The 30th percentile for the given data set is 5758.8, calculated by arranging the data in ascending order and interpolating between the 3rd and 4th values.
To find the 30th percentile for the given data set, first arrange the data in ascending order and then calculate the rank of the 30th percentile. The formula to find the kth percentile for a data set with n observations is:
Rank = (k/100) * (n + 1)
For the given data set of 10 values, the 30th percentile rank would be:
Rank = (30/100) * (10 + 1) = 3.3
Since the rank is not a whole number, the 30th percentile lies between the 3rd and 4th values in the ordered set. After arranging the data:
5581
5700
5700
5896
5972
5993
6075
6274
6283
6381
The 3rd and 4th values are 5700 and 5896. We must interpolate to find the exact 30th percentile:
30th Percentile = 5700 + 0.3 * (5896 - 5700) = 5700 + 0.3 * 196 = 5700 + 58.8 = 5758.8
The 30th percentile is 5758.8.
Find the function h(x) = f(x) ∘ g(x) if f(x) = x(2 - x) and g(x) = 3x.
h(x) = 0
h(x) = -32x
h(x) = 2(32x)
h(x) = 3x(2 - 3x)
Answer: h(x) = 3x(2 - 3x)
Step-by-step explanation:
Here the given functions are,
[tex]f(x) = x(2-x)[/tex]
[tex]g(x) = 3x[/tex]
[tex]h(x) = f(x) \circ g(x) = (f\circ g)(x) = f[g(x)][/tex]
[tex]= f( 3x )[/tex]
[tex]= (3x)[2-(3x)][/tex]
[tex]= 3x(2-3x)[/tex]
Hence,
[tex]h(x) = 3x(2-3x)[/tex]
⇒ Fourth option is correct.
The average weight of 5 students is 150.4 pounds. if no student weighs less than 130 pounds and if no two students' weights are within 5 pounds of each other, what is the most, in pounds, that any one of the students can weight
The wildflowers at a national park have been decreasing in numbers. There were 300 wildflowers in the first year that the park started tracking them. Since then, there have been one fourth as many new flowers each year. Create the sigma notation showing the infinite growth of the wildflowers and find the sum, if possible.
I chose C, but can someone check for me? Thanks :)
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
Initial wildflowers in the first year = 1200
Every year, the number of wildflower is one fourth of the previous year.
So, it form a geometric series:
1200,300,75............
so, using sigma notation we can express the infinite growth of the wildflowers:
[tex]\sum ^{\infty}_{i=1}1200(\dfrac{1}{4})^{i-1}[/tex]
As we know that sum of infinite terms in case of geometric series is given by
[tex]S_{\infty}=\dfrac{a}{1-r}\\\\S_{\infty}=\dfrac{1200}{1-0.25}\\\\S_{\infty}=\dfrac{1200}{0.75}\\\\S_{\infty}=1600[/tex]
Therefore, there are 1600 wildflowers.
Hence, Third option is correct.
A wooden roller coaster at a theme park has a height restriction: passengers must be at least 45 inches tall.
a.Write an inequality to represent the height restriction.
b.Using complete sentences, describe how to graph your inequality on a number line.
What is -4x - 5x <18 need help
What are the coordinates of the center of the circle whose equation is x^2+y^2-16x+6y+53=0?
suppose you randomly choose an integer n between 1 to 5, and then draw a circle with a radius of n centimetres. What is the expected area of this circle to the nearest hundredths of a square centimetres?
To find the expected area of a circle when randomly selecting an integer n between 1 to 5 as the radius, calculate the area of each possible circle and find the average. The expected area, rounded to the hundredths, is approximately 34.54 cm².
Explanation:When you randomly choose an integer n between 1 to 5, and then draw a circle with a radius of n centimetres, the expected area is calculated by taking the average of the areas for all possible radii.
The area of a circle is given by the formula A = πr². Since the integer n can be 1, 2, 3, 4, or 5, we calculate the area for each of these radii and then find the average.
For n=1: A = π(1)² = π cm²For n=2: A = π(2)² = 4π cm²For n=3: A = π(3)² = 9π cm²For n=4: A = π(4)² = 16π cm²For n=5: A = π(5)² = 25π cm²Add all the areas and divide by the number of possible radii:
Expected Area = (π + 4π + 9π + 16π + 25π) / 5
Expected Area = (55π) / 5
Expected Area = 11π cm²
Now, use the value of π up to two decimal places (3.14) to get the expected area in hundredths of a square centimetre:
Expected Area ≈ 11 × 3.14 cm²
Expected Area ≈ 34.54 cm²
The expected area of the circle, to the nearest hundredths of a square centimetre, is approximately 34.54 cm².
A carpenter is building a bookcase. The perimeter of the top is 108 in. If the width is 8 in., what is the length of the shelf?
The tangent of an angle is 3.4. what is the measure of the angle to the nearest tenth? 99.8° 73.6° 68.2° 52.9°
A basket contains six apples and five peaches. Three times, you randomly select a piece of fruit, return it to the basket, and then mix the fruit. All three times, the fruit is an apple. Find the probability of this occuring.
Answer:
16.22%
Step-by-step explanation:
A basket contains six apples and five peaches.
Total fruits in the basket = 6 + 5 = 11
The probability of selecting a piece of fruit is an apple [tex]P_{1}=\frac{6}{11}[/tex]
Now return it to the basket and select a fruit. so all events are independent.
Therefore, the probability of each time selecting an apple is same.
Probability=[tex]P_{1}\times P_{2}\times P_{3}[/tex]
P =[tex]\frac{6}{11}[/tex]× [tex]\frac{6}{11}[/tex]×[tex]\frac{6}{11}[/tex]
=[tex]\frac{216}{1331}[/tex] = 16.22%
The probability of all three times the fruit is an apple is 16.22%
Find the length of the missing side. The triangle is not drawn to scale.
A. 36
B. 6
C. 4
D. 13
An item sells for 2 for 66 cents. What would 5 items sell for?
Answer:
5 items sells for 165 cents
Step-by-step explanation:
An item sells for 2 for 66 cents
2 items cost 66 cents
1 item cost 66 divide by 2 is 33 cents
So 1 item cost 33 cents
WE need to find the cost of 5 items
1 item cost 33 cents
so 5 item costs [tex]5 \cdot 33= 165[/tex]
The cost of 5 items = 165 cents
What is the simplified form of the quantity of x plus 5, all over the quantity of 9 − the quantity of x plus 4, all over the quantity of x plus 6
Segment TR is a mid-segment of triangle ABC. What is the length of segment RC?
A) 5 inches
B) 6 inches
C) 8 inches
D) 10 inches
Which inequality is correctly represented by this graph
A) 3x-y>3
B) x-3y>=2
C) 3x-y<=3
D)x-3y>2
You should first solve each equation for y.
Eliminate answer choices with wrong slopes or y intercepts.
Then, because it is a dotted line, the answer will only be < or >.
And because the area is shaded to the right, it would mean that x > y.
So the answer is A) 3x - y > 3
Answer:
The correct option is A.
Step-by-step explanation:
If a line passing through two points then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
From the given graph it is clear that the related line passing through the points (0,-3) and (1,0). So, the equation of related line is
[tex]y-(-3)=\frac{0-(-3)}{1-0}(x-0)[/tex]
[tex]y+3=3x[/tex]
The (0,0) is not in the solution set. So check the equation be (0,0).
[tex]0+3=3(0)[/tex]
[tex]3=0[/tex]
This condition is false if the sign of inequality is < or ≤. Since the related line is a solid line, therefore the sign of inequality must be <.
The required inequality is
[tex]y+3<3x[/tex]
[tex]3<3x-y[/tex]
It is also written as
[tex]3x-y>3[/tex]
Therefore the correct option is A.
Alive the equation 2 k+2= k+1
help me please help me
Suppose $x$,$y$, and $z$ form a geometric sequence. if you know that $x+y+z=18$ and $x^2+y^2+z^2=612$, find the value of $y$.
We use the information that $x$, $y$, and $z$ forms a geometric sequence, and that $x + y + z = 18$ and $x^2 + y^2 + z^2 = 612$ to set up two equations in terms of $y$. These can be solved simultaneously to get the value of $y$.
Explanation:The problem involves a geometric sequence and two simultaneous equations in mathematics. Given $x$, $y$, and $z$ are in a geometric sequence, then they can be represented as $x=y/r$, $y=y$, $z=yr$, where $r$ is the common ratio. This sequence gives us the first equation, $ x + y + z = 18 $.
We have another given equation which is $ x^2 + y^2 + z^2 = 612 $. Substituting $x$, $y$ and $z$ with the terms of the geometric sequence in the second equation, we have $y^2(1/r^2+1+r^2)=612$. Now we have two equations: $ y(1/r+1+r)=18 $ and $ y^2(1/r^2+1+r^2)=612 $, which we can solve simultaneously to find the value of $ y $.
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The human eye blinks about 6.25x10 to the 6th power times each year. A seal blinks about 1.01x10 to the 3rd power times per year. How many times do a human and a seal blink in one year?
The human eye blinks about [tex]\( 6.25 \times 10^6 \)[/tex] times each year, and a seal blinks about [tex]\( 1.01 \times 10^3 \)[/tex] times per year.
To find out how many times a human and a seal blink in one year, we simply take the given values for each. The question provides us with the number of times a human eye blinks in one year as [tex]\( 6.25 \times 10^6 \)[/tex]times. Similarly, it gives us the number of times a seal blinks in one year as [tex]\( 1.01 \times 10^3 \)[/tex] times.
Therefore, without the need for any additional calculations, we can state that in one year:
- A human blinks [tex]\( 6.25 \times 10^6 \)[/tex] times.
- A seal blinks [tex]\( 1.01 \times 10^3 \)[/tex] times.
These values are already given in the question and represent the total number of blinks for each species in a year. No further calculations are required to answer the question as it is asking for the number of blinks in one year, which is directly provided.
The sum of three numbers is 132 . the third number is 7 less than the first. the second number is 3 times the third. what are the numbers?
The given problem can be solved by setting up and solving a system of linear equations. By assigning variables x, y, and z to represent the three unknown numbers and translating the relationships given in the problem into equations, we can then solve for the unknowns.
Explanation:The subject of this question is algebra and it involves a system of linear equations. Let's denote the three numbers as x, y, and z. We have the following equations based on the problem:
The sum of the three numbers is 132, which gives us the equation: x + y + z = 132. The third number (z) is 7 less than the first (x), which gives us the equation: z = x - 7. The second number (y) is 3 times the third (z), which give us the equation: y = 3z.
Now, let's substitute the second and the third equations into the first to solve for the variables:
Substituting z = x - 7 into y = 3z gives y = 3(x - 7). Substituting z = x - 7 and y = 3(x - 7) into x + y + z = 132 gives x + 3(x - 7) + (x - 7) = 132.
Solving this equation will give the values for x, y, and z that represent the three numbers.
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Find all complex solutions of x^2-3x+4=0.
(If there is more than one solution, separate them with commas.)
Final answer:
Complex solutions of a quadratic equation are found using the quadratic formula. The solutions to x²-3x+4=0 are complex numbers.
Explanation:
The solutions to the equation x²-3x+4=0 are complex numbers.
To find the complex solutions, we can use the quadratic formula where a=1, b=-3, and c=4. Plugging these values into the formula, we get:
x = (3 ± √(-7))/2
Therefore, the complex solutions are x = (3 ± i√7)/2.
PLEASE HELP!!!!!
Which function has the following domain and range?
Domain: {−7,−3,0,4,12}
Range: {−5,1,2}
Select one:
a. {(−7,12),(−5,2)}
b. {(−7,−5),(−3,1),(0,2),(−4,5),(3,−1)}
c. {(4,1),(−3,−5),(12,2),(0,−5),(−7,1)}
d. {(−5,4),(2,12),(1,−3),(−5,−7),(1,0)}
The table below represents the displacement of a horse from its barn as a function of time:
Time(hours) x.
0
1
2
3
4
Displacement from barn (feet) y
8
58
108
158
208
part a: what is the y-intercept of the function, and what does this tell you about the horse? part b: calculate the average rate of change of the function represented by the table between x=1 to x=3 hours, and tell what the average rate represents. part c: what would be the domain of the function of the horse continued to walk at this rate until it traveled 508 feet from the barn?
PLEASE HELP!! WILL RATE BRAINLIEST!!
A. The y-intercept (b) of a linear equation is obtained when x = 0. Therefore from the given table,
y - intercept = 8
Since at time zero the displacement is 8 ft, this means that the horse was already outside the barn initially.
B. The average rate of change of the function represents the slope of the linear equation (m). This can be calculated using the formula:
average rate of change = m = (y2 – y1) / (x2 – x1)
m = (158 – 58) / (3 – 1)
m = 50
C. Since we have determine the y-intercept and the slope, we can formulate the linear equation:
y = m x + b
y = 50 x + 8
The domain is the value of x. When y = 508, x is equivalent to
508 = 50 x + 8
x = 10 hrs
PLEASE HELP!!! IMAGE ATTACHED FIND THE VALUE OF X
What value of x is the solution of the equation 1/7+2x/3 = 15x-3/21?
A. 6
B. 0
C. 4/13
D. 6/29
Answer:A=6
Step-by-step explanation:
A class of 24 students is planning a field trip to a science museum. A nonrefundable deposit of $50 is required for the day-long program, plus a charge of $4.50 per student. Determine a linear function that models the cost, c, and the number of students, s. Which statements about the linear function and its graph are correct? Check all that apply.
A. The linear model is f(s) = 4.5s + 50.
B The linear model is f(c) = 54.5c + 24.
C.The domain is {x| 0 ≤ x ≤ 24}.
D.The range is {y| 50 ≤ y ≤ 158}.
E.The graph is continuous.
Two dice are rolled. if the total showing is odd, you pay your friend $8. otherwise, your friend pays you $4. what is the (expected) value of the game to you?
If a price is 70$ and the price is now 56$ what is the percent decrease
70-56 = 14
14/70 = 0.2
0.2 = 20%
Find the number of ways to listen to 4 different cds from a selection of 15 cds.
Answer:
The First person who answered it was wrong! Its 32,760 I took the test lol!
Step-by-step explanation:
nPr = n!/(n-r)! <-- The equation used for this.
fgh is a right triangle
Answer:
there is no picture
Step-by-step explanation: