Step-by-step explanation:
So a three digit number can be expressed as: [tex]100a + 10b + c[/tex] where a is the third digit, b is the second digit, and c is the first digit. Or in other words a is the hundreds place, b is the tens place, and c is the ones place. When something "increases" by 30%, it is 130% it's original value, and to calculate how much that is, you simply convert 130% to a decimal by dividing by 100, which gives you 1.30. And since all the digits are increased by 1, you have the equation:
[tex]100(a+1) + 10(b+1) + 1(c+1) = 1.30(100a+10b+c)[/tex]
Distribute the multiplication on the left side:
[tex]100a+100+10b+10+c+1=1.30(100a+10b+c)[/tex]
Distribute the multiplication on the right side:
[tex]100a+100+10b+10+c+1=130a+13b+1.3c[/tex]
Add like terms on the left side:
[tex]100a+10b+c+111=130a+13b+1.3c[/tex]
Subtract 100a, 10b, and c from both sides
[tex]111=30a+3b+0.3c[/tex]
So "technically" you can just plug in any two values, and then solve for the last value, but since you have a 3 digit number, you have the restriction of a < 10, b < 10, and c < 10, and also a, b, and c, should only be integers and all have the same sign or it wouldn't be a 3 digit number.
So let's start with a, since it has the highest coefficient, well you can fit 30 into 111, 3 times without going over so that's the first value
111 = 30(3) + 3b + 0.3c
111 = 90 + 3b + 0.3c
Now subtract the 90 from both sides
21=3b+0.3c
Well 3 can fit into 21, 7 times!
21 = 3(7) + 0.3c
21 = 21 + 0.3c
subtract 21 from both sides
0 = 0.3c
and now obviously c is 0, if you want you can divide both sides by 0.3 but it's a bit redundant
c = 0
This gives you the three values, a=3, b=7, c=0. which is the number 370. Now let's double check. Adding 1 to each digit would give you 481 and 481/370 = 1.3, so it is correct!
part b:
So to prove there is no three digit number, is to realize there is no solution, given the restriction or integers, greater than or equal to 0, and less than 10, and all of them must have the same sign.
So let's start with the same equation except this time instead of 1.3 it's 1.4
[tex]100(a+1) + 10(b+1) + 1(c+1) = 1.40(100a+10b+c)[/tex]
Distribute on the left side;
[tex]100a+100+10b+10+c+1=1.40(100a+10b+c)[/tex]
Distribute on the right side:
[tex]100a+100+10b+10+c+1=140a + 14b + 1.4c[/tex]
Add like terms on left side:
[tex]100a + 10b + c + 111 = 140a + 14b + 1.4c[/tex]
Subtract 100a, 10b, and c from both sides:
[tex]111 = 40a + 4b + 0.4c[/tex]
Now to do the same process, let's start by finding how many times we can fit 40 into 111, and if you're wondering why we start with 40, it's because let's say for example I just say, I can fit another 40 into it, but I decide not to, and let b do that, well even if it's just 40, b will have be at least 10, which does not fit our restrictions, so you have to fit as many 40's into the number first then go the other numbers.
So only 2 40's can fit in 111 without going over the value
111 = 40(2) + 4b + 0.4c
Subtract 80 from both sides
[tex]31=4b+0.4c[/tex]
4 can fit into 31, 7 times
31 = 4(7) + 0.4c
31 = 28 + 0.4c
subtract 28 from both sides
3 = 0.4c
divide both sides by 0.4
7.5 = c.
Since c is not an integer there is no 3 digit number that exists that increases by 40% whenever you increase it by 1.
a student
multiplied 4552 by 175 instead of multiplying by 157 how much was his product greater than the correct product
The student product is 81936 greater than the correct product
How to multiply numbers?The student was suppose to multiply 4552 by 157 but instead he multiplied 4552 by 175.
Therefore, let's find how much his product is greater than the correct product.
incorrect product = 4552 × 175 = 796600
Correct product = 4552 × 157 = 714664
Therefore,
difference = 796600 - 714664 = 81936
Therefore, his product is 81936 greater than the correct product.
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Given the following information, determine which lines, if any, are parallel. State the
postulate or theorem that justifies your answer.
Answer:
parallel lines a and b
parallel lines l and m
Step-by-step explanation:
25 A.
Angles 3 and 7 are alternate interior angles of lines a and b cut by transversal l.
Since angles 3 and 7 are congruent, lines a and b are parallel by the theorem:
If two lines are cut by a transversal such that alternate interior angles are congruent, then the lines are parallel.
25 B.
Angles 5 and 12 are same side interior angles of lines l and m and transversal b.
Since the sum of the measures of the angles 5 and 12 is 180, then angles 5 and 12 are supplementary angles making lines l and m parallel by the theorem:
If two lines are cut by a transversal such that same side interior angles are supplementary, then the lines are parallel.
Find the distance CD rounded
to the nearest tenth.
C = (4,7) D= (7,11)
CD= [?]
HINT: Use the distance formula:
d = √(x₂-x₁)² + (Y2 − 1)²
Enter
√(x₂-x₁)² + (Y2 − 1)²
√(7-4)² + (11− 7)²
√(3)² + (4)²
√(9)+ (16)
√(25) = 5
Thus, CD = 5
Hope this helps!
Multiply Conjugates Using the Product of Conjugates Pattern
In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern
333. (4 − 6y)(4 + 6y)
Answer:
The product is the difference of squares is[tex]$$\left(4-6y\right)\left(4+6y\right)=16-36{{y}^2}$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (4-6 y)(4+6y).We have to multiply the given expression.Square the first term 4. Square the last term 6y.[tex]$$\begin{aligned}&(4-6 y)(4+6 y)=(4)^{2}-(6 y)^{2} \\&(4-6 y)(4+6 y)=16-36 y^{2}\end{aligned}$$[/tex]
I need help :(:(:(:(
The resulting matrix of the row operation is given as follows:
[tex]R = \left[\begin{array}{ccc}7&4.5&-6\\-6&-3&12\end{array}\right][/tex]
How to find the resulting matrix?We apply the row operation on the original matrix, given as follows:
[tex]A = \left[\begin{array}{ccc}4&3&0\\-6&-3&12\end{array}\right][/tex]
The operation is given by:
[tex]R_1 = R_1 - 0.5R_2[/tex]
That is, applying to each element, we have that:
4 - 0.5(-6) = 7.3 - 0.5(-3) = 4.5.0 - 0.5(12) = -6.Hence the resulting matrix is:
[tex]R = \left[\begin{array}{ccc}7&4.5&-6\\-6&-3&12\end{array}\right][/tex]
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The mean output of a certain type of amplifier is 498 watts with a standard deviation of 12 watts. If 86 amplifiers are sampled, what is the probability that the mean of the sample would be less than 494.7 watts
Mean (m) = 498
Standard deviation (σ) = 12
Sample size (n) = 86
The probability that the sample mean would differ from Population mean by less than 494.7 watts
P(m - s < Z < m + s)
P(498-494.7 < Z < 498+ 494.7)
Using the Z formula :
Zscore = (x - m) / (σ/√n)
x = 498 - 494.7 = 3.3 , x = 498 + 494.7 = 992.7
Z = (3.3 - 498) / (12/√86) = -383.48
P(Z < -383.48)
Z = (992.7 - 498 ) / (12/√86) = 383.48
P(Z<383.48)
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A white tailed deer can sprint at speeds up to 30 miles per hour. American bison can run at speeds up to 3,520 feet per minute. Which animal is faster and by how many miles per hour ? There are 5,289 feet in one mile
We will see that the bison is faster, by 9.9 miles per hour.
Which animal is faster?
We know that the deer's speed is:
D = 30 mi/h
The bison's speed is:
B = 3,520 ft/min.
We want to convert the second speed to miles per hour, then we can use:
1 hour = 60 min
1 mile = 5289 ft
So, to get the speed in miles per hour, we need to multiply by 60 and divide by 5289, we will get:
B = 3,520 ft/min = 3,520*(60/5289) mi/h = 39.9 mi/h
So we can see that the bison is faster, by 9.9 miles per hour.
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When you are determining the probability of an event, why must the probablilty be between 0 and 1? explain your answer.
Probability is the ratio of the desired outcomes to all possible outcomes.
If there are no desired outcomes, the ratio is 0 over all possible outcomes, thus 0.
If the event is all possible outcomes, the ratio is all possible outcomes over all possible outcomes, thus 1.
Probability can never be below zero or negative because desired outcomes can never be negative. If an event is impossible that means there are no desired outcomes meaning that probability is zero, thus couldn't fall below
Probability can never exceed 1 as desired outcomes can never be greater than total outcomes.
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The graph of a linear function is shown,
Which word describes the slope of the line?
O positive
O negative
O zero
undefined
Answer:
postive
Step-by-step explanation:
im asian
For the graph of a linear function the slope of the line is positive, option A is correct.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Let the line is passing through points (-4, -1) and (0, 0)
m=1/4
The slope value is positive
Hence, for the graph of a linear function the slope of the line is positive, option A is correct.
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Can someone help me out on this
Answer:
Step-by-step explanation:
Help pleaseeeeeeeeeeeee
Answer:
B.$120
Step-by-step explanation:
find 8 on the bottom, and go up until you find the dot. then look to the left to see what number matches it on the left side.
What is 72,910 / 10^2
2x-5
-------- = 2
8
(2x-5/8 = 2)
Step-by-step explanation:
2×-5=-8 and 2×-5/8=-1.25
Answer:
x = 10.5
Step-by-step explanation:
I'll assume this is the equation: (2x-5)/8 = 2
(2x-5)/8 = 2
(2x-5) = 16 [Multiply both sides by 8]
2x = 21 [Add 5 to both sides]
x = (21/2) [Divide both sides by 2]
or x = 10.5
Enter the correct answer in the box. Divide f(x) = | x + 20| by g(x) = x + 1.
the quotient will be:
[tex](f/g)(x) = \frac{|x + 20|}{x + 1}[/tex]
with x ≠ -1
How to get the quotient of functions?
For two functions f(x) and g(x), the quotient:
(f/g)(x) is equal to f(x)/g(x).
Here we have:
[tex]f(x) = |x + 20|\\\\g(x) = x + 1[/tex]
Taking the quotient, we get:
[tex](f/g)(x) = \frac{|x + 20|}{x + 1}[/tex]
Where we also need to add the restriction that x must be different than -1, as we can divide by zero.
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A given line passes through the points (2,3) and (2,−3). Determine the equation of the line that is perpendicular to the given line and passes through the point (−1,5).
could someone break this down for me? multiple choice in attachment
The required equation of the line is y = 5
Equation of a lineThe equation of a perpendicular line to a line in point-slope form is expressed as:
y-y1 = -1/m(x-x1)
m is the slope
(x1, y1) is any point on the line
Determine the slope
Slope = -3-3/2-2
y = ∞
Since there is no slope, hence the equation of the line will be in the form y = b
where b is the y-coordinate of the point. Hence the required equation of the line is y = 5
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3/8-2/7=2/7-3/8 is the statement true
Answer:
The statement is not true.
Step-by-step explanation:
[tex]\frac{3}{8} -\frac{2}{7} =\frac{2}{7} -\frac{3}{8}[/tex]
First, let us solve the left side.
[tex]\frac{3}{8} -\frac{2}{7} \\\\\frac{3*7}{8*7} -\frac{2*8}{7*8}\\\\\frac{21}{56} -\frac{16}{56}\\\\\frac{21-16}{56} \\\\\frac{5}{56}[/tex]
And now let us solve the right side.
[tex]\frac{2}{7}-\frac{3}{8} \\\\ \frac{2*8}{7*8}-\frac{3*7}{8*7} \\\\\frac{16}{56}-\frac{21}{56}\\\\\frac{16-21}{56}\\\\\frac{-5}{56}[/tex]
Therefore, it is clear that the left side is not equal to the right side.
∴ Left side ≠ Right side
∴ [tex]\frac{5}{56}[/tex] ≠ [tex]\frac{-5}{56}[/tex]
f(x) = sin(x² + 2x - 1)²
f'(x) = ?
Need Best Answer? Give the explanation!
ok thx.
It depends if you mean
[tex]f(x) = \sin(x^2+2x-1)^2 = \sin^2(x^2+2x-1)[/tex]
i.e. the sine part is getting squared, or
[tex]f(x) = \sin(x^2+2x-1)^2 = \sin\left((x^2+2x-1)^2\right)[/tex]
i.e. the argument to sine is getting squared. I'll assume the first case, since it's fairly common convention to write [tex]g(x)^2 = \bigg(g(x)\bigg)^2[/tex].
Now if
[tex]f(x) = \sin^2(x^2+2x-1)[/tex]
• by the power and chain rules we have
[tex]f'(x) = 2 \sin(x^2 + 2x - 1) \left(\sin(x^2+2x-1)\right)'[/tex]
• using the derivative of sine and the chain rule again we have
[tex]f'(x) = 2 \sin(x^2+2x-1) \cos(x^2+2x-1) \left(x^2+2x-1\right)'[/tex]
• with the power and chain rules we have
[tex]f'(x) = 2 \sin(x^2+2x-1) \cos(x^2+2x-1) (2x+2)[/tex]
Recalling the double angle identity for sine,
[tex]\sin(2x) = \sin(x) \cos(x)[/tex]
we can rewrite the derivative among several other ways as
[tex]\boxed{f'(x) = (2x+2) \sin(2x^2+4x-2)}[/tex]
Which graph represents the solution set of the inequality x+2 less than or equal to 6
The solution to the given inequality expression is x ≤ 4
Graphing inequalitiesInequality are expressions not separated by an equal sign. Given the inequality expression
x + 2 ≤ 6
Find the solution
Subtract 2 fro both sides
x + 2. - 2 ≤ 6 - 2
x ≤ 4
Hence the graph of the solution is given as shown in the attachment
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What is the perimeter of ABC when AB=6
What is the answer to the question down below
Answer:
I'm pretty sure the answer is 4
Step-by-step explanation:
Because SQ is 4 and it looks like QT is the same length
Use natural logarithms to solve the equation. Round to the nearest thousandth.
7e^2x + 10 = 29
Answer:
x ≈ 0.499
Step-by-step explanation:
The value of x can be found by undoing the operations done to it.
SolutionThe operations done to the variable are ...
multiply it by 2use that as the exponent with a base of emultiply the result by 7add 10We undo these operations in reverse order:
7e^(2x) + 10 = 29 . . . . given
7e^(2x) = 19 . . . . . . . . . subtract 10
e^(2x) = 19/7 . . . . . . . . . divide by 7
2x = ln(19/7) . . . . . . . . take the natural logarithm
x = (ln(19/7))/2 . . . . . . divide by 2
The rounded result is ...
x ≈ 0.499
The time t required to empty a tank varies inversely as
the rate r of pumping. If a pump can empty a tank in
45 minutes at a rate of 300 gallons per minute, how
long will it take to empty a tank at 500 gallons per
minute?
k
If [tex]t[/tex] and [tex]r[/tex] are inverse proportional to one another, then for some constant volume [tex]V[/tex] we have
[tex]V = tr[/tex]
It takes 45 min to empty a tank containing at 300 gal/min, so the tank contains
[tex]V = (45\,\mathrm{min}) \left(300\dfrac{\rm gal}{\rm min}\right) = 13500\,\mathrm{gal}[/tex]
of liquid.
If it's emptied at 500 gal/min, it would take
[tex]13500\,\mathrm{gal} = t \left(500\dfrac{\rm gal}{\rm min}\right) \implies t = \boxed{27\,\mathrm{min}}[/tex]
Which of the following appear in the diagram below?
Check all that apply.
z
A. YX
B. ZXYZ
C. ZYXZ
D. YW
Answer:
A , B, D
Step-by-step explanation:
YX is the segment joining points Y and X and is defined (A)
∠ XYZ is the angle between XY and YZ and is defined (B)
∠ YXZ is the angle between YX and XZ
However there is no segment joining XZ ← not defined
YW is the segment joining points Y and W and is defined (D)
Convert from Decimal Notation to Scientific Notation
In the following exercises, write each number in scientific notation.
557. 0.00000103
Answer:
Hence, 0.00000103 can be expressed as [tex]$1.03 \times 10^{-6}$[/tex].
Step-by-step explanation:
- Given 0.00000103
- Move the decimal point so that the factor is greater than or equal to 1 but less than 10 .
- Then count n and write no. as a product with a power of 10 .
Step 1 of 1
Consider 0.00000103,
1.03
Decimal has moved 6 places to right.
The power will be negative as the original no. is less than 1 .
[tex]$$\begin{array}{r}1.03 \times 10^{-6} \\0.00000103=1.03 \times 10^{-6}\end{array}$$[/tex]
The diagram shows the cross-section of a wall of a cinema. It is to be painted. Paint cost £6 for a tin which covers 25m^2. How much will it cost to paint?
Answer:
53.04 pounds
Step-by-step explanation:
We find the area of the shape:
10*13=130 is the rectangle
(10+6)*8/2=16*8/2=16*4=64 (area of the right trapezoid)
(10+8)*3/2=18*3/2=9*3=27 (area of the left)
130+27+64=221 is the total area
221/25*6=53.04 pounds
sharon is participating in basketball practice with her basketball team. She knows that running 40 laps around the rectangular basketball court is equal to running a kilometer (3,280 feet). In addition, the court has an area of 408 square feet. If Sharon's coach tells her to run the length of the longer edge of the basketball court, how many feet must Sharon run
Answer:
Sharon would have to run 24 ft.
Step-by-step explanation:
Begin by finding the perimeter by dividing 3,280 by 40.
Then eliminate D and E because they are larger than the total perimeter, and then plug in the remaining values into the perimeter and then see which also gives you the area.
This is how you get the answer 24 ft.
Hope this helped :D
Which is equivalent to 16^3/4 x?
Answer:
The answer is A
The playing time X of classical CDs has the normal distribution with mean 54 and standard
deviation 5; the N(54, 5) distribution. What is the relative frequency of classical CDs with playing
time X between 49 and 69 minutes?
Using the normal distribution, it is found that the relative frequency of classical CDs with playing time X between 49 and 69 minutes is 0.8403 = 84.03%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 54, \sigma = 5[/tex]
The relative frequency of classical CDs with playing time X between 49 and 69 minutes is the p-value of Z when X = 69 subtracted by the p-value of Z when X = 49, hence:
X = 69:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{69 - 54}{5}[/tex]
Z = 3
Z = 3 has a p-value of 0.9987.
X = 49:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{49 - 54}{5}[/tex]
Z = -1
Z = -1 has a p-value of 0.1584.
0.9987 - 0.1584 = 0.8403.
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Select the correct answer.
Which statement is true about the effects of the transformations on the graph of function f to obtain the graph of function g.
g(x) = f(x − 3) + 4
A.
The graph of function f is shifted left 3 units and up 4 units.
B.
The graph of function f is shifted right 3 units and up 4 units.
C.
The graph of function f is shifted right 3 units and down 4 units.
D.
The graph of function f is shifted left 3 units and down 4 units.
=============================================================
Explanation:
When going from f(x) to f(x-3), we replaced x with x-3.
Doing this shifts the xy axis 3 units to the left since each x input is three units smaller than before. If we had the f(x) curve fixed in place while the axis moves like this, then it gives the illusion of the curve moving 3 units to the right.
The +4 at the end adds 4 to each y coordinate to shift things 4 units up.
If −6x+y=−4 and −8x−10y=3 are true equations, what would be the value of 2x+11y?
=========================================================
Reason:
The equation −8x−10y=3 is the same as 8x+10y = -3 after multiplying both sides by -1
We have this system of equations
[tex]\begin{cases}-6x+y = -4\\8x+10y = -3\end{cases}[/tex]
Add the equations straight down.
-6x+8x becomes 2xy+10y becomes 11ythe right hand sides combine to -4+(-3) = -7Therefore, we end up with the equation 2x+11y = -7
An alternative is to solve the system using substitution to get the (x,y) intersection point. Then use those coordinates to compute 2x+11y and you should get -7 as a result.