Answer:
a. 45/1024
b. 1/4
c. 15/128
d. 193/512
e. 9/256
Step-by-step explanation:
Here, each position can be either a 0 or a 1.
So, total number of strings possible = 2^10 = 1024
a) For strings that have exactly two 1's, it means there must also be exactly eight 0's.
Thus, total number of such strings possible
10!/2!8!=45
Thus, probability
45/1024
b) Here, we have fixed the 1st and the last positions, and eight positions are available.
Each of these 8 positions can take either a 0 or a 1.
Thus, total number of such strings possible
=2^8=256
Thus, probability
256/1024 = 1/4
c) For sum of bits to be equal to seven, we must have exactly seven 1's in the string. Also, it means there must also be exactly three 0's
Thus, total number of such strings possible
10!/7!3!=120
Thus, probability
120/1024 = 15/128
d) Following are the possibilities :
There are six 0's, four 1's :
So, number of strings
10!/6!4!=210
There are seven 0's, three 1's :
So, number of strings
10!/7!3!=120
There are eight 0's, two 1's :
So, number of strings
10!/8!2!=45
There are nine 0's, one 1's :
So, number of strings
10!/9!1!=10
There are ten 0's, zero 1's :
So, number of strings
10!/10!0!=1
Thus, total number of string possible
= 210 + 120 + 45 + 10 + 1
= 386
Thus, probability
386/1024 = 193/512
e) Here, we have fixed the starting position, so 9 positions remain.
In these 9 positions, there must be exactly two 1's, which means there must also be exactly seven 0's.
Thus, total number of such strings possible
9!/2!7!=36
Thus, probability
36/1024 = 9/256
Is the sequence arithmetic? If so, how do you know? Given the sequence: 20, 26, 32, 38, . . .
Answer:
yes
Step-by-step explanation:
it is
because difference between each two consecutive terms are equal
26-20=32-26=38-32
for the formula:
20 is the first term.
6 is the difference between each two consecutive terms
so:
[tex]y = 6(x - 1) + 20 \\ y = 6x + 14[/tex]
Set up and evaluate the optimization problem. You are constructing a cardboard box from a piece of cardboard with the dimensions 4 m by 8 m. You then cut equal-size squares from each corner so you may fold the edges. What are the dimensions (in m) of the box with the largest volume
Answer:
[tex]Shorter\ side=4-2\times 0.845=2.31\ m\\Longest\ side=8-2\times 0.845=6.31\ m\\Height=0.845\ m[/tex]
Step-by-step explanation:
Given that , dimension of the cardboard is 4 m by 8 m.
Lets the dimensions of the square is x m by x m.
The volume after cutting the equal size of square from all the four corners is given as
[tex]V=x\times (4-2x)\times (8-2x)\\V=x\times (32-16x-8x+4x^2)\\V=x\times (4x^2-24x+32)\\V=4x^3-24x^2+32x\\[/tex]
For the maximum volume
[tex]\dfrac{dV}{dx}=12x^2-48x+32=0\\3x^2-12x+8=0\\[/tex]
For maximum value of volume , the value of x will be 0.845
x= 0.845
Therefore the dimensions will be
[tex]Shorter\ side=4-2\times 0.845=2.31\ m\\Longest\ side=8-2\times 0.845=6.31\ m\\Height=0.845\ m[/tex]
The volume of a shape is the amount of space in the shape.
The dimensions that produce the largest volume are: 2.31 m by 6.31 m by 0.845 m
The dimensions of the cardboard is given as:
[tex]\mathbf{Length = 4m}[/tex]
[tex]\mathbf{Width = 8m}[/tex]
Assume the cut-out is x.
So, the dimension of the box is:
[tex]\mathbf{Length = 4 - 2x}[/tex]
[tex]\mathbf{Width = 8 - 2x}[/tex]
[tex]\mathbf{Height = x}[/tex]
So, the volume of the box is:
[tex]\mathbf{V = (4 - 2x)(8 - 2x)x}[/tex]
Expand
[tex]\mathbf{V = 32x -24x^2 + 4x^3}[/tex]
Differentiate
[tex]\mathbf{V' = 32 -48x + 12x^2}[/tex]
Set to 0
[tex]\mathbf{32 -48x + 12x^2 = 0}[/tex]
Divide through by 4
[tex]\mathbf{8 -12x + 3x^2 = 0}[/tex]
Rewrite as:
[tex]\mathbf{3x^2-12x +8 = 0}[/tex]
Using a calculator, we have:
[tex]\mathbf{x = 0.845,\ 3.155}[/tex]
3.155 is greater than the dimension of the box.
So, we have:
[tex]\mathbf{x = 0.845}[/tex]
Recall that:
[tex]\mathbf{Length = 4 - 2x}[/tex]
[tex]\mathbf{Width = 8 - 2x}[/tex]
[tex]\mathbf{Height = x}[/tex]
So, we have:
[tex]\mathbf{Length = 4 - 2 \times 0.845 = 2.31}[/tex]
[tex]\mathbf{Width = 8 - 2 \times 0.845 = 6.31}[/tex]
[tex]\mathbf{Height = 0.845}[/tex]
Hence, the dimensions that produce the largest volume are: 2.31 m by 6.31 m by 0.845 m
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Find the area of the figure. Round to the nearest tenth if necessary. Use 3.14 for pi . 47.3 units2 41.1 units2 57.1 units2 66.2 units2
Answer:
41.1 units
Step-by-step explanation:
find the area of the triangle
1/2BH
1/2*8*4
4*4=16
find the area half of the circle
pi*R^2
3.14*4^2
3.14*16
50.24/2
^because it is a half circle you divide by 2
25.12+16=41.1
In a right triangle, one leg is 7 feet long. The other leg is 24 feet long. What
is the length of the hypotenuse?
Answer:
25
Step-by-step explanation:
C^2=A^2+B^2
C^2=24^2 + 7^2
C^2=576+49
C^2=625
C=√625
c=25
1. Find the value of x
37.5
17
52.5
a. 39.5
b. 75
c. 40
d. 42.5
Answer:
d
Step-by-step explanation:
The segment inside the triangle bisects the angle and divides the opposite sides into segments that are proportional to the other two sides, that is
[tex]\frac{x}{17}[/tex] = [tex]\frac{37.5}{52.5-37.5}[/tex] = [tex]\frac{37.5}{15}[/tex] ( cross- multiply )
15x = 637.5 ( divide both sides by 15 )
x = 42.5 → d
The weight of a particle of unobtainium is 2.66 x 10−6oz. The weight of a grain of spice is 9.17 x 10−4oz. About how much more does a grain of spice weigh than the particle of unobtainium? A 6.51 × 10–3 oz B 6.51 × 10–2 oz C 9.1 × 10–2 oz D 9.1 × 10–4 oz
Answer:
the answer is D
Step-by-step explanation:
leshawna should've won season 1 PERIODT
6.51 × [tex]10^{-2}[/tex] oz grain of spice weighs more than the particle of unobtainium.
Given that, the weight of a particle of unobtainium is [tex]2.66\times10^{-6}[/tex] oz and the weight of a grain of spice is [tex]9.17\times10^{-4}[/tex] oz.
We need to find how much more grain of spice weighs than the particle of unobtainium.
What is scientific notation?To determine the power or exponent of 10, let us understand how many places we need to move the decimal point after the single-digit number.
If the given number is multiples of 10 then the decimal point has to move to the left, and the power of 10 will be positive.If the given number is smaller than 1, then the decimal point has to move to the right, so the power of 10 will be negative.Now, [tex]9.17\times10^{-4}[/tex] - [tex]2.66\times10^{-6}[/tex]
=9.17-2.66 × [tex](10^{-4}-10^{-6})[/tex]
=6.51 × [tex]10^{-2}[/tex]
Therefore, 6.51 × [tex]10^{-2}[/tex] oz grain of spice weighs more than the particle of unobtainium.
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Write 0000 using the am/pm clock.
Answer:
12am
Step-by-step explanation:
Answer:
12:00 am or midnight
Step-by-step explanation:
00 00 hrs in 12-hours clock is 12:00 am or 12:00 o'clock midnight.
Macy is trying to construct an isosceles triangle. She assigns an angle measurement of 40° to the unique angle of the triangle. She wants the length of the opposite side (the base) to be 6 centimeters. How many isosceles triangles can Macy construct using this information?
Answer:
https://brainly.com/question/8847227
Step-by-step explanation:
In triangle ΔABC, ∠C is a right angle and CD is the altitude to AB . Find the measures of the angles of the ΔCBD and ΔCAD if: Chapter Reference a m∠A = 20°
Answer:
1. ∆CBD: ∠B = 70°; ∠BCD = 20°; ∠ BDC = 90°
2. ∆CDA: ∠ACD = 70°; ∠A = 20°; ∠ ADC = 90°
Step-by-step explanation:
1. ∆DBC
In ∆ABC
∠A + ∠B + ∠C = 180°
20° + ∠B + 90 ° = 180°
∠B + 110 ° = 180°
∠DBC = ∠B = 70°
In ∆CBD
∠BDC = 90°
∠B + ∠BCD + ∠CBD = 180°
70° + ∠BCD + 90 ° = 180°
∠BCD + 160° = 180°
BCD = 20°
2. ∆CAD
∠A + ∠ACD + ∠ADC = 180°
20° + ∠ACD + 90° = 180°
∠ACD + 110° = 180°
∠ACD = 70°
For a large sporting event the broadcasters sold 51 ad slots for a total revenue of $136 million. What was the mean price per ad slot?
Answer:
$2.67 million
Step-by-step explanation:
Average price per slot is found by dividing total price by total slots:
($136 million)/(51 slots) ≈ $2.67 million/slot
The mean price per ad slot was $2.67 million.
Which is the graph of the equation v- 1 = (-3)?
Step-by-step explanation:
The equation is v-1 = -3
V-1 = -3 add one in both sides v -1 +1 = -3+1 v = -2Here is the graph :
By about how much will f (x comma y comma z )equalsln StartRoot x squared plus y squared plus z squared EndRoot change if the point Upper P (x comma y comma z )moves from Upper P 0 (6 comma 4 comma 12 )a distance of dsequals0.1 unit in the direction of 3 Bold i plus 6 Bold j minus 2 Bold k?
Answer:
pls format
Step-by-step explanation:
It is believed that 11% of all Americans are left-handed. In a random sample of 100 students from a particular college with 10123 students, 14 were left-handed. Find a 98% confidence interval for the percentage of all students at this particular college who are left-handed.
Answer:
Step-by-step explanation:
We can calculate this confidence interval using the population proportion calculation. To do this we must find p' and q'
Where p' = 14/100= 0.14 (no of left handed sample promotion)
q' = 1-p' = 1-0.14= 0.86
Since the requested confidence level is CL = 0.98, then α = 1 – CL = 1 – 0.98 = 0.02/2= 0.01, z (0.01) = 2.326
Using p' - z alpha √(p'q'/n) for the lower interval - 0.14-2.326√(0.14*0.86/100)
= -2.186√0.00325
= -2.186*0.057
= 12.46%
Using p' + z alpha √(p'q'/n)
0.14+2.326√(0.14*0.86/100)
= 0.466*0.057
= 26.5%
Thus we estimate with 98% confidence that between 12% and 27% of all Americans are left handed.
Manuel ordered pizza for a party. A vegetable pizza has 6 slices per pie. A cheese pizza has 8 slices per pie. Manuel ordered four times as many cheese pizzas as vegetable pizzas, for a total of 152 slices. How many pizzas did Manuel order? 15 20 30 40
Answer:
20 Pizza
Step-by-step explanation:
Let the number of vegetable pizza be x
Given that
Manuel ordered four times as many cheese pizzas as vegetable pizzas
the number of cheese pizza = 4x
1. no of slice in 1 vegetable pizza pie = 6
no of slice in x vegetable pizza pie = 6x
2. no of slice in 1 cheese pizza pie = 8
no of slice in 4x cheese pizza pie = 8*4x = 32x
Total no of slice for x vegetable pizza and 4x cheese pizza = 6x+32x = 38x
Given that
total no. of 152 slices, therefore
38x = 152
=> x = 152/38 = 4
Thus, no. of vegetable pizza ordered = 4
no. of cheese pizza ordered = 4x = 4*$ = 16
Total no of pizza ordered = 16+4 = 20 (answer)
Answer:
B
Step-by-step explanation:
Drag each equation to show if it could be a correct first step to solving the equation 2(x+7) =36
Answer:
(2.x) + (2.7) = 36
Step-by-step explanation:
Solving the given equation with the distributive property,
A(B + C) = (A.B) + (A.C)
So that,
2(x+7) = 36
(2.x) + (2.7) = 36
2x + 14 = 36
2x = 36 - 14
2x = 22
x = 11
From the given expressions, the option that is the correct first step to solving this equation is;
(2.x) + (2.7) = 36
Answer:
Here you go
Step-by-step explanation:
What is the value of d in the equation?
1 3/4d=14
4
8
18 2/3
24 1/2
Answer:
its 13/56.
Step-by-step explanation:
13/4d= 14
or , 13 = 14×4d
or, 13=56 d
or, d = 13/56.
Answer:
The answer is D
Step-by-step explanation:
1 3/4d= 14
7/4d = 14
d = 8
Hope I helped pls tell me if i'm wrong :D
Determine the location and value of the absolute extreme values of f on the given interval, if they exist. f (x )equals2 sine squared x on [0 comma pi ]Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Type an exact answer, using pi as needed. Use a comma to separate answers as needed.) A. The absolute maximum is nothing at xequals nothing, but there is no absolute minimum. B. The absolute minimum is nothing at xequals nothing and the absolute maximum is nothing at xequals nothing. C. The absolute minimum is nothing at xequals nothing, but there is no absolute maximum. D. There are no absolute extreme values for f (x )on [0 comma pi ].
Answer:
A. The absolute maximum is nothing at x equals nothing, but there is no absolute minimum.
Step-by-step explanation:
The equation is :
f(x) = 2x2 + x2
The function has not absolute maximum value and it has absolute minimum value 0. The both function has maximum value as nothing.
Need some help on this whole unit to be honest but any help with this one ?
answer:
i believe they all are identical
Step-by-step explanation:
i used a website called desmos graphing calculator and typed each one out and this is what it looked like
Jenna worked 13 hours more than Jose last month. If Jenna worked 9 hours for every 4 hours that Jose worked, how many hours did they each work?
I travelled at 60km/h and took 2 hours for a certain journey. How long would it have taken me if I had travelled at 50km/h?
Answer:
2 hours and 24 minutes
Step-by-step explanation:
2 hours at 60 km/h means you have travelled 2*60=120 km
120 km at 50 km/h takes 120/50 = 2.4 hours
2.4 hours is 2 hours and 0.4*60 = 24 minutes.
3) BRAINLIEST & 10+ POINTS!!! If a 4 foot blade of a propeller completes 22 revolutions per second, find the angular speed of the blade in radians per second. ~Round your answer to the nearest hundredth. Angular speed = _______________ radians/second
Answer:
44π rads per seconds
Step-by-step explanation:
Already the speed of the 4 foot blade is given as 22 revolutions per sec.
What we have to do is just to convert the 22 revolutions per second to radians.
1 rev = 360°
360° = 2π
So the speed is actually equal to
22 *360 = 7920° per second
Or
22*2π = 44π rad per seconds
What ever way the answers are both same.
the principal p is borrowed at a simple interest rate r for a period of time t. find the simple interest owed for the use of the money
Answer:
The simple interest is Prt
The simple interest on the money will be $24300
Step-by-step explanation:
The complete question is shown below
The principal P is borrowed at simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume 360 days in a year. P=$18,000, r=7.5%, t=18 months
Principal = P
Interest rate = r
Time period = t
simple interest owed for the use of the money will be gotten as below
The percentage of the principal that will be owed per unit period is the rate r
The total rate that it will be involved in this time period will be the product of the rate and the time = r x t = rt
Finally, to know the amount of interest that this rate will result to, we multiply the total rate in the time period by the original principal borrowed
Total interest = Prt
For a simple interest on the principal P = $18,000,
the interest rate = 7.5% = 7.5/100 = 0.075,
time period = 18 months
we assume the interested is calculated on a monthly basis
Simple interest = Prt
==> 18000 x 0.075 x 18 = $24300
Solve the following equation for X.
3x – 9 = -33
Answer:
-8Option D is the right option
solution,
[tex]3x - 9 = - 33 \\ or \: 3x = - 33 + 9 \\ or \: 3x = - 24 \\ or \: x = \frac{ - 24}{3} \\ x = - 8[/tex]
Hope this helps...
Good luck on your assignment..
Answer:
-8
Step-by-step explanation:
3x-9=-33
transpose 9 to RHS
->3x=-33+9=> 3x=-24
transposing 3 to RHS
=> x=-24÷3
=> x=-8
Which is NOT supported by this graph?
30
25
20
15
10
Profit
5
(dollars)
0
-10
-15
Cars Washed
Answer:
D -price of car wash keeps getting higher
Answer: The price of a car wash keeps getting higher
Step-by-step explanation:
19.25 tons equal Lbs
Answer:
38500lbs
Step-by-step explanation:
2000 lbs is one tone
if we have 19.25 tons, we need to multiply 19.25x2000
The answer is 38500 lb
Answer:
38,500 pounds
Step-by-step explanation:
Every ton is 2,000 pounds.
We want to find out how many pounds are in 19.25 tons.
Set up a proportion.
pounds/tons=pounds/tons
2,000 pounds/ 1 ton= x pounds / 19.25 tons
2,000/1= x /19.25
x is being divided by 19.25. The inverse of division is multiplication. Multiply both sides by 19.25.
19.25*2,000/1= x/19.25 *19.25
19.25*2000=x
38,500=x
There are 38,500 pounds in 19.25 tons.
Hope this was hard enough not to be illogical or simple. 3x=66 Solve for x
Answer: x = 22
Step-by-step explanation: To get x by itself, we divide both sides by 2 and we have x = 22 which is the solution to this equation.
Answer:x=22
Step-by-step explanation:divide 3 by both sides makes x=22
Simplify.
35 - (42 + 5)
━━━━━━━☆☆━━━━━━━
▹ Answer
-12
▹ Step-by-Step Explanation
35 - (42 + 5)
35 - 47 = -12
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer:
Hello!
~~~~~~~~~~~~~~~~~~~~~~~~~
35 - (42 + 5) =
-12
~~~~~~~~~~~~~~~~~~~~~~~~~
Step-by-step explanation: Simplify the expression.
Hope this helped you! Brainliest would be nice. ❤︎
What type of relationship has his teacher discovered?
Answer: positive correlation likely causal
Step-by-step explanation:
REFERENCE: LESSO
Estimate the difference of 645 and 273.
Answer:
350
Step-by-step explanation:
In this situation it seems like we should be rounding to 50 because the numbers work well that way, and it is nice number commonly unsed in these situaltions. So, 645 rounded to the nearentest 50 would be 650. And 273 rounded to the nerent 50 would be 300. Now if we subtract 300 from 650, (650-300) we will get 350.
Is the following statement true or false? Integration and differentiation are inverse processes. Group of answer choices
True.
Integration is also called anti-differentiation, mathematically its an inverse function of differentiation.
For example, one of the first equalities learned is:
[tex]f(x)=g'(x)\Longleftrightarrow\int g'(x)dx=f(x)[/tex].
Which explains that if you differentiate a function (get its derivative) and then integrate the derivative you will obtain the original function.
Hope this helps.