Answer:
[tex]10 ^ {3m-2n} = 10 ^ z[/tex]
Where z = 3m-2n
Step-by-step explanation:
An important mathematical property about the powers is that when powers of equal base are divided, the same base is placed and the exponents are subtracted.
Then we can write 1000m and 100n as powers of the same base:
[tex]1000 ^ m = (10 ^ 3) ^ m = 10 ^ {3m}\\ 100 ^ n = (10 ^ 2) ^ n = 10 ^ {2n}[/tex]
Now we perform the division of powers of the same base (10)
[tex]\frac{10 ^ {3m}}{10 ^ {2n}} = 10 ^ {3m-2n}[/tex]
Finally
[tex]10 ^ {3m-2n} = 10 ^ z[/tex]
Where z = 3m-2n
To express z in terms of m and n, rewrite the equation: 1000m / 100n = 10z. Then, simplify to 100m / 10n = z. So, z can be expressed as 10m/n.
Explanation:The given equation is 1000m divided by 100n equals to 10z. To express z in terms of m and n, we need to isolate z. Let's proceed step by step:
First, rewrite the equation: 1000m / 100n = 10z;Then, eliminate the 10 on the right side by dividing both sides by 10, we get: 100m / 10n = z; Then, simplify the left side, we get: 10m/n = z;So, z can be expressed as 10m/n.
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Claire is considering investing in a new business. In the first year, there is a probability of 0.2 that the new business will lose $10,000, a probability of 0.4 that the new business will break even ($0 loss or gain), a probability of 0.3 that the new business will make $5,000 in profits, and a probability of 0.1 that the new business will make $8,000 in profits. a. Claire should invest in the company if she makes a profit. Should she invest? Explain using expected values.
The expected value of business profit is the sum of probability times profit:
... 0.2×(-10,000) + 0.4×0 + 0.3×5,000 + 0.1×8,000
... = -2000 + 1500 + 800
... = 300 . . . dollars
The expected value of the business return is slightly positve, so Claire should invest in the business.
Answer:
The answer above is correct
Celine observed that 80% of patrons at the local library liked reading sci-fi novels. If 35 patrons did not like reading sci-fi novels, how many patrons did enjoy sci-fi novels?
Part A: Write an equation in one variable that can be used to find the total number of patrons at the library? Define the variable used in the equation.
Part B: How many patrons enjoy reading sci-fi novels? Show your work.
Part A. Let the total number of patrons be x. Then the number of patrons that liked reading sci-fi novels is x-35. Now
x-35 is 80%
35 is 100%-80%=20%.
Mathematically, you can write a proportion:
[tex]\dfrac{x-35}{80}=\dfrac{35}{20},\\ \\x-35=\dfrac{35\cdot 80}{20},\\\\x-35=140,\\\\x=175.[/tex]
Part B. The total nuber of patrons is 175, 35 did not like the sci-fi novels, then 140 liked.
Final answer:
To find the total number of library patrons, set up an equation using the given information. Then, solve the equation to determine the number of patrons who enjoy reading sci-fi novels.
Explanation:
Part A: Let's represent the total number of patrons at the library as 'x'. Since Celine observed that 80% of the patrons liked reading sci-fi novels, we can say that 80% of 'x' patrons enjoy reading sci-fi novels.
Therefore, the equation to find the total number of patrons can be written as: 0.8x = x - 35.
Part B: To find the number of patrons who enjoy reading sci-fi novels, we can solve the equation from Part A. First, let's simplify the equation: 0.8x = x - 35.
Then, we'll subtract 'x' from both sides of the equation: 0.8x - x = -35.
Combining like terms, we have: -0.2x = -35.
Finally, we'll divide both sides of the equation by -0.2 to solve for 'x': x = (-35)/(-0.2).
Plugging in the values, we get: x = 175. Therefore, there are 175 patrons who enjoy reading sci-fi novels.
Find the values of x and y in the following equation
(x+yi)+(4+9i)=9-4i
A. x = 9 and y = -4
B. x = 5 and y = -13
C. x = -9 and y = 4
D. x = 5 and y = 13
Answer:
B. x = 5 and y = -13
Step-by-step explanation:
Equating real parts, we have ...
... x + 4 = 9
... x = 9 - 4 . . . . subtract 4
... x = 5
___
Equating imaginary parts, we have ...
... yi +9i = -4i
... yi = -4i -9i = -13i . . . . subtract 9i
... y = -13 . . . . . . . . . . . divide by i
[tex](x+yi)+(4+9i)=9-4i \\\\x+4+yi+9i=9-4i\\\\x+4+(y+9)i=9-4i\\\\x+4=9 \wedge y+9=-4\\\\x=5 \wedge y=-13 \Rightarrow \text{B}[/tex]
The functions f(x) and g(x) in the table below show Kim's and Ben's savings respectively, in dollars, after x days. Some values are missing in the table.
x(years) 1 2 3
g(x) = 3x
Kim's savings in dollars 3 9
f(x) = 3x + 5
Ben's savings in dollars 8 11
Which statement best describes Kim and Ben's savings in the long run?
The savings will increase by the same factor for both.
The savings will increase by the same amount for both.
Kim will save more than Ben.
Ben will save more than Kim.
pleaseeee help will give brainliest
The table can be filled in as follows:
[tex]\begin{array}{r|cccc}x(days)&1&2&3&4\\g(x)=3^x&3&9&27&81\\f(x)=3x+5&8&11&14&17\end{array}[/tex]
After 3 days, Kim's savings already exceeds Ben's, and is increasing at a faster rate. The appropriate descriptor is ...
... Kim will save more than Ben
_____
An exponential function increases faster than any polynomial function. (A linear function is a polynomial function.)
If Kim keeps up her savings for 28 days, her account balance will exceed the US Gross National Product of more than $20 trilliion. (Exponential functions tend to increase very rapidly!) Meanwhile, Ben's savings will be $89 on day 28.
_____
Please note the discrepancy in the problem statement. The verbiage says "days", but the table shows "years".
A kite is flying on 39 feet of string. How high is it above the ground if it’s height is 22 feet more than the horizons distance from the person flying it. Assume that the string is being held at ground level.
Answer:
about 36.3 feet
Step-by-step explanation:
Let x represent the height of the kite in feet. Then (x-22) is the horizontal distance to the kite. The Pythagorean theorem tells you the string length is related to these distances by ...
... 39² = x² + (x-22)²
... 2x² -44x -1037 = 0 . . . . rearrange to standard form
Using the quadratic formula, the positive solution is ...
... x = (-b+√(b²-4ac))/(2a) . . . . for a=2, b=-44, c=-1037
... x = (44 + √((-44)² -4(2)(-1037)))/(2·2)
... x = 11 + √639.5 ≈ 36.288
The kite is about 36.3 feet above the ground.
While in college, why did Euler work through advanced math books on his own? His father required it. The quality of education offered was not satisfactory. His teacher advised it because he did not have time to tutor Euler privately. He wanted to come up with a method that would help builders find the best arrangement for a ship’s masts.
The correct answer is "His teacher advised it because he did not have time to tutor Euler privately." I just did the assignment and got it correct.
While in college, Euler work through advanced math books on his own because his teacher advised it because he did not have time to tutor Euler privately.
Leonhard Euler was a renowned Swiss mathematician who made significant contributions to various branches of mathematics. While in college, Euler worked through advanced math books on his own not because of his father or the quality of education, but because his tutor, Johann Bernoulli, advised it. Bernoulli recognized Euler's talent and encouraged him to pursue mathematics independently, as Bernoulli did not have enough time to tutor Euler privately.
PLEASE KNOW BEFORE YOU ANSWER. I CAN'T GET THIS WRONG.
Identify and EXPLAIN the ERROR
Show CORRECT WORK and SOLUTION
Show CORRECT WORK and SOLUTION
THE FIRST PIC IS THE QUESTION!!!!
Answer:
a) Error: Moving the decimal point without changing the exponent changes the value of the number. The final number reported is different from the one computed.
b) Correct work: (see below)
... Correct solution: 1.035×10¹¹
Step-by-step explanation:
a) When the decimal point is moved to the left in the mantissa, its value is divided by 10 for each place the decimal point is moved. To keep the overall value of the number the same, the power of 10 must be increased to compensate. The increase in the exponent is the number of places the decimal point is moved left.
In this problem, the decimal point is moved 1 place left, so the exponent needs to be increased from 10 to 11.
b) Correct work:
[tex]\displaystyle(7.14\cdot 10^{10})+(3.21\cdot 10^{10})=(7.14+3.21)\cdot 10^{10}\\\\=10.35\cdot 10^{10}=1.035\cdot 10^{11}[/tex]
Write the equation of the line parallel to the given line and passing through the given point. y= 1/2 x+2 through (0,4)
Parallel lines have the same slope, so the slope of the new line is 1/2.
The line passes through (0,4), and this gives the y-intercept, which would equal 4.
The equation now would be: y = 1/2x + 4
The graph of an inequality has a closed circle at 2.6, and the ray moves to the left. What inequality is graphed?
x Greater-than-or-equal-to 12
A closed circle is used on the graph.
The arrow on the graph points right.
The inequality representation is x ≤ 2.6 and has been graphed.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of before example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given,
The graph of inequality has a closed circle at 2.6, and the ray moves to the left.
The closed circle represents that point x = 2.6 is included.
Suppose the variable is x then x ≤ 2.6 represents the inequality.
Hence "The inequality representation is x ≤ 2.6 and has been graphed".
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WILL GIVE BRAINLIEST Patrick decided to start his own business. his business made 35,000 the first year his profits have increased annually by an average of 2.5%
a. write and iterative (explicit) rule to model the sequence formed by patricks profits each year. Show your work
b. use the rule you wrote to determine what the profits will be after twelve years from the start of his business. round your answer to the nearest dollar. do not round until the end! show all fo your work
(a)
his profits increase annually by 2.5%, thus the profits each year form a geometric sequence with r = 1.025
that is 100 + 2.5 = 102.5% = 1.025
[tex]a_{n}[/tex] = 35000 × [tex](1.025)^{n-1}[/tex] ← explicit rule
(b)
[tex]a_{12}[/tex] = 35000 × [tex](1.025)^{11}[/tex] = 45923....
Profits after 12 years ≈ $46000
What method would you choose to solve the equation 2x2 – 7 = 9? Explain why you chose this method.
I would add 7 to get ...
... 2x² = 16
then divide by 2 to get
... x² = 8
Now, I would take the square root, recognizing that both positive and negative values will solve the problem.
... x = ±√8
The root can be simplified, so we have ...
... x = ±2√2
_____
The above method seemed the most obvious method to me. One could use the quadratic formula, but that seems to involve more operations.
... 2x² -16 = 0 . . . . subtract 9
... x = (-0 ± √(0² -4·2·(-16)))/(2·2) . . . . put the coefficients into the formula
... x = ±(√128)/4 = ±√8 = ±2√2 . . . . . simplify the result
Sample Response/Explanation: I would use the square root property of equality. Because there is no x term, I would just add and divide to get x2 by itself. Then I would take the square root.
plz help asap geometry
Answer:
i think its d
Step-by-step explanation:
Answer:
I think it is C triangle ABD and triangle ADC. I hope that helped.
Perform the indicated operation and write the result in the form a+bi. -9i(-9i+4)+3(8+8i)
- 57 - 12i
distribute the parenthesis
= 81i² - 36i + 24 + 24i
[ note that i² = (√- 1 )² = - 1 ]
= - 81 - 36i + 24 + 24i ( collect like terms )
= - 57 - 12i
Answer:
D^^
Step-by-step explanation:
Edge
Partial results of a survey about students who wear glasses are shown in the two-way table.
Which of the following statements are true? Check all that apply.
225 students were surveyed.
25 girls always wear glasses.
15 girls sometimes wear glasses.
52 boys never wear glasses.
75 boys were surveyed.
65 students sometimes wear glasses.
Answer:
a. True, b. False, c. True, d. True, e. False, f. True
Step-by-step explanation:
Partial results of a survey about students who wear glasses are shown in the two-way table.
First we complete the table to understand options easily
Always Sometimes Never Total
Boys 25 50 52 127
Girls 35 15 48 98
Total 60 65 100 225
Now we can solve all the options easily.
a. 225 students were surveyed - True
b. 25 girls always wear glasses - False (35)
c. 15 girls sometimes wear glasses - True
d. 52 boys never wear glasses - True
e. 75 boys were surveyed - False (127)
f. 65 students sometimes wear glasses -True
Please Help ASAP 20 points
Find the slope of the line through the given points.
(−1, 2) and (−5,10)
(1,3) and (0,−9)
(18, 6) and (−7, 7)
(−7, 10 ) and (1, 10)
if the x-intercept (–68, 0), and the y-intercept (0, –34), what is the equation?
y = - [tex]\frac{1}{2}[/tex] x - 34
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 68, 0 ) and (x₂, y₂ ) = (0, - 34 )
m = [tex]\frac{-34-0}{0+68}[/tex] = [tex]\frac{-34}{68}[/tex] = - [tex]\frac{1}{2}[/tex]
the y-intercept = (0, - 34 ) ⇒ c = - 34
y= - [tex]\frac{1}{2}[/tex] x - 34
Answer:
Y=-.5x-34
Step-by-step explanation:
this is because you can do y2-y1/x2-x1 to get slope
-34/68
Which equals one half so currently
Y=-1/2x
To get the y intercept we can look at the number when x=0 so it would be -34. So here is the equation
Y=-.5x-34
Charlotte has invited 75 people to her party. The buffet menu below is for 25 people. Work out how many of the following she will need:
Charlotte will need 3 buffet menus to host 75 people!
Micheal's mean score for five tests was 82. if four of those tests were 83,75,93, and 67, what was the fifth score on his test?
Let T represent the fifth test score. The average is the sum of scores divided by their number.
... 82 = (83 +75 +93 +67 +T)/5
... 410 = 318 +T . . . . . . . multiply by 5
... 92 = T . . . . . . . . . . . . subtract 318
The fifth score was 92.
_____
One of the ways I like to work problems like these is to add the differences from the mean. Those are ...
1, -7, 11, -15
so their sum is -10.
The final score must be 10 above the mean in order for this total to be zero. 10 above the mean is 92.
If the federal reserve sells 80000 in a treasury bond to a bank at 7% what is the immediate effect in the money supply
"It is decreased by $80,000" is the one among the following choices given in the question that would be an immediate effect on the money supply. The correct option among all the options that are given in the question is the first option or option "A". I hope that this is the answer that has actually come to your desired help.
mark brainliest plssss
help pls with math pls
slope = [tex]\frac{4}{3}[/tex] and equation of line is
y = [tex]\frac{3}{2}[/tex] x + 3
calculate the slope m using the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = 2, 7 ) and (x₂, y₂ ) = (- 1, 3 )
m = [tex]\frac{3-7}{-1-2}[/tex] = [tex]\frac{-4}{-3}[/tex] = [tex]\frac{4}{3}[/tex]
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
calculate m using the gradient formula
with (x₁, y₁ ) = (- 4, - 3) and (x₂, y₂ ) = (0, 3 )
m = [tex]\frac{3+3}{0+4}[/tex] = [tex]\frac{6}{4}[/tex] = [tex]\frac{3}{2}[/tex]
the line crosses the y-axis at (0, 3 ) hence c = 3
y = [tex]\frac{3}{2}[/tex] x + 3 ← equation of line
help please...........
1. y = 3 x
y = -8x
2. y = - 7x
y =-4x - 12
(1)
both equations express y in term of x, hence equate the right sides
- 8x = 3x ( subtract 3x from both sides )
- 11x = 0 ( divide both sides by - 11 )
x = 0
substitute x = 0 into y = 3x → y = 0
solution is : (x, y ) → (0, 0)
(2)
both equations express y in terms of x, hence equate the right sides
- 4x - 12 = - 7x ( add 7x to both sides )
3x - 12 = 0 ( add 12 to both sides )
3x = 12 ( divide both sides by 3 )
x = 4
substitute x = 4 into y = - 7x → y = - 28
solution is : (x, y ) = (4, - 28 )
Gina is making pancakes for breakfast. Each batch of pancakes calls for 1/4 of a teaspoon of salt. Gina has 9/10 of a teaspoon of salt left. How many batches of pancakes can she make?
Divide the total amount she has by how much she needs per batch.
When dividing fractions, flip the second one over and then multiply straight across.
9/10 / 1/4 becomes: 9/10 x 4/1
9/10 x 4/1 = 36/10 = 3 6/10 = 3 3/5
She can make 3 more batches and have 3/5 of a teaspoon left over.
Solve for x. 5x−2(x+1)=1/4 Enter your answer in the box. x =
x = [tex]\frac{3}{4}[/tex]
distribute the parenthesis on left side of equation and simplify
5x - 2x - 2 = [tex]\frac{1}{4}[/tex]
3x - 2 = [tex]\frac{1}{4}[/tex] ( add 2 to both sides )
3x = [tex]\frac{1}{4}[/tex] + 2 = [tex]\frac{9}{4}[/tex] ( divide both sides by 3 )
x = [tex]\frac{9}{4}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{3}{4}[/tex]
Point M belongs to AN , point N belongs to BM , AB = 18 in and AM : MN : NB = 1:2:3. Find MN.
MN = 6 in
add the parts of the ratio, 1 + 2 + 3 = 6
divide AB by 6 to find 1 part of the ratio
[tex]\frac{18}{6}[/tex] = 3 ← 1 part
AM = 3 in ← 1 part
MN = 2 × 3 = 6 in ← 2 parts
NB = 3 × 3 = 9 in ← 3 parts
and 3 + 6 + 9 = 18 in = AB
A sociologist randomly selects single adults for different groups of three, and the random variable x is the number in the group who say that the most fun way to flirt is in person. Determine whether a probability distribution is given. If a probability distribution is not given, identify the requirements that are not satisfied. Probability Distribution 0 1 2 3 0 0.1 0.2 0.3 0.4 0.5 P(x)
Does the table show a probability distribution? Select all that apply.
A.
Yes, the table shows a probability distribution.
B.
No, the sum of all the probabilities is not equal to 1.
C.
No, the random variable x's number values are not associated with probabilities.
D.
No, the random variable x is categorical instead of numerical.
E.
No, not every probability is between 0 and 1 inclusive.
x P(x)
0 0.092
1 0.338
2 0.418
3 0.152
Answer:
A.
Yes, the table shows a probability distribution.
Step-by-step explanation:
Given that a sociologist randomly selects single adults for different groups of three. And the random variable x is the number in the group who say that the most fun way to flirt is in person.
Since sample size is only 3, x cannot be more than 3.
So x can take values as 0 1 2 3
Prob distribution is given as
x P(x)
0 0.092
1 0.338
2 0.418
3 0.152
We find that x values are from 0 to 3.
Each probability is positive but less than 1.
Also total probability = 1
So this is a perfect probability distribution.
A.
Yes, the table shows a probability distribution.
Calculate the quotient of 54256/45
3.5x10^-2 of salt in one liter of water this is how much
2.64x10^20of liters water
Answer:
Total liters of salt in [tex]2.64*10^20[/tex] liters of water is [tex]9.24*10^18[/tex].
Step-by-step explanation:
If 1 liter of water contains [tex]3.5*10^-2[/tex] amount of salt,
Then,
[tex]2.64*10^20[/tex] liters of water will contain,
[tex]3.5*10^-2[/tex] should be multiplied by [tex]2.64*10^20[/tex].
Therefore,
Total liters of salt in [tex]2.64*10^20[/tex] liters of water is [tex]9.24*10^18[/tex].
HELP!! WORTH 20 POINTS
( anything )² = anything × anything
5² = 5 × 5 = 25
Which of the following is 2/11 closest to?
0.
1/2.
1.
2/11 is 0.181818 as a decimal so closest to 0.
Answer:
The answer is the first one which is 0
HHELLLP IDEK HOW TO DO THIS THIS IS DUE TODAY!!!!!
The slope is 8/5 because you are increasing 8 units in the y axis and 5 units in the x direction. So the equation here would be d = 8/5t which means for every increase in t by 1, d will increase by 8/5.