Line Segment DE is parallel to side BC of right triangle ABC. CD = 3, DE = 6, and EB = 4. Compute the area of quadrilateral BCDE.

Answer:

(x + 7)² = 0

Step-by-step explanation:

Given

x² + 14x + 49 = 0 ( subtract 49 from both sides )

x² + 14x = - 49

To complete the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(7)x + 49 = - 49 + 49

(x + 7)² = 0

Answer:

\( {6}^{ - 3} \\ = \frac{1}{ {6}^{3} } \\ = \frac{1}{216} \)

Answer:

1/6^3

Step-by-step explanation:

6^-3

1/6^3

Note if any base has it's power negative then just do its reciprocal the exponent will be positive.

For example:

5^-y

1/5^y

Length of  side CD is given by the property of similar triangle and the value is 10 inch.

What is similar triangle?

Similar triangles are the triangles when both the triangles  look similar to each other but their sizes might not be exactly the same. In general sense, two objects are similar if they have the same shape but might vary in size. This property of similar shapes is defined to as "Similarity". The symbol of similar triangle is   '∼'

Given FE= 36 inch and FG= 15 inch

Then, GE= 36-15= 21 inch

Now ΔFEC ∼ ΔGED [ By the similarity of triangle]

Let, CD = x inch

so, length of DE = x+4 inch

So by the property of similarity of triangle ,

\(\frac{CE}{CD} =\frac{FE}{FG} \\\\\)

⇒ (2x+4)/x = 36/15

⇒ 15( 2x+4) = 36x

⇒ 30x+ 60=36x

⇒ 6x= 60

⇒ x= 10

Hence, the length of the side CD is 10 inch.

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Answer:

256 DIVIDE BY 8 THEN PLUS 1

Step-by-step explanation:

The statement "the heights of the bars represent relative class frequencies" is true. The correct answer is C.

A histogram is a graphical representation of the distribution of numerical data. It is commonly used to display the frequency distribution of continuous data in a graphical form.

The horizontal axis of the histogram represents the range of values of the variable being measured, and this range is divided into equal intervals called bins. The vertical axis represents the frequency, or the number of times a value appears in each bin.

The statement "the heights of the bars represent relative class frequencies" is also true. In a histogram, the height of each bar represents the frequency or count of data points that fall within each bin. This height is proportional to the frequency of data points within each bin, and it is often normalized to show the relative frequency of each bin.

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The five elements to be assessed during sample selection in audit sampling are Sapmlinf Frame, Sample Size, Sampling Method, Sampling Interval, Sampling Risk.

1. Sampling Frame: The sampling frame is the list or source from which the sample will be selected. It is important to ensure that the sampling frame represents the entire population accurately and includes all relevant elements.

2. Sample Size: Determining the appropriate sample size is crucial to ensure the sample is representative of the population and provides sufficient evidence for drawing conclusions. Factors such as desired confidence level, acceptable level of risk, and variability within the population influence the determination of the sample size.

3. Sampling Method: There are various sampling methods available, including random sampling, stratified sampling, and systematic sampling. The chosen sampling method should be appropriate for the objectives of the audit and the characteristics of the population.

4. Sampling Interval: In certain sampling methods, such as systematic sampling, a sampling interval is used to select elements from the population. The sampling interval is determined by dividing the population size by the desired sample size and helps ensure randomization in the selection process.

5. Sampling Risk: Sampling risk refers to the risk that the conclusions drawn from the sample may not be representative of the entire population. It is important to assess and control sampling risk by considering factors such as the desired level of confidence, allowable risk of incorrect conclusions, and the precision required in the audit results.

During the sample selection process, auditors need to carefully consider these elements to ensure that the selected sample accurately represents the population and provides reliable results. By assessing and addressing these elements, auditors can enhance the effectiveness and efficiency of the audit sampling process, allowing for meaningful generalizations about the population.

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The statement that best describes what a p-value is in terms of hypothesis testing is: It is a measure of the strength of the evidence against the null hypothesis.

What is a p-value?

In statistics, the p-value is the likelihood of obtaining the observed results of a test, or anything more extreme, assuming that the null hypothesis is true.

The null hypothesis is a statistical hypothesis that assumes that the statistical data used in the analysis are insignificant and that the observed differences can only be due to chance.

The p-value is a critical measure in hypothesis testing since it determines the statistical importance of the evidence against the null hypothesis.

The p-value is a percentage value that ranges from 0 to 1.

When p ≤ 0.05, we reject the null hypothesis because the observed evidence is statistically significant. If p > 0.05, we accept the null hypothesis because the observed evidence is not statistically significant.

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The probability of at least one is a Samsung in the purchase collection of two independent LED HDTV is equal to 0.376.

Percent of all LED display manufactured by Samsung = 21%

Probability that at least one purchase is Samsung

= 1 - Probability that both purchases are not Samsung

Probability that the first purchase is not Samsung is 1 - 0.21 = 0.79.

The probability that the second purchase is also not Samsung is also 0.79.

Since the purchases are independent,

Multiply these probabilities to get the probability that both purchases are not Samsung,

P(neither is Samsung)

= 0.79 x 0.79

= 0.6241

The probability that at least one purchase is Samsung is,

P(at least one is Samsung)

= 1 - P(neither is Samsung)

= 1 - 0.6241

= 0.3759

Rounding to 3 decimal places, we get,

P(at least one is Samsung) = 0.376

Therefore, the probability that in a collection of two independent LED HDTV purchases, at least one is a Samsung is 0.376.

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Answer: (-2, -5)

Step-by-step explanation:

When reflecting over the y axis, (x, y) becomes (-x, y).

So A(2, -5) turns into (-2, -5).

According to the combination, The value of the Two blue pebbles is a 3 red pebbles and 1 yellow pebbles.

According to the statement

We have to find that the value of the combination.

So, For this purpose, we know that the

A combination could be a mathematical technique that determines the quantity of possible arrangements in an exceedingly collection of things where the order of the choice doesn't matter.

From the given information:

A red pebble is capable 3 yellow pebbles. A blue pebble is adequate a red pebble and a couple of yellow pebbles. Therefore, the blue pebbles will be:

= 3 yellow pebble + 2 yellow pebbles

= 5 yellow pebbles or 15 red pebbles

And

Two blue pebbles will be:

= 10 yellow pebbles

= 3 red pebbles and 1 yellow pebbles.

So, According to the combination, The value of the Two blue pebbles is a 3 red pebbles and 1 yellow pebbles.

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Question:

A red pebble is equal to 3 yellow pebbles A blue pebble is equal to a red pebble and 2 yellow pebbles. A green pebble is equal to 3 red pebbles

Using the smallest number of pebbles possible and without using blue pebbles, what is the value in pebbles of 2 blue pebbles?

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Answer:

15

Step-by-step explanation:

To solve this equation, let's assume that the number you're referring to is represented by the variable "x." The problem states that eight times the number is equal to 120. Therefore, we can write the equation as:

8x = 120

To isolate the variable "x," we need to divide both sides of the equation by 8:

8x/8 = 120/8

This simplifies to:

x = 15

Hence, the number you are referring to is 15.

This distribution of inequities ensures that the total amount of ticket sales revenue stays within the budget, that no more than 150 tickets are sold overall, and that no negative ticket sales occur.

Let x represent the quantity of single tickets sold and y represent the quantity of pair tickets sold. The entire revenue from ticket sales, R, is then calculated as follows:

R = 45x + 70y

The entire amount of ticket sales revenue is limited by the budget to $5000:

45x + 70y ≤ 5000

No more than 150 tickets may be sold in total.

x + y ≤ 150

X and Y must both be non-negative since we cannot sell negative tickets:

x ≥ 0\sy ≥ 0

As a result, the system of disparities that best captures this circumstance is:

5000 x + y 45x + 70y 150x 0y 0

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Using the Probability formula ,

the probability that first card is odd and second card is greater than 8 is 1/10.

Probability is defined as the total number of favourable outcomes divided by total numbers of outcomes.

We have total 10 cards between 1 to 10 there are 5 even and 5 odd numbers.

so, Total possible outcomes = 10

= {1,2,3,4,5,6,7,8,9,10}

two different cards are drawn out of 10 cards favourble outcomes ( odd card drawn on first draw) = 5

probability that first card is odd(P₁) = 5/10

numbers greater than 8 = {9,10 } = 2

probability that second card is greater than 8 (P₂)

= 2/10

Now , probability that first card is odd and second one is greater than 8 = P₁×P₂ = (5/10)×(2/10) = 1/10

Hence, total probability that first card is odd and second one is greater than 8 is 1/10 .

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The probability from the odds is 3/7

The value of the odds is given as

Odds = 3 to 4

Represent the odds as a fraction

So, we have the following representation

Odds = 3/4

To convert the odds to probability, we make use of the following equation

Probability = Odds/(1 + Odds)

Substitute the known values in the above equation, so, we have the following representation

Probability = (3/4)/(3/4 + 1)

Evaluate the sum

Probability = (3/4)/(7/4)

Evaluate the quotient

Probability = 3/7

Hence, the probability is 3/7

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The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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B (23x5)-s

1) Gathering the data:

5 6th grade classes of 23 students

S= absent students

2) Since S represent the absent students. The question is How many went to the museum.

Then the expression that represents the absent students

is

5 classes of 23 students:

(23 x 5)

Minus the number of absent students, so:

(23x5)-s

Area between the lines = 57.5 sq.units

Whats is the area under a curve?

Area under a curve is the area enclosed by the curve and one of the axes      .

from plotting the graphs the area enclosed is found to be a trapezium.

Area of trapezium = (a+b)*h/2

where a and b are the parallel sides and h is the distance between them.

here a = distance between points 2,2 and 10,2 = 8 units

and b = distance between points (0,-3) and (15,-3) = 15 units

and h = distance between the parallel lines y=2 and y= -3   = 5 units.

hence area = (8+15)*5/2 = 57.5 sq units.

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Answer:

2 times the shortest leg (leg oppo. the 30 degree angle)

Answer:n

Step-by-step explanation:

====================================================

Explanation:

We're told that "Christopher  says that all Rational (Q) numbers are Whole (W)", which makes Christopher not correct. Some rational numbers are whole numbers. For instance, the number 7 = 7/1 is rational and it's a whole number as well.

However something like 1/2 is rational, but it's not a whole number. A whole number doesn't have any fractional or decimal part to it. It can be thought of the number of something.

Comelia is correct because all whole numbers are rational. If x is some whole number, then x = x/1 is rational as well. Replace x with any whole number you want. Her statement does not work in reverse as shown above.

When drawing a Venn diagram, the circle for "whole numbers" will be entirely inside the circle for "rational numbers", and not the other way around.

Answer: 39

Step-by-step explanation:

i = 1  iv = 4  ix = 9  xxi = 21

Answer:

Already in simplilest form

A hypothesis test on a regression coefficient fails to reject the null hypothesis at the 5% significance level. This means that the test was not able to provide enough evidence to support the idea that the regression coefficient is significantly different from zero.

A hypothesis test is a statistical test that is used to determine whether there is enough evidence to support or reject a claim about a population based on the sample data. In a regression analysis, the regression coefficient represents the slope of the regression line that shows the relationship between the dependent variable and the independent variable(s).The null hypothesis for a regression coefficient is that the population slope is zero, which means that there is no linear relationship between the dependent variable and the independent variable(s). The alternative hypothesis is that the population slope is not zero, which means that there is a linear relationship between the dependent variable and the independent variable(s).The level of significance (α) is the probability of making a Type I error, which is the rejection of the null hypothesis when it is actually true. The commonly used value for α is 0.05 (or 5%).If a hypothesis test on a regression coefficient fails to reject the null hypothesis at the 5% significance level, it means that there is not enough evidence to support the alternative hypothesis that the population slope is not zero. Therefore, it can be concluded that the regression coefficient is not significantly different from zero and there is no linear relationship between the dependent variable and the independent variable(s).

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Consumer surplus $5 as we solve the Q by given data

Consumer surplus is the difference between the consumer's willingness to pay and the price of the commodity.

Consumer surplus in economics, also called social surplus or consumer surplus, is the difference between the price a consumer pays for a commodity and the price the consumer is willing to pay in exchange for giving it up.

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

Consumer Surplus = Willingness to Pay - Price of the Good.

Item Price = $35 - $10 = $25

$30 - $25 = $5

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

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Answer:

17 = k

Step-by-step explanation:

d(x) = 7x – k

Let  d(3) = 4

4 = 7*3 -k

4 = 21 -k

Subtract 21 from each side

4 -21 = 21-k-21

-17 = -k

Multiply each side by -1

17 = k

Answer:

k=17

4= 7*3 -k

k=21-4

k= 17

A drill-down report is a type of report that displays a greater level of detail as the user navigates through it.

A drill-down report is a type of report that allows the user to access a greater level of detail as they navigate through it. It is an interactive report that presents a summary of data initially and then allows the user to drill down to more detailed information.

The report provides a visual representation of data that can be explored at different levels of granularity, providing a deeper understanding of the underlying information. Drill-down reports are useful for decision-making because they provide insights into the root causes of issues or trends.

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Answer:

a is (7,6)

b is (3,-1)

c is (1,3)

d is (5,5)

Step-by-step explanation:

The domain of the quotient function (f/g)(x) consists of all numbers that belong to both the domain of f and the domain of g which is false.

A statement, opinion, or rule that forms a linking of two variables is characterized as a function. Mathematics has functions, which are necessary for the design of meaningful relationships.

The range refers to all potential values of y, and the domain refers to all conceivable values of x.

The denominator of the rational function shouldn't be 0. The function is not defined if the denominator is 0.

Thus, the given statement is false.

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To simplify the equations so that there would be no fractions, we

1. Multiply both sides by 8

2. Multiply both sides by 12

3. Multiply both sides by 10

4. Multiply both sides by 30

From the question, we are to determine what we could do first to each side of the equations so that there would be no fraction

1. (4x -4)/8 = (x +2)/4

Multiply both sides by the LCM of the denominators

The denominators are 8 and 4

The LCM of 8 and 4 is 8

Thus,

Multiply both sides by 8

8 × (4x -4)/8 = 8 × (x +2)/4

4x -4 = 2(x +2)

2. 3(4 - r)/6 = (4 + r) /4

Multiply both sides by the LCM of the denominators

The denominators are 6 and 4

The LCM of 6 and 4 is 12

Thus,

Multiply both sides by 12

12 × 3(4 - r)/6 = 12 × (4 + r) /4

2 × 3(4 - r) = 3(4 + r)

6(4 - r) = 3(4 + r)

3. (5q + 3)/10 = (q + 2)/5

Multiply both sides by the LCM of the denominators

The denominators are 10 and 5

The LCM of 10 and 5 is 10

Thus,

Multiply both sides by 10

10 × (5q + 3)/10 = 10 × (q + 2)/5

(5q + 3) = 2(q + 2)

4. 4(b - 7)/15 = (b + 3)/10

Multiply both sides by the LCM of the denominators

The denominators are 15 and 10

The LCM of 15 and 10 is 30

Thus,

Multiply both sides by 30

30 × 4(b - 7)/15 = 30 × (b + 3)/10

2 × 4(b - 7) = 3(b + 3)

8(b - 7) = 3(b + 3)

Hence, we will multiply both sides of the equation by 30

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The quadratic regression equation that best fits the data set is \(y = -1.62x^2 + 34.89x - 5.57.\)

To determine which quadratic regression equation best fits the data set, we can use a graphing calculator or other technology to perform a quadratic regression analysis on the given data.

Using a graphing calculator, we can enter the data set as follows:

Press the STAT button.

Press ENTER to select 1:Edit.

Enter the x-values in L1 and the y-values in L2.

Press STAT again and choose CALC.

Choose option 5:QuadReg.

Press ENTER to select the regression equation.

The calculator will display the quadratic regression equation in the form y = \(ax^2 + bx + c.\)

After performing the quadratic regression analysis, we get the following equation:

y = \(-1.62x^2 + 34.89x - 5.57\)

Therefore, the quadratic regression equation that best fits the data set is \(y = -1.62x^2 + 34.89x - 5.57.\)

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Full Question: Use a graphing calculator or other technology to answer the question. 4.5 122 Which quadratic regression equation best fits the data set? 6.2 145 7.0 155 8.9 189 O Û = 1.62x2 + 34.89x +5.57 10.1 171 © = -5.5722 + 34.89x – 1.62 14.8 170 O Û = -1.62x2 + 34.89x 15.7 133 © y = -1.62x2 + 34.893 – 5.57

Answer:

Step-by-step explanation:

A. y < 5/3 x-2

B. y < -5/3 x + 1

C. y > 5/3 x + 2

D. y > -5/3 x + 2

\(y > \frac 53x +2\) will not have a shared solution set with the graphed linear inequality

From the graph, we have the equation of the line to be:

\(y < \frac 53x +1\)

The equation that have a shared solution must intersect with the line of the inequality.

From the list of options, we have:

\(y < \frac 53x -2\) --- has the same slope, but a smaller y-intercept.

This means that the region of \(y < \frac 53x -2\) is within the region of \(y < \frac 53x +1\)

\(y < -\frac 53x + 1\)

This has a different slope to the graph.

So, it will have a shared solution

\(y > \frac 53x +2\) --- has the same slope, but a bigger y-intercept and a different inequality sign

This means that the region of \(y > \frac 53x +2\) is outside the region of \(y < \frac 53x +1\), and it will not have a shared solution

Hence, \(y > \frac 53x +2\) will not have a shared solution set with the graphed linear inequality

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