The solution to the limit expression [tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} [/tex] is 6
The limit expression is given as:
[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5}[/tex]
Express 25 as 5^2
[tex] \lim_{x \to 1} \frac{x^2 - 5^2}{x - 5}[/tex]
Express the numerator as the difference of two squares
[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} = \lim_{x \to 1} \frac{(x - 5)(x +5)}{x - 5}[/tex]
Evaluate the quotient
[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} = \lim_{x \to 1} (x +5)[/tex]
Remove bracket
[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} = \lim_{x \to 1} x +5\\ [/tex]
Substitute 1 for x
[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} = 1 +5[/tex]
[tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} = 6[/tex]
Hence, the solution to the limit expression [tex] \lim_{x \to 1} \frac{x^2 - 25}{x - 5} [/tex] is 6
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How do you balance a firm’s need to succeed and the need for not asking the workers for perfection?
The way to balance a firm's need to succeed and the need for not asking the workers for perfection is through the offering of training to workers, which allows them to notably improve their performances autonomously, without this being directly instigated by the company's directory.
That is, through the education of workers in the different areas of their jobs, the level of the same will be improved and better results will be obtained.
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A crew of highway workers paved 1/5 mile in 1/8
hour. If they work at the same rate, how much
will they pave in one hour?
Answer: 2/5 Step-by-step explanation: The easiest approach is to realize that one hour is 3 times longer than 20 minutes. The longer the time, the more they will pave.
Help help help help math ASAP
Answer:that is 0.01541
Step-by-step explanation:
The combined area of the photo and mat needs to be 224 square inches. The equation that represents the combined area is
(2w +8)(2w + 10) = 224, where w represents the width of the mat around the photo.
What should the width of the mat be?
Enter your answer as the correct value, including units, like this: 42 meters
Be sure to use the correct units from the context of the problem
The width of the mat around the photo is 3 inches
The combined area of the of the photo and math = 224 square inches
The combined area is represented as:
(2w +8)(2w + 10) = 224
Expand the equation using the distributive rule
[tex]4w^2+20w+16w+80=224\\\\4w^2+36w+80-224=0\\\\4w^2+36w-144=0[/tex]
Divide through by 4
[tex]w^2+9w-36=0[/tex]
Factorize the resulting quadratic equation to solve for w
[tex]w^2-3w+12w-36=0\\\\w(w-3)+12(w-3)=0\\\\(w-3)(w+12)=0[/tex]
w - 3 = 0
w = 3
w + 12 = 0
w = -12
The width of the mat around the photo is 3 inches
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The width of the mat around the photo is 3 inches
Combined area:
2w +8)(2w + 10) = 224
where,
w = width of the mat around the photo
(2w +8)(2w + 10) = 224
open parenthesis
4w² + 20w + 16w + 80 = 224
4w² + 36w + 80 - 224 = 0
4w² + 36w - 144 = 0
divide through by 4
w² + 9w - 36 = 0
solve quadratic equation using factorization method
w² + 12w - 3w - 36 = 0
w(w + 12) - 3(w + 12) = 0
(w + 12) (w - 3) = 0
w + 12 = 0 or w - 3 = 0
w = -12 or w = 3
The width of the mat around the photo cannot be a negative value.
Therefore, the width of the mat around the photo is 3 inches
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En el siguiente trapecio calcular el valor de la base mayor x
Answer:
x = 20°
Step-by-step explanation:
OA = OB
so 140°+x°+x° = 180°
140+2x = 180
2x = 40
x = 20°
100 POINTS!!! Please solve this question step by step and explain each step for 100 points.
[tex]2\dfrac 29 = -\dfrac 45 m \\\\\implies 2+ \dfrac 29 =- \dfrac 45 m \\\\\implies \dfrac{20}9 = -\dfrac 45 m \\\\\implies 5(20) = (-4m)9\\\\\implies 100 = -36m\\\\\implies m = -\dfrac{100}{36} \\\\\implies m = -\dfrac{25}9\\\\\implies m=-2\dfrac 79[/tex]
Therefore, the answer is m = -25/9.
Hoped this helped.
[tex]-BrainaicUser1357-[/tex]
Which numbered choice shows a set of numbers whose product is -20 and whose sum is +1?
Question Two :
A discrete random variable X has negative binomial distribution,
with 6 successes required each with probability of success 0.4
Determine the value of ...
a) ...E(X).
b) ... Var( X)
c) ... P ( X = 12).
Using the negative binomial distribution, it is found that:
a) [tex]E(X) = 15[/tex]
b) [tex]Var(X) = 6.67[/tex]
c) [tex]P(X = 12) = 0.0883[/tex]
Negative binomial distribution:
It is the number of trials until q successes of a binomial variable, with p probability of success.
The expected value is:
[tex]E(X) = \frac{q}{p}[/tex]
The variance is:
[tex]Var(X) = \frac{pq}{(1 - p)^2}[/tex]
The probability mass function is:
[tex]P(X = x) = C_{x+q-1,q-1}(1 - p)^xp^q[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, the parameters are: [tex]q = 6, p = 0.4[/tex].
Item a:
[tex]E(X) = \frac{6}{0.4} = 15[/tex]
Item b:
[tex]Var(X) = \frac{6(0.4)}{(1 - 0.4)^2} = 6.67[/tex]
Item c:
[tex]P(X = 12) = C_{17,5}(0.6)^12(0.4)^6 = 0.0883[/tex]
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What is (3*7) divided by 5
Answer:
The answer is 4.2,
Hope that helped. x
Step-by-step explanation:
3 x 7 (3*7) = 21
21 divided by 5 = 4.2.
Answer:
4.2
Step-by-step explanation:
Using PEMDAS,
ParenthesisExponentsMultiplicationDivisionAdditionSubtractionWe know that to solve (3*7) divided by 5, we will need to solve what is in the parenthesis.
So, we need to figure out what is 7*3, which is 21.
This is what we have right now:
21 divided by 5
The next step is dividing,
We divide 21 by 5 to get 4Multiply the quotient digit (4) by the divisor 5Subtract 20 from 21Add a decimal place and a zero to the dividend, bring down the zero from the dividendDivided 10 by 5 to get 2Multiply the quotient digit (2) by the divisor 5Subtract 10 from 10The solution for the division is 4.2In the end, the answer is 4.2, hope this helped!
In one phase of a cycling race, a cyclist has covered three fifths of the total distance. If
there are still thirty km left, what's the total distance of the race?
Step-by-step explanation:
3/5 are done, that means 2/5 are still to do.
that means these 30 km are these 2/5.
2/5 x = 30
2x = 150
x = 75
the total distance is 75 km.
Answer:
75 km
Step-by-step explanation:
2/5 = 30 km
→ Find 1/5
1/5 = 15 km
→ Now find 5/5 or 1
1 = 75 km
While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After
returning to the United States he converts his money back to US dollars. How much of the original 250 US dollars
does Phelan now have? Round to the nearest cent.
1 European euro = 1,3687 US dollars
O 44.70 US dollars
O 73.06 US dollars
O 136.87 US dollars
O 140.41 US dollars
Answer:
$140.41
Step-by-step explanation:
250 * 1.3687 = 3412.175 Euros.
- 150 Euros = 192.175
192.175 1.3687 = $140.41
Help me please I don’t wanna fair math
Step-by-step explanation:
To find the equation you must first find the gradient and also look for the points on the graph.
I see point ( 0, 2) and point (4, 1)
Hence first find the gradient before equation
the gradient = y2-y1/x2-x1
y2 = 1
y1 = 2
x2 = 4
X1 =0
if you put in the values it will look like
1-2/4-0
-1/4
the gradient = -1/4
So for the equation the formula is
remember m is the gradient
y - y1 = m ( x - x1 )
so put in the value from only one point so you can choose either (0,2 ) or (4,1 )
I will go with (4, 1)
y - y1 = m ( x - x1 )
y - 1 = m ( x - 4 )
y -1 = -1/4 ( x - 4)
4 ( y-1) = -1(x-4)
4y- 4 = -1x +4
4y - 4 -4 = -1x
4y -8= -1x
4y + 1x -8 = 0
this is the equation.
thanks and good luck.
Need a little help on this
Answer:
Step-by-step explanation:
This is an isosceles triangle. You can tell because 2 of the sides are equal and the third is not equal to either of the other two.
x + x + 56 = 180 Combine the left
2x + 56 = 180 Subtract 56 from both sides.
2x = 180 - 56
2x = 124 Divide by 2
x = 124/2
x = 62
Suppose a special discount makes the price of Nike air max shoes 10% lower. As result, there is a 20% increase in the quantity demanded for the shoes, which statement is correct ____?
It is evident from the problem statement that an overall price reduction of Nike air max shoes will lead to an increase in the demand for the shoe.
In Economics, the relationship between price and demand is stated as follows "If all other factors remain equal, the higher the price of a good, the fewer people will demand that good. In other words, the higher the price, the lower the quantity demanded and vice versa."
In all, the Law of Demand tells us that if more people want to buy something, given a limited supply, the price of that thing will be bid higher, also of the price of something is low the demand will be high.
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Henry and Jose are gaining weight for football. Henry weighs 205 pounds and is gaining 2 pounds per week Jose weighs 195 pounds and is gaining 3 pounds per week.
Write an equation to represent when the weights will be the same. Let w represent the number of weeks.
what would be the equation?
Answer:
205+2w=195+3w
Step-by-step explanation:
:)
The equation to represent when the weights are the same will be 3w + 195 = 2w + 205 and the number of weeks is 10.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Henry and Jose are putting on weight for football. Henry weighs 205 pounds and is acquiring 2 pounds each week Jose weighs 195 pounds and is acquiring 3 pounds each week.
Let 'w' be the number of weeks and 'y' be the total weight. Then the equations are given as,
y = 2w + 205
y = 3w + 195
If the weight becomes the same. Then the number of weeks is given as,
3w + 195 = 2w + 205
Simplify the equation, then we have
3w + 195 = 2w + 205
3w - 2w = 205 - 195
w = 10
More about the linear equation link is given below.
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The ratio of the distances a driver and a 2-iron will drive a
golf ball is 5 to 4. If a golfer averages 240 yards with a 2-
iron, how far should she average with a driver?
The average distance is 300 yards
How to determine the average distance?The ratio is given as:
Driver : 2-iron = 5 : 4
When the iron driver is 240 yards, we have:
Driver : 240 = 5 : 4
Express as fraction
Driver/240 = 5/4
Multiply both sides by 240
Driver= 300
Hence, the average distance is 300 yards
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1
1.
A random variable X has expected value
and probability distribution as
12
follows:
X
-3
-2
-1
0
1
N
3
f(x)
a
2a
1
1
1
b
сле
b b
2
5
10
5
(a)
(b)
Find the values of a and b.
Find E[X2 + 1].
(8 marks)
Answer:
huh
Step-by-step explanation:
The body mass index, I, can be used to determine an individual's risk for heart disease. An index less than 25 indicates a low risk. The body mass index is given by
700W
the formula, or model, I=
where W= weight, in pounds, and H = height, in inches. Jerome is 70 inches tall. What weights will keep his body mass index
H2
between 20 and 28?
Using the BMI equation, it is found that weights between 139.4 and 195.2 pounds will keep his BMI between 20 and 28.
The BMI B, for a person of weight w(in pounds) and height h(in inches) is given by:
[tex]BMI = \frac{703w}{h^2}[/tex]
In this problem:
Height of 70 inches, hence [tex]h = 70[/tex].For a BMI of 20 inches, the weight is:
[tex]BMI = \frac{703w}{h^2}[/tex]
[tex]20 = \frac{703w}{70^2}[/tex]
[tex]w = \frac{20 \times 70^2}{703}[/tex]
[tex]w = 139.4[/tex]
For a BMI of 28 inches, the weight is:
[tex]BMI = \frac{703w}{h^2}[/tex]
[tex]28 = \frac{703w}{70^2}[/tex]
[tex]w = \frac{28 \times 70^2}{703}[/tex]
[tex]w = 195.2[/tex]
Weights between 139.4 and 195.2 pounds will keep his BMI between 20 and 28.
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Carry out the following integrals, counterclockwise, around the indicated contour
For the first integral, z = π/4 is a pole of order 3 and lies inside the contour |z| = 1. Compute the residue:
[tex]\displaystyle \mathrm{Res}\left(\frac{e^z\cos(z)}{\left(z-\frac\pi4\right)^3}, z=\frac\pi4\right) = \lim_{z\to\frac\pi4}\frac1{(3-1)!} \frac{d^{3-1}}{dz^{3-1}}\left[e^z\cos(z)\right][/tex]
We have
[tex]\dfrac{d^2}{dz^2}[e^z\cos(z)] = -2e^z \sin(z)[/tex]
and so
[tex]\displaystyle \mathrm{Res}\left(\frac{e^z\cos(z)}{\left(z-\frac\pi4\right)^3}, z=\frac\pi4\right) = - \lim_{z\to\frac\pi4} e^z \sin(z) = -\frac{e^{\pi/4}}{\sqrt2}[/tex]
Then by the residue theorem,
[tex]\displaystyle \int_C \frac{e^z\cos(z)}{\left(z-\frac\pi4\right)^3} \, dz = 2\pi j \left(-\frac{e^{\pi/4}}{\sqrt2}\right) = \boxed{-\sqrt2\,\pi e^{\pi/4} j}[/tex]
For the second integral, z = 2j and z = j/2 are both poles of order 2. The second poles lies inside the rectangle, so just compute the residue there as usual:
[tex]\displaystyle \mathrm{Res}\left(\frac{\cosh(2z)}{(z-2j)^2\left(z-\frac j2\right)^2}, z=\frac j2\right) = \lim_{z\to\frac j2}\frac1{(2-1)!} \frac{d^{2-1}}{dz^{2-1}}\left[\frac{\cosh(2z)}{(z-2j)^2}\right] = \frac{16\cos(1)-24\sin(1)}{27}j[/tex]
The other pole lies on the rectangle itself, and I'm not so sure how to handle it... You may be able to deform the contour and consider a principal value integral around the pole at z = 2j. The details elude me at the moment, however.
A house costs 36% more today than when it was built.If the cost of the house today is $333,200, find the cost when it was built.
Answer:
$245,000
Step-by-step explanation:
Let the intial cost = x
[tex]100\% + 36\% = 136\% = 1.36[/tex]
[tex]1.36x = 333200[/tex]
[tex]x = \frac{333200}{1.36} [/tex]
[tex]x = 245000[/tex]
What is the value of
8x2 + 3x when x = 4?
Answer:
28
Step-by-step explanation:
8*2=16
3*4=12
Then you add 16+12
hopefully it helps
Answer:
76
Step-by-step explanation:
plug in 4 in the equation:
8(4)2 + 3(4) = 76
Help meeeeeeeeeeeeedsddsss9
Answer:
2(x + 3) <9
Step-by-step explanation:
Two times the quantity of a number increased by 3 is less than 9
2 · (x + 3 ) < 9
= 2(x + 3) <9
Simplify 1.25 (-x -4)
Answer:
-1.25x-5
Step-by-step explanation:
Multiply using Distribution:
1.25(-x-4)
-1.25x-5
My answer can't be simplified anymore, since there isn't any like terms.
Help me with this question lol
Answer:
i think that it would be 0
PLS HELP ME WITH GEOMETRY PLSAND THANK YOU
Answer:
Yes
Step-by-step explanation:
They are equal acute triangles, are congurent. Your welcom
solve this: 23.769km-----?-----m
1 km = 1000 m, so:
23,769 km = 23,769 · 1000 m = 23 769 m
Answer:
23769m
Step-by-step explanation:
Basicly, 3.769x 1000= 23769m
Please mark brainliest
Mr. Hare left at 8:00 a.m. and is traveling 40 miles per hour. Mrs. Hare left at 9:00 a.m. and is traveling at 50 miles per hour. If Mr. and Mrs. Hare are traveling the same direction, what time will it be when Mrs. Hare is at the same location as Mr. Hare?
A. 11:00 a.m.
B. 1:00 p.m.
C. 2:00 p.m.
D. 3:00 p.m.
Answer:
The answer is b
Step-by-step explanation:
During the 8-9 , Mr hare travel 40miles
For the time 9 onwards they travel concurrently,
Let x be the distance covered by both since they can only meet if they covered the sams distance,
x/50 = x/40 -1 ,where the 1 is the (8-9) 1 hr
x/40 - x/50 = 1
x = 200
Time take by Mr Hare = 200/ 40 = 5
from 8 add 5 hours will be 1
Note, i took this answer from an answer from another answer.
A Biology test has 20 questions and is worth a total of 100 points. The test
consists of True/False questions worth 2 points each and multiple choice questions
worth 7 points each. How many of the test questions
are multiple choice and how
many of the test questions are True/ False?
# of true/false questions =
# of multiple choice questions =
THIS IS ALGEBRA PLEASE
Answer:
I've done alot of calculations on this but I cant get a definite answer I hope you got it I'm sorry I couldn't help you I tried but only got into a dead end
Morgan had 1/2 a box of candy left after the movie she ate 1/2 of that. On the way home and still had 8 pieces left. She give one to her Little brother. How many pieces of candy were in the box when Morgan bought it?
Answer:
16
Have a good day <3
PLEASE HELP!!!!!!!!!
Which of the following are properties of parallelograms? Select all that apply!
Consecutive angles are congruent.
One pair of parallel sides.
Consecutive angles are supplementary.
Both pairs of opposite sides are congruent.
Both pairs of opposite of angles are congruent.
Answer:
If I have to guess, I’ll say
Consecutive angles are congruent.
One pair of parallel sides.
Consecutive angles are supplementary.
Step-by-step explanation:
if I’m wrong, I’m sorry. If I’m right, mark me brainlest!
Answer:
Consecutive angles are supplementary.
Both pairs of opposite of angles are congruent.
Both pairs of opposite sides are congruent.
Step-by-step explanation:
I took the quiz and this was the correct answer.