Answers
The answer is: True.
Why?A counterexample is a way that we can prove that something is not true about a mathematical equation or expression, it's also considered as an exception to a rule.
So:
[tex]sec^{2}x-1=\frac{cosx}{cscx}\\\\tg^{2}x=\frac{cosx}{\frac{1}{sinx}}\\\\\frac{1-cos2x}{1+cos2x}=cosxsinx[/tex]
Then, evaluating we have:
[tex]\frac{1-cos(2*45)}{1+cos(2*45)}=cos(45)*sin(45)\\\\\frac{1-0}{1+0}=\frac{\sqrt{2} }{2}*\frac{\sqrt{2}}{2}\\\\1=\frac{(\sqrt{2})^{2} }{4}\\\\1=\frac{2}{4}\\\\1=\frac{1}{2}[/tex]
Hence, we can see that the equation is not fulfilled, so, 45° is a counterexample for [tex]sec^{2}x-1=\frac{cosx}{cscx}[/tex] and the answer is true.
Have a nice day!
Related Questions
The area of Mr.Birardis pool is 63x+81. If the width of his pool is 9,what is the length?
Answers
Answer:
The length is 7x+9
Step-by-step explanation:
We know that area equals length times width
A = l*w
63x+81 = l*9
The area is 63x+81 and the width is 9
Divide each side by 9
63x/9 +81/9 = 9l/9
7x +9 = l
The length is 7x+9
Answer:
The length should be 7x+9
Check all of the solutions to this equation PLS ANSWER!!
Answers
Answer:
D & E
Step-by-step explanation:
1/ they're the only ones in the right format
2/ they're both highlighted on the graph
(im not completely confident in my answer, so don't drag me if im wrong.)
Answer:
it is a and b
Step-by-step explanation:
Bart works 36 hr a week and makes $612.Charles worked 34hr a week and makes$663.Who makes more per he how do you know
Answers
Answer:
Charles
Step-by-step explanation:
Bart worked for 36 hours, and earned $612.
$612 / 36 = $17 is what he earned per hour
Charles worked for 34 hours, and earned $663.
$663 / 34 = $19.5 is what he earned per hour
You don't even need to solve for anything actually. Just looking at the given values, you will see that Charles earned more money despite working less hours compared to Bart.
Please help fast !!!!!
Answers
Answer:
Correct choice is D). -4.
Step-by-step explanation:
Given the following relation is a function where the relation is :
{(6,3),(-4,1),(8,-5),(x,1)}
Now we need to decide about which of the following cannot be a value for x.
Where given choices are:
A). 3
B). 1
C). -5
D). -4
E). 4
We know that a relation is called function if doesn't contains repeated values in domain or doesn't have repeated x-values.
In given relation, {(6,3),(-4,1),(8,-5),(x,1)}, we see that x-values are 6, -4 and 8.
So to prevent repetition, x can't be any of 6, -4 and 8.
Hence correct choice is D). -4.
Describe, in your own words, the identity sin^2(x) + cos^2(x) = 1.
Answers
Look at the attached figure. We define the unit circle as a circle with center [tex]A[/tex] in the origin (0,0) and radius 1.
Then, we consider a point P on the circumference. We call [tex]\alpha[/tex] the angle between the positive half of the x axis and the radius AP.
We define
[tex]\cos(\alpha) = \overline{AD},\quad \sin(\alpha) = \overline{AC}[/tex]
As you can see, ACD is a right triangle, and so we have
[tex]\overline{AD}^2+\overline{AC}^2=\overline{AP}^2[/tex]
But since we know that AD is the cosine, AC is the sine, and AP is the radius (which is 1, and remains 1 when squared), we have just found out that
[tex]\cos(\alpha)^2+\sin(\alpha)^2=1[/tex]
Luke is 5 years younger than 3 times Sydney's age, s. In this situation, what does 3s represent?
Answers
in this case, s is 5 years older than luke's age
Answer:
3s represents:
3 times of Sydney's age
Step-by-step explanation:
We are given that:
Luke is 5 years younger than 3 times Sydney's age, s.
i.e. Sydney's age is denoted by s
Then,
3s represents 3 times of Sydney's age
Hence, 3s represents:
3 times of Sydney's age
Two lengths of a triangle measure 6 feet and 10 feet what can the length of the third side
Answers
Answer:it could possibly equal 2[tex]\sqrt{x}[/tex]34 or 8Step-by-step explanation: by the pythagorean thoerm 6[tex]x^{2}[/tex]+10[tex]x^{2}[/tex] = 2[tex]\sqrt{x}[tex]34 or 6[tex]\sqrt{x}[/tex] +b[tex]x^{2}[/tex]=10[tex]x^{2}[/tex]
Final answer:
The length of the third side of the triangle is approximately 11.66 feet.
Explanation:
To find the length of the third side of a triangle, we can use the Pythagorean theorem. According to the theorem, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the lengths of the two sides given are 6 feet and 10 feet. So, we can calculate the length of the third side as follows:
a² + b² = c²
6² + 10² = c²
36 + 100 = c²
136 = c²
c = √136
c ≈ 11.66 feet
Brian wants to purchase a car wash "package" from his local car wash. He can either get unlimited car washes for a month for $35 with no additional charges. Or, he can buy a discount package, where he pays $22 for the month plus $1.50 per car wash. He wants to know how many car washes he would need to get in order to make the $35 deal a better choice.
y=22x+1.5 Substitute 35 for x: y=22(35)+1.5; y=771.5, which means it would take 772
car washes for the plans to be worth the same amount.
y=1.5x+22 Substitute 35 for y: 35=1.5x+22; y≈8.7, which means at 9 car washes, the unlimited package at $35
would be cheaper.
y=22x+1.5 Substitute 35 for y: 35=22x+1.5; y≈1.5, which means at 2 car washes, the unlimited package at $35
would be cheaper.
y=1.5x+22 Substitute 35 for x: y=1.5(35)+22; x=74.5, which means the discount package is cheaper unless Brian gets 75 car washes.
Answers
Answer:
y=1.5x+22 Substitute 35 for x: y=1.5(35)+22; x=74.5, which means the discount package is cheaper unless Brian gets 75 car washes. or d plz make Brainleist.
Step-by-step explanation:
The option that would make the $35 deal a better choice is 75 cars washes.
What makes the $35 deal better?The equation that can be used to determine the required value is:
$22 + $1.50x
Where x represents the number of car washes
Substitute x with 35
$22 + $1.5(35) = 74.5 = 75 cars
To learn more about mathematical equations, please check: https://brainly.com/question/26427570
Alexi's restaurant bill is $58, and he wants to leave a 20 percent tip. Which expression represents the total amount that Alexi needs to pay?
Answers
Answer:
8.00
Step-by-step explanation:
its all about moving over the decimal
Here is a list of numbers: 3.8, 5.3, 8.8, 1.6, 4.7, 8.8, 2.6 ,9.6 ,5.6 ,4 State the median.
Answers
A recent survey by the cancer society has shown that the probability that someone is a smoker is P(S)=0.19. They have also determined that the probability that someone has lung cancer, given that they are a smoker is P(LC|S)=0.158. What is the probability (rounded to the nearest hundredth) that a random person is a smoker and has lung cancer P(S∩LC) ?
0.35
0.03
0.02
0.83
Answers
Answer:
0.03
Step-by-step explanation:
The given question uses the concept of Conditional Probability. The general formula of conditional probability in terms of two events A and B is:
[tex]P(A|B) = \frac{P(A \cap B}{P(B)}[/tex]
In the given case, the two events are:
LC = Event that someone has lung cancer
S = Event that someone is smoker
The formula in terms of these events will be:
[tex]P(LC | S)=\frac{P(S \cap LC)}{P(S)}[/tex]
Using the given values, we can find the probability that a random person is a smoker and has lung cancer P(S∩LC).
[tex]0.158=\frac{P(S \cap LC)}{0.19} \\\\ P(S \cap LC) = 0.158 \times 0.19\\\\ P(S \cap LC) = 0.03[/tex]
Therefore, the probability (rounded to the nearest hundredth) that a random person is a smoker and has lung cancer P(S ∩ LC) is 0.03
Answer:
P (S∩LC) = 0.03
Step-by-step explanation:
It is known that the probability if someone is a smoker is P(S)=0.19 and the probability that someone has lung cancer, given that they are also smoker is P(LC|S)=0.158.
So using the above information, we are to find the probability hat a random person is a smoker and has lung cancer P(S∩LC).
P (LC|S) = P (S∩LC) / P (S)
Substituting the given values to get:
0.158 = P(S∩LC) / 0.19
P (S∩LC) = 0.158 × 0.19 = 0.03
The losing team in a baseball game scored 2 runs. Which inequality represents the number of runs, r , that the winning team could have scored? A. R?2 B. R>2 C. R<2 D. R=2
Answers
B. R>2 because to win the game they must have had more runs than the losing team
Final answer:
The inequality that represents the number of runs the winning baseball team could have scored is r > 2, since the winning team must score more than the losing team, which scored 2 runs.
Explanation:
The student is asking for the inequality that represents the number of runs, r, that the winning team could have scored in a baseball game, given that the losing team scored 2 runs. The condition to win a game is that the winning team must score more runs than the losing team. Therefore, if the losing team scored 2 runs, the inequality that represents the number of runs the winning team scored is r > 2. This is because the winning team must have scored more than 2 runs to win.
Y = 5x – 1 –15x – 3y = 3 How many solutions does this linear system have? one solution: (0, –1) one solution: (1, 4) no solution infinite number of solutions
Answers
Answer:
one solution: (0, –1)
Step-by-step explanation:
we have
[tex]y=5x-1[/tex] ----> equation A
[tex]-15x-3y=3[/tex] ----> equation B
isolate the variable y in the equation B
[tex]3y=-15x-3[/tex]
[tex]y=-5x-1[/tex] ----> equation C
Compare equation A and equation C
The equations are different
The slopes are different ( are not parallel lines)
therefore
The system has one solution
Solve the system
equate the equation A and equation C and solve for x
[tex]5x-1=-5x-1[/tex]
[tex]5x+5x=-1+1[/tex]
[tex]x=0[/tex]
Find the value of y
[tex]y=5(0)-1=-1[/tex]
The solution is the point (0,-1)
A circle with circumferemce 18 has a arc with a 120 degrees central angle. What is the length of the arc
Answers
360°=18
120°=x
x=120*18/360=6
What are the roots of the polynomial equation? Will mark brainliest.
Answers
Answer:
4 and -21
Step-by-step explanation:
When you factor it (x-4)(x+21)
You get 4 and -21
Fourteen percent of the town's population is over the age of 65. If there are 320 residents over the age of 65, approximately what is the town's population?
Answers
Answer:
Approximately the town´s population are 2285 people.
Step-by-step explanation:
1. Lets name the total population of the town as x, so the percentage of the population that is over the age of 65 can be expressed as:
[tex]P_{+65}=0.14x[/tex]
2. As there are 320 residens over the age of 65, means that the fourteen percent of the town´s population is equal to 14%, that is:
[tex]320=0.14x[/tex]
3. Solving for x it can be found the town´s population:
[tex]x=\frac{320}{0.14}[/tex]
[tex]x=2285people[/tex]
Two types of survey questions are open questions and closed questions. An open question allows for any kind of? response; a closed question allows for only a fixed response. An open question and a closed question with its possible choices are given below. List the advantages and disadvantages of each question.Open? question: What can be done to get students to eat healthier? foods?Closed? question: How would you get students to eat healthier? foods?1. Mandatory nutrition course2. Offer only healthy foods in the cafeteria and remove unhealthy foods3. Offer more healthy foods in the cafeteria and raise the prices on unhealthy foods
Answers
Answer:
Let's start with the open question.
Benefits
The benefits of using an open question is that it allows you to get a wide array of answers. People asked can come up with unique answers that the person who came up with the survey may not have thought of. This allows for more possibilities of finding a good solution.
Disadvantages
The disadvantage of this system is that you may get answers that would not work. For instance, if you wanted to incentivize students to each healthier, an open ended answer might suggest giving a monetary reward for those who eat healthy. This is not feasible in a school, so therefore getting this as an answer is a waste of time.
Now let's tack the close question.
Benefits
The key benefit of the closed question is that is allows you to settle between options that the surveyor has set on. Likely, if there are 3 answers, we know that these are the only ways that we can solve the problem with the resources that we have.
Disadvantages
If you ask a question this way, there is not chance that you'll be given alternative methods to solving the problem. Someone being surveyed may have a great idea on how to solve the problem that is not listed. Using this method will not garner you the response to inform you of this way.
Open questions in surveys capture rich data and offer depth of knowledge but are harder to analyze. Closed questions allow for easy analysis and comparison but tend to limit the respondents' answers.
Explanation:Open and closed questions in surveys convey their individual advantages and disadvantages. Open questions offer the advantage of capturing rich, detailed data that can provide profound insights. For instance, in response to 'What can be done to get students to eat healthier foods?' a variety of unforeseen ideas may surface, providing a depth of knowledge. However, open questions are harder to analyze due to the broad variety of responses, and they may confuse or overwhelm respondents with their open-ended nature.
On the other hand, closed questions, such as 'How would you get students to eat healthier foods?' with provided options, have the advantage of readily quantifiable answers which allows for easy comparison and analysis. These questions also guide respondents in formulating their answers. However, they may limit respondents' answers and may not provide the full perspective or nuanced responses that open questions can elicit.
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Find the polynomial M if 2x^2− 1/3 ax+by−M=0.
AND
Find the polynomial B if 3x^2y− 1/3 xy^3+cy+B=0.
Pls Help ASAP! Thanks
Answers
23/8 for the most part I think
What are the advantages and disadvantages of technological versus old-school methods for determining position at sea.
Answers
Answer:
A mere 15 years back, navigators would have scoffed at the idea of Paperless Navigation on big ocean going ships. After all, since centuries, navigational paper charts had been the heart and soul of ship navigation. Imagining that a day would come where we’d no longer have them onboard was nothing short of blasphemy.
Step-by-step explanation:
The advantages of technology versus old-school methods for determining the position at sea include ease of navigation and safety.
What is the ECDIS?The ECDIS is the abbreviated form Electronic Chart Display and Information System. It is a modern technology used for navigation through waters.
The advantages and disadvantages of technology versus old-school methods for determining the position at sea are as follows:With ECDIS as the dominant source of sailing, the Navigating Officer can plan and summarise the transition much more speedily than on Paper Charts.
This is the background that will sound an alarm if the ship is inside the limit stated.
This scene displays the non-traversable field and marks the confine save that the container can harmlessly cross.
Therefore, we have found that the advantages of technology versus old-school methods for determining the position at sea include ease of navigation and safety.
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Ivan has 15 yards of green felt 12 yards of blue felt to make 3 quilts, how many yards does he use for each quilt
Answers
Answer:
27
Step-by-step explanation:
I NEED HELP WITH A QUICK QUESTION! 30 POINTS!
For the circle with equation (x - 2)² + (y+3)² = 9 , answer each question.
(a) What are the coordinates of the center?
(b) What are the radius and diameter of the circle?
(c) Graph the circle.
Answers
Answer:
The center is (2 ,-3)
The radius is 3
The diameter is twice the radius = 2(3) = 6
Step-by-step explanation:
The equation of a circle is given by
(x-h)^2 + (y-k)^2 =r^2
where (h,k) is the center and r is the radius
(x - 2)² + (y+3)² = 9
(x - 2)² + (y- -3)² = 3^2
The center is (2 ,-3)
The radius is 3
The diameter is twice the radius = 2(3) = 6
The center of the circle is at (2, -3), the radius is 3 units, and the diameter is 6 units. To graph the circle, plot the center point (2, -3) and draw a circle with a radius of 3 units around it.
Explanation:(a) The coordinates of the center of the circle are (2, -3). The equation of the circle is in the form (x - h)² + (y - k)² = r², where (h, k) are the coordinates of the center and r is the radius. In this case, (h, k) = (2, -3).
(b) The radius of the circle is 3 units. The diameter is twice the radius, so the diameter of the circle is 6 units.
(c) To graph the circle, plot the center point (2, -3) and draw a circle with a radius of 3 units around it.
In the United States, it is possible for someone to give a gift up to how much money per year to another person without that money being taxed?
Answers
Answer:
I believe the correct answer is $10,000. I'm not positive, though.
Answer:
For years 2018 and 2019 the exclusion amount is $15000.
Step-by-step explanation:
In the United States, it is possible that you can give any individual a gift up to $15000 as per year 2018 and 2019, without having to file a gift tax return to report that gift.
Hence, for the years 2018 and 2019, the annual exclusion amount is $15,000.
Please help me with this
Answers
Center pole = SQRT(10^2 - 4.8^2)
Center pole = SQRT(100-23.04)
Center pole = SQRT(76.96)
Center pole = 8.8 feet
The National Football League (NFL) polls fans to develop a rating for each football game. Each game is rated on a scale from 0 (forgettable) to 100 (memorable). The fan ratings for a random sample of 12 games follow. 57 61 87 74 72 73 19 56 81 79 83 75 a. Develop a point estimate of mean fan rating for the population of NFL games (to 2 decimals). b. Develop a point estimate of the standard deviation for the population of NFL games (to 4 decimals).
Answers
The point estimates for the mean and standard deviation of the given data is respectively; 68 and 17.6
What is point Estimate?A) To find the point estimate of the mean, we add all up all the data and divide by the number of values.
Thus;
∑x = 57 + 61 + 86 + 87 + 72 + 73 + 19 + 56 + 81 + 79 + 83 + 75 = 816
n = 12 numbers
Thus;
mean = ∑x/n = 816/12
Mean = 68
B) To find the estimate of the standard deviation, we would get it from the formula;
s = √[(n*(∑x²) - (∑x)²)/n(n - 1)]
∑x² = 572 + 612 + 862 + ... + 742 = 59,010
s = √[ (12*(59,010) - (816)²)/(12)(11)]
s = 17.6
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Which is the equation in the slope-intercept form for the line that passed through (2, 8) And it is perpendicular to 4x + 2y= 6?
Answers
Answer: [tex]y=\frac{1}{2}x+7[/tex]
Step-by-step explanation:
The slope-intercept form of the equation of the line is the following:
[tex]y=mx+b[/tex]
Where m is the slope and b the y-intercept.
By definition, when two lines are perpendicular, their slopes are opposite reciprocals.
Then, to find the slope of the equation of the line given, you can solve for y:
[tex]4x+2y=6\\2y=-4x+6\\\\y=-2x+3[/tex]
As you can see, the slope of this line is -2.Then, the slope of the line that is perpendicular to it, must be:
[tex]m=\frac{1}{2}[/tex]
Substitute the slope and the point given, into the equation and solve for b:
[tex]8=\frac{1}{2}(2)+b\\8=1+b\\b=7[/tex]
Therefore, the equation of this line is:
[tex]y=\frac{1}{2}x+7[/tex]
Write an expression to represent: Four more than the product of three and a number x
Answers
Answer: 4+3x
Step-by-step explanation:
Find the measure of the line segment indicated.
Assume that lines which appear tangent are tangent.
A) 10
B) 6
C) 14
D) 7
Answers
Answer:
Option A. 10
Step-by-step explanation:
we know that
Applying the Intersecting Secants Theorem
[tex]QS*RS=CS*TS[/tex]
substitute the values
[tex](11x-1+8)*(8)=(9+7)*(9)[/tex]
solve for x
[tex](11x+7)*(8)=(16)*(9)[/tex]
[tex]88x+56=144[/tex]
[tex]88x=144-56[/tex]
[tex]88x=88[/tex]
[tex]x=1[/tex]
Find the measure of QR
[tex]QR=11x-1=11(1)-1=10[/tex]
The question also the answer options are below in the attachment. Please and thanks in advance! :)
Answers
Answer:
35 7/8.
Step-by-step explanation:
The total length of the wood before any cutting was done = 4 * the mean
= 4* 36 5/8 = 4* 293/8
= 146 1/2 feet.
So the length of the fourth piece = 146 1/2 - (36 3/4 + 36 3/8 + 37 1/2)
= 146 1/2 - 110 5/8
= 36 + 1/2 - 5/8
= 35 7/8 answer.
Turn the mean into an improper fraction.
36 5/8 = 293/8
Multiply the mean by four.
293/8 * 4/1 = 1172/8 or 146 1/2
Add all the sides together.
36 3/4 + 36 + 3/8 + 37 1/2 = 110 5/8 or 885/8
Subtract.
1172/8 - 885/8 = 287/8 or 35 7/8
Best of Luck!
Susan Sound predicts that students will learn most effectively with a constant background sound, as opposed to an unpredictable sound or no sound at all. She randomly divides twenty-four students into three groups of eight. All students study a passage of text for 30 minutes. Those in group 1 study with background sound at a constant volume in the background. Those in group 2 study with noise that changes volume periodically. Those in group 3 study with no sound at all. After studying, all students take a 10-point multiple choice test over the material. Their scores follow: Table Constant sound Random Sound No Sound 7 5 2 4 5 4 6 3 7 8 4 1 6 4 2 6 7 1 2 2 5 9 2 5 1. State the type of statistical test that you will use to conduct your hypothesis test.
Answers
Answer:
An ANOVA test
Step-by-step explanation:
You will use the ANOVA test, which is a test that compares the means of more than 2 samples. Since the teacher used 3 test groups, she would have to use this test if she wanted to do a hypothesis test to determine if the means are equal.
*This test only tells us if the means are equal, it won't say which is greater than the other. You would have to do 3 individual hypothesis tests comparing 2 means at a time in order to determine that.
An ANOVA (Analysis of Variance) is the appropriate statistical test to use when comparing the test scores of students studying under different sound conditions (constant sound, random sound, and no sound).
The type of statistical test to use for conducting a hypothesis test in this scenario would likely be an ANOVA (Analysis of Variance), which is specifically designed to compare the means of three or more groups. Since we have three independent groups of students (constant sound, random sound, and no sound) and we want to test if there is a significant difference in the test scores that could be attributed to the study condition, ANOVA is the appropriate choice of test.
The information provided about the music and sound conditions suggests that the volume of any background music should be low enough to not disrupt conversation and that it may serve as an auditory memory cue if used consistently. Additionally, the studies mentioned indicate various effects of background music on task performance among students, be it learning a passage, recalling information, or completing reading comprehension tasks. These factors would be considered when interpreting the results of the ANOVA.
If P(A)=0.35, then the probability of the complement of A is
0.55
-0.35
0.35
0.65
Answers
Answer:
P(A') = 0.65
Step-by-step explanation:
We are given that the probability P(A) = 0.35 and we are to determine the probability of the complement of A.
According to the Complement Rule of any probability, the sum of the probabilities of an event and its complement must be equal to 1.
So for for the event A,
P(A) + P(A') = 1
0.35 + P(A') = 1
P(A') = 1 - 0.35
P(A') = 0.65
The probability of the complement of A is 0.65
How to determine the probability of the complement of AThe probability of A is given as:
P(A) = 0.35
To calculate the probability of the complement of A, we make use of the following complement formula
P'(A) = 1 - P(A)
So, we have:
P'(A) = 1 - 0.35
Evaluate
P'(A) = 0.65
Hence, the probability of the complement of A is 0.65
Read more about probabiilty at:
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