Question 2 (2 points)Determine the following of the function y = 0.7log3(x).• DomainRange• X-intercept• Y-interceptAsymptote..
Answers
Recall that
\(\log _ax\)is defined for all positive real numbers, therefore:
\(\text{Dom}(0.7\log _3(x))=(0,\infty)\text{.}\)Also, since the range of log_3(x) is all real numbers, then:
\(Ran(0.7\log _3(x))=(-\infty,\infty).\)Now, to find the x-intercept, we set y(x)=0:
\(0.7\log _3(x)=0.\)Dividing the above equation by 0.7 we get:
\(\begin{gathered} \frac{0.7}{0.7}\log _3(x)=\frac{0}{0.7}, \\ \log _3(x)=0. \end{gathered}\)Solving the above equation for x we get:
\(\begin{gathered} 3^{\log _3(x)}=3^0, \\ x=1. \end{gathered}\)Therefore, the x-intercept has coordinates (1,0).
Since the function is only defined at (0,∞), there is no y-intercept.
Finally, the function has an asymptote at x=0.
Answer:
Domain:
\((0,\infty).\)Range:
\((-\infty,\infty).\)X-intercept:
\((1,0)\text{.}\)Y-intercept: There is no y-intercept.
Asymptote:
\(x=0.\)Related Questions
A barge of mass 4 tonnes is pulled in a straight line by two tugs with an acceleration of 0.6 ms ². The tension in one tow rope is 1800 N and the tension in the other is 1650 N. Given that the cables make angles of 20° and xº respectively, with the direction of the motion, find the value of x and the resistance to motion of the barge.
Answers
Answer:
Step-by-step explanation:
To solve this problem, we can start by analyzing the forces acting on the barge. There are two forces involved: the tension in the tow ropes and the resistance to motion.
1. Tension in the first tow rope:
The tension in the first tow rope is given as 1800 N, and it makes an angle of 20° with the direction of motion. Let's call this angle θ1 = 20°.
2. Tension in the second tow rope:
The tension in the second tow rope is given as 1650 N, and it makes an angle of xº with the direction of motion. Let's call this angle θ2 = xº.
Now, let's analyze the forces along the direction of motion:
1. Tension force along the first tow rope:
The component of the tension force along the direction of motion is T1cos(θ1).
2. Tension force along the second tow rope:
The component of the tension force along the direction of motion is T2cos(θ2).
The net force along the direction of motion is equal to the mass of the barge multiplied by its acceleration:
Net force = mass × acceleration
Since the acceleration is given as 0.6 m/s² and the mass is 4 tonnes (which is equivalent to 4000 kg), we have:
Net force = 4000 kg × 0.6 m/s²
Net force = 2400 N
Now, we can equate the net force to the sum of the tension forces along the direction of motion:
T1cos(θ1) + T2cos(θ2) = 2400 N
Substituting the given values:
1800cos(20°) + 1650cos(xº) = 2400
Simplifying the equation, we can solve for x:
1800cos(20°) + 1650cos(xº) = 2400
cos(xº) = (2400 - 1800cos(20°)) / 1650
xº = arccos((2400 - 1800cos(20°)) / 1650)
Using a calculator, we can find the value of xº.
To find the resistance to motion of the barge, we need to find the total force opposing the motion, which is the sum of the tension forces perpendicular to the direction of motion:
1. Tension force perpendicular to the first tow rope:
The component of the tension force perpendicular to the direction of motion is T1sin(θ1).
2. Tension force perpendicular to the second tow rope:
The component of the tension force perpendicular to the direction of motion is T2sin(θ2).
The resistance to motion is equal to the sum of these perpendicular tension forces:
Resistance = T1sin(θ1) + T2sin(θ2)
Substituting the given values, we can calculate the resistance to motion.
Sofia's audio player has 15,000 songs. the play time for the songs is skewed to the right, with a mean of 255 seconds and a standard deviation of 30 seconds. part a: can you accurately calculate the probability that the mean play time is more than 260 seconds for an srs of 15 songs? explain. (4 points) part b: if you take a random sample of 40 songs instead of 15, explain how the central limit theorem allows you to find the probability that the mean play time is more than 260 seconds. calculate this probability and show your work. (6 points)
Answers
Using the normal distribution and the central limit theorem, it is found that:
a) Since the distribution is skewed and the sample size is less than 30, the probability cannot be calculated.
b) There is a 0.1469 = 14.69% probability that the mean play time is more than 260 seconds.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation \(s = \frac{\sigma}{\sqrt{n}}\), as long as the underlying distribution is normal and the sample size is at least 30.The mean and the standard deviation are given by, respectively:
\(\mu = 255, \sigma = 30\)
In item a, according to the Central Limit Theorem, since the distribution is skewed and the sample size is less than 30, the probability cannot be calculated.
For item b, we have that n = 40 > 15, hence the standard error is given by:
\(s = \frac{30}{\sqrt{40}} = 4.74\)
The probability is one subtracted by the p-value of Z when X = 260, hence:
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{260 - 255}{4.74}\)
Z = 1.05
Z = 1.05 has a p-value of 0.8531.
1 - 0.8531 = 0.1469.
There is a 0.1469 = 14.69% probability that the mean play time is more than 260 seconds.
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An isosceles triangle has an angle that measures 134°. Which other angles could be in that isosceles triangle? Choose all that apply. 23 20 72 81
Answers
Answer:
23
Step-by-step explanation:
one angle = 134
Other two angles are the base angles which are same.
x + x + 134 = 180 {Angle sum property}
2x + 134 = 180
2x = 180 - 134
2x = 46
x = 46/2
x = 23
Other two angles are 23 , 23
another EASY question for y’all mathy people, easy points! Question in photo.
Answers
Answer:
the answer is c
Step-by-step explanation:
uh can someone help
Answers
Answer:
65
Step-by-step explanation:
<S = <t
x + 50 = 3x + 20
2x = 30, x = 15
. <t = <v
3x + 20 = 45 + 20 = 65
Answer:
b. 65 degrees.
Step-by-step explanation:
m < RST = m < STU (alternate angles), so
x + 50 = 3x + 20
50 - 20 = 3x - x
2x = 30
x = 15.
Now m < RVT = m < RST ( opposite sides of a parallelogram are equal).
So m < RVT = x + 50 = 15 + 50 = 65.
take all coins that are still on tails and keep flipping them until they land on heads. what is the expected number of total flips until all coins are on heads?
Answers
The probability that all coins show heads up is 1/16.
How to calculate the probabilityThe probability of one is 1/2: Half of the time (on average, as all numbers in this answer will be) it will show heads.
Of those times it shows heads, only half of the time will the second coin also show heads. We're down to a quarter of the time now.
Of those times the second coin shows heads, only half of the time will the third coin also show heads. This is 1/8.
And, of the times the third coin also shows heads, only half of the time will the fourth coin also show heads. Half of 1/8 is 1/16.
You can simplify this by calculating (1/2)^4.
= 1/16
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Take all coins that are still on tails and keep flipping them until they land on heads. We flip 4 coins simultaneously. What is the probability that all coins show heads up?
all the sides of a triangle are integers, and the perimeter is 12. how many different possible triangles are there
Answers
3 such difference triangle are possible when the perimeter of a triangle 12cm. if the lengths of the three sides are all integers (in cm).
Given that,
The perimeter of a triangle 12cm.if the lengths of the three sides are all integers (in cm).
We have to find how many such difference triangle are possible.
We know that,
Perimeter of the triangle is 12cm.
p=12
a+b+c=12
a+b≥c
b+c≥a
So,
a+b+c≥2c
12≥2c
c≤6
So,
a≤6,b≤6,c≤6
We get,
a=6,b=3,c=3
a=5,b=4,c=3
a=4,b=4,c=4
Therefore, 3 such difference triangle are possible when the perimeter of a triangle 12cm. if the lengths of the three sides are all integers (in cm).
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Please help!!!
D is f(x)=500(x+30000)
Answers
Answer:
The correct answer is A
Step-by-step explanation:
The books sold are 30,000, so that is our total sale for January. His sales are decreasing by an average of 500 books per month, which means he is losing sales so it is a negative value, and we multiply that by x (number of months) since the question has not stated the number of months. Therefore, the equation would be f(x) = 30,000 - 500x
Hope this is of help!
hey i need help with a math question thank you :)
Answers
Answer:
y = 60x + 20
y = 65x
0 = 5x - 20
5x = 20
x = 4 ---> 4 hours
Substitute x as 4:
y = 65 x 4
y = 260 ---> 260 miles
So the answer is A
The ratio of c:d is 1:3. The ratio of d:e is 2:3. What is the ratio of c:d:e?
Answers
The ratio of c:d:e is 1:3:2.
How The answer was obtainedTo find the ratio, you can multiply the first ratio by the second ratio: 1 * 2 = 2 and 3 * 3 = 9, so the ratio becomes 2:9:6, which can be simplified to 1:3:2.
A ratio is a comparison between two values. To calculate a ratio, divide the first value by the second value. For example, if you have three apples and seven bananas, the ratio of apples to bananas would be 3/7.
You can also simplify a ratio by dividing both values by their greatest common divisor. For example, if the ratio of apples to bananas is 6/14, you could simplify it to 3/7.
It's also possible to express a ratio as a fraction, decimal, or percentage. To convert a ratio to a fraction, simply divide the two values. To convert a ratio to a decimal, divide the numerator by the denominator. To convert a ratio to a percentage, multiply the ratio by 100.
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Five times the sum of a number n and seven
Hint- you need parenthesis
Answers
The equation of the problem is \(5(n+7)\)
The sentence is asking 5 times the sum of n+7, so you are multiplying (n+7) by 5.
christians money from his job increased from 12 hour to 21 hour what is the percent increase
Answers
Christian's hourly pay has increased by 75%.
To find the percent increase in Christian's hourly pay, we'll follow these steps:
Determine the difference between the new hourly pay and the old hourly pay.
Divide the difference by the old hourly pay.
Multiply the result by 100 to find the percent increase.
Difference between new and old hourly pay
21 (new hourly pay) - 12 (old hourly pay) = 9
Divide the difference by the old hourly pay
9 (difference) / 12 (old hourly pay) = 0.75
y - x = 21 - 12 = 9
So his salary have elevated by using $9 per hour. To categorical this extend as a proportion of his historic earnings, we use the following formula:
Percent extend = (difference / historical amount) x 100
In this case, the ancient quantity is $12 per hour, so:
The percent expand = (9 / 12) x a hundred = 75%
Multiply the result by 100 to find the percent increase
0.75 × 100 = 75%
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1. Express 0 .35 in the form of p/q
Answers
7/20 is your answer
0.35=7/20
The protection afforded to inventors for new inventions is restricted to a given length of time; once this time has elapsed the invention is said to be:
Answers
Once the protection period for a new invention expires, the invention is said to be in the public domain.
The invention without permission from the original inventor, and the inventor cannot prevent others from doing so.
In other words, the invention becomes freely available for anyone to use or benefit from, without any legal restrictions.
The length of time for which an invention is protected depends on the type of intellectual property protection granted, such as patents or trademarks, and the laws of the country or region where the protection is sought.
The creator cannot restrict others from using, manufacturing, or selling the innovation without the consent of the original inventor.
In other words, there are no longer any constraints on who can utilise or benefit from the idea.
The kind of intellectual property protection granted, such as patents or trademarks, as well as the legal framework of the nation or region where the protection is sought, determine the duration of an invention's protection.
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Two students in Ms. Romean's class are working on
finding the mean for the following set of numbers: 2,
12, 16, 4, 18, 24, 32. Susan states that the answer is
15.4 when rounded to the nearest tenth. She added all
of the numbers and divided by 7. Sam disagrees and
thinks the answer is 54. She added all of the numbers
and divided by 2. Which student is correct? How do
you know? Explain your thinking!
Answers
Answer:
susan is correct
Step-by-step explanation:
2+12+4+18+24+32=108
108 divided by 7=54
my reasoning is that the formula is add all and divide by how many numbers you added
Brainliest goes to whoever answers correctly try to show work ONLY if you can
Answers
Answer: COMPANY A HAS THE LOWEST COST PER SQUARE FOOT
Company A Chart below
1200 $2700
1400 $3150
1600 $3600
1800 $4050
2000 $4500
Company B
Sells it for $2.75 per square foot
A sofa is on sale for $816, which is 15% less than the regular price. What is the regular price?
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Answer:
100 - 15 = 85
816 = 85%
now work out 1%.
85/85 = 1% do the same to the other side
816/85 = 9.6
9.6 = 1%
now find 100%
1 X 100= 100%
9.6 X 100=960
regular price $960
PLEASE I NEED THE AWNSER IN 2 MIN
Match the situation with the correct ratio. Don't forget that you can write a ratio three ways! Also remember the different ways to find equivalent ratios (simplify, rename, table, graph, tape diagram). Make sure you pay attention to the order!! Only enter CAPITAL letters with no spaces or numbers. (Your answer should look something like this WTYUSR)
*
Answers
1. 6:15 has a ratio of 2:5
2. 10:40 has a ratio of 1:4
3. 6:28 has a ratio of 3:14 but it would be 12:56 based on the answer choices
4. 15:25 has a ratio of 3:5 but it would be 15:25 based on the answer choices
9) Fred is buying roses. The roses cost $1.68 each. How many roses did Fred buy if the bouquet cost
$25.20 in all?
Answers
Answer:
15
Step-by-step explanation:
1.68 divided 25.20 = 15
Annika spends $15.95, Tamara $18.46 and susan $22.80. they are dividing up the expenses equally. how much money should annika give Susan if there equllying the expenses equally
Answers
The amount Annika should give to Susan is $3.12
What is Algebra?
One of the many branches of mathematics is algebra. Algebra is a common thread that runs through nearly all of mathematics. It involves the study of mathematical symbols and the rules for using them in formulas.
Given,
The amount of money Annika spend = $15.95
The amount of money Tamara spend = $18.46
The amount of money Susan spend = $22.80
The total amount of money:
$15.95 + $18.46 + $22.80 = $57.21.
The average money spent :
= $57.21/3
= $19.07 , for each girl.
Thus Annika should give Susan
= $19.07 - $15.95
= $3.12
Hence, Annika should give $3.12 to Susan
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GEOMETRY GEOMETRY PLEASE HELP !!!!
The points N(3,1), O(9,1), and P(3,6) form a triangle. Plot the points then click the "Graph Triangle" button. Then find the perimeter of the triangle. Round your answer to the nearest tenth if necessary.
Answers
The perimeter of the triangle is approximately 18.2 units.
To plot the points N(3,1), O(9,1), and P(3,6), we will first draw the x and y-axes on the coordinate plane.
The x-axis is horizontal, and the y-axis is vertical.
The point N is located at x = 3 and y = 1, which means it is three units to the right of the y-axis and one unit above the x-axis.
The point O is located at x = 9 and y = 1, which means it is nine units to the right of the y-axis and one unit above the x-axis.
The point P is located at x = 3 and y = 6, which means it is three units to the right of the y-axis and six units above the x-axis. We can now plot these points on the coordinate plane.
To find the perimeter of the triangle, we need to find the distance between each pair of points and then add these distances together. Let's start with the distance between N and O. We can use the distance formula to find this distance:
d(NO) = √[(9-3)² + (1-1)²] = 6
The distance between N and O is 6 units. Now let's find the distance between O and P:
d(OP) = √[(3-9)² + (6-1)²] = √58
The distance between O and P is √58 units. Finally, let's find the distance between P and N:
d(PN) = √[(3-3)² + (1-6)²] = 5
The distance between P and N is 5 units. Now we can add these distances together to find the perimeter of the triangle:
Perimeter = d(NO) + d(OP) + d(PN)
Perimeter = 6 + √58 + 5
Perimeter ≈ 18.2 (rounded to the nearest tenth)
Therefore, the perimeter of the triangle is approximately 18.2 units.
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Does 2/3x+2/3+1/5=2/3x have a solution?
Answers
Answer:
no
Step-by-step explanation:
the town's population has increased for 80,000 to 90,000 in the past 10 years. what was the present increase.
Answers
The percentage increase in the population of the town is 12%.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Increase in population = 90,000 - 80,000 = 10,000
Percentage increase = 10,000/80,000 * 100 = 100/8 = 12.5%
Hence the percentage increase in the population of the town is 12%.
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class 9
if (x+1) is a factor of x³+2x²-5x-6, then factorise it.
please give me the answer fast...
Answers
9514 1404 393
Answer:
(x +3)(x +1)(x -2)
Step-by-step explanation:
A graphing calculator is a good tool for finding factors fast. Each zero (p) gives rise to a factor (x -p).
The graph shows zeros at -3, -1, and 2, so your factorization is ...
(x +3)(x +1)(x -2)
find the value of x
Answers
Answer:
117
Step-by-step explanation:
Sum of all angles of pentagon = 540
x + 86 + 140 + 138 + 59 = 540
x + 423 = 540
x = 540 - 423
x = 117
Answer:
x= 117°
Step-by-step explanation:
In a Pentagon the interior angles are equal to 540° so, first we take the values we have which is:
140°+138°+59°+86°= 423° in total
To find x all you do is take 423 away from 540
540 - 423 = 117°
x= 117°
Hope it helped, ask any questions if you are unsure:)
help with these two pages
Answers
A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral. The square's angles are at a straight angle or 90 degrees.
Explain about the square?Area of a square is measured in square units. The area of a square equals d22 square units when the diagonal, d, is known. For instance, a square with sides that are each 8 feet long is 8 8 or 64 square feet in area (ft2)
A square is a common polygon with four equal sides and angles that are each 90 degrees in length.
A square is a four-sided polygon with sides that are all the same length and angles that are all exactly 90 degrees. The square's shape ensures that both parts are symmetrical if it is divided down the middle by a plane. Then, each half of the square seems to be a rectangle with diagonal sides.
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easy one - giving brainly! show work!
not sure if the answer is 630 or 360???
Answers
Answer:
630
Step-by-step explanation:
There are 75 kids at camp. After 21 kids go swimming, a counselor separated the remaining kids into 6 teams so that each team had k kids. In the tape diagram, k represents the number of kids that the counselor put into each of the 6 teams. What is the value of k?
Answers
6 * k = 54
Now, divide both sides by 6:
k = 54 / 6
k = 9
So, the value of k is 9. The counselor put 9 kids into each of the 6 teams.
A linear function has an x-intercept of 8 and a y-intercept of 4 . which of these is an equation of the linear function?
Answers
The linear function is y = (-1/2)x + 4.
What is a linear function?
A linear function whose graph is a straight line and which is represented by an equation of the form y = ax + b where a and b are constants, a does not equal zero, and x is any real number.
Here, we have
Given,
A linear function has an x-intercept of 8 and a y-intercept of 4.
So, The two points on the line are (8, 0) and (0, 4).
Now, slope(m) = (4 - 0)/(0 - 8).
slope(m) = -4/8.
slope(m) = -1/2.
As it has a y-intercept of 4 it is the value of b, In y = mx + b.
Hence, the linear function is y = (-1/2)x + 4.
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i need the answer. (will give brainliest)
Answers
Answer:
30 degrees
Step-by-step explanation:
add the two together then subtract 180
Answer:
you have to the two together then subtract 180
Step-by-step explanation:
so your answer is 30