Evaluate each limit given that limit x->2 f(x)=9.
limit x->2 1/3[f(x)]^2= 27✔️
limit x->2 3f(x)+5= 32✔️
limit x->2 [f(x)]3/2= 27✔️
Answer:
27
32
27
Step-by-step explanation:
1) limit x->2 1/3[f(x)]^2= 27
2) limit x->2 3f(x)+5= 32
3) limit x->2 [f(x)]3/2= 27/2
What is limit?"A limit is the value that a function approaches as the input approaches some value."
Limit properties:If limit f(x) = m and constant 'a',
limit a (f(x)) = a × m
limit (f(x))^n = (m)^n
limit (a) = a
limit (f(x) + a) = m + a
Given: limit x->2 f(x)=9.
We need to evaluate each limit.
1) limit x->2 1/3[f(x)]^2
⇒ [tex]\lim_{x \to 2} \frac{1}{3} (f(x))^2[/tex]
= [tex]\frac{1}{3} \lim_{x \to 2} (f(x))^2[/tex]
= [tex]\frac{1}{3} (\lim_{x \to 2} f(x))^2[/tex]
= [tex]\frac{1}{3} \times (9)^2[/tex]
= [tex]\frac{81}{3}[/tex]
= 27
2) limit x->2 3f(x)+5
⇒ [tex]\lim_{x \to 2} (3f(x)+5)[/tex]
= [tex]\lim_{x \to 2} 3f(x)+ \lim_{x \to 2} 5[/tex]
= [tex]3\lim_{x \to 2} f(x) + 5[/tex]
= [tex](3 \times 9)+5[/tex]
=[tex]\bold{32}[/tex]
3) limit x->2 [f(x)]3/2
⇒ [tex]\lim_{x \to 2} (f(x))\frac{3}{2}[/tex]
= [tex]\frac{3}{2} \times (\lim_{x \to 2} f(x))[/tex]
= [tex]\frac{3}{2} \times 9[/tex]
= 27/2
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simplify 1/a+b + 1/a-b + 2b/a^2-b^2
Answer:
−a^2 b^2 + 2a + 2b
_________________
a^2
Step-by-step explanation:
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Solve the system by substitution.
x = - 4y - 5
2x + 10y = 8
Answer:
x = -41
y = 9
Step-by-step explanation:
Begin by multiplying the top equation by 2
2x = -8y - 10
The second equation requires a little more care.
Start by moving 10y to the right. Normally the y value is on the left, but we are going to be substituting for 2x.
2x = - 10y + 8
What I've done is not the usual practice, but there is nothing wrong with it.
Now since both right sides are equal to 2x, you can substitute for them
-8y - 10 = -10y + 8 Add 10y to both sides
-8y + 10y - 10 = 8
2y - 10 = 8 Add 10 to both sides
2y = 8+10
2y = 18 Divide by 2
y = 18/2
y = 9
Use the second original equation to solve for x
2x + 10y = 8
2x + 10*9 = 8
2x + 90 = 8 Subtract 20 from both sides
2x = 8 - 90
2x = - 82 Divide by 2
x = -822/2
x = - 41
There were 8 pizzas at the pizza party for two families. The Houston family ate 2 2/3 pizzas.
The Ozark family ate 2 5/6 pizzas.
What whole number is the closest estimate of how many pizza was left
Answer:2 pizzas
Step-by-step explanation:
2 2/3 and 2 5/6 can both be rounded to 3. Double that and you get 6. Since there were 8 pizzas originally,subtract 6 from 8 to get 2 remaining pizzas.
Answer:
2 pizzas
Step-by-step explanation:
IV
Evaluate the following:
a) A tea manufacturing company produces normal and green tea bags only. If 52.8% of 36850 total
production is normal tea bags, how many green tea bags are there?
b) If 61.6% of students out of 9855 total students are based in England, how many students are
based in England?
Answer:
A. Ans: Given,
Solution,
A tea manufacturing company produces normal and green tea bags only.
52.8% of 36850 production is normal tea bags.
Now,
Number of green tea bags=52.8% of 36850
=52.8/100×36850
=19456.8
Therefore, Number of normal tea bags=19456.8
The number of green tea bags is 17384
The number of students is 3071
What is Percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
Given data ,
a )
Total production of tea bags = 36850
Percentage of normal tea bags = 52.8 %
Total production of normal tea bags =
Percentage of normal tea bags x Total production
Total production of normal tea bags = ( 52.8 / 100 ) x 36850
= 19465.8 tea bags
Therefore , total amount of green tea bags = Total tea bags - Total normal tea bags
= 36850 - 19465.8
= 17384.2
≈≈ 17384
Hence , Total amount of green tea bags = 17384.2
b )
Total number of students = 9855
Percentage of students based in England = 61.6 %
Number of students based in England = Percentage of students x Total number of students
Number of students based in England = ( 61.6 / 100 ) x 9855
= 6070.68
≈ 6071
Hence , total number of students based in England = 6070.68
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Please help me, this is probably my 20th time doing this topic and I haven't passed it yet.
Thank you very much!
Answer:
infinitely many
Step-by-step explanation:
Answer:
there is an infinite number of triangles that can be created.
Step-by-step explanation:
To satart, you have a line, that is 8 cm, with a circle, with the center on one of its endpoints, that has a radius of 3 cm. s in this case, 2 sides of the triangle would be 8 and 3. now, with this combintion, you could have a triangle that the missing side is from 6 to 10. there is an infinite amount of numbers inbetween 6 and 10. for example, you could have 6, 6 1/4, 6 1/8, or 6 1/16.
The list goes on and on.
arrange the following fraction in descending order 1/2 5/7 1/4 or 1/8 11/12
Answer:
11/12, 5/7, 1,8, 1/4, 1/2
Step-by-step explanation:
Johanna can jog 24 feet in 5 seconds. If she jogs at the same rate, how many feet can she jog in 8 seconds? PLSS help!
Sybil has 1/2 of pizza left over. She wants to share the pizza with 3 of her friends. What fraction of the original pizza does sybil and her friends each receive.
Answer:
1/6
Step-by-step explanation:
Double the original amount: 1/3. Which is 1/6, not 2/6, if it was 2/6 then people waould get 1/3 instead (not equal).
Gary is cleaning windows. He sets his ladder 25 feet away from the wall of the house to reach the windows on the second story, which are at a height of 20 feet above the ground. He moves his ladder 15 feet closer to the wall to reach the windows on the third story of the house.
Approximately how high above the ground are the windows on the third story of the house?
A.33.5ft
B.28.3ft
C.30.4ft
D.32.0ft
The 28.3 feet high above the ground are the windows on the third story of the house.
It is required to find the height.
What is the Pythagorean Triple?The Pythagorean triple can be described as any three set of integers representing sides of a right triangle that are solutions to the Pythagorean Theorem, which is given as:
c² = a² + b².
Given that:
Distance between ladder and wall=25 feet
Height of window=20 feet
Closer distance between ladder and wall=15 feet
We know the Pythagoras theorem , we get
[tex]a^{2} +b^{2} =c^{2}[/tex]
we have
a=15 feet
b=?
c=25 feet
So,
[tex]a^{2} +b^{2} =c^{2}\\\\15^{2} +b^{2} =25^{2}\\\\225+b^{2} =625\\\\b^{2}=625-225\\\\b^{2}=400\\\\b=20 feet[/tex]≈28.3 feet
Therefore, the 28.3 feet high above the ground are the windows on the third story of the house.
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Please help !! If you help i’ll give 5 stars
Answer:
Imaginary
Step-by-step explanation:
After the last ice age began, the number of animal species in Australia changed rapidly.
The relationship between the elapsed time, t, in years, since the ice age began, and the total number of animal species, S(t), is modeled by the following function:
S(t)=4,200,000⋅(0.72)t
Complete the following sentence about the yearly percent change of the number of animal species.
Every year, _______ percent of species are SUBTRACTED/ADDED from the total number of animal species.
Answer:
Every year 28 percent of species are SUBTRACTED from the total number of animal species.
Step-by-step explanation:
Exponential growth or decay:
The equation for exponential growth or decay has the following format:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which A(0) is the initial amount and r is the growth/decay rate, as a decimal.
If r > 0, each year r percent is added to the total number, and if r < 0, each year, r percent is decreased from the total number.
In this question:
[tex]S(t) = 4200000(0.72)^t[/tex]
So
[tex]1 - r = 0.72[/tex]
[tex]r = 0.72 - 1 = -0.28[/tex]
Thus
Every year 28 percent of species are SUBTRACTED from the total number of animal species.
!!!!Plz Help!!!! How does the slop of AB compare with the slope of the parallel line as you move points A, B, and C? What conclusion can you draw about the relationship between the slopes of parallel lines?
Answer:
As points, A and B move, the slope of the two lines change but remain equal to each other. As point C moves, the slope does not change but remains equal to each other since the line through C is drawn parallel to AB.
I can canclude that slope of any two parallel lines are equal
Step-by-step explanation:
Help!!!!!!!!!!!!!!!!!!!!!!!
calculate the size of angle x
Answer:
16
Step-by-step explanation:
express 0.6 + 0.47 in the form p/q where p and q are integers q are not equal to 0
Answer:
[tex]0.6 + \bar 0.47 = \frac{532}{495}[/tex]
Step-by-step explanation:
Given
[tex]0.6 + \bar 0.47[/tex]
Required
Express as x/y
Let
[tex]x = \bar 0.47[/tex]
This implies that:
[tex]x = 0.4747[/tex] --- (1)
Multiply by 100
[tex]100x = 47.4747[/tex] --- (2)
Subtract 1 from 2
[tex]100x - x = 99x[/tex]
This gives
[tex]47.4747 - 0.4747 = 47[/tex]
So:
[tex]99x = 47[/tex]
Solve for x
[tex]x = \frac{47}{99}[/tex]
This implies that:
[tex]\bar 0.47 = \frac{47}{99}[/tex]
[tex]0.6 + \bar 0.47[/tex] becomes
[tex]0.6 + \bar 0.47 = 0.6 + \frac{47}{99}[/tex]
Express 0.6 as fraction
[tex]0.6 + \bar 0.47 = \frac{6}{10} + \frac{47}{99}[/tex]
Take LCM and solve
[tex]0.6 + \bar 0.47 = \frac{99*6+10*47}{990}[/tex]
[tex]0.6 + \bar 0.47 = \frac{1064}{990}[/tex]
Simplify
[tex]0.6 + \bar 0.47 = \frac{532}{495}[/tex]
Help pls I rlly need help it’s important
Answer:
2. 112
3. 78
5. 672
7. 149.8
9. 17.5
10. 19360
11. 64 000
13. 29
14. 350240
15. 386
16. 224
17. 0.9071847
Step-by-step explanation:
can anybody help me please
Answer:
Is B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Given : M, N, O are midpoints of AB, BC, AC Complete the following statements
MNOA is a
Somebody know the answer?
Present
earch and writ
storie
Answer:
What did you say?? i dont know what your trying to say?
Answer:
?
Step-by-step explanation:
In Exercises, we present descriptions of designed experiments. In each case, identify the
a. experimental units.
b. response variable.
c. factor(s).
d. levels of each factor.
e. treatments.
Oat Yield and Manure. In a classic study, described by F. Yates in The Design and Analysis of Factorial Experiments (Commonwealth Bureau of Soils, Technical Communication No. 35), the effect on oat yield was compared for three different varieties of oats and four different concentrations of manure (0, 0.2, 0.4, and 0.6 cwt per acre).
Answer:
Experimental unit = Oat
Response variable = Oat yield
Factors : Oat varieties ; Manure Concentration
Level of factors :
Oat = 3 levels
Manure concentration = 4 levels
Step-by-step explanation:
The experimental unit in this scenario is Oat, as it is the material or entity which we wish to research or learn about.
The response variable is what we intend to measure about the experimental unit, which is the yield of oat.
Factors here are the varieties of oat and the concentration of Manure which are the entities responsible for changes in the output or behavior of the dependent variable.
Level of factors : the different varieties of the factor variable, we have three Oat levels and 4 different Manure concentration levels.
Find value of x
A. 15
B. 18
C. 16
D. 19
Answer:
x = 19
Step-by-step explanation:
By the Supplementary Angle Theorem we can say that;
123 + 3x = 180
3x = 57
x = 19
Hope this helps!
Can somebody please help me out please my grads are bad
Write -9 9/16 as a decimal
Answer:
-8.4375
Step-by-step explanation:
convert -9 9/16 to a improper fraction.
-9 x 16 = -144
-144+9= -135
-135 divided by 16 = -8.4375
A mountain climber ascends hundred feet per hour from his original position. after six hours is fine opposition is 11,600 feet above the sea find climbers original position
Answer:
Original position =6,800 feet.
800 (ft per hour) x 6(hours) =4800 ft
11,600-4,800=6,800 feet
Step-by-step explanation:
Which statements are true? Select all that apply.
Answer:
A,B, D
Step-by-step explanation: I just took that test and i got it right
In the Formula SA=1/2PL+B
What does "L" Mean.
A. the height of the prism
B. the slanted height of the prism
C. the slanted height of the pyramid
D. the height of the pyramid
Please help
Answer:
L = the slanted height of the pyramid
Step-by-step explanation:
The surface area of a pyramid is given by :
[tex]SA=\dfrac{1}{2}PL+B[/tex]
Where
P is perimeter of base of pyramid
L is the slant height of the pyramid
B is the area of base.
So, the correct option is (c) "the slanted height of the pyramid".
Based on the definition of independence, which THREE statements are correct?
P(A) ,
A)
1
1
and B)
12
Events A and B are independent.
12
35
Events A and B are independent.
P(A) = 4, P(B) = , P(A and B) =
B)
1
1
P(A)
A B
10
Events A and B are independent.
P(A) = , P(B) = , P(A and B) =
7.
12
D)
Events A and B are dependent.
PLA) = }, PB) - to, P(A and B) - 1 2 3
E)
Events A and B are independent.
Answer: A, D, and E
Step-by-step explanation:
Which fraction is greater 2/5 or 4/10
They are equal. 2/5 is 4/10.