Final answer:
The integral of y/((y^2)-1) is (1/2) ln|y^2 - 1| + C.
Explanation:
To evaluate the integral of y/((y^2)-1), we can perform a substitution by letting u = y^2 - 1. Then, du = 2y dy, and the integral becomes:
∫ y/((y^2)-1) dy = (1/2) ∫ 1/u du = (1/2) ln|u| + C
Substituting back u = y^2 - 1, the final answer is (1/2) ln|y^2 - 1| + C.
A line and a plane are considered parallel if they have no points in common. True or False?
If 12 is replaced with 3 in the following set, what will happen to the value of the range?
28, 45, 12, 34, 36, 45, 19, 20
It will increase.
It will decrease.
It will stay the same.
Your correct answer is A: it will increase.
Hope this helps. :)
Find a ⋅ b. a = 4i - 4j, b = 4i + 5j
For this case we have the following vectors:
[tex]a = 4i - 4j\\b = 4i + 5j[/tex]
We must find the product point of both vectors.
To do this, we multiply component by component and add the results.
We have then:
[tex]a.b = (4) (4) + (-4) (5)\\a.b = 16 -20\\a.b = -4[/tex]
Answer:
The point product of both vectors is given by:
[tex]a.b = -4[/tex]
Ivan was given two data sets, one without an outlier and one with an outlier.
Data without an outlier: 108, 113, 105, 118, 124, 121, 109
Data with an outlier: 108, 113, 105, 118, 124, 121, 109, 61
How is the median affected by the outlier?
Answer:
Median is decreased by the outlier or Outlier made median lower.
Step-by-step explanation:
First we calculate median of the data without an outlier:
Data in Ascending or increasing order ,
105 , 108 , 109 , 113 , 118 , 121 , 124
Now there are 7 terms so
Median = [tex]\frac{7+1}{2}^{th}\:term[/tex] = 4th term = 113
Now we find median of the data with outlier:
Data in ascending or descending order,
61 , 105 , 108 , 109 , 113 , 118 , 121 , 124
here no of terms are 8.
So, Median = [tex]\frac{(\frac{8}{2})^{th}+(\frac{8}{2}+1)^{th}}{2}[/tex]
= [tex]\frac{4^{th}+5^{th}}{2}=\frac{109+113}{2}[/tex]
= 111
So, Median is decreased by the outlier or Outlier made median lower.
How long will it take for a sum of money, invested at 5% compounded annually, to double in value?
To determine the time needed for an investment to double at a 5% compounded annual rate, apply the Rule of 72 by dividing 72 by the interest rate, resulting in approximately 14.4 years.
The question pertains to the time it takes for an investment to double in value with compound interest. To calculate this, we can use the Rule of 72. This rule states that you can approximate the number of years it'll take for an investment to double by dividing 72 by the annual interest rate. In this case, with a 5% interest rate, it would be calculated as 72 \/ 5, which equals approximately 14.4 years.
Here's a step-by-step explanation:
Apply the Rule of 72 by dividing 72 by the interest rate: 72 ÷ 5 = 14.4.
Therefore, it will take roughly 14.4 years for the sum of money to double at an annual compounded interest rate of 5%.
This is a quick and efficient way to estimate the power of compound interest and make informed investment decisions.
A repairman charged $93.06. the price included 2 hours of labor and a $40 serive charge how much does the repaiman charge per hour for labor?
Solve each equation f over 28=24
Solve the equation x2 = 10.
Answer:
[tex]\large\boxed{x=-\sqrt{10}\ or\ x=\sqrt{10}}[/tex]
Step-by-step explanation:
[tex]x^2=10\iff x=\pm\sqrt{10}[/tex]
The solution of the equation is x = ±3. 162.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Parts of an Equation
There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators.
An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables.
Given:
x² = 10
Now to solve the above equation we have to take the square root on both side, we get
√x² = √10
x= ±√10
x= ±3. 162 ( because root provides two values one is positive and other is negative)
Hence, the value of x is ±3. 162.
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What is the diameter of a circle that has an area of 452.16 mm 2? 144 mm 12 mm 24 mm 6 mm
Answer:
the diameter is 24
Step-by-step explanation:
Divide 3x^2 -2x^2 -61x -20 by x -5
the number 0.4 can be written as 4/10 so it is a rational number
Answer: yes it's correct
Step-by-step explanation: yes it's correct
how many prime numbers are there between 0 and 25
Find the probability when a couple has 6 children at at least one of them is a boy
The probability when a couple has 6 children at at least one of them is a boy is 63/64
First step
Probability of all 6 girls=(1/2)^6
Probability of all 6 girls = 1/64
Second step is to determine the probability at least one of them is a boy
Let at least one boy means not all girls
Hence:
P(all girls)+P(not all girls)=1
P(at least 1 boy)=1-P(all girls)
P(at least 1 boy)=1-1/64
P(at least 1 boy)=63/64
Inconclusion The probability when a couple has 6 children at at least one of them is a boy is 63/64
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Can anyone please help me I will give you 13 points and make your answer the brainliest.Please help.
The true statements are ...
2. All squares are rectangles.
3. Not all parallelograms are rectangles.
_____
The attached diagram shows the relationships between various quadrilataral types. The line connecting a lower box to a higher box means "all of the lower box is a higher box." For example, all square are rectangles, and all rectangles are parallelograms.
However, it is typical for a higher box to have several different lower boxes. That is "a higher box may be any of the list of lower boxes or none of them" For example, a parallelogram may be a rhombus or a rectangle or neither.
Camelle manages her soccer team. She needs to order 4 practice jerseys for each player. There are y players. How many total practice jerseys does she need to order?
Answer:
The required number of total practice jerseys does she need to order is '4y'.
Step-by-step explanation:
Given : Camelle manages her soccer team. She needs to order 4 practice jerseys for each player. There are y players.
To find : How many total practice jerseys does she need to order?
Solution :
Let the total practice jerseys does she need to order be 'x'.
According to question,
She needs to order 4 practice jerseys for each player.
Number of players are y.
So, Total jerseys she needs is
[tex]x=4\times y[/tex]
[tex]x=4y[/tex]
Therefore, The required number of total practice jerseys does she need to order is '4y'.
If male and female college students work an average of 15 hours per week during the school year and the standard deviation is 5.4 for male students and 2.3 for female students, what may we conclude?
Answer: the male sample is more spread than the female sample
Step-by-step explanation:
The mean is the same for both genres, but the standard deviation form males is bigger than the one for females.
This means that the data of the male students is more spread than the female data (so there are more male students that study more hours, but there also are more male students that study less hours).
So the general conclusion is that the male sample is more spread than the female sample
Of the members of a student choir, 60% are boys. If there are 21 boys in the choir, how many members does the choir have in total?
Suppose there are x number of members in all.
Now we are given that 60% of these are boys.
So number of members who are boys = 0.6x
We are also given that there are 21 boys in the choir.
So making an equation ,
[tex] 0.6x =21 [/tex]
dividing both sides by 0.6,
x= 35
So there are total 35 members in the choir.
Kat has 19 coins, all quarters and dimes, that are worth a total of $4. The system of equations that can be used to find the number of quarters, q, and the number of dimes, d, she has is shown.
q + d = 19
0.25q + 0.1d = 4
How many quarters does she have?
4
5
14
15
To find the number of quarters, solve the system of equations. Kat has 14 quarters.
Explanation:To find the number of quarters Kat has, we can solve the system of equations given. The first equation states that the number of quarters (q) and the number of dimes (d) add up to 19.
The second equation represents the total value of the coins, where each quarter is worth $0.25 and each dime is worth $0.10.
By solving this system of equations, we can determine the value of q, which represents the number of quarters.
Using the first equation, we can solve for d by subtracting q from both sides: d = 19 - q.
Substituting this value of d into the second equation, we get: 0.25q + 0.1(19 - q) = 4.
Solving this equation, we find q = 14. Therefore, Kat has 14 quarters.
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The ice rink sold 95 tickets for the afternoon skating session, for a total of $828. General admission tickets cost $10 each and youth tickets cost $8 each. How many general admission tickets and how many youth tickets were sold?
By solving the system of linear equations formed from the scenario given, we find that the ice rink sold 34 general admission tickets and 61 youth tickets during the afternoon skating session.
Explanation:This problem is a simple linear algebra problem. We can represent the total number of tickets with the variable x (for the general admission tickets) and y (for the youth tickets). The scenario provides us with two equations:
The total number of tickets sold is 95, so x + y = 95.The total amount of money collected is $828, so 10x + 8y = 828.To solve the system of equations, we can multiply the first equation by 8 to have both equations involving '8y', which gives us 8x + 8y = 760.
Subtracting the first modified equation from the second gives: 2x = 68. Therefore, solving for x gives us x = 34. That means, there were 34 general admission tickets sold.
Substitute x=34 into x + y = 95, we get 34 + y = 95, which simplifies to, y = 61. That means, there were 61 youth tickets sold.
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what is the measure of C?
Express the complex number in trigonometric form. 3
The complex number 3, in trig form, would be 3 cos 0 degrees. This is a ray from the center, right, along the x-axis, for a distance of 3 units.
Answer:
Step-by-step explanation:
3(cos(0)+isin(0))
A box contains 3 cherry frozen treats and 2 grape frozen treats. Maggie takes a treat from the box without looking, gives it to her brother, and then selects another treat. What is the probability that her brother gets a grape treat and she gets a cherry treat?
Answer:
6/20 = 3/10
Step-by-step explanation:
Her brother gets the first treat. There are 2 grape treats out of 3+2 = 5 total; this is a probability of 2/5.
Maggie gets the second treat. There will still be 3 cherry treats left, but only 5-1 = 4 treats remaining; this is a probability of 3/4.
Together this gives us 2/5(3/4) = (2*3)/(5*4) = 6/20 = 3/10
Answer:
3/10 or 6/20
Step-by-step explanation:
Find an equation for the nth term of the arithmetic sequence.
9, 11, 13, 15, ...
Answer Choices
A) an = 9 + 2(n - 1)
B) an = 9 + 2(n + 1)
C) an = 9 + 2
D) an = 9 + 2(n)
Which statements are true?
Choose all answers that are correct.
A.
All quadrilaterals can be classified as either parallelograms or trapezoids.
B.
All rhombuses are parallelograms.
C.
Some trapezoids are parallelograms.
D.
Some parallelograms are squares.
Answer:
Step-by-step explanation:
B, C and D
what is the least common denominator of the rational expressions below?
6/x^2+7x - 8/x^2+10x+21
a. x(x+7)(x+3)
b. x+7
c. x(x+7)^2(x+3)
d. x(x+3)
Explanation of finding the least common denominator of rational expressions.
The least common denominator of the rational expressions provided is option (d): x(x+3).
To find the LCD, first factor each denominator completely. Then, identify the unique factors and their highest powers. The LCD will be the product of these unique factors raised to their highest powers.
Which of the following are the coordinates of the vertex of y=-x^2+2x+1
What is the equation of the line that contains the points (3, –6) and (–3, 0)?
A.
y = x – 3
B.
y = –x – 3
C.
y = –x + 3
D.
y = x + 3
To determine the equation of a line given two points, calculate the slope and then use one point to write the equation in slope-intercept form. The equation of the line through (3, -6) and (-3, 0) is B. y = -x - 3.
To find the equation of the line that contains the points (3,
-6) and (
-3, 0), we need to calculate the slope (m) of the line using the slope formula:
m = (y2 - y1) / (x2 - x1).
Plugging in the given points:
m = (0 - (-6)) / (-3 - 3)
m = 6 / -6
m = -1.
With the slope now known, we can use one of the points and the slope to write the equation of the line in point-slope form (y - y1) = m(x - x1) and then convert it to slope-intercept form (y = mx + b). Let's use the point (-3, 0):
y - 0 = -1(x + 3)
y = -1x - 3.
Therefore, the correct equation of the line is B. y =
-x - 3.
What are the zeros of the polynomial function f(x) = x3 – 4x2 – 12x
Crystal charges a flat fee of $10 plus an additional $5 per hour to babysit given the situation what is the range
Answer:
perhaps $10 to $10,810
Step-by-step explanation:
We assume Crystal may be willing to babysit for a period of up to 3 months (90 days), so 90×24 = 2160 hours. Her hourly fee for that period will be ...
... (2160 hours) × ($5/hour) = $10,800
That amount added her $10 initial charge may represent the upper limit of her pay. The lower limit will be the $10 initial charge.
_____
Comment on the question
Since no upper limit on hours is given, we conclude the problem is not well-specified.
We can make a variety of different assumptions regarding the upper limit of babysitting time.
We might choose to consider this a daily charge, so the upper limit is $130 per day. We might consider that Crystal is willing to babysit while the child's parents are on a 2-week vacation. We might consider that Crystal is willing to babysit for the duration of her summer vacation from school (about 3 months). This is the assumption we use here.Annie's cafe borrows $6100 at 6% for 290 days. Find the total amount that must be repaid after 290 days. (Use a 365 day year.)
General Idea:
The formula to find the Amount 'A' that need to be paid after ' t ' years for a Principal ' P ' with a annual rate of interest ' r ' is given below:
[tex] A= P(1+r \cdot t) [/tex]
Applying the concept:
Annie's cafe borrows $6100 at 6% for 290 days.
From the above statement we can conclude,...
[tex] P= \$6100\\ \\ r=6\%\\ \\ t=\frac{260}{365} [/tex]
Substituting the values of P, r and t in the formula, we get...
[tex] A=6100 \cdot (1+6 \% \cdot \frac{260}{365} )\\ \\ A=6100(1+\frac{6}{100} \cdot \frac{260}{365} )=6100(1+\frac{1560}{36500} ) \approx 6361 [/tex]
Conclusion:
The total amount that must be repaid after 290 days is approximately [tex] \$6361 [/tex]