Answer:
[tex]f(x)=3x^2+2[/tex] and the limit is 12
Step-by-step explanation:
we know that the derivative of the function f in x=a is the limit of this
[tex]\dfrac{f(a+h)-f(a)}{a+h-a}=\dfrac{f(a+h)-f(a)}{h}[/tex]
as the expression is
[tex][3(a+h)^2+2 ]-14[/tex]
we can say that
[tex]f(a+h)=3(2+h)^2+2 \\\\f(a)=14[/tex]
from the first equation we can identify a = 2 and then
[tex]f(x)=3x^2+2[/tex]
to verify that we are correct, we can compute f(2)=3*4+2=14
f'(x)=6x
so f'(2)=12
we can estimate it from the fraction as well
so the limit is 12
You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estimation for the population proportion. You would like to be 80% confident that you estimate is within 2.5% of the true population proportion. How large of a sample size is required?
Answer:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.025}{1.28})^2}=655.36[/tex]
And rounded up we have that n=656
Step-by-step explanation:
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 80% of confidence, our significance level would be given by [tex]\alpha=1-0.80=0.20[/tex] and [tex]\alpha/2 =0.10[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=\pm 1.28 [/tex]
Solution to the problem
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
Since we don't have prior info for the proportion of interest we can use [tex]\hat p=0.5[/tex] as estimator. And on this case we have that [tex]ME =\pm 0.025[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.025}{1.28})^2}=655.36[/tex]
And rounded up we have that n=656
Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the line y equals one third x comma above left by yequalsxplus4, and above right by yequalsminusx squaredplus10.
Answer:
The bounded area is: [tex]\frac{73}{6}\approx 12.17[/tex]
Step-by-step explanation:
Let's start by plotting the functions that enclose the area, so we can find how to practically use integration. Please see attached image where the area in question has been highlighted in light green. The important points that define where the integrations should be performed are also identified with dots in darker green color. These two important points are: (2, 6) and (3, 1)
So we need to perform two separate integrals and add the appropriate areas at the end. The first integral is that of the difference of function y=x+4 minus function y=(1/3)x , and this integral should go from x = 0 to x = 2 (see the bottom left image with the area in red:
[tex]\int\limits^2_0 {x+4-\frac{x}{3} } \, dx =\int\limits^2_0 {\frac{2x}{3} +4} \, dx=\frac{4}{3} +8= \frac{28}{3}[/tex]
The next integral is that of the difference between [tex]y=-x^2+10[/tex] and the bottom line defined by: y = (1/3) x. This integration is in between x = 2 and x = 3 (see bottom right image with the area in red:
[tex]\int\limits^3_2 {-x^2+10-\frac{x}{3} } \, dx =-9+30-\frac{3}{2} -(-\frac{8}{3} +20-\frac{2}{3} )=\frac{39}{2} -\frac{50}{3} =\frac{17}{6}[/tex]
Now we need to add the two areas found in order to get the total area:
[tex]\frac{28}{3} +\frac{17}{6} =\frac{73}{6}\approx 12.17[/tex]
What is the number of ways to
arrange 5 objects from a set of 8
different objects?
Answer:
6,720 ways
Step-by-step explanation:
Since in the problem arrangemnt is being asked this is a problem of permutation.
No . of ways of arranging r things out of n things is given by
P(n,r) = n!/(n-r)!
In the problem given we have to arrange 5 objects from set of 8 objects.
Here n = 8 and p = 5
it can be done in in
P(8,5) = 8!/(8-5)! ways
8!/(8-5)! = 8!/3! = 8*7*6*5*4*3!/3! = 8*7*6*5*4 = 6,720
Thus, number of ways to arrange 5 objects from a set of 8
different objects is P(8,5) = 8!/(8-5)! = 6,720 .
how much money do you earn in 1 hour if you earn 20 in 4 hours
Answer:
let’s make a Unit rate.
$20/4 hours = $5 per hour
So you earn $5 in 1 hour if you earn $20 in 4 hours.
hope this helps and pls mark me brainliest if it did ;)
Answer:
$5
Step-by-step explanation:
Let's set up a proportion using the following setup.
money/hours=money/hours
We know that $20 is earned in 4 hours. We don't know how much is earned in 1 hour, so we can say $x is earned in 1 hour.
$20/4 hours= $x/1 hour
20/4=x/1
x/1 is equal to x.
20/4=x
Divide 20 by 4.
5=x
$5 is earned in 1 hour.
If
f(x) = 13x + 1, then
f-1(x) =
Answer:
(x-1)/13
Step-by-step explanation:
y = 13x+1
To find the inverse, exchange x and y
x = 13y+1
Solve for y
Subtract 1 from each side
x-1 =13y+1-1
x-1 = 13y
Divide each side by 13
(x-1)/13 = y
The inverse is (x-1)/13
Answer:
f(x) = 13x + 1
To find the inverse let f(x) = y
y = 13x + 1
x = 13y + 1
13y = x - 1
y = (x-1)/13
The inverse is x-1/13.
Which theoretical probabilities are equal to 1/3? Check all that apply.
Answer:
2/6, 4/12, 8/24, 16/48, 32/96 ect....
Step-by-step explanation:
I hope this helps I really didnt know if this is what you were asking about
2)
Which of these objects are two-dimensional? Check all that apply.
A.Point
B.Segment
C.Square
D. Line
E. Solid
F. Plane
Answer:
Option C and F
Step-by-step explanation:
=> Square and Plane a two-dimensional objects.
Rest of the objects are either 1 - dimensional or 3- dimensional.
Please answer this correctly
Answer:
3| 4 4 7
4| 0 3 4
5| 5 5 5
6| 0 1 3 8 9
7| 9
8| 1 4 6 8
hope it helps!
Step-by-step explanation:
Check the numbers and list out the tens digit in stem (that is 3-8) and then write the corresponding leaf values
A simple random sample of 5 months of sales data provided the following information: Month: 1 2 3 4 5 Units Sold: 94 105 85 94 92 (a) Develop a point estimate of the population mean number of units sold per month. x = (b) Develop a point estimate of the population standard deviation. If required, round your answer to two decimal places. s =
Answer:
a) x = 94 units/month
b) s = 51.50 units/month
Step-by-step explanation:
The adequate point estimation of the population mean and standard deviation are the sample mean and sample standard deviation.
a) Point estimation of the population (sample mean)
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{5}(94+105+85+94+92)\\\\\\M=\dfrac{470}{5}\\\\\\M=94\\\\\\[/tex]
b) Point estimation of the population standard deviation (sample standard deviation)
[tex]s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2\\\\\\s=\dfrac{1}{4}((94-94)^2+(105-94)^2+(85-94)^2+(94-94)^2+(92-94)^2)\\\\\\s=\dfrac{206}{4}\\\\\\s=51.50\\\\\\[/tex]
Using statistical concepts, it is found that:
a) The point estimate for the population mean is of: [tex]\overline{x} = 94[/tex]
b) The point estimate for the population standard deviation is of: [tex]s = 7.18[/tex]
Item a:
The mean of a data-set is the sum of all observations in the data-set divided by the number of observations.The point estimate for the population mean is the sample mean.In this problem, the sample is: 94, 105, 85, 94, 92.
Thus, the mean is:
[tex]\overline{x} = \frac{94 + 105 + 85 + 94 + 92}{5} = 94[/tex]
Item b:
The standard deviation of a data-set is the square root of the sum of the differences squared between each observation and the mean, divided by one less than the number of values.The point estimate for the population standard deviation is the sample standard deviation.Then:
[tex]s = \sqrt{\frac{(94-94)^2+(105-94)^2+(85-94)^2+(94-94)^2+(92-94)^2}{4}} = 7.18[/tex]
A similar problem is given at https://brainly.com/question/13451786
Sixteen of 80 dogs in a rescue kennel are puppies.what percent of the dogs in the kennel are puppies?
Answer:
20%
Step-by-step explanation:
Answer:
20%
Step-by-step explanation: All you have to do is 16 divided by 80 which is 0.2. 0.2 as a decimal is 20%.
factorization of expression 4z(3a+2b-4c)+(3a+2b-4c)
Answer:
(3a+2b-4c)[4z+1]
Step-by-step explanation:
4z(3a+2b-4c)+(3a+2b-4c)
Factor out (3a+2b-4c)
(3a+2b-4c)[4z+1]
Answer:
3a+2b-4c)[4z+1]
Step-by-step explanation:
4z(3a+2b-4c)+(3a+2b-4c)
Factor out (3a+2b-4c)
(3a+2b-4c)[4z+1]
Question 2: The average price for a BMW 3 Series Coupe 335i is $39,368. Suppose these prices are also normally distributed with a standard deviation of $2,367. What percentage of BMW dealers are pricing the BMW 3 Series Coupe 335i at more than the average price ($44,520) for a Mercedes CLK350 Coupe? Round your answer to 3 decimal places.
Answer:
0.015 = 1.5% of BMW dealers are pricing the BMW 3 Series Coupe 335i at more than the average price ($44,520) for a Mercedes CLK350 Coupe
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 39368, \sigma = 2367[/tex]
What percentage of BMW dealers are pricing the BMW 3 Series Coupe 335i at more than the average price ($44,520) for a Mercedes CLK350 Coupe?
This is 1 subtracted by the pvalue of Z when X = 44520. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{44520 - 39368}{2367}[/tex]
[tex]Z = 2.18[/tex]
[tex]Z = 2.18[/tex] has a pvalue of 0.985
1 - 0.985 = 0.015
0.015 = 1.5% of BMW dealers are pricing the BMW 3 Series Coupe 335i at more than the average price ($44,520) for a Mercedes CLK350 Coupe
Any help would be great
Answer:
15
Step-by-step explanation:
38=10+13+c
c=38-10-13=15
Hope this helps!
The length of a 95% confidence interval for mean Age is which of the following? (Because of potential roundoff, choose the closest.) Click here to reference the data needed to answer the question. a. 3.37 b. 3.72 c. 4.27 d. 3.11
Answer:
The length of a 95% confidence interval for mean Age is 3.72.
Step-by-step explanation:
The data is provided for the age of 100 adults.
The mean and standard deviation are:
[tex]\bar x=47.8\\\\s=9.3744[/tex]
As the sample size is too large the z-interval will be used for the 95% confidence interval for mean.
The critical value of z for 95% confidence level is, z = 1.96.
The length of a confidence interval is given by:
[tex]\text{Length}=2\cdot z_{\alpha/2}\cdot\frac{s}{\sqrt{n}}[/tex]
[tex]=2\times 1.96\times\frac{9.3744}{\sqrt{100}}\\\\=3.6747648\\\\\approx 3.67\\\\\approx 3.72[/tex]
Thus, the length of a 95% confidence interval for mean Age is 3.72.
Replace eachwith <, >, or = to make a true sentence.
12 __ -6
A) <
B) >
C) =
Answer:
The answer is option B
Step-by-step explanation:
Since 12 is greater than - 6
Hope this helps
Answer:
12 > -6
Step-by-step explanation:
A positive number is always greater than a negative number
12 > -6
Can someone please help me
Answer:
20
Step-by-step explanation:
If the two triangles are similar, then corresponding sides must share a constant ratio. This means that:
[tex]\dfrac{10}{6}=\dfrac{25}{15}=\dfrac{x}{12}[/tex]
Let's use the second ratio:
[tex]\dfrac{25}{15}=\dfrac{x}{12}[/tex]
Multiply both sides by 12:
[tex]\dfrac{25\cdot 12}{15}=x \\\\x=20[/tex]
Hope this helps!
Please answer this correctly
Answer:
Step-by-step explanation:
Baltimore orioles : 1,000,000 + 1,000,000 + 500,000
Click 2 full bag and 1 half bag
Kansas city royals : 1,000,000 +500,000
Click 1 full bag and 1 half bag
Newyork Yankees : 1,000,000 + 1,000,000 + 1,000,000 +1,000,000 +1,000,000 + 500,000
Click 5 full bag + 1 half bag
which of these is a step constructing an inscribed square using technology?
Answer:
Mark the points of intersection between circle A and line AB.
Step-by-step explanation:
The attached shows an inscribed square created using technology. We started with point A and B, drew the circle with radius AB, and drew the line AB. Then we marked point C at the intersection of circle A and line AB.
We had a perpendicular to AB drawn through A, and marked its intersection with circle A as points D and E. Finally, we drew inscribed square BDCE.
__
Other answer choices may somehow be involved. We'd need to see the construction to be sure. The one shown above seemed most likely.
What is the answer? x^2-y^2=55
Answer:
To solve for x we can write:
x² - y² = 55
x² = y² + 55
x = ±√(y² + 55)
To solve for y:
x² - y² = 55
y² = x² - 55
y = ±√(x² - 55)
When 1760 is divided into 14 equal parts, the remainder is 10. What is a correct way to write the quotient?
Answer:
125 r. 10
Step-by-step explanation:
I Am Thinking of a number. 1/12 of it equals 6. 1/3 of it equals_________.
Answer:
24
Step-by-step explanation:
hello
let's note x the number we are looking for
[tex]\dfrac{x}{12}=6\\<=> x = 6*12=72[/tex]
so 1/3 of it equals
[tex]\dfrac{72}{3}=24[/tex]
another way to see it is that 12=4*3
so 1/3 of it equals 6*4=24
hope this helps
In the matrix equation below, what are the values of x and y?
Answer: x=3 y=1
Step-by-step explanation:
State the domain of f(a,b) = e^ab
Answer:
a2+b2=c2
Step-by-step explanation:
find the saqure roof of two
Answer:
(∞,∞), (a /a∉R)
Step-by-step explanation:
A kite is flying 85 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 52degrees. Find the length of the string. Round your answer to the nearest tenth.
Answer:
107.9 ft
Step-by-step explanation:
Imagine Kite is a point A. The person ,who keeps the string is point B.
The height of flying is AC=85 ft. So we have right triangle ABC :angle C=90 degrees, angle B is 52 degrees. Length of AB (triangle ABC hypotenuse) is the length of the string.
AB=AC/sinB=85/sin52=107.8665...=approx 107.9 ft
HELP!!!!!!!!!!!!
A random number generator is used to create a real number between 0 and 1, equally likely to fall anywhere in this interval of values. (For the instance, 0.3794259832... is a possible outcome). a. Sketch a curve of the probability distribution of this random variable, which is the continuous version of the uniform distribution.
Answer:
The graph of the probability density function is attached.
Step-by-step explanation:
The probability function for this random number generator will be like the uniform distribution and defined for X ∈ [0, 1].
The probability density function can be written as:
[tex]f(x)={\begin{cases}{\dfrac {1}{1-0}}=1&\mathrm {for} \ 0\leq x\leq 1,\\[8pt]0&\mathrm {for} \ x<0\ \mathrm {or} \ x>1\end{cases}}[/tex]
The graph of the probability density function is attached.
Calculate balloon volume for each balloon at maximum inflation from the circumference data. (You will have to assume that the balloon was a perfect sphere.) To calculate balloon volume, first find the radius (in cm) of the balloon by using the formula C = 2πr. Then, use the radius' value in the formula V = (4/3)πr3 to calculate volume (in cm3). Show all your work, place units on all numbers (even those within the calculations), and express your answers with appropriate sig figs. (12 pts)
Answer:
r₁ = 3.583cm
V₁= 192.55cm³
r₂= 5.176cm
V₂ = 580.283cm³
r₃ = 5.255cm
V₃ = 607.479cm³
Step-by-step explanation:
assuming circumferences of each balloons are given as follows C₁ = 22.5cm, C₂ = 32.5cm and C₃ = 33cm
Recall C = 2πr
volume of a sphere is 4/3πr³
Assume that the population proportion is 0.56. Compute the standard error of the proportion, σp, for sample sizes of 100, 200, 500, and 1,000. (Round your answers to four decimal places.)
Answer:
Standard errors are 0.049, 0.035, 0.022, and 0.016.
Step-by-step explanation:
The given value of population proportion (P) = 0.56
Given sample sizes (n ) 100, 200, 500, and 1000.
Now standard error is required to calculate.
Use the below formula to find standard error.
When sample size is n = 100
[tex]\sqrt{\frac{P(1-P)}{n}} = \sqrt{\frac{0.56(1-0.56)}{100}} =0.049[/tex]
When sample size is n = 200
[tex]\sqrt{\frac{P(1-P)}{n}} = \sqrt{\frac{0.56(1-0.56)}{200}} = 0.035[/tex]
When sample size is n = 500
[tex]\sqrt{\frac{P(1-P)}{n}} = \sqrt{\frac{0.56(1-0.56)}{500}} =0.022[/tex]
When sample size is n = 1000
[tex]\sqrt{\frac{P(1-P)}{n}} = \sqrt{\frac{0.56(1-0.56)}{1000}} = 0.016[/tex]
paulina plays both volleyball and soccer .the probability of her getting injured playing soccer is 0.10 and the probability of her getting injured playing soccer is 0.20 .which of the event is more likely
Step-by-step explanation:
While playing volleyball, probability of getting hurt is
P(A) = 0.1 = 1/10
and in the case of soccer, it is
P(B) = 0.2 = 2/10 = 1/5
Here we see, P(A) < P(B)
Answer: We can conclude that the probability of getting injured while playing soccer is more likely.
The area of a triangle is 80cm² and its base is 8cm. If its height is (6+k) cm, find the value if k.
(3marks)
Answer:
K=14
Step-by-step explanation:
A=1/2*b*h
80=1/2*8*(6+k) multiply by 2 on both sides
160=8*(6+k) distribute by 8
160=48+8k subtract 48 from both sides
112=8k divide by 8
14=K
Find the volume of a right circular cone that has a height of 4.2m and a base with a radius of 3.4m
Answer:
about 50.8 cubic meters
Step-by-step explanation:
The formula for the volume of a cone is ...
V = (1/3)πr²h
Put the given values into the formula and do the arithmetic.
V = (1/3)π(3.4 m)²(4.2 m) = 16.194π m³
__
For π to calculator precision, this is ...
V ≈ 50.84 m³
For π = 3.14, this is ...
V ≈ 50.82 m³