The answer accurate to the nearest hundredth is 38.5
How to find the nearest hundredth?
To find the nearest hundredth of a number, you can round it to the nearest hundredth. To do this, you need to look at the third digit after the decimal point.
If the digit is less than 5, you can round down.If the digit is greater than or equal to 5, you can round up.Regarding the rectangles, since the two rectangles are similar, we know that the ratio of their corresponding sides are equal.
W1/W2 = P1/P2 = k (where k is the proportionality constant)
So, P2 = (P1 * W2)/W1 = (34 * 14)/12 = 38.5
Hence, The answer accurate to the nearest hundredth is 38.5
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Last year, nicholas started babysitting to earn extra spending money. over the summer, he tracked how much money he earned at each babysitting job. this box plot shows the results.
The percent of the time Nicholas earned is the percent of the time 25%
The 5 values of the given box plot are;
The minimum fee = 20
In the first quartile, the 25th percentile point, Q₁ = 25
In the median or second quartile, the fiftieth percentile factor, Q₂ = 30
The 1/3 quartile, the 75th percentile point, Q₃ = 40
The maximum value = 55
The range = The most value - The minimal fee
The range = 55 - 20 = 35
We are aware that Nicholas earned $25 or less from the minimum value up to the first quartile, Q₁, which is the 25th percentile point, in which we've got 25 percent of the statistics points.
Consequently, the percentage of the time Nicholas earned $25 or much less is 25 percent of the time.
In mathematics, a percentage is a variety of ratios that can be expressed as a fraction of 100. If we have to calculate the percent of various, divide the wide variety by way of the whole and multiply by way of a hundred. For this reason, the shared approach is a component in line with a hundred. The phrase according to cent means in keeping with one hundred.
A relative cost indicates the hundredth component of any amount. One percent (symbolized 1%) is the hundredth part; for this reason, a hundred percent represents the whole lot and two hundred percent specifies two times the given amount.
Multiply the entire number amount through the decimal equal to the proportion. The end result is the share portion quantity. (consequently, this answers the question “How a whole lot is 24 percentage of 500,” you examine that 24 percent of 500 is a hundred and twenty).
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The figure shows lines r, n, and p intersecting to form angles numbered 1, 2, 3, 4, 5, and 6. All three lines lie in the same plane.
not to scale
Based on the figure, which of the individual statements would provide enough information to conclude that line r is perpendicular to line
p?
Select all that apply.
A m2 3 = m/6
OB. m2 3+m/4= 90°
Answer:
B.
Step-by-step explanation:
If the measures of angles 3 and 4 add to 90, then lines r and p meet at right angles making them perpendicular.
Answer: B.
Answer:
Step-by-step explanation:
Diamond went to lunch with her friends. The total bill came to $32.20. If Diamond tipped 19%, how much tip did she leave?
$6.12
Step-by-step explanation:A percentage is some portion of a whole number. Multiple methods can be used to find percentages.
Multiplication to Find Percentages
One of the easiest ways to find percentages is to multiply the original number by a decimal. To do this, one first needs to turn the percentage into a decimal.
For example,
19% = 0.19To convert a percentage to a decimal, just move the decimal point 2 places to the left.
Then, multiply this decimal by the whole number, and the answer, in this case, will be the tip.
19% of $32.20
Now, to solve we can just multiply.
0.19 * 32.20 = 6.118The exact answer is 6.118. However, since we are using money, we are going to round to the nearest hundredth place. This gives the final answer of $6.12.
a. Find the linear approximating polynomial for the following function centered at the given point a. b. Find the quadratic approximating polynomial for the following function centered at the given point a. c. Use the polynomials obtained in parts a. and b. to approximate the given quantity. -1/1.06
The required answers are:
a. The linear approximating polynomial at a = 1: P₁(x) = x - 2
b. The quadratic approximating polynomial at a = 1: P₂(x) = -3 + 3x - x²
c. Appromating the given quantity -1/1.06 for P₁(x) and P₂(x): -3.06 and -7.30 respectively.
Using Taylor polynomial series, the required approximating polynomials are calculated.
What is the Taylor polynomial series?The Taylor polynomial series is
Pₙ(x) = ∑ [tex]\frac{f^n(a)}{n!}[/tex](x - a)ⁿ; limits from 0 to n
Where fⁿ(a) is the nth derivation of f(x) at a
The first order(linear) Taylor polynomial series is
P₁(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a)¹
The second order(quadratic) Taylor polynomial series is
P₂(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a) + [tex]\frac{f''(a)}{2!}[/tex](x - a)²
Calculation:The given function is f(x) = -1/x at a = 1
f(a) = f(1) = -1
f'(x) = -(-1/x²) = 1/x²; f'(a) = f'(1) = 1
f''(x) = -2/x³; f''(a) = f''(1) = -2
a. Linear approximating polynomial:
From the Taylor series, we have
P₁(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a)¹
On substituting,
P₁(x) = -1 + (1/1!)(x - 1)¹
= -1 + (x - 1)
= x - 2
b. Quadratic approximating polynomial:
From the Taylor series, we have
P₂(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a) + [tex]\frac{f''(a)}{2!}[/tex](x - a)²
On substituting,
P₂(x) = f(1) + (1/1!)(x - 1) + (-2/2!)(x - 1)²
= -1 + (x - 1) - (x - 1)²
= -1 + x - 1 - (x² - 2x + 1)
= x - 2 - x² + 2x - 1
= -3 + 3x - x²
c. Approximating the given quantity -1/1.06:
Substituting x = -1.06 in P₁(x) and P₂(x),
P₁(x) = x - 2
⇒ P₁(-1.06) = (-1.06) - 2 = -3.06
P₂(x) = -3 + 3x - x²
⇒ P₂(-1.06) = -3 + 3(-1.06) - (-1.06)² = -7.30
Therefore, the approximating polynomials are calculated by using Taylor polynomial series.
Disclaimer: The given question is incomplete. Here is the complete question.
Question:
a. Find the linear approximating polynomial for the following function centered at the given point a.
b. Find the quadratic approximating polynomial for the following function centered at the given point a.
c. Use the polynomials obtained in parts a. and b. to approximate the given quantity.
f(x) = -1/x , a = 1; approximate -1/1.06
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A pile of cards contains 3 diamonds,
4 hearts, and 2 spades. Marianna randomly
selects two cards without replacing the
first. What is P(hearts, then spades)?
F. 8/81
G. 1/9
H. 2/3
J. 1/18
Answer:G
Step-by-step explanation:
4/9 times 2/8= 1/9
Answer:
G 1/9
Step-by-step explanation:
add all of the cards together that will get you 9 then you take the hearts overing it by total then times it by 2 overing by 8 or
4/9x2/8
You have fifteen blankets that each take up 557 cubic inches of space. How many blankets could you pack into a 14-inch moving box
You have fifteen blankets that each take up 557 cubic inches of space. In a 14-inch moving box, we can pack approximately 5 blankets.
The Volume that can take up by single blanket is 557 cubic inches.
The dimension of the moving box = 14 × 14 × 14
Hence, the volume of the moving box = 2744 cubic inches
The total number of blankets that can be packed in the given moving box = 2744/557 = 4.92 ≅ 5
Therefore, in a 14-inch moving box, there can be 15 blankets with 557 cubic inches of space of each can be packed.
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A bookshelf is 4-3/4 feet wide. how many 3-inch-wide books will fit on the shelf?
19 books can fit into a bookshelf that has a width of 19/4 feet
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
The bookshelf is 4 3/4 feet wide = 19/4 feet
1 ft = 12 in, hence:
19/4 feet = 19/4 feet * 12 in per feet = 57 inches
Number of books = 57 inches / 3 in = 19
19 books can fit into a bookshelf that has a width of 19/4 feet
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A yard with a tree is to be concreted. The owner wants to concrete the whole yard, but keep the tree in place and so concretes around the tree to its circumference. The tree has a circular cross section, with a diameter of 1 m. The yard is a rectangle, with sides of length 3 m and 4 m. What is the area of concrete required (to 1 d.p.)?
Answer:
11.2 square meters
Step-by-step explanation:
This is a very simple question. Basically, it's the area of a rectangle with the area of a circle subtracted. The area of a circle is calculated with the following formula:
[tex]\pi \times r^{2} [/tex]
Where r is the radius. We know the diameter is 1m, so we can simply halve this value to find the radius of 0.5m. Substituting in this value, we find the area of the circle to be:
[tex]\pi \times {0.5}^{2} \approx0.78539816339744830961566[/tex]
Now let's calculate the area of the rectangle, which is simply 3x4=12. Subtracting our earlier value from 12, we are left with an answer of 11.2 (to 1 d.p)
help im in a rush!!!!!!!
Answer:
Your answer should be 52!!
Step-by-step explanation:
Work included on the picture below.
Two friends are planning for a gathering. The food budget is modeled by 1/2(x-120)=10,where x is the amount spent on food. What are the least and greatest amounts that the two friends could spend on food
The least and greatest amounts that the two friends could spend on food are 100 and 140 respectively
Functions and values
Functions are expressions written in terms of letters known as variables. Given the equation that represents the food budget of two friends as shown;
1/2(x-120)=10
where x is the amount spent on food.
In order to determine the least and greatest amounts that the two friends could spend on food,
For the least amount
-(x-120) = 20
-x+120 = 20
x = 100
For the greatest amount
(x-120) = 20
x = 140
Hence the least and greatest amounts that the two friends could spend on food are 100 and 140 respectively
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Total slack is calculated by ____
Total slack is calculated by the late finish minus early finish and the late start minus the early start
What is the total slack?Total slack is simply the amount of time taken for a task to be delayed before the project finish date is delayed. It can be positive or negative.
It is calculated as the calculated as the value of the Late Finish minus the Early Finish field, and the Late Start minus the Early Start field.
Total slack = Late finish - early finish + late start - early start
Thus, the total slack is calculated by the late finish minus early finish and the late start minus the early start.
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The measure of one angle of an octagon is twice the measure of one of the other seven congruent angles. What is the measure of each angle?
Each one of the smaller angles x = 120 degrees and the larger angle = 2x = 2 × 120 = 240 degrees
How to find the angle of octagon?The angle of an octagon can be found as follows;
An octagon is a polygon that has 8 sides.
The sum of angles in an octagon is 1080 degrees.
Therefore,
x + x + x + x + x + x + x + 2x = 1080
Hence,
9x = 1080
divide both sides by 9
x = 1080 / 9
x = 120
Therefore, each one of the smaller angles x = 120 degrees and the larger angle = 2x = 2 × 120 = 240 degrees
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Read the excerpt from The Land.
"I'm ready to start getting to know him," I answered. "Not ready to mount him yet."
"Now, what you mean by that? Get on that horse."
"No, sir, I can't. You need to give me some time with him first."
"Well, I don't have none of that."
"It's important. Now, I said I'd ride your horse, Mister Sutcliffe, but I've got my own way of dealing with horses. You want me to win, then I've got to deal with this grey my way."
Based on this dialogue, which word best describes Paul’s approach to riding a new horse?
overbearing
carefree
methodical
informal
From the conversation it can be inferred that Paul's approach to getting on the horse is methodical (option c).
What is methodical behavior?A methodical attitude or behavior refers to the preference of people to use an organized method and sequences to perform an activity correctly.
According to the above, it can be inferred that Paul behaves in a methodical manner because he prefers to relate to the horse slowly and in a controlled manner before proceeding to mount it.
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The question is about unit circle in screenshot
The complete sentence for the unit circle is:
When t = 0, AP = 0, so sin t will begin at a value of 0. As t increases from 0 to π/2, sin t increases. Eventually, when t = π/2, OP will be 0, so sin t = AP will be 1.
How to complete a sentence with concepts from trigonometry
In this problem we have sentence to be completed by direct observation to the variables seen in a unit circle, a form used to teach trigonometric functions in a graphic manner. Now we proceed to present the complete sentence below:
When t = 0, AP = 0, so sin t will begin at a value of 0. As t increases from 0 to π/2, sin t increases. Eventually, when t = π/2, OP will be 0, so sin t = AP will be 1.
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Which point is a solution to the inequality shown in this graph? (urgent)
Answer: D
Step-by-step explanation:
sorry if its wrong
The graph of F(x) shown below resembles the graph of G(x) = x4, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
Using translation concepts, the equation of F(x) is:
A. [tex]F(x) = \frac{1}{3}x^4 - 2[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The parent function is:
[tex]G(x) = x^4[/tex]
For function F(x), we have that:
It was shifted down 2 units, hence F(x) = G(x) - 2.It was vertically compressed by a factor of 3, hence [tex]F(x) = \frac{1}{3}G(x) - 2[/tex]Then the equation is:
A. [tex]F(x) = \frac{1}{3}x^4 - 2[/tex]
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What's the difference between sampling with replacement and sampling without replacement? How should you account for this
using TI-84's or the "hat method"?
When sampling with replacement is used, an element that has already been chosen is put back into the sample frame and given the chance to be chosen again.
In the case of sampling without replacement, an element is eliminated from the sample frame after it has been chosen.
In this question, we are supposed to state the differences between sampling with replacement and sampling without replacement.
Generally speaking, sampling without replacement is more effective than producing representative samples using replacement sampling. It prevents the inclusion of the same population element in the sample several times.
By "drawing from a hat" or by using a computer program that simulates the same process, you select the sample at random using the lottery method.
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Which of the following correlation coefficients expresses the weakest relationship between two variables
The correct option is a) -0.15.
The weakest correlation relationship between two variables is given by -0.15.
What is correlation?With the aid of correlation, the strength of the relationship between two variables can be determined. We can tell from this study whether there is no correlation, weak correlation, or a strong correlation between the two variables.
Two different types of correlation exist:
positive correlation: Two variables that move together, or in the same direction, are said to have a positive correlation. When one variable rises while the other rises or when one variable falls while the other falls, there is a positive correlation.negative correlation: When two variables are correlated negatively, the other variable's value falls as the value of the first variable rises. The correlation coefficient, which expresses correlation on a scale from +1 to -1, is used. Values less than 0 indicate a negative connection.The correlation value (r) always lies between -1 and 1.
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The complete question is -
Which of the following is the weakest correlation relationship between two variables?
a) -0.15
b) 0.27
c) -0.70
d) 0.55
is flipped ten times, and he is asked to predict in advance the outcome. Our individual gets seven out of ten correct. What is the probability he would have done at least this well if he had no ESP
The required probability is 0.171.
What is probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
We can find required Probability as shown:
From 10 coins we choose 7 he guessed correct with probability of each 1/2. For three remaining coins he failed to predict the outcomes of the flip with the probability of 1/2 for each. Similarly for 8,9 or 10 successive trials. Let X denote number of successive trials
[tex]P(X\geq 7)= \tbinom{10}{7}.\frac{1}{2^{10}}+\tbinom{10}{8}.\frac{1}{2^{10}} +\tbinom{10}{9}.\frac{1}{2^{10}}+\tbinom{10}{10}.\frac{1}{2^{10}}[/tex]
[tex]=120.\frac{1}{2^{10}} +45.\frac{1}{2^{10}} +10.\frac{1}{2^{10}} +.\frac{1}{2^{10}}[/tex]
[tex]=\frac{120+45+10+1}{2^{10}}[/tex]
[tex]=\frac{176}{1024}[/tex]
=0.171
Hence, the required probability is 0.171.
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Given question is incomplete. This is complete question:
A man claims to have extrasensory perception. As a test, a fair coin is flipped 10 times and the man is asked to predict the outcome in advance. He gets 7 out of 10 correct. What is the probability that he would have done at least this well if he had no ESP?
A procedure for using sample data to find the estimated regression equation is _____. Group of answer choices point estimation interval estimation the least squares method extrapolation
c. the least squares method.
Regression equation:
In simple linear regression, the predicted value of the dependent variable is given by the equation = b0 + b1x. The values of b0 and b1 are calculated from the data so that the line = b0 + b1X minimizes the total sum of squared errors (error is the difference between the predicted value and the actual value of y).
Least squares method:
The least squares method is a statistical procedure to find the best fit for a set of data points by minimizing the sum of the offsets or residuals of points from the plotted curve.
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What is the image point of (-8, 3) after the transformation R2700 0 T-2,-1?
The transformation of the coordinate (-8, -3) R 270° and T-2,-1 is (-5, -9)
What is transformation?Transformation is the change of the coordinates of a shape either by rotation, reflection or translation.
Analysis:
When coordinates (x, y) rotate 270° the resulting coordinates become (-y, x)
so coordinates (-8, -3) after 270° rotation becomes ( 3, -8)
When it is translated 2 units to the left and 1 unit down, that is -3 + -2 = -5 and -8 + -1 = -9
Therefore the transformed coordinate becomes (-5, -9)
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The solution of the cubic function f(x) are −4,53, and 1. Identify a factor of this function.
Select one:
a. 3x+5
b. 5x+3
c. x+1
d. x+4
A factor of the polynomial function is (d) x + 4
How to determine the factor of the function?The solution of the cubic function f(x) are given as:
−4, 5/3, and 1.
This means that:
x = -4, x = 5/3 and x = 1
Set the above equations to 0
x + 4 = 0, x - 5/3 = 0 and x - 1 = 0
From the list of options, we have
(d) x + 4
Hence, a factor of the polynomial function is (d) x + 4
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If you apply the changes below to the quadratic parent function, f(x) = x²
what is the equation of the new function?
• Shift 3 units right.
• Vertically stretch by a factor of 4.
• Reflect over the x-axis.
A. g(x) = -4(x+3)²
B. g(x) = -4(x-3)²
C. g(x) = (-4x - 3)²
D. g(x) = 4x²+3
The equation of the unique function exists g(x) = -4(x-3)².
What is a quadratic equation?The polynomial of degree two exists named a quadratic polynomial and the equation corresponding to a quadratic polynomial P(x) exists named a quadratic equation.
Given: F(x) = x²
The vertical stretch by a factor of 4 exists can be satisfied by (b)
if we use a vertical stretch, it transforms the y-values which causes it to seem skinnier when graphed.
Multiply 4 by f(x) which provides 4x².
As the reflection over the x-axis, so multiply it by -1 to f(x), which results in -4x².
Shift the graph right 3 which exists by moving it right, so by adjusting the x values indicating use f(x-3), to obtain this subtract the value from x when you move right, and add the value to x when you move left.
Hence, the unique graph would be g(x) = -4(x-3)²
Therefore, the correct answer is option B. g(x) = -4(x-3)².
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What number is represented by the question mark?
111= 0, 3213=0, 7756= 1,7662= 2, 6855= 3, 8096= 5,6666=4 . 8193= 3,9313= 1,8639= 4,1234=0, 2581 = 2,7186= 3, 2679=?
The number that is represented by the question mark in the sequence is 2
What are sequence?Sequence are set of numbers that follow a predefined and predetermined patterns guided by a rule
How to determine the number represented by the question mark?The sequence of numbers is given as:
111= 0, 3213=0,
7756= 1, 7662= 2,
6855= 3, 8096= 5,
6666=4 8193= 3,
9313= 1, 8639= 4,
1234=0, 2581 = 2,
7186= 3, 2(6)7(9)=
From the complete question, the values of the sequence are determined by the count of numbers that are circled or in brackets
In the 2(6)7(9), two numbers are circled.
The numbers are 6 and 9
This means that the value of 2679 is 2
i.e. 2(6)7(9)= 2
Hence, the number that is represented by the question mark in the sequence is 2
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A group of scientists is conducting an experiment on the effects of media on children. they randomly select 100 children and randomly assign each child to one of four treatment groups. each treatment group has a specific amount of screen time during a one-week time frame. the first group has no screen time, the second group has two hours of screen time, the third group has four hours of screen time, and the fourth group has six hours of screen time. after the first week, the scientists conduct the same experiment, with the same subject groups, for three more weeks so that each group experiences each of the four treatments. which statements about this study are true?
The statements that are true about this study are
This study uses random samplingThis study uses a control groupThis study uses a repeated measures designThis is further explained below.
What is an experiment?Generally, a scientific technique is used to create a discovery, test a theory or show an established truth.
In conclusion, The following are accurate claims concerning this study:
Random sampling is used in this investigation. In this investigation, a control group is used. Repeated measurements are employed in this investigation.
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rewrite each expression without using absolute value notation |7m-56| if m<8
Considering the definition of the absolute value function, the expression is written as -7m + 56.
What is the definition of the absolute value function?The absolute value function is defined as follows:
[tex]|x| = x, x \geq 0[/tex].[tex]|x| = -x, x < 0[/tex]That is, where the expression is negative, it is multiplied by -1, while where it is not negative the expression is kept.
In this problem, the expression is:
|7m - 56|
For m < 8, we have that one example is m = 0:
7(0) - 56 = -56.
The expression is negative, hence the signal is changed, that is:
|7m - 56| = -(7m - 56) = -7m + 56.
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Which is the graph of a logarithmic function?
The domain and range of the graph of a logarithmic function are;
Domain; 0 < x < +∞Range; The set of real numbers.How can the graph that correctly represents a logarithmic function be selected?The basic equation of a logarithmic function can be presented in the form;
[tex]y = log_{b}(x) [/tex]
Where;
b > 0, and b ≠ 1, given that we have;
[tex]y = log_{1}(x)[/tex]
[tex] {1}^{y} = 1[/tex]
The inverse of the logarithmic function is the exponential function presented as follows;
[tex]x = {b}^{y} [/tex]
Given that b > 0, we have;
[tex] {b}^{y} = x > 0[/tex]
Therefore, the graph of a logarithmic function has only positive x-values
The graph of a logarithmic function is one with a domain and range defined as follows;
Domain; 0 < x < +∞
Range; -∞ < y < +∞, which is the set of real numbers.
The correct option therefore has a domain as x > 0 and range as the set of all real numbers.
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Answer:
3 or C
Step-by-step explanation:
The answer above is correct.
The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.15 gallons. A previous study found that for an average family the variance is 3.61 gallons and the mean is 19.4 gallons per day. If they are using a 95% level of confidence, how large of a sample is required to estimate the mean usage of water
The minimum sample size required to estimate the mean usage of water = 2225.07
What is Standard deviation?
In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.
We can find the minimum sample size required to estimate the mean usage of water as shown below:
Standard deviation [tex]\sigma =3.61[/tex]
Margin of error E=0.15
Critical value for 95% confidence interval = 1.96
Required minimum sample size: [tex]n=(\frac{Z_{\frac{\alpha}{2}}.\sigma }{E} )^2[/tex]
[tex]=(\frac{1.96\times 3.61}{0.15} )^2[/tex]
=2225.07
Hence, the minimum sample size required to estimate the mean usage of water = 2225.07
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The projectile motion of an object can be modeled using s(t) = gt2 + v0t + s0, where g is the acceleration due to gravity, t is the time in seconds since launch, s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is –4.9 m/s2.
An object is launched at an initial velocity of 19.6 meters per second from an initial height of 24.5 meters. Which equation can be used to find the number of seconds it takes the object to hit the ground?
A. 0 = –4.9t2 + 19.6t + 24.5
B 0 = –4.9t2 + 24.5t + 19.6
C. 19.6 = –4.9t2 + 24.5t
D. 24.5 = –4.9t2 + 19.6t
Answer: 0=-4.9t²+19.6t+24.5
Step-by-step explanation:
[tex]s(t)=gt^2+v_0t+s_0\\v_0=19,6\ \frac{m}{s} \ \ \ \ s_0=24,5\ m\ \ \ \ g=-4,9\ \frac{m}{s^2} \ \ \ \ S(t)=0\ (the\ object \ hitts\ the \ ground)\ \Rightarrow\\0=-4,9t^2+19,6t+24,5.[/tex]
Work out the area of the triangle.
Answer:
555.75m²Step-by-step explanation:
Triangle Area = 1/2b*h
1/2 57 * 19.5 =
28.5 * 19.5 =
555.75m²