Step-by-step explanation:
first term =6(a)
last term =750(b(
we know
m=a+b/2
or,m=6+750/2
or, m=756/2
or,
m =378
Describe the similarities and differences between solving an absolute value equation and solving an absolute value inequality.
Similarities and differences between solving an absolute value equation and solving an absolute value inequality are shown below.
Similarities and differences between solving an absolute value equation and solving an absolute value inequality:
1) The absolute value equation of a number is simply the number's distance from zero.
As a result, absolute values are always positive. This is due to the fact that they always employ the positive numbers contained within the absolute value sign. As a result, we can claim that they have a range that includes all positive values.Linear equations, on the other hand, specify values that can be negative, positive, or even zero. As a result, linear equations define all values.Another distinction is that the graph of an absolute value function is V-shaped, whereas the graph of a linear function is straight.2) Absolute value inequalities and linear inequalities share the fact that they both have two variables and so require a second equation to obtain the variables.
Therefore, the similarities and differences between solving an absolute value equation and solving an absolute value inequality are shown.
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SOLVE ASAP
X + x/3 = 4/9
solve for x!!
The value of 'x' from the expression is 1/3
How to determine the value
Given the expression;
[tex]x + \frac{x}{3} = \frac{4}{9}[/tex]
Find the LCM of the left side, we have
[tex]\frac{3x + x}{3} = \frac{4}{9}[/tex]
Cross multiply
[tex]9(4x) = 4 *3[/tex]
[tex]36x = 12[/tex]
Make 'x' the subject
[tex]x = \frac{12}{36}[/tex]
x = [tex]\frac{1}{3}[/tex]
Thus, the value of 'x' from the expression is 1/3
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Hello !
Answer:
[tex]\boxed{\sf x=\dfrac{1}{3} }[/tex]
Step-by-step explanation:
Our aim is to find the value of x that verifies the following equation :
[tex]\sf x+\frac{x}{3} =\frac{4}{9}[/tex]
Let's isolate x :
Multiply both sides by 3 :
[tex]\sf 3(x+\frac{x}{3} )=\frac{4}{9}\times 3\\ \sf 3x+x=\frac{4}{3}[/tex]
Now we can combine like terms :
[tex]\sf 4x=\frac{4}{3}[/tex]
Finally, let's divide both sides by 4 :
[tex]\sf \frac{4x}{4} =\frac{4}{3} \times \frac{1}{4} \\\boxed{\sf x=\dfrac{1}{3} }[/tex]
Have a nice day ;)
Label the midpoint of PQ as point S, the midpoint of QR as point T, and the midpoint of RP as point U.
Next, draw PT, QU, and RS.
Which statements are true?
m∠Q = m∠R
The length of QU is half the length of RP.
m∠P + m∠Q + m∠R = 180°
QU ≅ RS
PT, QU, and RS intersect at the same point.
The sum of the lengths of QU and RS is equal to the length of PT.
Step-by-step explanation:
1. Not neccesarily true
2. Not necessarily true
3. True because angles in a triangle add to 180°
4. Not necessarily true
5. True because the medians are being constructed, and the three medians of a triangle are always concurrent.
6. Not necessarily true
The statements that are true about the triangle are:
Option C: m∠P + m∠Q + m∠R = 180°
Option E: PT, QU, and RS intersect at the same point.
How to find the true statements of the triangle?1. m∠Q = m∠R: This is not true because there is no indication that the angles are equal.
2.The length of QU is half the length of RP: This is not true because there is no length given to show that measurement.
3. m∠P + m∠Q + m∠R = 180°:
This is true because the sum of angles in a triangle add to 180°
4. QU ≅ RS:
This is not true because we are not told that they are congruent
5. PT, QU, and RS intersect at the same point:
This is true because the medians are being constructed, and the three medians of a triangle are always concurrent.
6. The sum of the lengths of QU and RS is equal to the length of PT: This is not true because we are not told that.
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At a 95-percent confidence level, what should be the cutoffs from the left and right sides of a normal distribution?
The cutoffs from the left and right sides of normal distribution at a 95-percent confidence level are 1.96.
What is the confidence level?The confidence level, which is used in statistics, describes the likelihood that the estimation of a statistical parameter's location in a sample survey is also true for the population.
Confidence levels must be decided upon in advance when surveying since they affect the survey's essential scope and error margin. Confidence intervals of 90, 95, and 99 percent are widely employed in surveys.
If the confidence level were set at 95%, there is a very good likelihood that the population's arithmetic mean, as a statistical number, will fall within the survey's established margins of error.
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Using the table below, find the mean and median of the set of data.
Note: Round all numbers to the nearest tenth
The mean of the data set is 81.6.
The median of the data set is 80.
What is mean?The mean is the average of a data set. Therefore,
Mean = (70 x 2 + 75 x 8 + 80 x 6 + 85 x 3 + 90 x 9) / 28 = 81.6.
Hence,
mean = 81.6
What is a median?Median is a statistical measure that determines the middle value of a dataset listed in ascending order .
Therefore,
28 / 2 = 14
median = 80 + 80 / 2 = 160 / 2 = 80
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Freddie had saved 231 pennies.
Which statement best describes
the number of pennies he had?
he has 231 pennies..............
Order the set of numbers from least to greatest: -
--5, -√26.-31
6
Answer:
-31, /~26, -5, 6
Step-by-step explanation:
4. Find the solution to the equation below.
please finish
this
problem
Answer:
w = 12
Step-by-step explanation:
We are given the equation:
[tex]\displaystyle{\dfrac{w-2}{4} = \dfrac{2w+1}{10}}[/tex]
First, clear out the denominators by multiplying both sides by LCM. In this scenario, our LCM is 40. Thus, multiply both sides by 40:
[tex]\displaystyle{\dfrac{w-2}{4} \cdot 40= \dfrac{2w+1}{10} \cdot 40}[/tex]
Simplify the expressions/equations:
[tex]\displaystyle{(w-2)\cdot 10= (2w+1)\cdot 4}\\\\\displaystyle{10w-20= 8w+4}[/tex]
Isolate w-variable:
[tex]\displaystyle{10w-20= 8w+4}\\\\\displaystyle{10w-8w=4+20}\\\\\displaystyle{2w=24}\\\\\displaystyle{w=12}[/tex]
Hence, the solution is w = 12
If you have any questions regarding my answer or explanation, do not hesitate to ask away in comment!
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.
The polynomial approximate values are
a. The linear approximating polynomial is p1(x) = 2 - x
b.The quadratic approximating polynomial is p2(x) = x² - 3*x + 3
c. The approximating polynomial value is p1(0.97) = 1.03; p2(0.97) = 1.0309
According to the statement
we have given that the f(x) = 1/x
And we have to find that polynomial approximate values which are written below
The linear approximating polynomial And quadratic approximating polynomial And approximate the given quantity of polynomials obtained in parts a. and b.
So, the given function is f(x) = 1/x
And
f'(x) = -1/x²
f''(x) = 2/x³
a = 1
Now, we find the linear approximating polynomial
So,
a. The linear approximating polynomial is:
p1(x) = f(a) + f'(a)*(x - a)
p1(x) = 1/1 + -1/1² * (x - 1)
p1(x) = 1 - x + 1
p1(x) = 2 - x
And Now, we find the quadratic approximating polynomial
So,
b. The quadratic approximating polynomial is:
p2(x) = p1(x) + 1/2 * f''(a)*(x - a)²
p2(x) = 2 - x + 1/2 * 2/1³ * (x - 1)²
p2(x) = 2 - x + (x - 1)²
p2(x) = 2 - x + x² - 2*x + 1
p2(x) = x² - 3*x + 3
And Now, we find the approximating polynomial value
So,
c. approximate 1/0.97 using p1(x)
p1(0.97) = 2 - 0.97 = 1.03
approximate 1/0.97 using p2(x)
p2(0.97) = 0.97² - 3*0.97 + 3 = 1.0309
So, The polynomial approximate values are
a. The linear approximating polynomial is p1(x) = 2 - x
b.The quadratic approximating polynomial is p2(x) = x² - 3*x + 3
c. The approximating polynomial value is p1(0.97) = 1.03; p2(0.97) = 1.0309.
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Disclaimer: This question was incomplete. Please find the full content below
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 centeredat 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 1/0.97
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What is the range of the following set of ordered pairs?
{(-1,7), (6,2), (0,4), (5,2), (-3,1)}
O a. {7,2,4,1}
b.
O c.
O d.
{-1,6, 0, 5, -3}
{-1, -3, 1, 7,6}
{2, 0, 4, 5)
Answer:
range of the given set is { 7,2,4,2,1}
Step-by-step explanation:
. Hello !
When the above kind of set is given the second values of each elements belongs to the range or the y whereas, the first values of the elements belongs to the domain or x.
Thus, domain = {-1,6,0,5,-3}range ={7,2,4,2,1}GCSE MATHS PLEASE HELP
Answer:
A) y = 16/(x^2), B) 4/5
Step-by-step explanation:
For A, we can plug in some of the table values to check it. I will try 2 and 3
2. 4 = 16 / (2^2)
16/4 = 4
3. 16/9 = 16 / (3^2)
16/9 = 16/9
B) We can just input y into the formula 25 = 16 / (x^2)
This leaves us with +-4/5
Answer:
see explanation
Step-by-step explanation:
(a)
given y varies inversely as x² then the equation relating them is
y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation
to find k substitute any ordered pair from the table into the equation
using (2, 4 ) , then
4 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )
16 = k
y = [tex]\frac{16}{x^2}[/tex] ← equation of variation
(b)
when y = 25 , then
25 = [tex]\frac{16}{x^2}[/tex] ( multiply both sides by x² )
25x² = 16 ( divide both sides by 25 )
x² = [tex]\frac{16}{25}[/tex] ( take the square root of both sides )
x = ± [tex]\sqrt{\frac{16}{25} }[/tex] = ± [tex]\frac{4}{5}[/tex]
the positive value of x is x = [tex]\frac{4}{5}[/tex]
In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 50 and a standard deviation of 3. using the empirical rule, what is the approximate percentage of daily phone calls numbering between 47 and 53?
68% of the daily phone calls answered by the company are between 47 and 53.
What is empirical rule?Empirical rule states that for a normal distribution, 68% of the data are within one standard deviation from the mean, 95% of the data are within two standard deviation from the mean and 99.7% of the data are within three standard deviation from the mean.
Given mean of 50 and a standard deviation of 3
68% are within one standard deviation from mean = mean ± standard deviation = 50 ± 3 = (47, 53)
68% of the daily phone calls answered by the company are between 47 and 53.
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The error in the measurement of the radius of a sphere is 1%, then the error in the measurement of its volume is:
The error in the measurement of its volume is 3%.
What is the radius?The radius of a circle is the distance measured from its center to its edge.The radius of your cushion's corners can be determined by placing a framing square along the edges of your corners (see illustration) and measuring from the point where the curve begins to the corner of the square.The error in the measurement of its volume is:
Volume[tex]=\frac{4\pi r^{3} }{3}[/tex]
Δv/v*100=3 ΔR/R*100
[tex]3*\frac{1}{100} *100[/tex]
=3
The error in the measurement of its volume is 3%.
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Will mark brainliest
question-
jack jogs and rides his bike for a total of 75 minutes every day. he rides his bike 15 minutes more than he jogs.
part a: write a pair of linear equations to show the relationship between the number of minutes jack jogs (x) and the number of minutes he rides his bike (y) every day.
part b: how much time does jack spend jogging every day?
part c: is it possible for jack to have spent 60 minutes riding his bike every day? explain your reasoning.
The answers have been shown below.
To find the answers:Questions regarding the time spent by Jack jogging and bike riding are needed to be answered.
(A) The equations are [tex]x+y=75, y=15+x[/tex]
Time spent jogging is 30 minutes
The total time would be [tex]45+60=105[/tex] minutes which is not equal to 75 minutes.
(B) Let [tex]x[/tex] be the time spent jogging.
[tex]y[/tex] be the time spent bike riding.
[tex]x+y=75\\y=15+x\\x+15+x=75\\2x+15=75\\x=\frac{75-15}{2} =30[/tex]
Time spent jogging is 30 minutes.
[tex]y=60\\x+y=75[/tex]
(C) If he rides his bike 15 minutes longer than he jogs then he would have to jog [tex]60-15 = 45[/tex] minutes.
Therefore, the total time would be [tex]45+60=105[/tex] minutes which is not equal to 75 minutes.
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what is 4x-5/3+2x=7+2/9x+2
Simplifying the expression gives 36x^2 - 82x - 10 = 0
How to simplify the expressionGiven the expression;
4x-5/3+2x=7+2/9x+2
[tex]\frac{4x - 5}{3 + 2x} = \frac{9}{9x + 2}[/tex]
Cross multiply
[tex]4x - 5( 9x + 2) = 9 (3 + 2x)[/tex]
Expand the bracket
[tex]36x^2 + 8x - 45x - 10 = 27x + 18x[/tex]
Collect like terms
36x^2 + 8x - 45x - 27x - 18x = 0
Add the like terms
36x^2- 82x - 10 = 0
Thus, simplifying the expression gives 36x^2- 82x - 10 = 0
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What is the measure of angle g, in terms of x? x° x° x° 90° 180° – x° 180° – 2x°
The measure of angle G in terms of x is x+x degrees
Circle theoremThe measure of angle F and angle D is 90 degrees so that;
<GFD = <GDF = 90 - x
Since the sum of angle in a triangle is 180 degrees, hence;
<G + 90 - x + 90 - x = 180
<G + 180 - 2x = 180
<G = 2x
<G = x + x
Hence the measure of angle G in terms of x is x+x degrees
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Answer:A
Step-by-step explanation: math and me go together like mustard and pees
18. The area of a right triangle is 30 cm². The length
of one leg of the triangle is 5 cm. What is the
length of the other leg?
(A) 6 cm
(B) 12 cm
(C) 18 cm
(D) 24 cm
Answer:
12
Step-by-step explanation:
The area of a triangle is calculated with the following formula:
[tex]\frac{1}{2} *b*h[/tex] (b: base, h: height (or legs))
We can use this formula to find the length of the other leg:
30 = [tex]\frac{1}{2} *b*h[/tex] multiply both sides with 2 to get rid of fraction
60 = b*h one of the leg's length is given as 5 so
60 = 5*h divide both sides by 5
12 = h is the length of the missing leg.
Total area=
Help me please;! Asap thanks so much
The total area of the square based prism is 413.7 square units
How to determine the surface area?The given parameters are:
Base length, a = 10
Height, h = 11
The total surface area is calculated as:
[tex]A = a^2 + 2a\sqrt{\frac{a^2}{4} + h^2[/tex]
This gives
[tex]A = 10^2 + 2 *10\sqrt{\frac{10^2}{4}+11^2[/tex]
So, we have:
[tex]A = 100 + 20\sqrt{246[/tex]
Evaluate
A = 413.7
Hence, the total area of the square based prism is 413.7 square units
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When the bus leaves the station there are 29 passengers on board. at the first stop, 4 people get off and 11 get on. at the second step, 7 people get off and 23 get on. if the bus has 78 passenger seats and everyone is seating down, how many seats are now free?
When everyone is sitting down, the number of free seats is 26, using arithmetic addition and subtraction.
What is arithmetic addition and subtraction?The two main arithmetic operations that we learn to add and subtract two or more integers or other mathematical values are arithmetic addition and subtraction. The addition symbol is the plus sign (+), and the subtraction symbol is the minus sign (-). (minus sign).
The initial number of passengers on board=29
After 4 people get off at the first stop,
Using arithmetic addition and subtraction, we get,
Number of passengers left=29-4=25
After 11 people get on,
Number of passengers=25+11=36
At the second stop, when 7 people get off,
Number of passengers=36-7=29
When 23 people get on,
Number of passengers=29+23=52
Total number of passenger seats in the bus=78
Number of free seats, when everyone is sitting=78-52
=26
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Will Make BRAINLIEST!!!
In the figure below, parallel lines I and m are intersected by the transversal t. Based on the information given in the figure, what is the measure, in degrees, of x?
Answer:
there should have been names of every line and joining parts
Why would someone choose a 10-year term length on a student loan, rather than a 25-year length?
Answer:
See below
Step-by-step explanation:
To pay the loan off more quickly.
To pay less overall interest.
Often get a lower interest rate for a shorter term loan.
The function ƒ (x) = (?)* is shown on the coordinate plane. Select the drop-down menus to correctly describe the end behavior of f (x)
1. As x decreases without bound, the graph of f (x)
A. Increases without bound.
B. Approaches y=0
C. Decreases without bound
2. As x increases without bound, the graph of f (x)
A. Approaches y=0
B. Increases without bound
C. Decreases without bound
Answer: 1. A
2. A
Step-by-step explanation:
The field width of thestadium is 40m lessthan its length. The total length of the rectangular boundary of the open space in canopy is 420m. Frame a suitable
equation for the given situation and also find the length and width of the field in the stadium.
Answer:
I may have misubderstood the question, so review carefully.
width = 380 m
length is 420 m
Step-by-step explanation:
Let w and l stand for the width and length of the stadium.
We are told that w = l - 40 m
We also learn that l = 420 m
w = l - 40 m
w = (420 m) - 40 m
width = 380 m
length is 420 m
George is driving at an average speed of 707070 miles per hour. At this rate, how long, in minutes, will it take him to complete a 400400400-mile road trip
Given the average speed and distance covered, the time taken for the driver to complete the road trip is 5.7 hours
How long will it take the driver to complete a 400-mile road trip?Speed is simply referred to as distance traveled per unit time.
Mathematically, Speed = Distance ÷ time.
Given the data in the question;
Speed = 70 miles per hourDistance traveled = 400 mileElapsed time = ?We substitute into our equation above.
Speed = Distance ÷ time
70 miles per hour = 400 mile ÷ Elapsed time
Elapsed time = 400 miles ÷ 70 miles per hour
Elapsed time = 5.7 hours
Given the average speed and distance covered, the time taken for the driver to complete the road trip is 5.7 hours.
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Prediction of the value of the dependent variable outside the experimental region is called _____. Group of answer choices interpolation forecasting averaging extrapolation
Prediction of the value of the dependent variable outside the experimental region is called extrapolation.
According to the question,
Prediction of the value of the dependent variable outside the experimental region is called extrapolation.
Extrapolation is the statistical method beamed at understanding the unknown data from the known data.
Hence, prediction of the value of the dependent variable outside the experimental region is called extrapolation.
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Select all the correct answers.
The table shows points on the graph of the function f (x) = 3 sin (x- pi/2) + 1
Answer:
B,C and E
Step-by-step explanation:
The period can be calculated by dividing 2pi by the coefficfient of the x, so in this case 1. And we'll get 2pi/1 = 2pi.
The function clearly has a minimum of -2, you can see that from the table.
Same thing for the maximum = 4.
Answer:
See Photo
Step-by-step explanation:
Plato/Edmentum
bob baked 60 cookies and brownies. the number of cookies he baked was 4 less than 3 times the number of brownies he baked. how many cookies did bob bake
Answer:
Cookies = 44
Step-by-step explanation:
universal U=60
let the number of cookies be C,
n(C)=(3*b)-4
and the number of brownies be b,
n(b)=?
n(buc)=60
b+c=60
then, c=60-b
substitute for c=60-b.
60-b=3b-4
60+4=3b+b
64=4b
b=16
c=60-b
c= 60-16
c=44
Mr. smith has 5 courses he teaches at the community college. his course a has 102 students with an average tardiness of 3 students each day. another course has an average tardiness of 5 students each day with 85 enrolled. the average of these two courses receive a b+. what percent of students are tardy in course a? do not include % in answer and round to nearest hundredth. example, if answer is 19.567%, put 19.57.
The percentage of tardiness among the 102 pupils is 2.94.
Calculation of the percentageAccording to the query,
Course A: Total number of students = 102
Number of tardy students = 3
Percent of students tardy in course A = (number of tardy students/total
number of students) * 100
=(3/102)*100
= 2.941
≈2.94
In case of course B: Total number of students = 85 & tardy student = 5
So, the percent of tardy student = (5/85)*100 = 5.88 %
Therefore, it is concluded that the percentage of student tardiness in course A is 2.94.
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6. a. Sixty students in a class took an examination in Physics and Mathematics. If 17 of them passed Physics only, 25 passed in both Physics and Mathematics and 9 of them failed in both subjects, find i. the number of students who passed in Physics ii. the probability of selecting a student who passed in Mathematics 17
Let [tex]C[/tex] be the set of all students in the classroom.
Let [tex]P[/tex] and [tex]M[/tex] be the sets of students that pass physics and math, respectively.
We're given
[tex]n(C) = 60[/tex]
[tex]n(P \cap M') = 17[/tex]
[tex]n(P \cap M) = 25[/tex]
[tex]n((P \cup M)') = n(P' \cap M') = 9[/tex]
i. We can split up [tex]P[/tex] into subsets of students that pass both physics and math [tex](P\cap M)[/tex] and those that pass only physics [tex](P\cap M')[/tex]. These sets are disjoint, so
[tex]n(P) = n(P\cap M) + n(P\cap M') = 25 + 17 = \boxed{42}[/tex]
ii. 9 students fails both subjects, so we find
[tex]n(C) = n(P\cup M) + n(P\cup M)' \implies n(P\cup M) = 60 - 9 = 51[/tex]
By the inclusion/exclusion principle,
[tex]n(P\cup M) = n(P) + n(M) - n(P\cap M)[/tex]
Using the result from part (i), we have
[tex]n(M) = 51 - 42 + 25 = 34[/tex]
and so the probability of selecting a student from this set is
[tex]\mathrm{Pr}(M) = \dfrac{34}{60} = \boxed{\dfrac{17}{30}}[/tex]
Drag each statement to the correct location on the flowchart. Not all statements will be used.
Given: AB||CDand AD||BC
Prove: ZA ZC
D
B
Complete the flowchart proof.
m/ADC = m/ADB+ m/CDB m/BCD= m/DAC+m/ACD
m/DAB= m/BCD m/ABC= m/ABD+m/CBD
entum. All rights reserved.
pe here to search
m/DAB = m/DAC+m/ACD
C
m/DAB-m/DAC+m/BAC
MI
whetitution
The information to fill one the box regarding the proof include:
AB = CDAD = CBBD is common to both trianglesHow to illustrate the proof?It should be noted that when two triangles of each corresponding sides are equal, then it's said that they are similar.
Here AB = CD, and AD = CB as they illustrate the fact that they are parallel.
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