Based on the amount of money that Jerl had and then the amount that she put away, the possible values of the number of dollars in the original pile of money was ( 200, 440).
What was the amount in the original pile?The amount that was above $200 that she found can be x which means that the greater side of the inequality is:
= 200 + x
She then gave away $80:
= 120 + x
She gave away 1/3 of the money so the amount left is:
= 2/3 x (120 + x)
The lesser side of the inequality:
(x + 2) - 200 = x
So then:
((120 + x) x 2) / 3 > x
240 + 2x > 3x
240 > x
x < 240
The interval that shows the possible values of the original pile of money is therefore:
( 200, 440)
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If the first and the last term of an arithmetic progression, with common difference
[tex]1 \times 1\frac{1}{2} [/tex]
, are
[tex]? \times 2\frac{1}{2} [/tex]
and 19 respectively, how many term has the sequence?
The number of terms in the given arithmetic sequence is n = 10. Using the given first, last term, and the common difference of the arithmetic sequence, the required value is calculated.
What is the nth term of an arithmetic sequence?The general form of the nth term of an arithmetic sequence is
an = a1 + (n - 1)d
Where,
a1 - first term
n - number of terms in the sequence
d - the common difference
Calculation:The given sequence is an arithmetic sequence.
First term a1 = [tex]1\frac{1}{2}[/tex] = 3/2
Last term an = [tex]2\frac{1}{2}[/tex] = 5/2
Common difference d = 1/9
From the general formula,
an = a1 + (n - 1)d
On substituting,
5/2 = 3/2 + (n - 1)1/9
⇒ (n - 1)1/9 = 5/2 - 3/2
⇒ (n - 1)1/9 = 1
⇒ n - 1 = 9
⇒ n = 9 + 1
∴ n = 10
Thus, there are 10 terms in the given arithmetic sequence.
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Disclaimer: The given question in the portal is incorrect. Here is the correct question.
Question: If the first and the last term of an arithmetic progression with a common difference are [tex]1\frac{1}{2}[/tex], [tex]2\frac{1}{2}[/tex] and 1/9 respectively, how many terms has the sequence?
which function describes this table of value x -8, -4, 4, 8, y -2, 0, 4, 6
we conclude that the linear equation represented by the given table is:
y = (1/2)*x + 2
Which function is the one described by the table?A general linear equation is given by:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through (x₁, y₁) and (x₂, y₂), then the slope is given by:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we can use just the first two points on the given line:
(-8, -2) and (-4, 0)
Then the slope will be:
[tex]a = \frac{0 - (-2)}{-4 -(-8)} = \frac{2}{4} = \frac{1}{2}[/tex]
Then the linear equation is something like:
y = (1/2)*x + b
To find the value of b, we can use one of the two given points, I will use (-4, 0), then:
0 = (1/2)*(-4) + b
0 = -2 + b
2 = b
Then we conclude that the linear equation represented by the given table is:
y = (1/2)*x + 2
Then the correct option is the first one.
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d) The perimeter of room is 28 m. and the height is 3.5 m. Find the area of 4 walls.
it's hurry give me answer fast please
Answer: 98
Step-by-step explanation:
Area of four walls = Curved surface area
= perimeter × height
= 28 × 3.5
= 98 m square
Evaluate the integral. 3 f(x) dx −4 where f(x) = 3 if −4 ≤ x ≤ 0 4 − x2 if 0 < x ≤ 3
It looks like you have
[tex]f(x) = \begin{cases} 3 & \text{if } -4 \le x \le 0 \\ 4 - x^2 & \text{if } 0 < x \le 3\end{cases}[/tex]
and the integral you want to compute is
[tex]\displaystyle \int_{-4}^3 f(x) \, dx[/tex]
Split the integral up at [tex]x=0[/tex]. Then
[tex]\displaystyle \int_{-4}^3 f(x) \, dx = \int_{-4}^0 f(x)\,dx + \int_0^3 f(x)\,dx \\\\ ~~~~~~~~~~~~ = \int_{-4}^0 3 \, dx + \int_0^3 (4 - x^2) \, dx \\\\ ~~~~~~~~~~~~ = 3(0 - (-4)) + \left(4\cdot3 - \frac{3^3}3\right) = \boxed{15}[/tex]
After evaluating the integral we get 15
Integral is the representation of the area of a region under a curve. We approximate the actual value of an integral by drawing rectangles. A definite integral of a function can be represented as the area of the region bounded by its graph of the given function between two points in the line.
Given,
f(x) = 3 if - 4 ≤ x ≤ 0
f(x) = 4 - [tex]x^{2}[/tex] if 0 < x ≤ 3
Then,
[tex]f(x) = \left \{ {{3} \atop {4-x^{2} }}[/tex]
We need to solve the integral -[tex]\int\limits^3_4 {f(x)} \, dx[/tex]
Elaborate the integral with x = 0
-[tex]\int\limits^3_4 {f(x)} \, dx[/tex]
= -[tex]\int\limits^0_4 {f(x)} \, dx + \int\limits^3_0 {f(x)} \, dx[/tex]
= -[tex]\int\limits^0_4 {3} \, dx + \int\limits^3_0 {4-x^{2} } \, dx[/tex]
= 3 ( 0 - (-4)) + (4.3 - [tex]\frac{3^{3} }{3}[/tex])
= 15
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When followers' needs for______ are strong, it makes them vulnerable to the dictates of abusive leaders
When followers' needs for security and certainty, belonging, and feeling chosen or special are strong, it makes them vulnerable to the dictates of abusive leaders.
The epistemic attribute of beliefs that one cannot rationally reject is certainty, often known as epistemic certainty or objective certainty. Epistemic certainty is commonly defined as a belief being certain if and only if the person holding it could not be wrong in holding it.
In both public and private markets, securities are fungible, tradeable financial instruments used to raise capital.
The three main categories of securities are: equity, which gives holders ownership rights; debt, which is effectively a loan returned with recurring payments; and hybrids, which include features of both debt and equity.
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Maria was shopping for a camera and found one that was on sale for 30% off. As she went to pay for it, the store announced an instant sale that took an additional 10% off all items. If the final price Maria paid was $207.27, what was the original price (before all discounts) of the camera? Possible Answers: $290.18 $329.00 $518.18 $767.67 $82.91
Answer:
$329.00
Step-by-step explanation:
Let the original price be $x, then
x - 0.30x - 0.10(x - 0.30x) = 207.27
x - 0.30x - 0.10x + 0.03x = 207.27
0.63x = 207.27
x = 329.00.
Solve each pair of simultaneous equations by elimination method.
a) 2x+3y-1=0
5x+2y+3=0
Answer:
x = -1
y = 1
Step-by-step explanation:
PART I: Find the y-valueGiven expressions
1) 2x + 3y - 1 = 0
2) 5x + 2y + 3 = 0
Add 1 on both sides of the 1) equation:
2x + 3y - 1 + 1 = 0 + 1
2x + 3y = 1
Subtract 3 on both sides of the 2) equation:
5x + 2y + 3 - 3 = 0 - 3
5x + 2y = -3
Current System
1) 2x + 3y = 1
2) 5x + 2y = -3
Multiply 2.5 on both sides of the 1) equation
(2.5) 2x + (2.5) 3y = (2.5) 1
5x + 7.5y = 2.5
Current System
1) 5x + 7.5y = 2.5
2) 5x + 2y = -3
Subtract 2) equation from 1) equation
(5x + 7.5y) - (5x + 2y) = 2.5 - (-3)
Get rid of the parenthesis
5x + 7.5y - 5x - 2y = 2.5 + 3
Combine like terms
5x - 5x + 7.5y - 2y = 5.5
0 + 5.5y = 5.5
5.5y = 5.5
Divide 5.5 on both sides
5.5y / 5.5 = 5.5 / 5.5
[tex]\boxed{y=1}[/tex]
PART II: Find the x-valueSubstitute the y-value back to one of the equations to find the x-value
2x + 3y - 1 = 0
2x + 3(1) - 1 = 0
Combine like terms
2x + 3 - 1 = 0
2x + 2 = 0
Subtract 2 on both sides
2x + 2 - 2 = 0 - 2
2x = -2
Divide 2 on both sides
2x / 2 = -2 / 2
[tex]\boxed{x=-1}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Mean: about 25.1
Standard deviation: about 2.4
What is the z-score of the value 29,rounded to the nearest tenth
The z-score to the normal distribution table is 1.625
z-score of distribution tableThe standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is being observed or measured.
The formula for calculating the z-score is expressed as;
z = x-μ/σ
where
μ is the mean of the data
σ is the standard deviation
x is the value
Given the parameters
μ = 25.1
σ = 2.4
x = 29
Substitute the given parameters
z = 29-25.1/2.4
z = 3.9/2.4
z = 1.625
Hence the z-score to the normal distribution table is 1.625
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I will give you 10 pts if you teach me
Answer:
time required = 26 min
Step-by-step explanation:
To solve this, let's first list all the given information, and change the units to millimeters (mm) if required (because the discharge rate is given in mm/s):
○ diameter of pipe = 64 mm ⇒ radius = 32 mm
○ water discharge rate = 2.05 mm/s
○ diameter of tank = 7.6 cm = 76 mm ⇒ radius = 38 mm
○ height of tank = 2.3 m = 2300 mm.
Now, let's calculate the cross-sectional area of the pipe:
Area = πr²
⇒ π × (32 mm)²
⇒ 1024π mm²
Next, we have to calculate the volume of water transferred from the pipe to the tank per second. To do that, we have to multiply the pipe's cross-sectional area and the discharge rate of the water:
Volume transferred = 1024π mm² × 2.05 mm/s
⇒ 6594.83 mm³/s
Now. let's find the volume of the cylindrical tank using the formula:
Volume = π × r² × h
⇒ π × (38)² × 2300
⇒ 10433857 mm³
We know that 6594.83 mm³ of water is transferred to the tank every second, so to fill up 10433857 mm³ with water,
time required = [tex]\frac{10433857 \space\ mm^3}{6594.83\space\ mm^3/s}[/tex]
⇒ 1582.12 s
⇒ 1582.13 ÷ 60
≅ 26 min
Answer:
26 minutes
Step-by-step explanation:
The rate of filling the tank matches the rate of discharge from the pipe. Each rate is the ratio of volume to time. Volume is jointly proportional to the square of the diameter and the height.
VolumeFor some constant of proportionality k, the volume of discharge in 60 seconds from the pipe is ...
V = k·d²·h . . . . d = diameter; h = rate×time
V = k(0.64 dm)²(0.0205 dm/s × 60 s) = k·0.503808 dm³
For the tank, the height (h) is the actual height of the tank. The volume of the tank is ...
V = k(0.76 dm)²(23 dm) = k·13.2848 dm³
ProportionThen the proportion involving (inverse) rates is ...
time/volume = (fill time)/(k·13.2848 dm³) = (1 min)/(k·0.503808 dm³)
fill time = 13.2848/0.503808 min ≈ 26.369
__
Additional comments
1 dm = 100 mm = 10 cm = 0.1 m
1 dm³ = 1 liter, though we don't actually need to know that here.
We have used 1 decimeter (dm) as the length unit to keep the numbers in a reasonable range. We have worked out the rate numbers, but that isn't really necessary (see attached).
__
The value of k is π/4 ≈ 0.785398. We don't need to know that because the values of k cancel when we solve the proportion.
The population of a certain city can be modeled by the exponential * 1 poi
function below, where x represents the number of years since 2010. The graph for the function is also shown below. Which of the following statements are true? SELECT ALL THAT APPLY. I need help now please
The true statements about the functions are:
b. The population of the city in 2010 is 25000c. The rate at which the population decreases every year is 4% f. The function value would approach 0 as it decreasesHow to determine the true statement?The function is given as:
f(x) = 25000 * 0.96^x
Set x = 0 to determine the initial value of the function
f(0) = 25000 * 0.96^0
Evaluate
f(0) = 25000
This means that the population of the city in 2010 is 25000 i.e. option (B) is correct
Also, we have:
f(x) = 25000 * 0.96^x
The rate at which the population decreases every year is calculated as:
r = 1 - 0.96
Evaluate the difference
r = 0.04
Express as percentage
r = 4%
This means that the rate at which the population decreases every year is 4% i.e. option (C) is correct
The population after 5 and 10 years are:
f(5) = 25000 * 0.96^5
f(5) = 20384
f(10) = 25000 * 0.96^10
f(10) = 16621
Divide these populations by the initial population in 2010
20384/25000 = 82%
16621/25000 = 66%
This means that the population decreased by 82% and 66% in 5 years and 10 years since 2010, respectively.
So, options (d) and (e) are false
Lastly, because the population function is an exponential decay function;
The function value would approach 0 as it decreases
This means that option (f) is correct
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The table shows the temperature of a cooling cup of coffee.
Minutes 1 2 3 4
Temperature (degrees C) 97 95.1 93.2 91.3
What is the common ratio of the sequence? Express your answer as a decimal rounded to the nearest hundredth.
Write an explicit formula for the nth term of the sequence where n represents the number of minutes and T(n) represents the temperature of the coffee.
If the pattern continues, what will be the temperature of the coffee after 15 minutes? Express your answer as a decimal rounded to the nearest tenth.
Based on the given table, the common ratio, explicit formula and temperature of the coffee after 15 minutes is 0.98, Tn = 97 × 0.98^(n-1) and 73.1°C
Geometric sequenceCommon ratio, r = second minutes / first minutes
= 95.1 / 97
= 0.98041237113402
Approximately,
r = 0.98
nth term of the sequence, Tn = ar^n -1
Tn = 97 × 0.98^(n-1)
Temperature of the coffee after 15 minutes, T15 = 97 × 0.98^(n-1)
= 97 × 0.98^(15-1)
= 97 × 0.98^14
= 97 × 0.7536419414749019520643907584
= 73.1032683230654893502459035648
Approximately,
T15 = 73.1°C
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f(x)=4x^(3)+6x^(2 )-3x-4
g(x)=4x-3
Find (f - g) (x)
The value of (f - g)(x) is as follows:
(f - g)(x) = 4x³ + 6x² - 7x - 1
How to solve functions?f(x) = 4x³ + 6x² - 3x - 4
g(x) = 4x - 3
Let's find the function:
(f - g)(x)
Therefore,
(f - g)(x) = 4x³ + 6x² - 3x - 4 - ( 4x - 3)
Hence, let's open the bracket
(f - g)(x) = 4x³ + 6x² - 3x - 4 - 4x + 3
Let's combine like terms
(f - g)(x) = 4x³ + 6x² - 3x - 4x - 4 + 3
Therefore,
(f - g)(x) = 4x³ + 6x² - 7x - 1
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A candlemaker uses 240 cubic centimeters of wax to create a scented candle using a cylindrical mold. he decides to offer a larger-sized candle, which uses twice as much wax as the smaller-sized candle. which mold can he use to make the larger-sized candle?
The mold the candlemaker can use to make the larger-sized candle is 480 cubic centimeters.
CylinderA cylinder is a surface created by projecting a closed two-dimensional curve along an axis intersecting the plane of the curve.
smaller-sized candle = 240 cubic centimeterslarger-sized candle = 2(smaller-sized candle)
= 2(240 cubic centimeters)
= 480 cubic centimeters
Therefore, the mold the candlemaker can use to make the larger-sized candle is 480 cubic centimeters.
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Answer:
A cylinder with a height that is double the height of the original mold, and a radius that is the same as the radius of the original mold.
Hope this helps!
Step-by-step explanation:
Machine a can make 350 widgets in 1 hour, and machine b can make 250 widgets in 1 hour. if both machines work together, how much time will it take them to make a total of 1000 widgets?
If machine a can make 350 widgets in 1 hour and machine b can make 250 widgets in 1 hour then by forming equation we will get that both machines have to work for one hour and 40 minutes to make 1000 widgets.
Given that machine a can make 350 widgets in 1 hour, and machine b can make 250 widgets in 1 hour.
How much time will both machines take to make 1000 widgets?
Suppose the time taken by both machines be x hours. Time is equal because both the machines need to work together.
According to the question the equation will be as under:
350x+250x=1000
600x=1000
x=1000/600
x=10/6
x=5/3
x=1.67
Converting 0.67 to minutes 0.67*60=40.2
Adding will result 1 hour and 40 minutes.
Hence if machine a can make 350 widgets in 1 hour and machine b can make 250 widgets in 1 hour then by forming equation we will get that both machines have to work for one hour and 40 minutes to make 1000 widgets.
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4x+10=-2x + 4
y - 4 (2y - 5) = -4
Solve the 2 equations
(ignore image)
The solutions to the equations are x = 7/3 and y = 24/7
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
4x + 10 = -2x + 4
y - 4(2y - 5) = -4
Considering the first equation
4x + 10 = -2x + 4
Collect the like terms
4x + 2x = 10 + 4
Evaluate the like terms, by adding them
6x = 14
Divide both sides of the equation by 6
x = 7/3
Considering the second equation
y - 4(2y - 5) = -4
Expand the bracket in the above equation
y - 8y + 20 = -4
Collect the like terms
y - 8y = -20 -4
Evaluate the like terms, by adding them
-7y = -24
Divide both sides of the equation by -7
y = 24/7
Hence, the solutions to the equations are x = 7/3 and y = 24/7
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Consider this quadratic equation.
2x²2²-1=3x+4
Which equation correctly applies the quadratic formula?
COA
OB.
OC.
OD.
2=
H=
H=
-(-3) ± √(-3)²-4(2)(-5)
-(-3);
2
-(-3) ± √(-3)²-4(-5)
(2)
-(-3) ± √(-3)²(2)(-5)
(2)
-(-3) ± √(-3)²-4(2)(-5)
2(2)
Answer:
-(-3) ± √(-3)^2 - 4(2)(-5) / 2(2) (the last choice).
Step-by-step explanation:
Im ignoring the 2^2 in the equation
The equation transforms to
2x^2 - 3x - 5 = 0 (standard form)
So x = -(-3) ± √(-3)^2 - 4(2)(-5) / 2(2)
Draw a diagram to show that the square root of 121 is 11.
Answer:
i think this may help you
The diagram to show that the square root of 121 is 11 attached below
What is a perfect square?A perfect square is a number system that can be expressed as the
square of a given number from the same system.
Assume that x-a be the closest perfect square less than x,let x+b be the closest perfect square more than x, then we get: x-a < x < x+b (no perfect square in between x-a and x+b, except possibly x itself).
Then, we get:
[tex]\sqrt{x-a} < \sqrt{x} < \sqrt{x+b}[/tex]
Thus, [tex]\sqrt{x-a} and \sqrt{x+b}[/tex] are the closest integers, less than and more than the value of {x}. (assuming x is non-negative value).
Herewe are given the number as 121
It is perfect root then ;
√121 = 11
The solution that show that the square root of 121 is 11 attached below
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Which inequality is represented by the graph below? Check all that apply. A number line going from 4 to 14. An open circle is at 9. Everything to the left of the circle is shaded. x greater-than 9 x less-than 9 any rational number greater than or including 9 any rational number less than or including 9 any rational number greater than 9 any rational number less than 9
the correct inequality is"any rational number less than 9"
x < 9
Which inequality is represented by the graph?Remember that when we have a number line, an open circle means that we can use the symbols > or <.
While a closed circle uses the symbols ≤ or ≥.
Here we know that we have an open circle at 9, ant everything to the left of the circle is shaded.
To the left of 9 there are the numbers smaller than 9, then the inequality would be:
x < 9
Then the correct option is "any rational number less than 9"
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Answer: x<9
any rational number less than 9"
Step-by-step explanation:
Out of the total respondents, the percentage of respondents from the 46–55 age group who rated the film excellent is %. write your answer up to two decimal places.
Missing data:
Viewer's Age Group Excellent Good Average Poor Marginal Total
16–25 52 42 12 7 113
26–35 33 50 5 9 97
36–45 58 12 28 34 132
46–55 25 17 22 12 76
56 + 12 5 3 8 28
Marginal Total 180 126 70 70 446
A rating of good or excellent indicates the audience liked the movie, while a rating of poor indicates the audience disliked the movie.
How to determine the rating of the film from the 46–55 age group?A movie producer accomplished a survey behind a preview screening of her latest movie to estimate how the film would be accepted by viewers from various age groups. The table displays the numbers of viewers in various age groups who ranked the film excellent, good, average, and poor.
25/446 = 0.05605
0.05605 [tex]*[/tex] 100% = 5.605%
Out of the entire respondents, the percentage of respondents from the 46–55 age group who ranked the film excellent exists at 5.605%.
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If a2 = i, where i is the identity matrix, which matrix correctly represents matrix a?
[tex]A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]
We can find the A as shown below:
Given A^2=I
We know that A^2=A×A
And [tex]I=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]
So, [tex]A^2=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]
Let [tex]A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]
[tex]A^2=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right] \left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]
[tex]A^2=\left[\begin{array}{ccc}9-8&-6+6\\12-12&-8+9\end{array}\right][/tex]
[tex]A^2=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]
Hence, [tex]A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]
Hence, option C is correct
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Disclaimer: Given question is incomplete. Complete question is attached.
What is 6x^2 + 4(x^2 - 1)? Like terms.
The value of x for the given equation is 0.632 and -0.632.
According to the statement
We have given that the equation and we have to a find the value of the x.
So, The given quadratic equation are:
Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power solve for x in the quadratic equation
The given terms are
[tex]6x^2 + 4(x^2 - 1) = 0[/tex]
Solving the equation the the outcome equation is
[tex]6x^2 + 4x^2 - 4 = 0\\10x^2 - 4 = 0\\10x^2 = 4\\x^2 = 4/10[/tex]
The value of x is 0.632 and -0.632.
So, The value of x for the given equation is 0.632 and -0.632.
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5. Which point is a solution to this system of equations.
(3x - y = 7
(2x + 3y = 1
O (2,-1)
0 (2,1)
O (-2,-1)
O (-2,1)
Answer:
(2, - 1 )
Step-by-step explanation:
3x - y = 7 → (1)
2x + 3y -= 1 → (2)
multiplying ( 1) by 3 and adding to (2) will eliminate y
9x - 3y = 21 → (30
add (2) and (3) to eliminate y
11x = 22 (divide both sides by 2 )
x = 2
substitute x = 2 into either of the 2 equations and solve for y
substituting into (2)
2(2) + 3y = 1
4 + 3y = 1 (subtract 4 from both sides )
3y = - 3 ( divide both sides by 3 )
y = - 1
solution = (2, - 1 )
pls help me urgent pls help me
The answers to the questions are:
43.22 minutes15 km/hr6 km0.37 = 37/1000.086 = 86/1000What is distance?This defined as the total number of points that a person has been able to cover at a given period. It is calculated by taking the time and the speed of takeoff into consideration. The speed that a person used and the time it took them to get to their destination is what is used to calculate distance
The time it takes for sunlight to reach is given as
distance/speed
778000000000/300000000
=2593.33 * 60
= 43.22 minutes
The formula for distance is given as speed * time
speed = 15km/hr
time = 1 hour
The distance = 15 * 1
= 15 km/hr
If the time is 2*1/2
the distance = 15 / 2.5
= 6 km
Expressed as a fraction we have the following
0.37 = 37/100
0.086 = 86/1000
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Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. y = 2 x , y = 2 x2 , x = 4
The region enclosed by the given curves are integrated with respect to x and the area is 4.2724 square units.
In this question,
The curves are y = 2/x, y = 2/x^2, x = 4
The diagram below shows the region enclosed by the given curves.
From the diagram, the limit of x is from 1 to 4.
The given curves are integrated with respect to x and the area is calculated as
[tex]A=\int\limits^4_1 {\frac{2}{x} } \, dx -\int\limits^4_1 {\frac{2}{x^{2} } } \, dx[/tex]
⇒ [tex]A=2[\int\limits^4_1 {\frac{1}{x} } \, dx -\int\limits^4_1 {\frac{1}{x^{2} } } \, dx][/tex]
⇒ [tex]A=2[\int\limits^4_1( {\frac{1}{x} } - {\frac{1}{x^{2} } } )\, dx][/tex]
⇒ [tex]A=2[lnx-\frac{1}{x} ] \limits^4_1[/tex]
⇒ [tex]A=2[(ln4-\frac{1}{4} )-(ln1-\frac{1}{1} )][/tex]
⇒ A = 2[(1.3862-0.25) - (0-1)]
⇒ A = 2[1.1362 + 1]
⇒ A = 2[2.1362]
⇒ A = 4.2724 square units.
Hence we can conclude that the region enclosed by the given curves are integrated with respect to x and the area is 4.2724 square units.
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What is the z-score of the value 55.2?
Chris buys 4 more shirts than p number of pants. Shirts cost $18 each and pants cost $25 each. What does each term in the expression 25p+18(p+4) represent? What does the entire expression represent?
The expression 25p+18(p+4) represents the total amount spent on shirts and pants
How to interpret the terms of the expression?The given parameters are:
Shirts = 4 more than pants (p)
Cost of shirt = $18
Cost of pant = $25
The above means that:
p + 4 represents the number of shirts Chris buys, while p represents the number of pants
The terms of the expression 25p + 18(p+4) are
25p and 18(p+4)
This means that:
25p = The total cost of pants
18(p+4) = The total cost of shirts
Hence, the expression 25p+18(p+4) represents the total amount spent on shirts and pants
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Consider the line y equals 2 over 5 x plus 4.
Find the equation of the line that is parallel to this line and passes through the point left parenthesis 5 comma negative 1 right parenthesis.
the parallel linear equation is:
y = (2/5)*x - 3
How to find the parallel line?Two lines are parallel if the lines have the same slope but different y-intercept.
Here we know the line equation:
y = (2/5)*x + 4
Then a parallel line is of the form:
y = (2/5)*x + c
Where c is different than 4.
We want this line to pass through (5, -1), then:
-1 = (2/5)*5 + c
-1 = 2 + c
-1 - 2 = -3 = c
Then the parallel linear equation is:
y = (2/5)*x - 3
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A positive five-digit integer is in the form ; where , and are each distinct digits. What is the greatest possible value of that is divisible by eleven
The the biggest 5 digit number based on the computation will be 87,978.
How to compute the value?The difference between the sum of the odd-numbered digits (1st, 3rd, 5th...) and the sum of the even-numbered digits (2nd, 4th...) is divisible by 11.
An example is that 34871903 is divisible by 11
3+8+1+0=12
4+7+9+3=23
23-12=11
Here, we want (b + b) - (a + c + a) to be divisible by 11.
2b - (2a + c) to be divisible by 11
ab,cba (using 7 and 8 and 9 since they biggest)
78 987 --> 2*8 - (2*7 + 9) = 16 - (14 + 9) = 16 - 23 = -7 NO
87 978 --> 2*7 - (2*8 + 9) = 14 - (16 + 9) = 14 - 25 = -11 YES
79 897 --> 2*9 - (2*7 + 8) = 18 - (14 + 8) = 18 - 22 = -4 NO
97 879 --> 2*7 - (2*9 + 8) = 14 - (18 + 8) = 14 - 26 = -12 NO
89 798 --> 2*9 - (2*8 + 7) = 18 - (16 + 7) = 18 - 23 = -5 NO
98 789 --> 2*8 - (2*9 + 7) = 16 - (18 + 7) = 16 - 25 = -9 NO
Therefore, the biggest 5 digit number is 87,978.
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What is the product?
StartFraction 4 n Over 4 n minus 4 EndFraction times StartFraction n minus 1 Over n + 1 EndFractiontartFraction 2 Over x EndFraction
Based on the given task content; the product of StartFraction 4 n Over 4 n minus 4 EndFraction times StartFraction n minus 1 Over n + 1 EndFractiontartFraction 2 Over x EndFraction is (4n² - 8n) / (4n²x - 5nx - x)
ProductProduct of numbers refers to the multiplication of two or more values to arrive at a single result.
4n / (4n - 1) × (n - 1) / (n + 1) 2/x
= 4n / (4n - 1) × 2(n - 1) / x(n + 1)
= 4n / (4n - 1) × (2n - 2) / (nx + x)
= 4n(2n - 2) / (4n - 1) (nx + x)
= 4n² - 8n / (4n²x - 4nx - nx - x)
= (4n² - 8n) / (4n²x - 5nx - x)
Therefore, the product of 4n / (4n - 1) × (n - 1) / (n + 1) 2/x is (4n² - 8n) / (4n²x - 5nx - x)
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what do I check off