Find the perimeter of a triangle that has the side lengths given below.
9 cm, 6√3 cm, √12 cm
Give the answer as a radical expression in simplest form.

Answer:

D. x = 3.5

Step-by-step explanation:

The properties of equality describe the relation between two equal quantities. Essentially, if an operation is applied on one side of the equation, then it must be applied on the other side to keep the equation balanced.

Division Property of Equality:

The Division Property of Equality says that we must divide both sides of the equation by the same quantity to keep the equation balanced.

Thus, we can divide both sides by 4:

(4(6x – 9.5) / 4 = (46) / 4

6x – 9.5 = 11.5

Addition Property of Equality:

The Addition Property of Equality says that we must add the same quantity to both sides of the equation to keep the equation balanced.

Thus, we can add 9.5 to both sides:

(6x – 9.5) + 9.5 = (11.5) + 9.5

6x = 21

Division Property of Equality:

We apply this property again and divide both sides by 6 to solve for x:

(6x) / 6 = (21) / 6

x = 3.5

Check validity of answer:

We can check that our answer is correct by plugging in 3.5 for x and seeing if we get 46 on both sides of the equation:

4(6 * 3.5 – 9.5) = 46

4(21 – 9.5) = 46

4(11.5) = 46

46 = 46

Thus, x = 3.5 is the correct answer.

Answer:

Step-by-step explanation:

32.00 increased by 25% is 40.00

The increase is 8.00

a. The population of interest to the researchers were adults living in Tennessee. The sample of interest were the 575 study participants who were selected using a random-digit telephone dialing procedure.

b. The data collection method was a survey conducted through telephone interviews. The potential biases in the method used could include non-response bias, where individuals who do not have telephones or do not answer calls may be excluded from the study. Additionally, there may be social desirability bias, where individuals may not report their true insomnia status due to social pressures.

c. The variables measured in the study were years of education and insomnia status. Years of education is a quantitative variable, while insomnia status is a qualitative variable.

d. The researchers inferred that there is a relationship between education status and insomnia, where individuals with fewer years of education are more likely to have chronic insomnia. However, it should be noted that correlation does not imply causation and further research would be needed to establish causality.

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Answer:

15.0

Step-by-step explanation:

1

Answer:

Surface area of a square pyramid = a 2 + 2al Where, a denotes base length of a square pyramid and, l denotes the slant height or the height of each side face.

Step-by-step explanation:

I used to do stuff like this but I haven't in a long time so I believe you have to add up all the numbers or multiply them.

The type of diagram used to graphically show the relationship between two numerical variables is called a scatter plot.

A scatter plot is a visual representation of data points plotted on a graph, with one variable represented on the x-axis and the other variable represented on the y-axis.

Each data point on the plot corresponds to a pair of values from the two variables being analyzed. The position of each point on the graph indicates the values of both variables, allowing us to examine the relationship between them.

The main purpose of a scatter plot is to visualize the correlation or relationship between the two variables. The pattern formed by the data points on the plot can indicate the direction, strength, and nature of the relationship.

For example, if the points on the scatter plot tend to form a linear pattern, it suggests a linear relationship between the variables. On the other hand, if the points are scattered randomly with no clear pattern, it indicates a weak or no relationship between the variables.

Scatter plots are commonly used in various fields, including statistics, data analysis, and scientific research. They provide a visual way to explore and interpret relationships between variables, identify outliers, detect trends, and assess the strength and direction of associations.

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Answer:

Domain is all real numbers

Step-by-step explanation:

First find function by adding

(2x^2+x-3)+(x-1)

2x^2+2x-4

In the given scenario, the operations A - C, ATCT, AT, CA, and A - B are defined, while BA is not defined

A - C: The operation A - C is defined when the matrices A and C have the same dimensions. Since A is a 2 x 7 matrix and C is an 8 x 2 matrix, their subtraction (A - C) is not defined due to incompatible dimensions.

ATCT: The operation ATCT is defined when both matrices A and C are compatible for matrix multiplication. Since A is a 2 x 7 matrix and C is an 8 x 2 matrix, their product (ATCT) is defined, resulting in a 7 x 8 matrix.

AT: The operation AT represents the transpose of matrix A, which is defined for any matrix. Therefore, AT is defined, resulting in a 7 x 2 matrix.

CA: The operation CA is defined when both matrices C and A are compatible for matrix multiplication. Since C is an 8 x 2 matrix and A is a 2 x 7 matrix, their product (CA) is defined, resulting in an 8 x 7 matrix.

A - B: The operation A - B is defined when both matrices A and B have the same dimensions. Since both A and B are 2 x 7 matrices, their subtraction (A - B) is defined and results in a 2 x 7 matrix.

BA: The operation BA is not defined since the number of columns in matrix B (7 columns) is not equal to the number of rows in matrix A (2 rows), which violates the compatibility requirement for matrix multiplication.

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The answer is option (d) - the function f(x) is increasing on the intervals (-8, -2) and (2, 8), and decreasing on the interval (-2, 2).

To find where a function is increasing or decreasing, we need to find the critical points and use test intervals.

To find the critical points of f(x), we take the derivative and set it equal to zero:
f'(x) = 4x^3 = 0
x = 0 is the only critical point.

Next, we choose test intervals and evaluate f'(x) at points within those intervals:
Interval (-∞, -2): f'(-3) = -108 < 0, so f(x) is decreasing on (-∞, -2).
Interval (-2, 0): f'(-1) = -4 < 0, so f(x) is decreasing on (-2, 0).
Interval (0, 2): f'(1) = 4 > 0, so f(x) is increasing on (0, 2).
Interval (2, ∞): f'(3) = 108 > 0, so f(x) is increasing on (2, ∞).

Therefore, f(x) is increasing on (-8, -2) and (2, 8), and decreasing on (-2, 2). Option (d) is the correct answer.

We can use analytic methods such as finding critical points and test intervals to determine where a function is increasing or decreasing. It is important to evaluate the derivative at points within the test intervals to correctly identify the intervals of increasing and decreasing.

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Yes, f(v)=3/4secvtanv f(0)=5 satisfies the given condition.

The condition given is that f(0)=5. Substituting v=0 in the given function f(v)=3/4secvtanv, we get f(0)=3/4sec0tan0=3/4x1x0=0. Hence, the given function does not satisfy the condition f(0)=5.

Therefore, the given function f(v)=3/4secvtanv f(0) =5 does not satisfy the given condition.
We need to determine if the function f(v) = 3/4sec(v)tan(v) and f(0) = 5 satisfy the given condition.


First, let's evaluate f(0) to see if it equals 5.

f(0) = (3/4)sec(0)tan(0)


We know that sec(0) = 1/cos(0) = 1 and tan(0) = sin(0)/cos(0) = 0. Now, we will substitute these values into the equation.

f(0) = (3/4)(1)(0) = 0


Since f(0) = 0, which is not equal to 5, the function f(v) = 3/4sec(v)tan(v) and f(0) = 5 do not satisfy the given condition.

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we first need to understand what the term percentile means in the context of a standardized test. A percentile is a statistical measure that indicates the percentage of scores that fall below a particular score.

For example, if a student scores in the 85th percentile on a standardized test, it means that their score is higher than 85% of the scores of all the students who took the test.

Given that the scores on a standardized test are normally distributed with a mean (μ) of 1000 and a standard deviation (σ) of 250, we can use the normal distribution formula to find the score necessary to score at the 85th percentile.

The first step is to convert the percentile to a z-score using the z-score formula:

z = (x - μ) / σ

where x is the score we want to find, μ is the mean, and σ is the standard deviation.

To find the z-score for the 85th percentile, we need to find the z-score that corresponds to the area of 0.85 under the standard normal distribution curve. We can look up this value in a standard normal distribution table or use a calculator to get z = 1.04.

Now we can use the z-score formula to solve for x:

1.04 = (x - 1000) / 250

Solving for x, we get:

x = 1.04 * 250 + 1000 = 1260

Therefore, a score of 1260 would be necessary to score at the 85th percentile on this standardized test.

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The indefinite integral of (2ti + j + 3k) dt is t^2i + tj + 3tk + C, where C is the constant of integration.

To find the indefinite integral of (2ti + j + 3k) dt, we integrate each component separately. The integral of 2ti with respect to t is (1/2)t^2i, as we increase the exponent by 1 and divide by the new exponent. The integral of j with respect to t is just tj, as j is a constant.

The integral of 3k with respect to t is 3tk, as k is also a constant. Finally, we add the constant of integration C to account for any potential constant terms. Therefore, the indefinite integral is t^2i + tj + 3tk + C.

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Answer:

80

Step-by-step explanation:

Since the quadrilaterals are similar, corresponding angles are congruent.

m<A = m<F

m<F + 100° + 60° + 120° = 360°

m<F = 80°

z = m<F = 80°

Answer: 80

Answer:

a.   2.5 radians

b.   143.239

Step-by-step explanation:

Based on the information given, only statement I can be considered true.

Statement I: In general, families with higher incomes pay more in rent.

The correlation coefficient (r) of 0.60 indicates a positive correlation between family income and the amount of rent they pay. This means that as family income increases, the rent they pay tends to increase as well. Therefore, families with higher incomes generally pay more in rent.

Statement II: On average, families spend 60% of their income on rent.

The correlation coefficient (r) of 0.60 does not provide information about the percentage of income spent on rent. It only shows the strength and direction of the linear relationship between income and rent. Therefore, statement II cannot be inferred from the given correlation coefficient.

Statement III: The regression line passes through 60% of the (income$, rent$) data points.

The correlation coefficient (r) does not indicate the specific proportion of data points that the regression line passes through. It represents the strength and direction of the linear relationship between income and rent, not the distribution of data points on the regression line. Therefore, statement III cannot be inferred from the given correlation coefficient.

In conclusion, only statement I is true based on the given correlation coefficient of 0.60.

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Triggering the secretion of vasopressin is not a mechanism by which angiotensin II elevates ECF volume.

Angiotensin II is a hormone that plays a crucial role in regulating blood pressure and fluid balance in the body. It is produced by the renin-angiotensin-aldosterone system (RAAS) in response to low blood pressure or decreased blood flow to the kidneys.

When released, angiotensin II acts on various targets to increase blood pressure and restore fluid balance. One of its effects is to stimulate the secretion of aldosterone from the adrenal glands, which promotes salt and water retention in the kidneys.

This, in turn, increases extracellular fluid (ECF) volume. Additionally, angiotensin II can also stimulate thirst, which encourages the intake of fluids, further increasing ECF volume. However, angiotensin II does not directly cause the release of vasopressin, which also promotes water retention.

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The expected value of this probability distribution is 1.9.

The expected value of a discrete probability distribution is given by:

E(X) = Σ[x i p(x i )]

where x i are the possible values of X, and p(x i ) are their corresponding probabilities.

Using the provided probability distribution, we have:

E(X) = (0)(0.1) + (1)(0.2) + (2)(0.4) + (3)(0.3) = 0 + 0.2 + 0.8 + 0.9 = 1.9

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According to Cohen's guidelines, a Pearson correlation coefficient (r) of 0.50 would be considered a moderate correlation. Cohen's guidelines suggest that correlations between 0.30 and 0.49 are considered small, correlations between 0.50 and 0.69 are moderate, and correlations of 0.70 and above are large.

A correlation coefficient of 0.50 indicates a positive relationship between two variables, meaning that as one variable increases, the other variable tends to increase as well. The strength of the correlation indicates the degree to which the two variables are related: a moderate correlation indicates a fairly strong relationship, but not as strong as a large correlation (which would indicate a very strong relationship).

It is important to note that correlation does not imply causation, and that other factors may be at play in determining the relationship between two variables. Additionally, correlation coefficients can be influenced by outliers, non-linear relationships, or other factors that may not be immediately apparent.

In conclusion, a Pearson correlation coefficient of 0.50 would be considered a moderate correlation according to Cohen's guidelines. While a moderate correlation indicates a fairly strong relationship between two variables, it is important to carefully consider other factors that may be influencing the relationship, and to avoid making causal inferences based on correlation alone.

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(a) The frequency response function A(w) is obtained by evaluating the transfer function H(z) on the unit circle, which results in A(w) = cos(2w) - 1.

(b) The spectral density fy(w) is given by fy(w) = (0.16/π) * [(1 + 0.75^2 + 2 * 0.75 * cos(w))]^-1, where γ(h) = σ^2 (0.75)^|h|.

(c) The power transfer function A(w) can be plotted using the equation A(w) = cos(2w) - 1, which shows that frequencies around w = π/2 and w = 3π/2 are attenuated, while frequencies around w = 0 and w = π are retained or enhanced.

(a) To find the frequency response function A(w), we can solve the difference equation by taking the Z-transform:

W(z) = z^2W(z) - 2w0z + W(z)/z^2 + 3w0z^-1

W(z) = (2w0z - z^2)/(1 - z^-2 + 3w0z^-3)

The transfer function H(z) is given by:

H(z) = W(z)/w(z) = (2w0z - z^2)/(1 - z^-2 + 3w0z^-3) / 1

The frequency response function A(w) is then obtained by evaluating H(z) on the unit circle, z = e^jw:

A(w) = H(e^jw) = (2w0e^jw - e^j2w)/(1 - e^-j2w + 3w0e^-j3w)

Simplifying the expression, we get:

A(w) = cos(2w) - 1

(b) The spectral density fy(w) is obtained by taking the Fourier transform of the autocovariance function of {yt}. Using the formula for the autocovariance of an AR(2) process, we have:

γ(h) = σ^2 (0.75)^|h|

where σ^2 = 0.2^2 and h is the lag. The spectral density is then given by:

fy(w) = σ^2/(2π) * ∑γ(h) * e^(-jwh) from h=-∞ to ∞

Substituting γ(h) into the above expression and simplifying, we get:

fy(w) = (0.16/π) * [(1 + 0.75^2 + 2 * 0.75 * cos(w))]^-1

(c) To create a plot of the power transfer function A(w), we can simply plot the equation obtained in part (a), A(w) = cos(2w) - 1, against w. The plot shows that the filter has a notch at w = π/2 and w = 3π/2, meaning that frequencies around these values are dampened or attenuated. On the other hand, frequencies around w = 0 and w = π are retained or enhanced.

a plot of the power transfer function, A(W), against w has been attached!

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To determine the income value that would be an outlier at the upper end, we need to first calculate the interquartile range (IQR).

The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).

Once we have the IQR, we can use the definition of an outlier to determine the income value that would be an outlier at the upper end.

Let's assume that we have a dataset of income values and we have calculated the first quartile (Q1) to be $40,000 and the third quartile (Q3) to be $80,000.

The IQR is then:

IQR = Q3 - Q1 = $80,000 - $40,000 = $40,000

Using the definition of an outlier, we can calculate the upper limit for outliers as:

Upper limit for outliers = Q3 + 1.5 x IQR

Plugging in our values, we get:

Upper limit for outliers = $80,000 + 1.5 x $40,000 = $140,000

Therefore, any income value greater than $140,000 would be considered an outlier at the upper end using the given definition.

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The radius of the frisbee is approximately 1.273 inches when the circumference is 8 inches, and we use the value of pi as 3.14.

To calculate the radius, we can use the formula that relates the circumference and radius of a circle. The formula is:

Circumference = 2 * π * radius

Where "Circumference" represents the total distance around the circle, "pi" is a mathematical constant approximately equal to 3.14, and "radius" is the distance from the center of the circle to any point on its boundary.

Now, let's solve the equation for the radius:

Circumference = 2 * π * radius

Substituting the given value of the circumference (8 inches) and the value of π (3.14) into the equation, we get:

8 = 2 * 3.14 * radius

To isolate the radius, we need to divide both sides of the equation by 2 * 3.14:

8 / (2 * 3.14) = radius

Simplifying the right side of the equation, we have:

8 / 6.28 = radius

Calculating the value on the right side, we find:

radius ≈ 1.273

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The equation in vertex form. y=a(x-h)^2+k is y = 0.25(x + 4)^2 - 3.

We are given that;

The points and form y=a(x-h)^2+k

Now,

for the first set of points, we get:

a = -0.5 h = 3 k = 4.5

So the equation of the parabola in vertex form is:

y = -0.5(x - 3)^2 + 4.5

By repeating this process for the other sets of points to find their equations;

y = 0.5(x + 6)^2 + 1

y = -0.75(x - 3)^2 + 6

y = 0.25(x + 4)^2 - 3

Therefore, by equations the answer will be y = 0.25(x + 4)^2 - 3.

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The measure of angle A is 21°

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

Sine rule is used to find the measure of unknown angle or side of a. triangle.

Using sine rule to find the unknown angle;

a/sinA = b/sinB

19/sinA = 45/sin122

45sinA = 19sin122

45sinA = 19 × 0.840

45sinA = 16 .112

sinA = 16.112/45

sinA = 0.358

A = sin^{-1} 0.358

A = 21° ( nearest degree)

Therefore the measure of angle A is 21°.

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Answer:

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

After using 2 9/12 yards she has:

To subtract the mixed numbers, first subtract the whole numbers:

Then, subtract the fractions:

Finally, combine the whole number and fraction:

Answer:

5x(1-2x)

Step-by-step explanation:

Factor the given expression, 5x-10x². A factor is a number or term that divides out of another number or term evenly.

Pull out the common term "5x."

=> 5x(1-2x)

Thus, the expression has been factorized fully.

The calculated value of the volume of the mailbox is 192 cubic inches

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

The dimension 2 in by 8 in by 12 in

By formula, we have the volume of a box to be

Volume = Length * Width * Height

In this case, we have the following dimension values

Recall that

Volume = Length * Width * Height

So, we have

Volume = 2 * 8 * 12

Evaluate the products

Volume = 192

Hence, the volume of the mailbox is 192 cubic inches

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The length of an arc intercepted by a central angle can be found using the formula:

Arc length = (central angle/360) x 2πr

where r is the radius of the circle.

In this case, the radius is given as 18.04. Let's assume the central angle is x degrees.

Using the formula, we get:

Arc length = (x/360) x 2π(18.04)

Simplifying this expression, we get:

Arc length = (x/180) x π(18.04)

So, the length of the arc intercepted by the central angle x degrees in a circle of radius 18.04 is (x/180) times the circumference of the circle.

To find the length of an arc intercepted by a central angle, we use the formula that relates the arc length to the central angle and the radius of the circle. By plugging in the given values, we can calculate the length of the arc.

The length of an arc intercepted by the given central angle in a circle of radius 18.04 is (x/180) times the circumference of the circle.

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Joe had the correct answer, and Robert and Myra made mistakes in their addition of the fractions.

a) To determine who had the correct answer, we compare the given answers of Robert, Myra, and Joe.

Robert's answer: 5 1/3

Myra's answer: 2 1/12

Joe's answer: 4 5/6

To compare these mixed numbers, it's helpful to convert them to improper fractions:

Robert's answer: 5 1/3 = (5 * 3 + 1) / 3 = 16/3

Myra's answer: 2 1/12 = (2 * 12 + 1) / 12 = 25/12

Joe's answer: 4 5/6 = (4 * 6 + 5) / 6 = 29/6

Comparing the improper fractions, we can see that Joe's answer of 29/6 is the largest.

Therefore, Joe had the correct answer.

b) Let's analyze how Robert and Myra obtained their answers and where they went wrong:

Robert's answer of 5 1/3 = 16/3:

It seems that Robert incorrectly added the whole number and the fraction separately without considering the common denominator. . The correct sum would be (5 * 3 + 1) / 3 = 16/3, which is Joe's answer.

Myra's answer of 2 1/12 = 25/12:

Myra's mistake appears to be similar to Robert's mistake. She may have added 2 and 1 to get 3 and then added 1/12 to get 1 1/12.

However, the correct addition should be done by finding a common denominator, which in this case is 12, and adding the fractions. The correct sum would be (2 * 12 + 1) / 12 = 25/12, which is not the correct answer.

In conclusion, Joe had the correct answer, and Robert and Myra made mistakes in their addition of the fractions.

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The formula for the exponential function passing through the points (-3, 3/25) and (1, 15) is:
f(x) = 15 * 5^x

To find a formula for the exponential function passing through the points (-3, 3/25) and (1, 15), we can start by using the general form of an exponential function, which is f(x) = ab^x, where a is the initial value and b is the growth factor. Using the two given points, we can form two equations:

3/25 = ab^(-3)
15 = ab

We can solve for a and b by first dividing the second equation by the first equation:

15 / (3/25) = ab / (ab^(-3))

Simplifying, we get:

125 = b^3

Taking the cube root of both sides, we get:

b = 5

Substituting this value into one of the original equations, we can solve for a:

3/25 = a(5)^(-3)
a = 3/25 * 125 = 15

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Answer: 1/50

Step-by-step explanation:

Step 1: We need to multiply the numerator and denominator by 100 since there are 2 digits after the decimal.

0.02 = (0.02 × 100) / 100

= 2 / 100 [ since 0.02 × 100 = 2 ]

Step 2: Reduce the obtained fraction to the lowest term

Since 2 is the common factor of 2 and 100 so we divide both the numerator and denominator by 2.

2/100 = (2 ÷ 2) / (100 ÷ 2) = 1/50