If DE = 4 x + 10, EF = 2 x -1, and DF = 9 x - 15, what is the length of DF?

Answer:

The top left one is a pentagon, the lower left is a quadrilateral, the top right is a rhombus, and the bottom left is a parallelogram.

Step-by-step explanation:

Answer:

From left to right:

pentagon

quadrilateral

rhombus

parallelogram

Step-by-step explanation:

From left to right:

First polygon:

5 sides, pentagon. This pentagon has two sets of congruent sides, but there is no special name for it.

Second polygon:

4 sides, quadrilateral. This quadrilateral has 3 congruent sides, but there is no special name for it.

Third polygon:

4 sides, quadrilateral. All sides are congruent. It is a rhombus. A rhombus is also a parallelogram.

Fourth polygon:

4 sides, quadrilateral. There are two pairs of congruent sides. It is a parallelogram.

\(\bold{\huge{\purple{\underline{ Solutions }}}}\)

\(\bold{\dfrac{ 7}{6}}{\bold{ + }}{\bold{\dfrac{ 2}{5}}}\)

\(\sf{ = \:}{\sf{\dfrac{ 35 + 12 }{30}}}\)

\(\sf{ =\: }{\sf{\red{\dfrac{ 47 }{30}}}}\)

Hence, The answer is 47/30

\(\bold{\dfrac{ 1}{7}}{\bold{ + }}{\bold{\dfrac{ 1}{8}}}\)

\(\sf{ =\: }{\sf{\dfrac{ 8 + 7 }{56}}}\)

\(\sf{ =\: }{\sf{\red{\dfrac{ 15}{56}}}}\)

Hence, The answer is 15/56

\(\bold{\dfrac{ 7}{13}}{\bold{ + }}{\bold{\dfrac{ 5}{10}}}\)

\(\sf{=\:}{\sf{\dfrac{ 70 + 65 }{130}}}\)

\(\sf{ = \:}{\sf{\dfrac{ 135}{130}}}\)

\(\sf{ =\:}{\sf{\red{\dfrac{ 27}{26}}}}\)

Hence, The answer is 27/26

\(\bold{\dfrac{ 7}{5}}{\bold{ - }}{\bold{\dfrac{ 1}{3}}}\)

\(\sf{ =\:}{\sf{\dfrac{ 21 - 5 }{15}}}\)

\(\sf{ = \:}{\sf{\red{\dfrac{ 16}{15}}}}\)

Hence, The answer is 16/15

\(\bold{\dfrac{ 8}{7}}{\bold{ - }}{\bold{\dfrac{ 9}{11}}}\)

\(\sf{=\:}{\sf{\dfrac{ 88 - 63}{77}}}\)

\(\sf{=\:}{\sf{\red{\dfrac{ 25}{77}}}}\)

Hence, The answer is 25/77

\(\bold{\dfrac{ 11}{4}}{\bold{ - }}{\bold{\dfrac{ 1}{9}}}\)

\(\sf{=\:}{\sf{\dfrac{ 99 - 4}{36}}}\)

\(\sf{ =\: }{\sf{\red{\dfrac{ 95}{36}}}}\)

Hence, The answer is 95/36

Answer:

Mt Bueno esta alejandro Si

Well the y-intercept is +2

And the slope of the blue line is 1/2

So y=1/2x+2

Slope is rise/run (up then ((right)))

And the intercept is found where the line intercects the y line.

As per the given statement, the quadratic equation is to be used to find the exact solutions to this equation, and the quadratic equation is given by \(ax² + bx + c = 0\).

To solve the quadratic equation, we can use the quadratic formula given by\(x = (-b ± sqrt(b² - 4ac)) / 2a\) Where x is the variable, a, b, and c are coefficients with a ≠ 0, and sqrt is the square root symbol.To find the exact solutions to this equation, we can use the quadratic formula with a = 2, b = 6, and c = 12.

Substituting these values in the quadratic formula, we get

\(x = (-6 ± sqrt(6² - 4 × 2 × 12)) / 2 × 2= (-6 ± sqrt(36 - 96)) / 4= (-6 ± sqrt(-60)) / 4= (-6 ± i√60) / 4= (-3 ± i√15) / 2\)

Hence, the exact solutions to the given equation are \((-3 + i√15) / 2 and (-3 - i√15) / 2.\)

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Answer:

y = 3x + 6

Step-by-step explanation:

Since the line is parallel, it has the same slope -- 3

y = 3x + b, sub point (1, 9)

9 = 3(1) + b

9 = 3 + b

b = 9 - 3

b = 6

y = 3x + b -- y = 3x + 6

The 98% confidence interval for the mean account valuation of the population of customers is between approximately $29,086 and $36,314.

To calculate the confidence interval, we can use the t-distribution since the population standard deviation is unknown and the sample size is relatively small (26 customers). With a 98% confidence level, we need to find the critical value from the t-distribution table. For a two-tailed test, the degrees of freedom would be n - 1, which is 26 - 1 = 25.

Using the t-distribution table or statistical software, we find that the critical value for a 98% confidence level with 25 degrees of freedom is approximately 2.787.

Next, we can calculate the margin of error, which is obtained by multiplying the critical value by the standard error of the mean. The standard error of the mean (SE) is given by the sample standard deviation divided by the square root of the sample size. In this case, SE = 9000 / √26 ≈ 1766.088.

The margin of error is then 2.787 * 1766.088 ≈ 4917.936.

Finally, we can construct the confidence interval by subtracting and adding the margin of error to the sample mean. The lower bound of the confidence interval is the sample mean minus the margin of error: 32700 - 4917.936 ≈ 29,086. The upper bound is the sample mean plus the margin of error: 32700 + 4917.936 ≈ 36,314.

Therefore, the 98% confidence interval for the mean account valuation of the population of customers is approximately $29,086 to $36,314.

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Answer:

more info please

Step-by-step explanation:

Answer:4^2≈50.26548

Step-by-step explanation:

   πr2.

   Where r is the radius and π≈3.14 , the ratio of a circle's circumference to    its diameter.

   Plugging in 4 from the radius, we get.

   42π

   ⇒16π inches.

   This is our exact answer. Alternatively, we can plug in 3.14 for π to get.

   50.26 inches.

Answer:

$76.95

Step-by-step explanation:

Amber worked for 2.2 hours on Monday and she makes $9.50 per hour, so that means you multiply 9.50 x 2.2 and it equals 20.9, then it says she works 5.9 hours on Tuesday, so that means you multiply 9.50 x 5.9 and it equals 56.05, so in total you add 20.9 from Monday and 56.05 from Tuesday and it equals 76.95, which means $76.95 is how much Amber will be paid.

Answer:

76.95

Step-by-step explanation:

The value of the correlation coefficient is 0.34. Thus, the option (B) 0.34 is the correct answer.

Given that a researcher measures the relationship between two variables, X and Y.

If SS(XY) = 340 and SS(X)SS(Y) = 320,000, then we need to calculate the value of the correlation coefficient.

Correlation coefficient:

The correlation coefficient is a statistical measure that determines the degree of association between two variables.

It is denoted by the symbol ‘r’.

The value of the correlation coefficient lies between -1 and +1, where -1 indicates a negative correlation, +1 indicates a positive correlation, and 0 indicates no correlation.

How to calculate correlation coefficient?

The formula to calculate the correlation coefficient is as follows:

r = SS(XY)/√[SS(X)SS(Y)]

Now, substitute the given values, we get:

r = 340/√[320000]r = 0.34

Therefore, the value of the correlation coefficient is 0.34. Thus, the option (B) 0.34 is the correct answer.

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The point (9, -7) is the only solution to the system of linear inequalities given.

To determine which point would be a solution to the system of linear inequalities, let's substitute the given points into the inequalities and see which point satisfies both inequalities.

The system of linear inequalities is:

y > -4x + 6

y > (1/3)x - 7

Let's test each given point:

For the point (9, -7):

Substituting the values into the inequalities:

-7 > -4(9) + 6

-7 > -36 + 6

-7 > -30 (True)

-7 > (1/3)(9) - 7

-7 > 3 - 7

-7 > -4 (True)

Since both inequalities are true for the point (9, -7), it is a solution to the system of linear inequalities.

For the point (-12, -2):

Substituting the values into the inequalities:

-2 > -4(-12) + 6

-2 > 48 + 6

-2 > 54 (False)

-2 > (1/3)(-12) - 7

-2 > -4 - 7

-2 > -11 (False)

Since both inequalities are false for the point (-12, -2), it is not a solution to the system of linear inequalities.

For the point (12, 1):

Substituting the values into the inequalities:

1 > -4(12) + 6

1 > -48 + 6

1 > -42 (True)

1 > (1/3)(12) - 7

1 > 4 - 7

1 > -3 (True)

Since both inequalities are true for the point (12, 1), it is a solution to the system of linear inequalities.

For the point (-12, -7):

Substituting the values into the inequalities:

-7 > -4(-12) + 6

-7 > 48 + 6

-7 > 54 (False)

-7 > (1/3)(-12) - 7

-7 > -4 - 7

-7 > -11 (True)

Since one inequality is true and the other is false for the point (-12, -7), it is not a solution to the system of linear inequalities.

In conclusion, the point (9, -7) is the only solution to the system of linear inequalities given.

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The given problem involves a machine that issues lottery tickets and experiences breakdowns at different frequencies. The costs associated with repairs and preventive maintenance options are provided.

To find the most cost-effective option, we need to compare the total costs of each option considering the frequency of breakdowns. Option #1 covers all repairs for a fixed cost of $500, regardless of the number of breakdowns. Option #2, on the other hand, charges $360 for the first repair and any subsequent repairs, making it more favorable for machines with a higher frequency of breakdowns.

To calculate the total costs, we multiply the frequency of breakdowns by the repair cost for each occurrence and sum them up. For option #1, the total cost is obtained by multiplying the frequency of each breakdown by $500 and summing them. For option #2, we calculate the total cost as the sum of $360 plus the product of the frequency of breakdowns after the first one and $230 (average repair cost).

After performing the calculations, we can compare the total costs of both options and choose the option with the lowest cost. The chosen option will provide the most cost-effective preventive maintenance for the machine issuing lottery tickets.

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Answer: D; B

Step-by-step explanation: 1 and 4 are alternate exterior angles if you use process of elimination, all the other pairs are, alternate exterior, corresponding or same side interior angles. angles 1 and 4 are in between lines a and b when lines a and b have the transversal of c. with process of elimination, c is the only logical answer, as 1 and 4 both lie on that line. which leaves you with two answers. if you draw out lines a and b with a transversal of c and the lines b and e with the transversal of c, then B is the only logical answer. goodluck :) i just finished this unit :D

The terms are "organize, simplify, and summarize data" and "use sample data to reach general conclusions about populations."

Based on these terms, the first term refers to data visualization techniques such as charts, graphs, and infographics. These visual representations help to organize, simplify, and summarize data, making it easier to understand and interpret. On the other hand, the second term refers to statistical inference.

Statistical inference involves using sample data to draw conclusions or make predictions about larger populations. By analyzing a subset of data (sample), we can make generalizations or inferences about the entire population.

This is a common practice in various fields, including market research, social sciences, and public health. Overall, data visualization techniques help us understand data, while statistical inference allows us to make broader conclusions based on sample data.

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The slope m of a linear equation is given by

where (x_1, y_1) and (x_2, y_2) are two points on a line.

Now, to find the slope, we choose any two points from the table and put them into the above formula.

Let us choose the first point

and the second point

The slope, therefore, is

Therefore, the slope of the line is m = 2.

The y-intercept of the line is where the line intersects the y- axis. This happens when x =0. Now, from the table we have the ordered pair (0, 7); therefore, the y-intercept is 7.

a. The correct answer is: There is insufficient evidence to reject H0.

b. The correct answer is: There is insufficient evidence to reject H0.

c. The correct answer is: There is insufficient evidence to reject H0.

d. The correct answer is: There is sufficient evidence to reject H0.

(a). In hypothesis testing, if the p-value is greater than the chosen significance level (α), we fail to reject the null hypothesis H0. In this case, the p-value is 0.1094, which is greater than α = 0.04. Therefore, we do not have enough evidence to reject the null hypothesis that the population mean (μ) is equal to 75.

(b). Similar to the previous situation, the p-value of 0.1094 is greater than the significance level α = 0.09. Hence, we do not have enough evidence to reject the null hypothesis that μ is equal to 75 when the alternative hypothesis Ha states that μ is less than 75.

(c). Once again, the p-value of 0.1094 is greater than the significance level α = 0.09. As a result, we do not have enough evidence to reject the null hypothesis that μ is equal to 75, given that the alternative hypothesis Ha states that μ is greater than 75.

(d). In this scenario, the p-value is 0.1094, which is greater than the significance level α = 0.01. Therefore, we do not have enough evidence to reject the null hypothesis that μ is equal to 75, considering the alternative hypothesis Ha, which states that μ is not equal to 75.

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The range of the data is determined by the minimum and maximum values.

In this case, the minimum value is 102 (lower whisker) and the maximum value is 115 (upper whisker).  Therefore, the range of the data is 115 - 102 = 13.To determine where a number is in relation to another number on a number line, we need to compare their positions. If is seven units to the left of , we can represent this as: = - 7. Therefore, is to the right of on the number line. Similarly, if a number is to the left of another number, it means that it has a smaller value and its representation would have a negative sign. For example, if the number is three units to the left of , we can represent it as: = - 3.

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Answer:

3/10 is greater

Step-by-step explanation:

2/7 is equal to 0.29... and 3/10 is equal to 0.3

So, 0.3 is bigger than 0.29

There are more boxes shaded in the picture to the right than the picture to the left. 21 > 20

The direction angle of the vector Ū is approximately 16.26°.

A vector's direction angle is the angle, measured anticlockwise, between the positive x-axis and the vector in standard position.

Trigonometry can be used to determine the direction angle of the vector = (-7, 2).

The direction angle is determined by:

θ = tan^-1(y/x)

where y is the vector's vertical component and x is its horizontal component (in this example, -7). (in this case, 2).

θ = tan^-1(2/-7)

We can determine: Using a trigonometric table or a calculator

θ ≈ 16.26°

As a result, the vector's direction angle is roughly 16.26°.

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There will  total of 987 outcomes involving at least 8 heads when a coin is tossed ten times

We will be using the formula of combination for calculating the outcomes. Since we have tossed a coin 10 times , so total number of possible outcomes: 2¹⁰ = 1024 .Since at least 8 heads means we will get tail, exactly after two tosses exactly. we will find the outcomes for no head, one head, and 2 head .So, the number of outcomes involving will be 8 heads :

= 1024 - ⁸C₀ ( + ⁸C₁ + ⁸C₂ )

= 1024 - ( 1+8+28) = 1024 - 37

= 987

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The formula for D2 to be placed in order to find the unit price is D2 = B2/C2.

What is the unit price?

The average price of a product is calculated by dividing the total sales revenue by the total units sold. Managers must define "comparable" units when a single product is sold in variants, such as bottle sizes.

To find the unit price of an object, You divide the price by the Object. We need to find how much an object cost per unit.

Let, us consider an Example we have 50lbs of Kulfi (Object) that cost 8.00 dollars(price).

To find the Unit cost, We take the 8.00 and divide it by 50, which results in 0.16 cents per pound. We can check this by multiplying 0.16 by 50=8.00

So, Object= Number of units in cell = C2

Price of Object = B2

Unit Price Formula = D2

Therefore, by considering the above example.,

Object = C2 = 50

Price = B2 = 8.00

D2 Formula= Price of Object/ Number of Units

Therefore, The formula for D2 to be placed in order to find the unit price is D2 = B2/C2.

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The probability of selecting none of the correct six integers is given by:

Probability = (number of unfavorable outcomes) / (total number of possible outcomes)

= C(n - 6, 6) / C(n, 6)

The probability of selecting none of the correct six integers in a lottery can be calculated by dividing the number of unfavorable outcomes by the total number of possible outcomes. Since the order in which the integers are selected does not matter, we can use the concept of combinations.

Let's assume there are n positive integers not exceeding the given integers. The total number of possible outcomes is given by the number of ways to select any 6 integers out of the n integers, which is represented by the combination C(n, 6).

The number of unfavorable outcomes is the number of ways to select 6 integers from the remaining (n - 6) integers, which is represented by the combination C(n - 6, 6).

Therefore, the probability of selecting none of the correct six integers is given by:

Probability = (number of unfavorable outcomes) / (total number of possible outcomes)

= C(n - 6, 6) / C(n, 6)

To obtain the value of probability in decimals, we can evaluate this expression using the given value of n and round the answer to two decimal places.

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Value of ∫90f(x)dx is 2/3. By property 1 of integration ∫f(x)dx  = ∫f(t)dt Because f(x) is a continuous function ,so we can apply property 1.

A function f(x) is said to be a continuous function in calculus at a point x = a if the curve of the function does NOT break at the point x = a. The mathematical definition of the continuity of a function is as follows. A function f(x) is continuous at a point x = a if

f(a) exists;

limₓ → ₐ f(x) exists;

[i.e., limₓ → ₐ₋ f(x) = limₓ → ₐ₊ f(x)] and

Both of the above values are equal. i.e., limₓ → ₐ f(x) = f(a).

Is this definition really giving the meaning that the function shouldn't have a break at x = a? Let's see. "limₓ → ₐ f(x) exists" means, the function should approach the same value both from the left side and right side of the value x = a and "limₓ → ₐ f(x) = f(a)" means the limit of the function at x = a is same as f(a). These two conditions together will make the function to be continuous at that point.

A function is said to be continuous over an interval if it is continuous at each and every point on the interval. i.e., over that interval, the graph of the function shouldn't break or jump.

∫90f(x)dx = 4

Therefore,   ∫f(x)dx = 4/90  

Let,    X² = t

By differentiate both side ,

We get,

2xdx = dt

so, 30/2 ∫f(t)dt

from property 1 : ∫f(x)dx = ∫f(t)dt    

15∫f(t)dt = (4/90) × 15 = 2/3

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First, we need to understand what Fourier Trigonometric and Exponential Forms are.

Fourier Trigonometric Form refers to expressing a periodic function as a sum of trigonometric functions, such as sine and cosine. This is done using Fourier Series.
Exponential Form, on the other hand, refers to expressing a complex number as a product of a magnitude and an exponential term with an imaginary exponent. This is also known as Euler's Formula.
Now, let's move on to solving the problem using these forms.
We are not given the function we need to find the Fourier series for, so I will assume it is a periodic function with period 2π.
Using the Fourier Trigonometric Form, we can express the function as a sum of sine and cosine terms:
f(x) = a0/2 + Σ[an cos(nx) + bn sin(nx)]
where a0, an, and bn are coefficients that can be found using the following formulas:
a0 = 1/π ∫[0,2π] f(x) dx
an = 1/π ∫[0,2π] f(x) cos(nx) dx
bn = 1/π ∫[0,2π] f(x) sin(nx) dx
Now, to solve using the Exponential Form, we can rewrite the Fourier Trigonometric Form as:
f(x) = Σ[cn e^(inx)]

where cn is a complex coefficient given by:
cn = (an - ibn)/2
Using Euler's Formula, we can write:
e^(inx) = cos(nx) + i sin(nx)
Substituting this into the Fourier Series equation, we get:
f(x) = Σ[(an - ibn)/2 (cos(nx) + i sin(nx))]
Simplifying, we get:
f(x) = Σ[(an/2 + i bn/2) cos(nx) + (an/2 - i bn/2) sin(nx)]
Finally, we can write this in the Exponential Form as:
f(x) = Σ[dn e^(inx)]
where dn is a complex coefficient given by:
dn = an/2 + i bn/2

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c. t = -7/15  the value of t that makes the vectors ū(-4, 3t, -1) and v(-2, 5, 1) orthogonal, we need to check if their dot product is zero.

The dot product of two vectors is given by the sum of the products of their corresponding components:

ū · v = (-4)(-2) + (3t)(5) + (-1)(1)

      = 8 + 15t - 1

      = 15t + 7

For the vectors to be orthogonal, their dot product should be zero:

15t + 7 = 0

Solving this equation for t, we have:

15t = -7

t = -7/15

Therefore, the correct answer is:

c. t = -7/15

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The fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way. So the correct option is D.

Correlational method is a research technique used to explore the relationship between two or more variables. In this method, researchers collect data on the variables of interest and analyze their patterns of association. The fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way. This means that researchers are interested in exploring whether changes in one variable are associated with changes in another variable.

For instance, a researcher may be interested in exploring the relationship between stress and job performance. The researcher may collect data on the levels of stress and job performance in a sample of employees and then use statistical analysis to determine if there is a systematic relationship between the two variables. If the results show that higher levels of stress are associated with lower levels of job performance, then the researcher can conclude that there is a negative correlation between the two variables.

It is important to note that correlation does not imply causation. While a correlation between two variables indicates that they are related, it does not necessarily mean that changes in one variable are causing changes in the other variable. Therefore, researchers must be cautious when interpreting correlational data and should consider other factors that may be influencing the relationship between variables.

Therefore, the fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way, and researchers must be cautious when interpreting correlational data and should consider other factors that may be influencing the relationship between variables.

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Answer:

-0.333333333

Step-by-step explanation:

Hope this helps

The function A is a linear function.

The function B is not a linear function.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Function A.

The coordinates:

(0, 1), (1, 0), (2, -1), (3, -2), (4, -1)

The rate of change of a linear function between any two points is the same.

Rate of change:

= (0 - 1) / (1 - 0) = -1/1 = -1

= (-1 - 0) / (2 - 1) = -1/1 = -1

= (-2 + 1) / (3 - 2) = -1/1 = -1

The function A is a linear function.

Function B.

The linear function graph is a straight line.

Function B graph is not a straight line.

Thus,

Function A is a linear function but function B is not a linear function.

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