Answer: there is a relationship between study hours and test score. as the hours of studying increase, the test scores increase.
Answer:
C) There is a relationship between study hours and test score. As the hours of studying increase, the test scores increase.
Step-by-step explanation:
In the scatter plot, I can see that when the hours increase, so does the test scores. Thus, the answer is C
Are the two figures necessarily similar? Type "yes" or "no".
Two rhombuses =
Two circles =
Two isosceles triangles =
Two regular hexagons =
Answer:
Two rhombuses are not necessarily similar , No
Two circles are always similar , Yes
Two isosceles are similar , Yes
Two regular hexagons will be similar , Yes
The similar figures are Circle, Isosceles triangle and regular hexagons.
Geometric shapes are the figures which demonstrate the shape of the objects we see in our everyday life. In geometry, shapes are the forms of objects which have boundary lines, angles and surfaces. There are different types of 2d shapes and 3d shapes.
Two rhombuses are not necessarily similar: NoTwo circles are always similar: YesTwo isosceles are similar: YesTwo regular hexagons will be similar: YesTherefore the similar figures are Circle, Isosceles triangle and regular hexagons.
To Learn more about, Geometric shapes, refer:
https://brainly.com/question/16176111
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What's the present value of $11,000 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually?
Select the correct answer.
a. $7,083.20
b. $7,025.60
c. $7,040.00
d. $7,068.80
e. $7,054.4
Answer:
Step-by-step explanation:
A = P[1 + (r/n)]^(nt)
Look the formula up online to find out what each variable represents if needed.
We are solving for P, which is the principal amount 5 years back.
Substitute 11,000 for A (total amount), 4.5% for r(rate), 2 for n(number of times -- in this case, semiannually), and 5 for t(time -- 5 years).
11000 = P[1+(0.045/2)]^(2x5)
11000 = P (1.0225)^10
11000 = P (1.2492) approx.
Divide both sides by 1.2492 to find P.
P = $8805.64 (approx)
I know that the answer I got is not an option listed. However, I feel that my workings may help other people to answer this question or give them inspiration to answer similar questions. Therefore, I will leave this answer up.
Thanks, and sorry I couldn't do much.
Consider writing onto a computer disk and then sending it through a certifier that counts the number of missing pulses. Suppose this number X has a Poisson distribution with parameter μ = 0.2. (Round your answers to three decimal places.)
Required:
a. What is the probability that a disk has exactly one missing pulse? (Round to four decimal places)
b. What is the probability that a disk has at least two missing pulses? (Round to four decimal places)
c. If two disks are independently selected, what is the probability that neither contains a missing pulse?(Round to four decimal places)
Answer:
a) 0.164 = 16.4% probability that a disk has exactly one missing pulse
b) 0.017 = 1.7% probability that a disk has at least two missing pulses
c) 0.671 = 67.1% probability that neither contains a missing pulse
Step-by-step explanation:
To solve this question, we need to understand the Poisson distribution and the binomial distribution(for item c).
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!} [/tex]
In which
x is the number of sucesses
[tex] e = 2.71828[/tex] is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Binomial distribution:
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Poisson mean:
[tex]\mu = 0.2[/tex]
a. What is the probability that a disk has exactly one missing pulse?
One disk, so Poisson.
This is P(X = 1).
[tex]P(X = 1) = \frac{e^{-0.2}*0.2^{1}}{(1)!} = 0.164 [/tex]
0.164 = 16.4% probability that a disk has exactly one missing pulse
b. What is the probability that a disk has at least two missing pulses?
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!} [/tex]
[tex]P(X = 0) = \frac{e^{-0.2}*0.2^{0}}{(0)!} = 0.819[/tex]
[tex]P(X = 1) = \frac{e^{-0.2}*0.2^{1}}{(1)!} = 0.164 [/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.819 + 0.164 = 0.983[/tex]
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.983 = 0.017[/tex]
0.017 = 1.7% probability that a disk has at least two missing pulses
c. If two disks are independently selected, what is the probability that neither contains a missing pulse?
Two disks, so binomial with n = 2.
A disk has a 0.819 probability of containing no missing pulse, and a 1 - 0.819 = 0.181 probability of containing a missing pulse, so [tex]p = 0.181[/tex]
We want to find P(X = 0).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.181)^{0}.(0.819)^{2} = 0.671[/tex]
0.671 = 67.1% probability that neither contains a missing pulse
What’s the correct answer for this question?
Answer:
21/100
Step-by-step explanation:
By looking at the table, we can find the box that has information on people who have dogs but do not walk. The number is 21. The total number of people is 100. To find probability, divide 21 by 100.
21/100
This fraction is in its simplest form and cannot be simplified any further.
Does consuming beer attract mosquitoes? A study done in Burkino Faso, Africa, about the spread of malaria investigated the connection between beer consumption and mosquito attraction.1 In the experiment, 25 volunteers consumed a liter of beer while 18 volunteers consumed a liter of water. The volunteers were assigned to the two groups randomly. The attractiveness to mosquitoes of each volunteer was tested twice: before the beer or water and after. Mosquitoes were released and caught in traps as they approached the volunteers. For the beer group, the total number of mosquitoes caught in the traps before consumption was 434 and the total was 590 after consumption. For the water group, the total was 337 before and 345 after. 1Lefvre T, Gouagna L-C, Dabir KR, Elguero E, Fontenille D, et al. 2010 Beer Consumption Increases Human Attractiveness to Malaria Mosquitoes. PLoS ONE 5(3): e9546. doi:10.1371/journal.pone.0009546 (a) State the null and alternative hypotheses for a test to see if, after consumption, the average number of mosquitoes is higher for the volunteers who drank beer. Let group 1 be the people who drank beer and let group 2 be the people who drank water. SHOW HINT (b) Compute the average number of mosquitoes per volunteer before consumption for each group. Round your answers to two decimal places. Beer group: Water group: Are the two sample means different? Do you expect that this difference is just the result of random chance? SHOW HINT (c) Compute the average number of mosquitoes per volunteer after consumption for each group. Round your answers to two decimal places. Beer group: Water group: Are the two sample means different? Do you expect that this difference is just the result of random chance? SHOW HINT (d) If the difference in part (c) is statistically significant, do we have evidence that beer consumption increases mosquito attraction?
Answer:
Take u1 = average number of mosquitoes attracted after drinking beer
u2 = average number of mosquitoes attracted after drinking water
a) The null and alternative hypotheses:
H0 : u1 = u2
H1 : u1 > u2
b) i) The average number of mosquitoes per volunteer before drinking (beer group) :
[tex] x'1 = \frac{x_1}{n} = \frac{434}{25} = 17.36 [/tex]
Sample mean for mosquitoes attracted before consumption for beer group is 17.36
The average number of mosquitoes per volunteer before drinking (water group) :
[tex] x'2 = \frac{x_2}{n} = \frac{337}{18} = 18.72 [/tex]
Sample mean for mosquitoes attracted before consumption for water group is 18.72
The two means are different.
The difference in the two means are as a result of random choice.
c) i) The average number of mosquitoes per volunteer after drinking (beer group) :
[tex] x'1 = \frac{x_1}{n} = \frac{590}{25} = 23.60 [/tex]
Sample mean for mosquitoes attracted after consumption for beer group is 23.60
ii) The average number of mosquitoes per volunteer after drinking (water group) :
[tex] x'2 = \frac{x_2}{n} = \frac{345}{18} = 19.17[/tex]
Sample mean for mosquitoes attracted after consumption for water group is 19.17
The two sample means are different.
This difference here is likely not to be as a result of random choice, because the mean difference here is greater than the mean difference before consumption.
d) A statistically significant difference provides evidence that beer consumption increases mosquito attraction, as the average number of mosquitoes attracted when drinking beer is higher than the mean number of mosquitoes attracted when drinking water.
Matt bought 4 pie molds at a cost of $0.53 per mold. He also bought 4 pre-
made crusts at a cost of $0.72 per crust. How much did Matt spend on pie
molds? Do not include $ in your answer.
Answer:
2.12
Step-by-step explanation:
He spent 4*0.53 on pie molds.
4*0.53=2.12
To save money for a sabbatical to earn a master’s degree, you deposit $2000 at the end of each year in an annuity that pays 7.5% compounded annually. a) How much will you have saved at the end of five years? b) Find the interest.
Answer:
The amount he will have at the end of five years is $11,616.8
Interest on the amount is $1,616.8
Step-by-step explanation:
Kindly check the attached picture for explanation.
4. Candice leaves on a trip driving at 25 miles per hour. Four hours later, her sister
Liz starts from the same location driving at 50 miles per hour. How long after Liz
leaves home will she catch up to Candice?
A 9 hours
B 4 hours
C 8 hours
D 7 hours
Answer: B. 4 hours
Step-by-step explanation:
Please answer this correctly
Answer:
Area = 2.33 mm²
Explanation:
Perimeter of quarter circle = 14.28
But
Perimeter of quarter circle = 2πr+2r
So
2πr+2r = 14.28
6.3r+2r = 14.28
8.3r = 14.28
r = 14.28/8.3
r = 1.7 mm
Now the Area
Area of quarter circle = 1/4(πr²)
= 1/4(3.14)(1.7)²
= 1/4(3.14)(2.97)
= 1/4(9.34)
= 2.33 mm²
A trapezoid was broken into two congruent triangles and a rectangle. A trapezoid is broken into 2 triangles and 1 rectangle. The triangles both have a base of 3 centimeters and a height of 12 centimeters. The rectangle has a height of 12 centimeters and a width of 14 centimeters. What is the base length, b, of one of the triangles? 3 cm 4 cm 6 cm 7 cm
complete question:
The picture below is the complete question.
Answer:
base of the triangles = 3 cm
Step-by-step explanation:
The trapezoid was broken into 2 congruent triangles and a rectangle. The 2 triangle have a height of 12 cm . The rectangle has a height of 12 cm and width of 14 cm .
The base length of the triangle can be computed as follows.
Note a congruent triangle have exactly the same three sides and exactly the same three angles.
area of a triangle = 1/2 × base × height
From the area of the trapezoid one can calculate the sides of the triangle.
area of the trapezoid = 1/2 × (a + b)h
where
a = top side
b = base side
h = height
area of the trapezoid = 1/2 × (a + b)h
area of the trapezoid = 1/2 × (14 + 20)12
area of the trapezoid = 1/2 × 34 × 12
area of the trapezoid = 34 × 6
area of the trapezoid = 204 cm²
204 = area of the triangles + area of the rectangle
204 =2 (1/2bh) + lw
where
b = base of triangle
h = height of triangle
l = length of rectangle
w = width of rectangle
204 = bh + (14 × 12)
204 = 12b + 168
12b = 204 - 168
12b = 36
divide both sides by 12
b = 36/12
b = 3 cm
base of the triangles = 3 cm
Answer:
3
Step-by-step explanation:
I got 4cm wrong in the unit test and it showed me that the answer was 3cm
What can you conclude from a box plot where the length of the left box and whisker is the same as the length of the right box and whisker?
Answer/Step-by-step explanation:
The length of the boxes and whiskers of a box plot tells us more about the spread the data being represented is and as well as the shape of the spread.
Invariably, if the length of the left box and left whiskers is of the same length as the right box and right whiskers, this implies that the distribution of the data point is close to being symmetric, or approximately symmetrical.
An urn contains 78 slips of paper. Each slip bears a number from 1 to 26. Each number appears on 3 different slips. A child selects two slips of paper at random and without replacement. Find the probability that the drawn slips have the same number. Write your answer as a reduced fraction.
Answer:
2 / 77
Step-by-step explanation:
Each number appears 3 times in the urn.
After picking any number, the number picked will appear only two more times in the urn, and the total slips of paper will be 77.
So for any first number we pick, the probability of the second number picked being the same number as the first pick is the number of times the same number appears in the urn (2) over the total number of slips in the urn (77):
Probability = 2 / 77
Rathaus thinks all the factors of even numbers are even which explains wether Rathan is correct
Answer:
Incorrect
Step-by-step explanation:
It is incorrect because all even numbers have a factor of 1.
That is odd.
Answer:
False
Step-by-step explanation:
even numbers has odd & even factors
6 is an even number
Factors of 6 = 2 , 3
Where 3 is a odd number
Answer with Explanation please! Thank you!
Answer:
B)
Step-by-step explanation:
Slope = -3
Y-intercept = 3
So
Equation is
y = mx+b
Where m is slope and b is y-intercept
y = -3x+3
The diagram shows the scores given by the panel of judges
during a dancing competition.
a) Which score was the mode?
8
7
6
b)
Frequency
There were 5 judges.
They each gave one score in each
round of the competition.
3
2
How many rounds were there?
+
o
0 1 2 3 4 5
Score
Note: Please make sure your final answer says ... rounds.
Answer:
a) 4b) 6 roundsPlease Help I will mark as brainliest
Answer:
A. True
B. True
C. False
D. True
Step-by-step explanation:
A) To find the probability of the letters spelling CAT go to the letter C, then A, and finally T. there is only one sequence that does this, so the numerator will be 1. There are 6 outcomes overall, so the denominator will be 6. The probability of the letters spelling CAT would be 1/6. The answer is true.
B) To find the probability of T being the first letter go to the letter T. All sequences after the letter T will all be included in the answer. TAC and TCA are both possible solutions, this means there are 2 correct outcomes, so 2 is the numerator. Again, there are 6 outcomes overall, so the denominator will be 6. The probability of T being the first letter is 2/6, which is equal to 1/3. The answer is true.
C) To find the probability of A being the first letter go to the letter A. All sequences after the letter A will all be included in the answer. ACT and ATC are both possible solutions, this mean there are 2 correct outcomes, so 2 is the numerator. Again, there are 6 outcomes overall, so the denominator will be 6. The probability of A being the first letter is 2/6. The answer is false.
D) To find how many total outcomes are possible go to the tree diagram and look to the far right. Go down each of the rows to find all of the outcomes, there is T,C,T,A,C, and A. That means there are six possible outcomes. The answer is true.
A circle is centered on point BBB. Points AAA, CCC and DDD lie on its circumference.
If \blue{\angle ABC}∠ABCstart color #6495ed, angle, A, B, C, end color #6495ed measures 124^\circ124
∘
124, degrees, what does \orange{\angle ADC}∠ADCstart color #ffa500, angle, A, D, C, end color #ffa500 measure?
Answer:
[tex]\angle ADC=62^\circ[/tex]
Step-by-step explanation:
Given the circle centered on point B with points A, C and D on its circumference.
[tex]\angle ABC[/tex] is the angle subtended by arc AC at the centre.
Since D is on the circumference, [tex]\angle ADC[/tex] is the angle subtended by arc AC on the circumference.
Circle Theorem: The measure of the angle subtended by an arc at the center is twice the measure of the angle subtended by same arc at the circumference.
By the theorem stated above:
[tex]\angle ABC = 2 X \angle ADC\\Since \angle ABC=124^\circ\\124^\circ = 2 X \angle ADC\\ \angle ADC=124^\circ \div 2\\\\ \angle ADC=62^\circ[/tex]
Answer:
The real answer is 20 its not that high of a number
Step-by-step explanation:
Element X decays radioactively with a half life of 8 minutes. If there are 980 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 43 grams?
y=a(.5)^t/h
Answer:
[tex]t \approx 36.1\,min[/tex]
Step-by-step explanation:
The time constant for the isotope decay is:
[tex]\tau = \frac{8\min}{\ln 2}[/tex]
[tex]\tau \approx 11.542\,min[/tex]
Now, the decay of the isotope is modelled after the following expression:
[tex]m (t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex]
The time is now cleared with some algebraic handling:
[tex]\frac{m(t)}{m_{o}} = e^{-\frac{t}{\tau} }[/tex]
[tex]t = -\tau \cdot \ln \frac{m(t)}{m_{o}}[/tex]
Finally, the time need for the element X to decay to 43 grams is:
[tex]t = - (11.542\,min)\cdot \ln\left(\frac{43\,g}{980\,g} \right)[/tex]
[tex]t \approx 36.1\,min[/tex]
What is the value of x?
65°, 79° , X
Answer:
x=36 degrees
Step-by-step explanation:
Remember that all angles of a triangle must add up to 180 degrees due to the Angle Addition Postulate. So let's plug it in! x+65+79=180
Now you solve, x=180-79-65
x=36!
x=36 degrees
Answer:
Option B
Step-by-step explanation:
All interior angles of a triangle add up to 180°.
[tex]79+65+x=180\\144+x=180 \\144-144+x=180-144\\\boxed {x=36}[/tex]
The missing angle is 36°.
Option B should be your correct answer.
Select the statement that is true. Group of answer choices There are integers s and t such that 2=102⋅s+72⋅t . here are integers s and t such that 8=102⋅s+72⋅t . There are integers s and t such that 1=102⋅s+72⋅t . There are integers s and t such that 6=102⋅s+72⋅t .
Answer:
Step-by-step explanation: true
find the equation in standard form of the line passing through the points (2, negative 3) and (4, 2)
A.5x-2y=16
B.2x-3y=9
C.y=5/2x+8
D.5x+2y=16
Answer:
Step-by-step explanation:
(2 + 3)/(4 - 2)= 5/2
y + 3 = 5/2(x - 2)
y + 3 = 5/2x - 5
y = 5/2x - 8
2y = 5x - 16
5x - 2y = 16
Evaluate the expression 6•14-(9+8)2
Answer:
50
Step-by-step explanation:
First things first, use PEMDAS.
Parenthesis is first.
(9+8) is in parenthesis. 9+8 is obviously 17.
The equation now looks like this:
6 x 14 - 17 x 2
There is no exponents, but there is multiplication. 6 x 14 is 84 and 17 x 2 is 34. They both are multiplication equations.
The equation now looks like this:
84 - 34
84-34 is 50. 50 is your answer.
In the figure below, the polygons are similar. Find the value of x and y. Have a nice day
Answer:
x is 4 and y is 3.
Step-by-step explanation:
The scale factor between the triangles is 2, as you can see. The hypotenuse of the small triangle is 5 while the hypotenuse of the larger one is 10, so the scale factor between the triangles is 2. This means you can divide the other leg lengths of the large triangle by 2 to find the lengths for the corresponding legs of the small one.
Billy’s Restaurant ordered 200 flowers for Mother’s Day. They ordered carnations at
$1.50 each, roses at $5.75 each, and daisies at $2.60 each. They ordered mostly
carnations, and 20 fewer roses than daisies. The total order came to $589.50. Write
a system of linear equations that can be used to find c, the number of carnations, r,
the number of roses, and d, the number of daisies.
Answer:
c+r+d= 200
1.50c+5.75r+2.60d= 589.50
r=d-20
Step-by-step explanation:
From the information given you have that Billy's restaurant ordered roses, daisies and carnations that total 200 flowers. The first equation is:
c+r+d= 200
c= number of carnations
r= number of roses
d= number of daisies
Also, you can say that the sum of the results of multiplying the price of each flower for its quantity is equal to $589.50. The second equation is:
1.50c+5.75r+2.60d= 589.50
Besides, from the statement you know there are 20 fewer roses than daisies and from that you can write the third equation:
r= d-20
The system of linear equations that can be used to find c, the number of carnations, r, the number of roses, and d, the number of daisies is:
c+r+d= 200
1.50c+5.75r+2.60d= 589.50
r=d-20
Fahim is 6 feet tall. At noon, he stands with the sun behind him casting a shadow. The distance from the top of Fahim’s head to the furthest tip of the shadow is 13 feet. A right triangle with side length 6 feet, s, and hypotenuse 13 feet. [Not drawn to scale] What is the length of Fahim’s shadow? Round to the nearest tenth of a foot.
Answer:
11.5
Step-by-step explanation:
using Pythagoras theorem
the square of 13 equals the square of 6 and the unknown side
Answer:
11.5 feet
Step-by-step explanation:
I just took the quiz on edge
A company is planning a four-year project, with an initial cost of $1.67 million. This investment cost is amortised to zero over four years on a straight-line basis. However, the asset could be disposed of for $435,000 in four years. The project requires $198,000 in working capital initially and is fully recoverable after the project is completed. The project generates $1,850,000 in sales and $1,038,000 in costs each year. If the tax rate is 21% and the required return rate is 16.4%, what is NPV?
Answer:
The Net Present Value = $451180.733
Step-by-step explanation:
Given that:
the initial cost of the project is $1670000
the initial increase in working capital is $198000
The total investment will be ; initial cost of the project + initial increase in working capital
The total investment = $1670000 + $198000
The total investment = $1868000
So, This investment cost is amortised to zero over four years; This implies that the project will depreciate in four years;
Now; lets determine the rate of the annual depreciation
The annual depreciation = [tex]\dfrac{Initial \ cost \ of \ project }{life \ of \ project}[/tex]
The annual depreciation = [tex]\dfrac{1670000}{4}[/tex]
The annual depreciation = $417500
Over to the annual operating cash flow; the annual operating cash flow can be calculated as follows:
annual operating cash flow = (sales - cost) × (1 - tax rate )+ (annual depreciation × tax rate )
Given that the tax rate = 21% = 0.21
annual operating cash flow = (1850000 -1038000)×(1-0.21)+(417500× 0.21)
annual operating cash flow = 812000 × 0.79 + 87675
annual operating cash flow = 641480 + 87675
annual operating cash flow = $729155
So; let's calculate the after tax salvage value for the project
We know that the sales values for the project in four years is $435,000 (i.e the disposal rate of the asset after four years)
Thus; the book value is zero
The after tax salvage value for the project can now be determined by the relation:
after tax salvage value = sale value - tax (sale value - book value)
after tax salvage value = 435000 - 0.21 (435,000 -0)
after tax salvage value = 435000 - 91350
after tax salvage value = $343650
Similarly; given that the recovering rate of the project is $198000;
The cash flow in year 4 will be: annual operating cash flow + after tax salvage + recovery working capital
cash flow in year 4 = $(729155 + 343650 + 198000)
cash flow in year 4 = $ 1270805
This implies that the cash flow from year one to three is : 729155
the cash flow in year four is : 1270805
Given that the Required return rate = 16.4% = 0.164
We can therefore determine the Present cash inflows by using the relation:
[tex]Present \ Value = \dfrac{c_1}{(1+r)^1}+ \dfrac{c_2}{(1+r)^2}+ \dfrac{c_3}{(1+r)^3}+ \dfrac{c_4}{(1+r)^4}[/tex]
[tex]Present \ Value = \dfrac{729155}{(1+0.164)^1}+ \dfrac{729155}{(1+0.164)^2}+ \dfrac{729155}{(1+0.164)^3}+ \dfrac{1270805}{(1+0.164)^4}[/tex]
[tex]Present \ Value = \dfrac{729155}{1.164^1}+ \dfrac{729155}{1.164^2}+ \dfrac{729155}{1.164^3}+ \dfrac{1270805}{1.164^4}[/tex]
Present Value = $(626421.8213 + 538163.0767 + 462339.413+692256.4225)
Present Value = $2319180.733
Finally, The net present value = Present Value - Total Investment
Net Present Value = $(2319180.733 - 1868000)
Net Present Value = $451180.733
Therefore; The Net Present Value = $451180.733
omar has 5 liters of water he divides the water evenly between 4 buckets. how many milliters does omar pour in each bucket
Answer:
1250 milliliters
Step-by-step explanation:
Omar has 5 liters of water. He divides evenly between 4 buckets.
5/4 = 1.25
He pours 1.25 liters in each bucket.
Convert 1.25 liters into milliters.
1.25 × 1000
1250 milliliters.
Omar pours 1250 milliliters in each bucket.
What is the range of the function f(x)= 1/2sin(2x-pi)
The answer is [-1/2-1/2]
The range of the function f(x) is [-1/2, 1/2].
What is the range of a function?The range is the set of possible output values, which are shown on the y-axis. The range of a function, f is the set of all values f(x) , such that x is in the domain of f. Graphically speaking, the range is the set of all y such that (x,y) is a point on the graph of f.
For the given situation,
The function f(x) = 1/2sin(2x-π)
The graph below shows the range of the function f(x) = 1/2sin(2x-π) graphically.
As the range of sinx function is [-1, 1], the range of sin2x is also [-1, 1].
Let us consider [tex]\theta = 2x-\pi[/tex]
⇒ Then, [tex]sin \theta[/tex] lies in the range [tex][-1,1][/tex]
⇒ [tex]-1\leq sin(2x-\pi )\leq 1[/tex]
⇒ [tex](\frac{1}{2} )(-1)\leq sin(2x-\pi )\leq( 1)(\frac{1}{2} )[/tex]
⇒ [tex]\frac{-1}{2} \leq sin(2x-\pi )\leq\frac{1}{2}[/tex]
Hence we can conclude that the range of the function f(x) is [-1/2, 1/2].
Learn more about range of a function here
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2.34−1.7*0.2 = I am very confused
Answer:
2.34-1.7*0.2=2
Step-by-step explanation:
Well to solve this, we need to use PEMDAS:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Multiplication comes first before subtraction. You can do long multiplication for this and multiply 1.7 and 0.2 together. Once done that, the product of those 2 numbers are 0.34.
Now 2.34-0.34=2.00
Our answer is 2.
Answer:
2
Step-by-step explanation
1.7 x 0.2 = 0.34
2.34-0.34=2
A single card is drawn at random from a standard 52 card deck. Work out in its simplest
Answer:
1/52
Step-by-step explanation:
