Answer:
a) 910
b) 828100
c) 144320
Step-by-step explanation:
a. ∑y
This is the sum of all values of y. So
[tex]\sum y = 216 + 184 + 35 + 92 + 142 + 175 + 9 + 57 = 910[/tex]
b. (∑y)^2
This is the square of the sum, so the square of 910, that we found in the previous item.
910² = 828100
c. ∑y^2
This is the sum of the squares of each amount spent. So
[tex]\sum y^2 = 216^2 + 184^2 + 35^2 + 92^2 + 142^2 + 175^2 + 9^2 + 57^2 = 144320[/tex]
NO LINKS!!!! URGENT HELP PLEASE!!!!!
Find the area of ΔABC
5. B= 141°, a = 7, c = 8
6. C=70°, a=30, b= 24
7. A = 100°, b = 20, c = 25
Answer:
5) 17.62 units² (2 d.p.)
6) 338.29 units² (2 d.p.)
7) 246.20 units² (2 d.p.)
Step-by-step explanation:
To find the area of a triangle given two sides and the included angle, use the Sine Rule (Area of a Triangle) formula:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Sine Rule (Area of a triangle)}\\\\$A=\dfrac{1}{2}ab \sin C$\\\\\\where: \\ \phantom{ww}$\bullet$ $a$ and $b$ are adjacent sides. \\ \phantom{ww}$\bullet$ $C$ is the includ\:\!ed angle.\\\end{minipage}}[/tex]
[tex]\hrulefill[/tex]
Question 5Given values:
a = 7c = 8B = 141°The two sides of the triangle are 'a' and 'c', and the included angle is 'B'.
Substitute the given values into the formula and solve for area:
[tex]\begin{aligned}\implies \textsf{Area}\; \triangle ABC&=\dfrac{1}{2} ac \sin B\\\\&=\dfrac{1}{2} \cdot 7 \cdot 8 \cdot \sin 141^{\circ}\\\\&= 28 \sin 141^{\circ}\\\\& = 17.6209709...\\\\&= 17.62\; \sf square\;units\;(2\;d.p.)\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Question 6Given values:
a = 30b = 24C = 70°The two sides of the triangle are 'a' and 'b', and the included angle is 'C'.
Substitute the given values into the formula and solve for area:
[tex]\begin{aligned}\implies \textsf{Area}\; \triangle ABC&=\dfrac{1}{2} ab \sin C\\\\&=\dfrac{1}{2} \cdot 30\cdot 24 \cdot \sin 70^{\circ}\\\\&= 360\sin 70^{\circ}\\\\&= 338.289343...\\\\& = 338.29\; \sf square\;units\;(2\;d.p.)\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Question 7Given values:
b = 20c = 25A = 100°The two sides of the triangle are 'b' and 'c', and the included angle is 'A'.
Substitute the given values into the formula and solve for area:
[tex]\begin{aligned}\implies \textsf{Area}\; \triangle ABC&=\dfrac{1}{2} bc \sin A\\\\&=\dfrac{1}{2} \cdot 20 \cdot 25 \cdot \sin 100^{\circ}\\\\&= 250 \sin 100^{\circ}\\\\&= 246.201938...\\\\& = 246.20\; \sf square\;units\;(2\;d.p.)\end{aligned}[/tex]
1. Drag the cards so that each number sentence is true. (You will have one card left over.)
2. Describe your thinking.
The numbers arranged in the correct order are:
-3 = -3
-3 < | -1 |
0 < | 1 |
2 > | 0 |
3 > | 1 |
We have,
-3 = -3:
This is a true statement because -3 is indeed equal to -3.
-3 < | -1 |:
This is also a true statement.
The absolute value of -1 is 1, so we are comparing -3 and 1.
Since -3 is less than 1, the inequality is true.
0 < | 1 |:
Again, this is a true statement.
The absolute value of 1 is 1, so we are comparing 0 and 1.
Since 0 is less than 1, the inequality holds true.
2 > | 0 |:
This is also a true statement.
The absolute value of 0 is 0, so we are comparing 2 and 0.
Since 2 is greater than 0, the inequality is true.
3 > | 1 |:
Once again, this is a true statement.
The absolute value of 1 is 1, so we are comparing 3 and 1.
Since 3 is greater than 1, the inequality holds true.
Therefore,
By arranging the given numbers in this order: -3, -3, -1, 0, 1, 2, 3, all of the number sentences become true.
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This exercise uses the normal probability density function and requires the use of either technology or a table of values of the standard normal distribution. The cash operating expenses of the regional phone companies during the first half of 1994 were distributed about a mean of $29.96 per access line per month, with a standard deviation of $2.25. Company A's operating expenses were $28.00 per access line per month. Assuming a normal distribution of operating expenses, estimate the percentage of regional phone companies whose operating expenses were closer to the mean than the operating expenses of Company A were to the mean. (Round your answer to two decimal places.)
The probability of the values of X that are less than 21 is 0.97725.
We have,
The term "standard deviation" refers to a measurement of the data's dispersion from the mean.
A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Given:
u = 20
and SD = 2.25
To find P(X < 21)
So, P(X < 21 )
= 1 - P(X > 21)
Now, P(X > 21)
= P(Z > [(21–20)/2.25]
= P( Z > 1/2.25)
= P(Z > 0.444)
= 0.02275
So, the required probability = P(Z < 21) = 1 - 0.02275= 0.97725
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complete question:
Let X be a normally distributed random variable with a mean of 20 and a standard deviation of 2.25. Using Excel, find the proportion of the values of X that are less than 21.
Solve the system of equations :-)
Thank you
Which represents "5 subtracted from 3 times p"? A. 5 - 3p B. (5 - 3)p C. 3p - 5 D. p3 - 5
The algebraic expression for the sentence "5 subtracted from 3 times p" is given as follows:
A. 5 - 3p.
How to obtain the algebraic expression?
The sentence in the context of this problem is defined as follows:
"5 subtracted from 3 times p"
The expression that represents 3 times p is given as follows:
3p.
(that is, 3 and p are multiplied).
Then 5 subtracted from 3 times p means that the number 5 subtracts the above expression, hence the expression is given as follows:
5 - 3p.
Meaning that option A gives the correct answer in the context of this problem.
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Use the image to determine the type of transformation shown.
A. Reflection across the x-axis
B. 90° clockwise rotation
C. Horizontal translation
D. Vertical translation
Answer:
the answer is C. Horizontal translation
Step-by-step explanation:
trust fr
50 Points! Multiple choice algebra question. Photo attached.
The period of the function is given as follows:
C) 4.
How to obtain the period of the function?A periodic function is a function that has the behavior repeating in intervals over the domain.
Then the period of the function is defined as the difference between two points in which the function has the same behavior.
The function in this problem has the behavior repeating at these following points:
x = 0, x = 4, x = 8, ...
Hence the period is given as follows:
4 - 0 = 8 - 4 = 4.
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At Chairs and More, assemblers are paid according to the following differential piece rate scale: 1−25 chairs in a week, $10 each; 26−40 chairs, $13 each; and $17.50 each for every chair over 40. Salina Grant assembled 47 chairs in one week. Find her gross pay.
Answer:
To find Salina Grant's gross pay, we need to calculate the pay for each range and add them together.
For the first 25 chairs, Salina will be paid $10 for each chair, so her pay for this range is:
25 chairs x $10 per chair = $250
For the next 15 chairs (26-40), Salina will be paid $13 for each chair, so her pay for this range is:
15 chairs x $13 per chair = $195
For the remaining 7 chairs (over 40), Salina will be paid $17.50 for each chair, so her pay for this range is:
7 chairs x $17.50 per chair = $122.50
Adding up all three ranges, Salina's gross pay is:
$250 + $195 + $122.50 = $567.50
Therefore, Salina Grant's gross pay for assembling 47 chairs in one week is $567.50.
Step-by-step explanation:
What half of 4 fourths in a decimal
Answer:
0.5
Step-by-step explanation:
So what do we mean by half? Half means there are two of the thing, and so all you need to do is divide it by two. Half of 4/4 is just another way of saying 4/4 divided by 2:
: 4/4 ÷ 2
Now we know that "half" means to divide by 2, how do we half 4/4? Remember that a fraction a part of the whole, so the higher the denominator is, the smaller the piece. The answer is that the numerator stays the same and we multiply the denominator by 2:
: 4/4 x 2 = 4/8
Here's a little bonus calculation for you to easily work out the decimal format of half 4/4. All you need to do is divide the numerator by the denominator and you can convert any fraction to decimal:
: 4/8 = 0.5
A track coach recorded the time it took for each of her athletes to run a mile. She plans to display the results with a histogram. Which of the following will it show? Select all that apply. (please help as soon as possible. thanks :))
The histogram will show the distribution of the athletes' mile running times. It will provide a visual representation of the frequency or count of athletes falling within different time intervals.
1. Determine the time intervals or "bins" for the histogram. For example, you might have bins of 5-second intervals, such as 0-5 seconds, 5-10 seconds, and so on.
2. Count the number of athletes who fall within each bin. For instance, if three athletes completed the mile in the 0-5 second bin, and five athletes completed it in the 5-10 second bin, record those counts.
3. Plot the bins on the x-axis of the histogram and the corresponding frequency or count on the y-axis.
4. Draw rectangles (or bars) on the histogram, with the height of each bar representing the frequency or count of athletes within each bin.
5. Label the axes and add a title to the histogram for clarity.
The resulting histogram will provide a visual representation of how the athletes' mile running times are distributed, allowing you to observe any patterns or trends.
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Triangle ABC is shown. Use the graph to answer the question.
triangle ABC on a coordinate plane with vertices at 1 comma negative 2, 9 comma negative 2, 5 comma 2
Determine the coordinates of the image if triangle ABC is translated 5 units down.
A′(−4, −2), B′(4, −2), C′(0, 2)
A′(1, −7), B′(9, −7), C′(5, −3)
A′(1, 3), B′(9, 3), C′(5, 7)
A′(6, −2), B′(14, −2), C′(10, 2)
If triangle ABC is translated 5 units down, the coordinates of the image vertices are A′(1, −7), B′(9, −7), C′(5, −3).
The correct option among the given choices is A′(1, −7), B′(9, −7), C′(5, −3).
To determine the coordinates of the image if triangle ABC is translated 5 units down, we need to subtract 5 from the y-coordinate of each vertex of the triangle.
The given vertices of triangle ABC are A(1, -2), B(9, -2), and C(5, 2).
To translate the triangle 5 units down, we subtract 5 from the y-coordinate of each vertex.
The new coordinates of the vertices after the translation are:
A': (1, -2 - 5) = (1, -7)
B': (9, -2 - 5) = (9, -7)
C': (5, 2 - 5) = (5, -3)
Therefore, the correct option among the given choices is A′(1, −7), B′(9, −7), C′(5, −3).
In summary, if triangle ABC is translated 5 units down, the coordinates of the image vertices are A′(1, −7), B′(9, −7), C′(5, −3).
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HELP PLS !% POINTS!!
Answer:
149 sq. ft
Step-by-step explanation:
For the triangle:
Base = 16-9 = 7 ft
Area of Triangle = 1/2 of b.h
= 1/2 of 7 * 6
= 21 sq. ft
Area of Rectangle = l.b
= 5 * 16
= 128 sq. ft
Total Area = 149 sq. ft
Southside High School found that 80% of last year's sold-out plays occurred
during weekend performances. Based on this information, the drama teacher
decided to add another performance time on Saturday. This decision is a
result of
OA. describing data
OB. making an inference
OC. creating involvement
D. collecting data
Answer:
B. making an inference.
Step-by-step explanation:
The drama teacher's decision to add another performance time on Saturday is a result of making an inference based on the information that 80% of last year's sold-out plays occurred during weekend performances. By observing this pattern, the drama teacher infers that adding another performance on Saturday will likely attract a larger audience and increase the chances of having a sold-out show.
Which graph represents the solution to the following problem? y < |x+3|
The graph that shows the solution set of the inequality is the second one.
Which graph represents the solution set of the inequality?Here we have the following inequality:
y < |x + 3|
Notice that we have the symbol "<", then we know that the graph of the absolute value must be with dashed lines (because the points that lie on the graph aren't solutions).
Also, y is smaller than that, then the shaded region must be below the graph.
With that in mind, we conclude that the correct option is the second one.
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What is the X intercepts of f(x) =-2x^2 + 10x - 7
8. For positive real numbers a, b, and c, the expressions albici and Vabac are equivalent. What are the values
of p, q, and r?
Answer:
Step-by-step explanation:
To find the values of p, q, and r in the expression albici = Vabac, we need to equate the corresponding parts on both sides.
From the given equation, we have:
p * (a * b) * (c * i) = q * (a * b * a * c)
Comparing the exponents of a, b, and c on both sides, we get:
p = q * a^2
1 = q * c
To determine the value of r, we can use the fact that albici and Vabac are equivalent. The radical symbol (√) represents taking the square root.
√(a * b * c * i) = √(a * b * a * c)
This implies that:
√(a * b * c * i) = √(a^2 * b * c)
Comparing the exponents of a, b, and c on both sides, we get:
1/2 = 2 * p * q * r
Combining all the equations, we have:
p = q * a^2
1 = q * c
1/2 = 2 * p * q * r
To find the specific values of p, q, and r, we need additional information or equations involving a, b, and c. Without more context or equations, it is not possible to determine the exact values of p, q, and r.
30 POINTS, MULTIPLE CHOICE, TIME SENSITIVE!!
Select the correct answer.
Use a graphing tool to solve the equation for x.
-4x-1= 5x + 4
Answer: x= —5/9
Step-by-step explanation:
Please help me anwser this
The values are given as:
a. Mean = 19
Median = 20
Mode = 22
Standard deviation = 7.2
Range = 24
b. Mean = 75
Median = 80
Mode = 90
Standard deviation = 16
Range = 100
What the measures of central tendency?The three measures of central tendency include;
MeanModeMedianThe measures of dispersions are;
Rangeinterquartile range standard deviationFrom the information given, if 4 is added to all the measures, we get;
Mean = 15 + 4 = 19
Median = 16 + 4 = 20
Mode = 18 + 4 = 22
Standard deviation = 3.2 + 4 = 7.2
Range = 20 + 4 = 24
If the values are multiplied by 5
Mean = 15(5) = 75
Median = 16(5) = 80
Mode = 18(5) = 90
Standard deviation = 3.2(5) = 16
Range = 20(5) = 100
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helpppppppppp meeeeee please
Answer: D. <4 and <7
Step-by-step explanation:
Consecutive means one after the other
Interior means within the parallel lines
So we are looking for 2 to angles inside the parallelel lines that are 1 after the other on the same side
D. <4 and <7
100 tickets are sold for $1 each. there’s a $25 prize and a $10 prize.what is the expected value for a person that buys a ticket? round to the nearest cent
The expected value for a person who buys a ticket is $0.35.
We have,
Number of tickets sold = 100
Price of each ticket = $1
Prize value (1st prize) = $25
Prize value (2nd prize) = $10
Let's calculate the expected value step by step:
Calculate the probability of winning each prize:
Since there is only one 1st prize and one 2nd prize, the probability of winning each prize is:
Probability of winning the 1st prize = 1/100
Probability of winning the 2nd prize = 1/100
Calculate the expected value:
Expected value = (Probability of winning 1st prize x Value of 1st prize) + (Probability of winning 2nd prize x Value of 2nd prize)
= (1/100 x $25) + (1/100 x $10)
= $0.25 + $0.10
= $0.35
Therefore, the expected value for a person who buys a ticket is $0.35.
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NO LINKS!! URGENT HELP PLEASE!!!
O is the center of the decagon below. Find its area. Round to the nearest tenth if necessary.
Answer:
752.4
Step-by-step explanation:
Here we are provided with a decagon which has 10 sides.
The total interior angle is 360°.
So each will have 360/10 = 36 degrees
Half of that is 18 degrees inside the triangle.
Refer to the attachment below.
opposite = 16sin(18)
adjacent = 16cos(18)
Find the area of this triangle:
= 1/2 × 16sin(18) × 16cos(18)
= 37.61825
There are 20 triangles just like this so the total area is (37.61825 × 20) = 752.365 ≈ 752.4 unit2
Which point would be a solution to the system of linear inequalities shown below?
Answer:
(-2, 10)
Step-by-step explanation:
You want the point that would be a solution to the inequalities ...
y ≥ 5/2x +2y ≥ -4x -7GraphIt can be useful to graph the inequalities, or develop a mental picture of what the graph would look like. Both boundary line slopes are fairly steep, and the lines cross in the third quadrant. The V-shaped space above that intersection is the solution space.
The attachment shows the point (-2, 10) is a solution.
Try the answersFrom the shape and location of the solution space, we can eliminate the choices ...
(-8, 2) — too close to the x-axis in the far left part of the 2nd quadrant
(10, -3) — no part of the 4th quadrant is in the solution space
General formIt can work nicely to rewrite the inequalities as a comparison to zero.
5x -2y +4 ≤ 0 . . . . . the first inequality in general form
point (-2, 10): 5(-2) -2(10) +4 = -10 -20 +4 = -26 ≤ 0 . . . a solution
point (4, 9): 5(4) -2(9) +4 = 20 -18 +4 = 6 > 0 . . . . . . . not a solution
4x +y +7 ≥ 0 . . . . . . the second inequality in general form
point (-2, 10): 4(-2) +(10) +7 = -8 +10 +7 = 9 ≥ 0 . . . . . . a solution
point (4, 9): don't need to test (already known not a solution)
Point (-2, 10) is a solution.
__
Additional comment
We chose the use of "general form" inequalities for evaluating answer choices because ...
the arithmetic is mainly with positive integers (no fractions)the comparison to zero does not require a lot of mental effort<95141404393>
Consider the following symbolic logic statement: ¬ (∃x)(P(x) ∧ Q(x)) ∧ (∀y)(R(y) → P(y))
a) Translate the statement into English using proper syntax and semantics.
b) Identify and explain any potential ambiguities in the translated statement.
c) Rewrite the statement in a way that eliminates any ambiguities and maintains the original meaning.
a) The given symbolic logic statement can be translated into English as follows:
"Not exists x such that (P(x) and Q(x)), and for all y, if R(y) then P(y)."
b) Potential ambiguities in the translated statement:
The scope of the negation symbol "¬" is not explicitly defined. It can be interpreted as applying only to the first part of the statement or to the entire statement.
The scope of the quantifiers (∃x) and (∀y) is not explicitly defined. It is unclear which parts of the statement they apply to.
c) To eliminate ambiguities while maintaining the original meaning, the statement can be rewritten as follows:
"(∀x)(¬(P(x) ∧ Q(x))) ∧ (∀y)(R(y) → P(y))"
How to explain the informationIn the revised statement: The negation symbol "¬" applies to the entire first part of the statement, indicating that there does not exist any x for which both P(x) and Q(x) are true.
The quantifiers (∀x) and (∀y) explicitly indicate that the following predicates apply universally to all values of x and y.
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Explain what is meant by a positive relationship between two variables and a negative relationship between two variables. Give an example of a situation in which you would expect to find a positive relationship and when you would expect to find a negative relationship.
Answer: A positive relationship between two variables means that as the value of one variable increases, the value of the other variable also increases. In other words, there is a direct association or correlation between the two variables. Graphically, a positive relationship is represented by an upward-sloping line or curve.
For example, let's consider the relationship between studying time and exam scores. In general, if a student spends more time studying for an exam, their exam score is likely to increase. This implies a positive relationship between studying time and exam scores.
On the other hand, a negative relationship between two variables means that as the value of one variable increases, the value of the other variable decreases. In this case, there is an inverse association or correlation between the two variables. Graphically, a negative relationship is represented by a downward-sloping line or curve.
For instance, let's consider the relationship between hours of sleep and levels of fatigue. As the number of hours of sleep decreases, the level of fatigue tends to increase. This indicates a negative relationship between hours of sleep and levels of fatigue.
It's important to note that these examples describe typical scenarios, but individual variations and other factors can also influence the relationships between variables.
Brandon has 4 cups of powdered sugar. He sprinkles 1/10 of the sugar onto a plate of brownies and sprinkles the rest onto a plate of lemon cookies. How much sugar does Brandon sprinkle on the brownies?
Based on the fraction of the sugar sprinkled on the Brownies, Brandon sprinkles 0.4 cups of sugar on the brownies
How much sugar does Brandon sprinkle on the brownies?The amount of sugar sprinkled on the Brownies by Brandon is determined as follows:
Data given:
Brandon sprinkles 1/10 of the sugar onto the plate of brownies
Since he has 4 cups of powdered sugar in total
The amount of sugar he sprinkles on the brownies can be calculated as:
amount of sugar = fraction of sugar sprinkled * total amount of sugarThe amount of sugar he sprinkles on the brownies = 1/10 * 4 cups
The amount of sugar he sprinkles on the brownies = 0.4 cups
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3. How does the percentage of people who would borrow from some financial institution compare to
the percentage of people who would borrow from friends or family?
The percentage of people borrowing from financial institutions generally exceeds borrowing from friends or family due to formality, legal protection, larger loan amounts, privacy, expertise, and long-term implications.
The percentage of people who would borrow from a financial institution compared to the percentage of people who would borrow from friends or family can vary depending on various factors such as cultural norms, economic conditions, individual preferences, and access to financial services. However, in general, borrowing from financial institutions is often more common and prevalent than borrowing from friends or family for several reasons.
Formality and Legal Protection: Borrowing from financial institutions offers a more formal and legally protected process. When individuals borrow from a financial institution, they enter into a contractual agreement that outlines the terms and conditions of the loan. This agreement provides a legal framework that protects both the borrower and the lender. In contrast, borrowing from friends or family often lacks the same level of formality and legal protection, which can lead to ambiguity and strain personal relationships.
Access to Larger Loan Amounts: Financial institutions typically have more capital and resources to lend larger amounts of money compared to friends or family members. If someone requires a substantial loan, such as for purchasing a home or starting a business, they are more likely to turn to a financial institution. These institutions have processes in place to evaluate creditworthiness, collateral, and other factors, allowing them to provide loans that meet the borrower's specific needs.
Privacy and Independence: Borrowing from a financial institution offers a level of privacy and independence that may be preferred by individuals. Some people might feel uncomfortable disclosing personal financial details or discussing their financial challenges with friends or family. Financial institutions provide a professional environment where individuals can maintain privacy and retain control over their financial matters.
Expertise and Financial Advice: Financial institutions employ professionals with expertise in lending and financial management. When borrowing from a financial institution, borrowers can benefit from the advice and guidance of these professionals. They can help borrowers understand the terms of the loan, explore different options, and make informed financial decisions. Friends and family members may not possess the same level of financial knowledge or experience, limiting their ability to provide comprehensive advice.
Long-Term Implications: Borrowing from friends or family can have long-term implications for personal relationships. Financial transactions have the potential to create tension, conflicts, or misunderstandings among individuals, especially if there are difficulties in repaying the borrowed amount. Relying on financial institutions can help maintain healthy personal relationships, as the borrowing and lending processes are conducted on a professional level, minimizing the emotional and relational strain that can arise from borrowing from loved ones.
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Bill checked out 5 books from the library. Hazel checked out b fewer books than Bill. Choose the expression that shows the number of books Hazel checked out.
The solution is : (5-b ) is the expression that shows the number of books Hazel checked out.
Here, we have,
given that,
Bill checked out 5 books from the library.
Hazel checked out b fewer books than Bill.
now, we have to find the expression that shows the number of books Hazel checked out.
let,
that shows the number of books Hazel checked out = x
so, we have,
that shows the number of books Hazel checked out = b fewer books than Bill.
as, Bill checked out 5 books from the library.
so, we get,
the number of books Hazel checked out = 5 - b
so, we have,
x = 5-b
Hence, The solution is : (5-b ) is the expression that shows the number of books Hazel checked out.
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Select the correct answer from each drop-down menu. A graph of quadrilateral 1 with the nodes of (minus 3, 7), (minus 4, 9), (minus 7, 9), and (minus 4, 5). Transformation of quadrilateral 2 with the nodes of (3, minus 4), (3, 6), (8, 2.8), and (7.2, minus 1.9). Quadrilateral 1 and quadrilateral 2 are polygons that can be mapped onto each other using similarity transformations. The transformation that maps quadrilateral 1 onto quadrilateral 2 is a followed by a dilation with a scale factor of .
This transformation of the polygon ABCD to A'B'C'D' is a by a factor of 2√5.
The coordinates are given as:
First polygon: A (-3, 7), B (-4, 9), C (-7, 9), and D (-4, 5).
Second polygon: A' (3, -4), B'(3, 6), C'(8, 2.8), and D'(7.2, -1.9)
Calculate the distance AB and A'B' using:
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
⇒ AB = √ (-4 + 3)² + (9 - 7)²
⇒ AB = √1 + 4
⇒ AB = √5
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
⇒ A'B' = √ (3 - 3)² + (6 + 4)²
⇒ A'B' = 10
This gives, Divide A'B' by AB to determine the scale factor (k)
k = 10 / √5
k = 2√5
Hence, this transformation is a by a factor of 2√5
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Answer:
Reflection and 2
Step-by-step explanation:
for plato
Based on the picture above, what is the solution to the system of equations?
Type a response
Step-by-step explanation:
The 'solution ' is the point where the two lines intersect : ( 0,-1)
Arizona license plates are designed so there
are three letters followed by four digits.
How many different license plates are
possible if letters and digits cannot be
repeated?
A. 175,760,000
B. 47,174,400
C. 78,624,000
D. 115,316,136
78,624,000 different license plates are possible if letters and digits cannot be repeated.
For the letters:
There are 26 letters in the English alphabet, and we need to choose three of them without repetition.
This can be calculated as a permutation of 26 letters taken 3 at a time:
P(26, 3) = 26! / (26 - 3)!
= 26! / 23!
= 26 x 25 x 24
= 15,600
For the digits:
There are 10 digits (0-9), and we need to choose four of them without repetition.
This can be calculated as a permutation of 10 digits taken 4 at a time:
P(10, 4) = 10! / (10 - 4)! = 10! / 6!
= 10 x 9 x 8 x 7
= 5,040
To find the total number of different license plates possible, we multiply the number of possibilities for the letters by the number of possibilities for the digits:
Total possibilities = P(26, 3) x P(10, 4)
= 15,600 x 5,040
= 78,624,000
Learn more about Combination here:
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