Answer:
10 centimeters.
Step-by-step explanation:
First, we need to remember what's the formula to get the volume of a rectangular solid and a cube.
The volume of the first equals:
Volume = Length x Width x Height
While the volume of the cube is:
[tex]Volume = a^{3}[/tex] where a is the edge.
We are given the measures of the rectangular solid so we can calculate its volume:
[tex]Volume= (20)(5)(10)=1000[/tex] cubic cms.
Now, we know that both the volume of the rectangular solid and the cube are the same so we will use this information to calculate the edge of the cube.
[tex]1000=a^3 \\\sqrt[3]{1000} =\sqrt[3]{a^3} \\10=a[/tex]
Thus the length of an edge of the cube is 10 centimeters
in a 10 team league, each teams play every other team exactly twice. find the total number of games played in the league
Addition can be defined as the process of adding two numbers. The total number of games played in the league is 90.
What is Addition?Addition can be defined as the process of adding two numbers such that the result is the combined value of the two numbers.
Given that in a 10-team league, each team play every other team exactly twice. Therefore, the total number of games that will be played by the first team is 18, similarly, the number of games that will be played by the second team is 16.
Therefore, as mentioned above the series will continue with a common difference of -2 and will continue till 0. Thus, the total number of games played in the league is,
Total number of games = 18 + 16 + 14 + 12 + 10 + 8 + 6 + 4 + 2 = 90
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Helpppppppppppppppp plzzz
Answer:
$0.56, or 56¢.
Step-by-step explanation:
According to the picture, there are two dimes, two nickels, a penny, and a quarter.
A penny is worth $0.01.
A nickel is worth $0.05.
A dime is worth $0.10.
A quarter is worth $0.25.
2(0.1) + 2(0.05) + (0.01) + (0.25) = 0.2 + 0.1 + 0.01 + 0.25 = 0.3 + 0.26 = 0.56.
So, Vivian is using $0.56, or 56¢, to buy a toy. That's a cheap one!
Hope this helps!
NASA is painting the nose cone of a sounding rocket with a special sealant which reduces the air-drag on the rocket. If they need to do two coats of the sealant, how many square feet are they painting? Use π = 3.14.
Answer:
The formula for the lateral surface area (LSA) of a right cone is:
LSA = π x r x l
where: r as radius, and l as the slant height of the cone
If NASA need to do two coats of the sealant, the number of square feet that they are painting is: 2 x LSA = 2 x π x r x l
Step-by-step explanation:
Answer:
56.5 ft^2
Step-by-step explanation:
After you calulate the the surface area and double it, subtract the area of the circle.
Please help me understand this. Thank you! Gina has borrowed 100 songs from her friend. She plans to download an equal number of songs on her music player each week for 5 weeks. The graph shows the number of songs left to download, y, for a certain number of weeks, x: A graph titled Song Downloading shows the Number of Weeks on x-axis and Number of Songs Left to Download on the y-axis. The x-axis scale is shown from 0 to 5 at increments of 1, and the y-axis scale is shown from 0 to 140 at increments of 20. A straight line joins the ordered pairs 0, 100 and 1, 80 and 2, 60 and 3, 40 and 4, 20 and 5, 0. Part A: What is the rate of change and initial value of the function represented by the graph, and what do they represent in this scenario? Show your work to find the rate of change and initial value. (6 points) Part B: Write an equation in slope-intercept form to model the relationship between x and y. (4 points)
Answer:
Rate of Change/Slope = -20
Equation: y= -20x +100
Step-by-step explanation:
A. We know the rate of change is also known as the slope. If we used the slope formula to find the slope we can find the Rate of Change.
[tex]\frac{y2 - y1}{x2 - x1} = \frac{100-80}{1-2} = \frac{20}{-1} = -20[/tex]
B. Since we know the slope and 1 point on the graph we can substitute them in for 'b'
(0,100)
(100)=-20(0) + b
b = 100
Since we know the slope and the b value we can write the equation:\
y = -20x +100
The rate of change refers to the slope of the line, that is the change in y-axis per unit change in the value on the x-axis. Hence, the rate of change is :
Slope = - 20y = -20x + 100Slope = Rise / Run Rise = (y2 - y1) = (0 - 100) = - 100Run = (x2 - x1) = (5 - 0) = 5Slope = - 100 / 5 = - 20
General form of a slope - intercept relation :
y = bx + cThe intercept, c can be calculated thus:
100 = - 20(0) + c
100 = 0 + c
c = 100
Hence, the slope - intercept equation will be y = - 20x + 100
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A club has 16 members, included Mary and Peter. If two representative are
randomly selected from those members, find the probability that
(d) Mary or Peter is chosen.
Answer:
12.5 percent; 2/16; 1/8
Step-by-step explanation:
Peter and Mary make up 2 of the clubs members, so the probability that they are chosen is 2/16. This simplifies to 1/8, and in decimal form is .125. Therefore, the percentage form of the probability they are chosen is 12.5 percent.
Two students use different methods to solve this multiplication problem:
3/4*-4 2/9
Read each of their methods below and then enter numbers to correctly complete their
work.
Answer/Step-by-step Explanation:
Given, [tex]\frac{3}{4}*-4\frac{2}{9}[/tex]
Ivy solves this problem by writing each number as a fraction and then multiplies as shown below:
[tex] \frac{3}{4}*-4\frac{2}{9} = \frac{3}{4}* -\frac{38}{9} [/tex]
[tex] = \frac{3}{4}*-\frac{38}{9} = -\frac{3*38}{4*9} = -\frac{1*19}{2*3}[/tex]
[tex]= -\frac{19}{6}[/tex]
Fabian solves this problem by writing the mixed number as a sum and applies the distributive method of multiplication as shown below:
[tex] \frac{3}{4}*-4\frac{2}{9} = \frac{3}{4}(-4 + -\frac{2}{9}) [/tex]
[tex] = \frac{3}{4}*-4 + \frac{3}{4}*-\frac{2}{9} [/tex]
[tex] = -\frac{3}{1} + \frac{1}{2}*-\frac{1}{3} [/tex]
[tex] = -3 + (-\frac{1}{6}) [/tex]
[tex] = -3 - \frac{1}{6} = -3\frac{1}{6} [/tex]
At the beginning of the day the stock market goes up 60 1/2 points and stays at this level for most of the day. At the end of the day the stock market goes down 100 1/4 points from the high at the beginning of the day. What is the total change in the stock market from the beginning of the day to the end of the day?
Answer: it would be 40/2 or 20, but im not sure.
Step-by-step explanation: so what I did was: 100 1/4 - 60 1/2: 100 - 60 = 40 and then I subtracted 1-1 which is 0 then 4-2 which is 2, and got 40/2 or just simplify which will be equal to 20
If the geometric mean of a and 120 is 60, find the value of a.
Answer:
The answer is option 4.
Step-by-step explanation:
Given that the mean formula is total score/number of score. So we can assume that total score is (a+120), number of score is 2 and the mean value is 60. Then you have to find the value of a :
[tex] \frac{a + 120}{2} = 60[/tex]
[tex]a + 120 = 60 \times 2[/tex]
[tex]a + 120 = 120[/tex]
[tex]a = 120 - 120[/tex]
[tex]a = 0[/tex]
[tex] \text{ Geometric mean of two numbers } a \text{ and } b , \text{ where } a,b>0 \text{ is given by } G= \sqrt{ab}[/tex]
[tex] \sqrt{a\cdot120}=60 [/tex]
[tex] \implies 60 \cdot 2 \cdot a=60\cdot 60 \qquad \text{Squaring both sides} [/tex]
[tex] \implies a =30 [/tex]
help8b2 • 2b3 a) 16b-2 ,b) 16b6 ,c) 16b-4 ,d) 16b5
Answer:
16b^5
Step-by-step explanation:
8b^2×2b^3
= 16b^2+3
= 16b^5
Answer:
D)16b5
Step-by-step explanation:
8b2×2b3
= 16b2+3
= 16b5
Please, i need answer fast :< no steps, ILL GIVE BRAINLIEST TOO :)
Answer:
[tex]\huge\boxed{Area = 24\ square\ units}[/tex]
Step-by-step explanation:
Area of parallelogram = Base * Height
Where Base = 6 , Height = 6
Area = 6 * 4
Area = 24 square units
Answer:
24 square units
Step-by-step explanation:
the area formula is A=bh
b=6
h=4
A=4*6
A=24
A student is given three triangles and must determine which triangles are
congruent. The student is also told that B= ZE = ZY. Which of the
following statements is true?
Answer:
D.
Step-by-step explanation:
From the given triangles above, there are just 2 triangles that look the same, that is ∆ABC and ∆XYZ.
∆ABC has two sides (AB and BC), and an included angle (angle B), which are equal to the two sides (YZ and YX) and the included angle (angle Y) of ∆XYZ as ∆ABC is a reflection of ∆XYZ.
Therefore, according to the SAS Theorem of congruency, ∆ABC is congruent to ∆XYZ.
Which of the following are natural numbers? There may be more than one correct answer. Select all that apply. If only one answer is correct, select "only" and the answer that applies. A.) only B.) −1,−2,−3,… C.) 7,8,9,… D.) fractions E.) 22
Answer:
Option C and option E
Step-by-step explanation:
C.) 7,8,9,…
E.) 22
Natural numbers are also called counting numbers.
They begin from 1, 2, 3 to infinity.
Natural numbers are greater than zero (0)
They do not have decimal point in them.
They are positive integers, as such they do not have minus
Natural numbers can include commas when they are large like 3,000
Alonso went to the market with \$55$55dollar sign, 55 to buy eggs and sugar. He knows he needs a package of 121212 eggs that costs \$2.75$2.75dollar sign, 2, point, 75. After getting the eggs, he wants to buy as much sugar as he can with his remaining money. The sugar he likes comes in boxes that each cost \$11.50$11.50dollar sign, 11, point, 50.
Answer:
2.75+11.50S[tex]\leq[/tex]55
4
Step-by-step explanation:
The Total amount of money Alonso went to the market with is: = $55
Items to be bought includes:
eggssugarAlonso knows that:
A pack of 12 eggs costs = $2.75 Now, he wants to use the remaining amount to purchase as much sugar as possibleRequirement for his taste for sugar:
a box of sugar he likes = $11.50From this information, the objective would be to determine the number of sugar he can purchase with the money left after he has already bought the eggs.
To start with, the amount of money left after buying the eggs is:
= $55 - $2.75
= $52.25
Now, if a box of sugar he likes cost = $11.50
Then he will be able to purchase (x( bost of sugar with = $52.50
Now, to determine the number of boxes of sugar he can purchase, we have:
1 box of sugar = $11.50
x(box) of sugar = $52.25
∴
[tex]\mathbf{x (box) of sugar = \dfrac{\$52.25 \times 1 box of sugar }{\$11.50}}[/tex]
x = 4.5 box of sugar
Therefore, after buying a pack of 12 eggs for = $2.75, Alonso will be able to buy [tex]\mathbf{ 4\dfrac{1}{2}}[/tex] or 4.5 boxes of sugar.
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help plz I think the first one is correct but I'm not sure
The left side 10x+25 is the cost expression for Black Diamond, while the right hand side 5x+50 is for Bunny Hill. The x is the number of hours.
7 kids on the basketball team return sick from a weekend playing games at Lakenheath High school with a virus. The aggressive virus spreads at 130% each day. How long many days till 500 students are sick at school?
Answer:
It would take 6 days for 500 students to be affected.
Step-by-step explanation:
Given that:
1. Seven kids returned with the virus.
2. The aggressive virus spreads at 130% each day.
We want to find how many days until 500 students are infected by the virus.
First day:
7 students have the virus, 130% of 7 student will contract the virus again.
130% of 7 = (130/100) × 7
= 1.3 × 7 = 9.1 ≈ 9
9 new students are affected
New total affected = 7 + 9 = 16 students.
Day 2:
Affected = 1.3 × 16 = 20.8 ≈ 20
New total affected = 20 + 16 = 36
Day3
Affected = 1.3 × 36 = 46.8 ≈ 46
New total affected = 36 + 46 = 82
Day4
Affected = 1.3 × 82 = 106.6 ≈ 106
New total affected = 106 + 82 = 188
Day5
Affected = 1.3 × 188 = 244.4 ≈ 244
New total affected = 244 + 188 = 432
Day6
Affected = 1.3 × 432 = 561.6 ≈ 561
New total affected = 561 + 432 = 993
Therefore, it would take 6 days for 500 students to be affected.
Complete the table. At least the first few so I understand how to do it
Answer:
What we need to do is simply multiply the values in both columns e.g 4 * 3/36 = 12/36
Please check explanation for complete answer
Step-by-step explanation:
Here, we are concerned about filling the empty columns of the table.
What we want to do here is simply straightforward. All we need to do is to
multiply the values of x by the values of P(x) in each of the individual rows.
Also recall, we do not need to reduce the fractions.
So we have;
2. 3 * 2/36 = 6/36
3. 4 * 3/36 = 12/36
4. 5 * 4/36 = 20/36
5. 6 * 5/36 = 30/36
6. 7 * 6/36 = 42/36
7. 8 * 5/36 = 40/36
8. 9 * 4/36 = 36/36
9. 10 * 3/36 = 30/36
10. 11 * 2/36 = 22/36
11. 12 * 1/36 = 12/36
33. Find the area of the parallelogram above?
Answer:
120
Step 1: Value of triangle's sides
First, we need to find out the height of the parallelogram, since the equation to find the area is b * h. To find the height, we must use the Pythagorean Theorem to find the sides of the triangle on the right. Since the base is 15 cm, we know that the top is also 15 cm, so we subtract 9 from 15 to get 6. One of the sides of the triangle is 6, and the hypotenuse (longest side of the triangle) is 10.
Step 2: Pythagorean Theorem
[tex]a^2+b^2=c^2[/tex]. This is the equation we always use if we want to find the sides of a right triangle. Here, a = 6 and c = 10. In the formula, a and c needs to be squared to find b.
[tex]10^2 (10*10)=100\\6^2 (6*6)=36\\\\c^2=100\\a^2=36[/tex]
Now, we have to subtract c^2 from a^2 to get b^2.
[tex]100-36=b^2\\100-36=64\\b^2=64[/tex]
Finally, we find the square of 64 and that is 8.
8 is our height.
Step 3: Finding the area
This last step is really simple. to find the area of this parallelogram, we just have to multiply the height (8) by the base (15).
[tex]8*15=120\\Area=120[/tex]
Our area is 120.
Answer:
120
Step-by-step explanation:
at first you need to calculate h Using the Pythagorean relation
10
[tex]10 { }^{2} = 6 {}^{2} + x {}^{2} [/tex]
[tex] x {}^{2} = 100 - 36 = 64[/tex]
[tex]x = 8 = h[/tex]
area=
[tex]8 \times 15 = 120[/tex]
. A salesman sold 300 bags of maize to a retailer at Kshs .2000 each .He was given a commission of 3%.The salesman allowed a discount of 0.2% on the maize sold. This discount was deducted from his commission. (a) Calculate (i) The discount allowed
Answer:
The discount allowed per bag is kshs 4
while the discount allowed on all the 300 bags is kshs 1,200
Step-by-step explanation:
Here, we are interested in calculating the discount allowed on the sales of the bag of maize.
From the question, we are told that the sales man allowed a discount of 0.2% on the maize sold.
Now, to find the amount of this, we proceed as follows;
What we simply need to do is to find 0.2% of the each of the price of the maize bags, and then we can proceed to find the total discount given on all maize bags sold.
The discount on each bag of maize would be;
0.2% of kshs 2000
That would be;
0.2/100 * 2,000 = 400/100 = kshs 4
Since there are 300 bags, the total amount of discount allowed is 300 * kshs 4 = kshs 1,200
Sum and Product of zeroes of the quadratic polynomial 16s² - 16s + 4 respectively is:Sum and Product of zeroes of the quadratic polynomial 16s² - 16s + 4 respectively is:
Answer:
The sum and product of zeroes are 1 and 1/4, respectively.
Step-by-step explanation:
To determine the zeroes of the quadratic polynomial, let equalize the polynomial to zero and solve in consequence:
[tex]16\cdot s^{2}-16\cdot s + 4 = 0[/tex]
By the General Quadratic Formula:
[tex]s_{1,2} = \frac{16\pm \sqrt{(-16)^{2}-4\cdot (16)\cdot (4)}}{2\cdot (16)}[/tex]
[tex]s_{1,2} = \frac{1}{2}[/tex]
Which means that zeroes are [tex]s_{1}=s_{2}=\frac{1}{2}[/tex].
The sum and product of zeroes are, respectively:
[tex]s_{1}+s_{2} =\frac{1}{2}+\frac{1}{2}[/tex]
[tex]s_{1}+s_{2} = 1[/tex]
[tex]s_{1}\cdot s_{2} = \left(\frac{1}{2} \right)^{2}[/tex]
[tex]s_{1}\cdot s_{2} = \frac{1}{4}[/tex]
The sum and product of zeroes are 1 and 1/4, respectively.
which of the following could be the value of |x-3|+4 for some value of x? A) -2 B) 1 C) 3 D) 5
Answer:
5
Step-by-step explanation:
|x-3|+4
The minimum value that an absolute value can take is zero
0+4
4
The smallest value is 4
The answer must be 4 or greater
The only answer that is possible is 5
what is 0.7619047619 as a fraction?
Answer:
7619047619
10000000000
Step-by-step explanation:
Yeah big numbers:
To write 0.7619047619 as a fraction you have to write 0.7619047619 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
0.7619047619 = 0.7619047619/1 =
7.619047619/10 = 76.19047619/100 =
761.9047619/1000 = 7619.047619/10000 =
76190.47619/100000 = 761904.7619/1000000 =
7619047.619/10000000 = 76190476.19/100000000 = 761904761.9/1000000000 = 7619047619/10000000000
Hope this helps, have a good day :)
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85 POINTS! PLEASE HELP! Explain how to write an equation parallel to the equation y = 2x + 3 and the new line also includes the ordered pair (1,-2).
Answer:
[tex]\huge\boxed{\sf y = 2x -4}[/tex]
Step-by-step explanation:
The given equation is:
y = 2x + 3
Where Slope = m = 2 , Y-intercept = b = 3
Parallel lines have equal slopes
So, Slope of new line = m = 2
Now, Finding y-intercept:
Given Point = (x,y) = (1,-2)
So, x = 1 , y = -2
Putting m, x and y in standard form of equation to get b:
[tex]\sf y = mx+b[/tex]
[tex]\sf -2 = (2)(1) + b\\-2 = 2 + b\\[/tex]
Subtracting 2 to both sides
[tex]\sf b = -2-2\\[/tex]
b = -4
So, the standard form og equation for the new line is :
[tex]\sf y = mx+b[/tex]
[tex]\sf y = 2x -4[/tex]
Answer:
y = 2x - 4
Step-by-step explanation:
the problem is called (slope-intercept form)
the equation of the line is y = mx + b
the equation of a line is given as y = 2x + 3
slope = 2
b = y-intercept is where the line crosses the y-axis = 3
so point (x1, y1) = (1, -2)
by using the equation.
y = mx + b
-2 = 2 (1) + b
-2 -2 = b
therefore b = -4
writing the new equation using the slope intercept form
y = mx + b would be y = 2x + 4
so the equation parallel to the equation y = 2x + 3 is y = 2x - 4
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Addition property of Equality
Step-by-step explanation:
Adding same quantity to both sides of equation is called addition property of equality
WILL GIVE BRAINLIEST
Question 8(Multiple Choice Worth 1 points) (06.04 LC) Choose the correct product of (6x − 2)(6x + 2). A.36x2 + 4 B.36x2 − 24x + 4 C. 36x2 + 24x + 4 D. 36x2 − 4
Answer:
D) 36x²-4
Step-by-step explanation:
36x²+12x-12x-4
36x²-4
[tex](6x - 2)(6x + 2) \\ = {(6x)}^{2} - {(2)}^{2} \\ = {36x}^{2} - 4[/tex]
Answer:
D.
[tex] {36x}^{2} - 4[/tex]
Hope you could understand.
If you have any query, feel free to ask.
Mia’s average driving speed is 6 kilometers per hour faster than Kirk’s. In the same length of time it takes Mia to drive 558 kilometers, Kirk drives only 522 kilometers. What is Mia’s average speed?
Answer:
93km/hr
Step-by-step explanation:
Using the formula Speed = Distance/Time. From the formula we can substitute for time as shown;
Time = Distance/Speed
Let the distance and speed travelled by Mia be Dm ans Ds respectively
Distance travelled by Kirk be Km and and Ks respective.
Time taken be Mia to travel Tm = Dm/Sm
Time taken be Kirk to travel Tk = Dk/Sk
Since it takes the same length of time for both of them to travel, then Tm = Tk. Hence Dm/Sm = Dk/Sk
Given parameters
Dm = 558 kilometers
Dk = 522 kilometres
If Mia’s average driving speed is 6 kilometers per hour faster than Kirk’s, then Mia's driving speed Sm = 6 + Sk
Required
Mia’s average speed (Sm)
Since Dm/Sm = Dk/Sk
Substituting the given values to get Sk first we have;
558/6+Sk = 522/Sk
Cross multiply
558Sk = 522(6+Sk)
open the parenthesis
558Sk = 3132 + 522SK
558Sk-522Sk = 3312
36Sk =3132
Sk = 3132/36
Sk =87km/hr
SInce Sm = 6+Sk
Sm = 6+87
Sm = 93km/hr
Hence Mia's average speed is 93km/hr
(2x^0y^2)^-3 multiply 2yx^3
Answer:
[tex]\frac{x^{3} }{4y^{5} }[/tex]
Step-by-step explanation:
Simplifica la expresión
WILL GIVE BRAINLY PLEASE HELP!!!!!!!
Describe the type of correlation between two variables on the scatterplot. How do you know? Does the correlation between the variables imply causation? Explain
contains points:
(0.7,1.11)
(21.9,3.69)
(18,4)
(16.7,3.21)
(18,3.7)
(13.8,1.42)
(18,4)
(13.8,1.42)
(15.5,3.92)
(16.7,3.21)
Answer:
r² = 0.5652 < 0.7 therefore, the correlation between the variables does not imply causation
Step-by-step explanation:
The data points are;
X, Y
0.7, 1.11
21.9, 3.69
18, 4
16.7, 3.21
18, 3.7
13.8, 1.42
18, 4
13.8, 1.42
15.5, 3.92
16.7, 3.21
The correlation between the values is given by the relation
Y = b·X + a
[tex]b = \dfrac{N\sum XY - \left (\sum X \right )\left (\sum Y \right )}{N\sum X^{2} - \left (\sum X \right )^{2}}[/tex]
[tex]a = \dfrac{\sum Y - b\sum X}{N}[/tex]
Where;
N = 10
∑XY = 499.354
∑X = 153.1
∑Y = 29.68
∑Y² = 100.546
∑X² = 2631.01
(∑ X)² = 23439.6
(∑ Y)² = 880.902
From which we have;
[tex]b = \dfrac{10 \times 499.354 -153.1 \times 29.68}{10 \times 2631.01 - 23439.6} = 0.1566[/tex]
[tex]a = \dfrac{29.68 - 0.1566 \times 153.1}{10} = 0.5704[/tex]
[tex]r = \dfrac{N\sum XY - \left (\sum X \right )\left (\sum Y \right )}{\sqrt{\left [N\sum X^{2} - \left (\sum X \right )^{2} \right ]\times \left [N\sum Y^{2} - \left (\sum Y \right )^{2} \right ]}}[/tex]
[tex]r = \dfrac{10 \times 499.354 -153.1 \times 29.68}{\sqrt{\left (10 \times 2631.01 - 23439.6 \right )\times \left (10 \times 100.546- 880.902\right )} } = 0.7518[/tex]
r² = 0.5652 which is less than 0.7 therefore, there is a weak relationship between the variables, and it does not imply causation.
un automóvil recorre 90 km con 2 galones de gasolina cuantos kilómetros recorre con 11 galones de gasolina y cuantos galones de gasolina necesita para recorrer 650 km
Answer:
Recorrera 495 km con 11 galones de gasolina
Y necesitara 14.44 galones para recorrer 650 km
Step-by-step explanation:
k g k g
90 2 90 2
x 11 650 x
=(11 x 90)/2 =(650x2)/90
=990/2 =1300/90
=495 km =14.44
simplify 3/7
into a whole number
Answer:
You can't because it's not a "full fraction" like 7/7. The best you can do is turn that into a decimal like 0.43
Step-by-step explanation:
What is the difference between sin^-1 and sin?
Answer:
Step-by-step explanation:
sin of angle x is the trig ratio sine of x.
sin-1 x is the angle whose sine is x.
sin-1 x can also be written as arcsin x.
