The median element of a dataset is the middle element of the dataset.
There are 3 runs above and below the sample median
What is the median of a data set ?
The median of a data set is the value that falls in the middle, indicating that 50% of the data points have values that are lower or equal to the median and 50% of the data points have values that are higher or equal to the median. When working with a small data collection, you must first count the number of data points (n) and organize them in ascending order.
The information is given as:
Observations 1 2 3 4 5 6
Defects 10 18 13 15 9 12
In ascending order, the information is represented as:
Defects 9 10 12 13 15 18
Observations 5 1 6 3 4 2
The total number of observations is:
n=5+1+6+3+4+2 = 21
The median element is calculated as:
Median = (n+1)/2 th
Substitute 21 for n
Median = (21+1)/2 th
Median = 11th
The 11th element is 12.
So, the median is:
median = 12
Considering the given information;
Observations 1 2 3 4 5 6
Defects 10 18 13 15 9 12
The defects greater than the median (i.e. 12) are above (A) the median, while the defects less than the median are below (B)
So, we have:
Observations 1 2 3 4 5 6
Defects 10 18 13 15 9 12
Status B A A A B -
Next, we take a count of the number of times the status changes, i.e. from B to A, from A to B, from A or B to -
The count is 3.
Hence, there are 3 runs above and below the sample median
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Composition of functions worksheet
using f(x) = 8x squared and g(x) (2x+8), find:
The composition of the function are as follows:
(g ∘ g) (x) = 4x + 16
(f ∘ g) (x) = 16x + 64
f [g(7)] = 6x - 28
g [f(3)] = -30x - 10
What is a Composite Function?
If we are given two functions, we can compose one function into the other to produce a third function. The steps needed to complete this operation are the same as those needed to solve any function for any given value. These are referred to as composite functions.
We have,
i] f(x) = 8x and
g(x) = (2x+8)
(g ∘ g) (x) = g[g(x)]
Substitute x with (2x+8) in the function g(x) = (2x+8).
= 2((2x+8))+8
= 4x + 16
(f ∘ g) (x) = f [g (x)]
Substitute x with (2x+8) in the function f(x) = 8x.
(f ∘ g) (x) = 8(2x+8)
= 16x + 64
ii] f(x) = 6x + 2 and g(x) = x -5
f [g(7)] = 6(x-5) + 2
= 6x - 28
g [f(3)] = (6x + 2 ) - 5
= -30x - 10
Hence, the composition of the function is:
(g ∘ g) (x) = 4x + 16
(f ∘ g) (x) = 16x + 64
f [g(7)] = 6x - 28
g [f(3)] = -30x - 10
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The table shows the weights of apples at a grocery store.
Answer:
Is that all
_______
_______
Write an equation for a rational function with:
Vertical asymptotes at x = -5 and x = -2
x intercepts at x = -1 and x = 6
y intercept at 4
y =
The rational equation with the desired asymptotes and intercepts is given by: f(x) = [-20(x²-5x-6)] / [3(x² 7x + 10)].
What are the asymptotes of a function f(x)?Vertical asymptotes are x values that are outside the domain and, in a fraction, are the denominator zeroes.
As long as this value differs from infinity, the horizontal asymptote is the value of f(x) as x approaches infinity.
The vertical asymptotes are related to the denominator roots, so:
f(x) = a / ( x + 5)( x + 2 )
f(x) = a / ( x² + 7x + 10 )
The x-intercepts are related to the function's numerator, so:
f(x) = [a( x + 1 )( x - 6) ] / [x² + 7x + 10 ]
The y-intercept is to find a, hence, when x = 0, y = 5, thus:
4 = a(-6)/ 10
a = (-40/6)
a = -20 / 3
The equation will be written as,
f(x) = [-20(x²-5x-6)] / [3(x² 7x + 10)].
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Gianna is going to use a computer at an internet cafe. The cafe has an initial charge of $10 to use a computer and an additional charge of $0.60 for every minute of use. Make a table of values and then write an equation for C , C, in terms of t , t, representing the total cost of using a computer for t t minutes at the internet cafe.
A table of values and an equation for C, in terms of t, representing the total cost of using a computer for t minutes at the internet cafe are as follows:
C t
$10.60 1
$11.20 2
$11.80 3
C = 0.60t + 10.
How to write an equation for the total cost?In order to write an equation for the total cost, we would assign variables to the amount of time used and the total cost of using a computer, and then translate the word problem into algebraic equation as follows:
Let the variable C represent the total cost in dollars.Let the variable t represent the amount of time in minutes.Since the cafe has an initial charge of $10 to use a computer and an additional charge of $0.60 for every minute of use, an equation for the total cost is given by:
C = 0.60t + 10
When t = 1, we have:
Total cost, C = 0.60(1) + 10
Total cost, C = $10.60.
When t = 2, we have:
Total cost, C = 0.60(2) + 10
Total cost, C = $11.20.
When t = 3, we have:
Total cost, C = 0.60(3) + 10
Total cost, C = $11.80.
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does a gasoline additive improve mileage? drivers logged their mileage on a tank of gas with and without the additive. the sample of 10 drivers had an average difference (with additive - without) in mileage of 4.1 mpg with a standard deviation of 5 mpg. what is the test statistic for this test?
The test statistic for the given test is t = 2.59.
What is a standard deviation?
The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.
Given data:
[tex]\bar D[/tex] = 4.1, Sd = 5, n = 10, μd = 0
Now the test statistic can be computed as
[tex]t=\frac{\bar D-\mu_d}{S_d/\sqrt{n} }[/tex]
[tex]t=\frac{4.10-0}{5/\sqrt{10}} \\\\t=2.59[/tex]
Hence, the test statistic for the given test would be t = 2.59.
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What is the solution to the equation One-fourth x minus one-eighth = Start Fraction 7 Over 8 End Fraction + one-half x?
x = negative 5
x = negative 4
x = 4
x = 5
The solution to the equation represented by One-fourth x minus one-eighth = Start Fraction 7 Over 8 End Fraction + one-half x is (b) x = negative 4
How to determine the solution to the equation?The statement in the question is given as
One-fourth x minus one-eighth = Start Fraction 7 Over 8 End Fraction + one-half x
Mathematically, this statement can be represented as
1/4x - 1/8 = 7/8 + 1/2x
Multiply through the equation by 8
So, we have:
2x - 1 = 7 + 4x
Collect the like terms
4x - 2x = -1 - 7
Evaluate the like terms
2x = -8
Divide both sides by 2
x = -4
Hence, the solution is -4
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How do you write 760 percent as a fraction or as a mixed number?
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
760% can be written in fraction form as 38/5.
760% can be written in mixed form as 7(3/5).
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
760%
This can be written as a fraction.
760/100
= 76/10
= 38/5
or
= 7(3/5)
Thus,
760% can be written in fraction form as 38/5.
760% can be written in mixed form as 7(3/5).
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a publisher reports that 54t% of their readers own a personal computer. a marketing executive wants to test the claim that the percentage is actually different from the reported percentage. a random sample of 200200 found that 44d% of the readers owned a personal computer. is there sufficient evidence at the 0.100.10 level to support the executive's claim? step 1 of 7 : state the null and alternative hypotheses.
hybrids research When she does, the camden depositor is actually higher than the reported percentage. Here, we have the report 126 percent, the winners on the portion computer. It indicates that the proportion of the underling hypothesis at noon will be equal to 26.
The abon 26 point notte will be greater than the b of the means 10. In this question, which is the right-hand exam, we will provide the sembiante 340, which will be equal to 31 percent, and we must contend with the statistical test. The test is therefore equal to the z moving forward. It will be calculated using the following formula: hat: minus b over square root, times: 1 minus p over the hot equal to 131 p equal to 261 square 261 minus 26. If we compare it to my 340 point, we get 126 times 74 divided by 340, then we take the square root of that number. The 131 minus 7.26 is then divided by the industry standard.I respond with a number equal to 2.10, rounding up to two decimal places before moving on to the step's following inquiry. 3. This is the 110 test since the test pair is on 1 here and then the next 1 in his right hand. The choice must be made hypotheses, though. Rule and we need to identify the critical value, and since that will be the right hand, we must make sure that the critical value is both equal to and far beyond that. 05. It will check the z table to see if the value equals 1.645, and if it does, we'll use the decision rule to reject the null hypothesis. If so, the test result will exceed the cutoff of 1.645 points, and we will observe Because the test we determined to be equivalent to 2.10 is higher than the 1.645 point, we can observe that. We will thus rule out the known hypothesis and come to the conclusion that there is sufficient evidence to back up the prediction that the proportion will be higher than 26%.
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Has the marrying age of a man changed over the years? the united states bureau of the census takes a formal count of everyone in the u. S. Every 10 years and has provided the following data that gives the median age of an american man at the time of his first marriage. Year 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 median age 25. 1 24. 6 24. 3 24. 3 22. 8 22. 8 23. 2 24. 7 26. 1 26. 8 determine the average rate of change in median age per year from 1950 to 1990.
The average rate of change in median age per year from 1950 to 1990 is 0.085 years of age per year.
The median is the mid-value in a set of data. to find it we first arrange the data set from smallest to largest, then pick the middle value which divides the data set in half.
From the given table,
The median age at the time of the first marriage in 1950 = 22.8 years,
While the median age in 1990 = 26.1 years,
Hence, the average rate of change in median age per year from 1950 to 1990
= (22.8-26.1)/(1950-1990)
= (-3.3)/(-40)
= 0.0825 years of age per year.
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The interior angles of a polygon are the angles formed inside a polygon by two adjacent sides. The sum S of the measures of the interior angles of a polygon with n sides can be found using the formula S = 180(n - 2). The sum of a polygon’s interior angle measures is 1260°. How many sides does the polygon have?
The number of sides in the polygon that has 1,260° as the sum of the interior angles, found using the formula for the sum of the interior angles in the polygon, S = 180·(n - 2) is 9 sides
What is a polygon in geometry?A polygon is a figure consisting of a specified number of straight sides such that they form a closed loop. The number of sides in a polygon are three or more.
The formula for the sum of the interior angles of a polygon, S, can be be used to find the number of sides in the polygon as follows;
S = 180·(n - 2)
Where;
n = The number of sides the polygon has
The sum of the interior angles in the specified polygon = 1,260°
The number of sides in the polygon can be found by equating the formula for S to 1,260° as follows;
When S = 1.260°, we get;
1,260 = 180·(n - 2)
Which indicates;
n - 2 = 1,260 ÷ 180 = 7
Therefore; n - 2 + 2 = 7 + 2 = 9
n = 9
The number of sides in the polygon that has a sum of the interior angles as 1,260° is therefore, n = 9 sidesLearn more about polygons here:
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Factorise fully the following:
4x³ + 24x²
Answer:
4 x^3 + 24 x^2 = 4 (x^3 + 6 x^2) = 4 x^2 (x + 6)
4 x^2 (x + 6) seems to be the lowest factor
is the statement a valid null hypothesis?
A null hypothesis is a particular kind of statistical hypothesis that asserts that no statistical significance can be found in a given set of observations.
What is meant by null hypothesis?A null hypothesis is a particular kind of statistical hypothesis that asserts that no statistical significance can be found in a given set of observations. The use of sample data in hypothesis testing allows one to judge a hypothesis' veracity.
The null hypothesis states that the estimate is only based on chance. If the observed data (in the sample) do not differ from what would be predicted solely by chance, then the null hypothesis is true. The alternative hypothesis is what the null hypothesis has as its counterpart.
Two population parameters, such as an independent variable and a dependent variable, are said to be unrelated under the null hypothesis. It's possible that an experimental or sampling error caused the result if the hypothesis indicates a relationship between the two parameters.
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JE
Write an equation for a line perpendicular to y = 3a + 3 and passing through the point (-6,6)
Answer:
Step-by-step explanation:
A line that is perpendicular to another will have the opposite slope.
y = [tex]-\frac{1}{3}[/tex]a + b
To find b, substitute y and a with the given values
6 = [tex]-\frac{1}{3}[/tex](-6) + b
6 = 2 + b
-2 -2
4 = b
thus
y = [tex]-\frac{1}{3}[/tex]a + 4
Which expression is equivalent to (6x^-9x) - (2x - 3)?
The equivalent expression of (6x² - 9x) - (2x -3) is 6x² - 11x + 3
What is an equivalent expression?Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
In other words, equivalent expressions are expressions that have similar value or worth but do not look the same.
To find equivalent expression we can simplify the expression.
Therefore,
(6x² - 9x) - (2x -3)
open the brackets
6x² - 9x - 2x + 3
combine like terms
Therefore,
(6x² - 9x) - (2x -3) = 6x² - 11x + 3
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Find the solution(s) of the system of equations. y = x2 + 4x y + x2 = –4x
A)
(0, 0)
B)
(–4, 0) and (4, 0)
C)
(–4, 0) and (0, 0)
D)
(0, 0) and (4, 0)
Scott bought a desktop computer and a laptop computer. Before finance charges and the laptop cost $350 more than the desktop. He paid for the computers using two different financial plans. For the desktop the interest rate was 6.5% per year and for the laptop it was 9% per year. The total finance charges for one year for $388. How much did each computer cost before finance charges
The cost of laptop and cost of desktop are; $1,800 and $2,100 respectively.
What are mathematics operations?A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value.
From the question , we are given that the laptop costs $350 more than the desktop, therefore,
let x represent the cost of the laptop thus, x-350 will be the cost of the desktop .
The total finance charge of $388 is equal to 8% of the cost of the laptop and 7.5% of the cost of the desktop, we solve as;
388 = 0.08(x) + 0.075(x - 350)
252 = 0.08x + 0.075x - 26.25
278.75 = 0.155x
x = 278.75/0.155
x = 1798
Recall that the cost of desktop = x -350
therefore:
1,798- 350 = 1448
The cost of laptop = $1798
The cost of desktop = $1448
Thus, the cost of laptop and cost of desktop are; $1,800 and $2,100 respectively.
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Write the given expression as a single trigonometric function. 2 sine (startfraction 3 pi over 8 endfraction) cosine (startfraction 3 pi over 8 endfraction)
The single trigonometric function form of the expression is 2sin(3π/8) cos(3π/8).
Trigonometric function:
In math, trigonometric functions are the periodic functions which denote the relationship between angle and sides of a right-angled triangle.
Given,
Here we need to write the given expression as a single trigonometric function. 2 sine (start fraction 3 pi over 8 end fraction) cosine (start fraction 3 pi over 8 end fraction)
Here we have the expression,
2 sine (start fraction 3 pi over 8 end fraction) cosine (start fraction 3 pi over 8 end fraction)
Now, we have to convert this into the form of trigonometric function,
For that we have to rewrite the given expression based on the arithmetic operators, then we get the resulting function as,
=> 2sin(3π/8) cos(3π/8).
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Answer:C
Step-by-step explanation:
did it on edge
read questions A and B... Must give 2 answers
For a student with a shoe size of 9, the student's height is equal to 65 inches.
For a student with a height of 60 inches, the student's shoe size is equal to 6.5.
How to determine the approximate of a student?From the information provided, an equation for the line of best fit that represents or models the heights x (in inches) and shoe sizes y of several student is given by this mathematical expression:
y = 0.50x - 23.5
Where:
x represents the height of a student.y represents the shoe size of a student.For a student with a shoe size of 9, the student's height is given by:
y = 0.50x - 23.5
0.50x = y + 23.5
Student's height, x = (y + 23.5)/0.50
Student's height, x = (9 + 23.5)/0.50
Student's height, x = 32.5/0.5
Student's height, x = 65 inches.
For a student with a height of 60 inches, the student's shoe size is given by:
y = 0.50x - 23.5
y = 0.50(60) - 23.5
y = 30 - 23.5
y = 6.5
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Put the following equation of a line into slope-intercept form, simplifying all fractions.
6x + 4y = 16
Answer:
y = - [tex]\frac{3}{2}[/tex] x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
6x + 4y = 16 ( subtract 6x from both sides )
4y = - 6x + 16 ( divide through by 4 )
y = [tex]\frac{-6}{4}[/tex] x + [tex]\frac{16}{4}[/tex] , that is
y = - [tex]\frac{3}{2}[/tex] x + 4 ← in slope- intercept form
In an Arithmetic Progression (AP), the first
term is 3, and the sum of the first and the sixth
terms is 20. What is the 8th term
Answer:
The 8th term of the AP= 113/5 or 22.6
Answer:
22.6
Step-by-step explanation:
Given:
a = 3a + a₆ = 20Find the value of a₆:
[tex]\implies a+a_6=20[/tex]
[tex]\implies a_6=20-a[/tex]
[tex]\implies a_6=20-3[/tex]
[tex]\implies a_6=17[/tex]
Therefore:
a = 3a₆ = 17General form of an arithmetic sequence:
[tex]\boxed{a_n=a+(n-1)d}[/tex]
Where:
[tex]a_n[/tex] is the nth term.a is the first term.d is the common difference between terms.n is the position of the term.Substitute a = 3 and a₆ = 17 into the formula and solve for d:
[tex]\begin{aligned}\implies a_6=3+(6-1)d&=17\\3+5d&=17\\5d&=14\\d&=2.8\end{aligned}[/tex]
Therefore, the equation for the nth term is:
[tex]\implies a_n=3+(n-1)2.8[/tex]
[tex]\implies a_n=3+2.8n-2.8[/tex]
[tex]\implies a_n=2.8n+0.2[/tex]
To find the 8th term, substitute n = 8 into the equation for the nth term:
[tex]\implies a_8=2.8(8)+0.2=22.6[/tex]
Factorise this equation + workings out!! Please help!!!!
Answer:(2x+1)(3x-4)
Step-by-step explanation:Factor the expression out first by getting 6x^2+3x-8x-4. From there, factor again to 3x(2x+1)-4(2x+1) to get the answer (2x+1)(3x-4)
Answer:
(3x - 4)(2x - 1)
Step-by-step explanation:
6x^2 - 5x - 4
When factoring, we want to first find the GCF. In this case, the GCF is one so we leave it as that. Next, we want to try and find the sum and the product. Additionally, we have a leading coefficient. We will multiply the leading coefficient by the last term, which is -4. (You will need to remember this to continue on later.)
x^2 - 5x - 24
Now, we can find the sum and the product. To do this, we need to list the factors of 24. (Remember negatives as well!)
24: 1 and 24, 2 and 12, 3 and 8, 4 and 6.
As -24 is also a negative, that means it will have one positive and one negative factor. This must also add up to -5.
One pair that does this is -8 and 3. They multiply together to -24 and add up to -5.
Now, since we multiplied the leading coefficient in the beginning, we must bring it back down into the parenthesis.
(6x - 8)(6x - 3)
We must divide out and try to simplify this as much as we can to match the leading coefficient. The divisors must multiply up to 6.
(6x - 8)/2 and (6x - 3)/3. 3*2 = 6
(3x - 4)(2x - 1)
An empty cubical carton i of ide 9cm. Can you fit in 1000 1cm cube in it? Jutify
Answer: Side of an empty cubicle carton = 9 cm.
Now as we know that volume of the cube is the cube of its side.
So the volume of an empty cubicle carton having side 9 cm, V = (9)3=729 cm3.
Now we have to find out can 1000 cubes of side 1cm fit in it.
So the volume of the cube of side 1 cm is, V’ = (1)3=1 cm3
So the volume of the 1000 such cubes = 1000 (1) = 1000 cubic centimeters.
Now if the ratio of the volume of the empty cubicle carton to the volume of 1000 cubes of 1 cm is greater than 1 then we can will 1000 cubes of side 1 cm into an empty cubicle carton otherwise not.
So the ratio of the volume of the empty cubicle carton to the volume of the 1000 cubes is,
⇒VV′=7291000=0.729 < 1
So as we see that the ratio is less than one so we cannot fit 1000 cubes of side 1 cm into an empty cubicle carton of side 9 cm.
Step-by-step explanation:
I really hope this works!
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Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
answer Asap!!!!!!!!!!!!
The three statements about his solution that are true include the following:
1. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.
2. He did not multiply the numerator and denominator by the correct number to equal 1,500.
5. He should have multiplied the numerator and denominator by 75, not 30, because 20 × 75 = 1,500.
How to determine the true solutions?Based on the information provided, a mathematical expression which models the number of songs of each genre on Josiah's MP3 player to be 300 songs:
10/20 = x/1500
Multiplying the mathematical expression by 75, we have the following:
75 × (10/20) = x/1,500
750/1500 = x/1500
1,500x = (750 × 1,500)
x = (750 × 1,500)/1,500
x = 750.
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consider a new dam where the height is doubled and the width is only one third of the original value. the ratio of the total force exerted on the new dam to that on the original dam fnew f is given by
the total force exerted on the new dam to that on the original dam f new is given by F = 624010000 lb.
What is Pascal's Principle.?
Consider a flat surface that is immersed vertically in a fluid whose weight density is p, according to Pascal's Principle.
A flat surface experiences fluid force (F) which is
F = ∫ph(x)w(x) dx
where h(x) is the height of the point x in the x-axis' vertical direction and w(x) is the surface's width.
to determine fluid force applied
Assume that x is equal to the height of the water. At height x on the dam, width of the dam is w(x) = 200 ft (given), and height is h(x) = x ft.
F = ∫ph(x)w(x) dx
F =0→100 ∫62.4 x 200 dx
F = 12480* 0 →100∫ x dx
F = 12480* 0 →100(x²/2)
F =
F = 6240((100)²- (0)²)
F= 6240(10000)
F = 624010000 lb
Hence the total force exerted on the new dam to that on the original dam f newf is given by F = 624010000 lb.
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What is the measure of m? 28 n 7 m = 7√ [?] Give your answer in simplest form. I would really appreciate your help.
Answer:
[tex]7\sqrt{5}[/tex]
Step-by-step explanation:
Using the geometric mean theorem, [tex]n=\sqrt{28 \cdot 7}=14[/tex].
Using the Pythagorean theorem, [tex]m=\sqrt{7^2+14^2}=7\sqrt{5}[/tex]
find the perimeter of the triangle. a triangle is drawn. all the angles of the triangle are marked with a single arc. three sides of a triangle are labeled (x plus 5 )inches, (2 x minus 3 )inches and (21 minus x )inches.
If the three sides of the triangle is (x + 5), (2x - 3), (21 - x), then the perimeter of the triangle is 23 + 2x
The perimeter of the triangle is the summation of all three sides of the triangle
Perimeter = a + b + c
= (x + 5) + (2x - 3) + (21 - x)
= 2x + 23
= 23 + 2x
Therefore, if the three sides of the triangle is (x + 5), (2x - 3), (21 - x) then the perimeter of the triangle 23 + 2x.
Any two-dimensional figure's perimeter is determined by the space surrounding it. By adding the lengths of the sides, we can determine the perimeter of any closed shape.
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Which statement best explains whether the equation y = 2x − 4 represents a linear or nonlinear function?
The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.
The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.
The equation represents a nonlinear function because it has an independent and a dependent variable, each with an exponent of 1.
The equation represents a nonlinear function because its graph contains the points (0, 2), (2, 3), and (4, 4), which are not on a straight line.
The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.
What is linear equation?
Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable.
Given, the equation y = 2x -4
Which is linear function and have y a dependent variable and x be the independent variable,
because value of y depends upon the value of x.
Hence, a is the correct answer.
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Answer: A
Step-by-step explanation: Trust me
Use a calculator to perform the indicated operations. Round the result to two decimal places.
[tex]
19.42-34.8(19.3)+10.23+5.78
[/tex]
Using PEMDAS to solve the mathematical expression, the result is -637.947
Mathematical OperationThe mathematical operation refers to calculating a value using operands and a math operator. The symbol of the math operator has predefined rules to be applied to the given operands or numbers.
In this kind of problem, we need to use the PEDMAS rule which is
Parenthesis, Exponents, Division, Multiplication, Addition and Subtraction.
The order in which this must be prioritized is from parenthesis and the least is subtraction.
Applying PEMDAS to this mathematical operation, we would have
19.42 - 34.89(19.3) + 10.23 + 5.78
Using a calculator which follows this rule, we would have;
19.42 - 34.89(19.3) + 10.23 + 5.78 = -637.947
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Under his cell phone plan, liam pays a flat cost of $69. 50 per month and $5 per gigabyte. He wants to keep his bill under $90 per month. Write and solve an inequality which can be used to determine xx, the number of gigabytes liam can use while staying within his budget.
The inequality given by 69.50 + 5x ≤ 90 and the maximum gigabyte he can buy is 4.1.
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
Let the number of gigabytes consumed be x,
The total cost per month will be 69.50 + 5x
accoding to the question the bill would not exceed $90.
So the inequality,
69.50 + 5x ≤ 90
Simplification for the maximum gigabyte he can buy,
5x ≤ 90 - 59.90
5x ≤ 20.5
x ≤ 4.1
Hence, the required inequality is given by 69.50 + 5x ≤ 90 and the maximum gigabyte he can buy is 4.1.
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The best fitting line is one where the intercept of the regression equation: a, is closest to zero. slope of the regression equation,
b, is closest to zero. residual sum of squares is closest to zero.
c. variance of Y is large.
The best fitting line is one where the intercept of the regression equationrResidual sum of squares is closest to zero. So the option c is correct.
In the given question,
The best fitting line is one where the intercept of the regression equation:
Intercept of the regression equation, a, is closest to zero. Slope of the regression equation, b, is closest to zero. Residual sum of squares is closest to zero.variance of Y is large.As we know that;
The slope of the line of best fit is the coefficient in a simple regression with a single independent variable. The slope is a mixture of the two coefficients in this example and in any regression with two independent variables. The y-intercept of the line of best fit is constant C.
So, the best fitting line is one where the intercept of the regression equationrResidual sum of squares is closest to zero. So the option c is correct.
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