Answer:
log(1/10) = -1
Step-by-step explanation:
Use the law of exponents and the meaning of logarithm.
1/10 = 10^-1
log(10^x) = x
So, you have ...
log(1/10) = log(10^-1)
log(1/10) = -1
find the domain of the graphed function.
B(n)=2^n A binary code word of length n is a string of 0's and 1's with n digits. For example, 1001 is a binary code word of length 4. The number of binary code words, B(n), of length n, is shown above. If the length is increased from n to n+1, how many more binary code words will there be? The answer is 2^n, but I don't get how they got that answer. I would think 2^n+1 minus 2^n would be 2. Please help me! Thank you!
Answer:
More number of words that can be made: [tex]\bold{2^n}[/tex]
Please refer to below proof.
Step-by-step explanation:
Given that:
The number of binary code words that can be made:
[tex]B(n) =2^n[/tex]
where n is the length of binary numbers.
Binary numbers means 2 possibilities either 0 or 1.
Here, suppose if we have 5 as the length of binary number.
And there are 2 possibilities for each digit.
So, total number of possibilities will be [tex]2\times 2\times 2\times 2\times 2 = 2^5[/tex]
If the length of binary number is 2.
The total words possible are [tex]2^2[/tex].
These numbers are:
{00, 01, 10, 11}
If the length of binary number is 3. (increasing the 'n' by 1)
The total words possible are [tex]2^3[/tex].
These words are:
{000, 001, 010, 100, 011, 101, 110, 111}
So, number of More binary words = 8 - 4 = 4 or [tex]2^2[/tex] or [tex]2^n[/tex].
So, the answer is [tex]2^n[/tex].
Let us try to prove in generic terms:
[tex]B(n) = 2^n[/tex]
Increasing the n by 1:
[tex]B(n+1) = 2^{n+1}[/tex]
Number of more words made by increasing n by 1:
[tex]B(n+1) -B(n)= 2^{n+1} -2^n\\\Rightarrow 2\times 2^{n} -2^n\\\Rightarrow 2^n(2-1)\\\Rightarrow \bold{2^n}[/tex]
Hence, proved that:
More number of words that can be made: [tex]\bold{2^n}[/tex]
if a point is chosen inside the large circle what is the probability that it will also be inside the small circle?
Answer:
1/4
Step-by-step explanation:
The probability will be equal to 1 - (probability that it will not be inside the small circle) = 1 - (pi*4-pi)/(pi*4)=1/4
Reduce to Standard form : (a) -21/91 (b) 32/(-256)
Answer:
a) -3/13
b) -1/8
Step-by-step explanation:
a) - (21 / 7) / (91 / 7) = 3/13
b) (32 / 32 ) / - (256 / 32) = -1/8
The sum of 8 times a number and 7 equals 9!
Answer:
0.25*8+7=9
Step-by-step explanation:
8x+7=9
2/8=x
0.25=x
The radius of a sphere is measured as 7 centimeters, with a possible error of 0.025 centimeter.
Required:
a. Use differentials to approximate the possible propagated error, in cm3, in computing the volume of the sphere.
b. Use differentials to approximate the possible propagated error in computing the surface area of the sphere.
c. Approximate the percent errors in parts (a) and (b).
Answer:
a) dV(s) = 15,386 cm³
b) dS(s) = 4,396 cm²
c) dV(s)/V(s) = 1,07 % and dS(s)/ S(s) = 0,71 %
Step-by-step explanation:
a) The volume of the sphere is
V(s) = (4/3)*π*x³ where x is the radius
Taking derivatives on both sides of the equation we get:
dV(s)/ dr = 4*π*x² or
dV(s) = 4*π*x² *dr
the possible propagated error in cm³ in computing the volume of the sphere is:
dV(s) = 4*3,14*(7)²*(0,025)
dV(s) = 15,386 cm³
b) Surface area of the sphere is:
V(s) = (4/3)*π*x³
dV(s) /dx = S(s) = 4*π*x³
And
dS(s) /dx = 8*π*x
dS(s) = 8*π*x*dx
dS(s) = 8*3,14*7*(0,025)
dS(s) = 4,396 cm²
c) The approximates errors in a and b are:
V(s) = (4/3)*π*x³ then
V(s) = (4/3)*3,14*(7)³
V(s) = 1436,03 cm³
And the possible propagated error in volume is from a) is
dV(s) = 15,386 cm³
dV(s)/V(s) = [15,386 cm³/1436,03 cm³]* 100
dV(s)/V(s) = 1,07 %
And for case b)
dS(s) = 4,396 cm²
And the surface area of the sphere is:
S(s) = 4*π*x³ ⇒ S(s) = 4*3,14*(7)² ⇒ S(s) = 615,44 cm²
dS(s) = 4,396 cm²
dS(s)/ S(s) = [ 4,396 cm²/615,44 cm² ] * 100
dS(s)/ S(s) = 0,71
A number is multiplied by 8, and that product is added to 2. The sum is equal to the product of 2 and 25. Find the number.
Answer: the number = 6
Step-by-step explanation:
Let x be the number.
Set equation according to the information given
2 + 8x = 2 × 25
Simplify by multiplication
2 + 8x = 50
Subtract 2 on both sides
2 + 8x - 2 = 50 - 2
8x = 48
Divide 8 on both sides
8x / 8 = 48 / 8
[tex]\boxed {x=6}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Find the center, vertices, and foci of the ellipse with equation 4x2 + 9y2 = 36. Center: (0, 0); Vertices: (-3, 0), (3, 0); Foci: Ordered pair negative square root 5 comma 0 and ordered pair square root 5 comma 0 Center: (0, 0); Vertices: (-9, 0), (9, 0); Foci: Ordered pair negative square root 65 comma 0 and ordered pair square root 65 comma 0 Center: (0, 0); Vertices: (0, -3), (0, -3); Foci: Ordered pair 0 comma negative square root 5 and ordered pair 0 comma square root 5 Center: (0, 0); Vertices: (0, -9), (0, 9); Foci: Ordered pair 0 comma negative square root 65 and ordered pair 0 comma square root 65
Answer:
Option A.
Step-by-step explanation:
The given equation of ellipse is
[tex]4x^2+9y^2=36[/tex]
Divide both sides by 36.
[tex]\dfrac{4x^2}{36}+\dfrac{9y^2}{36}=1[/tex]
[tex]\dfrac{x^2}{9}+\dfrac{y^2}{4}=1[/tex]
[tex]\dfrac{x^2}{3^2}+\dfrac{y^2}{2^2}=1[/tex] ...(1)
The standard form of an ellipse is
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex] ...(2)
where, (h,k) is center, (h±a,k) are vertices and (h±c,k) are foci.
On comparing (1) and (2), we get
[tex]h=0,k=0,a=3,b=2[/tex]
Now,
Center [tex]=(h,k)=(0,0)[/tex]
Vertices [tex]=(h\pm a,k)=(0\pm 3,0)=(3,0),(-3,0)[/tex]
We know that
[tex]c=\sqrt{a^2-b^2}=\sqrt{3^2-2^2}=\sqrt{5}[/tex]
Foci [tex]=(h\pm c,k)=(0\pm \sqrt{5},0)=(\sqrt{5},0),(-\sqrt{5},0)[/tex]
Therefore, the correct option is A.
How many 4 digit palidromes are there?
Divide 500 in the ratio 4:5:1
Answer:
200 : 250 : 50
Step-by-step explanation:
Sum the parts of the ratio, 4 + 5 + 1 = 10 parts
Divide the amount by 10 to find the value of one part
500 ÷ 10 = 50 ← value of 1 part of ratio , then
4 parts = 4 × 50 = 200
5 parts = 5 × 50 = 250
500 = 200 : 250 : 50
Answer:
200, 250 and 50.
Step-by-step explanation:
First find the 'multiplier'.
4 + 5 + 1 = 10
500/10 = 50 = multiplier.
So the answer is
4*50 = 200
5 * 50 = 250
and 1 * 50 = 50.
What is the answer to my question?
Answer:
2/3
Step-by-step explanation:
24/36
Divide the top and the bottom by 12
24/12 =2
36/12 = 3
2/3
A bag contains 4 white and 2 black balls of the same size and weight and two balls are selected at random without replacement,what are the possible outcomes ?
Answer:
Step-by-step explanation:
Total balls in bag = 4+2
= 6 balls
Total white balls = 4
Total black balls = 2
The possible outcomes are
Black and Black or White and White or White and Black or Black and White.
Probability of black and black = 2/6
= 1/3
Probability of white and white = 4/6
= 2/3
Probability of Black and white or White and black
= 1/3×2/3
= 2/9
please click thanks and mark brainliest if you like :)
possible outcomes will be white and black, white and white, black and white or black and black
How is multiplying 3 - 2i by ia represented on the complex plane?
Drag a term or measure into each box to correctly complete the statements
The complex number 3 - 2i lies in quadrant IV
of the complex plane. When any complex number is multiplied by the
imaginary unit, the complex number undergoes a
90°
rotation in a counterclockwise direction This means that
the complex product of 3 - 2i and 22 lies in
quadrant I
of the complex plane.
The equation is represented 3 units to the left of the complex plane and 2 units up.
What is complex equation?A complex equation is an equation that involves complex numbers when solving it. A complex number is a number that has both a real part and an imaginary part.
Well to see how this is represented, we first need to multiply it out so we can see how it looks when it is simplified!
[tex]=(3-2i)(i^2)\\\\\\i^2=-1\\\\\\=(3-2i)(-1)\\\\\\=(-3+2i)[/tex]
We know that on a complex plane, our imaginary numbers are represented on the vertical axis.
So the original expression, (3-2i) would have been 3 units to the right on a complex graph and 2 units downward!
The equation I input above should be pretty straightforward, but one thing I didn't mention was that i^2 should = -1 when dealing with complex numbers!
Therefore, the equation 3-2i * i^2 is equal to -3 + 2i, this is graphed 3 units to the left and to units upward!
To know more about complex numbers follow
https://brainly.com/question/10662770
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log, (x + y)=log, y, log, x .
Solve for question D only
Answer:
4.
Step-by-step explanation:
Change of base formula is
logb x = loga x / loga b
So logx 25 = log5 25 /log5 x
Now log5 25 = log5 5^2 = 2, so:
logx 25 = 2 / log5 x
So log5 x^2 * logx 25
= log5 x^2 * 2 /log5 x
= 2 log5 x * 2 / log5 x
= 4.
Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. , The mean, , is nothing. (Round to the nearest tenth as needed.)
Complete Question
Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. , The mean, , is nothing. (Round to the nearest tenth as needed.)
p = 0.6 n = 18
Answer:
The mean [tex]\mu = 10.5[/tex]
The standard deviation [tex]\sigma = 2.08[/tex]
The variance [tex]var = 4.32[/tex]
Step-by-step explanation:
From the question we are told that
The probability of success is [tex]p = 0.6[/tex]
The sample size is [tex]n = 18[/tex]
Generally given that the distribution is binomial, then the probability of failure is mathematically represented as
[tex]q = 1- p[/tex]
substituting values
[tex]q = 1- 0.6[/tex]
[tex]q =0.4[/tex]
Generally the mean is mathematically evaluated as
[tex]\mu = np[/tex]
substituting values
[tex]\mu = 18 * 0.6[/tex]
[tex]\mu = 10.5[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{npq}[/tex]
substituting values
[tex]\sigma = \sqrt{18 * 0.6 * 0.4}[/tex]
[tex]\sigma = 2.08[/tex]
The variance is evaluated as
[tex]var = \sigma^2[/tex]
substituting value
[tex]var = 2.08^2[/tex]
[tex]var = 4.32[/tex]
helppppppppppppppppp pllllzzzzz
a
b
c
Answer:
b rectángulo de la referencia de los números que están por debajo de la construcción de un triángulo obtusangulo
The cost of a daily rental car is as follows: The initial fee is $39.99 for the car, and it costs $0.20 per mile. If Julie's final bill was $100.00 before taxes, how many miles did she drive?
Answer:
300.05 miles
Step-by-step explanation:
initial fee= $39.99
final bill = $ 100
cost =$ 0.20 per mile
remaining amount = $ 60.01
solution,
she drive = remaining amount / cost
=60.01/0.20
=300.05 miles
Answer:
500 miles
Step-by-step explanation:
Let us use cross multiplication to find the unknown amount.
Given:
1) Cost for 1 mile=$0.20
2)Cost for x miles=$100
Solution:
No of miles Cost
1) 1 $0.20
2)x $100
By cross multiplying,
100 x 1= 0.20x
x=100/0.20
x=500 miles
Thank you!
Name the property of real numbers illustrated by the equation
Answer:
A. Commutative property
Step-by-step explanation:
The commutative property states that multiplication can be performed in any order. This means that a*b=b*a. Therefore, it does not matter whether [tex]\sqrt{2}[/tex] or 3 is first in the multiplication problem. So, the first answer is correct.
Which expression is equal to (1+6i)−(7+3i) ?
Answer:
- 6+3iStep-by-step explanation:
[tex](1+6i)-(7+3i) ?\\Group\:the\:real\:part\:and\:the\:imaginary\\\:part\:of\:the\:complex\:number\\\left(a+bi\right)\pm \left(c+di\right)=\left(a\:\pm \:c\right)+\left(b\:\pm \:d\right)i\\=\left(1-7\right)+\left(6-3\right)i\\1-7=-6\\6-3=3\\=-6+3i[/tex]
A man earns RS.95 in a day how much does we earn in 18 days
Answer:
RS 17.10
Step-by-step explanation:
If they earn 0.95 a day, you can multiply that income by the number of days, which is 18.
RS 17.10
A couple has a total household income of $84,000. The husband earns $18,000 less than twice what the wife earns. How much does the wife earn? Select the correct answer below:
Answer:
$34000
Step-by-step explanation:
We can set up a systems of equations, assuming [tex]h[/tex] is the husbands income and [tex]w[/tex] is the wife's income.
h + w = 84000
h = 2w - 18000
We can substitute h into the equation as 2w - 18000:
(2w - 18000) + w = 84000
Combine like terms:
3w - 18000 = 84000
Add 18000 to both sides
3w = 102000
And divide both sides by 3
w = 34000
Now that we know how much the wife earns, we can also find out how much the husband earns by substituting into the equation.
h + 34000 = 84000
h = 50000
Hope this helped!
Jeff is playing a racing game. The game awards him an initial of virtual money. In addition, he gets of virtual money for each race he wins. In the end, he calculates average earnings of for each race he won. If represents the number of races he won, which equation can be used to find the number of wins? A. B. C. D.
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Perform the following computation with radicals. Simplify the answer.
V6 18
311
123 45
6
7
8
+
x
Question: Perform the following computation with radicals. Simplify the answer. √6 • √8
Answer:
[tex] 4\sqrt{3} [/tex]
Step-by-step explanation:
Given, √6 • √8, to perform the computation, we would simply evaluate the radicals and try as much as possible to leave the answer in the simplest form in radicals.
Thus,
[tex] \sqrt{6}*\sqrt{8} = \sqrt{6*8} [/tex]
[tex] = \sqrt{48} [/tex]
[tex] = \sqrt{16*3} = \sqrt{16}*\sqrt{3}[/tex]
[tex] = 4\sqrt{3} [/tex]
PLEASE HELP FOR 70 POINTS!!!!!! Maria and Jackson like in adjacent neighborhoods. If they superimpose a coordinate grid on the map of their neighborhoods, Maria lives at (–9, 1) and Jackson lives at (5, –4). Each unit on the grid is equal to approximately 0.132 mile. 8. How far apart do Maria and Jackson live to the nearest thousandth? 9. If April lives equidistant to both Maria and Jackson, at what coordinate on the grid would she live? 10. How far apart would Maria and April live to the nearest thousandth?
Answer:
8) 1.962 miles
9) (-2, -1.5)
10) 0.515 miles
Step-by-step explanation:
√(-9 - 5)² + (1 - -4)² = 14.866
14.866 x .132 = 1.962
(-9+5)/2, (1 + -4)/2
-4/2, -3/2
-2, -3/2
√(-2 - 1)² + (-3/2 - -4)² = 3.905
3.905 x .132 = 0.515 miles
Pentagon ABCDE and pentagon A”B”C”D”E” are shown on the coordinate plane below. Which two transformations are applied to pentagon ABCDE to create A”B”C”D”E”?
Answer:
Translated according to the rule (x, y)⇒ (x+7, y+1) , reflected across the x-axis
Step-by-step explanation:
Transformation involves changing the orientation, or even size of a given figure or object to produce its image. The methods of transformation include; translation, rotation, reflection, and dilation.
Comparing the pentagon ABCDE and A”B”C”D”E”, the two transformations applied are reflection across the x-axis first, then translation.
1. Which word best describes how you feel when working on a math assessment? ( point)
bored
excited
anxious
confident
Answer:
math is really a difficult subject for me. sometimes i feel confident when i get my answers correct, but sometimes i feel bored when i dnt get my answer. Sometimes i feel anxious , sometimes i feel excited to solve the problems.
Learn more:
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Which equation represents a population of 210 animals that decreases at an annual rate of 14%
Answer:
The equation i.e. used to denote the population after x years is:
P(x) = 490(1 + 0.200 to the power of x
Step-by-step explanation:
This problem could be modeled with the help of a exponential function.
The exponential function is given by:
P(x) = ab to the power of x
where a is the initial value.
and b=1+r where r is the rate of increase or decrease.
Here the initial population of the animals are given by: 490
i.e. a=490
Also, the rate of increase is: 20%
i.e. r=20%
i.e. r=0.20
Hence, the population function i.e. the population of the animals after x years is:
P(x) = 490(1 + 0.200 to the power of x
So for this, we will be using exponential form, which is y = ab^x (a = initial value, b = growth/decay).
Since we start off with 210 animals, that is our a variable.
Next, since this is *decreasing* by 14%, you are to subtract 0.14 (14% in decimal form) from 1 to get 0.86. That will be your b variable.
Putting everything together, your equation is y = 210(0.86)^x
Identify the slope and y-intercept of the function y = –2x+1.
Answer:
Below
Step-by-step explanation:
The function is y= -2x +1
● the slope is -2
● the y-intercept is 1
Compute the flux H F of F(x,y) = hxy, x − yi across the boundary of the square given by −1 ≤ x ≤ 1, −1 ≤ y ≤ 1.
Answer:
4i.
Step-by-step explanation:
To find the flux through the square, we use the divergence theorem for the flux. So Flux of F(x,y) = ∫∫divF(x,y).dA
F(x,y) = hxy,x - yi
div(F(x,y)) = dF(x,y)/dx + dF(x,y)dy = dhxy/dx + d(x - yi)/dy = hy - i
So, ∫∫divF(x,y).dA = ∫∫(hy - i).dA
= ∫∫(hy - i).dxdy
= ∫∫hydxdy - ∫∫idxdy
Since we are integrating along the boundary of the square given by −1 ≤ x ≤ 1, −1 ≤ y ≤ 1, then
∫∫divF(x,y).dA = ∫₋₁¹∫₋₁¹hydxdy - ∫₋₁¹∫₋₁¹idxdy
= h∫₋₁¹{y²/2}¹₋₁dx - i∫₋₁¹[y]₋₁¹dx
= h∫₋₁¹{1²/2 - (-1)/2²}dx - i∫₋₁¹[1 - (-1)]dx
= h∫₋₁¹{1/2 - 1)/2}dx - i∫₋₁¹[1 + 1)]dx
= 0 - i∫₋₁¹2dx
= - 2i[x]₋₁¹
= 2i[1 - (-1)]
= 2i[1 + 1]
= 2i(2)
= 4i
For this problem, use the tables and charts shown in this section. (Use picture provided)
A United States Citizen returning to the States declares the following items at the customs office:
3 shirts at $8.50 each
2 dresses at $27.50 each
1 pair of gold cuff links at $17.50 per pair
If he has not used his duty free exemption yet, how much duty should he pay?
0 $0.00
$5.00
$10.00
$300
Answer:
0
Step-by-step explanation:
0 because there is a $100 duty free exemption.
answer:
For this problem, use the tables and charts shown in this section.
A United States Citizen returning to the States declares the following items at the customs office:
3 shirts at $8.50 each
2 dresses at $27.50 each
1 pair of gold cuff links at $17.50 per pair
If he has not used his duty free exemption yet, how much duty should he pay?
$0.00 !
$5.00
$10.00
$300