Answer:
[tex]x=\frac{1}{4}[/tex]
Step-by-step explanation:
We can use some logarithmic rules to solve this easily.
Note: Ln means [tex]Log_e[/tex]
Now, lets start with the equation:
[tex]ln(2x) + ln(2) = 0\\ln(2x) = -ln(2)[/tex]
Writing left side with logarithmic base e, we have:
[tex]Log_{e}(2x) = -ln(2)[/tex]
We can now use the property shown below to make this into exponential form:
[tex]Log_{a}b=x\\means\\a^x=b[/tex]
So, we write:
[tex]Log_{e}(2x) = -ln(2)\\e^{-ln(2)}=2x[/tex]
We recognize another property of exponentials:
[tex]a^{bc}=(a^{b})^{c}[/tex]
So, we write:
[tex]e^{-ln(2)}=2x\\(e^{ln(2)})^{-1}=2x[/tex]
Also, another property of natural logarithms is:
[tex]e^{(ln(a))}=a[/tex]
Now, we simplify:
[tex](e^{ln(2)})^{-1}=2x\\(2)^{-1}=2x\\\frac{1}{2}=2x\\x=\frac{\frac{1}{2}}{2}\\x=\frac{1}{4}[/tex]
This is the answer.
5/4 divided by 1 1/12
Answer:
1.36 or 34/25
Step-by-step explanation:
5/4=1.25
11/12=0.916
Answer:
15/13
Step-by-step explanation:
5/4 ÷ 1 1/12
= 5/4 ÷ 13/12
= 5/4 x 12/13
= (5 x 12) / (4x13)
= 60/52
=15/13
Maylin and Nina are making fruit baskets. They have 36 apples, 27 bananas, and 18 oranges. They want each basket to contain the same amount of each fruit. Maylin believes the greatest number of baskets they can make is 6, and Nina believes the greatest number of baskets they can make is 9. Determine who is correct. Explain how you know.
Nina is correct,
Hope this helped
XD XD XD XD XD
A student cost for last semester at her community college was 2000.She spent $220 of that on books.what percent of last semester college costs was spent on books??
11% of college costs was spent on books.
Step-by-step explanation:
Total cost for last semester = $2000
Amount spent on books = $220
Percent of amount spent on books = [tex]\frac{Amount\ spent\ on\ books}{Total\cost\ for\ semester}*100[/tex]
Percent of amount spent on books = [tex]\frac{220}{2000}*100\\[/tex]
Percent of amount spent on books = [tex]\frac{22000}{2000}[/tex]
Percent of amount spent on books = 11%
11% of college costs was spent on books.
Keywords: percentage, division
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$85 jeans; 7% tax
pls help
Answer:
sales tax is $5.95, total price of jeans is $90.95 I believe
Find the solution for 30 − 5n ≤ 25.
1 n ≤ -1
2 n ≤ -11
3 n ≥ -11
4 n ≥ 1
Answer:
n>=1
Step-by-step explanation:
30-5n<=25
5n<=30-25
5n<=5
n<=5/5
n<=1
n>=1
The tile back splash will be a mixture of colors of four inch square tiles. One fifth of the tiles will be indian red three tenths will be Tuscan blue one sixth will be eucalyptus and the rest will be the color of sand . What fraction of the tiles will be the color of sand .
=================================================
Explanation:
1/5 of the tiles are indian red
3/10 of the tiles are Tuscan blue
1/6 of the tiles are eucalyptus
x of the tiles are sand, where x is some fraction
The four fractions listed above add to 1. The "1" refers to a whole back splash, in which you can think of "1" as "100%"
-----------
We have the fractions 1/5, 3/10 and 1/6
To combine these fractions, we need a common denominator. In this case, the lowest common denominator (LCD) is 30 as this is the LCM of the denominators 5, 10, and 6.
Let's get each fraction to have a denominator of 30
1/5 = (6/6)*(1/5) = 6/30
3/10 = (3/3)*(3/10) = 9/30
1/6 = (5/5)*(1/6) = 5/30
-----------
So effectively we have these fractions: 6/30, 9/30, and 5/30
They add to the unknown fraction x to get 1
Let's solve for x.
-----------
(1/5) + (3/10) + (1/6) + x = 1
(6/30) + (9/30) + (5/30) + x = 1
(6/30 + 9/30 + 5/30) + x = 1
(6 + 9 + 5)/30 + x = 1
20/30 + x = 1
2/3 + x = 1
x + 2/3 = 1
x+2/3-2/3=1-2/3 ... subtract 2/3 from both sides
x = 1 - 2/3
x = 3/3 - 2/3
x = (3 - 2)/3
x = 1/3
------------
1/3 of the tiles are the color of sand
Final answer:
One third of the tiles will be the color of sand. This is found by adding the fractions of the other colors, simplifying, and subtracting from one whole set of tiles.
Explanation:
To find the fraction of the tiles that will be the color of sand, we first need to calculate the total fraction of tiles that have already been assigned colors: Indian red, Tuscan blue, and eucalyptus. Then we subtract this total from 1, which represents the whole set of tiles, to find the remaining fraction for the sand-colored tiles.
Indian red: ⅓ of the tilesTuscan blue: ⅗ of the tilesEucalyptus: ⅙ of the tilesAdding these fractions:
⅓ + ⅗ + ⅙ = ⅓ + (⅗ × 2/2) + (⅙ × 5/5)= ⅓ + ⅖ + ⅓= 10/15Now, we convert 10/15 to a simplified fraction:
10/15 = 2/3 (dividing both numerator and denominator by 5)To find the fraction for sand-colored tiles, subtract the total colored fraction from 1:
1 - 2/3 = 3/3 - 2/3= 1/3Therefore, one third of the tiles will be the color of sand.
There are 2 girls and 3 boys on a camping trip. What is the ratio of girls
to boys on the trip?
Answer:
2/3
Step-by-step explanation:
Answer:
2/3 is the answer
Step-by-step explanation:
n a recent election, Mark Benton received 780 votes for 12% of the total vote. How many people voted in the election?
A
65
B
936
C
6,500
D
9,360
Answer: Answer C
Step-by-step explanation:
12%___780 votes
100%___X= 6500 votes
(100*780)/12 = 6500
Alma brought pens of green and blue color. 35% of pens are blue. If she brought a total of 70 pens, how many green pens did she have?
Answer:
24.5% are green
Step-by-step explanation:
Which equation represents the horizontal line passing through (-1,2)
Answer:
y = 2
Step-by-step explanation:
When line is horizontal, all points on this line have the same value of y.
In this case , all points have to have y = 2.
y = 2, is an equation of horizontal line.
The equation of line y = 2 represents the horizontal line passing through (-1,2).
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have given a point (-1, 2) on a coordinate plane.
The distance from origin (0, 0) and (0, 2) is 2
And line y = 2 represents the horizontal line that passes through (-1, 2)
Thus, the equation of line y = 2 represents the horizontal line passing through (-1,2).
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16 factory workers made 40 pieces in a certain amount of time.
a)Do these quantities (number of workers and number of pieces produced) vary directly or inversely?
b)Find the constant of variation.
a) The quantities vary directly
b) The constant of variation is 2.5
Step-by-step explanation:
Lets us revise the direct and inverse variation
If y varies x directly, then y = kx, that means the ratio between them is constant ( [tex]\frac{y}{x}=k[/tex] ) , they increased together and decreased together, k is the constant of variationIf y varies x inversely, then yx = k, that means when x increased y must be decrease ( [tex]y=\frac{k}{x}[/tex] ) k is the constant of variation∵ 16 factory workers made 40 pieces in a certain amount of time
- If the number of worker increased, then the number of pieces
increased in the same certain time, if the number of worker
decreased, then the number of pieces also decrease in the
same certain time
∴ The the number of workers and the number of pieces produce
vary directly
∴ Number of pieces produced = k × number of worker
a) The quantities vary directly
∵ The number of worker = 16
∵ The number of pieces produced = 40
- Substitute these values in the equation of variation above
∴ 40 = k × 16
- Divide both sides by 16
∴ k = 2.5
b) The constant of variation is 2.5
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the difference of the product of 3 and 6 minus the quotient of 6 divided by 2
Jadas family has completed 30% of a trip. They have traveled 15 miles. How far is the trip
Answer:
50
Step-by-step explanation:
.3x=15
x=50
Answer:
The trip is 50miles far
Step-by-step explanation:
If they have travel 15miles which is equal to 30% of the trip.
To find how far the trip is.
Let x represent the trip in miles
Therefore:
30% of x is 15miles
30/100 * x = 15miles
x = 15 miles ÷ 30/100
x = 15 miles * 100/30
x = 1500miles/30
x = 50miles
I need help !
Write an equation in point slope form (-6,3) m= -1/5
Answer:
y-3=-1/5(x+6)
Step-by-step explanation:
Talia uses 10 strawberries and 4 oranges to make 8 servings of fruit salad.
Drag oranges and strawberries into the box to show how many Taila needs to make 12
servings.
Answer:
She needs 15 Strawberries and 6 Oranges to make 12 servings of fruit salad
Step-by-step explanation:
Strawberries : (12 x 10)/ 8 = 15
Oranges: (12 x 4)/8 = 6
12 servings = 8 and half of 8 (8+4=12)
15 strawberries =10 and half of 10 (10+5=15)
6 oranges= 4 and half of 4(4+2=6)
Answer:
15 strawberries
6 oranges
Step-by-step explanation:
The perimeter of a rectangle is 34cm.Find the breadth of the rectangle if its length is 12cm.
es - Multiply the binomials (5x - 1) and (2x - 8).
A)
10x2 - 42x - 8
B)
10x2 - 42x + 8
o
10x2 + 38x - 8
D)
10x2 – 38x - 8
Answer:
Our final answer is option B that is [tex]10x^2-42x+8[/tex]
Step-by-step explanation:
As we have to multiply the binomial.
Here is the work.
Using distributive law of multiplication.
Where [tex]a(b+c)=ab+ac[/tex]
⇒[tex](5x-1)(2x-8)[/tex]
[tex]5x(2x-8)-1(2x-8)[/tex]
[tex]10x^2-40x-2x+8[/tex]... [tex](-1\times -8 =8)[/tex]
As [tex]-40x[/tex] and [tex]-2x[/tex] are in negative so we will add these
numbers keeping the negative sign as it is.
[tex]10x^2-42x+8[/tex]
So the correct choice is option B that is [tex]10x^2-42x+8[/tex]
Benchmark 1 - Big Ideas Math - Grade 7
24. Jack's mother is 44 years old. She is 4 years older than 8 times Jack's age. The
equation 8a + 4 = 44 represents this situation.
How old is Jack?
A. 5
B. 6
c. 9
d.13
Answer:
Jack is five. so, it's A
Step-by-step explanation:
subtract 4 from both sides of the equation. You can cancel out the four on the left, and get 40 on the right (since you took four away from 44.)
Then, divide by 8 on both sides. The eight is canceled out on the left. eight goes into 40 five times, meaning a=5.
The correct option is (A) 5. To find Jack's age, subtract 4 from both sides of the equation 8a + 4 = 44 and then divide by 8. This results in a = 5, meaning Jack is 5 years old.
To solve the given equation, 8a + 4 = 44, for Jack's age, we first need to isolate the variable a, which represents Jack's age. This can be done by first subtracting 4 from both sides of the equation to undo the addition.
8a + 4 - 4 = 44 - 4
8a = 40
Next, we divide both sides of the equation by 8 to undo the multiplication and solve for a:
8a / 8 = 40 / 8
a = 5
Therefore, Jack's age is 5 years old, which corresponds to option A.
Find the surface area of a conical grain storage tank that has a height of 41 meters and a diameter of 16 meters. Round the answer to the nearest square meter.
Answer:
The surface area of a conical grain storage tank that has a height of 41 meters and a diameter of 16 meters is[tex]1250.9 m^2[/tex]
Explanation:
Height of the conical grain storage tanks =41 m
Diameter of the conical grain storage tank=16 m
Hence radius = diameter/2=8 m
Suppose h is height and r is radius
Formula used:
Surface area of a cone= A
A= [tex]\pi rl +\pi r^2[/tex]
= πr(l+r)
Where[tex]l =(r^2+h^2)^1^/^2[/tex]
=[tex]\pi r(r+(h^2+r^2)^1^/^2)[/tex]
Putting the values
=[tex]3.14 \times 8\left(8+\left(41^{2}+8^{2}\right)^{1 / 2}\right)[/tex]
=1250.9368
=[tex]1250.9 m^2[/tex]
[tex]1250.9 m^2[/tex] is the surface area of a conical grain storage tank
LabTech is a company that manufactures microscopes and other laboratory instruments . On occasion, one of the microscopes is defective when it comes off of the production line. The probability that a microscope is defective is 0.17%. Find the probability that one of the first 50 microscopes is defective .
To find the probability of at least one defective microscope in a batch of 50, we first calculate the probability of all 50 being non-defective and then subtract this from 1. The resulting probability of having at least one defective microscope in the batch is approximately 7.96%.
Explanation:The question is about finding the probability that one of the first 50 microscopes manufactured by LabTech is defective. Given the probability of a microscope being defective is 0.17%, we can calculate this by multiplying the probability of a single microscope being defective by the total number of microscopes.
Firstly, convert the 0.17% to a decimal by dividing by 100, which gives us 0.0017. This is the probability of a single microscope being defective. Then, to find out the probability of at least one out of 50 being defective, we would consider the opposite - the probability of all 50 microscopes being non-defective. If one microscope has a 0.0017 chance of being defective, it has a 1-0.0017 = 0.9983 chance of being non-defective.
The chance of all 50 microscopes being non-defective is [tex](0.9983)^{50} = 0.9204.[/tex] Therefore, the probability of at least one out of 50 being defective is 1 - 0.9204 = 0.0796 or 7.96%.
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Final answer:
The probability that at least one of the first 50 microscopes manufactured is defective is calculated using the complement rule, by subtracting the probability of none being defective from 1, the answer is 0.082
Explanation:
To find the probability that at least one of the first 50 microscopes LabTech manufactures is defective, we use the complement rule. The probability that a microscope is not defective is 1 - 0.0017 (since 0.17% as a decimal is 0.0017). To find the probability that none of the microscopes out of the 50 produced are defective, we raise this to the power of 50:
P(no defective microscopes) = [tex](1 - 0.0017)^{50[/tex]
Then, to find the probability that at least one microscope is defective, we subtract this from 1:
P(at least one defective microscope) = [tex]1 - (1 - 0.0017)^{50[/tex]
P(at least one defective microscope)= 1-0.918= 0.082
Write as one logarithm. Simplify.
log5 125 – log5 25
Answer:
log 5 5
= 1.
Step-by-step explanation:
Use the logarithm law loga b - loga c = loga b/c:
log5 125 – log5 25
= log5 125 / 25
= log5 5.
= 1.
The expression log5 125 - log5 25 simplifies to 1.
To combine the logarithms log5 125 and log5 25 as one logarithm and simplify, we can use the properties of logarithms. Specifically, we'll use the property that states logb(x) - logb(y) = logb(x/y). Applying this property, we have:
log5 125 - log5 25 = log5 (125/25)
We simplify the fraction 125/25 to get 5. So, we have:
log5 (125/25) = log5 5
The logarithm of a number to the base of itself is always 1, so:
log5 5 = 1
Therefore, the expression log5 125 - log5 25 simplifies to 1.
Sea equation below that represents the line passing through the .(1 ,-4)with a slope of 1/2
Answer:
f(x)=1/2x-4.5
Step-by-step explanation:
so I used Desmos, so your starting point is -4.5 down from the 0 on the y line, then just do rise over run with 1/2 and it should pass through (1,-4)
J(x)=3x+-1 find j(-2)
Answer:
-7
Step-by-step explanation:
j(x)=3x+(-1)
j(x)=3x-1
j(-2)=3(-2)-1
j(-2)=-6-1
j(-2)=-7
Answer:
-7
Step-by-step explanation:
plug in -2 for x
(3)(-2) = -6
and then add the -1
= -7
3x - 3y = -3
2x - y = -5
For this case we must solve the following system of equations:
[tex]3x-3y = -3\\2x-y = -5[/tex]
To solve we follow the steps below:
We multiply the second equation by -3:
[tex]-6x + 3y = 15[/tex]
Thus, we have the equivalent system:
[tex]3x-3y = -3\\-6x + 3y = 15[/tex]
We add the equations:
[tex]3x-6x-3y + 3y = -3 + 15\\-3x = -3 + 15\\-3x = 12\\x = \frac {12} {- 3}\\x = -4[/tex]
We look for the value of the variable "y":
[tex]2 (-4) -y = -5\\-8-y = -5\\-y = -5 + 8\\-y = 3\\y = -3[/tex]
Thus, the solution of the system is given by:
[tex](x, y): (- 4, -3)[/tex]
Answer:
[tex](x, y): (- 4, -3)[/tex]
(2, -3) and (6,-13)
What is the slope
Answer:
-5/2
Step-by-step explanation:
Slope = change in y over change in x or (y2-y1)/(x2-x1)
slope = (-13-(-3))/(6-2) = -10/4 = -5/2
Answer:
m=-5/2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-13-(-3))/(6-2)
m=(-13+3)/4
m=-10/4
simplify,
m=-5/2
What is the first term of the quotient of the following division problem ? (X^3-1)
Answer:
The question is incomplete, complete question is:
What is the first term of the quotient of the following division problem?
(x^3 – 1) ÷ (x + 2)
A. –0.5
B. 1
C. x^2
D. x^4
option C
Step-by-step explanation:
(x^3-1) divide by x+2
Use long division
x^2 -2x
-----------------------
x+2 x^3 + 0x^2 +0x -1
x^3 + 2x^2
-----------------------------------(subtract it)
- 2x^2 +0x - 1
-2x^2 - 4x
--------------------------------(subtract)
5x -1
Thus the first term of the quotient is x^2.
Am i doing this right?
y = -4
Answer:
Step-by-step explanation:
no but you are very close
you forgot to put the x next to the -4
because if you left it like that than it would be a horizontal line going through the y-axis at -4
the x is very important since it is the input value while y is the output
so y depends on the x
Answer:
[tex]\displaystyle YES[/tex]
Step-by-step explanation:
The equation you modeled here is [tex]\displaystyle y = -4x,[/tex]where the y-intercept and x-intercept are both located at the origin. This is what is called direct variation.
I am joyous to assist you anytime.
*Just attach the x to the equation because leaving it out would form a horizontal line [zero rate of change (slope)].
If the adult dosage of the medicine is 180 milligrams (mg), what is 1/3 of the adult dose?
The 1/3 of the adult dosage of the medicine will be 60 milligrams(mg).
What is a fraction?A fraction is a number that is less than 1.
For example, a number 0.5 than is called a fraction number because it is less than 1.
Given that the adult dosage of the medicine is 180 milligrams(mg).
The 1/3 of the 180 milligrams(mg) will be
⇒ 180×1/3
⇒ 60 hence, 60 milligrams(mg) is one-third of adult dosage.
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To find 1/3 of the adult dosage of 180 mg, you simply divide by 3, which results in a dose of 60 mg. This method ensures safe and accurate medication dosing.
If the adult dosage of the medicine is 180 milligrams (mg), then 1/3 of the adult dose can be calculated by dividing the adult dose by 3. So, you would perform the following calculation:
1/3 of 180 mg = 180 mg / 3 = 60 mg.
Therefore, 1/3 of the adult dosage of the medicine is 60 mg.
rounding 829+392 nearest hundred
Mohammad would like to graph the line that represents the total number of baseball cards he will
have collected, T, after m months, given that he buys 5 cards each month and he started with no
cards. He would like the graph to show the number of cards after 6 and 12 months
Select from the drop-down menus to correctly complete each statement
To best show this information, the scale for the T-axis of his graph should go from 0 to at least
(Answer)
and the m-axis of his graph should go from 0 to at least (Answer)
Answer:
To best show this information, the scale for the T-axis of his graph should go from 0 to at least 60.
To best show this information, the scale for the m-axis of his graph should go from 0 to at least 12.
Step-by-step explanation:
Mohammad will have collected T cards after m months, given that he buys 5 cards each month and he started with no cards.
The relationship describing this situation is
[tex]T=5m[/tex]
When [tex]m=6,[/tex] then [tex]T=5\cdot 6=30[/tex] cards.
When [tex]m=12,[/tex] then [tex]T=5\cdot 12=60[/tex] cards.
To best show this information, the scale for the T-axis of his graph should go from 0 to at least 60.
To best show this information, the scale for the m-axis of his graph should go from 0 to at least 12.