please give brainliest if I helped! :)

The mean of 3X is 6, and the variance of 3X is 36. To find the mean of 3X, we can use the property that the mean of a constant multiplied by a random variable is equal to the constant multiplied by the mean of the random variable.

Since X has a mean of 2, multiplying it by 3 gives us a mean of 6 for 3X. To find the variance of 3X, we can use the property that the variance of a constant multiplied by a random variable is equal to the constant squared multiplied by the variance of the random variable. Since X has a variance of 2^2 = 4, multiplying it by 3^2 = 9 gives us a variance of 36 for 3X. The mean of X + Y is 4, and the variance of X + Y is 13. To find the mean of X + Y, we can use the property that the mean of the sum of independent random variables is equal to the sum of their individual means. Since X and Y both have a mean of 2, their sum X + Y has a mean of 2 + 2 = 4. To find the variance of X + Y, we can use the property that the variance of the sum of independent random variables is equal to the sum of their individual variances. Since X and Y have variances of 2^2 = 4 and 3^2 = 9 respectively, their sum X + Y has a variance of 4 + 9 = 13. The mean of X - Y is 0, and the variance of X - Y is 13. To find the mean of X - Y, we can again use the property that the mean of the difference of independent random variables is equal to the difference of their individual means. Since X and Y both have a mean of 2, their difference X - Y has a mean of 2 - 2 = 0. To find the variance of X - Y, we can use the property that the variance of the difference of independent random variables is equal to the sum of their individual variances. Since X and Y have variances of 2^2 = 4 and 3^2 = 9 respectively, their difference X - Y has a variance of 4 + 9 = 13. In summary, for independent random variables X and Y with given means and variances, the mean and variance of 3X are 6 and 36 respectively, the mean and variance of X + Y are 4 and 13 respectively, and the mean and variance of X - Y are 0 and 13 respectively.

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The multiplication of the given equation i.e. \((5x + 4)^2\) should be considered as the \(25x^2 + 40x + 16\).

Since the given equation is \((5x + 4)^2\)

We have to break this equation

So, it can be like

\((5x)^2 + 2 \times 5x \times 4 + 4^2\)

\(25x^2 + 40x + 16\)

Hence, we can conclude that The multiplication of the given equation i.e. \((5x + 4)^2\) should be considered as the \(25x^2 + 40x + 16\).

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The measure of the hypotenuse of the triangle x = 41.04 units

Given data ,

Let the triangle be represented as ΔABC

Now , the base length of the triangle is BC = 12 units

From the given figure of the triangle ,

The measure of the angle ∠BAC = 17°

So , from the trigonometric relations:

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

sin 17° = 12 / x

On solving for x:

x = 12 / sin 17°

x = 41.04 units

Therefore , the value of x = 41.04 units

Hence , the hypotenuse of the triangle is x = 41.04 units

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The population is increasing for values of P between 0 and 4100.

The given differential equation, dP/dt = 1.1P(1 - P/4100), represents the rate of change of the population (P) with respect to time (t). To determine when the population is increasing, we need to find the values of P for which the derivative dP/dt is positive.

Let's analyze the factors in the equation to understand its behavior. The term 1.1P represents the growth rate, indicating that the population increases proportionally to its current size. The term (1 - P/4100) acts as a limiting factor, ensuring that the growth rate decreases as P approaches the maximum capacity of 4100.

To identify when the population is increasing, we need to consider the signs of both factors. When P is between 0 and 4100, the growth rate 1.1P is positive. Additionally, the limiting factor (1 - P/4100) is also positive, as P is less than the maximum capacity.

Therefore, when P is between 0 and 4100, both factors are positive, resulting in a positive value for dP/dt. This indicates that the population is increasing within this range.

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Answer:

A.)x=6

B.)x=16

did u mean to solve it or do something else if this is not the way u mean i can do another way if u like

Answer:

Larger number = 23; Smaller number = 14.

Step-by-step explanation:

Let's assign variables and numbers based on what we know from the world problem. *NOTE: It doesn't have to be x or y. It can be different letters like: s or t.*

Let x be smaller number =  y- 9 ;

Let y be larger number.

Problem: x + y = 37.

STEP 1: Since x = y- 9...

            (y-9) + y = 37

STEP 2: Open the brackets...

           y - 9 + y = 37

STEP 3: COLLECT LIKE TERMS (CLT)...

            2y - 9 = 37

STEP 4: Add 9 to both other sides...

            2y = 46

STEP 5: Bring divide 2 from both sides.

             y = 23.

STEP 6: Since y = 23 & x = y - 9

            x = 23 - 9

STEP 7: COLLECT LIKE TERMS (CLT)...          

            x = 14.

Let's check:

x = y - 9

x = 23 - 9

x = 14. ✔

x + y = 37

23 + 14 = 37. ✔

Credentials: Grade 12 knowledge. Studying at Ontario, Canada, for Grade 12 College Math.

False. The weight of a variable in a standardized predictor environment does not necessarily indicate that the variable has a higher discriminating power.

Discriminating power is determined by the correlation of a predictor variable with the outcome variable. We can calculate the correlation between a predictor variable and an outcome variable using Pearson's correlation coefficient, which is represented by the formula:

r = (NΣXY - (ΣX)(ΣY)) / √[(NΣX2 - (ΣX)2)(NΣY2 - (ΣY)2)].

In this formula, N is the sample size, ΣX is the sum of the predictor variable, ΣY is the sum of the outcome variable, ΣXY is the sum of the products of the predictor and outcome variables, and ΣX2 and ΣY2 are the sums of the squares of the predictor and outcome variables, respectively. The Pearson's correlation coefficient ranges from -1 to +1, with +1 indicating perfect positive correlation, 0 indicating no correlation, and -1 indicating perfect negative correlation. A higher correlation coefficient indicates a higher discriminating power.

Therefore, the weight of a variable in a standardized predictor environment does not indicate whether or not the variable has a higher discriminating power; this is determined by the correlation between the predictor and outcome variables.

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d) Tthe probability that there is a moving object given that both sensors detect motion is approximately 0.98.

(a) To find the probability that sensor L detects motion given that there is movement outside and sensor V does not detect motion, we can use Bayes' theorem.

Let's denote the events as follows:

A = Movement outside

B = Sensor V does not detect motion

C = Sensor L detects motion

We are given:

P(A) = 0.7 (probability of movement outside)

P(B|A) = 0.05 (probability of sensor V not detecting motion given movement outside)

P(C|A) = 0.8 (probability of sensor L detecting motion given movement outside)

We want to find P(C|A', B), where A' denotes the complement of event A.

Using Bayes' theorem:

P(C|A', B) = [P(A' | C, B) * P(C | B)] / P(A' | B)

We can calculate the values required:

P(A' | C, B) = 1 - P(A | C, B) = 1 - P(A ∩ C | B) / P(C | B) = 1 - [P(A ∩ C ∩ B) / P(C | B)]

             = 1 - [P(B | A ∩ C) * P(A ∩ C) / P(C | B)]

             = 1 - [P(B | C) * P(A) * P(C | A) / P(C | B)]

             = 1 - [P(B | C) * P(A) * P(C | A) / [P(B | C) * P(A) * P(C | A) + P(B | C') * P(A') * P(C | A')]]

P(B | C) = 0 (since sensor V does not detect motion when there is motion outside)

P(C | A') = 0 (since sensor L does not detect motion when there is no motion outside)

Substituting these values:

P(C | A', B) = 1 - [0 * P(A) * P(C | A) / (0 * P(A) * P(C | A) + P(B | C') * P(A') * P(C | A'))]

             = 1 - [0 / (0 + P(B | C') * P(A') * P(C | A'))]

             = 1 - 0

             = 1

Therefore, the probability that sensor L detects motion given that there is movement outside and sensor V does not detect motion is 1.

(b) To find the probability that the home security system alerts the police given that there is a moving object, we need to consider the different combinations of sensor detections.

Let's denote the events as follows:

D = The home security system alerts the police

M = There is a moving object

We need to calculate P(D | M). This can occur in two ways:

1. Both sensor V and sensor L detect motion.

2. Sensor L detects motion while sensor V does not.

Using the law of total probability:

P(D | M) = P(D, V detects motion, L detects motion | M) + P(D, V does not detect motion, L detects motion | M)

We know:

P(D, V detects motion, L detects motion | M) = P(V detects motion | M) * P(L detects motion | M) = 0.95 * 0.8 = 0.76

P(D, V does not detect motion, L detects motion | M) = P(V does not detect motion | M) * P(L detects motion | M) = (1 - 0.95) * 0.8 = 0.04

Substituting

these values:

P(D | M) = 0.76 + 0.04

        = 0.8

Therefore, the probability that the home security system alerts the police given that there is a moving object is 0.8.

(c) To find the probability of a false alarm, i.e., that there is no movement but the police are alerted anyway, we need to consider the different combinations of sensor detections.

Let's denote the events as follows:

D = The home security system alerts the police

NM = There is no movement

We need to calculate P(D | NM). This can occur in two ways:

1. Both sensor V and sensor L detect motion.

2. Sensor L detects motion while sensor V does not.

Using the law of total probability:

P(D | NM) = P(D, V detects motion, L detects motion | NM) + P(D, V does not detect motion, L detects motion | NM)

We know:

P(D, V detects motion, L detects motion | NM) = P(V detects motion | NM) * P(L detects motion | NM) = 0.1 * 0.05 = 0.005

P(D, V does not detect motion, L detects motion | NM) = P(V does not detect motion | NM) * P(L detects motion | NM) = (1 - 0.1) * 0.05 = 0.045

Substituting these values:

P(D | NM) = 0.005 + 0.045

         = 0.05

Therefore, the probability of a false alarm, i.e., that there is no movement but the police are alerted anyway, is 0.05.

(d) To find the probability that there is a moving object given that both sensors detect motion, we can use Bayes' theorem.

Let's denote the events as follows:

M = There is a moving object

V = Sensor V detects motion

L = Sensor L detects motion

We want to find P(M | V, L).

Using Bayes' theorem:

P(M | V, L) = [P(V, L | M) * P(M)] / [P(V, L)]

We can calculate the values required:

P(V, L | M) = P(V | M) * P(L | M) = 0.95 * 0.8 = 0.76

P(M) = 0.7 (given probability of movement)

P(V, L) = P(V, L | M) * P(M) + P(V, L | M') * P(M')

        = 0.76 * 0.7 + 0.04 * 0.3

        = 0.532 + 0.012

        = 0.544

Substituting these values:

P(M | V, L) = (0.76 * 0.7) / 0.544

           ≈ 0.98

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Answer:

y = 11x/13 + 36/13

Step-by-step explanation:

We can write the line using y = mx + b form.

To find the slope, m, we can use the formula (y1 - y2) / (x1 - x2):

(7-(-4)) / (5-(-8)) = (7+4) / (5+8) = 11 / 13.

To find b, we can plug in one of the points. Lets use (5, 7).

y = 11/13 * x + b

7 = 11/13 * 5 + b

7 - 55/13 = b

b = 91/13 - 55/13 = (91-55)/13 = 36/13.

Your equation is:

y = 11x/13 + 36/13.

Answer: y = \(\frac{11}{13}\)x + \(\frac{36}{13}\)

Step-by-step explanation:

First, we will find the slope.

       \(m=\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }=\frac{-4-7}{-8-5} =\frac{-11}{-13} =\frac{11}{13}\)

Next, we will substitute this slope and a given point in and solve for our y-intercept (b).

       y = \(\frac{11}{13}\)x + b

       (7) = \(\frac{11}{13}\)(5) + b

       (7) = \(\frac{11}{13}\)(5) + b

       7 = \(\frac{55}{13}\) + b

       b = 7 - \(\frac{55}{13}\)

       b = \(\frac{36}{13}\)

Final equation:

       y = mx + b

     y = \(\frac{11}{13}\)x + \(\frac{36}{13}\)

The correct option is the third one; (14, 4); The vertex represents the maximum profit.

For a general quadratic equation

y = ax² + bx + c

The vertex is at the x-value:

x = -b/2a

Here the quadratic function is:

f(x)=  -x² + 28x - 192

The vertex is at:

x = -28/2*-1 = 14

Evaluating in x= 14 we get:

f(14) = -14² + 28*14 - 192 = 4

So the vertex is at (14, 4), and because the leading coefficient is negative, this is the maximum profit.

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Answer:

a = \(\frac{12}{\sqrt{3} }\)

Step-by-step explanation:

Using the tangent ratio in the right triangle and the exact value

tan30° = \(\frac{1}{\sqrt{3} }\) , then

tan30° = \(\frac{opposite}{adjacent}\) = \(\frac{a}{12}\) = \(\frac{1}{\sqrt{3} }\) ( cross- multiply )

a × \(\sqrt{3}\) = 12 ( divide both sides by \(\sqrt{3}\) )

a = \(\frac{12}{\sqrt{3} }\)

Answer:

Well, 30% is equal to 0.3.

0.4 > 0.3

Step-by-step explanation:

Hope that this answers your question. If not please put any further questions below.

Have a great rest of your day/night!

Answer:

Explanation:

We want to write 47 in base 3

To do this, we follow the steps below:

47/3 = 15 Remainder 2

15/3 = 5 Remainder 0

5/3 = 1 Remainder 2

1/3 = 0 Remainder 1

Now, to base 3, we write the remainders, starting from the last one to the first one.

Answer:

30 ft

Step-by-step explanation:

Answer:

122 ft

Step-by-step explanation:

The 100 ft and the 70 ft are two legs of a right triangle....their distance apart is the hypotenuse of this triangle ....use Pythagorean theorem

d^2 = 100^2 + 70 ^2

  d = 122 ft

Answer:21

Step-by-step explanation:

L'effectif total de l'équipage est donc de 10 personnes. L'âge moyen des équipiers de ce voilier est donc de 22 ans. le milieu de 20 et 22 est 21. La médiane des âges des équipiers est donc de 21.

Answer:

60

Step-by-step explanation:

straight lines are 180

since all lines are parallel

180 - 120 = 60

For the given set of parallel lines measurement of angle 2 is equals to 60degrees.

" Parallel lines are defined as coplanar lines which do not intersect in the same plane. They are equidistant from each other in the same plane."

According to the question,

Given,

Line 'n' is parallel to line 'm'

Line 's' is parallel to line 't'

As diagram drawn we have,

AB is a part of line 'n'

BC is a part of line 't'

CD is a part of line 'm'

DA is a part of line 's'

From this we get,

AB parallel to CD

BC parallel to DA

Therefore,

ABCD is a parallelogram.

Opposite angles in a parallelogram are congruent we have,

∠1 ≅∠3 = 120°

∠2 and ∠3 are supplementary angles.

⇒∠2 + ∠3 = 180°

⇒∠2 + 120° = 180°

⇒∠2 = 180° - 120°

⇒∠2 = 60°

Hence, for given parallel lines measure of angle2 is equals to 60degrees.

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Answer: k = √27-i

Step-by-step explanation:

Each statement about integer is:

Statement A: If positive is subtracted from a negative integer, the difference is negative integer.

This statement is sometimes true.

If a positive integer is subtracted from a negative integer, the difference can be a negative integer or a positive integer. For example, if -5 is subtracted from -3, the difference is -8, which is a negative integer. However, if -3 is subtracted from -5, the difference is 2, which is a positive integer. The difference sign depends on which value is the bigger one.

Statement B: If a positive integer is subtracted from a positive integer, the difference is a positive integer.

This statement is sometimes true.

If a positive integer is subtracted from a positive integer, the difference can be a positive integer or a negative integer. For example, if 3 is subtracted from 5, the difference is 2, which is a positive integer. However, if 5 is subtracted from 3, the difference is -2, which is a negative integer.

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Answer:

1.91

Step-by-step explanation:

Duncan had 3.8 and used 1.89 obviously we can't subtract right now so we have to add a 0 to 3.8 so it would 3.80 - 1.89 = 1.91

Answer:

5 Hours

Step-by-step explanation:

The net present value (NPV) for a 25-year project with an initial investment of $5,000 and a cash inflow of $2,000 per year, assuming that the firm has an opportunity cost of 15%, is $9,474.23.

NPV is a method used to determine the present value of cash flows that occur at different times.

The net present value (NPV) calculation considers both the inflows and outflows of cash in each year of the project. The NPV is then calculated by discounting each year's cash flows back to their present value using a discount rate that reflects the firm's cost of capital or opportunity cost.

A 25-year project with an initial investment of $5,000 and a cash inflow of $2,000 per year has a total cash inflow of $50,000 ($2,000 × 25).

Summary: Thus, the net present value (NPV) for a 25-year project with an initial investment of $5,000 and a cash inflow of $2,000 per year, assuming that the firm has an opportunity cost of 15%, is $9,474.23.

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Answer: 3

Step-by-step explanation: Combine Like Terms:

=8x+4y+7+22y

=(8x)+(4y+22y)+(7)

=8x+26y+7    

Answer:

7 is the term

Step-by-step explanation:

the 7 is the term

because 22y is a coeifcent and a var and the rest of the equation is a coeifcent and a var. Besides 7 so 7 is the term

Answer:

y = \(\frac{36}{25}\)

Step-by-step explanation:

y ∝ \(\frac{1}{x^2}\)

=> y = \(\frac{k}{x^2}\) --------------(1)

Now, y = 4 and x = 3.

Putting in (1)

=> 4 = \(\frac{k}{9}\)

=> k = 4*9

=> k = 36

Now, y = ?, when x = 5

Putting in (1)

=> y = \(\frac{36}{5^2}\)

=> y = \(\frac{36}{25}\)