Answer:
The minimum y-value of f(x) is -3.
Step-by-step explanation:
To find the minimum y-value of f(x), we can plug in a value of x that will make the y-value as small as possible. In this case, we can plug in x = 0 to get f(0) = 3² - 3 = 0. Since 0 is the smallest possible value for f(x), the minimum y-value of f(x) is 0.
Similarly, we can find the minimum y-value of g(x) by plugging in a value of x that will make the y-value as small as possible. In this case, we can again plug in x = 0 to get g(0) = 7 * 0² - 3 = -3. Since -3 is the smallest possible value for g(x), the minimum y-value of g(x) is -3.
Therefore, the correct answer is option A: "The minimum y-value of f(x) is -3."
Answer:
Step-by-step explanation:
A. The minimum y-value of f(x) is -3.
D. The minimum y-value of g(x) is -3.
Write a linear function f with the values.
The equation of the line is f(X)=(-1/6)x—(19/6)
What is equation?
In arithmetic, an equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.
Main body:
first linear functions have their general form as y= mx + c, where y belongs to the range and X belongs to the domain, m is the slope, and c is the y-intercept.
So using f(x) =y
Given that f(—5)=-4 , X=—5 and y=-4, hence by substituting into the general eqn y= mx+c, You get
-4= -5m+c ------(1)
Also given that f(1)=—3, X=1 and y=—3, hence by substituting into the general eqn y= mx+c, You get
-3= m+c --—-(2)
Solve equation (1) and (2), simultaneously to find the value of m and c. After which you will substitute into y=mx+c or f(X)=mx+c to get your f(X).
Note: you will get m=—1/6 and c=-19/6, from the simultaneous equations.
Hence f(X)=(-1/6)x—(19/6) and correct option is D.
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matthew wants to estimate the mean height of students attending his college. he records the heights of 635 randomly selected students attending the college. what is the population?
The population in order to calculate the mean height will be all the students attending the college.
The population is the entire group of individuals being studied. In this case, the population is all the students who goes to the college.
Every member of a group constitutes a population. It is the inverse of a sample, which is a percentage or proportion of a group. It is sometimes possible to poll every member of a group. The U.S. Census is a quintessential example of a population, as it is required by law that every member of the U.S. population reply. In most circumstances, surveying everyone is unfeasible in statistics.
Consider how long it would take you to phone every dog owner in the United States to find out what brand of dog food they preferred. Furthermore, people may choose not to respond or may forget to respond, resulting in incomplete censuses. By definition, incomplete censuses become samples.
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A set of data items is normally distributed with a mean of 500 and a standard deviation of 30. Find the data item in this distribution that corresponds to we givenz-score
z= -7
The data item that corresponds to z= -7 is (Type an integer or a decimal.)
The data item in this distribution corresponding to a z-score of -7 will be 290.
What is Z-score?The standard score in statistics is the number of standard deviations that a raw score's value is above or below the mean value of what is being observed or measured. Raw scores that are higher than the mean have positive standard scores, whereas those that are lower than the mean have negative standard scores. The Z-score measures how much a particular value deviates from the standard deviation. The Z-score, also known as the standard score, is the number of standard deviations above or below the mean for a given data point. The standard deviation reflects the level of variability within a particular data collection.
Here,
z=(X-μ)/σ
-7=(X-500)/30
-210=X-500
X=290
The data item in this distribution that corresponds to we given z-score
z equals to -7 will be 290.
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r(x) = x^2 + 5x + 4 write r(x) in factored form. I would like an explanation as to how you get the answer please!
Answer: (x+1)(x+4)
Step-by-step explanation:
Step 1: Use the sum-product pattern
x^2 + 5x + 4
x^2 + 4x + x + 4
Step 2: Common factor from the two pairs
x(x+4) + x+4
Step 3: Rewrite in factored form
(x+1)(x+4)
Tom's school is selling tickets to a Christmas performance. On the first day of ticket sales the school sold 11 senior citizen tickets and 12 child tickets for a total of $113. The school took in $76 on the second day by selling 10 senior citizen tickets and 2 child tickets. What does each ticket cost?
Senior citizen tickets cost $7, while child tickets cost $3.
Define cost?A mathematical formula known as a cost function is used to visualize how manufacturing costs will vary depending on the output level. In other words, given a specified quantity produced, it calculates the entire cost of production.
Senior citizen tickets should equal ST.
CT = child tickets
The school sold 11 senior citizen tickets and 12 kid tickets on the first day of ticket sales for a total of $113.
11 senior citizens equals 11ST.
12 children equals 12CT a total $113
11ST + 12CT = $113 ( REFER AS 1 )
On the second day, the school sold 10 senior citizen tickets and 2 kid tickets, bringing in $76.
10 senior citizen =10ST
2 children = 2CT
total 76
10ST + 2CT = $76 ( REFER AS 2 )
So from 1 and 2 we do elimination method
multiply eq 2 with 6 and subtracted from eq 1
60ST + 12CT = 456
That is
(60 -11)ST + (12-12)CT = 456 - 113
49ST = 343
ST = 343/49
ST = $7
the cost of senior citizen ticket is $7
10ST + 2CT = $76
10*7 + 2CT = 76
70 +2CT = 76
2CT = 76 - 70
2CT = 6
CT = $3
the cost of child ticket is $3
Senior citizen tickets cost $7 each, while child tickets cost $3 each
( to recheck from eq 1
7*11 + 3* 12 should be equal to 113
77 + 36 = 113 )
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(-20, 12)
(17, 2)
(-11, 8)
(17, 8)
(11, 2)
Is this relation a function?
Answer:
No because x-coordinate 17 appears twice.
Step-by-step explanation:
In a function, no two ordered pairs can have the same x-coordinate.
Here, points (17, 2) and (17, 8) have 17 as the x-coordinate. Since the same x-coordinate, 17, is used more than once, this relation is not a function.
Fifty students in the seventh grade are trying to raise at least $2,000 for sports supplies. They have already raised $750. How much should each student raise, on average, in order to meet the goal?
On average the 50 students need to raise $25 each.
What is average?
In plain English, an average is a single number chosen to represent a group of numbers; it is typically the sum of the numbers divided by the number of numbers in the group. The average of the numbers 2, 3, 4, 7, and 9 is, for instance, 5.
Given: Fifty students in the seventh grade are trying to raise at least $2,000 for sports supplies. They have already raised $750.
To find the number of students should each student raise, on average, in order to meet the goal.
Let, $2000 - $750 = $1250
So,
$1250/50 = 25
Hence, on average the 50 students need to raise $25 each.
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In gym class, the yellow team and the blue team played soccer. Ali doesn't remember the final score of the game, but she does remember the following. what's the score There were six goals scored in total. Neither team scored more than two goals in a row at any point in the game. Determine all the possible final scores and the different ways each score could have been obtained. The blue team won the game.
Answer:
Step-by-step explanation:
i need help
Make a frequency distribution and find the relative frequencies for the following number set. Round the relative
frequency to the nearest tenth of a percent.
10 20 40 50 60 80
10 20 40 60 60 80
20 30 50 60 70 90
20 30 50 60 80 90
Number Frequency Relative Frequency
The relative frequencies for the following number set is 10 30 40 50 60 70 10 30 40 60 60 80 20 30 50 60 70 90 20 30 50 60 70 90
How do you find the relative frequency in a frequency distribution?
Divide the frequency by the total number of data values to obtain the relative frequency. Add all of the earlier relative frequencies to the relative frequency for the current row to obtain the cumulative relative frequency. Divide the total number of occurrences of the result you're interested in by the total number of occurrences if your data are observational. This may be expressed mathematically as relative frequency = frequency of the desired result / all occurrences.
There are 24 items.
Relative Frequency:
10 - (2) - 8.33%
20 - (1) - 4.17%
30 - (4) - 16.67%
40 - (2) - 8.33%
50 - (3) - 12.5%
60 - (5) - 20.83%
70 - (3) - 12.5%
80 - (1) - 4.17%
90 - (2) - 8.33%
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The rectangular floor of a classroom is 30 feet in length and 20 feet in width. A scale drawing of the floor has a length of 15 inches. What is the area, in square inches, of the floor in the scale drawing?
HURRY PLEASEEEEEEEE
The area of the floor in the scale drawing will be equal to 150 in².
What is the area?An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.
As per the given information in the question,
Length of the classroom, l = 30 feet and,
The width of the classroom, w = 20 feet.
As per the scale drawing, the length of the classroom, l' = 15 feet
Let the scale width, w' = x feet
As we can see that the original length is twice the scale drawing.
Then, the original width also is twice the scale drawing.
So, w' = 20/2 = 10 feet.
Now, the area of the floor in the scale drawing will be,
A = wl
A = (15)(10)
A = 150 in².
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In a box of chocolates, of the chocolates are white chocolate, are milk
chocolate, and the rest are dark chocolate.
What fraction of the chocolates are dark chocolate?
......................................................................
Big Ideas: Graph f(x) = 0.5x^3 - 2x + 2.5. Identify the x-intercepts and the points where the local maximums and local minimums occur. Determine the intervals for which the function is increasing or decreasing. Round to the nearest hundredth, if necessary.
The x-intercept is x = (blank).
The local maximum is (blank, blank).
The local minimum is (blank, blank).
The function is increasing when x < (blank) and x > (blank).
The function is increasing when (blank) < x < (blank).
Answer:
The x-intercept is x = 0.
The local maximum is (-0.38, -0.46).
The local minimum is (0.38, -0.46).
The function is increasing when x < -0.38 and x > 0.38.
The function is increasing when -0.38 < x < 0.38.
Step-by-step explanation:
To find the x-intercepts, we can set the function equal to 0 and solve for x. This gives us the equations:
0.5x^3 - 2x + 2.5 = 0
To find the points where the function has local maximums and minimums, we can take the derivative of the function and set it equal to 0. This gives us the equation:
1.5x^2 - 2 = 0
To find the intervals where the function is increasing or decreasing, we can take the derivative of the function and determine the sign of the derivative. A positive derivative indicates that the function is increasing, while a negative derivative indicates that the function is decreasing.
Based on the information above, we can fill in the blank answers as follows:
The x-intercept is x = 0.
The local maximum is (-0.38, -0.46).
The local minimum is (0.38, -0.46).
The function is increasing when x < -0.38 and x > 0.38.
The function is increasing when -0.38 < x < 0.38.
Part F: Order the integers from least to greatest. 12, -6, 20, -47, -11
The integers are -47, -11, -6, 12, 20 in order of least to greatest.
Explain about the integers?A whole number that can be positive, negative, or zero is called an integer. It is not a fraction. -5, 1, 5, 8, 97, and 3, 043 are some examples of integers. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers.
Positive numbers, negative numbers, and zero make up integers. Thus, integers include 0 through 3, as well as -1, -2, and -3. No further parts, such as fractions or decimals, are allowed in integers. Therefore, fractional and decimal numbers like 3 1/2 and -7.5 are NOT integers.
Integer is derived from the Latin integer, which means whole or untouched, from the prefix in (for "not") with tangere ("to touch"). The words "entire" and "integer" are both derived from the same root, which is the French word entire.
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Which equation is equivalent to the quadratic equation x^2− 8x +19 = 0 where k represents the absolute value of the maximum value of the function? options:A (x-4)^2+k=0 B:(x-4)^2-k=0 C:(x+4)^2+k=0 D:(x+4)^2-k=0
The equation that is equivalent to quadratic equation x^ 2-8x+19=0 is
(x-4)^ 2+k = 0 using quadratic equation properties .
What is quadratic equation ?
A quadratic equation is a second order equation written as ax2 + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.
Properties of graph of quadratic equation :
1. The shape of curve y = f(x) is a parabola.
2. If a>0, the parabola opens upwards.
3. If a<0, the parabola opens downwards.
4.The coordinates of vertex of parabola in all these cases is
(-b/2a , -D/4a).
The given equation is x^ 2-8x+19=0
a = 1,
b = -8,
c = 19.
As a>0, 2nd property is correct i.e. no maximum value , only minimum value can be find that will be at vertex.
So, the vertex = (4,3)
The minimum value = 3 at 4.
So, the value of k = 3,
Given equation can be written as x^ 2-8x+16+3 = 0.
= (x-4)^ 2 +3 = 0.
The option A is correct.
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A police officer is estimating the distance from one side of a street to the other. The actual distance is 13.4 m. The police officer’s estimate is 14 m. Find the absolute error and the percent error of the police officer’s estimate.
PLEASE HELP
The absolute error and the percent error of the police officer’s estimate will be 4.29%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A cop is assessing the separation from one side of a road to the next. The genuine distance is 13.4 m. The cop's gauge is 14 m.
The absolute error and the percent error of the police officer’s estimate are calculated as,
%error = [(14 - 13.4) / 14] x 100
%error = (0.60 / 14) x 100
%error = 4.29%
The outright mistake and the percent blunder of the cop's gauge will be 4.29%.
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What percentage of trains were late in this particular week? 27.6% 38.2% 40.0% 72.4%
Answer:
27.6•\• is the answer from me
Does 0.010110111011110... represent a
rational number or an irrational number?
Explain your reasoning.
Answer:
This is an irrational number.
Step-by-step explanation:
If you see the decimal, it has the values of 1 and 0, but are not constant.
If it were to be 0.010101010... it would be rational.
But this decimal does not look like that, so its irrational.
Hope this helps.
What is the distance between points m and n? meters
Answer: 9.8
Step-by-step explanation:
If anyone could help it would be much appreciated.
kylie works for a large nursery and is investigating whether to use a new brand of seeds. the new brand of seeds advertises that 93% of the seeds germinate, which is higher than the germination rate of the seeds she is currently using. she will change over to this new brand unless the actual germination rate is less than what is advertised. kylie conducts an experiment by randomly selecting 76 seeds of the new brand and plants them. she finds that 70 of those seeds germinated. what are the null and alternative hypotheses for this hypothesis test?
The null and alternative hypotheses for this hypothesis test is H₀ : p = 0.93, Hₐ : p > 0.93.
What is Hypothesis ?A hypothesis in a scientific context, is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.
What is Null and Alternative Hypotheses?Null and alternative hypotheses are used in statistical hypothesis testing. The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.
Let 'p' be the population proportion.
Given statement : The new brand of seeds advertises that 93% of the seeds germinate, which is higher than the germination rate of the seeds she is currently using.
Since null hypothesis shows that there is no significant difference between the quantities where as alternative hypothesis believes that there is some difference,
Hence, the null and alternative hypotheses for this hypothesis test will be :- H₀ : p = 0.93
Hₐ : p > 0.93
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Please hurry and help!
Graph the following linear equation using the intercepts.
\displaystyle -10 x-12 y=-60−10x−12y=−60
The x−intercept is 6 and the y-intercept is 5.
What is an equation of a line?
In high school algebra, "the equation of a line" is a crucial concept. This refers to an equation in the (x,y) plane with a line as its solution set. The "slope-intercept" form is the most widely used form in algebra. y = mx + b. In essence, x is used as a parameter in this formula, and y is written as a function of x: y = f(x) = mx+b.
Here, we have
The given equation of a line is:
−10x − 12y = −60
10x + 12y = 60
x/6 = y/5 = 1
Hence, the x−intercept is 6 and the y-intercept is 5.
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a random sample of size 36 is taken from a population with mean 17 and standard deviation 6. the probability that the sample mean is greater than 18 is?
The probability that the sample mean is greater than 18 as calculated is 0.8413.
Given data,
n = 36, sample size
μ = 17, population mean
σ = 6, population standard deviation
when x = 18
z = (18 - 17)/1 = 1
P(x <18) = 0.8413
Therefore , the probability = 0.8413
A population's standard deviation serves as a gauge for how widely distributed its individual data points are. It's a way to express how dispersed from the mean the data is.
While a large standard deviation indicates that the data is more spread, a small standard deviation indicates that the data points are often close to the mean.
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Find the 59th term of the arithmetic sequence 29, 37, 45,
The , t59=492th term in the arithmetical sequence.
What is arithmetical sequence?The series where the common difference between any two next words stays constant is known as an arithmetic sequence. Let's review what a sequence is.
A collection of numbers that follow a pattern is called a sequence.
As an illustration, the numbers 1, 6, 11, 16,... are an arithmetic sequence because they follow a pattern in which the preceding term is multiplied by 5 to produce each subsequent number. There are two formulas for arithmetic sequences.
The equation to determine the nth term in an arithmetic sequence
The formula for calculating the sum of an arithmetic sequence's first n terms
The arithmetic sequence formula can be used to discover any term in the arithmetic sequence.
According to our question-
AP = 29,37,45,...
d= t2-t1
=37-29
=8
n=59
tn=a+(n-1)d
t59=29+(59-1)8
t59=28+58×8
t59=28 + 464
t59=492
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1. you have three baskets of fruit. one has apples, one has oranges, and one is a mix of the two. all the baskets are mislabeled. how many fruits do you need to pull out of how many baskets to correctly label them all.
To label the three basket correctly , We have to pull out total two fruits from all of them
Let Say , We are drawing a fruit from a basket labelled "Mixture"
If this fruit is an apple, then indicate such on the label (Because this basket does not contain Mixture, so if one is apple, all are apples only). We've now discovered that the basket marked "Mixture" solely includes apples.
Therefore , the Correct Label is "apples"
Now, Drawing another fruit from basket labelled "Oranges," we can see that it either contains solely apples or mixture. The basket marked "Oranges" contains "Mixture," as we already know which basket only contains apples. Put "Mixture" on the label.
Oranges will be the name of the third basket.
The same reasoning holds true if you suppose that you initially chose an orange from the basket marked "Mixture."
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It's a mean and median frequency table
Pls answer
a) The mode is 2.
b) 32 Students were there altogether.
c) 15 dinners were served during the week.
d)The mean number of dinners is 2.5.
What is mode?This refers to the value that appears most often in a set of data values.
What is mean?
This refers to the average of the given set of numbers. It is calculated by dividing the sum of given numbers by the total number of numbers.
Given in the question:
a)The number of school dinners 2 has a frequency of 12.
Hence, the mode is 2.
b) To calculate the number of students altogether, we add then frequencies
Total number of students = 0 + 8+ 12 + 6+ 4 + 2
Total number of students = 32
c) To get the number of dinners served during the week, we add the number of dinners together.
Number of dinners served during the week= 0 + 1 + 2 + 3 + 4 + 5
Number of dinners served during the week = 15
D) The mean number of dinners =
1+1+1+1+1+1+1+1+2+2+2+2+2+2+2+2+2+2+2+2+3+3+3+3+3+3+4+4+4+4+5+5
32
The mean number of dinners = 80
32
The mean number of dinners = 2.5
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Tell whether the point (13, 17) is a solution to the system of linear equations?
y = -x + 30
y = x + 6
yes
no
Answer:
No
Step-by-step explanation:
When the 2 equations are graphed the point (13, 17) is not
a solution to the system of linear equations.
So the answer is no.
If you want to look for the solution**- the solution to the equation is (12, 18)
The median, or middle value, is 42 48 52 54 59 61 61 64 65 67 68 70 72 75 80
The median or the middle value of 42 48 52 54 59 61 61 64 65 67 68 70 72 75 80 is 64.
What is a median?It is the middle value of the given set of numbers after arranging the given set of numbers in order.
We have,
42 48 52 54 59 61 61 64 65 67 68 70 72 75 80
The given set of numbers is in ascending order.
There are 15 numbers.
The middle number will be the 8th number.
8th number = 64
Thus,
The median is 64.
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f(x) = x²+x-6
g(x) = 4x +9
Find: g(f(x))
The value of the function g(f(x))=4x²+4x-15 if f(x) = x²+x-6
g(x) = 4x +9.
What is meant by a function?An exact one of each element of Y is assigned to each element of X via a mathematical function from a set X to a set Y. The sets X and Y are denoted by the terms "domain" and "codomain," respectively.
The fundamental concept of functions was the connection between fluctuating quantities and other variables. One illustration of this is the impact of time on a planet's position. Beginning at the end of the 17th century and continuing until the 19th century, the concept was developed using the infinitesimal calculus.
Given,
f(x) = x²+x-6
g(x) = 4x +9
f(g(x))=f(4x+9)
g(f(x))=4(x²+x-6)+9
g(f(x))=4x²+4x-24+9
g(f(x))=4x²+4x-15
Therefore, the value of the function g(f(x))=4x²+4x-15 if f(x) = x²+x-6
g(x) = 4x +9.
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You are designing one last sandbag-dolly system for the performance. this time, two actors will be on the dolly. the mass of the dolly and actors combined is 94 kg, and the mass of the sandbag is 35 kg. the coefficient of kinetic friction between the dolly and the stage floor is 0.20. what is the acceleration?
The acceleration of the dolly-sandbag system is 1.23 m/s²
How to calculate the acceleration?Given parameters:
The mass of the dolly and actor combined is: M = 94 kg
the mass of the sandbag is: m = 35 kg.
The coefficient of kinetic friction between the dolly and the stage floor is 0.20.
Let the acceleration is a.
Hence, From Newton's 2nd law of motion, we can write that:
ΣF = (m+M) a
mg - μMg = (m+M) a
a = g (m- μM)/ (m+M)
= 9.8 (35 - 0.20 × 94)/(35 + 94)
= 9.8 (16.2)/(129)
= 1.23 m/s².
Hence, the acceleration of the dolly-sandbag system is 1.23 m/s².
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There were two candidate A and B conteting for the municipal corporation election in a town. The total number of voter in the town were 80,000. If 90% of the voter had voted and 60% of vote polled were cat in favour of A, find the number of vote received by B
There were two candidate A and B contesting for the municipal corporation election in a town. The total number of voter in the town were 80,000. If 90% of the voter had voted and 60% of vote polled were cat in favour of A, 28,800 the number of vote received by B.
What is municipal corporation election?A state-incorporated city, town, village, or county that has the power to manage local governmental matters, such as creating a police force. A municipal corporation is established by a state's legislature, which also determines its lifespan, privileges, and powers. likewise known as a municipality.
A local governing body, such as cities, counties, towns, townships, charter townships, villages, and boroughs, is referred to legally as a "municipal corporation." Municipally-owned companies can also be referred to as this
Regulation of building construction and land usage. Town planning is included in urban planning. preparing for social and economic progress. water supply for residential, commercial, and industrial uses.
Given that,
Total number voters = 80,000
Total number of votes polled = 90%
Thus,
= (90/100) × 80,000
= 72,000
So, total percent of votes received by B if A gets 60% of polled votes.
= 100% - 60%
= 40%
Hence, total number of votes received by B
= (40/100) × 72,000
= 28,800
Therefore, the number of votes received by B, out of total votes polled is 28,800 votes.
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