Answer:
a). [tex]4.86\times 10^{-15}[/tex] m
b). [tex]4.21\times 10^{-2}[/tex] m³
c). [tex]7.00\times 10^{3}[/tex] N²
Step-by-step explanation:
In this question we have to convert each option into SI units.
a). [tex]4.86(10^{-6})^{2}[/tex] mm
= [tex]4.86\times (10^{-12})\times (10^{-3} )[/tex] m
= [tex]4.86\times 10^{-15}[/tex] m
b). (348 mm)³
= [tex](348)^{3}\times (10^{-3})^{3}[/tex] m³
= [tex]42144192\times 10^{-9}[/tex] m³
= [tex]4.21\times 10^{-2}[/tex] m³
c). [tex](83700)^{2}\times (10^{-3})^{2}[/tex] N²
= [tex]700569\times 10^{4}\times 10^{-6}[/tex] N²
= [tex]7.00\times 10^{9}\times 10^{-6}N^{2}[/tex]
= [tex]7.00\times 10^{3}[/tex] N²
Suppose that Britain pegs the pound to gold at six pounds per ounce, whereas the exchange rate between pounds and U.S. dollars is $5 = £1. What would an ounce of gold be worth in U.S. dollars?
Given the exchange rate of $5 = £1 and the conversion rate of 6 pounds per ounce of gold, the equivalent amount for an ounce of gold would be $30.
Explanation:In this scenario, given that the exchange rate between pounds and U.S. dollars is $5 = £1 and the conversion rate of pound to gold is six pounds per ounce, we want to find the value of an ounce of gold in U.S. dollars. Firstly, we need to establish how many pounds per ounce of gold, which is set at six pounds. With the currency exchange rate, $5 equals one pound. Therefore, to find the value in dollars, simply multiply these two rates together. That comes to 6 (pounds per ounce of gold) * 5 (dollars per pound) = $30. Hence, an ounce of gold would be worth $30.
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In a trial of 167 patients who received 10-mg doses of a drug daily, 45 reported headache as a side effect.
(a) Obtain a point estimate for the population proportion of patients who received 10-mg doses of a drug daily and reported headache as a side effect. (round to two decimal places as needed)
(b) Verify that the requirements for constructing a confidence interval about p are satisfied
Answer:
a) [tex]\hat{p} = 0.27[/tex]
b) All the conditions are met for constructing a confidence interval.
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 167
Number of people who had side effects, x = 45
a) point estimate
[tex]\hat{p} = \dfrac{x}{n} = \dfrac{45}{167} = 0.27[/tex]
The point estimate for the population proportion of patients who received 10-mg doses of a drug daily and reported headache as a side effect is 0.27
b) Conditions for constructing a confidence interval
The data is a random sample from the population of interest.Individual observations can be considered independent.[tex]n\hat{p}>10\\167\times 0.27 = 45.09 > 10\\n(1-\hat{p})>10\\167(1-0.27) = 121.91 > 10[/tex]
Thus, all the conditions are met for constructing a confidence interval.
Without calculation, decide if each of the integrals below are positive, negative, or zero. Let W be the solid bounded by z=sqrt(x2+y2) and z=2.1. ∭(z−2)dV2. ∭e−xyzdV3. ∭(z−sqrt(x2+y2))dV
Answer:
1) ∭(z−2) dV negative.
2) ∭e^{−xyz} dV positive.
3) ∭( z-\sqrt{x²+y²}) positive.
Step-by-step explanation:
From Exercise we have:
z=\sqrt{x²+y²}
z=2
⇒2=\sqrt{x²+y²}
4=x²+y²
Therefore, we get that the solid bounded by:
\sqrt{x²+y²}≤z≤2
4=x²+y²
1) From initial condition we have that
\sqrt{x²+y²}≤z≤2
⇒ 2-z≤0
Therefore, we get that the triple integral is
∭(z−2) dV negative.
2) We know that e^{-xyz} is always positive number.
Therefore, we get that the triple integral is
∭e^{−xyz} dV positive.
3) From initial condition we have that
\sqrt{x²+y²}≤z≤2
⇒ z-\sqrt{x²+y²}>0
Therefore, we get that the triple integral is
∭( z-\sqrt{x²+y²}) positive.
The given triple integrals, when evaluated over the defined region, result in the first integral being zero, while the second and third integrals yield positive values. This determination is made based on the properties of the integrand over the given region, without resorting to complete calculation.
Explanation:Triples Integral EvaluationThe question involves the evaluation of triple integrals over a given region W bounded by the surfaces z = sqrt(x^2 + y^2) and z = 2.1. Without explicit calculations, we can determine the sign of the integrals by assessing the integrand function over the specified region.
∭(z − 2)dV: Here, the integral will be zero as over the specified region W, z varies from sqrt(x^2 + y^2) to 2.1 which implies for some portions of W, z-2<0 and for some portions, it's >0. Hence, it cancels each other.∭e^−xyz dV: It will be a positive value since exponential of a number is always positive. ∭(z − sqrt(x^2 + y^2))dV: This integral will be positive since over the region W, z ranges from sqrt(x^2 + y^2) to 2.1, and hence z - sqrt(x^2 + y^2) is always greater than 0.Therefore, the first integral would yield zero, while the second and third integrals would yield positive values.
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The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.63 inches and a standard deviation of 0.03 inch. If you select a random sample of 9 tennis balls,
a. What is the sampling distribution of the mean?
b. What is the probability that the sample mean is less than 2.61 inches?
c. What is the probability that the sample mean is between 2.62 and 2.64 inches?
d. The probability is 6-% that the sample mean will be between what two values symmetrically distributed around the population mea
Answer:
a) sample mean = 2.63 inches
sample standard deviation = [tex]\frac{standard \hspace{0.15cm} deviation}{\sqrt{n} } = \frac{0.03}{\sqrt{9} } = \frac{0.03}{3} = 0.01[/tex]
b) P(X < 2.61) = 0.0228
c.) P(2.62 < X < 2.64) = 0.6827
d.) Therefore 0.06 = P(2.6292 < X < 2.6307)
Step-by-step explanation:
i) the diameter of a brand of tennis balls is approximately normally distributed.
ii) mean = 2.63 inches
iii) standard deviation = 0.03 inches
iv) random sample of 9 tennis balls
v) sample mean = 2.63 inches
vi) sample standard deviation = [tex]\frac{standard \hspace{0.15cm} deviation}{\sqrt{n} } = \frac{0.03}{\sqrt{9} } = \frac{0.03}{3} = 0.01[/tex]
vii) the sample mean is less than 2.61 inches = P(X < 2.61) = 0.0228
viii)the probability that the sample mean is between 2.62 and 2.64 inches
P(2.62 < X < 2.64) = 0.6827
ix) The probability is 6-% that the sample mean will be between what two values symmetrically distributed around the population measure
Therefore 0.06 = P(2.6292 < X < 2.6307)
a) The sampling distribution of the mean is 2.63 inches and sample standard deviation = 0.01
b) P(X < 2.61) = 0.0228
c) P(2.62 < X < 2.64) = 0.6827
d) 0.06 = P(2.6292 < X < 2.6307)
Let's solve this step by step:
Step 1: The diameter of a brand of tennis balls is approximately normally distributed.
Given:
Mean = 2.63 inches
Standard deviation = 0.03 inches
For random sample of 9 tennis balls
Step 2: Sample mean = 2.63 inches
Sample standard deviation = [tex]\frac{\text{standard deviation}}{\sqrt{n} } =\frac{0.03}{\sqrt{9} } =\frac{0.03}{3} =0.01[/tex]
Step 3: The sample mean is less than 2.61 inches = P(X < 2.61) = 0.0228
Step 4: The probability that the sample mean is between 2.62 and 2.64 inches = P(2.62 < X < 2.64) = 0.6827
Step 5: The probability is 6-% that the sample mean will be between what two values symmetrically distributed around the population measure
Therefore 0.06 = P(2.6292 < X < 2.6307)
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An ice cream cone is filled with vanilla and chocolate ice cream at a ratio of 2:1. If the diameter of the cone is 2 inches and the height is 6 inches, approximately what is the volume of vanilla ice cream in the cone? (round to nearest tenth) A) 1.0 in3 B) 2.1 in3 C) 4.2 in3 D) 6.3 in3
Answer:
D. 6.3 in^3
Step-by-step explanation:
V= 1/3 (3.14)(r^2)(h)
V= 1/3 (3.14) (1^2)(6)
V=6.3 in^3
Answer:
c
Step-by-step explanation: it was on usa test prep and the answer that was there was wrong.
The table shows the depth
of a submarine over a 2
hour period. Did the sub rise
or fall in the water? By how
much?
| Time
Depth
10 am
410 ft
12 am
289 ft please help show work or give answer will mark brainest
Answer:
The sub rose 121 feet.
Step-by-step explanation:
The sub was less deep at 12 pm than at 10 am, so rose in the water. The amount it rose was ...
410 -289 = 121 . . . . feet
__
If you like, you can think of the sub's elevation relative to the surface as changing from -410 feet to -289 feet. The difference is then an increase in elevation (rise) of ...
-289 -(-410) = -289 +410 = 121 . . . feet
_____
12 am is midnight, 14 hours after 10 am. The time 2 hours after 10 am is 12 pm, noon.
Find all values of x in the interval [0, 2π] that satisfy the equation.
6sin²(x) = 3
Answer:
The solutions are π/4, 3π/4,5π/4,7π/4
Step-by-step explanation:
The given equation is
6sin²(x) = 3
Divide by 6 to get:
[tex] { \sin}^{2} (x) = \frac{1}{2} [/tex]
This implies that;
[tex] \sin(x) = \pm \frac{ \sqrt{2} }{2} [/tex]
If
[tex]\sin(x) = \frac{ \sqrt{2} }{2}[/tex]
[tex]x = \frac{\pi}{4} [/tex]
in the first quadrant
[tex]x = \frac{3\pi}{4} [/tex]
in the second quadrant.
If
[tex]\sin(x) = - \frac{ \sqrt{2} }{2}[/tex]
[tex]x = \frac{5\pi}{4} [/tex]
in the third quadrant
[tex]x = \frac{7\pi}{4} [/tex]
a caterpillar stated at point(-2.5 -5.5) on a coordinate plane.She crawled in a straight line through the origin to point (45,y)What is y-axis of this?
Answer:
99
Step-by-step explanation:
Since the caterpillar crawled through the origin, her movement can be described by a straight line equation modeled with the points (-2.5; -5.5) and (0; 0).
The slope of a linear equation is given by:
[tex]m=\frac{y-y_0}{x-x_0}\\m=\frac{-5.5-0}{-2.5-0}\\m=2.2[/tex]
For x = 45, the value of y is:
[tex]y= 2.2x\\y= 2.2*45\\y=99[/tex]
The value of the y-axis is 99.
Under what circumstances is the median likely to produce a better measure of central tendency than the mean?
Answer:
With a skewed distribution and data with outliers.
Step-by-step explanation:
There are three measures of central tendency.
Mean: It is the average value of data and affected by presence of outliers.Median: It is the value that divides the data into two equal parts. It is a position based measure of tendency.Mode: It is the most frequent observation in the data.For a symmetrical distribution for continuous data, the mean, median, and mode are equal. For such case mean is a better measure of central tendency because it includes all of the data in the calculations. Median is the best measure of central tendency when the data is not symmetrical because the median is position based.Advantage of the median:The median is not affected by outliers and skewed data as compared to the mean.
Thus, median likely to produce a better measure of central tendency than the mean with a skewed distribution and data with outliers.
Which of the following functions are solutions of the differential equation y+4y+4y=0? A. y(x) =e^-2x B. y(x) = e^+22 C. y(x) = xe^-2x D. y(x) = -2x E. y(x) = 0 F. g(x) = x^2e^-2x
Options A, C, and F are solutions to the differential equation.
Explanation:The given differential equation is y''+4y'+4y=0.
To check which of the given functions are solutions of the differential equation, we substitute each function into the equation and check if it satisfies the equation.
By substituting each function and simplifying, we find that options A, C, and F are solutions to the differential equation.
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A car rental company charges a one-time application fee of 20 dollars, 45 dollars per day, and 15 cents per mile for its cars. Write a formula for the cost, C, of renting a car as a function of the number of days, d, and the number of miles driven, m.
Answer:
[tex]C(d,m) = 20 + 45d + 0.15m[/tex]
Step-by-step explanation:
In this problem, we have that the cost of renting a car C is a function of the number of days d, and the number of miles driven, m.
There is also a fixed cost F.
So the equation for the cost of renting a car is:
[tex]C(d,m) = F + a*d + b*m[/tex]
In which a is the daily cost and b is the cost per mile.
A car rental company charges a one-time application fee of 20 dollars, 45 dollars per day, and 15 cents per mile for its cars.
This means that [tex]F = 20, a = 45, b = 0.15[/tex]
Write a formula for the cost, C, of renting a car as a function of the number of days, d, and the number of miles driven, m.
[tex]C(d,m) = 20 + 45d + 0.15m[/tex]
Systematic Sampling Technique is used to select 5 numbers between 1 and 200. The first selected number is 12. What should be next four numbers?
Answer: 52, 92 , 132, 172
Step-by-step explanation:
A systematic random sampling is a random sampling technique in which a sample from a large population are chosen according to a random beginning point and a fixed periodic interval (k).Given : Systematic Sampling Technique is used to select 5 numbers between 1 and 200.
⇒ Population size : N=200
Required Sample size : n=5
Since , Sampling interval is given by :-
[tex]k=\dfrac{N}{n}[/tex]
⇒ [tex]k=\dfrac{200}{5}[=40/tex]
If the first selected number is 12, then the next four numbers would be :
(12+K) , (12+2k) , (12+3k) , (12+4k)
Put value of k , we get
(12+40) , (12+2(40)) , (12+3(40)) , (12+4(40)) =(52, 92 , 132, 172)
Hence, the next four numbers are : 52, 92 , 132, 172
Complete the following statements. In general, % of the values in a data set lie at or below the median. % of the values in a data set lie at or below the third quartile (Q3). If a sample consists of 500 test scores, of them would be at or below the median. If a sample consists of 500 test scores, of them would be at or above the first quartile (Q1).
Answer:
Complete the following statements. In general, 50% of the values in a data set lie at or below the median. 75% of the values in a data set lie at or below the third quartile (Q3). If a sample consists of 500 test scores, of them 0.5*500 = 250 would be at or below the median. If a sample consists of 500 test scores, of them 0.75*500 = 375 would be at or above the first quartile (Q1).
Step-by-step explanation:
The median separates the upper half from the lower half of a set. So 50% of the values in a data set lie at or below the median, and 50% lie at or above the median.
The first quartile(Q1) separates the lower 25% from the upper 75% of a set. So 25% of the values in a data set lie at or below the first quartile, and 75% of the values in a data set lie at or above the first quartile.
The third quartile(Q3) separates the lower 75% from the upper 25% of a set. So 75% of the values in a data set lie at or below the third quartile, and 25% of the values in a data set lie at or the third quartile.
The answer is:
Complete the following statements. In general, 50% of the values in a data set lie at or below the median. 75% of the values in a data set lie at or below the third quartile (Q3). If a sample consists of 500 test scores, of them 0.5*500 = 250 would be at or below the median. If a sample consists of 500 test scores, of them 0.75*500 = 375 would be at or above the first quartile (Q1).
Suppose a parallelogram has sides of length a and b. Is this enough information to compute the area of the parallelogram? If not, what additional information is required?
Answer:
No. it's not enough
Step-by-step explanation:
1) No. it's not enough
2) To compute the area of a parallelogram it's necessary the height of the parallelogram, i.e. a perpendicular line segment from the base up to its parallel side.
3) Because a parallelogram is made up by two triangles and the area of it is calculated using the height. Then to cover the area of a parallelogram it's mandatory to calculate the height, the perpendicular distance between their horizontal sides.
No, the lengths of the sides of a parallelogram alone are not enough to compute its area. Additional information, such as the length of the perpendicular distance between the sides, is needed to calculate the area.
Explanation:No, the lengths of the sides of a parallelogram alone are not enough to compute its area. To calculate the area of a parallelogram, you need two pieces of information: the length of one of its sides and the length of the corresponding altitude (or height), which is the perpendicular distance between the side and the opposite side. With just the lengths of a and b, we don't know the height, so we can't calculate the area.
To find the area of a parallelogram, you can use the formula: Area = base x height. The base is one of the side lengths, and the height is the length of the perpendicular from the base to the opposite side.
For example, if side a is the base, the height is the distance between side a and the opposite side, which can be found by drawing a perpendicular line. Once you know the height, you can calculate the area using the formula: Area = a x height.
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Consider the system of linear equations.
x + y = 9.0 0.50 x + 0.20 y = 3.30
Find the values of x and y
Answer: x = 5.0, y = 4.0
We multiply the second equation by -2.
-2(0.50 x + 0.20 y)= -2(3.30)
-x - 0.40y = -6.60
Then we add it to x + y = 9.0.
So we get: -x - 0.40y + x + y = -6.60 + 9.0
or, 0.60y = 2.4
or, y = 4.0
From x + y = 9.0 we get:
x + 4.0 = 9.0
x = 5.0
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To solve the system of linear equations, we used the substitution method, resulting in the solution x = 5 and y = 4.
Explanation:The system of linear equations provided is:
x + y = 9.00.50 x + 0.20 y = 3.30To find the values of x and y, we can use the method of substitution or elimination. In this case, we'll use substitution:
Rearrange the first equation to isolate y: y = 9 - x.Substitute y in the second equation: 0.50x + 0.20(9 - x) = 3.30.Simplify the second equation: 0.50x + 1.8 - 0.20x = 3.30.Combine like terms: 0.30x + 1.8 = 3.30.Isolate x: 0.30x = 3.30 - 1.8.Solve for x: 0.30x = 1.50.Find x: x = 1.50 / 0.30.x = 5.Substitute x back into y = 9 - x: y = 9 - 5.Find y: y = 4.Therefore, the solution to the system of equations is x = 5 and y = 4.
A sample of 60 women is obtained, and their heights ( in inches ) and pulse rates ( in beats per minute ) are measured. The linear correlation coefficient is 0.234 and the equation of the regression line is ^y= 17.5 + 0.850x, where x represents height. The mean of the 60 heights is 63.4 in and the mean of the 60 pulse rates is 75.6 beats per minute. Find the best predicted pulse rate of a woman who is 74 inches tall. Use a significance level of a=0.01.
Answer:
The best predicted pulse rate of a woman who is 74 inches tall is 80.4 (beats per minute).
Step-by-step explanation:
The best predicted pulse rate of a woman who is 74 inches tall is obtained below:
Let x denotes height (in inches) and y denotes pulse rates (in beats per minute).
From the information, the regression equation is, the total number of women is 60 and the linear correlation coefficient between height and pulse rates is 0.234 and the mean of heights is 63.4 and the mean of pulse rates is 75.6. The estimated regression line is
^y= 17.5 + 0.850x
The required best predicted pulse rates is,
=17.5 + (0.850×74)
=17.5 + 62.9
= 80.4 beats per minute
The standard deviation is expressed in absolute terms (i.e. in the same unit of measure as the data: lbs;inches;dollars;etc) while the coefficient of variation is relative measure?
a. True.
b. False.
Answer:
a) True
Step-by-step explanation:
The given statement is true.
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
The standard deviation express the variation of data from the mean and therefore, have the same unit as the data like lbs, inches, dollars, etc.
Coefficient of variation on the other hand is the ratio of standard deviation and mean. It is also a measure of dispersion but since it is a ratio, the units cancel each other.
[tex]C.V = \dfrac{s}{\bar{x}}[/tex]
Thus, coefficient of variation is dimensionless.
Thus, it is a relative measure.
2. The beam of a lighthouse can be seen for up to 20 miles. You are on a ship that is 10 miles east and 16 miles north of the lighthouse. Write an inequality to describe the region lit by the lighthouse beam. Can you see the lighthouse beam on your ship?
Answer:
The person on the ship can see the lighthouse
Step-by-step explanation:
The Circle Function
A circle centered in the point (h,k) with a radius r can be written as the equation
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Any point (x,y) can be known if it's inside of the circle if
[tex](x-h)^2+(y-k)^2\leq r^2[/tex]
The question is about a beam of a lighthouse than can be seen for up to 20 miles. If we assume the lighthouse is emitting the beam as the shape of a circle centered in (0,0), then its radius is 20 miles. Thus any person riding a ship inside the circle can see the lighthouse. This means that
[tex]x^2+y^2\leq 20^2[/tex]
[tex]x^2+y^2\leq 400[/tex]
The ship's coordinates respect to the lighthouse are (10,16). We should test the point to verify if the above inequality stands
[tex]10^2+16^2\leq 400[/tex]
[tex]356 \leq 400[/tex]
The inequality is true, so the person on the ship can see the lighthouse
The inequality is:
√(x^2 + y^2) ≤ 20 mi.
And you can see the lighthouse beam from your ship.
How to write the inequality?
First, let's define our coordinate system, North will be the positive y-axis and east will be the positive x-axis. Such that the origin is the lighthouse.
The distance between a point (x, y) and the lighthouse is given by:
d = √(x^2 + y^2).
And we know that the lighthouse beam can be seen for up to 20 miles, so you can only see the lighthouse if your position (x, y) is such that the inequality is true.
√(x^2 + y^2) ≤ 20 mi.
Now, can you see the lighthouse beam from your ship?
Your ship's position is: (10 mi, 16 mi)
Replacing that in the inequality we get:
√((10mi)^2 + (16mi)^2) ≤ 20 mi
18.87 mi ≤ 20 mi
The inequality is true, then you can see the beam from the ship.
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As the sample size increases, the variation of the sample mean from the population mean becomes larger and larger
True/False
The correct answer is: False.
As the sample size increases, the variation of the sample mean from the population mean typically becomes smaller. This is known as the Central Limit Theorem, which states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution with a mean equal to the population mean and a standard deviation that decreases as the sample size increases. Therefore, with larger sample sizes, the sample mean tends to be a more accurate estimate of the population mean, and the variation around the population mean decreases.
Two new wind-farm tower projects are proposed for a small company that installs them in south western Wisconsin. Project A will cost $250,000 to complete and is expected to have an annual net cash flow of $75,000. Project B will cost $150,000 to complete and should generate annual net cash flows of $52,000. As a small company, the owner and senior management team are very concerned about their cash flow. Use the payback period method and determine which project is better from a cash flow standpoint. Can someone show me how I can help my son solve this problem so I can guide him through it?
Answer:
Step-by-step explanation:
The simplified formula for payback period (assuming even cashflow) is as follows:
Payback Period (in years) = Cost / cashflow per year
Generally, the choice which gives the shorter payback period is desired
For project A,
Cost = $250,000 and cashflow per year = $75,000
Payback Period for project A
= 250,000 ÷ 75,000 = 3.333 years
For Project B
Cost = $150,000 and cashflow per year = $52,000
Payback Period for project B
= 150,000 ÷ 52,000 = 2.88 years
comparing the PP for A & B, it is clear that B has the shorter payback period, and hence choice B is more desirable
The simplified formula for the payback period (assuming even cashflow) is as follows:
Payback Period (in years) = Cost / cashflow per year
Generally, the choice which gives the shorter payback period is desired
For project A,
Cost = $250,000 and cashflow per year = $75,000
Payback Period for project A
= 250,000 ÷ 75,000 = 3.333 years
For Project B
Cost = $150,000 and cashflow per year = $52,000
Payback Period for project B
= 150,000 ÷ 52,000 = 2.88 years
comparing the PP for A & B, it is clear that B has the shorter payback period, and hence choice B is more desirable
What is an example of a word problem?Word problem usually consists of mathematical modeling questions, where statistics and information about a sure machine are given and a student is required to expand a version. for example, Jane had $five.00, then spent $2.00. How lots does she have now?
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33. The standard deviation divided by the square root of the sample size n is equal to the _______________ of the mean. Sample error Sampling error Critical value Standard error
Answer:
Standard error
Step-by-step explanation:
Standard error: In statistics, the term standard error is also denoted as SE, and is reffered to as the estimate of a particular parameter.
It is defined as the standard deviation in statistics related to its sampling distribution or else the the standard deviation's estimate.
Therefore, if a particular parameter or statistic is considered as a mean then it would be denoted as the standard error of that mean.
The standard error of an estimate may also be defined as the square root of the estimated error variance √[tex]\sigma^{2}[/tex] of the quantity,
[tex]S_{e}[/tex] =√[tex]\sigma^{2}[/tex]
In the given question, the appropriate answer would be standard error.
The branch of Statistics concerned with using the sample data to make an inference about a large set of data is called
Answer:
Statistical Inference.
Step-by-step explanation:
Statistical Inference:
It is the procedure for approximating and estimating the parameters of a population with the help of a sample.The sample statistics are used to describe population parameters.It is the practice of forming judgement on the population based on the statistic of sample.Basically with the help of sample we describe a population.Thus,
The branch of Statistics concerned with using the sample data to make an inference about a large set of data is called statistical inference.
The formula for a buffer solution contains 1.24% w/v of boric acid. How many milli-liters of a 5% w/v boric acid solution should be used to obtain the boric acid needed in preparing 1 liter of the buffer solution?
Answer: 248mL
Step-by-step explanation:
Given:
Concentration of buffer solution Cs = 1.24%w/v of boric acid
Concentration of boric acid solution Cb = 5 % w/v boric acid
For 1 liter of buffer solution, the weight of boric acid needed is:
mb = 1 × 1.24 = 1.24 unit weight
mb = Cb × Vb .....1
Cb = concentration of boric acid solution.
Vb = volume of boric acid solution needed.
mb = weight of boric acid needed.
From equation 1.
Vb = mb/Cb
Vb = 1.24/5
Vb = 0.248L
Vb = 248mL
248 milli-liters of a 5% w / v boric acid solution should be used to obtain the boric acid needed.
Since the formula for a buffer solution contains 1.24% w / v of boric acid, to determine how many milli-liters of a 5% w / v boric acid solution should be used to obtain the boric acid needed in preparing 1 liter of the buffer solution, the following calculation must be performed:
1000 milliliters = 1 liter 5 = 1000 1.24 = X 1.24 x 1000/5 = X 1240/5 = X 248 = X
Therefore, 248 milli-liters of a 5% w / v boric acid solution should be used to obtain the boric acid needed.
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It takes you 47 seconds to walk from the first (ground) floor of a building to the third floor.
How long will it take you to walk from the first floor to the sixth floor (at the same pace, assuming all floors have the same height)?
Answer: 117.5 seconds
Step-by-step explanation:
Given : It takes you 47 seconds to walk from the first (ground) floor of a building to the third floor.
Since from first floor to third , a person need to pass two levels of staircase.
We assume that the person walk at the same pace and the height of all floors are same.
The time taken to pass each level = (Time taken to pass 2 levels) ÷ 2
= (47 seconds) ÷ (2) = 23.5 seconds
Also, the from first floor to sixth floor , a person need to pass 5 levels of staircase.
Then, the time taken to pass each level = 5 x (Time taken to pass one level)
= 5 x 23.5 =117.5 seconds
Hence, it will take 117.5 seconds to walk from the first floor to the sixth floor.
The water content of soil from a borrow site is normally distributed with a mean of 14% and a standard deviation of 2.5%. What is the probability that a sample taken from the site will have a water content above 16% or below 12%?
The probability that a sample taken from the site will have water content above 16% or below 12% is 0.3862.
Given that,
Mean = µ
= 14%
= 0.14
Standard deviation = σ
= 2.5%
= 0.025
[Using standard normal table]
16% or 12% = 0.16 or 0.12
P(X < 0.16 or X > 0.12)
Using standard normal table,
To see the z value -0.9 in the row and 0.06 in the column of the standard normal table the cumulative probability of z = -0.96 is = 0.1685
To see the z value 0.7 in the row and 0.08 in the column of the standard normal table the cumulative probability of z = 0.78 is = 0.7823
[tex]P(X < 0.6\ or \ x > 0.12)=1-[P(0.16 < X < 0.12)][/tex]
[tex]=1-{P[\frac{0.16-0.142}{0.023} < \frac{x-\mu}{\sigma} < \frac{0.12-0.142}{0.023}]}[/tex]
[tex]= 1-[P(0.78 < z < -0.96)][/tex]
[tex]= [P(z < -0.96)-P(z < 0.78)][/tex]
[tex]=1-(0.1685-0.7823)[/tex]
[tex]= 1-0.6138[/tex]
[tex]P(X < 0.16 \ or \ X > 0.12)=0.3862[/tex]
Therefore, the probability that a sample taken from the site will have water content above 16% or below 12% is 0.3862.
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The probability that a random sample’s water content will be higher than 16% or lower than 12% is calculated by converting the values to Z-scores and then using the standard normal distribution's cumulative probability. The values from a Z-table or calculator are used to determine this probability.
Explanation:The subject of this question is Probability and Statistics, specifically related to the normal distribution. In this scenario, the water content of soil from a borrow site is normally distributed with a mean (μ) of 14% and a standard deviation (σ) of 2.5%.
To find the probability of the soil having a water content above 16% or below 12%, we first need to calculate the Z-scores for these values. The Z-score represents how many standard deviations an element is from the mean. It is calculated as (X - μ)/σ.
For X = 16%, Z = (16 - 14) / 2.5 = 0.8
For X = 12%, Z = (12 - 14) / 2.5 = -0.8
Using a Z-table or a calculator function that outputs standard normal probabilities, we would find that P(Z > 0.8) or P(Z < -0.8). By convention, Z-tables only give values as P(Z < z), for z > 0, so to find P(Z > 0.8), we can do 1 - P(Z < 0.8). Same for P(Z < -0.8).
As such, the desired probability is the sum of these two probabilities.
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how many different license plates are possible if each contains 2 letters(out of the alphabet’s 26 letters) followed by 5 digits (from 0 to 9)? how many of these license plates contain no repeated letters and no repeated digits?
The total number of different license plates possible with 2 letters and 5 digits is 67,600,000. If no letter or digit can be repeated, the number reduces to 32,760,000.
Explanation:This problem involves combinations and permutations, which are fundamental concepts in discrete mathematics. If a license plate has 2 letters followed by 5 digits, each chosen independently, we consider the product of the number of possibilities for each space. There are 26 possible letters (A-Z) for each of the 2 letter spaces and 10 possible digits (0-9) for each of the 5 digit spaces. Therefore, the total number of different license plates is 26 * 26 * 10 * 10 * 10 * 10 * 10 = 67,600,000.
However, if no letter or digit can be repeated, the number of possibilities for the second letter space becomes 25 (since one letter has already been used), and similarly for the digits, it gets reduced by one with each additional digit. Hence, the total number of different license plates without repeated letters and digits would be 26 * 25 * 10 * 9 * 8 * 7 * 6 = 32,760,000.
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There are 67,600,000 total possible license plates with two letters and five digits. When restricting to plates with no repeated letters or digits, there are 165,765,000 possible plates.
Explanation:The possible license plates can be calculated using the principle of multiplication. This principle states that if there are m ways to do one thing, and n ways to do another, then there are m*n ways to do both. In this case, there are 26 options for the first letter, another 26 for the second letter, and 10 options for each of the 5 digits (0-9). So, we can multiply these options to get our answer.
To calculate the number of possible combinations, we use the formula 26*26*10*10*10*10*10 = 67,600,000. Therefore, there are 67,600,000 possible license plates.
For the plates with no repeated letters or numbers, we still use the principle of multiplication but reduce each subsequent option by one. It will be 26*25 (because one letter has been used already and it can't be reused) *10*9*8*7*6 (same as for digits). Our formula is 26*25*10*9*8*7*6 = 165,765,000 plates.
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On a run, Natasha ran for 1 1/4 hours at a speed of 6 miles per hour. She then rested for 1/4 hour before running another hour at a speed of 5 miles per hour. Which graph best represents the distance she traveled?
Answer:
The answer to your question is See the picture below
Step-by-step explanation:
Analysis of the graphs
a) In the first graph, we observe that Natasha is running after 1 h and 1/4, the comeback for to her origin, finally she continues running forward. This option is incorrect.
b) In the second graph, Natasha runs for 1 1/4 hours, after this time, she comes back to her origin, takes a rest and continues running forward. This answer is incorrect.
c) In the third graph, Natasha runs for 1 1/4 hour, takes a rest and comes back to the origin. This option is incorrect.
d) In the forth graph, Natasha runs for 1 1/4 hour, takes a rest and continues running upwards. This is the right option.
Answer:
the last one to the far right at the bottom
Step-by-step explanation:
A study was done to determine the age, number of times per week and the duration (amount of time) of resident use of a local park in San Jose. The first house in the neighborhood around the park was selected randomly and then every 8th house in the neighborhood around the park was interviewed. 'Duration (amount of time)' is what type of data?
The 'Duration (amount of time)' in the study is an example of quantitative data. Quantitative data is numerical data that can be measured or counted.
Explanation:
The 'Duration (amount of time)' in the study is an example of quantitative data.
Quantitative data is numerical data that can be measured or counted. In this case, the duration of resident use of the local park is being measured in terms of time (amount of time).
Examples of other quantitative data include age and number of times per week.
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Identify the following measures as either quantitative or qualitative:
a. The 30 high-temperature readings of the last 30 days.
b. The scores of 40 students on an English test.
c. The blood types of 120 teachers in a middle school.
d. The last four digits of social security numbers of all students in a class.
e. The numbers on the jerseys of 53 football players on a team.
Answer:
a. Quantitative
b. Quantitative
c. Qualitative
d. Qualitative
e. Qualitative
Step-by-step explanation:
a. The temperature readings can be quantify and can be represented numerically so, it is quantitative variable.
b. The scores in English test can be quantify and can be represented numerically so, it is quantitative variable.
c. The blood type can be categorized as O plus, O negative, A plus, A negative, AB plus, Ab negative, B plus, B negative and cannot be represented numerically so, it is qualitative variable.
d. The last four digit of social security number take numerical values, yet they are qualitative because these are used as identifiers and mathematical operations of social security don't have meaningful interpretation.
e. The number on the jerseys of 53 football players also takes numerical values yet they are qualitative because these are used as identifiers for players and mathematical operations of number on the jerseys of football players don't have meaningful interpretation.
The measures in question are classified as either quantitative or qualitative.
Explanation:a. The 30 high-temperature readings of the last 30 days - Quantitative. These temperatures are numerical values that can be measured and compared.
b. The scores of 40 students on an English test - Quantitative. The scores represent numerical values that can be added, averaged, and compared.
c. The blood types of 120 teachers in a middle school - Qualitative. Blood types are descriptive categories or labels that cannot be measured numerically.
d. The last four digits of social security numbers of all students in a class - Qualitative. The last four digits are specific identifiers that cannot be measured or compared numerically.
e. The numbers on the jerseys of 53 football players on a team - Qualitative. The numbers are labels or identifiers, not measurable quantities.
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supposee you start saving today for a $8000 down payment that you plan to make on a condo in 4 years. Assume that you make no deposits into the account after your initial deposit. The account has quarterly compounding and an APR of 6%. How much would you need to deposit now to reach your $8000 goal in 4 years
To reach a $8000 down payment in 4 years with an account that compounds quarterly at an APR of 6%, you would need to make an initial deposit of approximately $6304.05 today.
Explanation:To calculate the initial deposit needed to save for a $8000 down payment in 4 years with an account that offers quarterly compounding at an APR of 6%, we use the compound interest formula:
[tex]P = A / (1 + r/n)^{(nt)[/tex]
Where:
P is the principal amount (initial deposit)A is the future value of the investment/loan, including interestr is the annual interest rate (decimal)n is the number of times that interest is compounded per yeart is the time the money is invested/borrowed for, in yearsGiven:
A = $8000r = 6/100 = 0.06 (as a decimal)n = 4 (quarterly compounding)t = 4 yearsNow we can calculate the initial deposit:
[tex]P = $8000 / (1 + 0.06/4)^(4*4)P = $8000 / (1 + 0.015)^(16)P = $8000 / (1.015)^16P \approx $8000 / 1.26824179P \approx $6304.05[/tex]
Therefore, you would need to deposit approximately $6304.05 today to have $8000 in 4 years in the account with the given interest rate and compounding frequency.
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To reach an $8000 goal in 4 years with a 6% APR compounded quarterly, you need to deposit approximately $6307.17 now.
To determine how much to deposit now to reach your $8000 goal in 4 years with quarterly compounding and an APR of 6%, you can use the formula for compound interest:
[tex]P = A / (1 + r/n)^(nt)[/tex]
Where:
P = initial deposit (what we're solving for)A = future value ($8000)r = annual interest rate (6% or 0.06)n = number of times interest is compounded per year (4 for quarterly)t = number of years (4)Now, substitute the given values into the formula:
P = [tex]$8000 / (1 + 0.06/4)^(4*4)[/tex]
P = $8000 / [tex](1 + 0.015)^(16)[/tex]
P = $8000 / [tex](1.015)^(16)[/tex]
P = $8000 / 1.2682 (approximately)
P = $6307.17 (approximately)
So, you would need to deposit approximately $6307.17 now to reach your $8000 goal in 4 years with quarterly compounding at a 6% APR.