Given that,
The acceleration due to gravity on the surface of the earth = 32 feet/s²
We need to calculate the time
Using formula of time period
[tex]T=2\pi\sqrt{\dfrac{l}{g}}[/tex]
On differentiating with respect to l
[tex]\dfrac{dT}{dL}=2\pi\times\dfrac{1}{2}(\dfrac{l}{g})^{-\frac{1}{2}}\times\dfrac{1}{g}[/tex]
[tex]\dfrac{dT}{dL}=\dfrac{\pi}{g}\times(\dfrac{g}{L})^{\frac{1}{2}}[/tex]
Put the value into the formula
[tex]\dfrac{dT}{dL}=\dfrac{\pi}{32}\times(\dfrac{32}{4})^{\frac{1}{2}}[/tex]
[tex]\dfrac{dT}{dL}=0.277\ sec[/tex]
If the length of the pendulum is decreased to 3.97 feet.
We need to calculate the time
Using formula of time period
[tex]\dfrac{dT'}{dL}=\dfrac{\pi}{g}\times(\dfrac{g}{L})^{\frac{1}{2}}[/tex]
Put the value into the formula
[tex]\dfrac{dT'}{dL}=\dfrac{\pi}{32}\times(\dfrac{32}{3.97})^{\frac{1}{2}}[/tex]
[tex]\dfrac{dT'}{dL}=0.278\ sec[/tex]
We need to calculate the gain time
Using formula for time
[tex]\dfrac{dT''}{dL}=\dfrac{dT'}{dL}-\dfrac{dT}{dL}[/tex]
Put the value into the formula
[tex]\dfrac{dT''}{dL}=0.278-0.277[/tex]
[tex]\dfrac{dT''}{dL}=0.001\ sec[/tex]
Hence, The clock gain the time in 24 hours is 0.001 sec.
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]
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.
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
Suppose tossing a coin 8 times represents the 8 cups of tea, heads represents a correct identification of what was poured first, tea or milk, and tails represents an incorrect identification of what was poured first. Select the best conclusion you would draw about whether the woman was just guessing.
A. Repeat the process many times (1000). If 6 correct out of 8 cups rarely occurs, then it is most likely that the woman was just guessing as to what was poured first.
B. Repeat the process many times (1000). If 8 correct out of 8 cups rarely occurs, then it is unlikely that the woman was just guessing as to what was poured first.
C. Repeat the process many times (1000). If 8 correct out of 8 cups rarely occurs, then it is likely that the woman was just guessing as to what was poured first.
D. Repeat the process many times (1000). If 4 correct out of 8 cups rarely occurs, then it is unlikely that the woman was just guessing as to what was poured first.
Answer:
A. Repeat the process many times (1000). If 6 correct out of 8 cups rarely occurs, then it is most likely that the woman was just guessing as to what was poured first.
Step-by-step explanation:
Since tossing a coin 8 times implies 8 cups of tea, with the given conditions.
The sample space = 1000
Then;
[tex]\frac{6}{8}[/tex] × 1000 = 750
If 6 correct out of 8 cups occurs (750 out of 1000), the woman got 750 correctly. Thus it can be inferred that it is likely that she knew what was poured first, either the tea or milk.
But, if 6 correct out of 8 cups rarely occurs (i.e 250 out of 1000), then it is most likely that the woman was just guessing as to what was poured first.
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
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.
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:
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]
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
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
answer this please ????
Answer:
a. x = 4
b. x = 17.5
Step-by-step explanation:
a. 5x/2 + 1 = 11
5x/2 = 10
5x = 20
x = 4
b. 2x/7 - 3 = 2
2x/7 = 5
2x = 35
x = 35/2
Answer:
a) x = 4
b) x = 17.5
Step-by-step explanation:
a)
(5x)/2 + 1 = 11
(5x)/2 = 10
5x = 20
x = 4
b)
(2x)/7 - 3 = 2
(2x)/7 = 5
2x = 35
x = 17.5
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]
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 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 .
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
The measures of two angles of a triangle are 105 and 31 degrees. Find the measure of the third angle.
Answer: 44°
Step-by-step explanation:
Measures of the angles of a triangle
= 180°
Therefore, 180 - 105 + 31 = 44°
The measure of the third angle is 44 degrees.
We have,
To find the measure of the third angle in a triangle, we can use the fact that the sum of the measures of all three angles in a triangle is always 180 degrees.
Let's denote the measure of the third angle as "x".
We are given that the measures of the other two angles are 105 degrees and 31 degrees.
Using the sum of angles in a triangle, we can set up the equation:
105 + 31 + x = 180
Simplifying the equation:
136 + x = 180
To isolate "x", we subtract 136 from both sides of the equation:
x = 180 - 136
x = 44
Therefore,
The measure of the third angle is 44 degrees.
Learn more about triangles here:
https://brainly.com/question/25950519
#SPJ2
In the matrix equation below, what are the values of x and y?
Answer: x=3 y=1
Step-by-step explanation:
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!
If the mean of the four nurnbers 4, 8, x and
12 is 0, chen x is
Answer:
x= -24
Step-by-step explanation:
(4+8+x+12)/4=0
4+8+x+12=0
x= -24
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.
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
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)
The goalkeeper of the USA ice hockey National Team, Jonathan Quick, saved 91.6% of shots during his entire career in the NHL. Estimate the probability that he let through more than 2 goals if the opposite team made 60 shots on goal.
Answer:
88.93% probability that he let through more than 2 goals if the opposite team made 60 shots on goal.
Step-by-step explanation:
For each shot, there are only two possible outcomes. Either he lets it through, or he does not. Shots are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The goalkeeper of the USA ice hockey National Team, Jonathan Quick, saved 91.6% of shots during his entire career in the NHL.
So he let in a goal in 100 - 91.6 = 8.4% of the shots, so [tex]p = 0.084[/tex]
60 shots:
This means that [tex]n = 60[/tex]
Estimate the probability that he let through more than 2 goals if the opposite team made 60 shots on goal.
Either he lets two or less goals, or he lets more than 2. The sum of the probabilities of these outcomes is 1. So
[tex]P(X \leq 2) + P(X > 2) = 1[/tex]
We want [tex]P(X > 2)[/tex].
Then
[tex]P(X > 2) = 1 - P(X \leq 2)[/tex]
In which
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{60,0}.(0.084)^{0}.(0.916)^{60} = 0.0052[/tex]
[tex]P(X = 1) = C_{60,1}.(0.084)^{1}.(0.916)^{59} = 0.0285[/tex]
[tex]P(X = 2) = C_{60,2}.(0.084)^{2}.(0.916)^{58} = 0.0770[/tex]
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0052 + 0.0285 + 0.0770 = 0.1107[/tex]
[tex]P(X > 2) = 1 - P(X \leq 2) = 1 - 0.1107 = 0.8893[/tex]
88.93% probability that he let through more than 2 goals if the opposite team made 60 shots on goal.
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
There is a notion that early discrimination training increases the IQ of children; that is, color discriminations (particularly subtle ones), discriminations among musical tones, etc., if fostered in children, are expected to increase IQ. A group of identical twins is used in an experiment to test this theory. One member of each twin pair gets this early discrimination training, but the other does not. Then, at a later date, their respective IQ scores are obtained. Which statistic would be used to test the hypothesis?
1. Point Biserial r
2. Z-test
3. Eta-squared
4. Dependent groups t-test
5. One Sample t-test
6. r-squared or r
7. Two factor ANOVA
8. Independent groups t-test
9. Phi Coefficient
10. Chi-square test
11. t-test for r > 0
12. One Factor ANOVA
13. Cramer’s Phi
Answer:
Two factor ANOVA
Step-by-step explanation:
They two factor ANOVA is used to determined if there is an interaction between the two independent variables on the dependent variable which in this case study are
The two independent variables are:
One member of each twin pair gets this early discrimination training, but the other does not.
While the dependent variable is their respective IQ scores.
Thus, we can use this test to determine whether the effect of one of the independent variable is the same for all other values of the other independent variable and vice versa using their IQ scores.
Any help would be great
Answer:
15
Step-by-step explanation:
38=10+13+c
c=38-10-13=15
Hope this helps!
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
A sofa sells for $1255.00 on the installment plan, which includes the finance charge. The payment plan calls for 10 percent down and the balance in 12 equal payments. The amount of each payment is $125.50. $86.43. $94.13. $120.00.
Answer:
$94.125
Step-by-step explanation:
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.