Answer:
40
Step-by-step explanation:
The data is
21,24,25,28,29,35,37,43,44
To find the third quartile we have to arrange the data in increasing order
so the data in increasing order is
21,24,25,28,29,35,37,43,44
total number of values = 9
Median value = (n + 1 )/ 2
=(9+1)/2
=5th value
so the median is 29
Lower half of the data is the values before the median and upper half of the data is values after the median
so lower half = {21,24,25,28}
Upper half = {35,37,43,44}
so to find the third quartile we will use the upper half of the values
Third quartile means that the median of the values of upper half of the data
As the total No of value in upper half is 4 which is an even no
we will take the middle values of the upper half and take their mean
so
Third Quartile = [tex]\frac{37+43}{2}[/tex]
=[tex]\frac{80}{2}[/tex]
=40
so the value of third quartile is 40
Final answer:
The third quartile (Q3) of the data set is 40, calculated by finding the average of the two middle numbers of the upper half of the data after excluding the median.
Explanation:
To find the third quartile of a data set, which is also referred to as Q3 or the 75th percentile, one must identify the median of the upper half of the data. For the provided data set (21, 24, 25, 28, 29, 35, 37, 43, 44), with nine values, the median is 29, which is the fifth value. To calculate Q3, we take the upper half of the data set which does not include the median itself. The upper half includes (35, 37, 43, 44), and the median of this half is the third quartile. Since we have an even number of data points in the upper half, we must find the average of the two middle numbers, 37 and 43, which is (37+43)/2 or 40. Therefore, the third quartile of the provided data set is 40.
On a standardized test, a score of 82 falls exactly 1 standard deviation below the mean. If the standard deviation for the test is 4, what is the mean score for the test?
Answer:
The correct answer is 86.
Step-by-step explanation:
Because 82 is only one standard deviation below the mean, then to find the mean, only add 82 + 4 = 86
The mean score for the test is 86.
What do you mean by standard deviation?In statistics, Standard deviation is a measure of the variation of a set of values.
σ = standard deviation of population
N = number of observation of population
X = mean
μ = population mean
We are given that;
Score=82
Number of tests=4
Now,
We can substitute σ=4 and xi=82 into the formula. We also know that there is only one data point that satisfies this condition, so we can use N=1.
[tex]\mu = \frac{\sum_{i=1}^{N}(x_i - \mu)^2}{N\sigma^2} + \mu[/tex]
We get:
μ=(82−μ)^2/4^2 +μ
Simplifying and solving for μ, we get:
μ=86
Therefore, by standard deviation the answer will be 86.
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Sophie Ruth is eating a 50-gram chocolate bar with contains 30% cocoa. How many grams of cocoa are in the chocolate bar?
please answer asap for brainlist
Either Table L or Table M shows a proportional relationship. Table L
x −1 0 1 2
y −2 0 2 4
Table M
x −1 0 1 2
y −4 0 6 9
Which graph represents the polynomial function g(x)=x^3+5x^2-12x-36
[tex]g(x)=x^3+5x^2-12x-36\\\\y-intercept\ for\ x=0:\\\\g(0)=0^3+5(0)^2-12(0)-36=-36\\\\\text{First or fourth graph.}\\\\\text{If the answer is 4th graph, then g(-2)=0}\\\\g(-2)=(-2)^3+5(-2)^2-12(-2)-36=-8+5(4)+24-36\\\\=-8+20+24-36=0[/tex]
The polynomial function utilizes only non-negative integers powers or positive integer exponent of the variable in a solution, like the quadratic equation, cubic equation, and so on, further calculation can be defined as follows:
Given:
[tex]\bold{g(x)=x^3+5x^2-12x-36}[/tex]
To find:
Graph the polynomial function=?
Solution:
[tex]\bold{g(x)=x^3+5x^2-12x-36}[/tex]
putting the value "1,2, -1, -2" into the above given function and calculate its value:
[tex]\to \bold{g(1)=1^3+5(1)^2-12(1)-36= 1+5-12-36= -42}\\\\\to \bold{g(-1)=(-1)^3+5(-1)^2-12(-1)-36= -1+5+12-36= 17-37=-20}\\\\\to \bold{g(2)=(2)^3+5(2)^2-12(2)-36= 8+5(4)-24-36= 8+20-24-36=-32}\\\\\to \bold{g(-2)=(-2)^3+5(-2)^2-12(-2)-36= -8+5(4)+24-36= -8+20+24-36=0}\\\\[/tex]Therefore, the answer is "4 choice".
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what is equation of the perpendicular bisector of the line segment between ( -3,4)and(5,6)
Answer:
Hey There so i saw your question. Solving it is very easy so i'm gonna help you step by step.
Step-by-step explanation:
(-3,4) (5,6) the slope formula y2-y1 over x2-x1
so its 6-4/5-(-3) which you gonna get 2/8 which is 1/4 so thats your slope.
*just know that your slope will flip since it's perpendicular and not parallel
so now you gonna find "b" on the equation Y=mx=b so out of your 2 points, choose one. I choose (5,6) all you gotta do is plug it into y=mx+b
so it's gonna be 6= 4 (the flipped slope)*5+b {1.4*5 = 1.25}
so you gonna take 6 - 20 = -14 whcih is your b
so your new equation + the answer is Y= 4x-14
What is the value of x in the inequality 5-2x/-3 -4<-x
The solution to the inequality is [tex]\(x > -17\).[/tex]
To solve the inequality [tex]\(\frac{5-2x}{-3} - 4 < -x\)[/tex], let's first find a common denominator and then combine the fractions:
[tex]\(\frac{5-2x}{-3} - 4 < -x\)[/tex]
Multiply each term by -3 to clear the fraction:
[tex]\(5 - 2x + 12 < -3x\)[/tex]
Combine like terms:
[tex]\(-2x + 17 < -3x\)[/tex]
Add [tex]\(2x\)[/tex] to each side:
[tex]\(17 < -x\)[/tex]
Multiply each side by -1 (remember to reverse the inequality when multiplying by a negative number):
[tex]\(-17 > x\)[/tex]
So, [tex]\(x > -17\).[/tex]
The value of x in the inequality [tex]\(\frac{5-2x}{-3} - 4 < -x\) is \(x \in \left(-\infty, -\frac{7}{5}\right)\).[/tex]
Step 1: Start with the given inequality:
[tex]\[\frac{5-2x}{-3} - 4 < -x\][/tex]
Step 2: Multiply both sides of the inequality by -3 to clear the fraction:
[tex]\[5-2x + (-3) \cdot 4 > -3 \cdot (-x)\][/tex]
[tex]\[5-2x -12 > 3x\][/tex]
Step 3: Combine like terms:
[tex]\[-7-2x > 3x\][/tex]
Step 4: Add 2x to both sides:
[tex]\[-7 > 5x\][/tex]
Step 5: Divide both sides by 5 (remembering to reverse the inequality when dividing by a negative number):
[tex]\[\frac{-7}{5} < x\][/tex]
So, the solution to the inequality is:
[tex]\[x \in \left(-\infty, -\frac{7}{5}\right)\][/tex]
The value of x in the inequality [tex]\(\frac{5-2x}{-3} - 4 < -x\) is \(x \in \left(-\infty, -\frac{7}{5}\right)\).[/tex]
Y= 2/3x-5 and y= -2/3x+5 are they perpendicular , parallel or neither?
PPEERRPPEENNDDIICCUULLAARR
Marquise has 200 meters of fencing to build a rectangular garden. The gardens area (in square meters) as a function of the gardens width w (in meters) is modeled by:
Answer: 2500 meters²
Step-by-step explanation:
Perimeter: 200 = 4w
⇒ 50 = w
Area = w²
= (50)²
= 2500
The width of 50 meters will produce the maximum garden area of the rectangle of 2500 square meters.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
The perimeter of the rectangle = 2( length + Width)
200 = 2( length + Width)
100 - w = L
The area of the rectangle = length × Width
= w(100 - w)
= (-w)²+ 100w
So, (-w)²+ 100w where, a = -1 and b = 100
w = -100/2(-1)
w = 50
The area of the rectangle = (-w)²+ 100w
= (-50)²+ 100(50)
= 2500
Thus, The width of 50 meters will produce the maximum garden area of the rectangle of 2500 square meters.
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The perimeter of a rectangular playground is 46m. If the length of the park is 7m, what is the width of the park?
Answer:
16m
Step-by-step explanation:
Since the length of the park is 7m, then the other side is also 7m so 46-14 is 32. So 32/2 is 16.
Jared has a bag that contains 8 blue marbles, 6 red marbles, and 10 green marbles. He selects a marble, replaces it in the bag, and then selects another marble. What is the probability that both marbles are green?
Answer:
The probability is 17.36%
Step-by-step explanation:
In order to find this, we first need to find the probability of pulling one green marble. You can do this by dividing the number of marbles by the amount of marbles in the bag.
10/24 = 41.67%
Now in order to find the likelihood of doing this twice, you multiply that number by itself.
41.67% *41.67% = 17.36%
The radius of a circular track is 0.2 miles ellie ran around the track 3 times how many kilometers round to the nearest whole mile
Answer:
4 miles to the nearest mile.
Step-by-step explanation:
Circumference of the track = 2 pi r
= 2*pi*0.2 = 1.257 miles
Ellie ran 3 times around the track so
the distance she ran is 3* 1.257
= 4 miles
A farmhouse 75 acres of wheat. The farmer can harvest the wheat from 12 acres per day. In how many days will all the Field be harvested?
Answer:
6.25
Step-by-step explanation:
Because to know the answer we have to divide 75 by 12 which is 6.25
For every penny Sam puts into his bank, Tara puts 4 pennies into her bank. If Sam puts 10 pennies into his bank, how many pennies does Tara put into her bank? Answer options with 4 options
Answer
Tara puts 4 pennies if Sam puts 1 but Sam put 10 pennies in all so you multiply 10 by 4 and that gives you 40
Step-by-step explanation:
The distance between the cities Chicago and Toronto is 540 miles. A motorcycle's speed is 48 mph. For a car, it takes 2.25 hours less to cover the same distance than for the motorcycle. How long does it take them to meet, if they start moving towards each other simultaneously?
The answer is in hours.
PLEASE HELP ME
Answer:
5 hours
Step-by-step explanation:
given :
Distance between the cities = 540 miles
Speed of motorcycle =48 mph
TO CALCULATE THE TIME TAKEN BY MOTORCYCLE TO COVER THE TOTAL DISTANCE WE USE THE FORMULA :
[tex]\frac{DISTANCE}{SPEED}[/tex]
By putting given values in the formula we get :
[tex]\frac{540}{48}[/tex]
= 11.25 hours
Now, We are given that for a car to cover the same distance it takes 2.25 hours less than the time taken by motorcycle
⇒ 11.25 hours - 2.25 hours
⇒ 9 hours
Thus , Time taken by car to cover the same distance is 9 hours .
Now to calculate speed of car by using formula:
[tex]\frac{distance}{time}[/tex]
[tex]\frac{540}{9}[/tex]
= 60 mph
Let t be the time taken to meet if they start moving towards each other.
So distance covered by motorcycle in t hours is
speed\times time
= 48t miles
Distance covered by car in t hours is
speed\times time
= 60t miles
⇒ 60t + 48t =540
⇒ 108t = 540
⇒ t= 5 hours
Therefore, time taken to meet if they start moving towards each other is 5 hours.
Which statement about parallel lines is true
PLEASE HELP. WILL GIVE BRAINIEST AND 60 POINTS if you show work so I can understand these.
1. Find the slope of the line that passes through the
points (-1, 2), (0, 5).
2. Suppose y varies directly with x, and y = 15 and x = 5.
Write a direct variation equation that relates x and y.
What is the value of y when x = 9?
3. Write an equation in slope-intercept form of the line
that passed through (-3, 4) and (1. 4).
4. Use point-slope form to write the equation of a line
that has a slope of 2/3
and passes through (-3, -1).
Write your final equation in slope-intercept form.
5. Write the equation in standard form using integers
(no fractions or decimals): = −2/3 − 1
6. Write an equation of the line that passes through
(2, -1) and is parallel to the graph of y = 5x – 2. Write
your final equation in slope-intercept form.
7. Write an equation of
1. The slope of the line is 3.
2. The direct variation equation is y = 3x
3. The equation in slope-intercept form is:y = 4
4. The equation in slope-intercept form is y = 2/3x + 1.
5. The equation = −2/3 − 1
6. The equation of the parallel line is y = 5x - 11.
1. Slope of the line:
The slope (m) of the line passing through (-1, 2) and (0, 5) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
m = (5 - 2) / (0 - (-1))
m = 3 / 1
m = 3
Therefore, the slope of the line is 3.
2. Direct variation equation:
Since y varies directly with x, we can write their relationship as y = kx, where k is the constant of proportionality. We can find k using the given information:
y = 15 when x = 5
15 = k * 5
k = 3
Therefore, the direct variation equation is y = 3x
When x = 9, y = 3 * 9 = 27.
3. Equation in slope-intercept form: First, calculate the slope using the same formula as in question 1:
m = (4 - 4) / (1 - (-3))
m = 0 / 4
m = 0
Since the slope is 0, the line is horizontal. The equation in slope-intercept form is:
y = 4 (constant y-intercept because it passes through (1, 4))
4. Equation in slope-intercept form using point-slope form:
The point-slope form equation is:
y - y1 = m(x - x1)
Plug in the given values:
y - (-1) = 2/3(x - (-3))
y + 1 = 2/3(x + 3)
3y + 3 = 2x + 6
3y = 2x + 3 (subtract 3 from both sides)
y = 2/3x + 1 (divide both sides by 3)
Therefore, the equation in slope-intercept form is y = 2/3x + 1.
5. Writing the equation in standard form:
The equation = −2/3 − 1 is already in standard form (ax + by = c), where a = -2/3, b = 0, and c = -1.
6. Equation of the parallel line:
Since the parallel line has the same slope (5) as the given line, its equation will be of the form y = 5x + b. To find b, plug the point (2, -1) into this equation:
-1 = 5(2) + b
-1 = 10 + b
b = -11
Therefore, the equation of the parallel line is y = 5x - 11.
PLEASE HELP ASAP 30 POINTS ):
Answer:
c (0,-4)
Step-by-step explanation:
-5x+y = -4
4x - 4y =16
Solve the first equation for y since we are using substitution.
-5x+y = -4
Add 5x to each side
-5x+5x+y = -4+5x
y = 5x-4
Substitute this equation y = 5x-4 into the second equation.
4x -4(5x-4) = 16
Distribute the -4
4x - 4(5x) -4(-4) = 16
4x-20x +16 = 16
Combine like terms
-16x +16 =16
Subtract 16 from each side
-16x+16-16 = 16-16
-16x =0
Divide by -16
x=0
But we still need to find y
y = 5x-4
y = 5(0) -4
y = -4
My favorite song stress gives away 25% of the sales of her signature vagrants collection to her charity last month per sales were $1200 how much of her total sales did she donate
I have music you cannot hear, a flame that doesn't burn, I am over 40 years old with no specific birth date. Who am I?
Answer: statue of liberty
Step-by-step explanation:
Answer:
when it says music its kinda a metaphor to peace when it says a flame that does burn it means the torch shes holding. She is over 40 years old shes 143 years old and she doesn't have any birth date she is the statue of liberty
Alex buys 24 cans of vegtables. 80 cents for a can of tomatoes. 40 cents for a can of corn. His total is $12.80. How many cans of corn does he buy?
Answer:
16 cans of corn
Step-by-step explanation:
1.You roll a fair six sided die twice.What is the probability of rolling a 3 and then a 5? A.1/3 B.1/6 C.1/12 D.1/36 2.What is the number of possible outcomes if two marbles are picked out of a bag that contains three red marbles and three blue marbles? [Note: Order does not matter.] A) 2 B) 3 C) 4 D) 6
Answer:
1. The correct answer is D) 1/36
Step-by-step explanation:
WE can tell this because the chance of rolling either is 1/6. To find the total probability we multiply those together.
1/6 * 1/6 = 1/36
Marta's starting annual salary is 24,900. At the beginning of each new year, she receives a $2700 raise. Write a recursive formula to find Marta's salary f(n) after n years. What will Marta's salary be after 4 years? A. f(n)=f(n-1)-2700;35,700 B. f(n)=f(n-1)+2700; 33,000 C. f(n)= 2700f(n-1);33,000 D. f(n)=-2700f(n-1);35,700
The solution is Option B.
The recursive formula to calculate Marta's salary is given by the equation
f ( n ) = f ( n - 1 ) + 2700
The salary of Marta after 4 years will be $ 33,000
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
Let the initial salary of Marta be f ( 0 ) = $ 24,900
The increment in Marta's salary every year = $ 2700
So , the equation will be
f ( n ) = f ( n - 1 ) + 2700
when n = 1
Substitute the value of n = 1 in the equation , we get
f ( 1 ) = f ( 1 - 1 ) + 2700
f ( 1 ) = f ( 0 ) + 2700
f ( 1 ) = 24,900 + 2700
f ( 1 ) = $ 27,600
when n = 2
Substitute the value of n = 2 in the equation , we get
f ( 2 ) = f ( 2 - 1 ) + 2700
f ( 2 ) = f ( 1 ) + 2700
f ( 2 ) = 27,600 + 2700
f ( 2 ) = $ 30,300
when n = 3
Substitute the value of n = 3 in the equation , we get
f ( 3 ) = f ( 3 - 1 ) + 2700
f ( 3 ) = f ( 2 ) + 2700
f ( 3 ) = 30,300 + 2700
f ( 3 ) = $ 33,000
Hence , after 4 years the salary of Marta will be $ 33,000
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Marta's annual salary increases by $2700 each year. Applying the recursive formula: f(n) = f(n-1) + 2700; f(4)=f(3)+2700=f(2)+2700+2700=f(1)+2700+2700+2700=f(0)+2700+2700+2700+2700=24900+4*2700=35500, we determine that Marta's salary in 4 years would be $35,500.
Explanation:The subject of the question involves recursion, or constructing a sequence of numbers in a specific way. In Marta's case, her salary can be calculated using a recursive formula that builds upon her previous salary. This formula relies on the concept of numerical patterns and can be represented as follows: f(n) = f(n-1) + 2700; where f(n) is Marta's salary after n years and f(n-1) is her salary the previous year.
At the start, Marta's salary is 24,900, which serves as the base case for our recursive function. Therefore, her income increases by $2700 each year. To get Marta's salary in 4 years, we would use the recursive formula: f(4) = f(3) + 2700 = f(2) + 2700 + 2700 = f(1) + 2700 + 2700 + 2700 = f(0) + 2700 + 2700 + 2700 + 2700 = 24,900 + 4*2700 = 35,500. So, Marta's salary is $35,500 after 4 years.
Therefore, the correct option among choices provided is none from the given options.
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What is the equation of a line with a slope of -4 and a point (-2,5) on the line? Express the equation in the form of y=my+b where m is the slope and b is the y-intercept. Enter your answer in the box.
Answer:
y=-4x-3
Step-by-step explanation:
There are 20 questions if peter gets a 80% how many questions did he get correct
Answer:
16 correct.
Step-by-step explanation:
We need to change 80% to a decimal
80 % = .8
If there are 20 questions
20 * .80 = 16
He got 16 questions correct
A rectangular field has an area of 1764 m^2 the width of the field is 13 m more than the length what is the perimeter of the field
Answer:
hello : here is a solution
What is the perimeter of a triangle with the given side lengths? s1 = x + 4 cm s2 = 3x + 1 cm s3 = 7x + 3 cm P = x + cm
Answer:
11x+8 cm = Perimeter
Step-by-step explanation:
A triangle has 3 sides. We add up all three sides to get the perimeter.
s1+s2+s3 = Perimeter
(x+4) +( 3x+1) + (7x+3) = Perimeter
Combine like terms
11x+8 = Perimeter
Calling Joe 45 minutes to the airport he arrived 90 minutes before his flight departed and then he spent 17 minutes in the air once he landed Collins been 20 minutes Gathering his luggage and then he drove 35 minutes is Hotel what must be the true of any expression that represents the total time that Colin Spence traveling from his house to the hotel
Yuki bought a pound of confetti for \$12$12. What is the price, in dollars, per ounce of confetti? There are 1616 ounces in 11 pound.
Answer:
Price $0.75 per ounce of confetti
Step-by-step explanation:
Given the statement: Yuki bought a pound of confetti for $12.
⇒[tex]1 pound = \$ 12[/tex] ......[1]
Also, it is given that there are 16 ounces in 1 pound.
⇒ 16 ounces = 1 pound .....[2]
To calculate the price, in dollars per ounce of confetti.
From [1] and [2] we have;
[tex]16 ounces = \$12[/tex]
then;
1 ounces = [tex]\frac{12}{16} = \frac{3}{4} = \$0.75[/tex]
Therefore, the price, in dollars per ounce of confetti is, $0.75 per ounce.
How to solve this 25 points!!!
[tex]\mathsf{Given : \dfrac{(3x^2y^-^3)^3}{27(xy)^-^9}}[/tex]
[tex]\mathsf{\implies \dfrac{(3)^3(x^2)^3(y^-^3)^3}{27(x)^-^9(y)^-^9}}[/tex]
[tex]\mathsf{\implies \dfrac{27(x)^6(y)^-^9}{27(x)^-^9(y)^-^9}}[/tex]
[tex]\mathsf{\implies \dfrac{(x)^6}{(x)^-^9}}[/tex]
[tex]\mathsf{\implies x^6^+^9}[/tex]
[tex]\mathsf{\implies x^1^5}[/tex]
About 16/20 of a tomato is water what present of a tomato is water?
94.46% Is the amount of water in a tomato
16/20 = 80/100
multiply both top and bottom by 5 to go from 16/20 to 80/100
80/100 = 80% by definition of what "percent" means, which is "per 100" or "for every 100"
So 16/20 = 80% meaning 80% of the tomato is water
Note on a calculator, 16/20 = 0.80 which converts to 80% if you move the decimal point 2 spots to the right.