Answer:
A. All atoms of the same elements are identical
Step-by-step explanation:
Two atoms of the same chemical element are typically not identical. They can be different if their electrons are in different states,
In a test of a printed circuit board using a random test pattern, an array of 14 bits is equally likely to be 0 or 1. Assume the bits are independent.
(a) What is the probability that all bits are 1s? Round your answer to six decimal places (e.g. 98.765432). Enter your answer in accordance to the item a) of the question statement
(b) What is the probability that all bits are 0s? Round your answer to six decimal places (e.g. 98.765432). Enter your answer in accordance to the item b) of the question statement
(c) What is the probability that exactly 7 bits are 1s and 7 bits are 0s? Round your answer to three decimal places (e.g. 98.765). Enter your answer in accordance to the item c) of the question statement
Answer:
(a) 0.000061
(b) 0.000061
(c) 0.209
Step-by-step explanation:
An array of 14 bits is equally likely to be 0 or 1.
That is, P (0) = P (1) = 0.50.
(a)
Compute the probability that all bits are 1s as follows:
[tex]P(\text{All bits are 1s})=[P(1)]^{14}[/tex] ∵ the bits are independent
[tex]=(0.50)^{14}\\=0.00006103515625\\\approx 0.000061[/tex]
Thus, the probability that all bits are 1s is 0.000061.
(b)
Compute the probability that all bits are 0s as follows:
[tex]P(\text{All bits are 0s})=[P(0)]^{14}[/tex] ∵ the bits are independent
[tex]=(0.50)^{14}\\=0.00006103515625\\\approx 0.000061[/tex]
Thus, the probability that all bits are 0s is 0.000061.
(c)
Compute the probability that exactly 7 bits are 1s and 7 bits are 0s as follows:
Define X as the number of bits that 1s.
Then the random variable X will follows a binomial distribution with parameters n = 14 and p = 0.50.
The value of P (X = 7) is:
[tex]P(X=7)={14\choose 7}(0.50)^{7}(1-0.50)^{14-7}[/tex]
[tex]=\frac{14!}{7!\times 7!}\times (0.50)^{14}\\\\=3432\times 0.000061\\\\=0.209352\\\\\approx 0.209[/tex]
Thus, the probability that exactly 7 bits are 1s and 7 bits are 0s is 0.209.
Find the volume of the solid that lies under the plane 3x + 2y + z = 12 and above the rectangle. $$ R = \{(x,y) | 0\le x \le {\color{red}1}, -{\color{red}2} \le y \le {\color{red}4} \} $$
Answer:
51 cubic units
Step-by-step explanation:
[tex]3x+2y+z=12\\\Rightarrow z=12-3x-2y[/tex]
Now we integrate over volume integral over the range [tex]R = \{(x,y) | 0\le x \le {1}, -{2} \le y \le {4} \}[/tex]
[tex]V=\int_0^1\int_{-2}^4 12-3x-2y dydx\\ =\int_{-2}^4 12y-3yx-y^2|_4^{-2} dx\\ =\int_{0}^1 12\times4-3\times4x-16-[12\times-2-3\times-2x-4]dx\\ =\int_{0}^1 60-18xdx\\ =60x-9x^2|_{0}^1\\ =60-9\\ =51\ \text{cubic units}[/tex]
The volume of the solid is 51 cubic units.
Find the area of the surface. The part of the paraboloid z = 1 - x2 - y2 that lies above the plane z = -6
Answer:
π/6 [(29)^³/₂ − 1]
81.247
Step-by-step explanation:
Surface area is:
S = ∫∫ √(fₓ² + fᵧ² + 1) dA
The partial derivatives are:
fₓ = -2x
fᵧ = -2y
Substituting:
S = ∫∫ √(4x² + 4y² + 1) dA
To make this easier, we can convert to polar coordinates.
S = ∫∫ √(4r² + 1) dA
S = ∫∫ √(4r² + 1) r dr dθ
S = ⅛ ∫∫ 8r √(4r² + 1) dr dθ
The limits for θ are 0 to 2π. The minimum of r is 0. The maximum of r is:
-6 = 1 − x² − y²
-6 = 1 − r²
r² = 7
r = √7
Integrating the first integral:
S = ⅛ ∫ ⅔ (4r² + 1)^³/₂ |₀ᴿ dθ
S = ⅛ ∫ [⅔ (4(7) + 1)^³/₂ − ⅔ (4(0) + 1)^³/₂] dθ
S = ⅛ ∫ [⅔ (29)^³/₂ − ⅔] dθ
S = ¹/₁₂ [(29)^³/₂ − 1] ∫ dθ
Integrating the second integral:
S = ¹/₁₂ [(29)^³/₂ − 1] θ |₀²ᵖⁱ
S = ¹/₁₂ [(29)^³/₂ − 1] (2π − 0)
S = π/6 [(29)^³/₂ − 1]
S ≈ 81.247
The area of a shape is the amount of space it covers.
The surface area is approximately 81.3 unit squares
The given parameters are:
[tex]\mathbf{z = 1 - x^2 - y^2}[/tex]
[tex]\mathbf{z = -6}[/tex]
Calculate the partial derivatives of [tex]\mathbf{z = 1 - x^2 - y^2}[/tex]
[tex]\mathbf{f_x = -2x}[/tex]
[tex]\mathbf{f_y = -2y}[/tex]
So, the surface area is:
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(f_x^2 + f_y^2 +1 )}} \, dA }[/tex]
So, we have:
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{((-2x)^2 + (-2y)^2 +1 )}} \, dA }[/tex]
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4x^2 + 4y^2 +1 )}} \, dA }[/tex]
Factor out 4
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4(x^2 + y^2) +1 )}} \, dA }[/tex]
Substitute
[tex]\mathbf{r^2 = x^2 + y^2}\\\mathbf{dA = rdr d\theta}[/tex]
So, we have:
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4r^2 +1 )}} \, r\ dr\ d\theta }[/tex]
Multiply by 1
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4r^2 +1 )}} \, r \times 1\ dr\ d\theta }[/tex]
Express 1 as 8/8
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4r^2 +1 )}} \, r \times \frac{8}{8}\ dr\ d\theta }[/tex]
Rewrite as:
[tex]\mathbf{A =\frac{1}{8} \int\limits^a_b\int\limits^a_b {8r \sqrt{(4r^2 +1 )}}, \ dr\ d\theta }[/tex]
From the question,
[tex]\mathbf{z = -6}[/tex]
So, we have:
[tex]\mathbf{1 - r^2 = -6}[/tex]
Add 6 to both sides
[tex]\mathbf{7 - r^2 = 0}[/tex]
So, we have:
[tex]\mathbf{r^2 = 7}[/tex]
Integrate [tex]\mathbf{A =\frac{1}{8} \int\limits^a_b\int\limits^a_b {8r \sqrt{(4r^2 +1 )}}, \ dr\ d\theta }[/tex]
[tex]\mathbf{A =\frac{1}{8} \int\limits^a_b {\frac{8}{12} (4r^2 +1 )^{\frac 32}}, |\limits^R_0 d\theta }[/tex]
[tex]\mathbf{A =\frac{1}{8} \times \frac{8}{12} \int\limits^a_b { (4r^2 +1 )^{\frac 32}}, |\limits^R_0 d\theta }[/tex]
[tex]\mathbf{A =\frac{1}{12} \int\limits^a_b { (4r^2 +1 )^{\frac 32}}, |\limits^R_0 d\theta }[/tex]
[tex]\mathbf{A =\frac{1}{12} \int\limits^a_b { (4r^2 +1 )^{\frac 32} -(4 \times 0^2 +1 )^{\frac 32} }, d\theta }[/tex]
Substitute [tex]\mathbf{r^2 = 7}[/tex]
[tex]\mathbf{A =\frac{1}{12} \int\limits^a_b { (4\times 7 +1 )^{\frac 32} - 1^{\frac 32}}, d\theta }[/tex]
[tex]\mathbf{A =\frac{1}{12} \int\limits^a_b {29^{\frac 32} - 1}, d\theta }[/tex]
Rewrite as:
[tex]\mathbf{A =\frac{1}{12} (29^{\frac 32} - 1), \int\limits^a_b d\theta }[/tex]
Integrate
[tex]\mathbf{A =\frac{1}{12} (29^{\frac 32} - 1), \times \theta |\limits^{2\pi}_0}[/tex]
So, we have:
[tex]\mathbf{A =\frac{1}{12} (29^{\frac 32} - 1), \times (2\pi - 0) }[/tex]
[tex]\mathbf{A =\frac{1}{12} (29^{\frac 32} - 1), \times 2\pi}[/tex]
Rewrite as:
[tex]\mathbf{A =\frac{2\pi}{12} (29^{\frac 32} - 1)}[/tex]
[tex]\mathbf{A =\frac{\pi}{6} (29^{\frac 32} - 1)}[/tex]
[tex]\mathbf{A =81.3}[/tex]
Hence, the surface area is approximately 81.3 unit squares
Read more about surface areas at:
https://brainly.com/question/3621496
use long division by dividing 78 and 3
Answer:
26
Step-by-step explanation:
Answer:
26
Step-by-step explanation:
Step 1:
Start by setting it up with the divisor 3 on the left side and the dividend 78 on the right side like this:
3 ⟌ 7 8
Step 2:
The divisor (3) goes into the first digit of the dividend (7), 2 time(s). Therefore, put 2 on top:
2
3 ⟌ 7 8
Step 3:
Multiply the divisor by the result in the previous step (3 x 2 = 6) and write that answer below the dividend.
2
3 ⟌ 7 8
6
Step 4:
Subtract the result in the previous step from the first digit of the dividend (7 - 6 = 1) and write the answer below.
2
3 ⟌ 7 8
- 6
1
Step 5:
Move down the 2nd digit of the dividend (8) like this:
2
3 ⟌ 7 8
- 6
1 8
Step 6:
The divisor (3) goes into the bottom number (18), 6 time(s). Therefore, put 6 on top:
2 6
3 ⟌ 7 8
- 6
1 8
Step 7:
Multiply the divisor by the result in the previous step (3 x 6 = 18) and write that answer at the bottom:
2 6
3 ⟌ 7 8
- 6
1 8
1 8
Step 8:
Subtract the result in the previous step from the number written above it. (18 - 18 = 0) and write the answer at the bottom.
2 6
3 ⟌ 7 8
- 6
1 8
- 1 8
0
I need help please help me
$20,500 at 7% for 3 years,
Answer:
If it is simple interest then it is $24805
If it is a compound interest then it is $25113.38
Step-by-step explanation:
In the triangle below, what is the length of the side opposite the 60° angle?
Answer:
3
Step-by-step explanation:
Answer:
3 sqrt3
Step-by-step explanation:
AP3X
It is necessary to find the times when the temperature is 8° F. Which of the following is the correct equation to do this
(A) 9 - 1 = 8
(B) 9+2 = 8
(C) 9-12 = 8
You spend 5/6 of your money on new clothes for school. The amount you spend on jeans for school is 2/5 of the total amount you spend on all your school clothes.
What fraction of money do you spend on jeans?
A. 7/30 on jeans
B. 10/30 on jeans
C. 1/3 on jeans
D. 5/30 on jeans
Answer:
C
Step-by-step explanation:
well when we multiply to get a common denominator we get 25/30 and 12/30 so the only possible answer is 1/3
Twenty point question!
Answer:
yes
no
Step-by-step explanation:
i hope im correct please give me brainliest and some feedback if im correct or not :)
You have wanted a car you entire life (literally since you were born)!! It is time...you found the car of you dreams AND the car is marked as 80% of!!!! What a deal!!! "What could go wrong" you ask yourself. You buy the car for $625 (and the man in the hood walks off smiling). As your parent(s) drive you home after picking you up next to your broken down vehicle 3 hours later, they ask you what the original price of the car was before the price reduction. What was the original price of your.... "dream car"?
Answer:
200,000
Step-by-step explanation:
Calculating Rate of change
Answer/Step-by-step explanation:
We are given the following coordinates of two points on the line of the graph shown in the question as: A(2, 1) and B(4, 2)
Vertical change from point A = [tex] y_2 - y_1 = 2 - 1 = 1 [/tex]
Horizontal change from point A = [tex] x_2 - x_1 = 4 - 2 = 2 [/tex]
Rate of change = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{1}{2} = 0.5 [/tex]
John earns $437 a week after a 15% pay rise. What was his pay initially? Round your answer to the nearest dollar.
Answer:
380 dollars
Step-by-step explanation:
John earns $437 a week after a 15% pay rise.
Let the initially pay of John be x
x + (15% of x) = 437
x + 0.15x = 437
1.15x = 437
x = \frac{437}{1.15}
1.15
437
x = 380
Multiply the polynomial expressions.
-3x*(2x2 - 4x + 1)
Answer:
-15
Step-by-step explanation:the
Find the slope of the line that passes through the points (8, 2) and (4,4).
Helppp !!
Answer:
-[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
We can find the slope of the line by using the point slope formula: [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].
If we plug in your numbers, we get:
[tex]\frac{4-2}{4-8}[/tex], or -[tex]\frac{2}{4}[/tex], or -1/2.
A man earned wages of $30,600 , received $2900 in interest from a savings account, and contributed $2600 to a tax-deferred retirement plan.He was entitled to a personal exemption of $2500 and had deductions totaling $5020. Find his gross income, adjusted gross income, and taxable income
Answer:
So the answer is gonna be: 33,580. Hope this help!
Step-by-step explanation:
Last night, Hailey spent 1 2/5 hours on her math
homework, then 45 minutes on her science
homework. What is the total time she spent doing her
math and science homework? Write your answer in a
complete sentence.
Answer:
a = 2 hours and 9 minutes
Explanation:
(using fractions)
45 minutes + 1 2/5 hours = 3/4 hours + 7/5 hours = 15/20 + 28/20 = 43/20 = 2 3/20 = 2 9 /60 = 2 hours 9 minutes.
(using decimals)
45 minutes + 1 2/5 hours =
0.75 hours + 1.4 hours = 2.15 hours = 2 hours 9 minutes.
since .15 × 60 = 9 .
Also keep in mind that there are 60 minutes in an hour.
Answer:2 3/20
Step-by-step explanation:
1 2/5 + 45(3/4)
=2 3/20
Solve: 2/3x-7=17 please help
Answer:
x=36
Step-by-step explanation:
2/3x-7=17
2/3x-7+7=17+7
2/3x=24
2/3x(3)=24(3)
2x=72
2x/2=72/2
x=36
Find the value of a. Then find the angle measures of the quadrilateral.
Answer:
a = 60
Step-by-step explanation:
Since it is a quadrilateral, the sum of interior angles is equal to 360°. Now you have to create an equation to solve this question. To create an equation, you have to add all the interior angles to 360°.
The equation would be 2a°+a°+a°+2a° = 360°.
Then you would simplify it to 6a° = 360.
You would divide 6 on both sides to get to a° = 60.
Therefore, the value of a is 60.
Hope this helped! If not, please let me know! <3
What number is 30 percent of 50
Answer:
15 (50*0.3)
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
0.3*50 = 15
Write as a product:
25a^2−0.01b^10
Answer:
(5a + 0.1b^5)(5a + 0.1b^5)
Step-by-step explanation:
25a^2 − 0.01b^10 =
This follows the pattern: x^2 - y^2 = (x + y)(x - y)
= (5a + 0.1b^5)(5a + 0.1b^5)
50 twenties minus 1 twenty
-2/7 x 3/7 as fraction
Answer:
-6/49
Step-by-step explanation:
this is the answer it is very easy
Sam was asked to place the numbers shown below in order from greatest to least.
5, -0.5, 4, 350%, -13, 4.7, -66, 1.22
ANSWER ASAP
Answer:
5 > 4.7 > 4 > 350% > 1.22 > -0.5 > -13 > -66
Step-by-step explanation:
Express the ratio as a fraction in simplest form.
7 kilograms to 400 grams
Answer:
35:2
Step-by-step explanation:
7000 and 400 are each multiples of 100. 7000÷100=70
400÷100=4
70/4 is left
divide each by 2 as it is the only number that can go both in to 70 and 4
What’s 3 over 4 plus 1 over 8
Answer:
7/8
Step-by-step explanation:
3/4+1/8
give common denominators
6/8+1/8
add like terms
7/8.
Answer:
3/4 +1/8=
6/8+1/8=7/8
Hello Can someone help me please???
What is the factored form of 5x2 – 19x + 12?
A.) (5x – 3)(x – 4)
B.) (5x – 4)(x – 3)
C.) (5x – 12)(x – 1)
D.) (5x – 1)(x – 12)
Answer:
pretty sure its B
Step-by-step explanation:
hope this helps ;)
In Earnest's yard, the grass grew 2 inches. The next week, Earnest cut 2 inches off of the grass. The total change was 0 inches. Which of the following situations
also has a total change of 0?
I put 5 pounds of birdseed in the feeder. Then, birds ate 5 pounds of birdseed.
It rained 2 inches on Tuesday. Then, it rained 2 inches on Wednesday.
It Snowed 4 inches last week. Then, 8 inches of snow melted during this week.
A farmer sold 3 bushels of apples last week. Then, she sold 6 bushels of apples this week.
Answer:
The answer is the first one, I put 5 pounds of birdseed and he ate 5 pounds, leaving you with none, or zero.
Step-by-step explanation:
Help. Please, I will give you brainliest. Give me the right answers.
Step-by-step explanation:
[tex] \sf{\dfrac{5( \fbox{41} - 32)}{9} = C}[/tex]
[tex] \sf{\dfrac{5( \fbox{9})}{9} = C}[/tex]
[tex] \sf{ \dfrac{45}{9} = C}[/tex]
[tex] \sf{C = 5 }[/tex]
So,
41° F = [5]°C
Ram bought an article for rs. 148.75. He gave rs. 200 to the shopkeeper. What balance will he get ?
Answer:
his balance will be 51.25 rs.
Step-by-step explanation:
200 - 148.75 = 51.25
Answer:
51.25
Step-by-step explanation:
200-148.75
=51.25