If for an arithmetic-sequence, the terms are t₅ = -154 and t₉ = -274, then the first-three terms are t₁ = -274, t₂ = -244 and t₃ = -214.
An "Arithmetic-Sequence" is defined as a sequence of numbers in which the difference between any two consecutive terms is always the same, which is called the "common-difference".
To find first 3 terms of an "arithmetic-sequence" given the values of t₅ and t₉, we use formulas for "nth-term" of an arithmetic sequence, which is
⇒ tₙ = t₁ + (n - 1)d,
where tₙ = nth term, t₁ = first term, n = position of term in sequence, and d = common-difference,
Given that t₅ = -154 and t₉ = -274,
So,
⇒ t₅ = t₁ + (5 - 1)d = -154,
⇒ t₉ = t₁ + (9 - 1)d = -274,
We first find the "common-difference" by subtracting "t₁" from both sides of first equation and "t₉" from both sides of second-equation,
We get,
⇒ 4d = -154 - t₁,
⇒ 8d = -274 - t₁,
Simplifying further,
We get,
⇒ 4d = 120,
⇒ d = 30,
Now, we substitute it in "4d = -154 - t₁",
We get,
⇒ 4(30) = -154 - t₁,
⇒ 120 = -154 - t₁,
⇒ t₁ = -154 - 120,
⇒ t₁ = -274
So, the first term is = -274;
Now we use "d = 30" to find second and third terms of sequence,
We get,
⇒ t₂ = t₁ + (2 - 1)d = -274 + 30 = -244,
⇒ t₃ = t₁ + (3 - 1)d = -274 + 60 = -214,
Therefore, first three-terms of arithmetic sequence are -274, -244, and -214.
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The given question is incomplete, the complete question is
Find the first 3 terms of arithmetic sequence if t₅ = -154 and t₉ = -274. Find t₁, t₂, t₃.
On March 30, Century Television received an invoice dated March 28 from ACME Manufacturing for 51 televisions at a cost of $100 each. Century received a 8/5/5 chain discount. Shipping terms were FOB shipping point. ACME prepaid the $91 freight. Terms were 5/10 EOM. When Century received the goods, 3 sets were defective. Century returned these sets to ACME. On April 08, Century sent a $275 partial payment. Century will pay the balance on May 06. What is Century’s final payment on May 06? Assume no taxes
Century's final payment will be on May 06 is $4,028.
Total cost of televisions:
51 TVs at $100 each = $5,100
8% discount = $100 x 8% x 10 = $80
5% discount = $100 x 5% x 10 = $50
5% discount = $100 x 5% x 31 = $155
Total discount = $80 + $50 + $155 = $285
Cost after discount = $5,100 - $285 = $4,815
Shipping cost: no additional cost
Returned sets:
3 *$100 = $300
ACME will issue a credit to Century for $300
Total cost:
$4,815 + $0 - $300 = $4,515
Partial payment:
$275
Final payment:
Balance after partial payment = $4,515 - $275 = $4,240
5% discount if paid within 10 days after the end of the month = $4,240 x 5% = $212
Final payment on May 06 = $4,240 - $212 = $4,028
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Write down the size of angle ABC. Give a reason for your answer.
Answer:
∠ ABC = 90°
Step-by-step explanation:
∠ ABC is the angle on the circle subtended by the diameter AC
it is the angle in a semicircle and is 90°
a pair of fair dice is tossed. define the following events: a: 5you will roll a 7 1i.e., the sum of the numbers of dots on the upper faces of the two dice is equal to 7).6 b: 5at least one of the two dice is showing a 4.6 a. identify the sample points in the events a, b, a b, a b, and ac . b. find p1a2, p1b2, p1a b2, p1a b2, and p1ac 2 and by summing the probabilities of the appropriate sample points. c. use the additive rule to find p1a b2 . compare your answer with that for the same event in part b. d. are a and b mutually exclusive? why?
The sample points of events A, B, A ∩ B, A ∪ B and A' (complement of A) are given. The probability of event are 1/18, 11/36, 1/18, 7/18 and 17/18 respectively. The probability using additive rule of p(A ∩ B) is 1/36. Events A and B are not mutually exclusive as they have a non-empty intersection.
Sample points in the events
A: {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}
B: {(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (1, 4), (2, 4), (3, 4), (5, 4), (6, 4)}
A ∩ B: {(4, 3), (3, 4)}
A ∪ B: {(1, 4), (1, 6), (2, 4), (2, 5), (3, 4), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (6, 1), (6, 4)}
A' (complement of A): {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (5, 1), (5, 3), (5, 5), (6, 2), (6, 3), (6, 5), (1, 5), (1, 6), (2, 6), (3, 5), (3, 6), (5, 6), (6, 6)}
The probability of event A is
p(A) = 2/36 = 1/18.
The probability of event B is
p(B) = 11/36.
The probability of event
A ∩ B (i.e., A and B) is p(A ∩ B) = 2/36 = 1/18.
The probability of event
A ∪ B (i.e., A or B) is p(A ∪ B) = 14/36 = 7/18.
The probability of event A' (i.e., not A) is p(A') = 17/18.
By the additive rule, we have p(A ∪ B) = p(A) + p(B) - p(A ∩ B). Therefore, p(A ∩ B) = p(A) + p(B) - p(A ∪ B) = (1/18) + (11/36) - (7/18) = 1/36. This inconsistent with the answer we obtained in above part.
The events A and B are not mutually exclusive because it is possible to roll a 4 and a 3 at the same time, which satisfies both events.
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Alvin's new bag of 50 marbles of different
designs spilled in his backpack. On the way
home from school, he randomly selects one
marble from the backpack, records the
result, puts the marble back in the bag,
and selects again. Here are his results:
jasper, galaxy, cat's-eye, rainbow,
galaxy, sunburst, galaxy, cat's-eye,
sunburst, jasper
Based on the data, estimate how many of
the marbles in Alvin's backpack are galaxy
marbles.
If necessary, round your answer to the
nearest whole number.
Answer: 7
Step-by-step explanation:
i did it a weird way
Find all the values of k for which the equation 2x^2+x+4k has (a) two real solutions, (b) one real solution, and (c) no real solutions.
the values of k for which the equation 2x² + x + 4k has (a) two real solutions are k < 1/32, (b) one real solution is k = 1/32, and (c) no real solutions are k > 1/32.
How to solve the question?
The given equation is 2x² + x + 4k.
(a) For the equation to have two real solutions, the discriminant b² - 4ac must be positive.
Therefore, for this equation, b² - 4ac > 0
=> 1 - 4(2)(4k) > 0
=> 1 - 32k > 0
=> k < 1/32
Hence, all values of k less than 1/32 will give the equation 2x² + x + 4k two real solutions.
(b) For the equation to have one real solution, the discriminant b² - 4ac must be zero.
Therefore, for this equation, b² - 4ac = 0
=> 1 - 4(2)(4k) = 0
=> 1 - 32k = 0
=> k = 1/32
Hence, only the value of k equal to 1/32 will give the equation 2x² + x + 4k one real solution.
(c) For the equation to have no real solutions, the discriminant b² - 4ac must be negative.
Therefore, for this equation, b² - 4ac < 0
=> 1 - 4(2)(4k) < 0
=> 1 - 32k < 0
=> k > 1/32
Hence, all values of k greater than 1/32 will give the equation 2x² + x + 4k no real solutions.
In conclusion, the values of k for which the equation 2x² + x + 4k has (a) two real solutions are k < 1/32, (b) one real solution is k = 1/32, and (c) no real solutions are k > 1/32.
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Suppose we roll a red die and a green die. Let A be the event that the number of spots showing on the red die is three or less and B be the event that the number of spots showing on the green die is more than three. The events A and B are
Both events A and B have probabilities of 1/12, and they are independent events since the outcome on one die does not affect the outcome on the other die.
The event A consists of all outcomes in which the number of spots showing on the red die is three or less.
Since the red die has six equally likely outcomes (1, 2, 3, 4, 5, and 6), the probability of A is:
P(A) = the number of outcomes in A / the total number of possible outcomes.
Out of the six possible outcomes on the red die, three of them are three or less: 1, 2, and 3.
Therefore, the number of outcomes in A is three.
Since there are six equally likely outcomes for the green die as well, the total number of possible outcomes is 6 x 6 = 36.
Therefore, we have:
P(A) = 3/36 = 1/12.
The event B consists of all outcomes in which the number of spots showing on the green die is more than three.
There are also three outcomes on the green die that satisfy this condition: 4, 5, and 6.
Thus, we have:
P(B) = 3/36 = 1/12.
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missing number in this sequence 512;128;?;8;2
Answer:
32
Step-by-step explanation:
512 / 4 = 128
128 / 4 = 32
32 / 4 = 8
8 / 4 = 2
Simplify. (3/4)^2= ?
Answer:
9/16.
Step-by-step explanation:
To simplify (3/4)^2, we simply need to square the numerator (3) and the denominator (4) separately, and then simplify the result:
(3/4)^2 = (3^2)/(4^2) = 9/16
Therefore, (3/4)^2 simplifies to 9/16.
Answer:
0.5625
Step-by-step explanation:
(3/4)²
9/16
0.5625
Which of the following points is shown in the graph below?
A.(-1,5,3)
B.(1,-5,3)
C.(1,5,3)
D.(1,5,-3)
Answer:
b
Step-by-step explanation:
1) Dodger Stadium will hold 56,000 fans. Staples Center seats 18,964 Lakers fans. How many more people can attend a Dodger game?
Operation:
Solution:
2) The Alamodome in San Antonio has a normal capacity of 20,557 seats for Spurs' fans, but it can seat 35,000 for special events. How many more people can it seat for special events?
Operation:
Solution:
3) Lambeau Field in Green Bay, Wisconsin seats 60,890 Packers' fans. The Georgia Dome in Atlanta seats 71,228 Falcons fans. How many fans can be seated altogether in the two parks?
Operation:
Solution:
4) The Arrowhead Pond in Anaheim will accommodate 17,174 Mighty Ducks' fans. Staples Center will hold 18,118 L. A. Kings' fans. How many can be held altogether in the two arenas?
Operation:
Solution:
5) The United Center in Chicago will hold 21,500 Bulls' fans. How many 25-seat ticket packages could be sold for one game?
Operation:
Solution:
6) Comerica Park in Detroit will hold 40,000 Tigers fans. If tickets to one game were sold in 20-seat packages, how many of these packages could be sold?
Operation:
Solution:
7) Fenway Park in Boston will hold 33,871 Red Sox fans. Veterans Stadium in Philadelphia will hold 62,409 Phillies fans. How many more fans can attend a game in Philadelphia?
Operation:
Solution:
8) The Rams can fit 66,000 fans in their St. Louis Stadium. If all tickets were sold in packages of 8, how many ticket packages could be sold for one game?
Operation:
Solution:
9) The Miami Dolphins can fit 75,192 fans in their stadium. How many total fans could attend all 8 regular-season games?
Operation:
Solution:
10) Edison Field in Anaheim will hold 45,050 fans. How many tickets could they sell for their 81 regular-season games?
Operation:
Solution:
Dodger Stadium: 37,036 more people can attend a Dodger game., Lambeau Field + Georgia Dome: 132,118 fans can be seated altogether in the two parks.
Solutions to the aforementioned questions1) Dodger Stadium:
56,000 - 18,964 = 37,036 more people can attend a Dodger game.
2) Alamodome:
35,000 - 20,557 = 14,443 more people can be seated for special events.
3) Lambeau Field + Georgia Dome:
60,890 + 71,228 = 132,118 fans can be seated altogether in the two parks.
4) Arrowhead Pond + Staples Center:
17,174 + 18,118 = 35,292 fans can be held altogether in the two arenas.
5) United Center:
21,500 / 25 = 860 25-seat ticket packages could be sold for one game.
6) Comerica Park:
40,000 / 20 = 2,000 20-seat packages could be sold.
7) Fenway Park - Veterans Stadium:
62,409 - 33,871 = 28,538 more fans can attend a game in Philadelphia.
8) St. Louis Stadium:
66,000 / 8 = 8,250 ticket packages could be sold for one game.
9) Miami Dolphins stadium:
75,192 x 8 = 601,536 total fans could attend all 8 regular-season games.
10) Edison Field:
45,050 x 81 = 3,655,050 tickets could be sold for their 81 regular-season games.
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will give brainliest to first answer
space 1 options:
-maximum
-minimum
space 2 options:
0
-2
6
1
space 3 options:
0
-2
6
1
Thus, the function has a minimum value of -2 at x = -1.
Explain about the maxima and minima of function:There are "hills and valleys" in functions, or points where their value reaches a minimum or maximum.
Locally, it may not be the lowest or maximum for the entire function.
An "Absolute" meaning "Global" maximum as well as minimum is the value at which the function has reached its maximum or minimum.There can be more than a local maximum or minimum, but there is only single global maximum (one and global minimum).Stated function:
g(x) = 2x² + 4x
Differentiate the function to find the critical points with respect to x.
g'(x) = 4x + 4 ...eq 1
Put g'(x) = 0
4x + 4 = 0
4(x + 1) = 0
x = - 1 (critical point)
Again Differentiate the function to check for maxima or minima:
g'(x) = 4x + 4
g''(x) = 4
g''(x) > 0 (minimum function)
At x = -1 , the function will be minimum.
Minimum value : Put x = -1 in function.
g(x) = 2(-1)² + 4(-1)
g(x) = 2 - 4
g(x) = -2
Thus, the function has a minimum value of -2 at x = -1.
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continuation. to investigate the believability of my results (dr eh), a student conducted a separate interview (secretly and randomly) on 60 students and construct a 95% confidence interval using the similar approach. suppose that this interview also discover 75% of students favor a difficult final exam. what can you say about this 95% confidence interval based 60 students?
With the probability that 75% of students favor a difficult final exam, the 95% confidence interval based 60 students for sample proportion is ( 0.64, 0.86).
We have to investigate the believability of my results.
Sample size, n = 60
Confidence nterval = 95%
Sample proportion for students who favour the difficulty of exam, [tex] \hat p[/tex] = 75% = 0.75
We have to determine 95% confidence interval based 60 students. Using the confidence interval formula or sample proportion, [tex]CI = \hat p ± z^* \sqrt{\frac{\hat p ( 1 - \hat p )}{n}}[/tex]
Now, using the Z-distribution table, the value z- score for 95% of confidence interval is equals to 1.96.
Substitute all known values in above formula, [tex]= 0.75 ± 1.96 \sqrt{ \frac{ 0.75( 1- 0.75)}{60}}[/tex]
= 0.75 ± 0.11
= ( 0.64, 0.86)
Hence, required value of interval is ( 0.64, 0.86), i.e., 0.64 < p < 0.86.
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Dane is using two differently sized water pumps to clean up flooded water. The larger pump can remove the water alone in 240 min240min240, start text, m, i, n, end text. The smaller pump can remove the water alone in 400 min400min400, start text, m, i, n, end text. How long would it take the pumps to remove the water working together?
It would take the two pumps working together approximately 240 minutes to remove the water.
To determine how long it would take the two pumps to remove the water working together, we can use the concept of work rates. Specifically, we can determine the work rates of each pump and then add them together to find the combined work rate when both pumps are working together.
Let's start by defining some variables:
Let L be the rate of the larger pump, in units of water volume per minute.
Let S be the rate of the smaller pump, in the same units as L.
Let T be the time it takes for both pumps to remove the water working together, in minutes.
From the problem statement, we know that the larger pump can remove all the water alone in 240 minutes. This means that its work rate is 1/240, since it can remove 1 unit of water volume in 240 minutes. Similarly, the smaller pump has a work rate of 1/400.
When both pumps are working together, their work rates add up. Therefore, we can set up an equation as follows:
L + S = 1/T
Substituting the work rates we found earlier, we get:
1/240 + 1/400 = 1/T
Simplifying this equation, we get:
1/T = 0.0041667
Solving for T, we get:
T = 1/0.0041667 ≈ 240.001 minutes
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(a) Three squares have the areas of 7 cm², 17 cm² and 10 cm², (i) Will the squares exactly surround a right angled triangle? (ii) Explain your answer.
Answer:
(i) This equation is not true, which means that the three squares cannot exactly surround a right-angled triangle.
(ii) It is not always possible for three squares to surround a right-angled triangle. One way to see this is to note that the side lengths of a right-angled triangle satisfy the Pythagorean theorem, which means that they must be in a certain relationship to each other. On the other hand, the areas of three squares can take any values, so it is not always possible to find three squares whose side lengths satisfy the Pythagorean theorem.
Step-by-step explanation:
To determine whether the three squares can exactly surround a right-angled triangle, we need to use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Let's assume that the three squares have side lengths a, b, and c, with areas of 7 cm², 17 cm², and 10 cm², respectively. Then, we have:
a² = 7 cm²
b² = 17 cm²
c² = 10 cm²
We need to find out whether there exist values of a, b, and c that satisfy the Pythagorean theorem. If such values exist, then the three squares can surround a right-angled triangle.
We can rearrange the equations above to solve for a, b, and c:
a = √7 cm ≈ 2.65 cm
b = √17 cm ≈ 4.12 cm
c = √10 cm ≈ 3.16 cm
Now, we can check whether the Pythagorean theorem holds:
c² = a² + b²
(√10 cm)² = (√7 cm)² + (√17 cm)²
10 cm = 7 cm + 17 cm
This equation is not true, which means that the three squares cannot exactly surround a right-angled triangle.
In general, it is not always possible for three squares to surround a right-angled triangle. One way to see this is to note that the side lengths of a right-angled triangle satisfy the Pythagorean theorem, which means that they must be in a certain relationship to each other. On the other hand, the areas of three squares can take any values, so it is not always possible to find three squares whose side lengths satisfy the Pythagorean theorem.
Find the missing side. round to the nearest tenth.
Answer:
[tex]x = \sqrt{ {16}^{2} + {21}^{2} } = \sqrt{256 + 441} = \sqrt{697} = 26.4[/tex]
Which matrix is equal to [-6,-6. 5,1. 7,2,-8. 5,19. 3]
The equivalent matrix is [tex]\begin{bmatrix}-6 & -2\\ -6& -8 \\ 5& 5 \\ 1& 19 \\ 7&3 \end{bmatrix}[/tex]
A matrix is a rectangular array of numbers, arranged in rows and columns. Each number in the matrix is called an element, and the number of rows and columns determine the size of the matrix.
Now, to answer your question, the given set of numbers, [-6,-6, 5,1, 7,2, -8, 5,19, 3] can be arranged in a 2x5 matrix or a 5x2 matrix, depending on the order in which you place the numbers. To illustrate:
[tex]\begin{bmatrix}-6 & -6 &5 &1 &7 \\ 2& -8 & 5 & 19& 3\end{bmatrix}[/tex]
or
[tex]\begin{bmatrix}-6 & -2\\ -6& -8 \\ 5& 5 \\ 1& 19 \\ 7&3 \end{bmatrix}[/tex]
Both matrices have the same set of numbers but arranged differently. Hence, it is important to specify the order of the rows and columns to define a matrix uniquely.
In summary, the given set of numbers can be represented as a matrix, which is a rectangular array of numbers arranged in rows and columns. However, to define a matrix uniquely, we must specify the order of the rows and columns. Moreover, matrices can be added, subtracted, and multiplied just like regular numbers.
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For log normally distributed returns, the annual geometric average return is greater than the arithmetic average return. (True or False)
Given statement: For log normally distributed returns, the annual geometric average return is always greater than the arithmetic average return.
The given statement is true.
This is because log normal distribution assumes that the rate of return is compounded continuously, which leads to a higher final value of the investment.
For lognormally distributed returns, the geometric average return is greater than the arithmetic average return.
This is because the lognormal distribution has a positive skew, meaning that there are more small positive returns and fewer large negative returns.
This leads to compounding effects over time, which favor the geometric average return.
The geometric average return is calculated by taking the nth root of the product of (1+Ri),
where Ri is the return for the ith period.
The arithmetic average return is calculated by taking the average of the returns over a period.
Therefore, for lognormally distributed returns, the geometric average return is greater than the arithmetic average return.
The geometric average return takes into account the compounding effect, whereas the arithmetic average return does not.
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4. Find the area of the shaded region. 5 ft 9 ft 3 ft 4 ft A. 36 ft² B. 38 ft² C. 39 ft² D. 40 ft²
Due before 8:30
Answer:
C. 39 ft²
Step-by-step explanation:
Area of the outer rectangle which includes the white triangle
= length x width
= 5 x 9
= 45 ft²
Area of the white triangle
= 1/2 x base x height
= 1/2 x 4 x 3
= 6 ft²
Area of shaded region
= Area of rectangle - Area of triangle
= 45 - 6
= 39 ft²
The line plot shows the amount of liquid that is in 4 different beakers measured in liters.
Which point on the number line represents the amount each beaker will contain after the
liquid has been redistributed equally among the 4 beakers?
A) Point A
B)Point B
(C) Point C
D) Point D
The point on the number line that represents the amount of liquid each beaker will contain after the liquid has been distributed among the 4 beakers is the option B
(B) Point Bi
What is a number line?
A number line is a line that consists of numbers marked at intervals, which indicates quantities, and can be used for numerical operations.
The amount of liquid in the each of the four beakers are;
1/8, 1/8, 6/8, 6/8
The sum of the liquid in the four beakers is therefore;
1/8 + 1/8 + 6/8 + 6/8 = (1 + 1 + 6 + 6)/8 = 14/8
When the same amount of liquid are in each beaker, we get;
Liquid in each beaker = (14/8)/4 = 3.5/8The point on the number line corresponding to the point 3.5/8 is the point B, therefore, the correct option is the option B
(B) Option B
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Each statement can be represented with a fraction and a division expression. Move the correct fraction and division expression to each line.
There are 5 identical pieces cut from 3 feet of rope. The length, in feet, of each piece of rope is____ or ____
There are 2 muffins shared equally by 3 friends. The amount of muffin that each friend gets is ____ or ____
pls answer quick! I will give brainiest to whoever is right
Answer:
act back its also known as act or tactics
Which of the following are examples of rational numbers? Select all that apply.
√4+√16
√5 +√36
√9+√24
2* √4
√49 • √81
3√12
The rational numbers in the list of options are √4+√16, 2* √4 and √49 • √81
The examples of rational numbers among the given options are:
2√4: √4 is equal to 2, so 2√4 = 2*2 = 4, which is a rational number.√49 • √81: √49 is equal to 7 and √81 is equal to 9, so √49 • √81 = 7 • 9 = 63, which is a rational number.√4+√16: √4 is equal to 2 and √16 is equal to 4, so √4+√16 = 2 + 4 = 6, which is a rational number.The other options are not rational numbers:
√5+√36: √5 is an irrational number, so √5+√36 is not a rational number.√9+√24: √24 is an irrational number, so √9+√24 is not a rational number.3√12: √12 is equal to 2√3, so 3√12 = 3 • 2√3 = 6√3, which is not a rational number.Read more about rational numbers at
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Given that ZQRP = (2x + 20) and ZPSQ = 30°, find the value of x.
The value of x is 65. Please note that this solution is based on the assumption that the angles QRP and PSQ are supplementary. If this assumption doesn't hold, feel free to let me know.
We need to find the value of x in the equation ZQRP = (2x + 20)° given that ZPSQ = 30°. Since the question doesn't provide enough information about the relationship between angles QRP and PSQ, I'll assume that they are supplementary angles (angles that add up to 180°). This assumption is based on the possibility that the angles form a straight line or a linear pair.
If angles QRP and PSQ are supplementary, their sum is 180°:
(2x + 20)° + 30° = 180°
Now, we can solve for x:
2x + 50 = 180
Subtract 50 from both sides:
2x = 130
Divide by 2:
x = 65
You are playing a game where a quarter is tossed 4 times. What is the probability that the quarter lands on tails exactly one time?
PLEASE ANSWER FAST!
Find the area of the following triangle:
5
3
4
Answer
6
Step-by-step explanation:
Answer:
Step-by-step explanation:
To find the area of a triangle, we can use the formula:
Area = (1/2) × base × height
In this case, we have three sides of the triangle given: 5, 3, and 4. To use these to find the area, we need to first determine which side is the base and what the corresponding height is.
We can see that the side with length 5 is opposite the biggest angle, so this is likely the hypotenuse. The other two sides, 3 and 4, must then be the other two legs of a right triangle, with one of them being the base and the other the height.
To determine which is which, we can use the Pythagorean theorem:
c^2 = a^2 + b^2
where c is the hypotenuse and a and b are the other two sides. In this case, we have:
5^2 = 3^2 + 4^2
25 = 9 + 16
So we have confirmed that 3 and 4 are indeed the legs of a right triangle, with 5 as the hypotenuse. We can use the Pythagorean theorem again to find the height:
a^2 + b^2 = c^2
b^2 = c^2 - a^2
b = sqrt(c^2 - a^2) (taking the positive square root because b is a length)
b = sqrt(5^2 - 3^2)
b = sqrt(16)
b = 4
So the height of the triangle is 4. We can now use the formula to find the area:
Area = (1/2) × base × height
Area = (1/2) × 3 × 4
Area = 6
Therefore, the area of the triangle is 6 square units.
Solve 2x^2+x-3=0 by factoring.
Answer:
To solve the quadratic equation 2x^2 + x - 3 = 0 by factoring, we follow these steps:
Step 1: Write the equation in standard quadratic form, which is ax^2 + bx + c = 0. In this case, the equation is already in standard form: 2x^2 + x - 3 = 0.
Step 2: Factor the quadratic expression on the left-hand side of the equation. We look for two numbers that multiply to give us the constant term (c) and add to give us the coefficient of the linear term (b). In this case, c = -3 and b = 1.
The two numbers that satisfy these conditions are -3 and 1, as -3 * 1 = -3 and -3 + 1 = -2.
Step 3: Use the factored form to set each factor equal to zero and solve for x.
2x^2 + x - 3 = 0
(2x - 3)(x + 1) = 0 (factored form)
Setting each factor equal to zero:
2x - 3 = 0
2x = 3
x = 3/2
x + 1 = 0
x = -1
So the solutions to the equation are x = 3/2 and x = -1.
h(x)= 6/x-h+k
Oh no! He seems to be missing some parts though. He was "robbed" of his asymptotes!
Luckily, he can remember what they were:
1. This functions vertical asymptote was x = 4.
2. This functions horizontal asymptote was y = -15.
Please recreate this function with those identifying features! Please make sure it looks like the function at the beginning of this problem.
At a function x = 4 has a vertical asymptote and at y = -15 has a horizontal asymptote.
What are asymptotes?The general form of a function is x= a and y = b.
f(x) = (kx + m) / (x - a) + b
k and m are constants.
We require a factor of (x - 4) in the denominator to get a vertical asymptote at x = 4. It is necessary for the fraction to approach -15 when x approaches positive or negative infinity in order to obtain a horizontal asymptote at y = -15.
One potential function that meets these specifications is:
H(x) = 6/(x - 4) - 15 + k
where k is a constant that establishes the function's vertical shift (i.e., its value at x = 0).
By entering a point on the graph, such as the x-intercept (where y = 0), the value of k can be determined:
0 = 6/(x - 4) - 15 + k
15 - k = 6/(x - 4)
x - 4 = 6/(15 - k)
x = 6/(15 - k) + 4
We may enter this value of x into the original equation to find k since y = 0 at the x-intercept:
0 = 6/((6/(15 - k) + 4) - 4) - 15 + k
0 = 6/(6/(15 - k)) - 15 + k
0 = 15 - k - 15 + k
The x-intercept and asymptotes are unaffected by the value of k, and any value of k will result in a function with the same asymptotes. K does, however, have an impact on the function's vertical shift.
We can select a value for k and then search for a specific function that has the specified asymptotes.
For instance, if we select k = 0, we obtain:
H(x) = 6/(x - 4) - 15
This function has the same shape as the original function H(x) presented in the problem and asymptotes at x = 4 and y = -15, respectively.
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Use the form |x – b| < c or |x – b| > c to write an absolute value inequality that has the solution set x= < –9 or x>=-5.
Answer: |x + 9| > 0 or |x + 5| < 4
Step-by-step explanation: To begin with, ready to utilize the frame |x - b| > c to speak to the arrangement x < -9:
|x - (-9)| >
Rearranging this gives:
|x + 9| >
Another, we are able utilize the frame |x - b| < c to speak to the arrangement x ≥ -5. Ready to select a esteem of c that's more noteworthy than the remove from -5 to the closest endpoint of the arrangement set (which is -9):
|x - (-5)| < 4
Rearranging this gives:
|x + 5| < 4
Joining these two supreme esteem disparities with an "or" explanation gives:
|x + 9| > or |x + 5| < 4
Rearranging this gives:
x < -9 or -9 < x < -1
We will see that the primary portion of the arrangement set (x < -9) is as of now spoken to within the to begin with supreme esteem imbalance, and the moment portion (x ≥ -5) is spoken to by the moment supreme esteem imbalance.
A zoologist selected 12 black bears in a Canadian habitat at random to examine the relationship between the age in years, x, and the weight in tens of pounds, y. The 95 percent confidence interval for estimating the population slope of the linear regression line predicting weight in tens of pounds based on the age in years given by 1.272+/-0.570. Assume that the conditions for inference for the slope of the regression equation are met. Which of the following is the correct interpretation of the interval?
It can be concluded that we are 95 percent confident that the mean increase in the weight of a black bear for each one year increase in the age of the bear is between 7.0 and 18.4 pounds.
What is mean?
In statistics, the mean is one of the measures of central tendency which is nothing but simple average, apart from the mode and median. Mean is the average of the given set of values. Mean denotes the equal distribution of values for a given set of data.
A zoologist selected 12 black bears in a Canadian habitat at random to examine the relationship between the age in years, x, and the weight in tens of pounds, y. The 95 percent confidence interval for estimating the population slope of the linear regression line predicting weight in tens of pounds based on the age in years given by 1.272 ±0.570.
From the given data it is clear that the 95 confidence interval given by 1.272±0.570, or (0.702,1.842)
[ 1.272-0.570 = 0.702 and 1.272+0.570= 1.842]
It estimates the relationship between weight in tens of pounds and age in years. So the given data makes us 95 percent confident that the mean increase in the weight of a black bear must be in between 7.02 and 18.42 pounds and it is for each one-year increase in the age of the bear.
Hence, it can be concluded that we are 95 percent confident that the mean increase in the weight of a black bear for each one year increase in the age of the bear is between 7.0 and 18.4 pounds.
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A rhombus has a diagonals of 6 inches and 8 inches. what is the perimeter and the area of the rhombus?
the perimeter of the rhombus is 20 inches, and the area is 24 square inches.
How to solve the question?
To find the perimeter of a rhombus, we need to know the length of one side. Fortunately, we can use the properties of a rhombus to find the length of the sides. A rhombus has two pairs of equal-length sides, so we can use the Pythagorean theorem to find the length of each side.
Let's label the diagonals of the rhombus as d1 and d2. The diagonals of a rhombus bisect each other at right angles, so we can draw a right triangle with half of each diagonal as the legs and a side of the rhombus as the hypotenuse. Using the Pythagorean theorem, we can find the length of the sides:
(1/2)d1 = 3 inches
(1/2)d2 = 4 inches
Side length = √((1/2)d1² + (1/2)d2²) = √(9 + 16) = 5 inches
Now that we know the length of the sides, we can find the perimeter:
Perimeter = 4 x side length = 4 x 5 = 20 inches
To find the area of the rhombus, we can use the formula:
Area = (diagonal 1 x diagonal 2) / 2
Area = (6 x 8) / 2 = 24 square inches
So the perimeter of the rhombus is 20 inches, and the area is 24 square inches.
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HELP I GOT AN F IN MATH AND MY MOMMA AINT GONNA LIKE IT WHEN SHE FINDS OUT
The quadratic equation y = x²-6x+5 is minimum because the coefficient of x² is positive.
x = [tex]\frac{-b}{2a}[/tex], but a = 1 and b = -6
therefore x = [tex]\frac{-(-6)}{2(1)}[/tex] = 3
By plugging the value in the quadratic equation above, then we have
y = (3)² - 6(3) + 5 = -4 = -4
Note that y is the y-value of the vertex.
How to determine the minimum/maximum of a functionTo determine whether the function y = x^2 - 6x + 5 has a maximum or minimum value, we can use the vertex formula, which gives the x-coordinate of the vertex of a quadratic function as -b/2a.
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