What Is The Average Of The Points A, B, And C With Weights 1, 4 And 4 Respectively?A (8,-6) B(9,-5) C(-6,7) (2024)

Answer: Factor55out of5x5x.5(x)−5y5(x)-5yFactor55out of−5y-5y.5(x)+5(−y)5(x)+5(-y)Factor55out of5(x)+5(−y)5(x)+5(-y).5(x−y)

Answer: 5.

Step-by-step explanation: Please give Brainlist.

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The factor for 5x and 5y-2 is 1.

What are Factors?

An algebraic expression or number that divides another expression or number equally, leaving no remainder.

We have,

5x and 5y-2.

Now, factoriese the each term we get

5x = 5 . x

5y-2 = 5 . y - 2 . 1

As there is no common factor here.

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Theorem 9.6.1 states that when the origin is an asymptotically stable critical point, the system will approach the origin as t → ∞. In order for the origin to be asymptotically stable, the eigenvalues of the Jacobian matrix evaluated at the origin must have negative real parts.

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The mean absolute deviation of the data is of:

1.25.

It represents the average by which the shoe sizes deviate from the mean shoe size.

What is the mean absolute deviation of a data-set?

The mean of a data-set is given by the sum of all observations divided by the cardinality of the data-set, which is the number of observations in the data-set.The mean absolute deviation of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.The mean absolute deviation represents the average by which the values differ from the mean.

The mean of the data-set in this problem is given as follows:

Mean = (6 + 8.5 + 6 + 9 + 10 + 7 + 8 + 9.5)/8

Mean = 8.

Then the deviations are given as follows:

|6 - 8| = 2.|8.5 - 8| = 0.5.|6 - 8| = 2.|9 - 8| = 1.|10 - 8| = 2.|7 - 8| = 1.|8 - 8| = 0.|9.5 - 8| = 1.5.

Hence the MAD for the data-set is given as follows:

MAD = (2 + 0.5 + 2 + 1 + 2 + 1 + 0 + 1.5)/8

MAD = 1.25.

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Answer:

C

Step-by-step explanation:

the denominator of f(x) cannot be zero as this would make f(x) undefined.

Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non zero for this value then it is a vertical asymptote.

2x + 6 = 0 ( subtract 6 from both sides )

2x = - 6 ( divide both sides by 2 )

x = - 3

Thus x = - 3 is a vertical asymptote of f(x)

No, it is not likely that Penelope selects earrings of the same color.

We have,

Gold Earrings= 11

Silver Earrings= 16

Black Earrings = 13

So, if she picked a earring already of any of the color.

Then, there is chance if she picked the second earring then the earring can be different or same.

Thus, No it is likely that Penelope selects earrings of the same color as there 50% chance of getting different earrings too.

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At Ying Ying's bakery, there's an 8% probability that a customer will report a food allergy.

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Note that the system of graphs has two y-intersects hence the two solutions. Note tht in the graph there ar etwo parabolas.

What is a y-intercept?

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation meets the coordinate system's y-axis. This is done in analytic geometry using the usual convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points fulfill x = 0 because of this.

Replace x in the equation with 0 and then solve for y, keeping in mind that the y-intercept always has an associated x-value of 0. Finding the value of y at x=0 on a graph will reveal the y-intercept. The graph's intersection with the y-axis occurs at this location.

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a. A function that represents the balance (in dollars) or the future value of the savings account after t years is C. s(t) = 6,000(1 + 0.045/12)^12t.

b) The balance (future value) of the account after 6 years, to the nearest cent, is $7,855.82.

How the future value is computed?

The future value can be computed using the FV formula or function below:

s(t) = 6,000(1 + 0.045/12)^12t

s(t) = 6,000(1 + 0.045/12)^12(6)

= $7,855.8186

= $7,855.82

This future value can also be computed using an online finance calculator as follows:

N (# of periods) = 72 months (6 years x 12)

I/Y (Interest per year) = 4.5%

PV (Present Value) = $6,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $7,855.82

Total Interest = $1,855.82

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As the age of the bus increases, the annual maintenance cost generally increases as well. Therefore, the estimated regression model is: y = a + bx = 883.5 + 253.17x where y is the annual maintenance cost and x is the age of the bus.

(a) The correct scatter chart is (i) which has age of bus as the independent variable. The scatter chart indicates there may be a linear relationship between age of bus and annual maintenance cost.

(b) To develop an estimated regression equation, we can use the following steps:

X = (1+2+2+2+2+3+4+4+5+5)/10 = 3

Y = (350+370+480+520+590+550+750+800+790+950)/10

= 643

Calculate the deviations of age of bus (x) and annual maintenance cost (y) from their respective means (X and Y).

x - X: -2, -1, -1, -1, -1, 0, 1, 1, 2, 2

y - Y: -293, -273, -163, -123, -53, -93, 107, 157, 147, 307

Calculate the sum of the product of the deviations of x and y.

∑[(x - X)(y - Y)] = (-2)(-293) + (-1)(-273) + (-1)(-163) + (-1)(-123) + (-1)(-53) + (0)(-93) + (1)(107) + (1)(157) + (2)(147) + (2)(307)

= 4,557

Calculate the sum of the squared deviations of x.

∑[(x - X)²] = (-2)² + (-1)² + (-1)² + (-1)² + (-1)² + 0² + 1² + 1² + 2² + 2²

= 18

Calculate the estimated slope of the regression line, b.

b = ∑[(x - X)(y - Y)] / ∑[(x - X)²]

= 4,557 / 18

= 253.17

Calculate the estimated intercept of the regression line, a.

a = Y - bX

= 643 - (253.17)(3)

= 883.5

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The data values differ from the mean by an average of 4

Finding and interpreting the mean absolute deviation

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

8,12,4,3,14,1,9,13

The mean of the above data is

x = (8 + 12 + 4 + 3 + 14 + 1 + 9 + 13)/8

Evaluate

x = 8

The mean absolute deviation is calculated as

M = 1/n * sum of |data points - mean|

So, we have

M = (|8 - 8| + |12 - 8| + |4 - 8| + |3 - 8| + |14 - 8| + |1 - 8| + |9 - 8| + |13 - 8|)/8

Evaluate the absolute differences

M = (0 + 4 + 4 + 5 + 6 + 7 + 1 + 5)/8

So, we have

M = 4

Hence, the mean absolute deviation is 4

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The test statistic (42.19) falls between the lower and upper critical values (13.839 and 42.982) and the p-value (0.057) is greater than the significance level (0.05), we do not reject the null hypothesis.

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From the triangle, the values of α , β and Ф are 97⁰, 45⁰ and 38⁰

How to determine the values?

Recall that the sum of angles of a straight line is 180 degrees and the sum of angles of a triangle is 180 degrees also.

using the given properties of a triangle and angles,

We have that Y + β - 180 ( sum of angles on a straight line)

where β = 135 degrees

Y = 180-135

Y = 45⁰

Also, using the same properties,

α + <EAC = 180 (sum of <s of a straight line)

α + 83 = 180

α = 97⁰

Ф = 180 - (97 + 45)

Ф = 180 - 142

Ф = 38⁰

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To calculate the size of the next generation of a population undergoing exponential growth, we can use the following formula:

Nt = N0 * e^(rt)

where:
- Nt is the size of the population at some future time t
- N0 is the initial size of the population
- e is the mathematical constant approximately equal to 2.71828
- r is the growth rate of the population (expressed as a decimal)

Substituting the values given, we get:

Nt = 700 * e^(0.014)

Nt ≈ 710.4

Rounding to the nearest whole number, we get:

Nt ≈ 710

Therefore, the size of the next generation of this population is estimated to be approximately 710 individuals, assuming exponential growth at a rate of 1.4%.

The statements that must be true based on the histogram are as follows:

A. The range of the data set is 50 min.

C. The most common amount of exercise is 0 to 9 min.

E. The distribution is skewed right.

How to determine the distribution

You can say that the distribution of a histogram is skewed right if the highest point in the distribution lies towards the left-hand side of the graph.

The graph above is an example of a distribution that is skewed right. Also, the range of the dataset is between 0 to 50 and the most common amount of exercise engaged in by the students is 0 to 9 min.

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The probability of Event 1 is 5/36 and the probability of Event 2 is 1/2.

What is the probability of each of the given events?

The probability of each of the given events is determined by comparing the outcomes of the rolling of two dies:

There are 6 * 6 = 36 possible outcomes

Event 1: The sum is greater than 8.

There are 5 outcomes where the sum is greater than 8.

P(Event 1) = 5/36

Event 2: The sum is divisible by 2.

There are 18 possible outcomes where the sum is divisible by 2.

The probability of this event will be:

P(Event 2) = 18/36

P(Event 2) = 1/2

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Therefore, we can conclude that the changing cultural values have resulted in more Hispanic men grocery shopping by -3.81 percent.

To determine if a lower proportion of Hispanic grocery shoppers are women, we need to perform a hypothesis test using the given sample data.

Let p be the true proportion of Hispanic grocery shoppers who are women. The null hypothesis is that p = 0.94, while the alternative hypothesis is that p < 0.94. We will use a one-tailed test with a significance level of α = 0.05.

The test statistic is calculated as:

z = (x - np) / √(np(1-p))

where x is the number of women in the sample (606), n is the sample size (689), and p is the null hypothesis value (0.94).

z = (606 - 6890.94) / √(6890.94*0.06)

z = -3.81

The critical value for a one-tailed test with α = 0.05 and degrees of freedom of 688 is -1.645. Since the calculated z value of -3.81 is less than the critical value of -1.645, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that a lower proportion of Hispanic grocery shoppers are women.

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The possible number of times the binary search algorithm splits the list when searching for a term in the list varies depending on the length of the list and the position of the term within the list.

However, in general, the number of times the list is split during the binary search algorithm is proportional to the logarithm of the length of the list. So, for example, if the list has 8 items, the binary search algorithm may split the list up to 3 times (log base 2 of 8 is 3), while if the list has 1024 items, the binary search algorithm may split the list up to 10 times (log base 2 of 1024 is 10).

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Using a linear approximation (or differentials) we estimate 3√28 is 3.11111.

To estimate the cube root of 28 using linear approximation, we first need to find a nearby perfect cube. In this case, the closest perfect cube is 27, since [tex]3^3[/tex] = 27.
Let's use the function f(x) = [tex]x^{(1/3)}[/tex]. We want to approximate f(28) using linear approximation. To do this, we will find the tangent line to f(x) at x=27, which will give us a good approximation for f(28).
First, find the derivative of f(x):
f'(x) = [tex](1/3)x^{(-2/3)}[/tex]
Now, evaluate the derivative at x=27:
f'(27) = [tex](1/3)(27)^{(-2/3)}[/tex] = [tex](1/3)(3^{(-2)})[/tex] = 1/9
Next, find the value of f(27):
f(27) = [tex]27^{(1/3)}[/tex] = 3
Now, we can find the equation of the tangent line at x=27:
y = f(27) + f'(27)(x - 27)
y = 3 + (1/9)(x - 27)
Finally, approximate f(28) by plugging x=28 into the tangent line equation:
y ≈ 3 + (1/9)(28 - 27)
y ≈ 3 + (1/9)(1)
y ≈ 3 + 1/9
y ≈ 3.11111
So, using linear approximation, we estimate that the cube root of 28 is approximately 3.11111, rounded to five decimal places.

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The transformations of the exponential function are given as follows:

6f(x) = [tex]6(2^x)[/tex].f(6x) = [tex]2^{6x}[/tex]f(x + 6) = [tex]2^{x + 6}[/tex]f(x) + 6 = [tex]2^x + 6[/tex]

How to define an exponential function?

An exponential function has the definition presented as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

a is the value of y when x = 0.b is the rate of change.

Hence the transformations of the exponential function are given as follows:

6f(x) = [tex]6(2^x)[/tex] -> vertical stretch -> multiplies a by 6.f(6x) = [tex]2^{6x}[/tex] -> numeric value -> replace each instance of x by the desired value, in this case 6x.f(x + 6) = [tex]2^{x + 6}[/tex] -> same as above, just x + 6 instead of 6x.f(x) + 6 = [tex]2^x + 6[/tex] -> addition in the range -> vertical translation.

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We are given two sets of paired observations, which we will use to calculate the sample mean difference and the standard error of the mean difference:

Sample mean difference = x1 -x2 = (214+186+182+200+210+204+187+210+190+182+215+198)/12 - (188+210+199+209+207+195+203+191+190+211+199+181)/12 = 4.75

Sample standard deviation of the differences = s = √[(Σd²)/(n-1)] where d = (x1 - x2) - (x1 - x2), and n is the number of pairs.

d1 = (214 - 188) - 4.75 = 21.25

d2 = (186 - 210) - 4.75 = -28.75

d3 = (182 - 199) - 4.75 = -22.75

d4 = (200 - 209) - 4.75 = -9.75

d5 = (210 - 207) - 4.75 = -1.75

d6 = (204 - 195) - 4.75 = 3.25

d7 = (187 - 203) - 4.75 = -20.75

d8 = (210 - 191) - 4.75 = 13.25

d9 = (190 - 190) - 4.75 = -4.75

d10 = (182 - 211) - 4.75 = -28.75

d11 = (215 - 199) - 4.75 = 10.25

d12 = (198 - 181) - 4.75 = 12.25

Σd² = 1734.875

s = √(1734.875/11) = 5.076

Standard error of the mean difference = s/√n = 5.076/√12 = 1.469

Using a t-distribution with 11 degrees of freedom and a 99% confidence level (α = 0.01), we find the t-value to be 3.106. Therefore, the 99% confidence interval for the true mean difference between the cholesterol levels for people who take the new drug is:

(4.75 - 3.106(1.469), 4.75 + 3.106(1.469))

= (0.885, 8.615)

So we are 99% confident that the true mean difference between the cholesterol levels for people who take the new drug lies between 0.885 and 8.615 mg/dL.

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The expression x²-6x+9 is equal to the expression (x-3)², option A is correct.

The given expression is x²-6x+9

x is the variable in the expression

Plus and minus are the operators

We have to factor the expression

x²-6x+9

x²-3x-3x+9

x(x-3)-3(x-3)

(x-3)(x-3)

x²-6x+9 is equal to (x-3)²

(x-3)²

Hence, the expression x²-6x+9 is equal to the expression (x-3)², option A is correct.

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The solution to the given quadratic equation, m² + 8m + 16 = 0, is m = -4

Solving Quadratic equations

From the question, we are to solve the given quadratic equation.

The given equation is

m² + 8m + 16 = 0

We are to solve the equation using any method of our choice.

Using the factorization method

m² + 8m + 16 = 0

m² + 4m + 4m + 16 = 0

m(m+ 4) + 4(m + 4) = 0

(m + 4)(m + 4) = 0

Thus,

m + 4 = 0 OR m + 4 = 0

m = -4 OR -4

Hence,

m = -4

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The critical point of the two-dimensional system x' = Ax is asymptotically stable if all eigenvalues of matrix A have negative real parts, stable if all eigenvalues have non-positive real parts, and unstable if there exists at least one eigenvalue with a positive real part.

In a two-dimensional system described by x' = Ax, the stability of the critical point is determined by the eigenvalues of the matrix A. If all eigenvalues have negative real parts, the critical point is asymptotically stable, meaning the system will converge to the critical point as time goes to infinity.

If all eigenvalues have non-positive real parts (including zero), the critical point is stable, indicating that the system trajectories will remain bounded but may not necessarily converge to the critical point. Finally, if there exists at least one eigenvalue with a positive real part, the critical point is unstable, and the system trajectories will diverge away from the critical point over time.

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Answer: A ≈ 201.06 cm²

Step-by-step explanation:

We can use the given formula for a sphere's area to solve.

Given formula:

A = 4πr²

Subsiute given radius:

A = 4π(4 cm)²

Square:

A = 4π(16 cm²)

Multiply:

A = 201.0619298 cm²

Round:

A ≈ 201.06 cm²

The appropriate null hypothesis for the company to test depends on the specific study or experiment being conducted.

However, in the given options, option C is the appropriate null hypothesis for the company to test. This hypothesis states that the proportion of people in the population who trust each brand is the same for all five brands. This hypothesis can be tested using statistical methods to determine if there is a significant difference in trust levels between the five brands. Options A and B are not appropriate null hypotheses as they do not make a specific statement about the relationship between the variables being studied. Option D is an alternative hypothesis, which suggests that there is a difference in trust levels between at least one of the brands and the other four.

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He would fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim.

What is null hypothesis?

The null hypothesis is:

H0: p <= 0.58

The alternative hypothesis is:

Ha: p > 0.58

Where p represents the true proportion of adults who take a daily multivitamin.

The medical adviser could conduct a hypothesis test using a significance level (alpha) of 0.05. He would need to collect a sample of adults and determine the proportion who take a daily multivitamin. He could then calculate the test statistic, which in this case would be a one-sample z-test, using the following formula:

z = (p - p0) / sqrt(p0(1 - p0) / n)

Where p is the sample proportion, p0 is the hypothesized proportion under the null hypothesis, and n is the sample size.

If the test statistic falls in the rejection region (i.e. if the p-value is less than the significance level), the medical adviser would reject the null hypothesis and conclude that there is evidence to support the claim that the proportion of adults who take a daily multivitamin is more than 0.58. If the test statistic does not fall in the rejection region, he would fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim.

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Based on the number of doctors at the hospital who obtained results as extreme or more extreme than the results from the study, since 13 out of 20 samples have more than 7 adults who take a daily multivitamin, there is NOT evidence to suggest that the proportion of adults who take a multivitamin is more than 58%. the correct answer is b.

To determine whether there is evidence to suggest that more than 58% of adults take a daily multivitamin, we need to analyze the results from the 20 samples taken by the doctors.

The statement mentions that 13 out of the 20 samples have more than 7 adults who take a daily multivitamin. This means that in these 13 samples, the proportion of adults taking a multivitamin is higher than 7/12, which is equivalent to 58%.

To determine whether this difference is statistically significant, we typically perform a hypothesis test. The null hypothesis (H0) in this case is that the proportion of adults taking a multivitamin is 58% or less (p ≤ 0.58). The alternative hypothesis (Ha) is that the proportion is more than 58% (p > 0.58).

If the observed results are significantly different from what would be expected under the null hypothesis, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis.

Since 13 out of 20 samples have more than 7 adults who take a daily multivitamin, there is NOT evidence to suggest that the proportion of adults who take a multivitamin is more than 58% because it acknowledges that the observed results are not significantly different from the original study. The correct answer is B.

In hypothesis testing, we typically set a significance level (e.g., 0.05) to determine if the evidence is statistically significant. If the p-value (the probability of obtaining results as extreme or more extreme than the observed results) is less than the significance level, we reject the null hypothesis.

Your question is incomplete but probably your full question was attached below

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Answer:

Step-by-step explanation: can you possibly be more specific please.

Answer:

What do you need help with?

Step-by-step explanation:

give further info.

r u okay? or is it a math problem

This fraction gets smaller as m gets larger (holding n fixed), so a larger set A makes it less likely that a random binary relation from A to B will be a function.

a. To define a binary relation from A to B, we need to specify whether or not each ordered pair of elements in A and B is in the relation. Since there are m choices for the first element of each ordered pair, and n choices for the second element, there are a total of m × n possible ordered pairs. Therefore, there are 2^(mn) possible binary relations from A to B, since each ordered pair can either be in or not in the relation.

b. A function from A to B is a special kind of binary relation, where each element in A is paired with exactly one element in B. Therefore, to specify a function, we must choose an element of B for each of the m elements of A. For the first element of A, we have n choices, for the second element of A, we have n - 1 choices (since we cannot choose the same element as we did for the first element), and so on, until we get to the mth element of A, for which we have n - (m - 1) = n - m + 1 choices. Therefore, the total number of functions from A to B is given by:

n(n - 1)(n - 2) ... (n - m + 1) = n!/(n - m)!

c. Since a function is a binary relation where each element in A is paired with exactly one element in B, it follows that there are n possible choices for the second element of each ordered pair. Therefore, the fraction of binary relations that are functions is given by:

number of functions / total number of binary relations

= n!/(n - m)! / 2^(mn)

= n! / (n - m)! / (2^m)^n

= n! / (n - m)! / (2^m * n)^m

This fraction gets smaller as m gets larger (holding n fixed), so a larger set A makes it less likely that a random binary relation from A to B will be a function.

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