Answers
The geometric center of the graph under the function is 5/3
How to determine the geometric center of the graph under the function?The equation of the function is given as:
f(x) = 3 - |x - 2|
The interval is given as:
x ∈ [0, 3]
The geometric center (gc) of the graph under the function is calculated using
gc = ∫x f(x) dx/∫f(x) dx
Substitute the known values in the above equation
gc = ∫x * (3 - |x - 2|) dx/∫3 - |x - 2| dx
Integrate the numerator and the denominator of the above equation
gc = [-1/6(x - 2)((2|x -2| - 9)x + 2|x - 2| - 18)]/[3x - 1/2[|x - 2|(x - 2)]]
Recall that the interval is given as x ∈ [0, 3]
Substitute the interval values in the above equation.
The equation is then simplified using a graphing calculator.
So, we have
gc = (65/6)/(13/2)
Express the quotient expression as a product
gc = (65/6) * (2/13)
Divide 65 by 13
gc = 5/6 * 2
Divide 2 by 6
gc = 5/3
Hence, the geometric center of the graph under the function is 5/3
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Related Questions
Given the drawing as shown below and that plla, name a pair of
alternate interior angles.
le
A
B
C
D
Lc = 4f
Zb and Ze
Zd=48
Zd= Le
d
do
8
9
Answers
Answer:
Angle D & Angle E
Step-by-step explanation:
Angle C & Angle F are ALTERNATE EXTERIOR angles.
Angle B & Angle E are CONSECUTIVE angles.
Angle D & Angle G are CORRESPONDING angles.
15) Allie Young has to get a new car because someone hit and destroyed her old one. She feels she can afford to
pay $90 each month, and the best loan terms she has found offer her an 8.33 percent interest rate on a 4-year
loan. What is the maximum value of the car Allie should be looking for? Give answer to nearest hundred dollars.
a.) $3900
b.) $3800
c.) $3600
d.) $3700
Answers
Answer:I beleive the answer is c-3600
Step-by-step explanation:
90$ a month for 48 months=4320
Plus the interest rate of 8.33 so 4320x0.833=3598.56
Then you have to round up from 3598.56 to the nearest 100 dollars, so it would be 3600.
What is the equation of the line in slope-intercept form?
Answers
[tex]y=\frac{3}{5}x+3[/tex]
Step-by-step explanation:Slope-intercept form is the most common form of a linear function.
Formula
The formula for slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. In this question, we must find both m and b by looking at a graph.
Slope
The slope is the change in y over the change in x. So, one way to find the slope is to identify 2 points on the graph and count the difference between them.
For example, the points (-5,0) and (0,3). First, the y-value increases by 3. Then, the x-value increases by 5. This gives us the final slope, [tex]\displaystyle\frac{3}{5}[/tex].Another way to find the slope is to use the formula [tex]\displaystyle\frac{y_{2}- y_{1} }{x_{2}- x_{1} }[/tex]. You can plug in the values from both points and solve to get the same answer.
Y-Intercept
The y-intercept is easy to find from a graph. The y-intercept is wherever the line intersects with the y-axis (the vertical axis). In this case, the line intersects at y-value 3. So, 3 is the b-value in the equation.
Final Equation
Using the information above, we can say that the equation of the line in slop-intercept form is [tex]y=\frac{3}{5}x+3[/tex].
Tim wants to build a rectangular fence around his yard. He has 42 feet of fencing. If he wants the length to be twice the width. What is the largest possible length
Answers
Answer: The largest he can possibly build is x = 14
Step-by-step explanation:
ramon is a parking lot attendant. he estimates that 30% of the cars in the lot are sedans, 10% are minivans, and 20% are suvs. he designs a simulation. let 0,1, and 2 represent sedans. let 3 represent minivans. let 4 and 5 represent suvs. let 6,7,8 and 9 represent other cars. the table show the simulation results. what is the probability that at least one of the next four cars the enter the lot is a sedan?
Answers
The probability that the nest set of cars that would enter the lot is a sedan is given as 80 percent
How to solve for the probabilityThe total number of trials can be seen to be 20 in number. The numbers that represents the sedan are 0, 1, 2
Now we would have to count the number of trials in these 20 that have 0, 1, 2
In the table we have 16 of these 0, 1 or 2 numbers
Hence we would have
16 /20
= 0.8
= 80 percent
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Find the recursive rule for the following sequence. -3, 2, 7, 12, 17,
Answers
Answer:
+5
Step-by-step explanation:
There is a length of 5 between all numbers, meaning that 5 is added to each number to get the next one.
I hope this helps!
Find the area of the region enclosed by the curves yequals
xsquaredminus2x
and yequals
minusxsquaredplus2
x.
Answers
The area enclosed by the given 2 curves is; 8/3 or 2.67
How to Solve Integration with Limits?We want to find the area enclosed by the curves;
y = x² - 2x
y = -x² + 2x
The point of intersection of the parabola and the line is given by;
x² - 2x = -x² + 2x
2x² - 4x = 0
Solving this gives;
x = 0, 2
Therefore, the area bounded by the parabola and the line between x = 0 and x = 2 is given as;
A = ∫₀² (-x² + 2x - x² + 2x)
A = ∫₀² (-2x² + 4x)
Using online integration calculator here gives;
A = 2.67
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What is the simplified form of the quantity of x plus 6, all over the quantity of x plus 4 + the quantity of x minus 3, all over 3 ? (2 points) the quantity of x squared plus 3x minus 18, all over 3 times the quantity of x plus 4 the quantity of x squared plus 4x plus 6, all over the quantity of x plus 7 the quantity of x squared plus 3x minus 18, all over the quantity x plus 7 the quantity of x squared plus 4x plus 6, all over 3 times the quantity of x plus 4
Answers
The simplified expression of the given equation is [tex]\frac{x^{2} + 4x + 6}{3x + 12}[/tex]
There are three basic steps for addition or subtraction of two fractions
Step 1: Make sure the bottom numbers (the denominators) are the sameStep 2: Add the top numbers (the numerators), put that answer over the denominatorStep 3: Simplify the fraction (if possible)The given expression :- [tex]\frac{x+6}{x+4} +\frac{x-3}{3}[/tex]
Taking LCM or making the denominators same we get,
= {3(x+6) + (x-3)(x+4)}/3(x+4)
= {3x + 18 + x² +x -12}/3(x+4)
={x² + 4x + 6}/3x + 12
= [tex]\frac{x^{2} + 4x + 6}{3x + 12}[/tex]
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Answer:
i believe its B
Step-by-step explanation:
Simplify (x + 5)2 using the square of a binomial formula.
x² + 10x + 25
x²-10X-25
x²-10x+25
x² + 10x - 25
Answers
Answer:
[tex]x^2 + 10x + 25[/tex]
Step-by-step explanation:
Hello!
Formula: [tex](a +b)^2 = a^2 + 2ab + b^2[/tex]
a = xb = 5Plug it into the formula and simplify.
Simplify[tex](a +b)^2 = a^2 + 2ab + b^2[/tex][tex](x +5)^2 = x^2 + 2(x)(5) + 5^2[/tex][tex](x +5)^2 = x^2 + 10x + 25[/tex]The answer is the first option: [tex]x^2 + 10x + 25[/tex].
Answer:
x^2-10x+25
Step-by-step explanation:
This is the correct answer
You deposit $2000 in an account earning 2% interest compounded monthly. How much will you have in the account in 10 years?
Answers
Answer:Principal P = 2000
Amount= A
years=n 10.00
compounded 12 times a year t
Rate = 2.00 0.02
Amount = P*((n+r)/n)^n*t
Amount = = 2000 *( 1 + 0.02 /t)^ 10 * 12
Amount = 2000 *( 1 + 0 )^ 120
2000 *( 1 )^ 120
Amount = 2442.4
Step-by-step explanation:
The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65° E, and the two towers are 31 kilometers apart. A fire spotted by rangers in each tower has a bearing of N 80° E from the Pine Knob and S 70° E from Colt Station (see figure). Find the distance of the fire from each tower. (Round your answers to two decimal places.)
From Pine Knob:
Answers
The equation that can be used to find the height of the tree is as follows:
[tex]\frac{h}{sin 29} =\frac{40}{sin147}[/tex]
The height of the tree is 35.6 m
How to use sine rule to find height of the tree?Th equation that can be used to find the height of the tree uses the principle of sine rule.
Therefore,
[tex]\frac{h}{sin 29} =\frac{40}{sin(180-4-29)}[/tex]
[tex]\frac{h}{sin 29} =\frac{40}{sin147}[/tex]
Therefore,
[tex]\frac{h}{sin 29} =\frac{40}{sin147}[/tex]
cross multiply
h sin 147 = 40 sin 29°
h = 40 sin 29° / sin 147
h = 19.3923848099 / 0.54463903501
h = 35.6015636045
h = 35.6 m
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A study showed that low-intensity shock therapy reduces pain levels in patients with lupus. During each session, electrodes were placed on the pain site indicated by the patient. Pain reduction was measured through self-reporting after each session.
Another study is being designed to examine whether low-intensity shock therapy also reduces pain in patients suffering from bulging disks in the thoracic region of the back. Two hundred female patients are subjects in the new study.
Part A: What is an appropriate design for the new study? Include treatments used, method of treatment assignment, and variables that should be measured. (4 points)
Part B: If the study consisted of 100 male and 100 female patients instead of 200 female patients, would you change the study design? If so, how would you modify your design? If not, why not? (4 points)
Part C: Could your design be double-blind? Explain. (2 points)
Answers
The experiment is illustrated below.
How to explain the experiment?A. The type of experimental design is a completely randomized design experiment where experimental units of 200 female subjects which are allocated randomly to say 4 treatment groups with each treatment group consist of 50 female patients.
Here the treatment used is low-intensity shock therapy which is also factor or explanatory variable. After administrating above treatment for a period of say 2-3 weeks, the response in pain reduction can be measured among all patients in 4 treatment groups by comparing their earlier pain level for reduction in pain.
If the study consist of 100 male and female patients, the experimental design can be changed into randomized block design by blocking subjects by gender.
The above design can be double blinded by not letting either the patients or lab technicians aware about which treatment groups, each of these subjects are experimented against to keep the data confidential.
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The cost price was $10000 she made a down payment of 2500 and agreed to pay the balance in 24 monthly installments of $350 how much did Jen pay for microwave?
Answers
Answer:
in total she spent 10900
Step-by-step explanation:
We know she made a down payment of 2500 dollars and she agreed to pay the balance in 24 monthly installments of 350 dollars. Thus we can do simple multiplying of 24 x 350 which gives us 8400. We also need to add in her down payment which is 2500 so in total we got 10900
Interior and exterior triangle angles
Answers
Answer:
Step-by-step explanation:
f(x)= x+28/x-7 for inverse functions
Answers
The inverse function of the given function is [tex]\mathbf{= \dfrac{28+7x}{x-1}}[/tex]
What is the inverse of a function?A function g is the inverse of a function f, if and only if the values of y= f(x), x = g(y).
From the formula given:
[tex]\mathbf{y=f(x) = \dfrac{x+28}{x-7}}[/tex]
Let's substitute x with y;
[tex]\mathbf{y= \dfrac{x+28}{x-7}}[/tex]
[tex]\mathbf{x=\dfrac{y+28}{y-7}}[/tex]
Solve for y;
[tex]\mathbf{= \dfrac{28+7x}{x-1}}[/tex]
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Solve for x if sqrt (3x-8) + 1 = sqrt (x+5)
Answers
The solution of x in the given expression [tex]\mathbf{\sqrt{(3x-8)}+1 = \sqrt{(x+5)}}[/tex] is 4. However, if it is [tex]\mathbf{\sqrt{(3x-8)+1} = \sqrt{(x+5)}}[/tex], it is 6.
What is the solution to algebraic expression?The solution to the given algebra expression involving surds can be seen in the steps below.
Given that:
[tex]\mathbf{\sqrt{(3x-8)}+1 = \sqrt{(x+5)}}[/tex]
Remove the square roots, we have:
12x - 32 = 4x² - 48x + 144
Solving the quadratic equation at the RHS and equating it to LHS, we have:
x = 11, x = 4
Verifying the solutions by replacing the value of x with the given equation:
x = 11 Falsex = 4 TrueTherefore, we can conclude that the value of x = 4
NOTE:
Given that:
[tex]\mathbf{\sqrt{(3x-8+1)} = \sqrt{(x+5)}}[/tex]
Square both sides
3x - 7 = x +5
Solve for x
3x - x = 5 + 7
2x = 12
x = 6
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How would you describe the difference between the graphs of f(x) = 2x² and
g(x) = -2x²?
O A. g(x) is a reflection of f(x) over the line y = x.
B. g(x) is a reflection of f(x) over the line y = -1.
C. g(x) is a reflection of f(x) over the y-axis.
D. g(x) is a reflection of f(x) over the x-axis.
Answers
Answer:
D. g(x) is a reflection of f(x) over the x-axis.
Step-by-step explanation:
So when you have the equation: [tex]-2x^2[/tex] it's just negating the value of f(x), which is [tex]2x^2[/tex] and since f(x) represents the y-value, you're negating the y-value and the x-value is unchanged. So each point on f(x) was originally: (x, f(x)) and now it's (x, -f(x)). Since the y-value is changing, it's going to be reflecting across the x-axis. So g(x) is a reflection of f(x) over the x-axis.
what is the volume of the following rectangular prism
Answers
Answer:
[tex] \large{ \boxed{ \tt{336 \: units ^{3} }}}[/tex]- Please see the attached picture for full solution!:)
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Does this appear to be a regular polygon? Explain.
Answers
Answer:
Yes
Step-by-step explanation:
All sides and angles look equal and appears to be a regular hexagon
Hope this helped and have a good day
Answer:
Yes.
Step-by-step explanation:
Hello!
A regular polygon is a closed shape with sides of equal length, and angles of equal degree. A regular polygon also forms around a general center.
This seems to be a regular polygon as all side lengths and angles seem to be equivalent, and there is a center point to the .
This shape is a hexagon, so the measure of the angles are 120°.
Use a graphing calculator or other technology to write the quadratic equation that best fits the data set. X 0 -1 -2. y 3 -3 -5
Answers
The quadratic equation of the data is y = 7x^2 + 13x + 3
How to determine the quadratic equation?The table of values is given as:
X 0 -1 -2.
y 3 -3 -5
When the above values are added to the graphing calculator, we have the following summary
a = 7
b = 13
c = 3
A quadratic equation is represented as:
y = ax^2 + bx + c
So, we have:
y = 7x^2 + 13x + 3
Hence, the quadratic equation of the data is y = 7x^2 + 13x + 3
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Five times a number decreased by nine is equal to twice the number increased by 23. Which equation could be used to solve the problem?
Answers
Answer:
The equation is 5x - 9 = 2x + 23.
The answer is option A.
Step-by-step explanation:
what is the measure of this
Answers
Answer:
60
Step-by-step explanation:
140-80=60
A rock is dropped from a height of 100 feet. Calculate the time between when the rock was dropped and when it landed. If we choose "down" as positive and ignore air friction, the function is h (t) = 36t2 - 64
t= 3.56 seconds
t= 1.78 seconds
t= 1.33 seconds
t= 8 seconds
Answers
The time it takes between when the rock was dropped and when it landed is 1.33 seconds.
What is the time it takes for the rock to land?The time it takes the rock to land on the ground from where it is dropped can be determined by using the function given.
The height of the function when it hits the ground will be zero, so the function can be written as:
[tex]\mathbf{h(t) =36t^2 -64}[/tex]
[tex]\mathbf{0 =36t^2 -64}[/tex]
64 = 36t²
[tex]\mathbf{t^2 = \dfrac{64}{36}}[/tex]
t² =1.778
[tex]t = \sqrt{1.778}[/tex]
t = 1.333 seconds
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Assume that two fair dice are rolled. First compute P(F) and then P(FIE). Explain why one would expect the
probability of F to change as it did when the condition that E had occurred was added.
E: a three shows on at least one of the dice
F: the total is less than eight
...
Answers
The probability that a three shows on at least one of the dice is 11/36.
How to calculate the probability?It should be noted that of probability means the likelihood of the occurence of an event.
The probability that a three shows on at least one of the dice will be:
= 11/36
This can be seen from the table that is attached.
The probability that the total is less than 8 will be:
= 21/36
= 7/12
Here, there are 21 places where the total is less than 8.
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If $11,000 is invested in an account for 25 years. Find the value of the investment at the end of 25 years if the interest is:
Answers
If $11,000 is invested, $33,000 is the value of the investment at the end of 25 years if the interest is 8% simple interest and $75,333.23 is the value of the investment at the end of 25 years if the interest is 8% compounded annually. This can be obtained by using formulas for simple interest and compound interest.
What is the formulas of simple interest and compound interest?Simple interestA = P(1 +Rt/100) , P = principle amount ,R = rate of interest, t = time(in years)
Compound interest (annually)A = P(1 + R/100)^t , P = principal amount, R = rate of interest, t = time(in years)
What is the value of investment?
Given that,
P = $11,000 , R = 8%, t = 25 years
8% simple interestA = P(1 +Rt/100) = [tex]11000(1+\frac{(8)(25)}{100} )[/tex] = $33,000
8% compounded annuallyA = P(1 + R/100)^t = [tex]11000(1+\frac{8}{100} )^{25}[/tex] = [tex]11000(1.08 )^{25}[/tex] = $75,333.23
Hence If $11,000 is invested, $33,000 is the value of the investment at the end of 25 years if the interest is 8% simple interest and $75,333.23 is the value of the investment at the end of 25 years if the interest is 8% compounded annually.
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: If $11,000 is invested in an account for 25 years. Find the value of the investment at the end of 25 years if the interest is:
(a) 8% simple interest
(b) 8% compounded annually
how many 150-pound gas cylinders are uesd each year at a 500 gpm well that fequires a chlorine dosage of 1.5 mg/L?
Answers
The number of 150-pound gas cylinders are used each year for the well is 22.
Total volume of gallons used per year
V = 500 gal/min x 1 year x 525600 min/year
V = 262,800,000 gallons = 994,806,216.835 liters
Mass of the gas cylindersmass = density x volume
mass = 1.5 mg/L x 994,806,216.835 L
mass = 1,492,209,325 mg = 3289.75 lb
number of gas cylinders usedn = 3289.75 lb/150 lb
n = 21.9
n ≈ 22 gas cylinders
Thus, the number of 150-pound gas cylinders are used each year for the well is 22.
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The function h(x) is a transformation of the square root parent function,
f(t) = t. What function is H(x)?
Answers
Answer:
A. [tex]h(x)=\sqrt{x-3}[/tex]
Step-by-step explanation:
Step 1: DefinitionThe parent function of [tex]\sqrt{x}[/tex] is translated to the left when [tex]h[/tex] is positive in the transformation [tex]\sqrt{x+h}[/tex].
If [tex]h[/tex] is negative, the graph translates towards the left with the distance equal to the value of [tex]h[/tex].
Step 2: ImplementationHere the graph moved 3 units towards the right. This means that [tex]h[/tex] is negative and has the value of 3.
So, plugging that into the parent function for translation, the function becomes:
[tex]h(x)=\sqrt{x-3}[/tex]
If 4x+2=5y+3 then y =
Answers
Answer:4x/5-1/5 = y
Step-by-step explanation:
We need to get y by itself
4x+2=5y+3
subtract 3 from both sides
4x-1=5y
divide both sides by 5
4x/5-1/5 = y
Answer:
[tex]4x + 2 = 5y + 3[/tex]
[tex]5y + 3 = 4x + 2[/tex]
[tex]5y = 5x + 2 - 3[/tex]
[tex]5y = 4x - 1[/tex]
[tex] \frac{5y}{5} = \frac{4x - 1}{5} [/tex]
[tex]y = \frac{4x - 1}{5} [/tex]
An advertiser claims that 74% of people stream their TV, 12% have cable, and the rest do not watch TV. A test is conducted to evaluate the claim and the conclusion is fail to reject
using alpha = 0.1. What is your interpretation of the test result?
Answers
Considering the hypothesis tested, the interpretation is that there is not enough evidence to conclude that the percentages are different at a significance level of 0.1.
What are the hypothesis tested?At the null hypothesis, we test if the percentages are as advertised.At the alternative hypothesis, we test if the percentages are different than advertised.We fail to reject the null hypothesis, hence the interpretation is that there is not enough evidence to conclude that the percentages are different at a significance level of 0.1.
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Find the values of the variables in the parallelogram.
please help asap
tysm
Answers
Answer:
Step-by-step explanation: