Answer: 151
Step-by-step explanation:
if prior population proportion is unknown , then the formula is used to find the sample size :
[tex]n=0.25(\frac{z_{\alpha/2}}{E})^2[/tex]
, where [tex]z_{\alpha/2}[/tex] = Two tailed critical value for significance level of [tex]\alpha.[/tex]
E = Margin of error.
Given : margin of error = 8%= .08
For 95% confidence level , two tailed critical value = 1.96
Now, the required sample size :
[tex]n=0.25(\frac{1.96}{0.08})^2\\\\=0.25(24.5)^2\\\\=150.0625\approx151[/tex]
Hence, the size of the sample needed = 151.
Lee watches TV for 2 hours per day. During that time, the TV consumes 150 watts per hour. Electricity costs (12 cents)/(1 kilowatt-hour). How much does Lee's TV cost to operate for a month of 30 days?
Answer:
$1.08
Step-by-step explanation:
30 days × (2 hrs/day) × (150 W) × (1 kW / 1000 W) × (0.12 $/kWh) = $1.08
A toy falls from a window 80 feet above the ground. How long does it take the toy to hit the ground?
Answer:
2.24 s
Step-by-step explanation:
Given:
Δy = 80 ft
v₀ = 0 ft/s
a = 32 ft/s²
Find: t
Δy = v₀ t + ½ at²
80 ft = (0 ft/s) t + ½ (32 ft/s²) t²
t = 2.24 s
The volume of a gas in a container varies inversely with the pressure on the gas. A container of helium has a volume of 370in3 under a pressure of 15psi (pounds per square inch). Write the equation that relates the volume, V, to the pressure, P. What would be the volume of this gas if the pressure was increased to 25psi?
Answer:
Step-by-step explanation:
When two variables vary inversely, it means that an increase in one would lead to a decrease in the other and vice versa. Since the volume of a gas, V in a container varies inversely with the pressure on the gas, P, if we introduce a constant of proportionality, k, the expression would be
V = k/P
If V = 370 in³ and P = 15psi, then
370 = k/15
k = 370 × 15 = 5550
The equation that relates the volume, V, to the pressure, P would be
V = 5550/P
if the pressure was increased to 25psi, the volume would be
V = 5550/25 = 222 in³
Answer:
v=5550/p
222
Step-by-step explanation:
PLEASE ANSWER FAST, THANKS! :)
Answer:
Step-by-step explanation:
k = 3 ; 2k + 2 = 2*3 + 2 = 6 + 2 = 8
k = 4; 2k + 2 = 2*4 + 2 = 8 +2 = 10
k =5; 2k + 2 = 2*5 +2 = 10+2 = 12
k=6; 2k +2 = 2*6 + 2 = 12+2 = 14
k = 7 ; 2k + 2 = 2*7 +2 = 14 +2 = 16
k = 8 ; 2k + 2 = 2*8 + 2 = 16 +2 = 18
∑ (2k + 2) = 8 + 10 + 12 + 14 + 16 + 18 = 78
A car travelling from Ibadan to Lagos at 90 km/hr
takes 1 hour 20 min. How fast must one travel to
cover the distance in one hour?
Answer:
A velocity of 120km/h is needed to cover the distance in one hour
Step-by-step explanation:
The velocity formula is:
[tex]v = \frac{d}{t}[/tex]
In which v is the velocity, d is the distance and t is the time.
A car travelling from Ibadan to Lagos at 90 km/hr takes 1 hour 20 min.
This means that [tex]v = 90, t = 1 + \frac{20}{60} = 1.3333[/tex]
We use this to find d.
[tex]v = \frac{d}{t}[/tex]
[tex]90 = \frac{d}{1.3333}[/tex]
[tex]d = 90*1.3333[/tex]
[tex]d = 120[/tex]
The distance is 120 km.
How fast must one travel to cover the distance in one hour?
Velocity for a distance of 120 km(d = 120) in 1 hour(t = 1). So
[tex]v = \frac{d}{t}[/tex]
[tex]v = \frac{120}{1}[/tex]
[tex]v = 120[/tex]
A velocity of 120km/h is needed to cover the distance in one hour
The Ericsson method is one of several methods claimed to increase the likelihood of a baby girl. In a clinical trial, results could be analyzed with a formal hypothesis test with the alternative hypothesis of pgreater than0.5,which corresponds to the claim that the method increases the likelihood of having a girl, so that the proportion of girls is greater than 0.5. If you have an interest in establishing the success of the method, which of the following P-values would you prefer: 0.999, 0.5, 0.95, 0.05, 0.01, 0.001? Why?
Answer:
0.001
Step-by-step explanation:
Here, the aim is to support the null hypothesis, Ha. Where Ha: p > 0.5. Which means we are to reject null hypothesis H0. Where H0: p = 0.5.
The higher the pvalue, the higher the evidence of success. We know If the pvalue is less than level of significance, the null hypothesis H0 is rejected.
Hence the smallest possible value 0.001 is preferred as the pvalue because it corresponds to the sample evidence that most strongly supports the alternative hypothesis that the method is effective
The Ball Corporation's beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with a known thickness standard deviation σ = .000586 mm. Assume a random sample of 59 sheets of metal resulted in an x¯ = .2905 mm. Calculate the 95 percent confidence interval for the true mean metal thickness.
Answer:
The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{0.000586}{\sqrt{59}} = 0.0002[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 0.2905 - 0.0002 = 0.2903 mm
The upper end of the interval is the sample mean added to M. So it is 0.2905 + 0.0002 = 0.2907 mm
The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm
You want to install a 1 1 yd wide walk around a circular swimming pool. The diameter of the pool is 23 yd. What is the area of the walk? Use 3.14 for pi π.
Complete Question:
You want to install a 1 yd wide walk around a circular swimming pool. The diameter of the pool is 23 yd. What is the area of the walk? Use 3.14 for pi π.
Answer:
75.36 square yard
Step-by-step explanation:
From the question,
The diameter of this circular pool inside is 23 yd.
This means that the radius = Diameter/2 = 23yd/2 = 11.5 yd.
The formula for the area of a circle =
A = πr²
A = π(11.5)²
A =3.14 × 11.5²
A = 415.265 yd²
This is the Area of the inner circle.
We were told in the question also that he wants to install a walk of 1 yard
Hence, the radius of outer circle =
radius of inner circle +length of the walk
11.5yard + 1 yard
= 12.5 yard
A = πr²
A = 3.14 × (12.5)²
A = 490.625yd²
Area of the walk = Area of the Outer circle - Area of the inner circle
= (490.625 - 415.265)yd = 75.36 yd²
Therefore, the area of the walk is 75.36 square yards.
Perform the indicated operation.
Answer:
√75 = 5√3 and √12 = 2√3 so √75 + √12 = 5√3 + 2√3 = 7√3.
Answer:
[tex] 7\sqrt{3} [/tex]
Step-by-step explanation:
[tex] \sqrt{12} \: can \: be \: simplified \: as \: 2 \sqrt{3} \: and \: \sqrt{75} \: canbe \: simplified \: as \: 5 \sqrt{3} \\ after \: simplifying \: we \: can \: add \: them \: up \\ 2 \sqrt{3} + 5 \sqrt{3} = 7 \sqrt{3} [/tex]
Which of the following is false? Correlation coefficient and the slope always have the same sign (positive or negative). If the correlation coefficient is 1, then the slope must be 1 as well. If the correlation between two variables is close to 0.01, then there is a very weak linear relation between them. Correlation measures the strength of linear association between two numerical variables.
Answer:
If the correlation coefficient is 1, then the slope must be 1 as well.
Step-by-step explanation:
Coefficient of correlation is used in statistics to determine the relationship between two variables. Correlation coefficient and slope always have same sign. It measures the strength of linear relation between two variables. The values of correlation coefficient ranges between 0 to 1. where 0 determines that there is no relationship between two variables.
If the correlation coefficient is 1, then the slope must be 1 as well.
The correlation coefficient (ρ) is a measure that determines the degree to which the movement of two different variables is associated.
Correlation coefficient and the slope both quantify the direction and strength of the relationship between two numeric variables. When the correlation (r) is negative, the regression slope (b) will be negative. When the correlation is positive, the regression slope will be positive.If the correlation between two variables is close to 0.01, then there is a very weak linear relation between them.
So, the false statement is:
If the correlation coefficient is 1, then the slope must be 1 as well.
Learn more:https://brainly.com/question/16557696
Question 15 A party rental company has chairs and tables for rent. The total cost to rent 8 chairs and 3 tables is $38 . The total cost to rent 2 chairs and 5 tables is $35 . What is the cost to rent each chair and each table?
Answer:
Each table is $6 and each chair is $2.50
Step-by-step explanation:
A 12 sided die is rolled the set of equally likely outcomes is 123 456-789-10 11 and 12 find the probability of rolling a number greater than three
Answer:
6
Step-by-step explanation:
nerd physics
16. How much money will I need to have at retirement so I can withdraw $60,000 a year for 20 years from an account earning 8% compounded annually? a. How much do you need in your account at the beginning b. How much total money will you pull out of the account? c. How much of that money is interest?
Answer:
starting balance: $636,215.95total withdrawals: $1,200,000interest withdrawn: $563,784.05Step-by-step explanation:
a) If we assume the annual withdrawals are at the beginning of the year, we can use the formula for an annuity due to compute the necessary savings.
The principal P that must be invested at rate r for n annual withdrawals of amount A is ...
P = A(1+r)(1 -(1 +r)^-n)/r
P = $60,000(1.08)(1 -1.08^-20)/0.08 = $636,215.95
__
b) 20 withdrawals of $60,000 each total ...
20×$60,000 = $1,200,000
__
c) The excess over the amount deposited is interest:
$1,200,000 -636,215.95 = $563,784.05
Graph the line y=-1/3x+2
Answer:
Graphed below.
Step-by-step explanation:
The slope of the line is -1/3.
The y-intercept is at (0, 2).
The x-intercept is at (6, 0).
A scooter runs 40 km using 1 litre of petrol tje distance covered by it using 15/4 litres of petrol is
Answer:
150 km
Step-by-step explanation:
1 liter ............ 40 km
15/4 liter .........x km
x = 15/4×40/1 = 600/4 = 150 km
CAN SOMEONE HELP ME ASAP
A. 5
B. 53‾√53
C. 10
D. 103√3
Answer:
n = 5
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 30 = n/ 5 sqrt(3)
5 sqrt(3) tan 30 = n
5 sqrt(3) * 1/ sqrt(3) = n
5 = n
The population of Adamsville grew from 6000 to 13000 in 7 years. Assuming uninhibited exponential growth, what is the expected population in an additional 3 years?
Answer:
18107.32
Step-by-step explanation:
Set up the exponential function in the form:
[tex]P = P_0(R)^t[/tex]
so P is the new population, [tex]P_0[/tex] is the original population, R is the rate of increase in population, and t is the time in years.
You have to use the information given to find the rate that the population is increasing and then use that rate to find the new population after more time passes.
[tex]13000 = 6000(R)^7\\\\\\frac{13000}{6000} = R^7\\\\\sqrt[7]{\frac{13000}{6000} } = R\\\\\\ R = 1.116786872[/tex]
Now that you found the rate, you can use the function to find the population after another 3 years.
[tex]P = 13000(1.116786872)^3\\P = 18107.32317\\[/tex]
So the population is 18107, rounded to the nearest whole number.
Don’t know this one
Answer:
B
Step-by-step explanation:
The answer is B because in order for the square root of a number to be equal to another number, the answer squared should be the number under the square root.
B. [tex](-4)^2\neq -16[/tex].
Hope this helps.
What is the solution to the system of equations?
y=-3x – 2
5x + 2y = 15
0 (-40. 19)
(-19.55)
(19-40)
(55.-19)
Answer:
Step-by-step explanation:
y = -3x - 2
5x + 2y = 15
5x + 2(-3x -2) = 15
5x -6x - 4 = 15
-x - 4 = 15
-x = 19
x = -19
y = -3(-19) - 2
y = 57 - 2
y = 55
(-19, 55)
solution is b
The curvature of a plane parametric curve x = f(t), y = g(t) is $ \kappa = \dfrac{|\dot{x} \ddot{y} - \dot{y} \ddot{x}|}{[\dot{x}^2 + \dot{y}^2]^{3/2}}$ where the dots indicate derivatives with respect to t. Use the above formula to find the curvature. x = 6et cos(t), y = 6et sin(t)
Answer:
The curvature is modelled by [tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex].
Step-by-step explanation:
The equation of the curvature is:
[tex]\kappa = \frac{|\dot {x}\cdot \ddot {y}-\dot{y}\cdot \ddot{x}|}{[\dot{x}^{2}+\dot{y}^{2}]^{\frac{3}{2} }}[/tex]
The parametric componentes of the curve are:
[tex]x = 6\cdot e^{t} \cdot \cos t[/tex] and [tex]y = 6\cdot e^{t}\cdot \sin t[/tex]
The first and second derivative associated to each component are determined by differentiation rules:
First derivative
[tex]\dot{x} = 6\cdot e^{t}\cdot \cos t - 6\cdot e^{t}\cdot \sin t[/tex] and [tex]\dot {y} = 6\cdot e^{t}\cdot \sin t + 6\cdot e^{t} \cdot \cos t[/tex]
[tex]\dot x = 6\cdot e^{t} \cdot (\cos t - \sin t)[/tex] and [tex]\dot {y} = 6\cdot e^{t}\cdot (\sin t + \cos t)[/tex]
Second derivative
[tex]\ddot{x} = 6\cdot e^{t}\cdot (\cos t-\sin t)+6\cdot e^{t} \cdot (-\sin t -\cos t)[/tex]
[tex]\ddot x = -12\cdot e^{t}\cdot \sin t[/tex]
[tex]\ddot {y} = 6\cdot e^{t}\cdot (\sin t + \cos t) + 6\cdot e^{t}\cdot (\cos t - \sin t)[/tex]
[tex]\ddot{y} = 12\cdot e^{t}\cdot \cos t[/tex]
Now, each term is replaced in the the curvature equation:
[tex]\kappa = \frac{|6\cdot e^{t}\cdot (\cos t - \sin t)\cdot 12\cdot e^{t}\cdot \cos t-6\cdot e^{t}\cdot (\sin t + \cos t)\cdot (-12\cdot e^{t}\cdot \sin t)|}{\left\{\left[6\cdot e^{t}\cdot (\cos t - \sin t)\right]^{2}+\right[6\cdot e^{t}\cdot (\sin t + \cos t)\left]^{2}\right\}^{\frac{3}{2}}} }[/tex]
And the resulting expression is simplified by algebraic and trigonometric means:
[tex]\kappa = \frac{72\cdot e^{2\cdot t}\cdot \cos^{2}t-72\cdot e^{2\cdot t}\cdot \sin t\cdot \cos t + 72\cdot e^{2\cdot t}\cdot \sin^{2}t+72\cdot e^{2\cdot t}\cdot \sin t \cdot \cos t}{[36\cdot e^{2\cdot t}\cdot (\cos^{2}t -2\cdot \cos t \cdot \sin t +\sin^{2}t)+36\cdot e^{2\cdot t}\cdot (\sin^{2}t+2\cdot \cos t \cdot \sin t +\cos^{2} t)]^{\frac{3}{2} }}[/tex]
[tex]\kappa = \frac{72\cdot e^{2\cdot t}}{[72\cdot e^{2\cdot t}]^{\frac{3}{2} } }[/tex]
[tex]\kappa = [72\cdot e^{2\cdot t}]^{-\frac{1}{2} }[/tex]
[tex]\kappa = 72^{-\frac{1}{2} }\cdot e^{-t}[/tex]
[tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex]
The curvature is modelled by [tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex].
Please answer this correctly
Step-by-step explanation:
pnotgrt8rthan4 = 3 ÷ 7 × 100
= 42.8571428571 / 43%
Cheryl bought 3.4 pounds of coffee that cost $6.95 per pound . How many did she spend on coffee
Answer:
23.63
Step-by-step explanation:
multiply the cost by the pounds
Answer:
$23.63
Step-by-step explanation:
3.4 X 6.95 = 23.63
The mean and standard deviation of a random sample of n measurements are equal to 34.5 and 3.4, respectively.A. Find a 95 % confidence interval for μ if n=49.B. Find a 95% confidence interval for μ if n=196.C. Find the widths of the confidence intervals found in parts a and b.D. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?1. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 4.2. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 2.3. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the on confidence interval by a factor of 4.4. Quadrupling the sample size while holding the confidence coefficient fixed does not affect the width of the confidence interval.5. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.
Answer:
a. The 95% confidence interval for the mean is (33.52, 35.48).
b. The 95% confidence interval for the mean is (34.02, 34.98).
c. n=49 ⇒ Width = 1.95
n=196 ⇒ Width = 0.96
Note: it should be a factor of 2 between the widths, but the different degrees of freedom affects the critical value for each interval, as the sample size is different. It the population standard deviation had been used, the factor would have been exactly 2.
d. 5. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.
Step-by-step explanation:
a. We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=34.5.
The sample size is N=49.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{49}}=\dfrac{3.4}{7}=0.486[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=49-1=48[/tex]
The t-value for a 95% confidence interval and 48 degrees of freedom is t=2.011.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=2.011 \cdot 0.486=0.98[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 34.5-0.98=33.52\\\\UL=M+t \cdot s_M = 34.5+0.98=35.48[/tex]
The 95% confidence interval for the mean is (33.52, 35.48).
b. We have to calculate a 95% confidence interval for the mean.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{196}}=\dfrac{3.4}{14}=0.243[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=196-1=195[/tex]
The t-value for a 95% confidence interval and 195 degrees of freedom is t=1.972.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=1.972 \cdot 0.243=0.48[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 34.5-0.48=34.02\\\\UL=M+t \cdot s_M = 34.5+0.48=34.98[/tex]
The 95% confidence interval for the mean is (34.02, 34.98).
c. The width of the intervals is:
[tex]n=49\rightarrow UL-LL=33.52-35.48=1.95\\\\n=196\rightarrow UL-LL=34.02-34.98=0.96[/tex]
d. The width of the intervals is decreased by a factor of √4=2 when the sample size is quadrupled, while the others factors are fixed.