Answers
1) y = 3sin(x-π).
The function sine returns a value between -1 and 1, including those limits, so the range interal is [-1,1] no matter what the input be.
Multiplying the function by the factor 3, stretches the range by that factor.
So, the range of the given function is [-3,3].
2) y = 1 - sin(x)
Againt the range of sin(x) is [-1,1], then when you subtract that from 1, the limits of 1 - sin(x) are: 1 - (-1) = 2 and 1 - 1=0, and any other value wiill be in that range.
So, the answer is [0,2]
3) y = 3 + 4cos(x - π).
The range of the cosine function is also [-1,1], so the range of cos(x - π) is [-1,1].
By multiplying by 4 you stretch the range by that factor, so the new range is [-4,4].
By adding 3, the new borders are 3 - 4 = -1 and 3 + 4 = 7, so the range of the given function is: [-1, 7].
4) y = 2+cot(x)
The range of cot(x) is (-∞,∞), so adding 2 does not modify the range
So, the range for the given function is (-∞,∞).
Be sure to understand how this work. For both functions sine and cosine the range is [-1,1], when you mutiply by a constant factor you scale the range by that factor and when you add a constant you translate the range by that number of units.
Related Questions
Lee ann paid in advance for 20 hours of day care. After one week, she had used 12 3/4 hours. How many hours of day care does she have left!
Answers
the answer would be 7 1/4 hours
Enya is building a storage cupboard in the shape of a rectangular prism. The rectangular prism has a square base with side lengths of 2.4 feet and a height of 3.4 feet. Find the percentage of the amount of paint she would use to paint all but the bottom surface of the prism to the amount she would use to paint the entire prism. Round to the nearest tenth.
Answers
The sides have area (4*2.4 ft)*(3.4 ft) = 32.64 ft².
The the total area is (2*5.76 +32.64) ft² = 44.16 ft². All but the bottom area is then 44.16 ft² -5.76 ft² = 38.40 ft².
The ratio (all but bottom area)/(total area) is then
38.40/44.16 ≈ 87.0%
Which ordered pair is identified by the letter "G" on this coordinate grid?
Answers
When we say coordinate pair, we usually express our pair in the form of:
(x, y)
This means the point on the x axis is first, and the point on the y is second in the parenthetical format of coordinates. We know that the x coordinate is the horizontal one, while the y is vertical.
If we start with the x axis, we see that our point, G, is just below the number 2. That means our x coordinate is 2. For the y coordinate, we see that the point is directly lined up with the -3, therefore our y coordinate is -3.
Therefore, our coordinates are (2, -3).
Hope this helps!
Kim is reading a book with 380 pages. She read 20 pages each day until she reached Part 2 of the book. Part 2 of the book is 160 pages long. She uses the equation 380−20d=160 to represent the number of days, d, it took her to read Part 1. How many days did it take Kim to read Part 1 of the book?
Answers
part 1 of the book took 19 days
Milton got a paperweight like the one shown below. He needs to fill it with sand to give it weight.
If a = 2 inches, what is the volume of the paperweight?
A.24 in3
B.56 in3
C.16 in3
D.32 in3
Answers
4 x 2 x 2 = 16
16+8 = 24
Answer is A
Solution:
Given that, Milton got a paperweight like the one shown in the figure.
The Paper Weight is in the shape of a cuboid and a cube.
Length and breadth of cuboid is a and height of the cuboid is 2a, whereas side of cube is a.
The volume of sand required to fill in the Paper Weight , is equal to the volume of the Paper weight,
Volume of Paper Weight = Volume of cube + Volume of cuboid
We know that, Volume of cube =[tex] (side)^{3} [/tex]
and , Volume of Cuboid = [tex] length \times breadth \times height [/tex]
Volume of Paper Weight = [tex] a^{3}+ (a\times a \times2a)= a^{3} +2a^{3} = 3a^{3} [/tex]
Given that , a = 2 inches , then Volume of Paper Weight = [tex] 3 \times (2)^{3}= 3\times 8 = 24 [/tex]
[tex] 24 \: in^{3} [/tex] is the volume of the paperweight.
Option A is the correct solution.
The salesman has observed that many students are looking for cars that cost less
than $5,000. If he decides to also deal in cars that cost less than $5,000 and projects selling 200 of them over the next 10 years, how will the distribution be affected?
Answers
Introducing vehicles costing less than $5,000 will alter the supply curve by adding a new segment for lower-priced cars, likely leading to an increase in the quantity supplied for this market segment. This reflects market segmentation and aligns with the demand for cheaper vehicles.
The introduction of cars less than $5,000 into the salesman's inventory may affect the distribution of car sales. When discussing economic models, a supply curve (such as curve So) indicates the quantity of goods that sellers are willing to supply at various prices. According to the scenario provided, Point J on the supply curve So shows that if the price is $20,000, the quantity supplied will be 18 million cars. However, if the price drops to below $5,000, this will most likely introduce a new segment on the supply curve, as the current supply data relates to higher-priced vehicles.
Introducing lower-cost cars will attract a different consumer base, often overlooked in premium markets. This could lead to an increase in the quantity supplied of cheaper cars, as the demand for this segment is likely to be different from premium cars. If the projection of selling 200 cars in 10 years holds true, it will introduce a new point on the supply curve, which will represent cars at a lower price point and possibly a higher quantity compared to the original supply curve for higher-priced cars.
It cannot be determined from the given information whether the overall effect will pull market equilibrium towards the lower end, but it introduces the concept of market segmentation where different products and prices can co-exist, catering to different consumer needs and preferences.
B) the first marble is replaced, and another marble is chosen at random. if you're told the marble has the number 6 on it, what is the probability the marble is blue?
Answers
B) 1/2 (there is only 2 marbles with the number 1 on it. So its a 50/50 chance its red.)
Also ivorbigg has no clue what he/she is talking about. A probably never has a value higher than 1. If it did, that would mean that is more than 100% chance of that event happening which is impossible. All of your answers to anything probability related is 1 or less.
The probability that the marble is blue on the second draw, given that the first marble was replaced and had the number 6 on it, is 4 out of 7.
Explanation:The probability that the marble is blue on the second draw, given that the first marble was replaced and had the number 6 on it, can be found using conditional probability.
The probability of drawing a blue marble on the first draw is 4 out of 7 (4 blue marbles out of a total of 7 marbles). Since the first marble was replaced, the probability of drawing a blue marble on the second draw is still 4 out of 7. Therefore, the probability that the marble is blue on the second draw, given that the first marble had the number 6 on it, is also 4 out of 7.
donovan brought 5 1/2 kilograms of flour for $8.25.
TELL WHEATHER EACH STATEMENT IS TRUE OR FALSE.
A. The product (33/4) (2/11) gives the price of one kilograms of flour.
B. Donovan paid less than $1.25 per kilogram of flour.
C. $1.00 can purchase 2/3 kilogram of flour.
SHOW YOUR WORK
Answers
$8.25 for 5 1/2 kilograms of flour.
8.25 / 5.5 = 1.5 per kilograms.
The price of flour per kilograms is $1.5.
Choice A is TRUE.
(33/4) (2/11) = 33*2 / 4*11 = 66/44 = 1.5
Choice B is FALSE. Donovan paid 1.5 per kilo. It is not less than 1.25.
Choice C is TRUE. 2/3 kilograms of flour is priced as $1.
1.5 * 2/3 = (1.5*2) / 3 = 3/3 = 1
In the casino game roulette players bet on which of 38 equally likely outcomes will occur on a single spin of the wheel. The probability of the ball landing on black is 18/38. If you bet $100 on black, which of the following is the best choice for your expected value?
a)-$5.26
b)+$5.26
c)+$52.63
d)-$52.63
e)0.00
Answer is a) -$5.26, just not sure how to achieve that. I know it's asking to find the mean (mu).
Answers
P(winning) = 18/38
P(losing) = 1-18/38 = 20/38
Expected value = 100*18/38 - 100*20/38
1800/38 - 2000/38 = - 200/38 =-$5.26
the answer is the option a)-$5.26
Which of the following describes the graph of the equation
y = 2(x+2)
A. Line
B. Circle
C.Ellipse
D. parabold
Answers
Determine the values of n for which f(x)=x^2 has an inverse that is a function. Assume that n is a whole number.
Answers
Determine the values of n for which f(x)=x^n has an inverse that is a function.
a. n is even
b. n is odd
c. n < 0
d. n > 0
And if you have this answer option my answer would be B. N is odd
Four sets of data are shown in box-and-whisker plots. Which set has the largest MEDIAN?
Answers
Answer:
It’s c
Step-by-step explanation:
For a two week period, John and Amanda had the following transactions occur to their checking account: a deposit of $1,644.50; checks written for $190, $45, and $7.50; and debit card transactions for $30, $5.59, $7.20, and $21.30. What is the ending balance for this time frame? A. $1,352.24 B. $1,377.91 C. $1,234.56 D. $1,466.09
Answers
At the beginning of soccer practice a water cooler contained 5 gallons of water at the end of soccer practice the water cooler is only 1/4 full how many gallons of water are in the cooler at the end of practice explain
Answers
x= # gallons remaining
x= 5 * 1/4
x= (5*1)/4
x= 5/4
x= 1 1/4 gallons remaining
CHECK:
multiply 1 1/4 remaining gallons by number of quarters in a whole or in 100 (there are four 1/4s)
= 1 1/4 * 4
= 5/4 * 4
= (5*4)/4
= 20/4
= 5
ANSWER: 1 1/4 gallons remaining
Hope this helps! :)
Evaluate the expression. 9! − 5!
Answers
Evaluate means just solve it.
9! = 9x8x7x6x5x4x3x2x1 = 362880
5! = 5x4x3x2x1 = 120
362880 - 120 = 362760
There is your answer
This is the product of a number and below it until 1.
In mathematical language
a! = a * (a - 1)!
So,
5! = 5 * 4 * 3 * 2 * 1 = 120
9! = 9 * 8 * 7 * 6 * 5 *4 *3 * 2 *1 = 326 880
Therefore 9! - 5! = 326 880 - 120 = 326 760
Jason is decorating his house and decides to paint one of the bedrooms blue. One tin of 500mL blue paint costs $11.50. To finish the whole bedroom, he needs 4L of blue paint. How much will it cost Jason to paint this bedroom?
Answers
- One tin of 500 mL blue paint costs $11.50.
-Jason needs 4 L of blue paint.
2. First, you must convert 4 L to mL, as below:
1 L----1000 mL
4 L----x
x=4x1000/1
x=4000 mL
3. If 500 mL costs $11.50, how much will it cost 4000 mL?
500 mL-----$11.50
4000 mL---x
x=(4000 mL)($11.50)/500 mL
x=$92.00
How much will it cost Jason to paint this bedroom?
The answer is: $92.00
Jason needs 4L of blue paint to paint a bedroom. At 500mL per tin costing $11.50 each, he will need 8 tins, totaling $92.00 for the paint.
The question asks to calculate the total cost of blue paint Jason needs to paint a bedroom. Jason requires 4L (4000mL) of paint and one 500mL tin costs $11.50. Since 4000mL is eight times 500mL, we will need eight tins of paint. To find the total cost, we multiply the cost of one tin by the number of tins needed:
Cost of one tin of paint = $11.50
Number of tins needed = Total volume required / Volume of one tin = 8
Total cost = Cost of one tin times Number of tins = $11.50 times 8 = $92.00.
Therefore, it will cost Jason $92.00 to buy the blue paint needed to paint the bedroom.
A cell phone plan includes 450 anytime minutes for $35 per month, plus $18.85 for a cell phone and $25 for a one-time activation fee. let x represent the number of months of service. write an equation in the form y equals mx plus
b. find the ordered pair associated with the equation for xequals9. if you sign a 1-yr contract, how much will this cell phone package cost?
Answers
The cost of the cell phone plan over x months is represented by the equation y = 35x + 43.85. For 9 months, the total cost is $359.85, and for a 1-year contract, the total annual cost is $463.85.
The total monthly cost of the cell phone plan for x months of service can be represented by the linear equation y = 35x + 18.85 + 25. Here, y represents the total cost, x represents the number of months, 35 is the cost per month, 18.85 is the cost of the cell phone, and 25 is the one-time activation fee. The equation simplifies to y = 35x + 43.85, since the cost of the phone and the activation fee is a one-time charge, independent of the number of months.
For x = 9 months of service, the ordered pair is (9, y), where y = 35(9) + 43.85. Therefore, the ordered pair associated with x = 9 is (9, 359.85).
If you sign a 1-year contract, which is 12 months, you will pay y = 35(12) + 43.85, which results in a total cost of $463.85 for the year.
What is f(x)=8x2+4x written in vertex form
Answers
using completing the square:
f(x)=8(x^2+1/2x+1/16)-(8*1/16) -->since we added a 1/16 inside the parenthesis, we need to subtract that quantity times 8
f(x)=8(x+1/4)-1/2
Answer:
Vertex form:
[tex]f(x)=8(x+\frac{1}{4})^2-\frac{1}{2}[/tex]
Step-by-step explanation:
Given: [tex]f(x)=8x^2+4x[/tex]
We need to write in vertex form.
Vertex form:
[tex]y=a(x-h)^2+k[/tex]
vertex: (h,k)
[tex]f(x)=8x^2+4x[/tex]
Step 1: Take out 8 common from each term
[tex]f(x)=8(x^2+\frac{1}{2}x)[/tex]
Step 2: Add and subtract square of half of coefficient of x
[tex]f(x)=8(x^2+\frac{1}{2}x+\frac{1}{16}-\frac{1}{16})[/tex]
Step 3: Factor the term inside parentheses
[tex]f(x)=8(x^2+2\cdot \frac{1}{4}\cdot x+(\frac{1}{4})^2)-8\cdot \frac{1}{16})[/tex]
[tex]f(x)=8(x+\frac{1}{4})^2-\frac{1}{2}[/tex] [tex]\because (a^2+2ab+b^2)=(a+b)^2[/tex]
Hence, The vertex form of f(x)
[tex]f(x)=8(x+\frac{1}{4})^2-\frac{1}{2}[/tex]
Charlotte's annual salary is 29,354 dollars. She is hoping to win the World Lottery which has a grand prize of 6,156,782,221 dollars. Approximately how many times as large is the World Lottery's grand prize as Charlotte's annual salary?
Answers
The answer is approximately 209,742.53 times as large.
The World Lottery's grand prize is approximately 209,701 times larger than Charlotte's annual salary when dividing the grand prize amount by her annual salary.
To determine approximately how many times larger the World Lottery's grand prize is compared to Charlotte's annual salary, we perform a division of the two amounts. Charlotte's annual salary is $29,354, and the World Lottery grand prize is $6,156,782,221.
To find out how many times larger the lottery prize is than Charlotte's salary, we use the following calculation:
Lottery Prize to Salary Ratio = World Lottery Grand Prize / Charlotte's Annual Salary
Lottery Prize to Salary Ratio = $6,156,782,221 / $29,354 ≈ 209,701
This means that the World Lottery's grand prize is approximately 209,701 times larger than Charlotte's annual salary.
Note: This is a simplified approximation and does not take into account any deductions or taxes that would be applied to either the grand prize or the salary.
Jaclyn sells candles that are in the shape of cones. She makes a green candle that has a radius of 2.5 inches and a height of 9 inches. She sells each candle at a price of $0.25 per cubic inch of wax. Which statements about the green candle are true? Check all that apply. Use 3.14 for pie.
The volume of the green candle is about 23.55 in.(cubed)
The volume of the green candle is about 58.88 in. (cubed)
The diameter of the green candle is 5 in.
The diameter of the green candle is 1.25 in.
The base area of the green candle is about 19.63 in. (squared)
The base area of the green candle is about 7.85 in. (squared)
The price of one green candle is about $5.89.
The price of one green candle is about $14.72.
Answers
Since the radius is 2.5 in, the diameter is 2*2.5 = 5.
The base is a circle. Therefore the base area is found by the formula
A=πr²=(3.14)(2.5)²=19.625≈19.63in².
The volume of a cone is given by multiplying the base area by the height and then taking 1/3 of it:
19.625(9)/3 = 58.875≈58.88in³.
The cost would be 58.88*0.25 = $14.72.
Answer:
2,3,5,8
Step-by-step explanation:
edge 22
Help!!!100 students who are in 9th or 10th grade were asked if they participated in at least one extracurricular activity (sports, music, or drama). 40 of the students are in 10th grade, but only 18 of these participate in at least one extracurricular activity. 32 of the 9th grade students participate in at least one extracurricular activity. Create a two-way table
Identify the variable and the categories represented in this problem.
Set up and fill in a two-way table to represent the frequencies in this problem.
PLEASE HELP
Answers
The best approach to solve this question is to build a table and start entering the given information in it. When the given data has been entered fill the rest on basis of the data you have.
18 students from grade 10 participate in at least one Extracurricular activities. This means the rest students i.e. 22 students from grade 10 do not participate in Extracurricular activities.
32 students from grade 9 participate in at least one Extracurricular activities. This means total students who participate in at least one Extracurricular activities are 18 + 32 = 50 students.
The rest 50 students do not participate in at least one Extracurricular activities. From these 22 are from class 10. So the rest i.e. 28 are from class 9.
Based on this data we can fill the table as shown in image below.
Given: ABCD is a parallelogram m∠A = 60º ; BK ⊥ AD AK = KD; Perimeter of ABCD = 24 Find: BD.
Answers
Please, see the attached file.
Thanks.
What integer is equivalent to 9 3/2
Answers
[tex]\bf \stackrel{mixed}{9\frac{3}{2}}\implies \cfrac{9\cdot 2+3}{2}\implies \stackrel{improper}{\cfrac{21}{2}}\implies 10.5 \ne \mathbb{Z}[/tex]
an integer is a "whole" number, with no decimals.
The millers electric bill jumped from 84 to 105 what was the percent increase
Answers
21/84 = 0.25
0.25 = 25% increase
Kendra bought a magazine for $3 and four paperback books for $5 each the expression 3 + 4 x 5 represents the total cost in dollars of her purchases what are the terms in this expression
Answers
If the width of a rectangle is 3in less than the length, and the perimeter of the rectangle is 14in, find the length and width of the rectangle.
Answers
.. l -w = 3
.. 2(l +w) = 14
Divide the second equation by 2 and add the first equation.
.. (2(l +w))/2 +(l -w) = (14)/2 +3
.. 2l = 10
.. l = 5
Then
.. w = l -3 = 2
The length and width are 5 inches and 2 inches, respectively.
Factor 34 out of 34z+6
Answers
2 has to be outside the parenthesis, 34 divided by 2: 17, 6 divided by 2: 3
2(17z+3)
Answer:
[tex]34z+6=34(z+\frac{3}{17})[/tex]
Step-by-step explanation:
To find : Factor 34 out of [tex]34z+6[/tex] ?
Solution :
Factor out means taking common term from the given expression.
Expression is given as [tex]34z+6[/tex]
Taking 34 common from 34z is left with z.
Taking 34 common from 6 is left with [tex]\frac{6}{34}[/tex].
So, [tex]34z+6=34(z+\frac{6}{34})[/tex]
[tex]34z+6=34(z+\frac{3}{17})[/tex]
Therefore, The required expression is [tex]34z+6=34(z+\frac{3}{17})[/tex]
A car rental agency charges $16.00 per day plus $.15 per mile. Jim's bill for 4 days was $79.00. How many miles did he drive?
Answers
Answer:
Jim drove 100 miles
Step-by-step explanation:
Suppose a cake was cut into 8 equal size pieces and 6 people ate all the pieces. Explain how they could have divided the pieces so that everyone ate the same amount of cake
Answers
hope this helps :)
Of the computer games Lynne owns, 5-12 are sport games and 3-12 are educational. What fraction of the games are either sport games or educational games?
Answers
5/12 + 3/12= 8/12 or 2/3 are one or the other.
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
We have that:
Lynne owns 12 games.
Of those
5 are sports games
3 are educational
What fraction of the games are either sport games or educational games?
[tex]f = \frac{5}{12} + \frac{3}{12} = \frac{8}{12} = \frac{2}{3}[/tex]