Answer:
(a) The first quartile is 382.27 and it means that at least el 25% of the scores are less than 382.27 points.
The second quartile is 462 and it means that at least el 50% of the scores are less than 462 points.
The third quartile is 541.73 and it means that at least el 75% of the scores are less than 541.73 points.
(b) The 99th percentile is 739.27 and it means that at least el 99% of the scores are less than 739.27 points.
Step-by-step explanation:
The first, second the third quartile are the values that let a probability of 0.25, 0.5 and 0.75 on the left tail respectively.
So, to find the first quartile, we need to find the z-score for which:
P(Z<z) = 0.25
using the normal table, z is equal to: -0.67
So, the value x equal to the first quartile is:
[tex]z=\frac{x-m}{s}\\ x=z*s +m\\x =-0.67*119 + 462\\x=382.27[/tex]
Then, the first quartile is 382.27 and it means that at least el 25% of the scores are less than 382.27 points.
At the same way, the z-score for the second quartile is 0, so:
[tex]x=0*119+462\\x=462[/tex]
So, the second quartile is 462 and it means that at least el 50% of the scores are less than 462 points.
Finally, the z-score for the third quartile is 0.67, so:
[tex]x=z*s +m\\x =0.67*119 + 462\\x=541.73[/tex]
So, the third quartile is 541.73 and it means that at least el 75% of the scores are less than 541.73 points.
Additionally, the z-score for the 99th percentile is the z-score for which:
P(Z<z) = 0.99
z = 2.33
So, the 99th percentile is calculated as:
[tex]x=z*s +m\\x =2.33*119 + 462\\x=739.27[/tex]
So, the 99th percentile is 739.27 and it means that at least el 99% of the scores are less than 739.27 points.
find the quotient of (5+4i)/(6+8i) ans express in simplest forms
Answer:
Your correct answer is 31/50 + -4/25 i
Step-by-step explanation:
5+4i/6+8i = 31/50 + -4/25 i
Fill out the tables for each scenario and answer the question that follows. Use $7.25 as the minimum wage and remember that employees in the United States must be paid time-and-a-half (1.5 times the normal hourly rate) for each hour worked over 40 hours per week
Answer:
see below for the table valuesUS labor cost: $115275 per yearStep-by-step explanation:
The labor charge is for (6 days/week). In Mongolia, the charge per laborer is then ...
(6 days/week)($1.10/day) = $6.60/week
The three laborers working 50 weeks/year will have a labor cost of ...
(3 laborers)($6.60/week/laborer)(50 weeks/year) = $990/year
__
In the US, the labor charge per person per week is ...
(14 hr/day)(6 day/week) = 84 hr/week
That's 40 hours of straight pay and 44 hours of overtime pay, or ...
7.25(40 +1.5(44)) = 7.25(106) = 768.50
For 150 person-weeks per year, the total US labor charge is ...
($768.50/person/week)(3 persons)(50 weeks/year) = $115,275/year
__
The materials cost for a year is ...
($50/rug)(12 rugs/year) = $600/year
__
The revenue is ...
($2000/rug)(12 rugs/year) = $24,000/year
Profit is the difference between revenue and the total of costs:
profit = $24,000 -($990 +600 +10000) = $12410 . . . made in Mongolia
__
So, the table gets filled as follows:
(labor, material, fixed cost, revenue, profit)
Mongolian-made
($990, $600, $10000, $24000, $12410)
US-made
($115275, $600, $10000, $24000, -$101,875)
The US labor cost would be $115,275.
_____
Comment
For the given selling price, the break-even labor cost is about $1.06 per hour (on average). At US labor rates, the break-even selling price is about $10,490 per rug.
Find the volume of the rectangular prism.
8 ft
8 ft
8 ft
Answer:
V = 512 ft^3
Step-by-step explanation:
The volume of a prism is length * width * height
V = 8*8*8
V = 512 ft^3
The volume of a rectangular prism is lwh.
V=lwh
V=8*8*8
V=8^3
V=512
IT IS EXTREAMLY URGENT!!! I WILL GIVE BRANLIEST!!!!AT LEAST TAKE A LOOK!!!!!! HELPPPPPPPPP
Find the value of x in the figure below. (Round your answer to the nearest whole number)
A) 5 inches
B) 7 inches
C) 6 inches
D) 8 inches
YOU HAVE TO CLICK THE TRIANGLE TO EE IT BETTER, JUST IN CASE ON THE TOP LEFT SIDE IT IS 8IN AND THE BOTTOM OF THE TRIANGLE IS 10 IN
Answer: D) 8 inches
====================================================
Work Shown:
Refer to the diagram below.
A = 50 degrees
B = unknown
C = 80 degrees
-----
For any triangle, the three angles always add to 180
A+B+C = 180
50+B+80 = 180
B+130 = 180
B = 180-130
B = 50 degrees
Since angles B and C are the same measure, their opposite sides are the same length. Triangle ABC is isosceles. Therefore, a = x = 8
Answer: D) 8 inches.
Step-by-step explanation: The triangle has three angles: two were given (50º and 80º) and the other one can be calculated (50º). Therefore, this triangle is an isosceles triangle, it has one base and two congruent sides. Since the one side is 8in, then the other missing side must also be 8in according to the Isosceles Triangle Theorem.
A man starts walking from home and walks 3 miles at north of west, then 5 miles at west of south, then 4 miles at north of east. If he walked straight home, how far would he have to the walk, and in what direction
Answer:
Step-by-step explanation:
We shall find the solution of this problem with the help of vector notation of i , j , which show east and north direction .
The first displacement can be represented by the following
D₁ = - 3 cos 45 i + 3 sin45 j = - 3 / √2 i + 3 / √2 j
The second displacement can be represented by the following
D₂ = - 5 cos 45 i - 5 sin45 j = - 5 /√2 i - 5 /√2 j
The third displacement can be represented by the following
D₃ = 4 cos 45 i + 4 sin45 j = 4 /√2 i + 4 /√2 j
Total displacement D =
D₁ +D₂ + D₃
= i ( -3 -5 + 4 ) / √2 + j ( 3 - 5 + 4 ) / √2 j
= - 4 / √2 i + 2 / √2 j
D = - 2.8288 i + 1.414 j
Magnitude of D
= √ ( 2.8288² + 1.414² )
= 3.16 miles
For direction we calculate angle with X axis
Tanθ = 1.414 / 2.8288
θ = 26 °
As x is negative and Y is positive ,
the direction will be north of west .
Please answer this correctly
Answer:
4 because 6th floor has no office
Answer:
5 floors
Step-by-step explanation:
Fewer than 80 makes it 0-79
So,
0-79 => 5 floors
Need help please guysssssss
Answer:
C
Step-by-step explanation:
3x+2-x>8
2x+2>8
2x>8-2
2x>6
x>3
Answer:
C
Step-by-step explanation:
4 - (-5) + 04−(−5)+0
Answer:
18
Step-by-step explanation:
4 - (-5) + 04 - (- 5)+0
Negative times negative cancels.
4 + 5 + 4 + 5 + 0
Add the terms.
9 + 9 + 0
= 18
Answer:
Step-by-step explanation:
4-(-5)+04-(-5)+0
4+5+04+5+0
14+04
if you meant 0.4 then, it would be 14.4
if you mean 04 then, it would be 18
Scores on a recent national statistics exam were normally distributed with a mean of 82.2 and a standard deviation of 5.If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award
Answer:
The lowest score eligible for an award is 92.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 82.2, \sigma = 5[/tex]
If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award
The lowest score is the 100 - 2.5 = 97.5th percentile, which is X when Z has a pvalue of 0.975. So X when Z = 1.96. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 82.2}{5}[/tex]
[tex]X - 82.2 = 5*1.96[/tex]
[tex]X = 92[/tex]
The lowest score eligible for an award is 92.
Let R(x), C(x), and P(x) be, respectively, the revenue, cost, and profit, in dollars, from the production and sale of x items. If R(x) = 6x and C(x) equals = 0.002x^2+2.2x+40, find each of the following. a. p(x) b.p(100) c. P'(x) d.P'(100)
Answer:
[tex]a.\ P(x) = - 0.002x^2+3.8x-40[/tex]
b. 320
[tex]c.\ P'(x) = -0.004 x + 3.8[/tex]
d. 3.76
Step-by-step explanation:
Given that:
Revenue function:
[tex]R(x) = 6x[/tex]
Cost Function:
[tex]C(x) = 0.002x^2+2.2x+40[/tex]
We know that,
Answer a: Profit = Revenue - Cost
[tex]\Rightarrow P(x) = R(x) - C(x)\\\Rightarrow P(x) = 6x - (0.002x^2+2.2x+40)\\\Rightarrow P(x) = - 0.002x^2+3.8x-40[/tex]
Answer b:
P(100) = ?
Putting value of x as 100 in above equation:
[tex]P(100) = - 0.002\times 100^2+3.8 \times 100-40\\\Rightarrow P(100) = -20+380 -40\\\Rightarrow P(100) = 320[/tex]
Answer c:
P'(x) = ?
Differentiating the equation [tex]P(x) = - 0.002x^2+3.8x-40[/tex]
[tex]P'(x) = -2 \times 0.002 x^{2-1} + 3.8 + 0\\P'(x) = -0.004 x + 3.8[/tex]
Answer d:
P'(100) = ?
Putting x = 100 in equation [tex]P'(x) = -0.004 x + 3.8[/tex]
[tex]P'(100) = -0.004 \times 100 + 3.8\\P'(100) = -0.4 + 3.8\\P'(100) = 3.76[/tex]
Renee is making a scale diagram of her MP3 player. The length of her scale drawing is 8 inches, and the width is 14 inches. The actual length of the MP3 player is 4 centimeters, and the width is 7 centimeters. This is , and the scale factor is .
Answer:
2
Step-by-step explanation:
Scale Factor = [tex]\frac{AnySideOfDiagram}{AnySideOfMP3Player}[/tex]
So,
Scale Factor = [tex]\frac{8}{4} = \frac{14}{7}[/tex] = 2
So,
The scale factor is 2
eric has practiced more than 40 hours with his band. Write an inequality to express this situation. On the graph below, graph Erics situation
Answer:
We can call the variable e. "more than" is denoted by > so the inequality is e > 40. To graph it, draw a circle on the tick mark that has 40 underneath it but don't fill in the circle. Then, draw a continuous line to the right of the circle and draw an arrow at the end of it to show that it goes on forever.
According to the diagram, a 13-foot ladder leans against a 12-foot wall. The distance from the base of the wall is 5 feet. Based on this information, which trigonometric ratio has the value of 12/5
Answer:
Tangent
Step-by-step explanation:
if the angle in question is the bottom of the ladder and the ground, then tangent is opposite over adjacent... or 12/5
Hope this is right
Consider a binomial experiment with n = 20 and p = .70.
A. Compute f(12).
B. Compute f(16).
C. Compute P(x 16).
D. Compute P(x 15).
E. Compute E(x).
F. Compute Var(x).
Complete question:
Consider a binomial experiment with n = 20 and p = .70.
A. Compute f(12).
B. Compute f(16).
C. Compute P(x≥ 16).
D. Compute P(x≤15).
E. Compute E(x).
F. Compute Var(x).
Answer:
a) 0.1144
b) 0.1304
c) 0.2375
d) 0.7625
e) 14
f) 4.2
Step-by-step explanation:
Given:
n = 20
p = 0.70
q = 1 - p ==> 1 - 0.70 = 0.30
a) Use the formula:
[tex] P(x) = CC\left(\begin{array}{ccc}n\\x\end{array}\right) p^x q^(^n^-^x^) [/tex]
Thus,
[tex]P(12) = C\left(\begin{array}{ccc}20\\12\end{array}\right) (0.7^1^2) (0.3^(^2^0^-^1^2^) )[/tex]
[tex] = 125970*0.0138*0.00006 [/tex]
[tex] = 0.1144 [/tex]
b) [tex]P(16) = C\left(\begin{array}{ccc}20\\16\end{array}\right) 0.7^1^6 (0.3^(^2^0^-^1^6^))[/tex]
[tex] = 4845 * 0.0033 * 0.0081 [/tex]
[tex] = 0.1304 [/tex]
c) Compute P(x≥16):
P(x ≥ 16) = P(16) + P(17) + P(18) + P(19) + P(20)
[tex]= C\left(\begin{array}{ccc}20\\16\end{array}\right) 0.7^1^6 (0.3^(^2^0^-^1^6^)) + C\left(\begin{array}{ccc}20\\17\end{array}\right) 0.7^1^7 (0.3^(^2^0^-^1^7^) ) + C\left(\begin{array}{ccc}20\\18\end{array}\right) 0.7^1^8 (0.3^(^2^0^-^1^8^)) + C\left(\begin{array}{ccc}20\\19\end{array}\right) 0.7^1^9 (0.3^(^2^0^-^1^9^)) + C\left(\begin{array}{ccc}20\\20\end{array}\right) 0.7^2^0 (0.3^(^2^0^-^2^0^))[/tex]
[tex] = 0.1304 + 0.0716 + 0.0278 + 0.0068 + 0.0008 = 0.2375 [/tex]
d) P(x ≤ 15):
= 1 - P(x ≥ 16)
= 1 - 0.2375
= 0.7625
e) E(x): use the formula, n * p.
= n*p
= 20 * 0.7
= 14
f) Var(x)
Use the formula: npq
npq = 20 * 0.7 * 0.3
= 4.2
σ
Management at a home improvement store randomly selected 45 customers and observed their shopping habits. They recorded the number of items each of the customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the managers of the home improvement store.
Answer:
c. number of items - discrete; total time - continuous
Step-by-step explanation:
The question is incomplete due to the lack of the following options:
to. number of items - continuous; total time - discrete
b. number of items - continuous; total time - continuous
c. number of items - discrete; total time - continuous
d. number of items - discrete; total time - discrete
Knowing this, the type of variables recorded by managers of the home improvement store are,
c. number of items - discrete; total time - continuous
Discrete variables are those that are well defined and in the finite set of values and continuous variables are variables that can take a value between any of the other two values.
Which equation is the inverse of y = x2 + 16? y = x2 – 16 y = plus-or-minus StartRoot x EndRoot minus 16 y = plus-or-minus StartRoot x minus 16 EndRoot y = x2 – 4
Answer:
[tex]\pm \sqrt{x-16}[/tex] is the inverse of [tex]y = x^2 + 16[/tex]
Step-by-step explanation:
Given that:
[tex]y = x^2 + 16[/tex]
Let us proceed step by step to calculate the inverse:
Step 1: Put [tex]y = f(x)[/tex]
[tex]f(x) = y=x^2 + 16[/tex]
Step 2: Interchange [tex]x[/tex] and [tex]y[/tex]:
[tex]x = y^2 + 16[/tex]
Step 3: Solve the equation to find the value of [tex]y[/tex]:
[tex]y^2 =x- 16\\\Rightarrow y =\pm \sqrt{x- 16}[/tex]
Step 4: Replace [tex]y[/tex] with [tex]f^{-1}(x)[/tex]:
[tex]\Rightarrow y =f^{-1}(x)=\pm \sqrt{x- 16}[/tex]
So, the inverse of [tex]y = x^2 + 16[/tex] is [tex]\pm \sqrt{x- 16}[/tex].
The equation which is the inverse of y = x2 + 16 is; f-¹ = y = ±√(x -16)
To evaluate the inverse of the function, y = x2 + 16.
We must first make x the subject of the formula and swap x and y as follows;
x = ±√(y - 16)y = ±√(x - 16)Therefore, the inverse function is;
f-¹ = y = ±√(x -16)Read more on inverse function:
https://brainly.com/question/14391067
what set of Reflections and rotations could carry ABCD onto itself?
Reflect over y-axis,reflect over the X axis ,rotate 180°
Option D is the correct option.
Explanation:
Let's take point A which is (4,-1)
Reflection over y- axis will make this point (4,1)
Then, reflection over X axis will make this point (4,-1)
After rotation of 180 degree we will get (-4,1) .
Please see the attached picture....
Hope it helps...
Good luck on your assignment...
Answer: d) reflect over the x-axis, reflect over y-axis, rotate 180°
Step-by-step explanation:
A reflection over the x-axis and a reflection over the y-axis is the SAME as a rotation of 180°. Together they make a rotation of 360°, which results in the image staying at the same place.
Reflection over the x-axis changes the sign of the y-coordinate
Z = (x, y) → Z' = (x, -y)
Reflection over the y-axis changes the sign of the x-coordinate
Z' = (x, -y) → Z'' = (-x, -y)
Rotation of 180° changes the signs of both the x- and y-coordinates
Z'' = (-x, -y) → Z''' = (x, y)
A corporation must appoint a​ president, chief executive officer​ (CEO), chief operating officer​ (COO), and chief financial officer​ (CFO). It must also appoint a planning committee with four different members. There are 13 qualified​ candidates, and officers can also serve on the committee. A. How many different ways can the officers be​ appointed?B. How many different ways can the committee be​ appointed?
C. What is the probability of randomly selecting the committee members and getting the four youngest of the qualified​candidates?
Answer:
A) 715 ways
B) 715 ways
C) (1/715)
Step-by-step explanation:
This is a permutation and combination problem.
Since we want to select a number of people from a larger number of people, we use combination as the order of selection isn't important now.
A) How many different ways can the officers be appointed?
There are 4 officer positions.
There are 13 people in total.
We want to select 4 people from 13
Number of ways to select 4 people from 13 = ¹³C₄ = 715
B) How many different ways can the committee be appointed?
Number of committee members = 4
Total number of people available = 13
Number of ways to select 4 people from 13 = ¹³C₄ = 715
C) What is the probability of randomly selecting the committee members and getting the four youngest of the qualified candidates?
Selecting a group of the youngest candidates is just 1 amongst the total number of ways the 4 committee members can be picked,
Hence, the required probability = (1/715)
Hope this Helps!!!
a dock is 5 feet above water. suppose you stand on the edge of the dock and pull a rope to a boat at a constant rate of 2 ft/s. assume the boat remains at water level. at what speed is the boat approaching the dock when it is 4 feet from the dock
Answer:
The boat is approaching the dock at a speed of 3.20 ft/s when it is 4 feet from the dock.
Step-by-step explanation:
The diagram of the situation described is shown in the attached image.
The distance of the boat to the dock along the water level at any time is x
The distance from the person on the dock to the boat at any time is y
The height of the dock is 5 ft.
These 3 dimensions form a right angle triangle at any time with y being the hypotenuse side.
According to Pythagoras' theorem
y² = x² + 5²
y² = x² + 25
(d/dt) y² = (d/dt) (x² + 5²)
2y (dy/dt) = 2x (dx/dt) + 0
2y (dy/dt) = 2x (dx/dt)
When the boat is 4 ft from dock, that is x = 4 ft,
The boat is being pulled at a speed of 2 ft/s, that is, (dy/dt) = 2 ft/s
The speed with which the boat is approaching the dock = (dx/dt)
Since we are asked to find the speed with which the boat is approaching the dock when the boat is 4 ft from the dock
When the boat is 4 ft from the dock, x = 4 ft.
And we can obtain y at that point.
y² = x² + 5²
y² = 4² + 5² = 16 + 25 = 41
y = 6.40 ft.
So, to the differential equation relation
2y (dy/dt) = 2x (dx/dt)
when x = 4 ft,
y = 6.40 ft
(dy/dt) = 2 ft/s
(dx/dt) = ?
2 × 6.40 × 2 = 2 × 4 × (dx/dt)
25.6 = 8 (dx/dt)
(dx/dt) = (25.6/8) = 3.20 ft/s.
Hope this Helps!!!
What is the solution to this equation? 4x+x-15+3-8x=13
Answer:
x = -25/3
Step-by-step explanation:
The equation simplifies to -3x - 25 = 0, so
-3x = 25 =>
x = -25/3
The controller of a chain of toy stores is interested in determining whether there is any difference in the weekly sales of store 1 and store 2. The weekly sales are normally distributed. This problem should be analyzed using an independent means method. True or False
Answer:
True
Step-by-step explanation:
We know that sales of store 1 and store 2 will be two independent sample and given that weeky sales are normally distributed therefore we can use indepedence means method.
That is to say, we are affirming that what they say is correct therefore the correct answer is "true".
A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the baseball in meters t seconds after it is hit is given by the quadratic function h(t)= -4.9t^2 + 9.8t + 1. How long does it take for the baseball to reach its maximum height? What is the maximum height obtained by the baseball?
Answer:
Step-by-step explanation:
max can be found by the formula:
t=-b/2a
t=-9.8/2*(-4.9)
t=-9.8/-9.8
t=1
1 sec
to find maximum height obtained we find the vertex:
plug in 1 for t and simply solve:
h(t)= -4.9t^2 + 9.8t + 1
h(t)= -4.9*1^2 + 9.8*1 + 1
h(t)= -4.9*1 + 9.8 + 1
h(t)= -4.9 + 10.8
h(t)= 5.9
height is 5.9
Harriet has a square piece of paper. She folds it in half again to form a second rectangle (the high is not a square). The perimeter of the second rectangle is 30cm. What is the area of the original piece of paper?
Answer:
The area of the original piece of paper is 60cm
Answer:
the answer is 60
hope it helps :D
Step-by-step explanation:
Find the slope of the line graphed above. Question 2 options: A) –6 B) –10 C) –8 D) –5
Answer: -6
Step-by-step explanation: The slope of a line is rise divided by run. This is shown by the equation (y2-y1) / (x2-x1) = slope of a line.
For this specific line you can plug in two points such as (2,-4) and (1,2)
[2-(-4)] / (1-2) = -6
Hope this helps :)
2) A bike racer completed a 20.0 kilometer race. She pedaled the first 5.0 kilometers with an average speed of 20.0 km/hr. She pedaled the next 5.0 kilometers (which were uphill) at an average speed of 10.0 km/hr. She completed the next 5.0 kilometers (which were downhill) at an average speed of 25.0 km/hr and the final 5.0 kilometers she covered at an average speed of 20.0 km/houra) (2point) How long did it take the biker to complete the race
Answer:
Step-by-step explanation:
Time = distance/speed
Considering the first stage,
Speed = 20km/hr
Distance = 5km
Time = 5/20 = 0.25 hour
Considering the second stage,
Speed = 10km/hr
Distance = 5km
Time = 5/10 = 0.5 hour
Considering the third stage,
Speed = 25km/hr
Distance = 5km
Time = 5/25 = 0.2 hour
Considering the third stage,
Speed = 20km/hr
Distance = 5km
Time = 5/20 = 0.25 hour
Therefore, the time it took the biker to complete the race is
0.25 + 0.5 + 0.2 + 0.25 = 1.2 hours
How many cubes with side lengths of end fraction 1/2 cm does it take to fill the prism? btw anyone who answers this first will be marked the brainiest answer and get a thanks from me :)
How mant solutions are there for the equation? 12x+6=5x
Answer:
One solution
Step-by-step explanation:
12x+6=5x
7x+6=0
7x=-6
x=-6/7
Only one solution. Hope this helps!
Surface area of a cylinder: S = 2ar+2arh , solve for h.
Answer:
[tex]h = \frac{s - 2ar}{2ar} \\ [/tex]
Step-by-step explanation:
[tex]s = 2ar + 2arh \\ s - 2ar = 2arh \\ \frac{s - 2ar}{2ar} = \frac{2arh}{2ar} \\ h = \frac{s - 2ar}{2ar} [/tex]
hope this helps you
brainliest appreciated
good luck! have a nice day!
Find the equation of a line perpendicular to 4x – 4y = -4 that contains the point (-5, -2).
Answer:
Y = -X - 7
Step-by-step explanation:
y-y1 =m(x-x1)
y-(-2)= -1(x-(-5)
y+2 = -1(x+5)
Solve for y
subtract 2 from both sides
y=-x-5-2
Y = -x-7
Which expressions are equivalent to –9
(2/3x+1)? Check all that apply.
Answer:
-18/3x - 9
Step-by-step explanation:
-9(2/3x + 1)
Expand.
-18/3x + -9