Answer:
(1/10)∛100 ≈ 0.4642
Step-by-step explanation:
For a cube of volume V, the edge length is ...
s = ∛V
and the area is ...
A = 6s² = 6V^(2/3)
Then the ratio of area to volume is ...
r1 = A/V = 6V^(2/3)/V = 6V^(-1/3)
If the value of V is increased by a factor of 10, the ratio of area to volume is now ...
r2 = 6(10V)^(-1/3)
The factor by which the ratio changed is ...
r2/r1 = (6(10V)^(-1/3))/(6V^(-1/3)) = 10^(-1/3) = (1/10)∛100
The surface area per unit volume changes by a factor of (∛100)/10.
___
Example
For a cube of side length 2, the volume is 2³ = 8 and the surface area is 6·2² = 24. The ratio of surface area to volume is 24/8 = 3.
Multiplying the edge length by ∛10, we now have a volume of (2∛10)³ = 80, and a surface area of 6(2∛10)² = 24(10^(2/3)). The ratio of surface area to volume is ... 24(10^(2/3))/80 = 0.3∛100.
The ratio of area to volume changed by a factor of (0.3∛100)/3 = (∛100)/10, as above.
a) Find a recurrence relation for the number of bit strings of length n that contain a pair of consecutive 0s.
b) What are the initial conditions?
c) How many bit strings of length seven contain two consecutive 0s?
Answer:
A) [tex]a_{n} = a_{n-1} + a_{n-2} + 2^{n-2}[/tex]
B) [tex]a_{0} = a_{1} = 0[/tex]
C) for n = 2
[tex]a_{2}[/tex] = 1
for n = 3
[tex]a_{3}[/tex] = 3
for n = 4
[tex]a_{4}[/tex] = 8
for n = 5
[tex]a_{5}[/tex] = 19
Step-by-step explanation:
A) A recurrence relation for the number of bit strings of length n that contain a pair of consecutive Os can be represented below
if a string (n ) ends with 00 for n-2 positions there are a pair of consecutive Os therefore there will be : [tex]2^{n-2}[/tex] strings
therefore for n ≥ 2
The recurrence relation for the number of bit strings of length 'n' that contains consecutive Os
[tex]a_{n} = a_{n-1} + a_{n-2} + 2^{n-2}[/tex]
b ) The initial conditions
The initial conditions are : [tex]a_{0} = a_{1} = 0[/tex]
C) The number of bit strings of length seven containing two consecutive 0s
here we apply the re occurrence relation and the initial conditions
[tex]a_{n} = a_{n-1} + a_{n-2} + 2^{n-2}[/tex]
for n = 2
[tex]a_{2}[/tex] = 1
for n = 3
[tex]a_{3}[/tex] = 3
for n = 4
[tex]a_{4}[/tex] = 8
for n = 5
[tex]a_{5}[/tex] = 19
Which set is closed under subtraction?
the set of whole numbers
the set of natural numbers
the set of rational numbers
the set of irrational numbers
Answer:
Set of rational numbers
Step-by-step explanation:
Answer:
the set of rational numbers
Step-by-step explanation:
Edge 2021
Graphing form equation for y=x^3
Answer:
Step-by-step explanation:
In the U.S., 79,816,000 people age 25 and over have completed at least a bachelor’s degree. This is 36% of the population. How many people are age 25 and over in the U.S.?
Answer:
79,816,000 people
Step-by-step explanation:
Given:
People Age 25 above = 79,816,000 people
Required
Determine the population of people over 25
The first statement of the question reads:
"In the U.S., [tex]79,816,000[/tex] people age 25 and over......"
This statement answers your question;
Hence;
Required Population = 79,816,000 people
Jada is evaluating 8 × 3 × 4. She doesn't know the product of 24 and 4 off the top of her head, so she decides to multiply 3 by 4 first. Which property is Jada using? PLEASE HELP!!
Answer: Associative property
Step-by-step explanation:
From the question, we are informed that Jada is evaluating 8 × 3 × 4 and that she doesn't know the product of 24 and 4 off the top of her head, so she decides to multiply 3 by 4 first.
The property that Jada is using is the Associative property. This has to do with regrouping of the numbers and then multiplying the numbers in different groups.
Find the distance between the pair of points.(-6, -20) and (-17, -22)
Answer:
Use the distance formula to determine the distance between two points.
5 √ 5
The graph below shows the number of pages that Victor has left to read in his book at the end of the day over seven days. Pages Left to Read in Victor’s Book On a coordinate plane, the x-axis is labeled Day and the y-axis is labeled Pages left. On day 0 there were 220 pages; Day 1, 180; Day 2, 170; Day 3, 140; Day 4, 140; Day 5, 100; Day 6, 60; Day 7, 40. Which statement is supported by the graph? Victor read 0 pages on day 4. Victor read 170 pages on day 2. Victor read the same number of pages on day 1 and on day 2. Victor read the same number of pages on day 3 and on day 4.
Answer:
C
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
I had the same question and got it right
what is the median of 3 3 4 5 5 5 6 6 6 7 8
Answer:
5
Step-by-step explanation:
The median is the middle number of the list when put in order from smallest to largest
3 3 4 5 5 5 6 6 6 7 8
There are 11 numbers so the middle number is the 6th ( 5 on the left and 5 on the right
3 3 4 5 5 5 6 6 6 7 8
If x = -1 and y = 6, then x + 3xy
(A) 19
(B) 17
(C) 16
(D) -16
(E) -17
Choose
Answer:
D
Step-by-step explanation:
idk I just guessed tbh
Answer:
E -17
Step-by-step explanation:
3 times -1 is -3
-3 times 6 is -18
-18 + -1 is -17 (++)
Been working for 30 minutes can’t wrap my head around this, need help fast!
Answer:
It's D.
Step-by-step explanation:
If you want me to explain it, I will. But it seems like you need the answer fast. So if you still don't understand it later, then I will try to explain it...but it'll take some time. :)
All you have to do is move all the points to the right 6 numbers because it says x+6. For example, A is (-5,-1). Move to the right 6 times, so (-5+6,-1) which is (1, -1). So the new point of A is (1, -1). Do the same with the others. Now that we got the new rectangle in the fourth quadrant, you want to move it counterclockwise around the origin, which is 0. Clockwise is like a clock, it goes around the middle going to the right. Counterclowise is the same, except it goes to the left around the middle of the clock. You can sort of apply that to this. Go counterclockwise around the middle, in this case being the origin, 0. Move the rectangle up to the first quadrant because counterclockwise is going around to the left. So, if the rectangle goes around to the left, then that means that it is now vertical...because it turns to the left making it straight if you go counterclockwise. Now the point A is on the bottom left because the rectangle got turned. If you turned it properly, then A should be at (1,1). Apply the same thing to the other points. D is the only one with point A being at the point (1,1), so that is correct. Check the other points anyway.
Select the correct answer. A bottlenose dolphin is 10 feet below sea level. Then it begins to dive at a rate of 9 feet per second. What is the equation of the line that represents its elevation, y, after x seconds? A. y = 9x − 10 B. y = -9x − 10 C. y = 9x + 10 D. y = -9x + 10
Answer: y = -9x − 10
Step-by-step explanation: y represents the elevation of the bottlenose dolphin. The dolphin begins at 10 feet below sea level or -10. It then becomes to dive, go deeper under the water at a rate of 9 feet per second, or -9.
The equation y = -9x - 10 will equal the amount of feet below sea level that the dolphin is at. Below sea level will always be indicated with a negative number.
Find the equation of a line containing the given points (4,3) and (8,1). Write the equation in slope-intercept form. Please give step by step explanation.
Answer:
-1/2
Step-by-step explanation:
y2-y1 1-3 -1
x2-x1 8-4 2
Need help now Please help
Answer:
D is the correct answer.
Answer:
d
Step-by-step explanation:
taisha ran faster than 15.02 but slower than 14.65
Solve for x using
cross multiplication.
Answer:
Step-by-step explanation:
5X * 4-->20X
8(2X+3)--> 16X+24
20X=16X+24
4X=24
x=6
Answer:
x = 6
Step-by-step explanation:
(5x) ×4=8× (2x+3)
20x = 16x + 24
20x- 16x = 24
4x = 24
divide both sides by 4 to get the value of x
4x/4 = 24/ 4
x = 6
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 420 gram setting. It is believed that the machine is underfilling the bags. A 49 bag sample had a mean of 413 grams. Assume the population variance is known to be 676 . A level of significance of 0.1 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.
Answer:
The value is [tex]p-value = 0.0297[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 420 \ g[/tex]
The The sample size is [tex]n = 49[/tex]
The sample mean is [tex]\= x = 413 \ g[/tex]
The population variance is [tex]\sigma^2 = 676[/tex]
Generally the population standard deviation is mathematically represented as
[tex]\sigma = \sqrt{\sigma^2 }[/tex]
[tex]\sigma = \sqrt{676}[/tex]
[tex]\sigma = 26[/tex]
The null hypothesis is [tex]H_o : \mu = 420 \ g[/tex]
The alternative hypothesis is [tex]H_a : \mu < 420 \ g[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{ \= x - \mu }{ \frac{ \sigma }{\sqrt{n} } }[/tex]
=> [tex]z= \frac{ 413 - 420 }{ \frac{ 26 }{\sqrt{49} } }[/tex]
=> [tex]z = -1.884[/tex]
The p-value is obtained from the z-table table and the value is
[tex]p-value = P(Z < -1.885) = 0.029715[/tex]
[tex]p-value = 0.0297[/tex]
n/12 = 300 n = pls help again
Answer: 3600
Step-by-step explanation: N= 3,600
3,600/12= 300
Answer:
n=0, or n=3600
Step-by-step explanation:
If your question is n/12 = 300n, n=0
Otherwise n/12=300, n=3600
Multiply both sides by 12 to isolate variable
The question is on the picture.
Equation:
8-9 = 3(4-5a)
Solution:
16-a =6(4-5a) (step 1)
16-a=24-5a (step 2)
16+ 40 = 24 (step 3)
4a=8 (step 4)
a=2
(step 5)
which statement describes the error in the solution?
Answer:
the answer is 988 .........
Simplify the equation 9z-3z=48
Answer: z=8
Step-by-step explanation:
9z-3z=48
6z=48 ⇔ combine like terms
z=8
Hope this helps
Answer:
z = 8
Step-by-step explanation:
9z - 3z = 48
6z = 46
z = 8
g find the 2 components of vector b = 2i + j - 3k, one parallel to a = 3i - j and another one perpendicular to a
Answer:
The components of [tex]\vec{b}[/tex] parallel and perpendicular to [tex]\vec {a}[/tex] are [tex]\vec {b}_{\parallel} = \frac{3}{2}\,i-\frac{1}{2}\,j[/tex] and [tex]\vec b _{\perp} = \frac{1}{2}\,i+\frac{3}{2}\,j-3\,k[/tex], respectively.
Step-by-step explanation:
Let be [tex]\vec b = 2\,i+j-3\,k[/tex] and [tex]\vec a = 3\,i-j[/tex], the component of [tex]\vec b[/tex] parallel to [tex]\vec a[/tex] is calculated by the following expression:
[tex]\vec b_{\parallel} = (\vec b \bullet \hat{a}) \cdot \hat{a}[/tex]
Where [tex]\hat{a}[/tex] is the unit vector of [tex]\vec a[/tex], dimensionless and [tex]\bullet[/tex] is the operator of scalar product.
The unit vector of [tex]\vec a[/tex] is:
[tex]\hat{a} = \frac{\vec {a}}{\|\vec a\|}[/tex]
Where [tex]\|\vec {a}\|[/tex] is the norm of [tex]\vec a[/tex], whose value is determined by Pythagorean Theorem.
The component of [tex]\vec{b}[/tex] parallel to [tex]\vec {a}[/tex] is:
[tex]\|\vec {a}\| = \sqrt{3^{2}+(-1)^{2}+0^{2}}[/tex]
[tex]\|\vec {a}\| = \sqrt{10}[/tex]
[tex]\hat{a} = \frac{1}{\sqrt{10}} \cdot (3\,i-j)[/tex]
[tex]\hat{a} = \frac{3}{\sqrt{10}}\,i -\frac{1}{\sqrt{10}} \,j[/tex]
[tex]\vec{b}\bullet \hat{a} = (2)\cdot \left(\frac{3}{\sqrt{10}} \right)+(1)\cdot \left(-\frac{1}{\sqrt{10}} \right)+(-3)\cdot \left(0\right)[/tex]
[tex]\vec b \bullet \hat{a} = \frac{5}{\sqrt{10}}[/tex]
[tex]\vec b_{\parallel} = \frac{5}{\sqrt{10}}\cdot \left(\frac{3}{\sqrt{10}}\,i-\frac{1}{\sqrt{10}}\,j \right)[/tex]
[tex]\vec {b}_{\parallel} = \frac{3}{2}\,i-\frac{1}{2}\,j[/tex]
Now, the component of [tex]\vec {b}[/tex] perpendicular to [tex]\vec{a}[/tex] is found by vector subtraction:
[tex]\vec{b}_{\perp} = \vec {b}-\vec {b}_{\parallel}[/tex]
If [tex]\vec b = 2\,i+j-3\,k[/tex] and [tex]\vec {b}_{\parallel} = \frac{3}{2}\,i-\frac{1}{2}\,j[/tex], then:
[tex]\vec{b}_{\perp} = (2\,i+j-3\,k)-\left(\frac{3}{2}\,i-\frac{1}{2}\,j \right)[/tex]
[tex]\vec b _{\perp} = \frac{1}{2}\,i+\frac{3}{2}\,j-3\,k[/tex]
what’s the probability of drawing a jack on the first draw and a 3 on the second draw
Answer:
jgvi hhvh ihvyv
Step-by-step explanation:
what is 57/5as a decimal
Answer:
11.4
Step-by-step explanation:
57/5 as a mixed number is 11 2/5.
2/5 of a number is also known as 4/10 or 0.4, so add that to 11 to get 11.4.
Answer:
11.4
Step-by-step explanation:
57/5 = 11.4
last year frankie deli made an 11 foot 6 inch submarine this year they plan to make another one 2 feet and 3 inches longer how many feet long will this sandwich be? anserw
Answer:
13 feet 9 inches
Step-by-step explanation:
11 feet 6 inches + 2 feet 3 inches= 13 feet 9 inches
If you wish to have $60,000 in 8 years, how much do you need to deposit in the bank today if the account pays 9% using present value and future value.
Answer:
Amount to deposit= $26799.0
Step-by-step explanation:
Amount A = $60,000
Years t = 8 years,
Rate R = 9% .
A= p(1+r/n)^(nt)
60000= p(1+0.09/9)^(9*9)
60000= p(1+0.01)^(81)
60000= p(1.01)^81
60000= p(2.23888)
60000/2.23888= p
26799.1138= p
P= $26799.0
Amount to deposit= $26799.0
To be able to have $60,000 after 8 years at a rate of 9% per annum, the amount to deposit today is $30,111.98
You can solve this using the Future Value formula which is:
Future value = Present value x ( 1 + rate)^ number of years
You have everything except the present value so solve for it:
60,000 = PV x ( 1 + 9%)⁸
60,000 = PV x 1.9925626416901921
PV = 60,000 / 1.9925626416901921
PV = $30,111.98
In conclusion, you should deposit $30,111.98 today.
Find out more about this at https://brainly.com/question/14715827.
What is the quotient of 3,968 ÷ 32?
Answer:
124
Step-by-step explanation:
you just add 32 till u get 3968
Answer: The quotient of 3,968 ÷ 32= 124
Nidhi is thinking of a number n, and she wants her sister to guess the number. Her first clue is that eight less than three times her number is between one and nineteen. Write a compound inequality that shows the range of numbers that Nidhi might be thinking of
Answer:
The range of numbers that Nidhi might be thinking of is between 3 and 9.
Step-by-step explanation:
We are given that Nidhi is thinking of a number n, and she wants her sister to guess the number.
Her first clue is that eight less than three times her number is between one and nineteen.
Let the number Nidhi is thinking be 'n'.
So, eight less than three times her number means that;
[tex](3\times \text{n}) - 8 = 3\text{n}-8[/tex]
Now, according to the question; the above equation is between one and nineteen, so;
[tex]1< 3\text{n}-8 < 19[/tex]
Adding 8 to the whole expression;
[tex]1+8< 3\text{n}-8 +8< 19+8[/tex]
[tex]9< 3\text{n}< 27[/tex]
Dividing the whole expression by 3;
[tex]\frac{9}{3} < \frac{3\text{n}}{3} < \frac{27}{3}[/tex]
[tex]3< \text{n}< 9[/tex]
Hence, the range of numbers that Nidhi might be thinking of is between 3 and 9.
An Olympic swimming pool is 50 m long, 25 m wide, and 1.5 m deep. How many Olympic pools would be filled by the dollar bills spent by the U.S. federal government in 2011
Answer:
Number of dollars bills that can be fitted in Olympic pool = 1.67 billion.
Step-by-step explanation:
The dimensions of a dollar bill are 15.5956 cm by 6.6294 cm by 0.010922 cm. The U.S. federal government spent $3.8 trillion in fiscal year 2011.
An Olympic swimming pool is 50 m long, 25 m wide, and 1.5 m deep. How many Olympic pools would be filled by the dollar bills spent by the U.S. federal government in 2011
From above,
The volume for the dimension of the dollar bill = 15.5956 cm × 6.6294 cm × 0.010922 cm
The volume for the dimension of the dollar bill = 1.12922 cm³
The volume for the dimension of the dollar bill = 1.12922 × 10⁻⁶ m³
The volume of the pool = 50 m × 25 m × 1.5 m
The volume of the pool = 1875 m³
Number of dollars bills that can be fitted in pool = volume of the pool/volume of the dimension of dollar bills
Number of dollars bills that can be fitted in Olympic pool =1875 m³ / 1.12922 × 10⁻⁶ m³
Number of dollars bills that can be fitted in Olympic pool = 1,660,438,180
Number of dollars bills that can be fitted in Olympic pool = 1.67 billion.
[tex]2(4z - 2) = 44[/tex]
can you help me
2(4z−2) = 44
Simplify both sides of the equation.
Distribute:
(2)(4z)+(2)(−2) = 44
8z + −4 = 44
8z − 4 = 44
Add 4 to both sides.
8z − 4 + 4 = 44 + 4
8z = 48
Divide both sides by 8
8z/8 48/8
z = 6
Answer:
z=6
Step-by-step explanation:
12b + 9 = 12b + 11 what’s the answer
Answer: b∈∅
Step-by-step explanation:
Answer:
no solutions
Step-by-step explanation:
12b + 9 = 12b + 11
Subtract 12b from each side
12b-12b + 9 = 12b-12b + 11
9 = 11
This is never true, so there are no solutions
Which of the numbers below is less than zero? Select all that apply.
A) 1.2
B) 7/2
C)-3.5
D)-0.75
E)-1/3
C D E
Step-by-step explanation:
All the numbers above (C D E) are negative, making them less than 0.
Answer:
C, D, and E. They are all negative, which means they are less than zero.
1.2 and 7/2 are more than one. 7/2 simplifies to 3 1/2.