After taking into consideration the advantages in tax management, it will not be beneficial for Raphael and Martina to get married and avail tax benefits.
What are tax benefits?The individual taxable incomes of Raphael and Martina after availing the standard deductions will be $33,000 and $3,400 respectively. Now the computation of taxation liabilities will be computed as,
For Raphael, 10% of $33,000= $3,300;
For Martina, 10% of $3,400 = $340.
However, the joint income will be $61,200 and taxation liabilities of Raphael and Martina will be,
[tex]\rm Taxable\ Income = Total\ Income - Standard\ Deduction\\\\\rm Taxable\ Income =61200-24800\\\\\rm Taxable\ Income =\$36400[/tex]
Solving further,
[tex]\rm Joint\ Taxation = (\frac{10}{100}\ x\ 19750) + (\frac{12}{100}\ x\ 16650)\\\\\rm Joint\ Taxation = 1975+1998\\\\\rm Joint\ Taxation = \$3973[/tex]
Now, it can be compared that the joint taxation is higher than the summation of individual taxation of Raphael and Martina, and thus, tax benefits are not enough for Raphael and Martina to get married.
Hence, the tax benefits of Raphael and Martina after getting married are given as above.
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If the legs of a right triangle are 8 and 10, find the length of the hypotenuse.
Answer:
Given :-
Two legs of a rt. triangle : 8 and 10 respectively.
To find :-
Length of the hypotenuse
Solution :-
Using Pythagorean Theorem;
(hypotenuse)² = (8)² + (10)²
= 64 + 100
hypotenuse = √164
= 12.8 units
Answer:
12.80
Step-by-step explanation:
We have to use the Pythagoras theorem to find the value of the hypotenuse.
Let the value of the hypotenuse be c.
Let us use the below formula to find the length of the hypotenuse.
a² + b² = c²First, let us replace a and b with 8 and 10 ( the lengths of the legs of the right triangle) with a and b.
a² + b² = c²
8² + 10² = c²
64 + 100 = c²
And now let us solve the above and find the value of c.
164 = c²
√164 = c
12.80 = c
Therefore, the length of the hypotenuse is:
12.80 units
A restaurant will select 1 card from a bowl to win a free lunch, jimmy puts 10 cards in the bowl. The bowl has a total of 150 cards in it when they do the drawing. what are the odds of jimmy winning a free lunch
The odds of jimmy winning a free lunch is 0.066.
What is Probability ?Probability is the likeliness of an event to happen.
It is given that
A restaurant will select 1 card from a bowl to win a free lunch,
jimmy puts 10 cards in the bowl.
The bowl has a total of 150 cards in it
The odds of jimmy winning a free lunch is given by
= No. of chances / Total Outcomes
= 10/150
= 1/15
= 0.066
Therefore the odds of jimmy winning a free lunch is 0.066.
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Answer:
Step-by-step explanation:
1/1
An economy package of cups has 690 green cups. If the green cups are 30% of the total package, how many cups are in the package?
The total number of cups in the package is 2300.
What is Percentage?Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.
Here,
Let the total number of cups in the package be x.
Number of green cup = 690
Weightage of green cup in total = 30%
Now,
30% of x = 690
30/100 X x = 690
x = 690 X 100/30
x = 23 X 100
x = 2300
Thus, the total number of cups in the package is 2300.
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28.6% of city employees ride the bus to work. Last year, 29.7% of city employees rode the bus to work. What is the relative change from last year to this year?
(Express your answer rounded correctly to the nearest tenth of a percent!)
A percentage is a way to describe a part of a whole. The relative change from last year to this year is 3.7%.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
28.6% of city employees ride the bus to work, therefore, the final value is 28.6. While Last year, 29.7% of city employees rode the bus to work, therefore, the initial value is 29.7.
Since relative change means change with respect to some value. Thus, the relative value with respect to last year is,
Relative value = (29.7-28.6)/29.7 = 0.037 = 3.7%
Hence, the relative change from last year to this year is 3.7%.
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The system of equations y = one-fourth x minus 1 and y = negative one-half x minus one-fourth is shown on the graph below.
On a coordinate plane, 2 lines intersect at (1, negative three-fourths).
The solution of the system of equations is (1, -3/4)
How to solve the system of equations?
Here we have the system of equations:
y = (1/4)*x - 1
y = -(1/2)*x - 1/4
To solve it, we use the fact that the variable "y" is the same in both equations, then we can write:
(1/4)*x - 1 = -(1/2)*x - 1/4
Now we can solve that for x:
(1/4)*x - 1 = -(1/2)*x - 1/4
(1/4)*x + (1/2)*x = 1 - 1/4
(1/4)*x + (2/4)*x = 1 - 1/4
(3/4)*x = 3/4
x = 1
To get the y-value of the solution, we just evaluate x = 1 in any of the two given lines, using the first one:
y = (1/4)*(1) - 1 = -3/4
So the solution is (1, -3/4)
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The dot plot shows the number of books lent by a school library during a 10-day period.
What was the mean absolute deviation of the number of books?
F. 0
G.
H.
J.
1.04
1.96
..
23 24 25 26 27 28 29 30 31 32 33
2.19
The mean absolute deviation of the number of books is 1.84
How to determine the mean absolute deviation?The dot plot of the number of books is in the attached figure.
From the figure, we have:
x f
1 1
2 2
3 2
4 3
5 1
6 2
7 3
8 1
Start by calculating the mean using:
[tex]\bar x= \frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x= \frac{1 * 1 + 2 * 2 + 2 * 3 + 3 * 4 + 1 * 5 + 2 * 6 + 3 *7 + 1 * 8}{1 +2+2+3+1+2+3+1}[/tex]
Evaluate the sum and products
[tex]\bar x= \frac{69}{15}[/tex]
Divide
[tex]\bar x= 4.6[/tex]
The mean absolute deviation is then calculated as:
[tex]|\bar x| = \frac{\sum f|x - \bar x|}{\sum f}[/tex]
So, we have:
[tex]|\bar x|= \frac{1 * |1 -4.6|+ 2 * |2 -4.6| + 2 * |3 -4.6|+ 3 * |4 -4.6|+ 1 *| 5 -4.6|+ 2 * |6 -4.6|+ 3 *|7 -4.6|+ 1 * |8-4.6|}{1 +2+2+3+1+2+3+1}[/tex]
Evaluate the absolute difference
[tex]|\bar x|= \frac{1 * 3.6+ 2 * 2.6 + 2 * 1.6+ 3 * 0.6+ 1 *0.4+ 2 * 1.4+ 3 *2.4+ 1 * 3.4}{15}[/tex]
Evaluate the sum of products
[tex]|\bar x|= \frac{27.6}{15}[/tex]
Divide
[tex]|\bar x|= 1.84[/tex]
Hence, the mean absolute deviation of the number of books is 1.84
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Which set of values could be the side lengths of a 30-60-90 triangle?
Answer is B.
Step-by-step explanation:
Since we know that in 30-60-90 triangle, the side corresponding to angle 90 degrees is two times the length of side corresponding to 30 degree angle. The length of side corresponding to 60 degree angle is times the length corresponding to 30 degree angle.
We can see from our given choices that the side corresponding to 30 degree angle is 5 units.
Therefore, the side lengths of a 30-60-90 triangle will be and option B is the correct choice.
PLS MARK ME AS BRAINLIEST.
Given 4 c 5 not-equals 0 and c is a real number, what is the multiplicative inverse of 4 c 5 not-equals 0 0 1 startfraction 1 over 4 c 5 end fraction startfraction 1 over 4 c endfraction 5
The multiplicative inverse of the expression 4c + 5 is 1/(4c + 5)
Complete questionGiven 4c + 5 ≠ 0 and c is a real number, what is the multiplicative inverse of 4c + 5
How to determine the multiplicative inverse?The expression is given as:
4c + 5
The multiplicative inverse of an expression x is 1/x
This means that:
The multiplicative inverse of the expression 4c + 5 is 1/(4c + 5)
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3x + 4 divided by 2 = 9.5
Answer:
2.5
Step-by-step explanation:
First divide 4 by 2
Second, you want x on a side by itself. So you would move 2 over to 9.5. But since 2 is positive, you would subtract 2 from 9.5
Third, you need to get x by itself. So you would divide by 3 on both sides because division cancels out multiplication which is what 3x is. And then you end up with 2.5
3x + 4 / 2 = 9.5
3x + 2 = 9.5
3x = 7.5
3x/3 = 905/3
x = 2.5
And if you want to check it, just substitute 2.5 for x
3(2.5) + 4 / 2 = 9.5
7.5 + 4 / 2 = 9.5
7.5 + 2 = 9.5
9.5 = 9.5
Se encarga del estudio de los triángulos rectilíneos
Answer:
Rectilíneo generalmente indica una figura representativa de hacer una línea recta oa lo largo de una línea recta o en una línea recta. En términos matemáticos, es una figura plana delimitada por segmentos de línea. En otras palabras, una figura plana totalmente compuesta de segmentos de línea se conoce como figura rectilínea. Ahora bien, si te preguntas ¿qué es una figura plana? Entonces, sepa que cuando ponemos la punta de un lápiz en una hoja de papel y nos movemos de un punto a otro, sin levantar el lápiz, entonces las formas que se forman son lo que llamamos curvas planas.
MATH: Inverse function, 10 pts for your help!
The inverse of g(5) and the inverse of h(x) are 2 and [tex]h^{-1}=\frac{-x-13}{4}[/tex] respectively
Inverse of a function
Given the following coordinates and function
g = {(-6, -5), (2, 5), (5,6), (6,9)}
The inverse of "g" is determined by switching the coordinates to have:
g^-1(x) = {(-5, -6), (5, 2), (6, 5), (9,6)}
Since the value of the y-coordinate when x = 5 is 2, hence g^-1(5) = 2
Given the function expressed as:
h(x) = -4x - 13
y = -4x - 13
Replace y with x
x = -4y - 13
4y = -x - 13
y = (-x-13)/4
[tex]h^{-1}=\frac{-x-13}{4}[/tex]
Determine the composite function [tex](hoh^{-1})(-1)[/tex]
h(h(x)) = h(-4x-13)
h(h(x)) =[tex]\frac{-(-4x-13)-13}{4} \\[/tex]
[tex]h(h(x))=\frac{4x}{4} \\h(h(x)) = x\\h(h(-1)) = -1[/tex]
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Martha is late for class, so she races her 75 kg body up a 4.0 meter flight of stairs in only 2.3 seconds. What is Martha’s power?
Answer:
[tex]1.3\cdot 10^3\text{ J}[/tex]
Step-by-step explanation:
Power is defined by work over time. In physics, work can be defined as the energy transferred over from an applied force over some distance. As a formula:
[tex]W=Fd[/tex], where F = force applied and d = distance that force is applied over.
*It is worth noting that F must be parallel to the distance travelled. If it is perpendicular, no work is done, and if it is at an angle, find the parallel component and use that for F.
In this case, the force applied must counter the force of gravity on Martha, which is given by [tex]F_g=mg[/tex], where m = Martha's mass and g = gravitational constant 9.8 m/s/s. Therefore, [tex]F_g=75\cdot 9.8=735\text{ N}[/tex]. Since she raises her body 4.0 meters, the work done must be [tex]W=Fd=735\cdot 4=2940\text{ J}[/tex].
Since power is equal to work over time and t = 2.3 seconds, we have:
[tex]\displaystyle P=\frac{W}{t}=\frac{2940}{2.3}=\boxed{1278\text{ J}}\approx \boxed{1.3\cdot 10^3\text{ J}}[/tex] (to two significant figures)
a water tank is empty. Anil needs to fill the tank with 2400 litres of eater
Answer:
2400 liters in tank
Step-by-step explanation:
Company A would take 260 minutes more than Company B for filling 2400 liters of water in Anil's tank when the rate at which Company A fills is 8 liters in 1 minute and 40 seconds, while the rate at which Company B fills is 2.2 gallons per minute.
What is the meaning of rate?Rate is the ratio of quantity to time.
[tex]RATE = \frac{QUANTITY}{TIME}[/tex].
How to solve the question?In the question, we are asked to find the time which Company A takes more than Company B for filling a water tank of 2400 liters when Company A fills water at a rate of 8 liters in 1 minute and 40 seconds, while the rate at which Company B fills is 2.2 gallons per minute.
For Company A:
The capacity of the tank = 2400 liters
Rate = 8 liters in 1 minute and 40 seconds
Now, 1 minute and 40 seconds = 1 + 40/60 minutes = 1.67 minute
Therefore, the actual rate = 8/1.67 = 4.8 liters per minute.
Therefore, the time taken by Company A = 2400/4.8 minutes = 500 minutes.
For Company B:
The capacity of the tank = 2400 liters.
We know 1 gallon = 4.54 liters,
or, 1/4.54 gallons = 1 liter.
Therefore, the capacity of the tank = 2400 * (1/4.54) gallons = 528.634 gallons.
Rate = 2.2 gallons per minute.
Therefore, the time taken by Company B = 528.634/2.2 minutes = 240.288 minutes.
Therefore, the time that Company A takes more than Company B = 500 - 240.288 minutes = 259.712 minutes ≈ 260 minutes.
The given question is an incomplete question. The complete question is:
"A water tank is empty.
Anil needs to fill the tank with 2400 liters of water.
Company A supplies water at a rate of 8 liters in 1 minute and 40 seconds.
Company B supplies water at a rate of 2.2 gallons per minute.
1 gallon = 4.54 liters.
Company A would take more time to fill the tank than Company B would take to fill the tank.
How much more time?
Give your answer in minutes correct to the nearest minute."
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the equation of the line that goes through (3, 0) and (6, 2) in slope-intercept form???
the slope intercept form of the given points is y = 2/3 (x-3).
What is Straight Line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined on both sides of a point. A straight line does not have any curve in it.
Here, given passing points
(3, 0) and (6, 2)
We know that,
(y - y₁) = (y₂-y₁)/(x₂-x₁) (x - x₁)
(y - 0) = (2-0)/(6-3) (x-3)
y = 2/3 (x-3)
Thus, the slope intercept form of the given points is y = 2/3 (x-3).
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. The probability that a patient catches flu is 3/8, the probability that he has a headache
is 5/15, and the probability that he has asthma is 4/9. If we know the fact that the
probability that the patient will have at least one of the illnesses is 3/5, then what is
the probability that he will have flu, headache, and asthma?
Answer:
[tex]\boxed {\frac{343}{360}}[/tex]
Step-by-step explanation:
Probability Rule :
[tex]\boxed {P(A\cup B \cup C) = P(A) + P(B) + P(C) - P(A \cap B \cap C)}[/tex]
Solving :
⇒ 3/5 = 3/8 + 5/15 + 4/9 - P (A ∩ B ∩ C)
⇒ P (A ∩ B ∩ C) = 3/8 + 1/3 + 4/9 - 1/5
⇒ P (A ∩ B ∩ C) = 135/360 + 120/360 + 160/360 - 72/360
⇒ P (A ∩ B ∩ C) = (135 + 120 + 160 - 72) / 360
⇒ P (A ∩ B ∩ C) = 343/360
he following stem-and-leaf plot represents the test scores for 26 students in a class on their most recent test. Use the data provided to find the quartiles.
Test Scores by Student
Stem Leaves
6 2 4 4 6 7 9
7 1 2 4 7 8
8 4 4 5 5 6 7 7 8
9 0 0 1 3 4 7 8
Key: 6|2=62
Step 1 of 3 : Find the second quartile.
Considering the given stem-and-left plot, the median = second quaritle of the data set is of 84.5.
What is the median of a data-set?The median of a data-set is the 50th percentile, that is, the value that separates the bottom 50% of scores from the upper 50% of scores.
This data-set has even cardinality of 26, hence the median is the mean of the 13th and 14th scores, which, considering the key for the stem-and-leaf plot, are 84 and 85, hence:
Me = (84 + 85)/2 = 84.5.
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What is a real-world example of a relation that is a function?
How would you classify the following expression by the number of terms?
42−8+4
Solution
First, consider how many terms are in the expression.
This expression has ______ terms.
Therefore, this expression is called a trinomial.
Classify the expression by the number of terms: 43−8
Solution
First, consider how many terms are in the expression.
This expression has ____ terms.
The answer is a ______. (monomial, binomial, or trinomial)
Classify the expressions by the number of terms.
2+3+9 = (monomial, binomial, polynomial or trinomial)
6= (monomial, binomial, polynomail or trinomial)
Answer:
1. This expression has 3 terms.
2. This expression has 2 terms
3. Solution 43-8=35
3. binomial
2+3+9= trinomial
6=monomial
Step-by-step explanation:
The average of 4 numbers is 9. If one of the numbers is 7, What is the sun of the other 3 numbers?
Answer:
Step-by-step explanation:
Comment
If 4 numbers have an average of 9, then total of the 4 numbers is 4 * 9 = 36.
If one of the 4 numbers is a 7, then
7 + x = 36 where x is the sum of the other 3 numbers.
7 + x = 36 Subtract 7 from both sides
7- 7 +x = 36 - 7
x = 29
Answer 29
If m∠1 = 72º, then find the value of m∠2. vertical angles
If the angle 1 and angle 2 are vertical angles, hence they must be equal to each other, therefore m∠1 = m∠2 = 72º
What are vertical angles?Angles angle are angles that are equal to equal to each other in a line geometry.
Given the following parameters
m∠1 = 72º,
If the angle 1 and angle 2 are vertical angles, hence they must be equal to each other, therefore m∠1 = m∠2 = 72º
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Find area bounded between y=x^2 and y=-(x+2)^2+4
By applying definite integrals and integration rules, the area bounded between the curves f(x) = x² and g(x) = -(x+2)² + 4 is equal to 8 square units.
How to determine the between the two integrals
The points of intersection between the two curves are (x, y) = (0, 0) and (x, y) = (-2, 4). The curve is f(x) = x² and upper curve is g(x) = -(x+2)² + 4. The area between the two curves is defined by this definite integral:
[tex]A = \int\limits^{0}_{-2} {f(x) - g(x)} \, dx[/tex]
[tex]A = \int\limits^{0}_{-2} {f(x)} \, dx - \int\limits^{0}_{-2} {g(x)} \, dx[/tex]
[tex]A = \int\limits^0_{-2} {[-(x+2)^{2}+4]} \, dx -\int\limits^0_{-2} {x^{2}} \, dx[/tex]
[tex]A = -\frac{(x+2)^{3}}{3}|_{-2}^{0} + 4\cdot x|_{-2}^{0}-\frac{x^{3}}{3}|_{-2}^{0}[/tex]
[tex]A = - \frac{2^{3}}{3} + 0 + 4\cdot [0 - (-2)] - 0 + \frac{(-2)^{3}}{3}[/tex]
[tex]A = -\frac{8}{3} + 8 -\frac{8}{3}[/tex]
A = 8
By applying definite integrals and integration rules, the area bounded between the curves f(x) = x² and g(x) = -(x+2)² + 4 is equal to 8 square units.
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Tina's application for graduate school was ranked 54 out of 300 applications. Her twin sister's application to a
different graduate school was ranked 23 out of 175 applications.
a. Which sister had the higher percentile ranking?
b. If you had the data on the cumulative GPA of each student in each school in June 2019, which measure of
average would be the most meaningful - mean, median, mode? Explain
A percentage is a way to describe a part of a whole. The percentile ranking of Tina's sister is higher than her.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
A.)
The percentile ranking of Tine is,
Tina's Ranking = [1 - (54/300)] × 100% = 82%
Tina's soster Ranking = [1 - (23/175)] × 100% = 86.85%
Hence, the percentile ranking of Tina's sister is higher than her.
B.) It shows that you can succeed in the graduate examination if you exceed this value.
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how do you simplify
−(12st3+34s3t+t2−1)
Answer:
-34s^3t - 12st^3 - t^2 + 1
Step-by-step explanation:
hope this helps
How much vinegar would be in each container if the total amount in all cups were redistributed equally between the 8 containers?
Answer:
Step-by-step explanation:
1/8
Point A is at (3, 2.6) and Point B is at (3, 1.4) on a coordinate grid. The distance between the two points is
Answer:
oma cursos online gratis de chino para aprender a hablar y escribir en este idioma. Aprende chino con cursos de las mejores universidades en edX.
Step-by-step explanation:
Help me with this question please!!!
Answer: 98.5
Step-by-step explanation:
There were 942 people in total, 928 of which recognized Exxon.
So, the probability is 928/942, which is about 98.5%
The probability of random consumers knowing of exon will be 98.5%.
What is probability?Probability helps us to know the chances of an event occurring.
[tex]P =\dfrac{Desired \ Outcomes}{Possible outcomes}[/tex]
Given that:-
928 consumers knew exon and 14 did not.The probability will be calculated as:-
Total consumers are 942 out of which 928 knew exon and 14 did not.
P = 928 / 942
P = 0.985
P = 98.5%
Therefore the probability of random consumers knowing of exon will be 98.5%.
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Select the correct answer from each drop-down menu. y 11 10 Weight (kilograms) 9 00 7 CO 5 3 2 1 5 6 7 Age (months) The scatter plot shows the weight of a child each month. 1 rights reserved 2 3 4 The birth weight of the child is V X 8 9 10 11 kilograms. The child gains an average of per month. Select the correct answer from each drop - down menu . y 11 10 Weight ( kilograms ) 9 00 7 CO 5 3 2 1 5 6 7 Age ( months ) The scatter plot shows the weight of a child each month . 1 rights reserved 2 3 4 The birth weight of the child is (blank) kilograms . The child gains an average of(blank) per month .
Answer:
its wrong answer and question
The graphs below have the same shapes. What is the equation for the red graph?
The equation for the red graph is f(x)=-x^2.
The question is an incomplete graph of a function is missing
For a complete question refer to the graph attached below
we have [tex]g(x)=4-x^2[/tex]
The vertex of the function g(x) is the point (0,4)
The vertex of the function f(x) is the point (0,0)
What is the vertex?
This is typically a local maximum or minimum of curvature, and some authors define a vertex to be more specifically a local extremum of curvature.
So, the rule of the translation of g(x) to f(x) is
(x,y)------> (x,y-4)
The translation is 4 units down
The equation of the function f(x) is
[tex]f(x)=g(x)-4[/tex]
[tex]f(x)=(4-x^2)-4[/tex]
[tex]f(x)=-x^2[/tex]
Therefore, The answer is f(x)=-x^2
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Which expression is equivalent to (15²)(15^-7)?
A 15^-21
B -15^4
C 1/15^4
D 1/15^-4
Answer:
there is no answer
Step-by-step explanation:
If you multiply 15^x by 15^y, the answer is 15^(x+y) so 2 plus -7 is negitive 5.
but there is no answer equal to this.
The equivalent expression will be;
⇒ 15⁻⁵
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
The expression is,
⇒ (15²) × (15⁻⁷)
Now,
Since, The expression is,
⇒ (15²) × (15⁻⁷)
Hence, We solve as;
⇒ (15²) × (15⁻⁷)
⇒ 15²⁻⁷
⇒ 15⁻⁵
⇒ 1 / 15⁵
Thus, The equivalent expression is,
⇒ 15⁻⁵
⇒ 1 / 15⁵
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If you could please answer this that would be awesome!
Please graph it!
The graph is attached with the answer, This is looking like a horizontal staircase
What is a Step Function ?A step function is a piece wise function whose all pieces are horizontal line or a point.
It is given in the question to graph the interval
-2 ≤x≤2
for f(x) = |x+3|
-2 1
-1 2
0 3
1 4
2 5
The graph is attached with the answer.
This is looking like a horizontal staircase
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