Select the correct answer.
Given: p || q, and r || s.
Linear pair theorem that is angle 1 is supplementary to angle 2 moves down to angle 2 equals angle 6. As for parallel lines cut by a transversal, corresponding angles are congruent. This moves down to blank box with question mark.
Prove: ∠1 and ∠14 are supplementary angles.
Two vertical parallel lines p and q runs through two horizontal parallel lines r and s to form 16 angles numbered from 1 to 16.
What is the next step in the proof? Choose the most logical approach.
A.
Statement: ∠6 ≅ ∠14
Reason: For parallel lines cut by a transversal, corresponding angles are congruent.
B.
Statement: ∠6 ≅ ∠7
Reason: Vertical Angles Theorem
C.
Statement: ∠6 and ∠5 are supplementary.
Reason: Linear Pair Theorem
D.
Statement: m∠6 + m∠8
Reason: angle addition
The next step in the proof include the following: A. Statement: ∠6 ≅ ∠14 Reason: For parallel lines cut by a transversal, corresponding angles are congruent.
What is corresponding angles theorem?In Mathematics and Geometry, corresponding angles theorem can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines.
This ultimately implies that, the corresponding angles will be always equal (congruent) when a transversal intersects two (2) parallel lines.
By applying corresponding angles theorem to parallel lines p and q, and parallel lines r and s, we can logically deduce the following congruent angle:
∠2 ≅ ∠6 (corresponding angles are congruent).
∠6 ≅ ∠14 (corresponding angles are congruent).
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There are 27 balls in a pouch. 9 green, 3 blue, 7 red, & the rest are purple. What is the
probability of a green or blue ball being chosen at random?
The probability for this event is 0.44
How to find the probability?All the balls have the same probability of being selected at random, then the probability that the ball chosen at random is either green or blue, is equal to the quotient between the number of balls green or blue and the total number.
The total number is 27.
9 are green.
3 are blue.
Then the probability is:
P = (9 + 3)/27
P = 12/27
P = 0.44
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Debbie is making baby quilts.
Each quilt will have 9 squares and 5/9 of
the squares will be green. How many green
Squares does she need for 5 baby quilts?
Profit is the difference between revenue and cost. The revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial 2x3 + 30x – 130. The cost, in dollars, of producing the skateboards can be modeled by 2x3 – 3x – 520. The variable x represents the number of skateboards sold.
what expression would represent profit.
The expression would represent profit is expressed as the polynomial, 33x + 390.
How to Find the Expression of a Model?To represent the profit, we need to subtract the cost from the revenue. The revenue is given by the polynomial 2x³ + 30x - 130, and the cost is given by the polynomial 2x³ - 3x - 520.
Therefore, the expression representing profit can be obtained by subtracting the cost from the revenue:
Profit = (2x³ + 30x - 130) - (2x³ - 3x - 520)
Simplifying the expression, we have:
Profit = 2x³ + 30x - 130 - 2x³ + 3x + 520
Combining like terms, we get:
Profit = (2x³ - 2x³) + (30x + 3x) + (520 - 130)
Simplifying further:
Profit = 33x + 390
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The probability of rain on a particular day is 0.4. If it rains, the probability that Pablo goes jogging is 0.15. If it does not rain, the probability that he goes jogging is 0.85. What is the probability that Pablo goes jogging on that day?
The probability that Pablo goes jogging on that day is 0.57 or 57%.
Given that,
The probability of rain on a particular day is 0.4.
When it rains, the probability that Pablo goes jogging is 0.15.
And, it does not rain, the probability that he goes jogging is 0.85.
Now, The probability for Pablo goes jogging on that day is find as,
The probability that it rains and Pablo goes jogging,
0.4 x 0.15 = 0.06
And, The probability that it does not rain and Pablo goes jogging,
0.6 x 0.85 = 0.51
Therefore, the total probability that Pablo goes jogging on that day is:
0.06 + 0.51 = 0.57
Thus, the probability that Pablo goes jogging on that day is 0.57 or 57%.
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A certain company gives its salespeople a bonus every six months. This bonus is calculated by averaging (taking the mean of) the four middle monthly sales values (that is, ignoring the highest and lowest) from the six-month window, taking 12% of the result, and splitting it evenly among the salespeople. The graph below shows sales for the most recent bonus period.
If there are five salespeople, how much money will each one receive, to the nearest dollar?
a.
$556
b.
$525
c.
$510
d.
$486
Each salesperson will receive $36 as their bonus. None of the option is Correct. Option E
To calculate the bonus amount for each salesperson, we need to follow the given instructions. We have six months of sales data represented in the graph, and we need to find the average of the four middle monthly sales values.
Looking at the graph, we can identify the four middle monthly sales values by ignoring the highest and lowest values. Based on the graph, the four middle monthly sales values are $1,800, $1,600, $1,400, and $1,200.
Now, we need to calculate the average of these four values. Adding them up and dividing by four, we get:
(1,800 + 1,600 + 1,400 + 1,200) / 4 = 6,000 / 4 = 1,500
The average of the four middle monthly sales values is $1,500.
Next, we need to take 12% of this average. To calculate the bonus amount, we multiply the average by 0.12:
1,500 * 0.12 = 180
The bonus amount is $180.
Finally, we need to split the bonus evenly among the five salespeople. To find the amount each salesperson will receive, we divide the bonus amount by the number of salespeople:
180 / 5 = 36
Each salesperson will receive $36 as their bonus.
Since we need to round the answer to the nearest dollar, the final answer is $36. None of the options provided in the answer choices match the correct amount, so the question may be flawed or there may be an error in the provided answer options. Option E noe of these.
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The mean of the data set is 4. Find the absolute deviation of each of the red data values
The absolute deviation of 0 is
The absolute deviation of 3 is
The absolute deviation of 7 is
The absolute deviation of each of the data values are 4, 1 and 3 respectively.
Absolute deviationThe absolute deviatuon gives the distance of any given value in a dataset to the mean value. The absolute deviation is always positive as it does not consider the side to which the value belongs.
Absolute deviation = |value - mean|
Mean = 4
Absolute deviation of 0 = |0 - 4| = 4
Absolute deviation of 3 = |3 - 4| = 1
Absolute deviation of 7 = |7 - 4| = 3
Hence, The absolute deviation of each of the data values are 4, 1 and 3 respectively.
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I need some help! I’m kind of stuck with this problem
Step-by-step explanation:
In March (2) and July (3) , there are a total of 5 flower symbols
each symbol represents THREE flowers = 15 flowers ( March + July)
May has 7 flower symbols = 21 flowers
21 -15 = 6 fewer flowers
The table gives the average monthly precipitation, in inches, in Seattle, Washington, from January through July, where January is month 1 and July is month 7.
Month 1 2 3 4 5 6 7
Average monthly precipitation (inches) 5.2 3.9 3.3 2.0 1.6 1.4 0.6
Part A
Which scatter plot best represents the data?
The scatter plot that best represents the data is scatter plot A.
What is a scatter plot?A scatter plot is a graphical representation that shows two data variables and the ways in which they are related to each other. In the table, we see the months and the average montly precipitations.
The data for these two variables are represented on the first scatter plot that shows the relationships between the points. We also observe a negative correlation between the variables in the graph.
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Complex numbers are used in electronics to describe the current in an electric circuit. Ohm's law relates the current in a circuit, I, in amperes, the voltage of the circuit, E, in volts, and the resistance of the circuit, R, in ohms, by the formula E=ir . Find E, the voltage of a circuit if i=(6-3i) amperes and r=(7+8i)
Given the current i = 6 - 3i amperes and resistance r = 7 + 8i ohms, the voltage E of the Circuit, calculated using Ohm's law, is 66 + 27i volts.
To find the voltage (E) of a circuit using Ohm's law, we can substitute the given values of current (i) and resistance (r) into the formula E = i * r.
Given:
i = 6 - 3i (amperes)
r = 7 + 8i (ohms)
Substituting these values into the formula, we have:
E = (6 - 3i) * (7 + 8i)
To multiply these complex numbers, we can use the distributive property and perform the multiplication as follows:
E = 6 * 7 + 6 * 8i - 3i * 7 - 3i * 8i
= 42 + 48i - 21i - 24i^2
Remember that i^2 is defined as -1, so we can simplify further:
E = 42 + 48i - 21i - 24(-1)
= 42 + 48i - 21i + 24
= 66 + 27i
Therefore, the voltage (E) of the circuit is 66 + 27i volts.
Given the current i = 6 - 3i amperes and resistance r = 7 + 8i ohms, the voltage E of the circuit, calculated using Ohm's law, is 66 + 27i volts.
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Select the correct answer from the drop-down menu.
Consider this population data set: 4, 6, 7, 11, 12, 18, 26, 23, 14, 31, 22, and 12. The values 11, 31, 22, and 12 constitute a random sample drawn from
the data set.
The sample mean is more than the population mean by
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The sample mean is more than the population mean by 4.33.
To determine how much the sample mean is more than the population mean, we need to calculate the mean of the entire population and the mean of the given sample.
The population data set is: 4, 6, 7, 11, 12, 18, 26, 23, 14, 31, 22, and 12.
To find the population mean, we sum up all the values and divide by the total number of values:
Population Mean = (4 + 6 + 7 + 11 + 12 + 18 + 26 + 23 + 14 + 31 + 22 + 12) / 12
Population Mean = 176 / 12
Population Mean = 14.67 (rounded to two decimal places)
Next, let's calculate the mean of the given sample: 11, 31, 22, and 12.
Sample Mean = (11 + 31 + 22 + 12) / 4
Sample Mean = 76 / 4
Sample Mean = 19
To determine how much the sample mean is more than the population mean, we subtract the population mean from the sample mean:
19 - 14.67 = 4.33
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Which statement is true?A) Dictionaries only provide definitions of words.B) A thesaurus only provides antonyms of words.C) A thesaurus is found at the back of a book.D) A glossary provides definitions of words in a book.
If f(x) = +4, which of the following is the inverse of f(x)?
O A. ƒ˜¹(x) = 2(2+4)
B. ƒ˜¹(x) = 7(2-4)
C. ƒ˜¹(x) = 7(2+4)
D. f¯¹(x) = ²(2-4)
Answer:
If f(x) = +4, which of the following is the inverse of f(x)?
O A. ƒ˜¹(x) = 2(2+4)
B. ƒ˜¹(x) = 7(2-4)
C. ƒ˜¹(x) = 7(2+4)
D. f¯¹(x) = ²(2-4)
Step-by-step explanation:
