The value of "i" squared results in:
(-1) = i²
What are numeric sets?Numerical sets are groupings of numerical values that have a particularity in common, they can be integers, decimals, fractions, among others.
Among the numerical sets there is one that we call complex numbers, which include values that are not real, such as "i" a letter that denotes that it is an imaginary number.
In function to this type of numbers there is a particular value and it is the "i" which is the result of the square root of -1, then we have:
√(-1) = i[√(-1)]² = i²(-1) = i²Learn more about complex numbers at:
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when 110 is added to a certain number and the sum is divided by 3, the result is 4 times the original number.What is the original number.
Answer:
Step-by-step explanation:
Let X be the original number.
The problem can be written as the following equation:
(X + 110) / 3 = 4X
Multiplying both sides by 3 gives:
X + 110 = 12X
Subtracting X from both sides gives:
110 = 11X
Dividing both sides by 11 gives:
X = 10
Therefore, the original number is X = 10.
Answer:
(x + 110)/3 = 4x (multiple both side by 3)
x + 110 = 12x
110 = 11x
x = 10
CHECKING(x + 110)/3 = 4x
(10 + 110)/3 = 4(10)
120/3 = 40
40/40
Therefore the original number is 10.Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Tim needs a new car while he attends college in the United States for the next three years. The car he would like has a MSRP of $15,000. A local dealer can get him a 3-year loan with a 7% interest rate if Tim can give them a $1,500 down payment.
The same dealer offers the same car to lease with a money factor of 0.00271 and a residual value of 75%. The lease requires an additional fee of $1,250 to cover Tim’s security deposit and the acquisition and documentation fees for the car.
Tim is looking to drive the car home with the smallest initial out-of-pocket cost. Which of the following statements is true?
a.The initial out-of-pocket cost is less for the lease.
b.The initial out-of-pocket cost is less for the loan.
c.The initial out-of-pocket cost is the same for the lease and loan.
d.The initial out-of-pocket cost for a lease is not comparable to that of a loan.
Answer:
A
Step-by-step explanation:
To compare the initial out-of-pocket cost for the lease and loan options, we need to calculate the total cost for each option.
For the loan option, we can calculate the total cost as follows:
Total cost = MSRP + down payment + interest
= $15,000 + $1,500 + $1,050 (7% of MSRP)
= $17,550
For the lease option, we can calculate the total cost as follows:
Total cost = (MSRP x money factor x 36) + acquisition and documentation fees + security deposit
= ($15,000 x 0.00271 x 36) + $1,250
= $5,925 + $1,250
= $7,175
Since the total cost for the lease option is less than the total cost for the loan option, the initial out-of-pocket cost is less for the lease. Therefore, the correct statement is:
a. The initial out-of-pocket cost is less for the lease.
In Angle abc and angle pqr ab:pq=4:5 and a(angle pqr)=125cm² then find a(angle abc)
Answer:
Therefore, the measure of angle ABC is 55 cm².
Step-by-step explanation:
In order to solve this problem, we need to use the property of angles in a linear pair, which states that the measures of the two angles in a linear pair add up to 180 degrees.
If angle ABC and angle PQR form a linear pair, then the measure of angle ABC is 180 degrees minus the measure of angle PQR.
Since the measure of angle PQR is 125 cm² and the measure of angle ABC is 180 degrees minus the measure of angle PQR, the measure of angle ABC is:
180 degrees - 125 cm² = 55 cm²
What are the 4 graphs called?
The four basic graphs used in statistics include bar, line, histogram and pie charts.
What is meant by graphs?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph. Charts and graphs come in a variety of styles. Line graphs, bar graphs and histograms, pie charts, and Cartesian graphs are likely the four most popular types. They serve quite diverse purposes and are best suited for very different uses.Intercepts, intervals where the function is rising, falling, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity are important characteristics. Data that is readily apparent. appropriate unit-specific labeling for each axis.To learn more about graphs refer to:
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What is the nature of the roots 5x² 3x 2 0?
The nature of the roots of the equation 5x² + 3x + 2 = 0 are x = -7.123 and x = 0.878.
The equation 5x² + 3x + 2 = 0 has two solutions, or roots, which can be found using the quadratic formula:
x = [-b ± √(b² - 4ac)] / 2a
Where a = 5, b = 3 and c = 2,
x = [-3 ± √(3² - 4(5)(2))] / 2(5)
x = [-3 ± √17] / 10
x = (-3 ± 4.123) / 10
x = (-7.123) / 10, 0.878
The roots of the equation 5x² + 3x + 2 = 0 are x = -7.123 and x = 0.878.
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Using the diagram, find GT and TA:
Answer:
GT: 10
TA: 6
Step-by-step explanation:
use the ratio of GR:RE to find GT:TA
since the ratio of GR:RE is 5:3, the ratio of GT:TA=5:3. The total length of GT+TA=16.
5x+3x=16, 8x=16, x=2.
By plugging in the x value, it is shown that GT=10 and that TA=6
subtract ( – 8r–2)–( – 5r–9)
Answer:[tex]-3r+7[/tex]
Step-by-step explanation:
given the equation
[tex](-8r-2)-(-5r-9)[/tex]
Distribute the negative
[tex]-8r-2+5r+9[/tex]
Combine like terms
[tex](-8r+5r)+(-2+9)[/tex]
[tex](-3r)+(7)=[/tex]
[tex]-3r+7[/tex]
Hope this helps!
Most Algebra 1 Formulas for needed for CST
The below would be most important Algebra 1 Formulas for CST.
Linear Equation:
[tex]Ax + By + C = 0[/tex]
Equation of Straight Line or Slope:
[tex]y = mx+b[/tex]
Point-slope form:
[tex]y-y_{1} = m(x-x_1)[/tex]
Slope when 2 points are given:
[tex]m = \frac{(y_2 - y_1)}{(x_2-x_1)}[/tex]
Quadratic Equation:
[tex]Ax^2 + Bx +C = 0[/tex]
When lines are parallel:
Slope of both lines are equal. [tex]m_1 = m_2[/tex]
When lines are perpendicular:
Slope of perpendicular lines are opposite reciprocals, meaning if the slope of a line [tex]l_1[/tex] is [tex]\frac{1}{2}[/tex]. The line [tex]l_2[/tex] perpendicular to [tex]l_1[/tex] is [tex]-\frac{2}{1}[/tex].
Work Formula:
Total Work Done = Number of Days [tex]\times[/tex] Efficiency
where Efficiency is inversely proportional to Time Taken.
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Which expression can you use to find the number of ways to choose 5 cards from a 52-card deck?.
The expression that you can use to find the number of ways to choose 5 cards from a 52-card deck is 52!/(47! * 5!).
The expression that you can use to find the number of ways to choose 5 cards from a 52-card deck is 52 choose 5, which is equal to 52!/(47! * 5!), where the exclamation point indicates the factorial function. This is known as the binomial coefficient, and it represents the number of ways to choose a certain number of items from a larger set. In this case, the binomial coefficient is used to find the number of ways to choose 5 cards from a deck of 52 cards.
The order of the cards is irrelevant in card games like poker. A five-card draw of 1,2,7,9, K is equivalent to a draw of K,7,9,1,2. What counts is the fundamental overall group.
Order is irrelevant, therefore we utilize a combination (instead of a permutation)
We will substitute n = 52 and r = 5 into the nCr combination formula, which is n C r = (n!)/(r!*(n-r)!)
so we obtain:
n C r = r!*(n-r)!/(n!)
52 C 5 = (52!)/(5!*(52-5)!)
52 C 5 = (52!)/((52-5)!*5!)
The complete question is:-
Which expression can you use to find the number of ways to choose 5 cards from a 52-card deck?
a) (52-5)! / 52!5!
b) 52! / (52-5)!
c) 52! / (52-5)!5!
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A carpet cleaner charges $59 for the first room and $30 for each additional room. A customer does not want to spend no more than $125 for having the carpets in his house cleaned. If r represents the additional rooms, write an inequality that represents the situation
The inequality could be represented by 59 + 30r ≤ 125
According to the given information
Money charged for first room = $59
Money charged for per additional room = $30
The money that the customer could pay = $125
So
We need to write the inequality to determine the situation
Let the number of carpets be r
Firstly , determining an expression for the cleaner charges
59 + 30*r
Since
The customer cannot pay more than $125
Hence
According to the given situation
59 + 30r ≤ 125
30r ≤ 66
r ≤ 2.2
The inequality could be represented by 59 + 30r ≤ 125
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__________________energy that comes from the movement of particles.
Thermal energy that comes from the movement of particles.
What is meant by thermal energy ?The energy present in a system that determines its temperature is referred to as thermal energy. Thermal energy flows as heat. Thermodynamics is a whole field of physics that studies how heat is transmitted between various systems and how the procedure is carried out (see the first law of thermodynamics).
The energy that results from a substance's temperature is known as thermal energy. The amount of molecular vibration increases with temperature, increasing thermal energy.
Heat energy is another name for thermal energy. A moving object's kinetic energy is its energy. Thermal energy is a type of kinetic energy because it is produced by moving particles.
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What is a perpendicular slope example?
Examples of perpendicular slope are the sides of a fixed square, a window, and the Red Cross emblem.
Describe perpendicular slope.Lines that are vertical and horizontal are perpendicular to one another. In this instance, the perpendicular line's slope would be equal to a horizontal line's slope, which would be 0. The slope of the perpendicular line is zero, but the slope of the parallel line is unknown. By taking the negative reciprocal of the slope of the provided line, one can determine the slope of a perpendicular line from that line. We obtain m2 = -1/m1 if the slope of the provided line is m1 and the slope of a perpendicular line is m2.
Given
There are a lot of perpendicular lines that we may see in reality. The corners of the chalkboard, the arms of a clock at specific times of the day, the sides of a fixed square, a window, and the Red Cross emblem are a few examples.
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a new trendy restaurant is growing exponentially. after being open for 11 months the restaurant was serving an average of 310 customers a day. by month 15, the restaurant was serving about 456 customers a day. write an exponential function n(t) that models average number of customers, n, after t months of being open. if necessary, round any values to four decimal places (do not round on intermediate steps). write your answer in the form a(b)t
the exponential function is n(t) =n° (1+r)∧t, where t is the power refers the time in months after opening and n denotes average customer.
what means growing exponentially?when the rate of increases is occurred very rapidly. In this question, the trendy restaurant has earned reputation.
How will be the exponential function?Given, average number of customers after 11 months of opening = n(11) =310
average number of customers after 15 months of opening= n(15) =456
during this 4 month increases of customer =456 -310 =146
increasing rate of customer per month = 146/4 = 36.5
now increasing rate in percentages = 36.5 %
exponential growth rate, r= 0.365
let, n° is the initial number of customer while opening at t=0 month
now, the exponential function n(t) that model's average number of customers, n after t months of being open will be
n(t) = n° ( 1+r)∧t
we are given that after 11 months of opening average customer n(11) = 310
now, 310 = n° (1+ 0.365)∧11
n° = 10
hence, the exponential function = n(t) = 10(1+r)∧t
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Here are 2 triangles. One triangle has a 60 degree angle and a 40 degree angle. The other triangle has a 40 degree angle and an 80 degree
angle.
How long are the sides labeled x and y?
x= (blank) units and y= (blank) units.
Answer:
x=4.04 y=7.66
Step-by-step explanation:
Answer the question please
Answer:
81 degrees
Step-by-step explanation:
Because of exterior angles u=u-41+u-40
Solve:
u=2u-81
0=u-81
u=81
How do you tell the end behavior of a graph from an equation?
The end behavior of a graph can be determined by looking at the leading term in the equation. If the leading term is a positive or negative power of x, then the end behavior of the graph will be either a horizontal asymptoteor an oblique asymptote. If the leading term is a constant, then the end behavior of the graph will be a horizontal line at that constant value.
To determine the end behavior of a graph from an equation, we first look at the leading term in the equation. If the leading term is a positive or negative power of x, then the end behavior of the graph will be either a horizontal asymptote (positive or negative infinity) or an oblique asymptote (slanted line). If the leading term is a constant, then the end behavior of the graph will be a horizontal line at that constant value. For example, if the leading term of an equation is 3x2, then the end behavior of the graph will be a horizontal asymptote at positive infinity. If the leading term of the equation is 4, then the end behavior of the graph will be a horizontal line at y=4. To determine the exact shape of the asymptote, we must look at the coefficient of the leading term. A positive coefficient will create a positive asymptote (sloping up), while a negative coefficient will create a negative asymptote (sloping down). Additionally, if the graph oscillates around a single point, then the end behavior of the graph is a limit cycle.
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The ratio of trees to flowering plants in Marsha’s backyard is shown on the ratio table. What number completes the ratio table to make an equivalent ratio? [Type your answer as a number.]
trees 2 12
plants 5 ?
The ratio of trees to flowering plants in Marsha’s backyard is shown on the ratio table.
30 numbers complete the ratio table to make an equivalent ratio.
What is equivalent ratio?When we compare two ratios, they are said to be equivalent. To determine if two or more ratios are comparable, they can be compared to one another.
Equivalent ratios are two ratios with the same value. By multiplying or dividing the two amounts by the same number, you may get the corresponding ratio. Finding comparable fractions follows the same procedure.
Here in this case,
for trees: 2: 12 [ 2 to 12, 6 times more ]
for plants: 5: 30 [ 5 to 30, it is also 6 times more]
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What is mean median and mode 7th grade?
The three statistical measures of central tendency are mean, median, and mode. While describing a set of data, we point out its primary location. This is referred to as the central tendency measure.
The arithmetic mean of a given data is the sum of all observations divided by the number of observations.
The data set's median is the value in the center. Put all the numbers in ascending or descending order, and then choose the middle number to determine the median. There will only be one middle integer if the number of data points is odd. If the number of data points is even, you must choose the middle two numbers, add them together, and divide by two. Your median will be that value.
A mode is defined as the value that has a higher frequency in a given set of values. It is the value that appears the most number of times.
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Hamid is playing a trivia game with multiple choice questions. Each question has 2 22 correct answers among 5 55 answer choices. Hamid has no idea what the answers to a certain question are, so he needs to choose two different answers at random. What is the probability that hamid guesses both answers correctly? round your answer to two decimal places.
The probability that Hamid guesses both answers correctly is 10%.
Probability means that it is possible. It is a branch of statistics that deals with the occurrence of a random event. The number is expressed from 0 to 1 where 0 represents an impossible event and 1 represents a sure event.
Probability Formula
The probability formula is defined as the ratio of favorable outcomes to the ratio of total outcomes. For any event (E), this can be shown as
P(E)=Number of favorable outcomes /Number of total outcomes
Since Hamid is playing a trivia game with multiple choice questions, and each question has 2 correct answers among 5 answer choices, and Hamid has no idea what the answers to a certain question are, so he needs to choose two different answers at random, to determine what is the probability that Hamid guesses both answers correctly the following calculation must be performed:
2/5 x 1/4 = X
0.4 x 0.25 = X
0.1 = X
0.1 x 100 = 10
Therefore, the probability that Hamid guesses both answers correctly is 10%.
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Probability denotes possibility. The occurrence of a random event is the subject of this area of statistics. The number is expressed as a number between 0 and 1, where 0 denotes an improbable event and 1 denotes a certain event.
Statistical Formula
The ratio of favorable outcomes to the ratio of all outcomes is the definition of the probability formula. This can be shown as for any event (E) as
P(E) = Number of positive results / Number of total results
Given that each question in a multiple-choice trivia game has two correct answers out of a possible five, and that Hamid must choose two answers at random because he doesn't know what the answers are, the following calculation must be done to ascertain the likelihood that Hamid will correctly guess both answers:
2/5 x 1/4 = X
0.4 x 0.25 = X
0.1 = X
0.1 x 100 = 10
What is the slope of the line represented by the equation y − 3x 1?
Applying the derivative to the provided line with respect to "x," using the equation of the given line, The response is 3.
Why do you use the word "derivative"?In mathematics, the derivative of a function of a real variable measures the sensitivity of the function's value to changes in its argument. The derivative is the fundamental tool in calculus. a function's rate of evolution in respect to a variable Problems involving calculus and differential equations need the use of derivatives.
By slope, what do you mean?The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line. Calculate the percentage by dividing the elevation difference between two places by their separation. slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.
y(x) = 3x +1
derivate y(x) with respect to x. we get,
= 3
slope =3
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Let [tex]\displaystyle f(x)= \lim_{n\to \infty}\left( \dfrac{n^n (x+n)\left(x+\dfrac{n}{2}\right) \dots \left(x+\dfrac{n}{n}\right)}{n! (x^2+n^2)\left(x^2+\dfrac{n^2}{4}\right)\dots \left( x^2+\dfrac{n^2}{n^2}\right)}\right)^{\dfrac{x}{n}}[/tex] for all x > 0 , then;
[tex] A ) \ f\bigg(\dfrac{1}{2}\bigg) \geq f(1) \\\\ B)\ f\bigg(\dfrac{1}{3}\bigg) \leq f\bigg(\dfrac{2}{3}\bigg) \\\\ C) \ f'(2)\leq 0 \\\\ D) \ \dfrac{f'3(3)}{f(3)}\geq \dfrac{f'(2)}{f(2)} [/tex]
The solution is Option C.
The equation f'( 2 ) ≤ 0 is true
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
[tex]f ( x ) = \lim_{n \to \infty} [ \frac{( n^{n} ( x + n ) ( x + \frac{n}{2} ) ....( x + \frac{n}{n} )}{n! (x^{2}+n^{2}) ( x^{2} + \frac{n^{2}}{4} ) ....( x^{2} +\frac{n^{2}}{n^{2} } ) } ]^{\frac{x}{n} }[/tex]
Taking logarithm on both sides of the equation , we get
[tex]ln f ( x ) = \lim_{n \to \infty} \frac{x}{n} [\sum _{r=1}^nln\frac{1}{r/n} + \sum _{r=1}^nln\frac{(x + \frac{1}{r/n} )}{(x^{2} + (\frac{1}{r/n})^{2} ) }[/tex]
On simplifying the derivatives of the equation , we get
[tex]ln f ( x ) = x [\int\limits^1_0 {ln ( 1/t )} \, dt + \int\limits^1_0 {ln \frac{( x+1/t )}{(x^{2} + 1/t^{2} ) } } \, dt][/tex]
Now , substituting the limits in the equation , we get
[tex]ln f ( x ) = x [ \int\limits^1_0 {( - ln t+ ln (tx+1)-lnt-ln(t^{2} x^{2}+1)+lnt^{2}] } \, dt[/tex]
Substitute the value of tx = z in the equation , we get
[tex]ln f ( x ) = \int\limits^1_0 {ln\frac{(1+z)}{1+z^{2} } } \, dz[/tex]
Taking exponential on both sides of the equation , we get
[tex]f ( x ) = e^{\int\limits^x_0 {{ln\frac{(1+z)}{1+z^{2} } } \, dz} \, }[/tex]
Differentiating with respect to x , we get
[tex]\frac{f' (x ) }{f ( x ) } = ln\frac{1+x}{1+x^{2} }[/tex]
Now , on further simplification of the equation , we get
f ( x ) > 0 for x > 0
And , f' ( x ) > 0
[tex]ln\frac{1+x}{1+x^{2} } > 0[/tex]
And ,
x > x²
0 < x < 1
Therefore , f ( x ) is increasing ∀ x ∈ ( 0 , 1 )
Hence , the equation f' ( 2 ) ≤ 0 is true
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Explanation:
[tex] \rm f(x) = \lim \limits_{n \to \infty } \left( \dfrac{ \displaystyle \rm \prod \limits_{r = 1}^n \left(1 + \dfrac{rx}n \right ) }{\displaystyle \rm\prod \limits_{r = 1}^n \left(1 + \bigg(\dfrac{rx}n \bigg)^{2}\right )} \right)^{ \dfrac{x}{n} }[/tex]
[tex] \large \rm = {e}^{ x \int \limits_{0}^{1} ln(1 + xy)dy - ln(1 + (xy {)}^{2} ) dy }[/tex]
[tex]\rm f'(x)=f(x) \ln \bigg( \dfrac{1 + x}{1 + {x}^{2} } \bigg)[/tex]
[tex]\rm For \: x \in(0,1) \: it \: i s \: increasing \: function[/tex]
[tex]\rm f'(2) = f(2) \ln( \frac{3}{5} ) < 0[/tex]
[tex]\rm \dfrac{f'(3)}{f(3)} =ln \bigg( \dfrac{2}{5} \bigg), \dfrac{f'(2)}{f(2)} = ln \bigg( \dfrac{3}5 \bigg) [/tex]
How do you solve inverse questions?
In order to solve a inverse function question we switch the coordinates of x with that of y and the perform the required calculations.
The result which we get as is considered as a relation and not as a function.
We an calculate inverse for functions which are one to one .
A function is known as a one to one function only when every second element matches the first value.
The inverse question is a type of function , when we solve this function we get another function which is represented as , ‘g’ and is known as the inverse of function .
y = f(x) then,
x = g(y)
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Y = 1/3x + 4
3x+y=-6
Answer:
Step-by-step explanation:
x= -3
y= 3
Solve pls brainliest
I don't see the picture. Can you send it in the message.
Answer:
x 0 2 4 6
y 3 4 5 6
Step-by-step explanation:
y = x/2 + 3
x = 0
y = 0/2 + 3 = 0 + 3 = 3
x = 2
y = 2/2 + 3 = 1 + 3 = 4
x = 4
y = 4/2 + 3 = 2 + 3 = 5
x = 6
y = 6/2 + 3 = 3 + 3 = 6
How do you draw an inverse function?
Over the line y = x, a function and its inverse are reflected. It only takes one step to graph a function and its inverse: first, graph the function, then, to graph the inverse, switch all x and y values at each point.
Given,
Inverse function;
A function that can reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as "f-1" or "F-1."
Here,
To graph the inverse, you only need to alter the x and y values in each point on the function graph. Just take a look at all the numbers that are being reflected along the line y = x as they move from the f(x) function to its inverse g(x) and back again.
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6. If y = -2x² + 8x - 5 were put in vertex form y = a(x - h)² + k, then what is
the value of k?
A. -13
B. -3
C. 3
D. 1
Answer:
C. [tex]3[/tex]
Step-by-step explanation:
[tex]y=-2x^2 + 8x-5 \\ \\ =-2(x^2 -4x)-5 \\ \\ =-2(x^2-4x+4-4)-5 \\ \\ =-2((x-2)^2 -4)-5 \\ \\ =-2(x-2)^2 +8-5 \\ \\ =-2(x-2)^2 + 3[/tex]
a line ray or segment that divides a segment into two congruent parts at a 90° angle
A line, line segment, or ray that divides an angle into two congruent angles is called an angle bisector.
What are supplementary angles example?
Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°. Similarly, complementary angles add up to 90 degrees.
What do you mean by angle bisector?
If the angle is divided by the line and the angle is divided such that the angles are equal to each other then the line is called the angle bisector.
The word congruent means equal of the things. In this, the angles are congruent to each other which means the angles are equal to each other.
Thus, the black space is to be filled by the angle bisector.
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4. lisa wants to make a larger bandana similar to the bandana shown. if the shorter leg of the larger bandana is 15 inches, how long is its hypotenuse? a 10 in. c b 8 in.
Answer: 6 square root 23
Step-by-step explanation:
10^3 + 8^2
In a survey, one out of three people named blue as their favorite color. Two out of seven named red. If 1,092 people were included in the survey, how many named neither blue nor red as their favorite color?
By using fraction, it can be calculated that 416 people choose neither blue nor red as their favorite color.
What is fraction?
Suppose there is a collection and a part of the collection has to be taken. The part which is taken is called fraction. In other words, part of a whole is called fraction.
The upper part of the fraction is the numerator and the lower part of the fraction is called denominator.
This is a word problem on fraction.
Fraction of people choose blue as their favorite color = [tex]\frac{1}{3}[/tex]
Fraction of people choose red as their favorite color = [tex]\frac{2}{7}[/tex]
Fraction of people choose neither red nor blue as their favorite color =
[tex]1- (\frac{1}{3}+\frac{2}{7})\\\\1 - (\frac{7 + 6}{21})\\\\1-\frac{13}{21}\\\\\frac{21-13}{21}\\\\\frac{8}{21}[/tex]
Total number of people surveyed = 1092
Number of people choose neither red nor blue as their favorite color =
[tex]\frac{8}{21}\times 1092[/tex]
= 416
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Why is the slope called M?
In the equation y = mx + b, m is the slope of the line and b is the intercept.
What does the m represent in slope intercept form?The letter m is frequently used to represent slope; the reason for this usage is unclear, but it can be found in O'Brien's (1844) and Tod hunter's (1888) formulations of the equation for a straight line as "y = mx + b" and "y = mx + c," respectively.m is the line's slope and b is its intercept in the equation y = mx + b. The letters x and y stand for the line's separation from the x- and y-axes, respectively. When x = 0, the value of b equals y, and m indicates how steep the line is. The gradient of a line is another name for its slope.To learn more about slope intercept equation refer to:
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