the number of degrees in the smaller angle is 60 degrees.
The smaller angle is 60 degrees.
Let x = number of degrees in the smaller angle
Then the number of degrees in the larger angle = 3x
Given that the two angles are in the ratio of 2 to 3
2x = 3x
x = 60
Therefore, the number of degrees in the smaller angle is 60 degrees.
The two supplementary angles are supplementary angles because the sum of their angles is 180 degrees. This means that if we denote the number of degrees in the smaller angle as x, then the number of degrees in the larger angle must be 180-x. We know that their ratio is 2 to 3, which can be written as 2x = 3(180-x). Solving this equation gives us x = 60, so the number of degrees in the smaller angle is 60.
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What is the solution to 2log9(x)=log9 * + log9(x-2)
The solution to 2log9(x)=log9+ log9(x-2) is 4.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 2log9(x)=log^9(8)+log9(x-2)
Above equation can be written as below
Log₉x² = log₉8 + log₉(x-2)
Loga+Logb=Log ab from properties of logarithms
Log₉x² = log₉(8×(x-2))
Log₉x² = log₉8x-16
Log₉x² - log₉8x-16 = 0
Loga-logb=log(a/b)
Log₉(x²/(8x-16)) = 0
x²/(8x-16) = 9°
x² = 1 × 8x-16
x²-8x+16 = 0
x²-4x-4x+16 = 0
(x-4)(x-4) =0
x=4
Hence, the solution to 2log9(x)=log9+ log9(x-2) is 4.
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Using your knowledge of complementary, supplementary vertical, and adjacent angles, identify the pairs of angles named in each figure. For example, in Figure #1 you are to identify the supplementary angles, which are: >AFC and >CFB >AFD and >DFB >CFB and >BFD >BFD and >DFA >DFA and >AFC
The supplementary angles are (a) >AFC and >CFB
How to identify the supplementary anglesThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The figure
As a general rule, supplementary angles are angles that add up to 180 degrees
From the attached figure, we have
AFC + CFB = 180 degrees
This means that these angles are supplementary angles
Hence, the supplementary angles are (a) >AFC and >CFB
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A starship voyages to a distant planet 10 ly away. The explorers stay 4.0 yr , return at the same speed, and arrive back on earth 26 yr after they left. Assume that the time needed to accelerate and decelerate is negligible.
How much time has elapsed on the astronauts' chronometers?
Express your answer using two significant figures
The total time elapsed on the astronauts' chronometers is 20 years. This is calculated by subtracting the time spent traveling to and from the distant planet (2 * 10 years = 20 years) from the total time elapsed on Earth (26 years).
This result takes into account the time dilation effect of special relativity, which states that time passes more slowly for a moving object relative to a stationary observer. Since the astronauts were traveling at high speeds for much of their journey, the time elapsed on their chronometers would be less than the time elapsed on Earth.
The total time elapsed on the astronauts' chronometers is 20 years. This is calculated by subtracting the time spent traveling to and from the distant planet (2 * 10 years = 20 years) from the total time elapsed on Earth (26 years).
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which pair of segments in the figure below appear to be parallel?
determine which best describes lines g and k.
A. The pair of segments that is parallel will be AB & EF, DH & CG, and BC & FG. Then the correct option is A.
B. The line G and line K will be a skew line. Then the correct option is B.
What is Geometry?One of the first areas of mathematics is geometry, along with maths. It is preoccupied with spatial characteristics including the separation, form, size, and relative placement of objects. A geometer is a mathematician who specializes in shape.
A. The parallel edges of the rectangular is given below.
AB = CD = EF = GH
AE = DH = CG = BF
BC = AD = EH = FG
The pair of segments that is parallel will be AB & EF, DH & CG, and BC & FG. Then the correct option is A.
B. The line G and line K will be a skew lines. Then the correct option is B.
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Solve for X And stuff
The required value of the x in the given circle is given as,
5. x = 9 6. x = 4 7. x = 5 8. x = 8
Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
5.
For the given circle,
The sum of all sections should be equal to 360°.
65 + 34 + 41 + 16 +6x + 150 = 360
x = 9
Similarly,
6. x = 4
7. x = 5
8. x = 8
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on monday alex ran 2 2/3 miles. on wednesday she ran 1 5/6 more miles than she did on monday. how many miles did she run on wednesday
Given (x – 1)2 = 50, select the values of x. x = –49 x = 51
The values of x are 13 and 11
How to determine the valuesAlgebraic expressions are expressions having terms, variables, coefficients, constants and factors.
They are also made up of arithmetic operations.
Given that;
(x - 1)²= 50
expand the bracket
x² - x - x + 1 = 50
collect like terns
x² - 2x + 1 = 50
x² - 2x - 49
Factorize the expression
(x² - 13x) + (11x - 49)
Factor the common terms
x(x - 13) + 11(x - 13)
x = 13. x = -11
Hence, the values are 13 and 11
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If base of parallelogram is 7m and height is 12m what is area
Answer:
84m²
Step-by-step explanation:
Area if a parallelogram is base×height
base=7m
height=12m
area=7m×12m=84m²
Let die one have sides 0, 3, 3, 3. Let die 2 have sides 2, 2, 2, 5. Let die 3 have sides 1, 1, 4, 6. Fine the probabilities that a. die 1 beats die 2 b. die 2 beats die 3 c. die 3 beats die 1 Did something strange occur?
a. The probability that die 1 beats die 2 is 1/4\
b. The probability that die 2 beats die 3 is 2/4 or 1/2
c. The probability that die 3 beats die 1 is 1/4.
Nothing strange occurred because the probabilities found are all based on the number of sides of each die and their values, which followed the expected outcome for any fair dice.
What is probability?Probability is described as the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
The probability that die 1 beats die 2 is 1/4 because die 1 has three sides with the value of 3, and die 2 has only one side with a value which is greater than 3. Hence there is a 1 in 4 chance that the result of rolling die 1 will be greater than the result of rolling die 2.
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Marta is shopping where there is a sales tax of 8\%8%8, percent on any item she buys.
1. Write an equation that represents how much tax (ttt) Marta pays on an item whose price is ppp dollars.
2. How much tax does Marta pay on an item whose price is \$ 20$20dollar sign, 20?
\$$dollar sign
1. An equation that represents "the amount of tax on an item of price p",
t = p x X / 100
2. Marta does pay on an item whose price is $20, $1.6
What is the percentage?Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".
Given that,
Tax rate = 8%
1. Let's assume that the sales tax rate is X%.
Then, the equation that represents the amount of tax (t) Marta pays on an item whose price is p can be written as:
t = p x X / 100
2. If the price of the item is $20, the amount of tax Marta pays can be calculated as follows:
t = $20 x X / 100
t = $20 x 8 / 100
t = $1.6
So, Marta pays $1.6 in sales tax on an item whose price is $100.
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An amusement park has opened a new roller coaster. It is so popular that people are waiting for up to 3 hours for a 2-minute ride. Concerned about how people who might be willing to wait in line for 3 hours feel about this, they survey every 15th person in line for the roller coaster, starting from a randomly selected individual. a) What kind of sample is this? b) Is it likely to be representative of the people in line for the roller coaster? c) What is the sampling frame? O A. a simple random sample O B. a systematic sample OC. a convenience sample OD. a census b) Is the sample likely to be representative of the people in line for the roller coaster? O A. Yes OB. No c) Choose the correct sampling frame below. O A. all the patrons of the park OB. all the patrons willing to wait in line for the roller coaster OC. all the people who go to amusement parks OD. all the patrons who like roller coasters
a) The sample is a systematic sample., b) It may not be representative of all people in line for the roller coaster., c) The sampling frame is all the people who are willing to wait in line for the roller coaster.
a) A systematic sample is a sample where individuals are selected from a larger population at regular intervals or through a set pattern. In this case, the amusement park is selecting every 15th person in line, making it a systematic sample.
b) The sample may not be representative of the population of people in line for the roller coaster because by only including every 15th person, certain groups of people who are similar may be overrepresented or underrepresented in the sample, potentially leading to a biased representation of the opinions of the people waiting in line.
c) The sampling frame for this survey is the population of people waiting in line for the roller coaster. This is the group of individuals from which the sample will be taken. In this case, the sampling frame is not limited to just the patrons of the park, or all the people who go to amusement parks, but is specifically focused on the people waiting in line for the roller coaster.
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Alice wants to use the stack method to pay down her debts listed in the table below. If she applies an extra $150 a month to her debts, what will be the first debt she targets to pay off and what will be the monthly amount she applies to it?
Therefore , the solution of the given problem of linear equation comes out to be monthly amount she applies to it is $550.
What exactly is a linear equation?Using the formula y=mx+b, a simple regression curve is constructed. The slope is B, and the y-intercept is m. Even if y or y are separate portions, the foregoing sentence is frequently referred to as a "mathematical formula merging many variables." In bivariate linear equations, there are only two variables. Application problems involving linear equations have no known solutions.
Here,
Given :
=> $150 extra in her debt
her debt be x
y be the amount she already pays
=> amount left
=> x - y - 150
=> x- (y+150)
Let x be 1000
y be 300
=> 1000 -(300+150)
=> 1000 -450 = 550
Thus,
monthly amount she applies to it is $550
Therefore , the solution of the given problem of linear equation comes out to be monthly amount she applies to it is $550.
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PLEASE HELP ITS URGENT
A store is instructed by corporate headquarters to put a markup of 25% on all items. An item costing $24 is displayed by the store manager at a selling price of $6. As an employee, you notice that this selling price is incorrect. Find the correct selling price. What was the manager's likely error?
The correct selling price of an item will be $12.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a store is instructed by corporate headquarters to put a markup of 25% on all items. An item costing $24 is displayed by the store manager at a selling price of $6.
The selling price will be calculated as:-
Selling price = 25% of 24 + $6
Selling price = 6 + 6
Selling price = $12
Hence, the selling price of the item is $12.
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Five sisters' ages added up to 211. The oldest sister's age was 3 times
that of the youngest. The next to the oldest was 2 years younger than the
oldest and the middle sister was twice as old as the youngest. The
remaining sister was 3 years older than the youngest sister. What is the
age of the oldest sister?
Please have the answer as a worded answer!
(ex: there are 35 pounds of beans.)
Answer:
The oldest is 60 years olds.
Step-by-step explanation:
a+b+c+d+e=211
a=3e
b=a-2
c=2e
d=e-3
3e+3e-2+2e+e-3+e-6=211
10e-5=211
211-11=10e
200=10e
e=20
Can any one help with the circled ones
The reasoning based on the information will be:
a) Deductive reasoning.
b) Deductive reasoning.
What is a deductive reasoning?Deductive reasoning follows a top-down method, whereas inductive reasoning follows a bottom-up method. While deductive thinking involves drawing conclusions by moving from general premises to specific conclusions, inductive reasoning involves moving from the specific to the general.
A specific conclusion is reached by the logical process of inductive reasoning, which combines several premises that are all generally accepted as true or discovered to be true. Applications that involve prediction, forecasting, or behavior use inductive reasoning frequently. In both cases, deductions were made based on the information.
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A company charges a shippping dee that is 4.5% of the purchase price for all items it ships. What is the fee to ship an item costs $56?
The shipping charge of an item on the purchase $56 would be $2.52.
We are Given that, a company charges a shipping fee that is 4.5% of the purchase price for all items at ships.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
The Cost of an item =$56
So, shipping fee = 4.5% of 56
Therefore, we have
= 4.5/100 × 56
= 0.045 × 56
= $2.52
Hence, the shipping charge of an item is $2.52.
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consider a production process that produces batteries. a quality engineer has taken 20 samples each containing 100 batteries. the total number of defective batteries observed over the 20 samples is 200. the sample standard deviation is
The sample standard deviation is 0.03
As per the given data, a quality engineer has taken the 20 samples in which each containing of 100 batteries.
The total number of the defective batteries which are observed over the 20 samples is 200.
Here we have to calculate the value of the sample standard deviation
The number of samples, k = 20
The number of batteries in each sample:
The sample size = 100
The total number of batteries of the sample are:
The total number of samples, [tex]$\sum{n=20 \times 100=2000}$[/tex]
[tex]& \bar{n}=\sum_\frac{n}{k}} \\[/tex]
= [tex]$\frac{2000}{20}[/tex]
= 100
The total number of defective batteries = 200
Now we can calculate the proportion of the deflective battery:
Therefore, [tex]$\bar{p}=$[/tex] The total number of defectives ÷ The total number of samples
= [tex]$\frac{200}{2000}[/tex]
= 0.10
The standard deviation, [tex]$\sigma_{\mathrm{p}}=\sqrt{\frac{\bar{p} \bar{q}}{\bar{n}}}$[/tex]
= [tex]$ \sqrt{\frac{0.1 \times 0.9}{100}} \\[/tex]
= [tex]& \sqrt{0.0009} \\[/tex]
= 0.03
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The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the a. level of significance b. confidence level c. confidence coefficient d. error factor
The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the level of significance.
The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is known as the level of significance. The level of significance (α) is the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true. This is calculated by subtracting the confidence level from 1. For example, if the confidence level is 95%, then the level of significance is 1-0.95 = 0.05. This means there is a 5% chance of making a Type I error.
The confidence level is the probability that the interval will contain the actual value of the population parameter. It is calculated by 1 minus the level of significance. For example, if the level of significance is 0.05, then the confidence level is 1-0.05 = 0.95, which is 95%. This means there is a 95% chance that the interval will contain the actual value of the population parameter.
The confidence coefficient is the width of the interval, which is calculated by subtracting the lower bound from the upper bound of the interval.
The error factor is the difference between the estimated parameter value and the actual parameter value, which is calculated by subtracting the estimated parameter value from the actual parameter value.
The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the level of significance.
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Which of the following is the solution to the equation 25^(z + 4) = 125? Group of answer choices z = 5.5 z = 3.5 z = −2.5 z = −0.5
The value of 'z' in the equation [tex]25^{(z + 4)} = 125[/tex] is, z = - 2.5.
What are some rules of exponents?Some common rules of exponents are
xᵃ×xᵇ = xᵃ⁺ᵇ.
xᵃ/xᵇ = xᵃ⁻ᵇ.
Addition and subtraction of exponents are only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.
Given, An exponential equation [tex]25^{(z + 4)} = 125[/tex].
We know, 5² = 25 and 5³ = 125.
Therefore, [tex](5^2)^{(z + 4)} = 5^3[/tex] , Having the same base we can equate the exponents.
2(z + 4) = 3.
2z + 8 = 3.
2z = - 8 + 3.
2z = - 5.
z = - 2.5.
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A card is drawn randomly from a standard 52-card deck. Find the probability event. (a) The card drawn is 8 of the given 2 The probability is:______(b) The card drawn is a face card (Jack, Queen, or King) The probability is:______(c) The card drawn is not a face card The probability is:_______
The probability of selecting an 8 is [tex]\frac{4}{52}[/tex] since there are 4 total 8's available (8 of hearts/spades/diamonds/clubs) out of 52 cards. This simplifies to [tex]\frac{1}{13}[/tex]. The probability of selecting a face card is [tex]\frac{12}{52}[/tex] since there are 4 Jacks, 4 Queens, and 4 Kings. This simplifies to [tex]\frac{3}{13}[/tex]. 1 - [tex]\frac{3}{13}[/tex] = [tex]\frac{13}{13}[/tex] - [tex]\frac{3}{13}[/tex] =[tex]\frac{10}{13}[/tex].
There are four suits (hearts, spades, diamonds, and clubs), each with 13 cards from Ace to King, in a conventional 52-card deck of playing cards. As a result, there are four of each potential card.
(A) The probability of selecting an 8 is [tex]\frac{4}{52}[/tex] since there are 4 total 8's available (8 of hearts/spades/diamonds/clubs) out of 52 cards. This simplifies to [tex]\frac{1}{13}[/tex].
(B) The probability of selecting a face card is [tex]\frac{12}{52}[/tex] since there are 4 Jacks, 4 Queens, and 4 Kings. This simplifies to [tex]\frac{3}{13}[/tex].
(C) The probability of NOT selecting a face card is [tex]\frac{40}{52}[/tex] since there are 4 of each card from Ace through 10 that are not face cards. This simplifies to 10/13. The solution to part B's question can be used as another way to approach this issue. If the probability of selecting a face card is 3/13, then the probability of NOT selecting a face card has to be 1 - [tex]\frac{3}{13}[/tex] = [tex]\frac{13}{13}[/tex] - [tex]\frac{3}{13}[/tex] =[tex]\frac{10}{13}[/tex]. Recall that you must deduct from 1 since the probability of all conceivable outcomes must add up to 1, or 100%.
Therefore, the probability of selecting an 8 is [tex]\frac{4}{52}[/tex] since there are 4 total 8's available (8 of hearts/spades/diamonds/clubs) out of 52 cards. This simplifies to [tex]\frac{1}{13}[/tex]. The probability of selecting a face card is [tex]\frac{12}{52}[/tex] since there are 4 Jacks, 4 Queens, and 4 Kings. This simplifies to [tex]\frac{3}{13}[/tex]. the probability of NOT selecting a face card has to be 1 - [tex]\frac{3}{13}[/tex] = [tex]\frac{13}{13}[/tex] - [tex]\frac{3}{13}[/tex] =[tex]\frac{10}{13}[/tex].
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a dilation has center (0,0). find the image of the point b (7/2, -6/5) for the scale factor 1/9
The image of the point b(7/2 , -6/5) is (7/18,-2/15)
what is the Cartesian coordinate system?A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates,
Given here: A dilation has center (0,0) and image of the point b (7/2,-6/5)
Now it is given that the scale factor is 1/9
Thus the image of the given point is
x=7/2×1/9
x=7/18
y=-6/5×1/9
y=-2/15
Thus the image is (7/18,-2/15)
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consider the trial on which a 3 is first observed in successive rolls of a six-sided die. let a be the event that 3 is observed on the first trial. let b be the event that at least two trials are required to observe a 3. assuming that each side has probability 1/6, find (a) p(a), (b) p(b), and (c) p(a ub).
P(A) is the probability of observing 3 on first trial. P(B) is probability of observing 3 after at least 2 trials. P(A U B) is total probability of observing 3.
(a) The probability of observing a 3 on the first trial is 1/6. So, p(a) = 1/6.
(b) The probability of not observing a 3 on the first trial is 5/6.
If a 3 is not observed on the first trial, then the same experiment will be repeated with a 5/6 chance of not observing a 3 again.
This can be represented as (5/6)^2.
The probability of not observing a 3 on the first two trials is (5/6)^2.
So, the probability of observing a 3 on the third trial is
1 - (5/6)^2
This can be represented as
1 - (5/6)^n where n is the number of trials
The probability of requiring at least two trials to observe a 3 is the sum of the probabilities of observing a 3 on the third, fourth, fifth, etc. trials. This is equivalent to the sum of an infinite geometric series. The sum can be calculated using the formula
S = a/(1 - r) where S is the sum, a is the first term, and r is the common ratio.
In this case, a = 1 - (5/6)^2 and r = 5/6. So, the sum is S = (1 - (5/6)^2)/(1 - 5/6) = 6/36 = 1/6. Therefore, p(b) = 1/6.
(c) The probability of observing a 3 on the first trial or at least two trials is the sum of p(a) and p(b). So, p(a or b) = p(a) + p(b) = 1/6 + 1/6 = 1/3.
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Solve each equation:6x + __ = 10x+5
The complete equation is,
6x + 4x + 5 = 10x+5.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
We have an equation,
6x + __ = 10x+5.
Let the missing number is y.
Then,
6x + y = 10x+5.
y = 10x - 6x + 5
y = 4x + 5
Therefore, the missing term is 4x + 5.
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the markup over dealer’s cost of a new car ranges from 13% to 20%. if the sticker price is $15,000, over what range will the dealers cost vary? HELPP
Answer:
Step-by-step explanation:
2=35434567654321-34567887654321=2345678765-cwjbfd3
20 is to 28 as 3x-5 is to 3x-5+10
20 is 8 less than 28 as 3x-5 is 10 less than 3x-5+10.
What is comparison?Comparing numbers in math is defined as a process or method in which one can determine whether a number is smaller, greater, or equal to another number according to their values.
Given that, 20 is to 28 as 3x-5 is to 3x-5+10
We see, 28-20 = 8
That mean, we need to add 8 to 20 or subtract 8 from 28 to make both equal,
Therefore, we can say, 20 is 8 less than 28, or 28 is 8 more than 20,
Similarly,
3x-5 and 3x-5+10
We see, 3x-5+10 - (3x-5)
= 3x+5-3x+5
= 10
That mean, we need to add 10 to 3x-5 or subtract 10 from 3x-5+10 to make both equal,
Therefore, 3x-5 is 10 less than 3x-5+10, or 3x-5+10 is 10 more than 3x-5,
Hence, 20 is 8 less than 28 as 3x-5 is 10 less than 3x-5+10.
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write and equation for each system of equation as an ordered pair
(I think I know the answer s but I really want assurance please eand thank you)
The solution for each system of equations is given as follows:
1. (-2,-2).
2. (4,1).
How to obtain the solution to the system of equations?When a system of equations is plotted on graph, the solutions are the intersection points of all the functions that compose the system.
For the first system, the graphs intersect at a x-coordinate of -2 and an y-coordinate of -2, hence the coordinates are given as follows:
(-2,-2).
For the first system, the graphs intersect at a x-coordinate of 4 and an y-coordinate of 1, hence the coordinates are given as follows:
(4,1).
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Proving Vertical Angles Are Congruent
Given: 2 and Z4 are vertical
angles.
Prove: 42 44
4
1
P
3
E
2
n
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Statements Reasons
m22+ m23 = 180
m23+ m24 = 180
42 and 43 are a linear pair 23 and 24 are a linear pair
Statements
Reasons
22
anc
mz
me
a company records a journal entry that contains a debit to inventory. which of the following could be a valid entry to complete this journal entry?
When a journal entry contains a debit to inventory, a corresponding credit to an offsetting account, such as Cost of Goods Sold (COGS), is required.
A journal entry that contains a debit to inventory requires a corresponding credit to an offsetting account, such as Cost of Goods Sold (COGS). The formula for the entry would be:
Debit Inventory
Credit Cost of Goods Sold (COGS)
The calculation would depend on the cost of the inventory, the quantity purchased and the applicable tax rate. For example, if the cost of the inventory is $5,000, the quantity purchased is 500 and the applicable tax rate is 5%, the journal entry would look like this:
Debit Inventory $5,000
Credit Cost of Goods Sold (COGS) $4,750 ($5,000 x 95% = $4,750)
In this example, the total cost of the inventory was $5,000, but the credit to COGS was calculated by multiplying the cost of the inventory ($5,000) by 95% (the applicable tax rate of 5% was subtracted). The resulting amount of $4,750 was the amount credited to COGS.
In summary, when a journal entry contains a debit to inventory, a corresponding credit to an offsetting account, such as Cost of Goods Sold (COGS), is required. The formula for the entry is: Debit Inventory, Credit Cost of Goods Sold (COGS). The calculation for the entry depends on the cost of the inventory, the quantity purchased and the applicable tax rate.
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a sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape: 383 351 355 361 378 421 322 395 401 373 374 372 363 368 364 326 339 394 391 369 377 356 352 407 333 397
The sample mean is 358.54, and the sample median is 365. To keep the median unchanged, we could increase or decrease the largest value by up to 49 seconds. The values of mean and the median in minutes are 5.97 and 6.08.
The sample mean can be calculated as follows:
mean = (sum of all observations) / (number of observations)
mean = (373 + 370 + 364 + 366 + 364 + 325 + 339 + 393 + 356 + 359 + 363 + 375 + 424 + 325 + 394 + 402 + 392 + 369 + 374 + 359 + 356 + 403 + 334 + 397) / 26
mean = 358.54
The median can be calculated by arranging the observations in order and finding the middle value. With 26 observations, we'll find the average of the two middle values.
median = (364 + 366) / 2 = 365
To keep the median unchanged, we need to maintain the same number of observations on either side of the median. In this case, with 26 observations, there are 13 observations on either side of the median. To keep the median unchanged, we need to keep the range of the data the same, which means the difference between the maximum and minimum values should remain the same.
The range of the data is 424 - 325 = 99 seconds.
So, to keep the range the same, the largest value could be increased or decreased by up to half of the range, which is:
99 seconds / 2 = 49 seconds.
To express the observations in minutes, we'll divide each observation by 60.
mean in minutes = 358.54 / 60 = 5.97
median in minutes = 365 / 60 = 6.08
So, the values of mean and the median in minutes are 5.97 and 6.08, respectively.
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Your question is incomplete, but I suppose the question was:
"A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape: 373 370 364 366 364 325 339 393 356 359 363 375 424 325 394 402 392 369 374 359 356 403 334 397
a. Calculate the values of the sample mean and median.
b. By how much could the largest time, currently 424, be increased without affecting the value of the sample median? By how much could this value be decreased without affecting the value of the sample median?
c. What are the values of mean and the median when the observations are re-expressed in minutes?"
use the definition or identities to find the exact value of each of the remaining five trigonometric functions of the acute angle
The value of Sinθ 1/√197, cos θ = 14/√197, csc θ = H/P =√197, sec θ =√197/14, Cot θ = 14
Trigonometric functions are real functions in mathematics that connect an angle of a right-angled triangle to ratios of two side lengths. They are widely utilised in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more.
Trigonometry employs six fundamental trigonometric functions. These ratios are trigonometric functions. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities.
if triangle is form,
Then Perpendicular(P) = 1 and Base(B) = 14
Then Hypotenuse(H) = √(12 + 142)= √197
Then , sin θ = P/H = 1/√197
cos θ = B/H = 14/√197
csc θ = H/P = √197/1 = √197
sec θ = H/B =√197/14
Cot θ = B/P = 14/1 = 14
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The complete question should be:
use the definition or identities to find the exact value of each of the remaining five trigonometric functions of the acute angle, given that tan θ = 1/14 ,