This question is incomplete, the complete question is;
Assume that two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Which distribution is used to test the claim that women have a higher mean resting heart rate than men?
A.t
B.F
C.Normal
D. Chi-square
Answer:
A) t test
Step-by-step explanation:
A t-test uses sample information to assess how plausible it is for the population means μ1 and μ2 to be equal.
The formula for a t-statistic for two population means (with two independent samples), with unknown population variances shows us how to calculate t-test with mean and standard deviation and it depends on the assumption of having an equal variance or not.
If the variances are assumed to be not equal,
he formula is:
t = (bar X₁ - bar X₂) / √( s₁²/n₁ + s₂²/n₂ )
If the variances are assumed to be equal, the formula is:
t = (bar X₁ - bar X₂) / √ (((n₁ - 1)s₁² + (n₂ - 1)s₂²) / (n₁ + n₂ - 2)) ( 1/n₁ + 1/n₂)
it called t-test for independent samples because the samples are not related to each other, in a way that the outcomes from one sample are unrelated from the other sample.
hence option A is correct. t test
19. A game is played by rolling a group of at least 3 dice. The highest two numeric results are removed
from the table. If any 6s remain on the table the player wins. If only 3 dice are rolled then the
probability of winning is 1/216. As the number of dice used increases without bound what does the
probability of a winning roll approach?
Answer: Approaches to 1.
Step-by-step explanation:
If there are only 3 dice used, then the only chance that the player has to win is when the 3 dice have the same outcome, 6.
The probability will be:
p = (1/6)^3 = 1/216.
Now, if we add one more dice, we still need at least 3 sixes to win, but the other dice can have any other value. so now the probabilities are:
dice 1---- outcome = 6, prob = 1/6.
dice 2---- outcome = 6, prob = 1/6.
dice 3---- outcome = 6, prob = 1/6.
dice 4---- outcome = any number, prob = 1.
The probability for this arrangement is still:
p = 1/216.
But now we have permutations!.
The dice that can be any number has 4 possible positions, so the actual probability will be:
P = 4*p = 4/216.
Now remember that if we have N elements, the total number of combinations of K elements ( N ≥ K) is:
[tex]C(N, K) = \frac{N!}{(N - K)!K!}[/tex]
if we add other dice, then we will have 5 dices, and 2 of them that can not be 6 that can take any position, then the number of combinations will be:
[tex]C(5, 2) = \frac{5!}{(5 - 2)!2!} = \frac{5*4}{2} = 10[/tex]
Then the probability will be:
P = 10*p = 10/216.
So we can start to see a pattern here, if we have N dices, we still only need 3 of them to be strictly 6, then we have (N - 3) dices that can be any number.
Then the probabilty of winning if you have N dices is:
P = C(N, N - 3)*p = C(N, N - 3)*(1/216)
Then as N increases, we will see that the probability tends to 1, (it actually grows larger than that, but remember that the probability is a number between 0 and 1, so the maximum is 1)
Why? well... if you roll a lot of dice, suppose 1000 of them, is really likely to have at least 3 sixes in there, so as the number of dice increases, also does the probability.
Triangle ABC is a right triangle. The sides measure AB = 6 and BC = 8. Use the
Pythagorean theorem to find CA.
Answer:
AC = 10 units
Step-by-step explanation:
From the picture attached,
Triangle ABC is a right triangle.
Opposite side of the right angle B = Hypotenuse (AC)
and the other two legs are AB and BC
Pythagoras Theorem states
(hypotenuse)² = (leg 1)² + (leg 2)²
AC² = AB² + BC²
AC² = (6)² + (8)²
AC² = 36 + 64
AC² = 100
AC = √100
AC = 10
Therefore, length of the hypotenuse (AC) = 10 units will be the answer.
which statement is true regarding the graphed functions?
This is because the red and blue lines cross at (0,-2). We don't really need to worry about the y coordinate here. For this problem, all we care about is the x coordinate, which is x = 0.
When x = 0, the outputs of each function f(x) and g(x) are both the same value. So that's why we can say f(0) = g(0). It's the same as saying f(x) = g(x) has the solution x = 0.
Net to seller equals the ______ multiplied by the percent to seller.
I assumed you are referring to the Net (take away by the seller after removing their commissions).
Answer:
Selling price
Step-by-step explanation:
To determine what amount goes to the seller, we multiply the selling price of a commodity in question by the percentage (commissions) to the seller.
Note that the resulting amount is the value of the commission paid to the seller, the actual net is gotten by substracting the selling price from the commission paid.
The force of gravity on Mars is different than on Earth. The function of the same situation on Mars would be represented by the parabolic function shown below. On which planet would the ball go the highest? On which planet would the ball take the longest to return to the ground? Explain your reasoning.
Answer:
If thrown up with the same speed, the ball will go highest in Mars, and also it would take the ball longest to reach the maximum and as well to return to the ground.
Step-by-step explanation:
Keep in mind that the gravity on Mars; surface is less (about just 38%) of the acceleration of gravity on Earth's surface. Then when we use the kinematic formulas:
[tex]v=v_0+a\,*\,t\\y-y_0=v_0\,* t + \frac{1}{2} a\,\,t^2[/tex]
the acceleration (which by the way is a negative number since acts opposite the initial velocity and displacement when we throw an object up on either planet.
Therefore, throwing the ball straight up makes the time for when the object stops going up and starts coming down (at the maximum height the object gets) the following:
[tex]v=v_0+a\,*\,t\\0=v_0-g\,*\,t\\t=\frac{v_0}{t}[/tex]
When we use this to replace the 't" in the displacement formula, we et:
[tex]y-y_0=v_0\,* t + \frac{1}{2} a\,\,t^2\\y-y_0=v_0\,(\frac{v_0}{g} )-\frac{g}{2} \,(\frac{v_0}{g} )^2\\y-y_0=\frac{1}{2} \frac{v_0^2}{g}[/tex]
This tells us that the smaller the value of "g", the highest the ball will go (g is in the denominator so a small value makes the quotient larger)
And we can also answer the question about time, since given the same initial velocity [tex]v_0[/tex] , the smaller the value of "g", the larger the value for the time to reach the maximum, and similarly to reach the ground when coming back down, since the acceleration is smaller (will take longer in Mars to cover the same distance)
The vertices of triangle PQR are listed below.
P(-5, 3), Q(-13, -3), R(-5, -9)
What is the perimeter of triangle PQR?
A.
32 units
B.
51 units
C.
22 units
D.
48 units
Answer:
A. 32 units
Step-by-step explanation:
First, we need to find all of the side lengths of triangle using distance formula:
[tex]Distance = \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]Now, we can calculate length of PQ, QR and PR sides by using their vertices and above formula:
[tex]PQ=\sqrt{(-13-(-5))^2+(-3-3)^2} =\sqrt{8^2+6^2}=10[/tex] [tex]QR=\sqrt{(-5-(-13))^2+(-9-(-3))^2} =\sqrt{8^2+6^2}=10[/tex] [tex]PR=\sqrt{(-5-(-5))^2+(-9-3)^2} =\sqrt{0^2+12^2}=12[/tex]For perimeter we add up the length of all of its sides:
[tex]Perimeter = PQ +QR + PR=10+10+12=32[/tex]find the midpoint of (-1, -5) and (-5, 9)
Answer:
(-3,-2) is the midpoint
Step-by-step explanation:
To find the midpoint
Add the x coordinates and divide by 2 to find the x coordinate of the midpoint
(-1+-5) /2 = -6/2 = -3
Add the y coordinates and divide by 2 to find the y coordinate of the midpoint
(-5+-9) /2 = -4/2 = -2
(-3,-2) is the midpoint
Step-by-step explanation:
To solve, we have to use the midpoint formula:
[tex]M=(\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2})[/tex]
Our points:
(-1, -5) (-5, 9)
Our x1 is -1, and our x2 is -5. Our y1 is -5, and our y2 is 9.
[tex]M=(\frac{-1+(-5) }{2} ,\frac{-5+9 }{2})[/tex]
[tex]M=(\frac{-6 }{2} ,\frac{4}{2})[/tex]
[tex]M=(-3 ,2)[/tex]
Answer: our midpoint: (-3, 2)
The second side of a triangular deck is 6 feet longer than the shortest side, and the third side is 6 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 72 feet, what are the length of the three sides?
Answer:
let the shortest side be 'x' ft
length of second side = x + 6 ft
length of third side = 2(x+6) - 6 ft
perimeter of triangle = 72 feet
shortest side + second side + third side = 72 ft
x + x + 6 + 2(x+6) - 6 = 72
4x + 12 = 72
x = 15
length of shortest side = 15 ft
length of second side = 15 + 6 = 21 ft
length of third side = 2(15 + 6) - 6 = 36 ft
compare your answers from parts A and B. What connections can you make between the size and number of squares in part A and the prime factors in part B?
Answer:
In part A, 6 squares made up of 4 units represented an area of 24.
In part B, the prime factorization of 24 gave 24 = 2 ∙ 2 · 2 · 3, which is equal to 4 · 6.
The factor that is a perfect square, in this case 4, determines the size of squares needed for the visual model, and other factor, 6, determines the number of squares of that size.
Step-by-step explanation:
4. Write these fractions in the simplest form.
6
_
9
Answer:
Given fraction is 6/9 .
→What does fractions in simplest form means?
Fractions are said to be in simplest form if the HCF of numerator and denominator is equal to 1 .→ How to convert?
We will find the HCF of numerator and denominator and we will divide the numerator and denominator by that number.Now HCF of 6 and 9 is 3.
→ 6/9 = 6÷3/9÷3 = 2/3.
Hence the required answer is 2/3.
Answer:
[tex]\Large \boxed{\displaystyle \frac{2}{3}}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{6}{9}[/tex]
Factor out 3 from the numerator and denominator.
[tex]\displaystyle \frac{3(2)}{3(3)}[/tex]
Cancel the common factors.
[tex]\displaystyle \frac{2}{3}[/tex]
Find the indicated angle measures. pls help i’m dyin lol
Answer:
utv = 24° wtx=113°
Step-by-step explanation:
I solved in the picture
hope this helps ^-^
Explain how to use the distributive property to find an expression that is equivalent to 20+10
Answer: 2(10+5)
Step-by-step explanation: half of 20 is 10. half of 10 is five and i put them both in parentheses. outside the parenthesis i placed 2 so it is multiplied to the inner set of numbers.
Part of a regression output is provided below. Some of the information has been omitted.
Source of variation SS df MS F
Regression 3177.17 2 1588.6
Residual 17 17.717
Total 3478.36 19
The SS(Residual) is?
Answer:
301.189
Step-by-step explanation:
Given the table :
Source of Variation - - SS - - - df - - - MS - - - - F
Regression - - - - - -3177.17 - - -2 - - 1588.6
Residual - - - - - - - - ______ --17 - - -17.717
Total - - - - - - - - - - 3478.36 - - 19
Calculate the SSR, Sum of Square residual
The Sum of Square RESIDUAL (SSR), Mean Square Residual (MSR) and Degree of Freedom RESIDUAL (DFR) are related by the formular :
MSR = SSR / DFR
Hence,
SSR = MSR × DFR
Fr the table ;
MSR = 17.717 ; DFR = 17
SSR = (17.717 × 17)
SSR = 301.189
ILL GIVE YOU BRAINLIST !
b/2 - 1 as a verbal phrase
Answer:
b/2-1 has a verbal phrase can be one minus the quotient of b and 2.
3/8+1/8-1/6+1/4=? What is the answer? please!!!
Answer:
.58 repeating 3
Step-by-step explanation:
7/12=.58 repeating 3
Find an equation for the plane y=4x in cylindrical coordinates. (Type theta for θ in your answer.)
Answer:
sinθ - 4cosθ = 0Step-by-step explanation:
Given the equation of a plane in rectangular coordinates to be y = 4x.
The cylindrical coordinates of the axis is as given below;
x = rcosθ
y = rsinθ
z = z
Since there is no z coordinate in the equation of the plane given, we will only substitute x = rcosθ and y = rsinθ into the equation y = 4x and simply the result as shown;
y = 4x
rsinθ = 4( rcosθ)
rsinθ = 4rcosθ
sinθ = 4cosθ
sinθ - 4cosθ = 0
Hence the equation for the plane in cylindrical coordinate is expressed as sinθ - 4cosθ = 0
The equation of the plane y=4x in cylindrical coordinates is, [tex]sin\theta-4cos\theta=0[/tex]
Equation of plane:To find the equation of plane in cylindrical coordinates,
We have to substitute ,
[tex]x=rcos\theta\\\\y=rsin\theta\\\\z=z[/tex]
Given equation of plane is, [tex]y=4x[/tex]
Substitute values in equation of plane.
[tex]rsin\theta=4(rcos\theta)\\\\sin\theta=4cos\theta\\\\sin\theta-4cos\theta=0[/tex]
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Max’s car holds 18 gallons of gasoline. Driving on the highway, the car uses approximately 2 gallons per hour. Let h represent the number of hours Max has been riding on the highway. Write an expression that shows how many gallons of gasoline Max has left after driving h hours. Then find that number after Max drives 3.5 hours on the highway.
Answer:
y=18 gallons
Step-by-step explanation:
You can multiply how many hours he's been driving by the 2 gallons and subtract it from 18
Answer:
11 gallons
18=-2h h=3.5
Step-by-step explanation:
-2(3.5)=18
18-7=11, he has 11 gallons of gas left
In your gym class, your teacher can create teams of 4 for a
relay race and have no students left over. The next day, your
teacher creates teams of 5 for dodge ball and has no
students left over. What are some possible numbers of
students in your class?
Answer: 20, 40, 60, 80, 100,....
Step-by-step explanation:
Given that :
It is possible to create teams of 4 for a relay race with no student leftover
Also,
It is possible to create teams of 5 for dodgeball with no student left over from the same class
To deduce the possible number of students in the class, then the number of students should be a multiple of both 4 and 5
Multiples of 4 include = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100,....
Multiples of 5 : 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100,....
Multiples common to both 4 and 5 : 20, 40, 60, 80, 100,....
Sinplify x+3x-36. 3x-36 3x²-36 4x-36 4x²-36
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{4x - 36}}}}[/tex]Step-by-step explanation:
[tex] \sf{x + 3x - 36}[/tex]
Here, we have to collect like terms.
_________________________________
▪️What do you mean by like terms ?
⇒Like terms are those which have the same base. While adding or subtracting like terms, we should add or subtract the coefficients of like terms.
_________________________________
Let's add the like terms :
Answer : 4x - 36
Hope I helped!
Best regards!
Simplify each expression.
1) 7x - 9x
2) -2x - 7+ 8x - 10
3) 3 - 10x - 3-6x
4) 2m - 6+ m + 1
5) 10m - 8m
6) x - 4+x-5
7 4x + 5x
8) -x + 3 + 7x + 5
Answer:
1) -2x
2) 6x - 17
3) -16x
4) 3m - 5
5) 2m
6) 2x - 9
7) 9x
8) 6x + 8
Step-by-step explanation:
1) = x(7-9) = x(2) = 2x
2) x(-2+8) - 7 - 10 = x(6) - 17 = 6x - 17
3) x(-10-6) + 3 - 3 = x(-16) + 0 = 16x
4) m(2+1) - 6 + 1 = 3m - 5
5) m(10-8) = m(2) = 2m
6) x(1+1) - 5 - 4 = 2x - 9
7) x(4+5) = x(9) = 9x
8) x(7-1) + 3 + 5 = 6x + 8
Given the following definitions:
U = {1, 2, 3, 4, 5, 6, 7}
A = {1, 2, 4, 5)
B = {1,3,5,7)
How many elements are in A'n B?
Step-by-step explanation:
First,
(A intersect B) = {1,2,4,5} intersect {1,3,5,7}
= {1,5}
Now,
A'n B = (A) - (A intersect B)
= {1,2,4,5} - {1,5}
= {2,4}
I need to name the type of special pairs of angles shown. Please and thank you
Answer:
WXY is an obtuse angle, YXZ is an acute angle, and WXZ is a straight line.
Step-by-step explanation:
WXY is greater than 90 degrees, YXZ is lesss than 90 degrees, and WXZ is a straight 180 degree line.
The required name for a special type of pair of angles shown is supplementary angles.
What is the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
The figure, shown is pair of angles whose sum is equal to 180,
The by definitions of the angle where the sum is equal to 180° and adjacent angles are said to be supplymentary angles.
Thus, the required name for a special type of pair of angles shown is supplementary angles.
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Find the area of the region between the curve y= 2ln(x) and the horizontal axis for 1<= x <= 4
Answer:
5.09 units
Step-by-step explanation:
Given equation
[tex]y=2\ln x=f(x)[/tex] in the interval [tex]1\le x\le 4[/tex]
So we integrate [tex]y[/tex] in the given interaval
[tex]\int f(x)=2\int\limits^4_1 {\ln x}dx[/tex]
Let us integrate [tex]\ln x[/tex] first.
let
[tex]u=\ln x, dv=dx[/tex]
[tex]du=\dfrac{1}{x}, v=x[/tex]
[tex]\int\ln x dx=udv[/tex]
Using integration by parts we get
[tex]uv-\int vdu[/tex]
[tex]=x\ln x-\int x\dfrac{1}{x}dx[/tex]
[tex]=x\ln x-dx[/tex]
[tex]=x\ln x-x+C[/tex]
So here
[tex]\int f(x)=2\int\limits^4_1 {\ln x}dx\\ =2(x\ln x-x)_1^4\\ =2[(4\ln 4-4)-(1\ln 1-1)]\\ =2[4\ln 4-4+1]\\ =5.09\ units[/tex]
The area of the the region between the curve and horizontal axis is 5.09 units.
sheila___ her case, look .( had picked,have picked , picked.)
Answer:
picked
Step-by-step explanation:
It is the only one that sounds correct.
Answer:
hi,
i think the answer can be picked
Step-by-step explanation:
picked is the answer
The volume of a cube is 3,375 cubic inches. What is the measure of each side of the cube?
Answer:
l=w=h=15
Step-by-step explanation:
Volume of a cube= l*w*h
where l=w=h
[tex]l = {}^{3} \sqrt{ v} \: \: \: l = {}^{3} \sqrt{3375} = 15 [/tex]
15*15*15=3375
Hope this helps ;) ❤❤❤
The measure of each side of the cube will be 15 inches.
What is volume?The Volume of the cone is the amount of quantity, which is obtained in the 3-dimensional space. Volume is defined as the space occupied by an object in the three-Dimensions. All three parameters are required for the volume like length, width, and height of the cube or Cuboid
The cube has all the sides equal means that the length, width, and height of the cube will be the same. Let's suppose the length, width, and height of the cube is a.
The volume of a cube will be given by the formula:-
Volume = side³ = a³
a³ = 3375
a = ∛3375
a = ∛( 15 x 15 x 15 )
a = 15 cubic inches.
Therefore, the measure of each side of the cube will be 15 inches.
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Find the equation of the line passing through (0,5) with a slope of 2/3
Answer:
y= 2/3x +5
Step-by-step explanation:
(0,5) is the y intercept and the slope is 2/3 so we can use the y intercept form
y = mx+b where m is the slope and b is the y intercept
y= 2/3x +5
Answer:
y= 2/3x+5
Step-by-step explanation:
Okay, to write the equation of a line you need two values. The y intercept and the slope. The y intercept has an x coordinate of zero, and lucky us, the point you were given has an x coordinate of zero so that's done. You were also given the slope, so you don't have to calculate it. Anyways, the formula of a line is written in slope intercept form usually, so y=mx+b. Just fill in the gaps, m= the slope and b=the y intercept. The slope is 2/3, and the y intercept is 5. So, inserting in the variables you get y=2/3x+5.
Hope that helps!
Factorise:
( a²- 1) ( b²- 1) + 4ab
pls give a detailed explanation
pls answer it......
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]\boxed{ a^2 b^2 + -a^2 + -b^2 + 1 + 4ab}[/tex]
Let's simplify step-by-step.
[tex]( a^2 - 1 ) ( b^2 -1) + 4ab[/tex]
Distribute:
[tex]=( a^2) (b^2) + (a^2) (-1) + ( -1) (b^2) + (-1) (-1) + 4ab[/tex]
[tex]= a^2 b^2 + -a^2 + -b^2 + 1 + 4ab[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
Answer:
a²b² - a² - b² + 4ab + 1
Step-by-step explanation:
( a²- 1) ( b²- 1) + 4ab
(a²b² - a² - b² + 1) + 4ab
a²b² - a² - b² + 4ab + 1
A diver descended 20 feet in 5 seconds. What is the average rate per second that he traveled? Explain how you can use integer tiles to solve the problem and find the answer. Pls help
Answer:
The diver is moving down, so he moved −20 feet. Start with 20 negative tiles and separate them into 5 equal groups. There are 4 negative tiles in each group, so he traveled at a rate of −4 feet per second.
Step-by-step explanation:
Answer:
4 feet per second
Step-by-step explanation:
We can create a proportion:
[tex]\frac{20}{5} = \frac{x}{1}[/tex]
Cross multiply:
[tex]20\cdot1=20\\\\20\div5=4[/tex]
So he's travelling at a rate of 4 feet per second.
Hope this helped!
Express the formula P=2L+2W in terms of the width,W. Use the formula to find the width when the perimeter is 70 and the length is 22.
Answer:
The width is 13Step-by-step explanation:
From the question
P=2L+2W
where
L is the length
W is the width
To make W the subject move 2L to the left side of the equation
That's
2W = P - 2L
Divide both sides of 2 to make W stand alone
We have
[tex]W = \frac{P - 2L}{2} [/tex]
when
P = 70
L = 22
W is
[tex]W = \frac{70 - 2(22)}{2} \\ W = \frac{70 - 44}{2} \\ W = \frac{26}{2} [/tex]
We have the final answer as
W = 13Hope this helps you
Answer:
Width W = 13
Step-by-step explanation:
P = 2L + 2W
if the perimeter P = 70
and Length L = 22
find the Width W
P = 2L + 2W
70 = 2(22) + 2W
70 - 44 = 2W
26 = 2W
W = 26 / 2
W = 13
therefore,
the Width W = 13
check:
P = 2L + 2W
70 = 2(22) + 2(13)
70 = 44 + 26
70 = 70 --- OK
Convert the decimal expansion of each of these integers to a binary expansion.
a) 321
b) 1023
c) 100632
Answer:
[tex]321_{10} = 101000001_{2}[/tex]
[tex]1023_{10} = 1111111111_2[/tex]
[tex]100632_{10} = 11000100100011000_{2}[/tex]
Step-by-step explanation:
Given
a) 321
b) 1023
c) 100632
Required
Convert to decimal
To convert each of these to binary, we have to divide the quotient by 2 and we take note of the remainder;
Solving (a)
321 / 2 = 160 R 1
160 / 2 = 80 R 0
80 / 2 = 40 R 0
40 / 2 = 20 R 0
20 / 2 = 10 R 0
10 / 2 = 5 R 0
5 / 2 = 2 R 1
2 / 2 = 1 R 0
1 / 2 = 0 R 1
Hence;
[tex]321_{10} = 101000001_{2}[/tex]
Solving (b)
1023 / 2 = 511 R 1
511 / 2 = 255 R 1
255 / 2 = 127 R 1
127 / 2 = 63 R 1
63 / 2 = 31 R 1
31 / 2 = 15 R 1
15 / 2 = 7 R 1
7 / 2 = 3 R 1
3 / 2 = 1 R 1
1 / 2 = 0 R 1
Hence;
[tex]1023_{10} = 1111111111_2[/tex]
Solving (c)
100632 / 2 = 50316 R 0
50316 / 2 = 25158 R 0
25158 / 2 = 12579 R 0
12579 / 2 = 6289 R 1
6289 / 2 = 3144 R 1
3144 / 2 = 1572 R 0
1572 / 2 = 786 R 0
786 / 2 = 393 R 0
393 / 2 = 196 R 1
196 / 2 = 98 R 0
98 / 2 = 49 R 0
49 / 2 = 24 R 1
24 / 2 = 12 R 0
12 / 2 = 6 R 0
6 / 2 = 3 R 0
3 / 2 = 1 R 1
1 / 2 = 0 R 1
Hence;
[tex]100632_{10} = 11000100100011000_{2}[/tex]