IQR is shorthand for interquartile range
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Explanation:
The original list is {84,75,90,87,99,91,85,88,76,92,94}
It sorts to {75,76,84,85,87,88,90,91,92,94,99}
Pick out the middle most value, which is 88 in slot 6. A quick way to get here is to see that there are n = 11 values in this set. So n/2 = 11/2 = 5.5 which rounds to 6, and that tells us the slot number where the median is held. If n is an even number, then you'll need to use the midpoint formula for the two middle-most items.
After we determine the median is 88, we split the sorted data set as follows:
L = {75,76,84,85,87}
U = {90,91,92,94,99}
Everything in set L is below the median. L for lower.
Everything in set U is above the median. U for upper.
Sets L and U have 5 items each. Note that 5+1+5 = 11 = n.
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The median of set L is 84, so Q1 = 84
The median of set U is 92, so Q3 = 92
Q1 and Q3 are the first and third quartiles respectively. Subtracting them gets us the IQR (interquartile range)
IQR = Q3 - Q1
IQR = 92 - 84
IQR = 8
The IQR helps give us a sense how spread out the data set is. It's similar to the range, which is found by range = max - min. The larger the (interquartile)range, the more spread out the data set will be.
Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. Together they charged a total of $1400.
What was the rate charged per hour by each mechanic if the sum of the two rates was $165 per hour
Answer:
$115/hr The 10 hr mechanic
$50/hr The 5hr mechanic
Step-by-step explanation:
let the 10 hr mechanic charge x
then the 5 hr mechanic charges 165 - x
------------------------------
10x + 5(165 - x) = 1400
10x + 825 - 5x = 1400
5x = 575
x = 115 The 10 hr mechanic
165 - x = 50 The 5hr mechanic
What is the approximate value of sin C?
help me please this is due at 2:20
Answer:
94.2
Step-by-step explanation:
Answer:
C = pie x diameter
= 3.14 x 30
= 94.2 units
in a bag containing 3 black balls and 2 red balls , a ball is picked at random then replaced. A second ball is chosen.
What is the probability of :
I. both balls being black II.one is black ,the other is red.
2.in a class of 22 boys and 18 girls , two students are to be selected .
What is the probability of selecting two students of the same sex.
3 black and 2 red balls, total number is 5
i) Both balls are black:
P(BB) = 3/5*3/5 = 9/25ii) Black and red balls:
P(BR) = 2/5*3/5 = 6/25#222 boys and 18 girls, total number is 40
Combinations of 2 students:
40C2 = 40!/38!2! = 40*39/2 = 780Combination of 2 boys:
22C2 = 22!/20!2! = 22*21/2 = 231Combination of 2 girls:
18C2 = 18!/16!2! = 18*17/2 = 153Probability of selecting 2 students of the same sex:
P(BB or GG) = (231 + 153)/780 = 384/780 =96/195 ≈ 0.4923 = 49.23%What is the slope intercept equation for the line below?
Answer:
The answers is B
y=5/4x-4
Can someone help me pls
4. Find (5.8 104) + (7.17 x 10).
Express you answer in scientific
notation. Show your work.
Step-by-step explanation:
(5.8 x 10⁴) + (7.17 × 10^6) =
(5.8 × 10⁴) + ( 717 × 10⁴)
= (5.8 +717) × 10⁴
= 722.8 × 10⁴
= 7.228 × 10^6
Pls help! (don't give wrong answer pls)
Decide whether the sequence is Arithmetic, Geometric or Neither.
4, 9, 16, 25, ...
Check arithmetic
t4-t3 t3-t2
25-16 16-9
=9 =7
sequence is not arithmetic bcoz t4-t3 is unequal to t4-t3
check geometric
t4÷t3 t3÷t2
25÷16 16÷9
=1.6 1.7
sequence is not geometric bcoz t4÷t3 is unequal to t3÷t2
neither
What is the equation of the line?
Answer:
y = -7
Step-by-step explanation:
This is a horizontal line
The y value does not change
It is of the form y=
y = -7
Answer:
y = -7
Step-by-step explanation:
A horizontal line has an equation of the form
y = k
where k is the y-coordinate of every point on the line.
We see that every point on this line has y-coordinate -7, so the equation is
y = -7
Which of the following results from taking the square root of a negative
number?
A. Imaginary number
B. Negative number
C. Positive number
D. Irrational number
A construction crew has two 100ft. beams with which to form the walls of a tent that needs to be 80ft. high. At what angle do they need to place the beams into the ground in order to form their tent? Round your answer to the nearest tenth of a degree.
A. 14.0 degrees
B. 36.9 degrees
C. 38.7 degrees
D. 53.1 degrees
Robert ride his bike from home to school and back 3 days a week. He travels a total of 7.14 km in those three days what is the total distance travels he ride his bike 5 days a week
Answer:
11.9 km
Step-by-step explanation:
Distance travelled in 1 day = 7.14 / 3 = 2.38
distance he travels in 5 days = Distance travelled in 1 day x 5 = 11.9 km
PlZ HELP !!!! if you can AWNSER either one if those please
Problem 1
The two angles 6x and 30 are vertical angles, so they are congruent or the same in measure.
6x = 30
x = 30/6
x = 5 is the answer
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Problem 2
The two angles form a straight angle which is 180 degrees. We consider them a linear pair (since they are adjacent and supplementary).
So,
5x+(3x+12) = 180
8x+12 = 180
8x = 180-12
8x = 168
x = 168/8
x = 21 is the answer
Y is inversely proportional to the square of x. If Y = 9 when x = 2, then what is y, when x is 10?
Answer:
y = 0.36
Step-by-step explanation:
Given y is inversely proportional to x² then the equation relating them is
y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation
To find k use the condition y = 9 when x = 2 , then
9 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )
36 = k
y = [tex]\frac{36}{x^2}[/tex] ← equation of variation
When x = 10 , then
y = [tex]\frac{36}{10^2}[/tex] = [tex]\frac{36}{100}[/tex] = 0.36
if y is inversely proportional to x and y =5 when x = 2 find the value of y when x = 8
Answer:
y = 10/8 = 1.125 or 1 1/4
Step-by-step explanation:
Inverse proportion means
xy = a constant.
In this case, the constant is given by the example,
x = 2 when y=5, so
xy=10
when x = 8, then
y = 10/8 = 1.125 or 1 1/4
How to solve 48÷2(9+3)=?
Answer:
288
Step-by-step explanation:
48÷2=24(9+3=12) =24×12=288
A wildlife refuge has 200 birds when it is first established. It is so
successful that the number of birds increases by 25% every year.
Write a function to model the situation.
Find the number of birds present after 7 years.
Answer:
[tex](a)\ f(x) =200(1.25)^x[/tex]
(b) 954 birds after 7 years
Step-by-step explanation:
Given
[tex]a = 200[/tex] --- initial
[tex]r =25\%[/tex] --- rate
Solving (a): The function.
This is represented as:
[tex]f(x) =a(1+r)^x[/tex]
So, we have:
[tex]f(x) =200(1+25\%)^x[/tex]
Express percentage as decimal
[tex]f(x) =200(1+0.25)^x[/tex]
[tex]f(x) =200(1.25)^x[/tex]
Solving (b): Birds after 7 years
This implies that we calculate f(7)
[tex]f(7) =200(1.25)^7[/tex]
[tex]f(7) =953.67[/tex]
[tex]f(7) =954[/tex] --- approximated
Please help me ASAP!!
Answer:
its b The angles need to add up to 90 degrees and this fits the formula
Answer:
B is the right answer
Step-by-step explanation:
Hope this helps you!!
yes or noo ? ……………..
Answer:
no
Step-by-step explanation:
A circle will fail the vertical line test, which means a vertical lines intersects two or more points. If it fails the vertical line test, it is not a function
The school events committee is planning to buy a banner and some helium balloons for graduation night. A store charges them $35 for the banner and $3 for each helium balloon. If the committee has at most $125 to spend, how many helium balloons can they buy?
Answer:
30 balloons
Step-by-step explanation:
$125 - $35 = $90
$90 ÷ $3 = 30
The rectangles below are similar. Find the length of the missing side (giving brainliest and thanks to all!)
Answer:
A = 68/5 ≈ 13.6
Step-by-step explanation:
If they're similar, the fraction between their sides have to be the same:
5/2 = 34/A
34•2/5 = A
A = 68/5 ≈ 13.6
The school band has a goal of raising $800 for some new uniforms. If they have raised $512 so far, what percent of their goal have they raised?
Answer:
64%
Step-by-step explanation:
can someone tell me how to do this?
Answer:
x = 10
Step-by-step explanation:
(5x + 20) = 70
5(10) + 20 = 70
I will give u brainliest and 5 star and thanks if its correct
Answer:
1. the side length of the square is 3 when its perimeter is 12.
2. (20/21, 5/21)
Step-by-step explanation:
2. 20/21 ÷ 4 = 20/21 × 1/4 = 5/21(the side length of the square with the given perimeter of 20/21)
=> (20/21, 5/21)
Find the area of the shaded regions:
The green area is the shaded region.
Answer:
254.34cm^2
Step-by-step explanation:
area=πr^2
area=3.14*9^2
area=3.14*81
area=254.34 cm^2
The point (-5,3) lies on the graph of f(x). Which of the following points lies on
f-1(x)?
Answer:
(3, -5).
Step-by-step explanation:
By the definition of inverses:
[tex]\text{If $f(a) = b$, then $f^{-1}(b)=a$}[/tex]
In other words, the inverse of a function returns the input when given the output of the original function.
We know that the point (-5, 3) lies on the graph of f(x). In other words:
[tex]f(-5)=3[/tex]
Then by definition:
[tex]f^{-1}(3)=-5[/tex]
So, the point (3, -5) must lie on the graph of f⁻¹(x).
The graph of an absolute value function = a|x| includes the point (1,6). Complete the following statements. The value of a is ____
Answer:
6
Step-by-step explanation:
y = f(x)
6 = a |1 |
6 = a. 1
a = 6/1
a = 6
Answer:
[tex] \displaystyle a = 6[/tex]
Step-by-step explanation:
we are given a absolute value function
[tex] \displaystyle f(x) = a |x| [/tex]
we want to figure out the value of a
since we are a point which is on the function we can figure out a by using the point i.e (1,6) this point tell us when x is 1 f(x) is 6 thus
substitute:
[tex] \displaystyle 6= a \cdot |1| [/tex]
absolute value of any integer is positive therefore,
[tex] \displaystyle 6= a \cdot 1[/tex]
simplify multiplication:
[tex] \displaystyle 6= a [/tex]
hence,
the value of a is [tex]\underline{\quad 6 \quad}[/tex]
A grocery store sells apple and oranges by the pound the cost of the apples is $1.30 the cost of the oranges is $1.84 how much more is the cost for 1 and 1 half pound of oranges than the cost for 1 and 1 half pounds of apples?
Answer:
1.5 pounds of oranges cost $0.81 more than 1.5 pounds of apples
Step-by-step explanation:
1.5 pounds of apples = 1.5 × $1.30 = $1.95
1.5 pounds oforanges = 1.5 × $1.84 = $2.76
$2.76 - $1.95 = $0.81
Can someone help me with this
Answer:
2, 4, 6, and 8, respectively
Step-by-step explanation:
The rule says that 2 times the x value, which we are given, equals to y, which we must find. So all we hve to do is multiply each of the given x values by two to get the y value.
Answer:
y=2x
Step-by-step explanation:'
Multiply the x times 2
[tex]\frac{1}{2}[/tex] [tex]\frac{2}{4}[/tex] [tex]\frac{3}{6}[/tex] [tex]\frac{4}{8}[/tex]
2 4 6 8
. The temperature on Monday was −5∘C . By Tuesday the temperature rose to −2∘C. Find the change in temperature.
Answer: [tex]3^{\circ}C[/tex]
Step-by-step explanation:
Given
The temperature on Monday was [tex]-5^{\circ}C[/tex]
By Tuesday, it becomes [tex]-2^{\circ}C[/tex]
Change in temperature is the difference between the two temperatures.
[tex]\Rightarrow \Delta T=-2-(-5)\\\Rightarrow \Delta T=-2+5\\\Rightarrow \Delta T=3^{\circ}C[/tex]
Therefore, the change in temperature is [tex]3^{\circ}C[/tex].
What is the value of y?
Answer:
y =24
Step-by-step explanation:
The exterior angle is the sum of the opposite interior angles
y+18 + 3y -41 = y+49
Combine like terms
4y -23 = y+49
Subtract y from each side
4y -y -23 = y+49-y
3y -23 = 49
Add 23 to each side
3y -23+23 = 49 +23
3y = 72
Divide by 3
3y/3 = 72/3
y =24