Answer:
y = 15Step-by-step explanation:
Question:
4(y - 3) = 48
1. Distribute
4y - 12 = 48
2. Simplify Like terms
4y - 12 = 48
+ 12 + 12
4y = 60
3. Solve
4y = 60
/4 /4
y = 15
4. Check:
4(y - 3) = 48
4((15) - 3) = 48
4(12) = 48
48 = 48 Correct!
Hope this helped,
Kavitha
Answer:
[tex]y=15\\[/tex]
Step 1:
To find y, we first have to multiply [tex]4(y-3)[/tex]. When we do that (4 * y, 4 * - 3), we get [tex]4y-12[/tex].
Step 2:
Our equation looks like this now:
[tex]4y-12=48[/tex]
To solve this equation, we have to add 12 on both sides so we can cancel out the -12 on the left side of the equation.
[tex]4y-12(+12)=48(+12)[/tex]
[tex]4y=60[/tex]
Now, we can divide 4 on both sides to get y by itself.
[tex]4y/4\\60/4[/tex]
[tex]y=15[/tex]
Simplify 3 (2x + 1) - 2 (x + 1)
Let's simplify step-by-step.
3(2x+1)−2(x+1)
Distribute:
=(3)(2x)+(3)(1)+(−2)(x)+(−2)(1)
=6x+3+−2x+−2
Combine Like Terms:
=6x+3+−2x+−2
=(6x+−2x)+(3+−2)
=4x+1
4x+1 is the answer to the question
is any answers loading for you guys or is it just me
Answer:
not just you
Step-by-step explanation:
The distance S that a certain object falls from a height of 350 ft in T seconds is given by the following formula.
S = 350 - 16t^2 + vt
Find S when T = 2 and V = -4
S = ??ft
Answer:
278 feet.
Step-by-step explanation:
S = 350 - 16t^2 + vt
t =2; v = -4.
S = 350 - 16 * (2)^2 + 2 * (-4)
S = 350 - 16 * 4 - 8
S = 350 - 64 - 8
S = 350 - 72
S = 278 feet.
Hope this helps!
Antisocial personality disorder (ASPD) is characterized by deceitfulness, reckless disregard for the well-being of others, a diminished capacity for remorse, superficial charm, thrill seeking, and poor behavioral control. ASPD is not normally diagnosed in children or adolescents, but antisocial tendencies can sometimes be recognized in childhood or early adolescence. James Blair and his colleagues have studied the ability of children with antisocial tendencies to recognize facial expressions that depict sadness, happiness, anger, disgust, fear, and surprise. They have found that children with antisocial tendencies have selective impairments, with significantly more difficulty recognizing fearful and sad expressions.
Suppose you have a sample of 40 14-year-old children with antisocial tendencies and you are particularly interested in the emotion of surprise. The average 14-year-old has a score on the emotion recognition scale of 11.80. (The higher the score on this scale, the more strongly an emotion has to be displayed to be correctly identified. Therefore, higher scores indicate greater difficulty recognizing the emotion). Assume that scores on the emotion recognition scale are normally distributed.
You believe that children with antisocial tendencies will have a harder time recognizing the emotion of surprise (in other words, they will have higher scores on the emotion recognition test).
What is your null hypothesis stated using symbols? ________
What is your alternative hypothesis stated using symbols? _________
This is a ____ tailed test. Given what you know, you will evaluate this hypothesis using a _______ statistic.
Using the Distributions tool, locate the critical region for a = 0.05.
Answer:
Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 11.80
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 11.80
Step-by-step explanation:
We are given that you have a sample of 40 14-year-old children with antisocial tendencies and you are particularly interested in the emotion of surprise. The average 14-year-old has a score on the emotion recognition scale of 11.80.
Assume that scores on the emotion recognition scale are normally distributed.
Let [tex]\mu[/tex] = true average score on the emotion recognition scale
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 11.80
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 11.80
This a right-tailed test because the higher the score on this scale, the more strongly an emotion has to be displayed to be correctly identified. Therefore, higher scores indicate greater difficulty recognizing the emotion.
We can evaluate this hypothesis using One-sample t-test statistics or One-sample z-test statistics depends on the information given in the question.
If the z-test statistic is used, then the critical region at 0.05 level of significance will be an area more than the critical value of 1.645.
And if the t-test statistic is used, then the critical region at 0.05 level of significance with 39 degrees of freedom will be an area more than the critical value of 1.685.
The null hypothesis should be considered as the [tex]H_0: \mu = 11.80[/tex]
The alternative hypothesis should be considered as the [tex]H_A: \mu > 11.80[/tex]
It is the right-tailed test.
Calculation of the null hypothesis & alternative hypothesis:Since The average 14-year-old has a score on the emotion recognition scale of 11.80.
So here the null hypothesis should be [tex]H_0: \mu = 11.80[/tex]
And, here it is the right-tailed test since there should be higher the score on the given scale, due to this it should strongly an emotion that represent for rightly identified. Also high scores represent the high difficults for recording the emotion.
Learn more about hypothesis here: https://brainly.com/question/18831983
FIRST ANSWER GETS BRAINLIEST!!!
How do you write 0.00696 in scientific notation?
Answer:
6.96x10^-3
Step-by-step explanation:
0.00696
We move the decimal point to between 6 and 9
since the number with the decimal point should be between 0 and 9.
Then we count the numbers.
6.96x10^-3.
Hope this helps. ❤❤❤
Answer: 6.96 * 10^(-3)
Step-by-step explanation:
In scientific notation, you multiply a number that has a value in the ones place and no value in the tens place by 10 raised to an exponent.
Hope it helps <3
If ABC~DEF and the scale factor from ABC to DEF is 3/4, what is the length of DF?
Answer:
the length of DF = 3/4 AC
see below for explanation
Step-by-step explanation:
ABC is said to be approximately equal to DEF
The scale factor from ABC to DEF = 3/4
From the question, we can tell the original and new shape is a triangle because the lettering to indicate the vertices for both are 3.
We can deduce from the question, ΔABC was dilated to form ΔDEF
In dilation, the length of each of the corresponding side of the new figure is equal to the multiplication of each of the corresponding sides of the old figure and thee scale factor.
In the absence of cordinates for each vertices and length of each sides, ΔABC has 3 sides :
AB, BC and AC
ΔDEF has 3 sides : DE, EF and DF
If AB corresponds to DE
BC corresponds to EF
AC corresponds to DF
Then:
length DE = scale factor × AB = 3/4 AB
length EF = scale factor × BC = 3/4 BC
length DF = scale factor × AC = 3/4 AC
Therefore, the length of DF = 3/4 AC
what is the world smallest number that is divisible by all the numbers 1,2,3,4,5,6,7,8,9,10?
Answer:
1
Step-by-step explanation:
1 ÷ 1 = 1
2 ÷ 1 = 2
3 ÷ 1 = 3
4 ÷ 1 = 4
5 ÷ 1 = 5
6 ÷ 1 = 6
7 ÷ 1 = 7
8 ÷ 1 = 8
9 ÷ 1 = 9
10 ÷ 1 = 10
Answer:
The world smallest number that is divisible by all the numbers 1,2,3,4,5,6,7,8,9,10 means that all the above numbers can divide that number without a remainder.
From the question the world smallest number that is divisible by the above numbers is
2520Hope this helps you
Karen has 6 more than twice as many newspaper customers as when she started selling newspapers. She now has 98 customers. How many did she have when she started?
Answer:
46 customers
Step-by-step explanation:
If the number of original customers is n, we can write the following equation:
98 = 2n + 6
92 = 2n
46 = n
Please help
ASAP
ANSWERS
A-48.21
B-66.35
C-53.68
D-28.34
Answer:
B
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos54° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{39}{AB}[/tex] ( multiply both sides by AB )
AB × cos54° = 39 ( divide both sides by cos54° )
AB = [tex]\frac{39}{cos54}[/tex] ≈ 66.35 → B
Eight women and six men apply for a job at Google. Four of the applicants are selected for interviews. Let X denote the number of women in the interview pool. a) Give (explicitly) the probability mass function for X. Also describe a plot of F(x). b) Give (explicitly) the cdf, F(x), for X. Also show a plot of it. c) Determine the probability that more women are interviewed than men.
Answer:
See below
Step-by-step explanation:
images attached showing all working
a) The possible values of X are as follows
X = {0,1,2,3,4}
P(x) = P(X=x)
b) The cdf in this case, as in the F(x), comes out to be a step function graph on the basis of values obtained from the probability mass function.
c) To find out the probability when more women are interviewed than me, add together the matrices from when value of X is equal to 2, 3 and 4 (from part a).
helppppppppppppp pleaseeeeeeeeeeeeee
Answer:
work is shown and pictured
Factor d^2-10d+10 by grouping
Answer:
(d-5-√15)(d-5+√15)
Step-by-step explanation:
Which is the recommended method for reading your math textbook most effectively? a. read, question, summarize, practice b. highlight, skim, ask, and review c. preview, read, summarize, and review
Answer: a. read, question, summarize, practice
Step-by-step explanation:
This may be subjective, but the most efficient method usually is:
> Read:
Obviously the first step is read, if there is something that you do not understand, keep reading (but take note of all the things that you don't understand), is important that you have a complete overview on the topic that you are studying
> Question:
Now is time to ask about the things that you did not understand in the first read, always when you do not fully understand something, is a good habit to ask about it, this is the best and easiest way to learn.
> Summarize:
Now that you understand all the text (or at least most of it) is the moment to summarize your new knowledge: Write all the new equations that you learned, also write for what they are for, when they can be useful, etc.
This is what you will use to solve exercises, so you should be clear when writing.
> Practice:
This is one of the most important parts, here is where you put in practice your new knowledge. Here you may find some problematic situations where you need to be inventive with your equations, which will allow you to learn new ways to use your equations, so this is a really important step.
So the correct option is A.
PLEASE HELP Two prisms are composed to form a V shape. The thickness of each prism is 1 unit, and width of each prism is 2 units. If the length of one prism is greater than the length of the other prism by 1 unit and the total volume of the figure is 30 cubic units, what are the lengths of the prisms?
Answer:
7 units, 8 units
Step-by-step explanation:
Apparently, the cross section of each prism is a rectangle 1 unit by 2 units. Hence the total length will be ...
(30 units³)/((1 unit)(2 units)) = 15 units
Two numbers that differ by 1 and have a sum of 15 are 7 and 8.
The lengths of the prisms are 7 units and 8 units.
Click on the solution set below until the correct one is displayed.
Answer:
{ } or empty set.
Step-by-step explanation:
The solutions should be where the two lines intersect, but in this case, the parallel lines never intersect. That means that they have no solutions.
Hope this helps!
Answer:
{ } or empty set
Step-by-step explanation:
It's because these lines are parallel so they don't intersect to give you a coordinate.
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Third-degree, with zeros of −3, −1, and 2, and passes through the point (1,10).
Answer:
[tex]\Large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}[/tex]
Step-by-step explanation:
Hello,
Based on the indication, we can write this polynomial as below, k being a real number that we will have to identify (degree = 3 and we have three zeroes -3, -1, and 2).
[tex]\Large \boxed{k(x+3)(x+1)(x-2)}[/tex]
We know that the point (1,10) is on the graph of this function, so we can say.
[tex]k(1+3)(1+1)(1-2)=10}\\\\4*2*(-1)*k=10\\\\-8k=10\\\\k=\dfrac{10}{-8}=-\dfrac{5}{4}[/tex]
Then the solution is:
[tex]\large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A study reports the mean change in HDL (high-density lipoprotein, or "good" cholesterol) of adults eating raw garlic six days a week for six months. The margin of error for a 95% confidence interval is given as plus or minus 7 milligrams per deciliter of blood (mg/dl). This means tha:_________a) There is a 95% probability that the true population mean is within 7 mg/dl. b) The study used a method that gives a results within 7 mg/dl of the truth about the population in 95% of all samples. c) 95% percent of the population has changed their HDL after eating raw garlic six days a week for six months. d) We can be certain that the study results is within 7 mg/dl of the truth about the population. e) We could be certain that the study result is within 7 mg/dl of the truth about the population if the conditions for inferences were satisfied.
Answer:
Option B
Step-by-step explanation:
The margin of error describes how many percentage points the results will differ from the real population value, thus 'the margin of error for a 95% confidence interval is given as plus or minus 7 milligrams per deciliter of blood (mg/dl)' can be interpreted as 'The study used a method that gives a results within 7 mg/dl of the truth about the population in 95% of all samples.'
Applications of exponential functions need help ASAP PlZ
Answer:
Second choice is correct.
Step-by-step explanation:
Simple interest = $12600
Compounded interest = $14656
Best Regards!
Adam is going to cook a turkey for 14 people
Answer:
they divied the turkey into 14 pices
Step-by-step explanation:
A positive integer is 2 less than another. If the sum of the reciprocal of the smaller and twice
the reciprocal of the larger is 11/15,
then find the two integers.
Answer:
Step-by-step explanation:
Let x represent the smaller integer.
Let y represent the larger integer.
A positive integer is 2 less than another. It means that
y = x + 2
If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 11/15, it means that
1/x + 2/y = 11/15- - - - - - - - - - 1
Substituting y = x + 2 into equation 1, it becomes
1/x + 2/(x + 2) = 11/15
Considering the left hand side of the equation, it becomes
(x + 2 + 2x)/x(x + 2)
Therefore,
(3x + 2)/(x² + 2x) = 11/15
Cross multiplying, it becomes
15(3x + 2) = 11(x² + 2x)
45x + 30 = 11x² + 22x
11x² + 22x - 45x - 30 = 0
11x² - 23x - 30 = 0
11x² + 10x - 33x - 30 = 0
x(11x + 10) - 3(11 + 10) =℅0
(x - 3)(11x + 10) = 0
x - 3 = 0 or 11x + 10 = 0
x = 3 or x = - 10/11
Since it us a positive integer, the smaller integer is 3 and the larger integer is 3 + 2 = 5
Answer: Let x represent the smaller integer.Let y represent the larger integer.A positive integer is 2 less than another. It means that y = x + 2 If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 11/15, it means that 1/x + 2/y = 11/15- - - - - - - - - - 1Substituting y = x + 2 into equation 1, it becomes 1/x + 2/(x + 2) = 11/15Considering the left hand side of the equation, it becomes(x + 2 + 2x)/x(x + 2) Therefore,(3x + 2)/(x² + 2x) = 11/15Cross multiplying, it becomes15(3x + 2) = 11(x² + 2x)45x + 30 = 11x² + 22x11x² + 22x - 45x - 30 = 011x² - 23x - 30 = 011x² + 10x - 33x - 30 = 0x(11x + 10) - 3(11 + 10) =℅0(x - 3)(11x + 10) = 0x - 3 = 0 or 11x + 10 = 0x = 3 or x = - 10/11Since it us a positive integer, the smaller integer is 3 and the larger integer is 3 + 2 = 5
Step-by-step explanation:
what is the measure of SR?
Answer:
RS = 8
Step-by-step explanation:
Given:
Secant QU = internal secant segment PU + external secant segment PQ = 7 + 9 = 16
Secant QS = internal secant segment RS + external secant segment RQ = (3x - 5) + 8
To find the measure of RS, we need to find the value of x.
Thus, recall the "Two Secant Theorem"
According to the theorem,
(RS + RQ)*RQ = (PU + PQ)*PQ
Thus,
[tex] (3x - 5 + 8)*8 = (7 + 9)*9 [/tex]
[tex] (3x + 3)*8 = (16)*9 [/tex]
[tex] 24x + 24 = 144 [/tex]
Subtract 24 from both sides
[tex] 24x + 24 - 24 = 144 - 24 [/tex]
[tex] 24x = 120 [/tex]
Divide both sides by 24
[tex] \frac{24x}{24} = \frac{120}{24} [/tex]
[tex] x = 5 [/tex]
Plug in the value of x into (3x - 5) to find the measure of RS
RS = 3(5) - 5 = 15 - 7
RS = 8
The soldering iron’s highest temperature setting is 400 °F. What is the soldering iron’s temperature in Centigrade?
Answer:
204.4(repeating) degrees
Step-by-step explanation:
The equation to go from F to C, is (F-32)×5/9. So 400-32 is 368.
368×5=1840
Than 1840/9=204.44 degrees. The 4 is repeating at the end.
The assistant principal set up chairs in the auditorum for graduation. She placed
the chairs in 24 rows with 28 chairs in each row. How many chairs are set up in
the auditorium
Answer:
672 chairs
Step-by-step explanation:
24 × 28 = 672
hope this helps
Can you figure out the missing number in this sequence? Type your answer below!
88511,16351,?,10251
Answer:
731`55
Step-by-step explanation:
*Step-by-step explanation:*
The given sequence:
88511, 16351, ?, 10251
To find, the missing number (?) = ?
The pattern follow:
1. To Add the first 2 digits in the number .
2. Subtract digit 3 from Digit 2 .
3. The multiply digit 3 and 4 .
4. To divide digit 4 by 3.
16351 ⇒ 8 + 8 = 16, 8 - 5 = 3, 5 × 1 = 5 and \dfrac{1}{1} =111=1
= 16351
? ⇒ 1 + 6 = 7, 6 - 3 = 3, 3 × 5 = 15 and \dfrac{5}{1}15 = 5
= 73155
10251 ⇒ 7 + 3 = 10, 3 - 1 = 2, 1 × 5 = 5 and \dfrac{5}{5}55 = 1
= 10251
∴ The missing number of the given sequence = 73155
Thus, the missing number of the given sequence is 73155.
The third number in the sequence is : 73155
The given sequence is:
88511, 16351, ?, 10251
Now the pattern to find the missing value is:
Add, subtract, multiply and then divide.
These patterns are applied on the previous number's double digits to get the next number of the sequence.
Example:
Take 88511.
First pair (8,8): Add them: 16
Second pair (8,5): Subtract them: 8-5 = 3
Third pair: (5,1): Multiply them: 5
Fourth pair(1,1): Divide them: 1/1 = 1
Thus the next number of the sequence we get is 16351.
Similarly, doing it on 2nd term (16351) to find the missing third term:
Add (1,6): 7
Subtract (6,3): 3
Multiply (3,5): 15
Divide (5,1): 5
Thus the third number in the sequence is : 73155
Learn more here:
https://brainly.com/question/3000144
The height of an object dropped from the top of a 144-foot building is given by . How long will it take the object to hit the ground?
They left off the equation but we can know it's
y(t) = h₀ - g t² / 2
That's
y(t) = 144 - 16 t²
It hits the ground when
0 = 144 - 16 t²
16 t² = 144
t² = 144 / 16 = 9
t = 3 seconds
Answer: 3 seconds
Values for relation g are given in the table. Which ordered pair would be found in the inverse of g? X Y 2 2 3 5 4 9 5 13 A: (4,9) B:(-3.-5) C:(13,5) D:(-2,-2)
Answer:
D (13,5)
Step-by-step explanation:
X 2 3 4 5
Y 2 5 9 13
So the ordered pairs are (2,2),(3,5), (4,9), (5,13)
and the ordered pairs for the inverse are
(2,2),(5,3), (9,4), (13,5)
from which D (13,5) is found among the options.
Answer:
b
Step-by-step explanation:
Could someone answer the question with the photo linked below? Then explain how to solve it?
Answer:
Hey there!
Pythagorean Theorem:
[tex]a^2+b^2=c^2\\[/tex]
Let 6 be a, and 11 be b.
[tex]6^2+11^2=c^2\\[/tex]
[tex]36+121=c^2\\[/tex]
[tex]157=c^2[/tex]
[tex]\sqrt{157} =c[/tex]
Hope this helps :)
Answer:
[tex]12.529[/tex]
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {6}^{2} + {11}^{2} = {c}^{2} \\ 36 + 121 = {c}^{2} \\ 157 = {c}^{2} \\ \sqrt{157} = {c}^{2} \\ c = 12.529[/tex]
[tex]hope \: it \: helps \: < 3[/tex]
A city council consists of eight Democrats and eight Republicans. If a committee of six people is selected, find the probability of selecting two Democrats and four Republicans.
(Type answer a fraction Simplify your answer.)
Answer:
The probability is [tex]P[ D n R] = 0.196[/tex]
Step-by-step explanation:
From the question we are told that
The number of Democrats is [tex]D = 8[/tex]
The number of republicans is [tex]R = 8[/tex]
The number of ways of selecting selecting two Democrats and four Republicans.
[tex]N = \left {D} \atop {}} \right. C_2 * \left {R} \atop {}} \right. C_1[/tex]
Where C represents combination
substituting values
[tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1[/tex]
[tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8!}{(8-2)! 2!} * \frac{8! }{(8-4)! 1 !}[/tex]
=> [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8!}{(6)! 2!} * \frac{8! }{(6)! 1 !}[/tex]
=> [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8 * 7 * 6!}{(6)! 2!} * \frac{8*7 *6! }{(6)! 1 !}[/tex]
=> [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8 * 7 }{ 2*1 } * \frac{8*7 }{ 1 *1 }[/tex]
=> [tex]N = 1568[/tex]
The total number of ways of selecting the committee of six people is
[tex]Z = \left {D+R} \atop {}} \right. C_6[/tex]
substituting values
[tex]Z = \left {8+8} \atop {}} \right. C_6[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6[/tex]
substituting values
[tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16! }{(16-6) ! 6!}[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16 *15 *14 * 13 * 12 * 11 * 10! }{10 ! 6!}[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16 *15 *14 * 13 * 12 * 11 }{6* 5 * 4 * 3 * 2 * 1}[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6 = 8008[/tex]
The probability of selecting two Democrats and four Republicans is mathematically represented as
[tex]P[ D n R] = \frac{N}{Z}[/tex]
substituting values
[tex]P[ D n R] = \frac{1568}{8008}[/tex]
[tex]P[ D n R] = 0.196[/tex]
what is the average when you add 122.99%, 108.46% and 102.65%? I don't know how to add percentages.
Answer:
111.33667
Step-by-step explanation:
You add percentages just like you would any other number.
122.9% + 108.46% + 102.65% = 334.01%
334.01%/3 = 111.33667
Luke is organising a camping trip for the youth club. He is looking at the temperature and rainfall charts for Brighton and Newquay. What is the probability of it raining in July in Brighton? Give your answer as a fraction.
Answer:
The answer is 15.6/31 or 1/2
Step-by-step explanation:
The data in the question is sufficient to find an answer for it.
1. I look at the temperature and rainfall chart for Brighton, United Kingdom.
2. Check for rainy season and dry season.
3. The rainy season lasts approximately 5 months while the dry season (which still has some rainfall) lasts approximately 7 months. All together, 12 months of the calendar year.
4. July happens to fall within the dry season. The temperature and rainfall statistics are observed.
The number of rainfall days is 15.6 and we know there are 31 days in July.
If the approximate number of days it rains in Brighton, in July, is 15.6 then the probability of rainfall in the month is 15.6/31 which is = 0.503 or 0.5
Therefore, there's a 50% chance of having rainfall in Brighton, on any day in the month of July.
In fraction, 0.5 = 1/2