Looks like the limit is
[tex]\displaystyle\lim_{(x,y)\to(0,0)}\frac{x^4-36y^2}{x^2+18y^2}[/tex]
Let [tex]y=x^m[/tex] with [tex]m\ge1[/tex], so the limit is equivalent to
[tex]\displaystyle\lim_{x\to0}\frac{x^4-36x^{2m}}{x^2+18x^{2m}}=\lim_{x\to0}\frac{x^2-36x^{2(m-1)}}{1+18x^{2(m-1)}}=0[/tex]
Now let [tex]x=y^n[/tex] with [tex]n\ge1[/tex], so the limit is
[tex]\displaystyle\lim_{y\to0}\frac{y^{4n}-36y^2}{y^{2n}+18y^2}=\lim_{y\to0}\frac{y^{2(2n-1)}-36}{y^{2(n-1)}+18}=-\dfrac{36}{18}=-2[/tex]
The value of the limit evidently depends on path of approach, so the limit does not exist.
Suppose that early in an election campaign, a telephone poll of 800 registered voters shows that 460 favor a particular candidate. Just before Election Day, a second poll shows that 520 of 1,000 registered voters now favor that candidate. At the 0.05 significance level, is there sufficient evidence that the candidate's popularity has changed?
Answer:
Yes. At the 0.05 significance level, there is enough evidence to support the claim that the proportion that support the candidate has significantly changed.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the proportion that support the candidate has significantly changed.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
The significance level is 0.05.
The sample 1, of size n1=800 has a proportion of p1=0.58.
[tex]p_1=X_1/n_1=460/800=0.58[/tex]
The sample 2, of size n2=1000 has a proportion of p2=0.52.
[tex]p_2=X_2/n_2=520/1000=0.52[/tex]
The difference between proportions is (p1-p2)=0.05.
[tex]p_d=p_1-p_2=0.58-0.52=0.05[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{464+520}{800+1000}=\dfrac{980}{1800}=0.54[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.54*0.46}{800}+\dfrac{0.54*0.46}{1000}}\\\\\\s_{p1-p2}=\sqrt{0.00031+0.000248}=\sqrt{0.000558}=0.02[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.05-0}{0.02}=\dfrac{0.05}{0.02}=2.33[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]\text{P-value}=2\cdot P(z>2.33)=0.02[/tex]
As the P-value (0.02) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportion that support the candidate has significantly changed.
Random walk. A Java programmer begins walking aimlessly. At each time step, she takes one step in a random direction (either north, east, south, or west), each with probability 25%. She stops once she is at Manhattan distance r from the starting point. How many steps will the random walker take
Step-by-step explanation:
Hi, your question isn't totally complete. Here's the likely full question:
Random walk. A Java programmer begins walking aimlessly. At each time step, she takes one step in a random direction (either north, east, south, or west), each with probability 25%. She stops once she is at Manhattan distance r from the starting point. How many steps will the random walker take? This process is known as a two-dimensional random walk.
Write a program RandomWalker.java that takes an integer command-line argument r and simulates the motion of a random walk until the random walker is at Manhattan distance r from the starting point. Print the coordinates at each step of the walk (including the starting and ending points), treating the starting point as (0, 0). Also, print the total number of steps taken.
Evaluate. Write your answer as a fraction or whole number without exponents. 3^–4 =
Answer:
1/81.
Step-by-step explanation:
3^-4 = 1 /3^4
= 1/81.
Pls help me I’ll mark brainLiest
Answer:y times 20 p
Step-by-step explanation:
a rectangle has a length that is 5 inches grater than is width and is area is 104 square inches, The equation (x+5) x=104 represent the situation, where x represents the width of the retangle
Answer:
width = 8 inches; length = 13 inches
Step-by-step explanation:
(x + 5)x = 104
x^2 + 5x - 104 = 0
(x - 8)(x + 13) = 0
x - 8 = 0 or x + 13 = 0
x = 8 or x = -13
Since the width of a rectangle cannot be a negative number, we discard the answer x = -13.
x = 8
The width is 8 inches.
The length is 8 + 5 = 13.
The length is 13 inches.
if C=(a,b,x,y) and D=(m,n,o,p) then c union d is
Step-by-step explanation:
here,
C={ a,b,x,y}
D ={ m,n,o,p}
now,
C union D ={a,b,x,y} union {m,n,o,p}
= {a,b,x,y,m,n,o,p}
therefore C union D ={ a,b,x,y,m,n,o,p}
hope u get it...
Please answer this correctly
Answer:
0
Step-by-step explanation:
3 cards
P( odd) = 1 odd/ 3 cards = 1/3
No replacement
2 cards 6,8
No odds
P( odd) = 0/2
P( odd, no replacement, odd) = 1/2 * 0 = 0
Can somebody help me with this math question?
Answer:
8s^3
Step-by-step explanation:
In the question it says, triple the product which typically means triple using exponents. It is asking for you to do 8s x 8s x 8s or 8s to the power of 3
What is the solution to the equation below? Round your answer to two decimal places. 4+4•log2 x=4
Answer:
Option (C)
Step-by-step explanation:
Given expression is,
[tex]4+4\times \text{log}_2(x)=14[/tex]
By subtracting 4 from both the sides of the equation.
[tex]4\times \text{log}_2(x)=14-4[/tex]
Now divide the equation by 4
[tex]\text{log}_2(x)=\frac{10}{4}[/tex]
[tex]\text{log}_2(x)=2.5[/tex]
[If [tex]\text{log}_ab=x[/tex] , then [tex]b=a^{x}[/tex]]
[tex]x=(2)^{2.5}[/tex]
[tex]x = 5.657[/tex]
x ≈ 5.66
Therefore, Option C will be the correct option.
4+4•log2 x=14
x= 5.66
Find an equivalent ratio where the total number of students is 250
Answer: 125 boys and 125 girls = 1:1
Step-by-step explanation:
An equivalent ratio means there will be an equal number of boys and girls.
Since there are 250 students,
Boys = 250/2 = 125
Girls = 250/2 = 125
The ratio of boys to girls = 125 : 125
1 : 1 when simplified
a zero dimensional object that defines a specific location on a plan
Answer:
This is correct! Great Job!
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the given function.
Answer:
to determine the inverse of the given function, change f(x) to y, switch [tex]\boxed{x}[/tex] and y and solve for [tex]\boxed{y}[/tex]
The resulting function can be written as
[tex]f^{-1}(x)=x^2+\boxed{4}[/tex] where [tex]x\geq\boxed{0}[/tex]
Step-by-step explanation:
Hello,
f is defined for [tex]x\geq 4[/tex] as x-4 must be greater or equal to 0
and [tex]f(x)\geq 0[/tex]
so [tex]f^{-1}[/tex] is defined for [tex]x\geq 0[/tex]
and then we can write
[tex]x=(fof^{-1})(x)=f(f^{-1}(x))=\sqrt{f^{-1}(x)-4} \ so\\f^{-1}(x)-4=x^2 <=> f^{-1}(x)=x^2+4[/tex]
hope this helps
FOR BRAINLIEST ANSWER IF CORRECT The production supervisor finds that it takes 3 hours to manufacture a particular office chair and 6 hours to manufacture a particular office desk. A total of 1200 hours is available to produce office chairs and desks of this style. The linear equation that models this situation is 3x + 6y = 1200, where x represents the number of chairs produced and y represents the number of desks produced. (Do you see why?)
Answer:
[tex]3x + 6y = 1200[/tex] is the correct linear equation.
Step-by-step explanation:
Given:
Time taken to manufacture an office chair = 3 hours
Number of office chairs produced = [tex]x[/tex]
Time taken to manufacture an office desk = 6 hours
Number of office desks produced = [tex]y[/tex]
Let us calculate, Total Time taken to manufacture [tex]x[/tex] chairs.
Suppose we manufacture 2 chairs, time taken = 3 hours + 3 hours i.e. = 6 hours
Suppose we manufacture 3 chairs, time taken = 3 hours + 3 hours + 3 hours i.e. = 9 hours
Now, we are manufacturing [tex]x[/tex] number of chairs so we have to add 3 for [tex]x[/tex] number of times:
OR
simply multiply 3 with [tex]x[/tex].
i.e. Total time taken in producing [tex]x[/tex] chairs = 3[tex]x[/tex] hours
Similarly Total time taken in producing [tex]y[/tex] desks = 6[tex]y[/tex] hours
We have a total of 1200 hours to produce this type of office chairs and desks:
So, 1200 = Total time taken in producing [tex]x[/tex] chairs + Total time taken in producing [tex]y[/tex] desks
Putting the values, we get the following:
[tex]3x+6y=1200[/tex] is the correct linear equation for the situation.
Write the trigonometric expression in terms of sine and cosine, and then simplify. sin(u) cot(u) cos(u)
Answer:
[tex]sin(u) cot(u) cos(u) = cos^{2}(u)[/tex]
Step-by-step explanation:
[tex]sin(u) cot(u) cos(u)[/tex]
First, let us simplify cot(u) as follows:
cot (u) = [tex]\frac{1}{tan(u)}[/tex]
also, [tex]tan (u) = \frac{sin (u)}{cos(u)}[/tex]
∴ [tex]\frac{1}{tan(u)} = \frac{1}{\frac{sin(u)}{cos(u)} } = \frac{cos(u)}{sin(u)}[/tex]
Hence the original expression becomes:
[tex]sin(u).\frac{cos(u)}{sin(u)} .cos(u)[/tex]
Next, sin(u) will cancel each other out, leaving the expression below:
[tex]cos(u) . cos(u) = cos^{2} (u)[/tex]
hence:
[tex]sin(u) cot(u) cos(u) = cos^{2}(u)[/tex]
I also found a similar expression with a plus (+) sign after the "sin(u)" online, and if this was your question, the solution will be as follows:
sin(u)+ cot(u) cos(u)
[tex]sin(u) + \frac{cos(u)}{sin(u)} . cos (u)[/tex]
[tex]= sin(u) + \frac{cos^{2} (u)}{sin(u)}[/tex]
[tex]sin(u).\frac{sin(u)}{sin(u)} + \frac{cos^{2}(u) }{sin(u)} \\[/tex] (note that [tex]\frac{sin(u)}{sin(u)} = 1[/tex], hence multiplying it with sin(u) does not change anything in the expression.)
[tex]\frac{sin^{2} (u)}{sin(u)} + \frac{cos^{2}(u) }{sin(u)} = \frac{sin^{2}(u) + cos^{2}(u) }{sin(u)}[/tex]
Now the relationship sin²(u) + cos²(u) = 1
Therefore:
[tex]\frac{sin^{2}(u) + cos^{2}(u) }{sin(u)} = \frac{1}{sin(u)}[/tex]
Hence, [tex]sin(u)+ cot(u) cos(u) = \frac{1}{sin(u)}[/tex]
Planes A and B both intersect plane S. Vertical plane S intersects horizontal plane A and horizontal plane B. Plane S and plane A intersect at line f. Line f contains points N and K. Plane S and plane B intersect at line g. Line g contains points P and Q. Line d intersects plane A at point L. Which statements are true based on the diagram? Select three options.
Answer:
first second third
Step-by-step explanation:
Answer:
A,B,C
Step-by-step explanation:
I took the course
what is 2 3/7- 5 6/7
Answer:
-24/7please see the attached picture for full solution...
Hope this helps...
Good luck on your assignment..
A survey of enrollment at 35 community colleges across the United States yielded the following figures:
6414; 1550; 2109; 9350; 21828; 4300; 5944; 5722; 2825; 2044; 5481; 5200; 5853; 2750; 10012; 6357; 27000; 9414; 7681; 3200; 17500; 9200; 7380; 18314; 6557; 13713; 17768; 7493; 2771; 2861; 1263; 7285; 28165; 5080; 11622
a. Organize the data into a chart with five intervals of equal width. Label the two columns "Enrollment" and "Frequency."
b. Construct a histogram of the data.
c. If you were to build a new community college, which piece of information would be more valuable: the mode or the mean?
d. Calculate the sample mean.
e. Calculate the sample standard deviation.
f. A school with an enrollment of 8000 would be how many standard deviations away from the mean?
Answer: (a) The chart is in the first attachment named table frequency.
(b) The histogram is in the second attachment named frequency vs. enrollment
(c) Mode
(d) x = 9071.4
(e) s = 6677.64
(f) It is -0.16 standard deviation away
Step-by-step explanation:
(c) Mode is the number in the data set which appears more often. When thinking about builiding a new community college, if you choose mode will have which college enrollment will appear more often, i.e., which courses have more students wanting to enroll.
(d) To calculate sample mean of a frequency data:
1) Find the midpoint for each interval;
2) Multiply each midpoint for its correspondent frequency;
3) Sum up each multiplication obtained in the previous step;
4) Sum up all the frequencies;
5) Divide the sum in step 3 by the sum in step 4;
For this chart:
x = [tex]\frac{3000.10+7500.16+12500.3+17500.3+22500.1+27500.2}{35}[/tex]
x = 9071.4
(e) To find the standard deviation:
1) With each midpoint, calculate its square;
2) Multiply the midppoint square by its correspondent frequency;
3) Use the following formula to determine the sample standard:
s = √∑f.M² - n(μ)² / n-1
For this chart:
s = [tex]\sqrt{\frac{4396250000 - 35*(9071.4)^{2}}{34} }[/tex]
s = 6677.64
(f) To find how many standard deviations away is the enrollment:
z = [tex]\frac{8000-9071.4}{6677.64}[/tex]
z = - 0.16
8000 enrollments are -0.16 standard deviations away from the mean.
Which one doesn’t belong? Why? Explain. please help me
Hi! So, the one that doesn't belong is a) y = 4x.
I think that this doesn't belong because every other option has a number after the variable (I forget the exact term for it but it's like +7, +4, and -1 for the rest of the options)
Please let me know how I can further help you :)
(
Answer:
I think the answer is y = -2x + 4 because that is the only one that has a negative slope. The other choices all have positive slopes.
Find the value of
3y when y= -7
Answer:
-21
Step-by-step explanation:
3×(-7) = - 21
Three times minus seven equals minus twenty one.
Answer:
Step-by-step explanation:
y = -7
3y = 3 * -7
= (-21)
Which type of energy refers to the sum of potential and kinetic energies in the particles of a substance?
Answer:internal
Step-by-step explanation:
Answer:
internal
Step-by-step explanation:
took the test
Prime factorization of 45
A. 2³×5
B. 3²×5
C. 5²×3
D. 5²×9
Answer:
Hello, your answer is:
B. 3²×5
Step-by-step explanation:
Prime factorization of 45 is:
45 = 9 x 5
= 3²×5
Hope this helps you.. Good Luck
Answer:
B. 3² × 5
Step-by-step explanation:
45 can be written as a product of its prime factors.
45 = 3 × 3 × 5
45 = 3² × 5
what is 18576939*47 Thanks!!!!!
Answer:
873116133
Step-by-step explanation:
18576939 × 47
Multiply the numbers.
= 873116133
Answer: 873116133
Step-by-step explanation:
‘Hope this helps:)
One-eighth of the students in Martha's class are left handed. One-fourth of the left-handed students wear glasses. What fraction of Martha's class is left-
handed and wears glasses?
Answer:
1/32
Step-by-step explanation:
Multiply the fractions together
1/8 * 1/4 = 1/32
1/32 are left handed glass wearers
What is the 20th digit after the decimal point of the sum of the decimal equivalents for the fractions $\frac{1}{7}$ and $\frac{1}{3}$?
Answer:
7
Step-by-step explanation:
1/7+1/3= 3/21+7/21= 10/21= 0.476190
the 6 digits after the decimal point get repeated
6*3= 18- three full cycles and the second digit after 3 cycles = 7 so the 20th digit is 7
This person was correct.
Answer:
7
Step-by-step explanation:
1/7+1/3= 3/21+7/21= 10/21= 0.476190
the 6 digits after the decimal point get repeated
6*3= 18- three full cycles and the second digit after 3 cycles = 7 so the 20th digit is 7
a bag contains only red and blue counters the probability that a counter is blue is 0.58 A counter is picked at random What is the probability that it is red
Answer:
0.42
Process:
1 - 0.58
0.42
factor the polynomial expression x^4+18x^2+81
Answer:
Step-by-step explanation:
Hello,
please consider the following
[tex]x^4+18x^2+81=(x^2)^2+2*(3^2)x^2+(3)^4\\\\=(x^2+9)^2[/tex]
hope this helps
Answer: The answer is shown in the picure
Jimmie invested $13,000 at 5.23% compounded monthly.
What will Jimmie's account balance be in 42 years?
Answer:
116370.197$
Step-by-step explanation:
Jimmie invested $13,000 at 5.23% compounded monthly.
Jimmie's account balance (B) after 42 years:
B = principal x (1 + rate)^time
= 13000 x (1 + (5.23/100)/12)^(42 x 12)
= 116370.197$
A farmer divided his land into 2 groups of sections randomly. There is no difference in the quality of the soil between the 2 groups of land. He used Type A seeds in the first group and Type B seeds in the second group. After 3 months, the heights of the crops are measured across the two groups of land sections. Is the study observational or experimental? If it is an experiment, what is the controlled factor?
Answer:
Experiment
Time..
Step-by-step explanation:
It is an experimental study. An experimental study is a type of study in which all conditions are under the control of the researcher.
The control factor in this case may includes the time...before measurements.
Here we must answer different things about the experiment that the farmer performed. We will see that this is an experiment and the controlled factors are:
Quality of the soil.Wheater.Hours of daylight.What he did is divide his land in two equal parts, and then use different types of seeds in each one of the two parts.
After 3 months, he measures the height of the crops.
The questions are:
Is the study observational or experimental?
It is experimental, because the farmer assigned two areas and he decided what type of seed went into each area.
If it is an experiment, what are the controlled factor?
The controlled factors are the things that are the same for both of the groups of sections and that are relevant for the growth of the seeds. These things are:
Quality of the soil.Wheater.Hours of daylight.If you want to learn more about experiments, you can read:
https://brainly.com/question/11256472
What is the solution to this inequality -13x> - 39
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form: x < 3
Interval Notation:
( − ∞ , 3 )
Answer:
x<3
Step-by-step explanation:
-13x>-39
-13x>-39 (Divided by Negative Thirteen)
-13>-13
x<3 (The great sign changes to less than when divided or multiplied by a negative number.)
x={...0,1,2}
Hope this helps ❤
please help me with this
Answer:
Volume = 160 cm³ (Unit = cm³)
Step-by-step explanation:
Length = 4 cm
Width = 4 cm (Because it's a square based cuboid!)
Height = 10 cm
Now, Volume:
Volume = [tex]Length * Width*Height[/tex]
Volume = 4 * 4 * 10
Volume = 160 cm³
Answer:
160 cm³
Step-by-step explanation:
The base is a square. The side length of the base is 4 cm.
The volume of a square-based cuboid is the area of square × height or length.
4² × 10
16 × 10
= 160
The volume of the square-based cuboid is 160 cm³.