The limit of the given function if [tex]\lim_{x \to 0} f(x)=4[/tex] is 64
Limit of a functionGiven the following limit of a function expressed as;
[tex]\lim_{x \to 0} f(x)=4[/tex]
We are to determine the value of the function
[tex]\frac{1}{4} \lim_{x \to 0} [f(x)]^4[/tex]
This can also be expressed as
[tex]\frac{1}{4} \lim_{x \to 0} [f(x)]^4\\ = \frac{1}{4}(4)^4 \\=1/4\times 256\\=64[/tex]
Hence the limit of the given function if [tex]\lim_{x \to 0} f(x)=4[/tex] is 64
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simplify (x^3+2x-3)-(x^2-2x+4)
Answer:
x³ - ((x+1)(x+1))
Step-by-step explanation:
x³ + 2x -3 - x² - 2x + 4
x³ - x² + 1
x³ - ((x+1)(x+1))
Answer:
x^3−x^2+4x−7
Step-by-step explanation:
Hope this helps! Have a great day!!
Determine the marginal distribution of Gender. In paragraph form, how you calculated the marginal distribution. Include your calculations in your explanation.
The marginal distribution for gender tells you the probability that a randomly selected person taken from this sample is either male or female, regardless of their blood type.
In this case, we have total sample size of 714 people. Of these, 379 are male and 335 are female. Then the marginal probability mass function would be
[tex]\mathrm{Pr}[G = g] = \begin{cases} \dfrac{379}{714} \approx 0.5308 & \text{if }g = \text{male} \\\\ \dfrac{335}{714} \approx 0.4692 & \text{if } g = \text{female} \\\\ 0 & \text{otherwise} \end{cases}[/tex]
where G is a random variable taking on one of two values (male or female).
What segment is the altitude to side AC?
Segment CR
Segment BT
Segment BL
Please Help I Don't Understand!
Answer:
D) None of the choices are correct.
Explanation:
Given triangles AHL and NKG
Sides which are congruent:
AH and NKHL and KGAL and NGSo, AHL ≅ NKG. There are no such options.
Nick wants to write a 1,260 page science-fiction novel.
How many pages will Nick need to write each month to finish his novel in 1 year?
1 year = 12 months
Pages to write in 12 months = 1260
Pages to write in 1 month = 1260/12
= 105 pages per month
what is the answer to −1.4+(−1.2)
Answer:
-2.6
Step-by-step explanation:
-1.4+(-1.2)
-1.4-1.2=-2.6
Hope this helps!
If not, I am sorry.
Evaluate the expression below when x = 3 54 ÷ 2•3-x²
Answer:
72
Step-by-step explanation:
54/2(3)−3^2
= 54/2(3)−3^2
=72
A dog eats 3 cans of dog food in 12 days. Write an equation to represent th
proportional relationship. Then find k, the constant of proportionality.
Let c =
Let d =
Equation:
= k•
k=-
The equation to represent the proportional relationship is c = 0.25d
How to determine the equation?Let c = the number of cans
Let d = the number of days
So, we have:
c = kd
Where k represents the constant of proportionality.
From the given parameters, we have:
3 = 12k
Divide both sides by 12
k = 0.25
Substitute k = 0.25 in c = kd
c = 0.25d
Hence, the equation to represent the proportional relationship is c = 0.25d
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According to a survey, 48% of adults in the united states believe that unidentified flying objects (ufos) are observing our planet. you ask 8 randomly chosen adults whether they believe ufos are watching earth.
The expected number of adults that believe ufos are watching earth is 4
How to determine the number of adults?The given parameters are:
p = 48%
Sample size, n = 8
The expected number of adults that believe ufos are watching earth is calculated as:
E(x) = np
This gives
E(x) = 8 * 48%
Evaluate
E(x) = 3.84
Approximate
E(x) = 4
Hence, the expected number of adults that believe ufos are watching earth is 4
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The population in the United States was roughly 161,000,000 in 1950. By 2000, it had grown to roughly 291,000,000. Assume that the population in the United States grew linearly during that period. Find a linear equation which models the population in the United States during the period 1950 to 2000
to get the equation of any straight line, we simply need two points off of it, so let's use the ones provided in the table above.
[tex]\begin{array}{|cc|ll} \cline{1-2} \stackrel{millions}{population}&year\\ \cline{1-2} 161&1950\\ 291&2000\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{161}~,~\stackrel{y_1}{1950})\qquad (\stackrel{x_2}{291}~,~\stackrel{y_2}{2000}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2000}-\stackrel{y1}{1950}}}{\underset{run} {\underset{x_2}{291}-\underset{x_1}{161}}} \implies \cfrac{ 50 }{ 130 }\implies \cfrac{5}{13}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1950}=\stackrel{m}{\cfrac{5}{13}}(x-\stackrel{x_1}{161}) \\\\\\ y-1950=\cfrac{5}{13}x-\cfrac{805}{13}\implies y=\cfrac{5}{13}x-\cfrac{805}{13}+1950\implies y=\cfrac{5}{13}x+\cfrac{24545}{13}[/tex]
there is 1 litre of tea in a teapot, alex pours 275ml of the tea into a cup what percentage of the tea has alex poured
Answer:
27.5%
Step-by-step explanation:
Given:
1 Liter In TeapotAlex poured 275 milliliters of the tea into a cupReview:
1,000 Milliliters = 1 LiterConcepts:
A liter is a noun meaning a unit of capacity redefined in 1964 by a reduction of 28 parts in a million to be exactly equal to one cubic decimeter. It is equivalent to 1.0567 U.S. liquid quarts and is equal to the volume of 1 kilogram of distilled water at 4°C.A millimeter is a noun meaning a unit of capacity equal to one thousandth of a liter, and equivalent to 0.033815 fluid ounce, or 0.061025 cubic inch.Formula:
The mℓ to ℓ formula is [L] = [mL] / 1000.Now we must convert 275 milliliters to liters.
1. Divide the volume by 1,000.
275 ÷ 1000 = 0.275
2. Add the Unit Symbol for Liter.
0.275 ⇒ 0.275 L
Now we have to find how much of 1 liter- 0.275 liters as a percentage is.
To convert 0.275 to percent multiply 0.275 by 100. The result is 27.5 percent, or, using the percent sign, 27.5 %.
helppppppppppppppppppppppppp
Answer:
reason 1.) This is the original expression
reason 2.) you subtract 4 from both sides
reason 3.) you divide both sides by 2 to get x=5
2. Calculate the amount of compound interest paid on $7300 at the end of 3 years for each
rate. [2 marks each]
a) 10% compounded semi-annually
b) 8% compounded monthly
The compound interest when $7300 when interest is compounded semi annually is $2482.70.
The compound interest when $7300 when interest is compounded monthly is $1972.73.
What is the compound interest?An investment earns compound interest when both the amount invested and the interest accrued increases in value at predetermined time intervals.
The formula to represent compound interest is :
FV - amount invested
FV = P (1 + r)^nm
FV = Future value P = Present value R = interest rate m = number of compoundingN = number of yearsa. 7300 x [1 + (0.1/2)]^(3 x 2) = 9782.70
Compound interest = 9782.70 = 7300 = $2482.70
b. 7300 x [1 + (0.08/12)]^(12 x 3) = 9272.73
9272.73 - 7300 = $1972.73
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Brett draws the shape shown below.
He says the shape can be classified as a quadrilateral, parallelogram, rhombus, and square.
Is Brett correct? Explain.
The given figure is quadrilateral, parallelogram, and a rhombus but not a square. So brett is not correct.
What is a square?A square is a quadrilateral with all the sides equal and all the four sides are perpendicular to each other.
We know that it is a quadrilateral as a quadrilateral is having four sides and the sum of the angles is 180 degrees.
The given figure is a parallelogram as opposite sides of the figure are parallel and equal.
The given figure is a rhombus as all the sides are parallel and equal.
The given figure can not be a square as in the square all the four sides are perpendicular to each other.
Therefore given figure is quadrilateral, parallelogram, and a rhombus but not a square. So brett is not correct.
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Maria says the mean of the scores 7, 8, 3, 0, 2 is 5, because she added the scores and divided by 4. Is she correct? Explain why or why not.
Answer:
She is wrong.
Step-by-step explanation:
The mean score is
7 + 8 + 3 + 0 + 2= 20
We then divide it by the number which is 5
20/5= 4.
Therefore, Maria is wrong.
This is because she divided by 4 instead of 5, as she didn't include the rational number 0.
Solve the equation for x
z=m+x-y a)x=-z+m+y b)x=z-m+y c)x=z+m-y d)x=z+y+m
Answer:
x = z - m + y
Step-by-step explanation:
Given:
[tex]\displaystyle \large{z = m+x-y}[/tex]
To solve for x-term, we have to isolate it. We can do by subtracting m-term both sides and add y-term both sides.
[tex]\displaystyle \large{z-m+y=m+x-y-m+y}\\\\\displaystyle \large{z-m+y=x}\\\\\displaystyle \large{x=z-m+y}[/tex]
Therefore, the answer to this question is x = z - m + y
Please let me know if you have any questions regarding my answer or explanation!
If f(x) = |x| + 9 and g(x) = -6, which describes the range of (f+g)(x)
The range exist on all real values. This can be written as (-infty, infty)
Range of a functionThe range is the value of the dependent variable for which it exists. Given the following functions
f(x) = |x| + 9 and;
g(x) = -6
Determine the sum
(f+g)(x) = |x| + 9 + (-6)
(f+g)(x) = |x| + 9 -6
(f+g)(x) = |x| + 3
Determine the range of the function
The range exist on all real values. This can be written as (-infty, infty)
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Evaluate the functions for the given input values.
f(x) = x² + 1
g(x) = 2f(x)
g(-3) =
g(2) =
g(7) =
Answer:
g(-3) = 20
g(2) = 10
g(7) = 100
Step-by-step explanation:
g(x) = 2f(x) tells us that g(x) is two times f(x). Instead of f(x) we can write (x² + 1).
g(x) = 2f(x)
g(x) = 2(x² + 1)
Multiply.
g(x) = 2x² + 2
Now that we have g(x) we just substitute values in the function.
g(-3) = 2(-3)² + 2
= 2(9) + 2
= 18 + 2
= 20
g(2) = 2(2)² + 2
= 2(4) + 2
= 8 + 2
= 10
g(7) = 2(7)² + 2
= 2(49) + 2
= 98 + 2
= 100
How many different sequences of 3 playing cards (from a single 52-card deck) exist?
22,100
140,608
132,600
24,804
There 1,32,600 possibilities to withdrawn 3 different sequence of playing cards from 52 cards.
What is Permutations?A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.
Here, total number of cards = 52
Number of Withdrawn cards = 3
Possibilities of different sequences of 3 playing cards = 52 X 51 X 50
= 132600
Thus, there 1,32,600 possibilities to withdrawn 3 different sequence of playing cards from 52 cards.
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Answer:
132,600
Step-by-step explanation:
To determine the number of different sequences of 3 playing cards from a 52-card deck, we can use the formula for permutations, which is given by:
P(n, k) = n! / (n-k)!
Where n is the total number of items (in this case, the number of cards in the deck) and k is the number of items chosen (in this case, 3 cards).
Plugging in the values:
n = 52 (total number of cards in the deck)
k = 3 (number of cards chosen)
P(52, 3) = 52! / (52-3)!
Calculating the factorial terms:
52! = 52 x 51 x 50 x ... x 3 x 2 x 1
(52-3)! = 49! = 49 x 48 x ... x 3 x 2 x 1
Simplifying the equation:
P(52, 3) = 52 x 51 x 50
P(52, 3) = 132,600
Therefore, there are 132,600 different sequences of 3 playing cards that can be formed from a single 52-card deck.
When graphing f(x)=a sin(bx) you would determine the functions period using which of the following?
A. The period is 2pi/b
B. The period is a
C. The period is pi/b
Explanation:
The value of 'a' out front in y = a sin(bx) determines the amplitude.
The b term helps us compute the period, which is 2pi/b for sine, cosine, secant, and cosecant functions.
For example, y = 2sin(3x) has an amplitude of 2 and period of 2pi/3
For tangent and cotangent functions, the period would be pi/b.
Given that 2x³-5x² - 4x+8 = (Ax - 1)(x-B)(x + 1) + C for all values of x, find the
values of A, B and C.
Answer:
A=2, B=3, C=5
Step-by-step explanation:
Two polynomials are equal for all values of the variable if the corresponding coefficients are the same. The way to solve the problem is to multiply the RHS, rewrite it in a more orderly way
[tex](Ax-1)(x-B)(x+1)+C = \\Ax^3+(A-AB-1)x^2+(B-AB-1)x +B+C[/tex]
Now, for the two polynomials to be the same we need to have, at the same time
[tex]x^3: A=2\\x^2: A-AB-1= -5\\x:B-AB-1=-4\\1: B+C=8[/tex]
You might notice that we have more conditions than variables, but you can consider one of the two in the middle as a "check" option.
Now, grabbing the value from the first condition into the second we get B=3. Replacing both value in the third we see that the equality still holds, and replacing into the fourth we get C =5.
The box-and-whisker plot represents a data set. Which statements are never true for this data set?
The statement that can never be true is the data set contains a value of 3.
What is box plot?A box plot is used to study the distribution of a dataset. The box plot consists of two lines and a box. The two lines are known as whiskers. The end of the first line represents the minimum number and the end of the second line represents the maximum number.
minimum number = 8
maximum number = 22
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Answer the follwing grade 5 questions of HFC and LCM
Answer:
give clear image is next question
Step-by-step explanation:
i will give you the answer
A certain population of bacteria has an initial population of 225. the bacteria triples every hour. determine the multiplier that would allow you to predict the population of bacteria after 2 hours.
Using an exponential function, it is found that the multiplier that would allow you to predict the population of bacteria after 2 hours is of 9.
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
a is the initial value.b is the growth rate.In this problem, the bacteria triples every hour, hence the rate of change is b = 3, and the equation is:
[tex]y = a(3)^x[/tex]
Hence, after 2 hours:
[tex]y = a(3)^2 = 9a[/tex]
Which means that the multiplier is of 9.
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what is the center of the circle given by the equation (x-2)2+(y+4)2=6
Answer:
(2,-4)
Step-by-step explanation:
Here, h=2 and k=-4, so the center is (2,-4)
what is the slope of y=-9x-8?
The slope of the linear equation, y = -9x - 8 is determined as: -9.
How to Identify the Slope in an Equation?If the equation of a line is given in a slope-intercept form, y = mx + b, the slope value is represented as m.
Thus, given the equation y = -9x - 8, the slope in the linear equation is -9.
Therefore, slope of y = -9x - 8 is: -9.
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A group of students from your school is part of the audience for a TV game show. The total number of people in the audience is . What is the theoretical probability of students from your school being selected as contestants out of possible contestant spots?
A group of students from your school is part of the audience for a TV game show, the theoretical probability of students is mathematically given as
P=2.7%
What is the theoretical probability of students from your school being selected as contestants out of possible contestant spots?Generally, the equation for Probability is mathematically given as
[tex]P=\frac{Desired outcomes}{Total outcomes}[/tex]
Where Desired outcomes
D=40C5 *110C3
D=1420112865560
And Total outcomes
T=150C8 *
T=5.2572*10^10{12}
Hence, Probability
[tex]P=1420112865560/ 5.2572*10^10{12}[/tex]
P=0.0270
P=2.7%
In conclusion, the theoretical probability
P=2.7%
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Based on the information in the table what is the probability of being a girl and choosing lemonade?
Select one:
a.
21%
b.
.20
c.
20%
d.
38%
e.
.38
Using it's concept, it is found that the probability of being a girl and choosing lemonade is given by:
b. 0.2.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, out of 130 people, 26 are girls who choose lemonade, hence the probability is given by:
p = 26/130 = 0.2, which means that option b is correct.
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what is the value of the digit 5in the number 734.95?
Answer:
0.05
explanation
value means total value
so it's 5*0.01
=0.05
Select the correct answer. in which career would you most likely apply concepts from geometry? a. food critic b. social worker c. radio dj d. computer game designer
Answer:
Computer game designer.
Step-by-step explanation:
If you want to design a game, you need to have some basic shapes and stuff in it. I'm not sure what else needs to be explained here lol