The required solution of the nonlinear equation is (4, 13) and (2, 1).
Given that,
To solve the nonlinear system of equations for real solutions. y =x²-3, 6x-y=11.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
y =x²-3 - - - - - [1]
6x-y=11
From equation 1,
6x -x² + 3 = 11
x² - 6x + 8 = 0
x = 4, and 2
Substitute this x's in equation 1
That gives for the above x's,
y = 13 and 1
Thus, The required solution of the nonlinear equation is (4, 13) and (2, 1).
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24. The following fractions compare the number of free throws made to the number taken by
basketball players:
Smith:
13
19
Haller:
12/20
Dennis:
14/17
Ballard:
17/22
Rank the free throw accuracy of these players from lowest to highest. Justify.
The free throw accuracy of these players can be ranked from lowest to highest as Haller, Smith, Ballard, and Dennis.
What is a fraction?
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, or three-quarters.
To rank the free throw accuracy of these players from lowest to highest, we need to compare the fraction of free throws made to the total number of free throws taken by each player.
The fraction of free throws made to the total number of free throws taken is called the free throw percentage.
The free throw percentage for each player can be calculated by dividing the number of free throws made by the number of free throws taken and expressing the result as a decimal.
For example, the free throw percentage for Smith can be calculated as follows:
Free throw percentage = 13/19 = 0.68
We can use this same method to calculate the free throw percentage for the other players:
Haller: Free throw percentage = 12/20 = 0.6
Dennis: Free throw percentage = 14/17 = 0.82
Ballard: Free throw percentage = 17/22 = 0.77
Based on these calculations, the free throw accuracy of these players can be ranked from lowest to highest as follows:
Haller: Free throw percentage = 0.6
Smith: Free throw percentage = 0.68
Ballard: Free throw percentage = 0.77
Dennis: Free throw percentage = 0.82
Hence, the free throw accuracy of these players can be ranked from lowest to highest as Haller, Smith, Ballard, and Dennis.
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Draw the graph for y=2x-3 for -2<=x<=3
The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
The graph is shown below.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
y = 2x - 3 for -2 ≤ x ≤ 3.
The x values are between -2 and 3
For x = -2,
y = 2 x (-2) - 3 = -4 - 3 = -7
For x = 3,
y = 2 x 3 - 3 = 6 - 3 = 3
Now,
The graph is shown below.
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The drama club sold 800 tickets to their spring play. Floor seats cost 110 each and balcony seats cost 8$ each. Tickets sales were 7740. How many floor seat tickets were sold
There were 14-floor seat tickets sold to their spring play.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
Let's assume x be floor seat tickets and y be balcony seats
As per the given formation, the equation would be as:
x + y = 800 ....(i)
110x + 8y = 7740 ...(ii)
Multiply by 8 into equation (i), and subtract into equation (ii),
110x + 8y - 8x - 8y = 7740 - 6400
102x = 1340
x = 1340/102
x = 13.7 ≈ 14
Therefore, there were 14-floor seat tickets sold.
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b) Since Barrow is looking for a good batter for his team, do you think that the batting average or the
slugging average is more indicative of a good batter? Answer the question and explain your
reasoning in 2-3 sentences.
Slugging average is more indicative of a good batter rather than batting average.
Define slugging average.The total number of bases a player accumulates per at-bat is represented by slugging percentage. In contrast to on-base percentage, which takes walks and hit-by-pitch pitches into account, slugging percentage simply considers hits. Slugging average is distinct from batting average in that not every hit is worth the same amount.
Given
Since Barrow is looking for a good batter for his team
In my point of view, Slugging average is more indicative of a good batter.
The slugging percentage is a player's average number of bases per at-bat. Slugging percentage, unlike on-base percentage, solely accounts for hits and excludes walks and hit-by-pitch pitches from its computation. In contrast to batting average, slugging percentage does not reward every hit equally.
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100 Points + Brainliest if correct and well explained:
A recent survey at a local recreation center reported that 79% of the participants played pickleball. Of those who play pickleball, 6% are female. Of those who do not play pickleball, 21% are male. Based on this information, construct a two-way relative frequency table. Round all values to the nearest whole percentage.
Male Female Total
Plays pickleball 77% 2% 79%
Does not play pickleball 6% 15% 21%
Column Totals 83% 17% 100%
Male Female Total
Plays pickleball 74% 5% 79%
Does not play pickleball 4% 17% 21%
Column Totals 78% 22% 100%
Male Female Total
Plays pickleball 75% 4% 79%
Does not play pickleball 4% 17% 21%
Column Totals 79% 21% 100%
Male Female Total
Plays pickleball 76% 3% 79%
Does not play pickleball 4% 17% 21%
Column Totals 80% 20% 100%
Answer:
[tex]\begin{array}{|l|c|c|c|}\cline{1-4} \vphantom{\dfrac12}& \sf Male & \sf Female & \sf Total\\\cline{1-4} \vphantom{\dfrac12}\sf Plays \; pickleball & 74\%& 5\% & 79\%\\\cline{1-4} \vphantom{\dfrac12}\sf Does\;not\;play\; pickleball &4\% & 17\%& 21\%\\\cline{1-4} \vphantom{\dfrac12}\sf Column\;Totals&78\%&22\%& 100\%\\\cline{1-4}\end{array}[/tex]
Step-by-step explanation:
Create a blank frequency table:
[tex]\begin{array}{|l|c|c|c|}\cline{1-4} \vphantom{\dfrac12}& \sf Male & \sf Female & \sf Total\\\cline{1-4} \vphantom{\dfrac12}\sf Plays \; pickleball & & &\\\cline{1-4} \vphantom{\dfrac12}\sf Does\;not\;play\; pickleball & & &\\\cline{1-4} \vphantom{\dfrac12}\sf Column\;Totals&&& 100\%\\\cline{1-4}\end{array}[/tex]
If 79% of the participants played pickleball, then 21% of the participants do not play pickleball.
Input these percentages into the table:
[tex]\begin{array}{|l|c|c|c|}\cline{1-4} \vphantom{\dfrac12}& \sf Male & \sf Female & \sf Total\\\cline{1-4} \vphantom{\dfrac12}\sf Plays \; pickleball & & & 79\%\\\cline{1-4} \vphantom{\dfrac12}\sf Does\;not\;play\; pickleball & & & 21\%\\\cline{1-4} \vphantom{\dfrac12}\sf Column\;Totals&&& 100\%\\\cline{1-4}\end{array}[/tex]
Of those who play pickleball, 6% are female.
Therefore, of those who play pickleball, 94% must be male.
The total percentage of those who play pickleball is 79%, so find 6% and 94% of 79%:
[tex]\begin{aligned}\textsf{Plays pickleball (female)}&=6\% \; \sf of \; 79\%\\&=0.06 \times 0.79\\&=0.0474\\&=5\%\; \sf (nearest\;percent)\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Plays pickleball (male)}&=94\% \; \sf of \; 79\%\\&=0.94 \times 0.79\\&=0.7426\\&=74\%\; \sf (nearest\;percent)\end{aligned}[/tex]
Input the found percentages into the table:
[tex]\begin{array}{|l|c|c|c|}\cline{1-4} \vphantom{\dfrac12}& \sf Male & \sf Female & \sf Total\\\cline{1-4} \vphantom{\dfrac12}\sf Plays \; pickleball & 74\%& 5\% & 79\%\\\cline{1-4} \vphantom{\dfrac12}\sf Does\;not\;play\; pickleball & & & 21\%\\\cline{1-4} \vphantom{\dfrac12}\sf Column\;Totals&&& 100\%\\\cline{1-4}\end{array}[/tex]
Of those who do not play pickleball, 21% are male.
Therefore, of those who do not play pickleball, 79% must be female.
The total percentage of those who do not play pickleball is 21%, so find 21% and 79% of 21%:
[tex]\begin{aligned}\textsf{Does not play pickleball (male)}&=21\% \; \sf of \; 21\%\\&=0.21 \times 0.21 \\&=0.0441\\&=4\%\; \sf (nearest\;percent)\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Does not play pickleball (female)}&=79\% \; \sf of \; 21\%\\&=0.79 \times 0.21\\&=0.1659\\&=17\%\; \sf (nearest\;percent)\end{aligned}[/tex]
Input the found percentages into the table and calculate the column totals:
[tex]\begin{array}{|l|c|c|c|}\cline{1-4} \vphantom{\dfrac12}& \sf Male & \sf Female & \sf Total\\\cline{1-4} \vphantom{\dfrac12}\sf Plays \; pickleball & 74\%& 5\% & 79\%\\\cline{1-4} \vphantom{\dfrac12}\sf Does\;not\;play\; pickleball &4\% & 17\%& 21\%\\\cline{1-4} \vphantom{\dfrac12}\sf Column\;Totals&78\%&22\%& 100\%\\\cline{1-4}\end{array}[/tex]
Answer:
c
Step-by-step explanation:
i took the test :)
Find the area of the following parallelogram:
3cm,5cm, and 4.5
What is the area of the parallelogram?
Please show your work.
Step-by-step explanation:
Area of parallelogram = base • height
Where,
Base = 4.5 cm
Height = 5 cm.
Area = 4.5 cm • 3 cm
Area = 13.5 cm²
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Mr. Cruz drove 70 miles in March. He drove 7 times as many miles in March as he did in January. He drove 4 times as many miles in February as he did in January. How many miles did Mr. Cruz drive in February?
The number of miles that Mr.Cruz drive in February is 40 miles .
In the question ,
it is given that ,
Mr.Cruz drove 70 miles in March .
let the number of miles that Mr.Cruz drive in January is "x" miles .
He drive 4 times as many miles in February as he did in January ,
So , the number of miles driven in February is = 4x .
he also drive 7 times as many miles in march as he did in January .
So , the number of miles driven in March is = 7x
According to the question ,
7x = 70
x = 10
So , miles driven in February is = 4(10)
= 40 miles .
Therefore , the number of miles driven is February is 40 miles .
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find the minimum sample size needed if we wish to be 92% confiodent and error to be within 5 years of the true mean age
To find the minimum sample size needed to estimate the mean of a population with a certain level of confidence and margin of error, you can use the following formula: n = (Z^2 * p * (1 - p)) / e^2
What is mean?
The mean, also known as the arithmetic average, is a measure of central tendency that represents the average value of a set of data. To calculate the mean of a set of numbers, you add up all the numbers in the set and then divide the sum by the number of numbers in the set.
n is the minimum sample size
Z is the z-score corresponding to the desired level of confidence (e.g. for a confidence level of 92%, the z-score would be approximately 1.75)
p is the estimated proportion of the population that has the characteristic of interest (e.g. if you are trying to estimate the mean age of a population and you believe that about 50% of the population is within 5 years of the true mean age, then p would be 0.5)
e is the margin of error (e.g. if you want the error to be within 5 years of the true mean age, then e would be 5)
Plugging in the values given in the problem, we get:
n = (1.75^2 * 0.5 * (1 - 0.5)) / 5^2
= (3.0625 * 0.5 * 0.5) / 25
= 0.122 / 25
= 0.0049
Since sample size must be a whole number, we would need to round up to the nearest integer, which would be a minimum of 1 sample. However, it is generally recommended to use a larger sample size to increase the precision and reliability of the estimate.
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Use the graph of f(x) to find the following values.
a)f(-4)
b)f(-5)
c)f(3)
d)f(4)
a) [tex]f(-4)[/tex] is equal to the output when [tex]x=-4[/tex]. Therefore, [tex]f(-4)=-7[/tex].
b) [tex]f(-3)=-11[/tex]
c) [tex]f(3)=-3[/tex]
d) [tex]f(4)=-1[/tex]
i need this asap pleaseee
The correct option using linear equations is [tex]y\leq 2.85x[/tex].
What are linear equations?
A linear equation is one with variables of power 1, such as ax+b = 0, where x is the variable and a and b are fundamental values. Equations are claims that two mathematical expressions comprising one or more variables are equal. The term "linear equation" refers to an equation where the greatest power of the variable is one.
Since the budget is y, the total amount spent on fuel must be less than or equal to the budget. Since it is $2.85 per gallon, the correct equation would be [tex]y\leq 2.85x[/tex].
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A school sold 461 tickets for the school play. Student tickets cost $3 and adult tickets cost $4. Ticket sales totaled $1624.
Part A. Write and solve a system of equations to model this situation.
Part B. Then explain the meaning of your solution.
The system of equations to model this situation is given by;
x + y = 461
3x + 4y = 1624
The school sold 220 students tickets and 241 adult tickets.
How to write and solve equation?let
Number of students tickets = x
Number of adults tickets = y
x + y = 461
3x + 4y = 1624
From (1)
x = 461 - y
Substitute into (2)
3x + 4y = 1624
3(461 - y) + 4y = 1624
1383 - 3y + 4y = 1624
- 3y + 4y = 1624 - 1383
y = 241
Substitute into (1)
x + y = 461
x + 241 = 461
x = 461 - 241
x = 220
In conclusion 220 students tickets and 241 adults tickets were sold.
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RST and WXY are similar triangles. RS = 2, WX = 5, ST = x + 1, and XY = 3x-1
Solve for x. HELP PLEASE ANYONE
Answer: x=7
Step-by-step explanation:
2/5=x+1/3x-1
find the LCD
15x-5
multiply 2/5 by 3x-1
multiply x+1/3x-1 by 5
6x-2=5x+5
x=7
Find the sum of 2x2 + 5x + 7 and - 1022 - 7x + 1.
[tex](2x^2 + 5x + 7) + ( - 1,022 - 7x + 1)\\\\2x^2 + 5x + 7 - 1,022 - 7x + 1\\\\2x^2 + 5x + 7 - 1,022 - 7x + 1\\\\2x^2-2x-1,014[/tex]
ayúdenme por favor...
Answer:
konsi bhasha h bhai ye?
Step-by-step explanation:
i dont understand
un camion lleva 2 646 kilos de naranja en 147 cajas. ¿ cuantos kilos pesa cada caja?
por faaaa ayuda....
18 Kilos
Step-by-step explanation:
2646 /147 = 18
In the problem on the previou page uppoe alex wanted to know how many week it would take him to work 51 hour alex work 3 hour a day and 4 day a week
Since you cannot have a partial week, it would take Alex at least 5 weeks to work 51 hours at this rate.
What is time and work?Time and work is a mathematical concept that includes determining the amount of time necessary to do a specific quantity of labor. This idea is frequently applied in daily life and a number of industries, including manufacturing, construction, and project management.
Problems with time and work include two factors: the quantity of employees and the amount of time needed to finish a task. The quantity of effort is fixed and unchanging. The formula Work = Time * Number of Workers must be applied in order to overcome these issues.
For instance, if a task requires three people to finish it in six hours, the total quantity of work completed is six hours multiplied by three, or 18 hours.
How to solve?
If Alex works 3 hours a day and 4 days a week, he works a total of 3 hours * 4 days = 12 hours per week.
To work 51 hours, it would take Alex 51 hours / 12 hours/week = 4.25 weeks.
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Tamar's house is greater than 472 and less than 500 which number can be on Tamar's house?
490
472 <490<500
it fits the criteria
If CD represents 100%, what is the length of a line segment that is 25%? Explain.
Answer: (1/4)CD
Step-by-step explanation:
CD is 100% when the line segment is 25% of it or 1/4 of it! Then the line segment is (1/4)CD.
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The diagram shows a sector of a circle radius 10 cm.
Find the perimeter of the sector, giving your answer correct to 1 decimal place.
Answer:
P ≈ 43.6 cm
Step-by-step explanation:
the perimeter (P) is the sum of the 2 radii and the arc
arc length = circumference of circle × fraction of circle
= 2πr × [tex]\frac{135}{360}[/tex]
= 2π × 10 × 0.375
= 20π × 0.375
≈ 23.6 cm ( to 1 decimal place )
Then
P = 23.6 + 10 + 10 = 43.6 cm
Sophia scored 92% on a math test. If the test had 50 questions, how many did she get correct?
Answer:46 answers :)
Step-by-step explanation:
The seating capacity of the gym at Union Hill is 550. So far, there are 210 fans already at the basketball game. How many more fans can attend the game?
Answer:
340
Step-by-step explanation:
550 - 210 = 340
An item is regularly priced at $30 . it is on sale for 70% off the regular price. how much (in dollars) is discounted from the regular price?
The amount in dollars discounted from the regular price is $21
Calculating discounted amountFrom the question, we are to determine the amount that is discounted from the regular price
From the given information,
The regular price is $30
and
The item is on sale for 70% off the regular price.
Thus,
The amount discounted from the regular price = 70% of $30
The amount discounted from the regular price = 70% × $30
The amount discounted from the regular price = 0.7 × $30
The amount discounted from the regular price = $21
Hence, the amount is $21
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The chart shows Maria's workout schedule. Today she worked out with weights and then had a long run. When is the next time Maria will do both workouts on the same day?
The next time Maria will do both workouts on the same day is 15 days
When next Maria will do both workouts on the same day?Weights = every 3 days Long run = every 5 daysFind the lowest common multiple (LCM) for both weight days and long-run days
3 = 3 , 6, 9, 12, 15, 18, 21
5 = 5, 10, 15, 20, 25, 30
The lowest common multiple (LCM) for both weight days and long-run days is 15
Therefore, Maria will do both workout again in 15 days time.
Complete question:
The chart shows Maria's workout schedule. Today she worked out with weights and then had a long run. When is the next time Maria will do both workouts on the same day? Weights every 3 days and long run every 5 days
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Choose the graph of the linear equation.
y = −2x − 8
The equation of line is y = -2x - 8 and the slope is -2
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
y = -2x - 8 be equation (1)
The equation is of the form y = mx + b where m is the slope and b is the y-intercept
Substituting the values in the equation , we get
The slope of the line m = -2
The y intercept of the line b = -8
Now , the graph of the linear equation is given below
Hence , the equation of line is y = -2x - 8
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The table represents some points on the graph of linear
function f.
Answer: None of these
Step-by-step explanation:
The slope of the graph of [tex]f[/tex] is [tex]\frac{-224-64}{-2-1}=96[/tex].
Using point-slope form,
[tex]f(x)-64=96(x-1)\\\\f(x)-64=96x-96\\\\f(x)=96x-32[/tex]
Therefore, none of the options are correct. This can be confirmed by an online calculator.
A store has apples on sale for $21.00 for 6 pounds.if an apple approximately 5 ounces,how many apples can you buy for $168.00?
Part 1 The cost per pound of the apples on sale is ——-
Part 2 you can buy————pounds of apples for $168.00
Part 3 since 1 pound =16 ounces,so there are about ____apples in each pound
Part 4 you can buy approximately——— apples for $168.00
Help pls
Answer:
A store has apples on sale for $21.00 for 6 pounds.if an apple approximately 5 ounces,how many apples can you buy for $168.00?
you can buy approximately 256 apples
Step-by-step explanation:
Part 1 The cost per pound of the apples on sale is —3.50—-
Part 2 you can buy——48——pounds of apples for $168.00
Part 3 since 1 pound =16 ounces,so there are about __3__apples in each pound
Part 4 you can buy approximately—256— apples for $168.00
the gold prospector panned for gold 1000 times and actually found some 53 of those times. what is the probability that he will find the gold the next time he pans for gold?
Probability is the possibility of happening an event.
Given that, the gold prospector panned for gold 1000 times and actually found 53 times of those times.
The probability that he will find the gold next time is:
53/1000
= 0.053
Hence, the probability that he will find the gold the next time he pans for gold is 0.053.
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Suppose a sale price is $18 and the discount is 25%. Explain how to find the regular price.
Answer:
Step-by-step explanation:
x - 0.25x = 18
3/4x = 18
x = 24
EXPERT NEEDED!! please help me with these! much appreciated
The value of a is -4 from the given system of linear equations.
The system of given equations are ax+12y=-6 and 2x-6y=4.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Here, ax+12y=-6 -------(I) and 2x-6y=4 -------(II)
Given, no solution for the system
So, (a1/a2) = (b1/b2) ≠ (c1/c2)
Now, a/2 = 12/(-6)
a=-4
Hence, the value of a is -4 from the given system of linear equations.
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Solve:
3x/2-5= 7
Please give full explanation
Answer:x=8
Step-by-step explanation:
3x/2-5=7
Move all terms not containing x to the right side of the equation by adding 5 to both sides
3x/2-5+5=7+5
3x/2=12
Multiply both sides of the equation by 2/3 to isolate x.
3x/2*2/3=12*2/3
x=24/3
x=8
Answer: x= 8
Step-by-step explanation:
3x/2-5=7
3x/2 = 12
3x = 24
x= 8
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