Step-by-step explanation:
1 × 10 ^7 - 8 × 10 ^ 6
2 × 10 ^ 6 which is also equivalent to 2,000,000
An English professor assigns letter grades on a test according to the following scheme. A: Top 13% of scores B: Scores below the top 13% and above the bottom 61% C: Scores below the top 39% and above the bottom 20% D: Scores below the top 80% and above the bottom 10% F: Bottom 10% of scores Scores on the test are normally distributed with a mean of 72.8 and a standard deviation of 7.3. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.
Solution :
The test is distributed normally with mean of 72.8 and the standard deviation of 7.3
Finding numerical limits for the D grade.
D grade : Scores below the top 80% and above the bottom 10%.
Let the bottom limit for D grade be [tex]$D_1$[/tex] and the top limit for D grade be [tex]$D_2$[/tex].
First find the bottom numerical limit for a D grade is :
[tex]$P(X<D_1)= 0.10$[/tex]
[tex]$P(X\leq D_1)= 0.10$[/tex]
[tex]$P\left(\frac{X-\mu}{\sigma} \leq \frac{D_1-\mu}{\sigma}\right) = 0.10$[/tex]
[tex]$P\left(Z \leq \frac{D_1-72.8}{7.3}\right) = 0.10$[/tex] ..........(1)
From (1)
[tex]$\frac{D_1 - 72.8}{7.3} = -1.28$[/tex]
[tex]$D_1 = -1.28(7.3)+72.8$[/tex]
= 63.45
≈ 64
Now the top numerical limit for D grade :
[tex]$P(X>D_2)= 0.80$[/tex]
[tex]$1-P(X\leq D_2)= 0.80$[/tex]
[tex]$P(X\leq D_2)= 1-0.80$[/tex]
[tex]$P(X\leq D_2)= 0.20$[/tex]
[tex]$P\left(\frac{X-\mu}{\sigma} \leq \frac{D_2-\mu}{\sigma}\right) = 0.20$[/tex]
[tex]$P\left(Z \leq \frac{D_2-72.8}{7.3}\right) = 0.20$[/tex] ..........(2)
From (2)
[tex]$\frac{D_2- 72.8}{7.3} = -0.84$[/tex]
[tex]$D_12= -0.84(7.3)+72.8$[/tex]
= 66.668
≈ 67
Therefore, the numerical limit for a D grade is 64 to 67.
my question is in the picture
Answer:
x = 1
y = -1
Step-by-step explanation:
-5x + 5y = -10
rewrite the order:
5y = 5x - 10
6x + 5y = 1
rewrite the order:
5y = 1 - 6x
substitute for 5y:
5x - 10 = 1 - 6x
simplify:
11x = 11
x = 1
5y = 1 - 6(1) = -5
y = -1
A kite is shown below with given dimensions in inches. What is the area in square units
Answer:
320
80
Step-by-step explanation:
2. In triangle ABC, SA is a right angle, and m B = 45°
(1 point)
C
16 ft
A
B.
What is the length of BC? If your answer is not an integer, leave it in simplest radical form.
O 16 ft
O 16.2 ft
O 16.5 ft
O 32 ft
Answer:
[tex]16\sqrt{2}[/tex]
Step-by-step explanation:
The given triangle shown is a 45-45-90. We can use this picture attached to figure out BC.
n in this case is 16ft
Based on the picture, we can get BC's length, which is n[tex]\sqrt{2}[/tex]
BC = [tex]16\sqrt{2}[/tex]
Use the multiplier method to decrease £56 by 14% show your working
Answer: £46.44
Step-by-step explanation:
£56 × 0.86 or (1 - 0.14)
find the value of b in rectangle
the speed of the current in a creek is 2 mph. A person can kayak 4 mi upstream in the same time that it takes him to kayak 8 mi downstream. What is the speed of the persons kayak in still water?
Answer:
I think 6 mph
Step-by-step explanation:
I needore characters so ingnor this sentence.
Write an equation to represent the total cost y for x days of renting a mid-size car from each of these companies. *
Answer:
Step-by-step explanation:
Hindi ko alm hehe
Which one is a unit rate?
sk
5 pounds in 2 bags
15 miles per gallon
$8.00 for 3 boxes of oranges
22gallons of water in 5 days
math HELPPP MEEEEEEEE
Answer: I HAVE YOUR ANSWER!!!!!
Step-by-step explanation:
51x + 26y + 17
Your test scores in one class are 79 and 83. What possible scores can you earn on your next test to have a test average between 81 and 87, inclusive?
Answer:
83 and 84
Step-by-step explanation:
these numbers will both work because if you make an equation 79+83+x=y, with 87≥y≥81, and plug in these numbers for x, the answers are around 82 which is within the range.
Simplify the expression 1/2(h+4) - 1/8(h+4) by combining like terms.
A. 1/6 (h+4)
B. 3h/8 + 2/10
C. 3/8 (h-4)
D. 3/8 (h+4)
WILL GIVE BRAINLIEST IF THE ANSWER IS CORRECT.
Answer:
3h/8+3/2
Step-by-step explanation:
Answer:
D. should be the correct answer.
Can you help with this I don’t know how to solve this.
Answer:
[tex]arclength = 13.44 ft[/tex]
Step-by-step explanation:
We are given PS = 28 feet, which is the length of the diameter.
The formula for arc length is [tex]2\pi r\frac{x}{360}[/tex], where x is the degrees.
So, we need to find the radius. We know that the radius is half of the diameter, so:
[tex]\frac{28}{2}=14 ft[/tex]
We also need to find ∠TXS. Since we know the diameter is a line that crosses the center point of the circle, we also know that ∠PXT and ∠TXS add up to 180°. So:
∠PXT + ∠TXS = 180
125 + ∠TXS = 180
∠TXS = 180 - 125
∠TXS = 55°
Now, we can use the arc length formula:
[tex]arclength=2\pi r\frac{x}{360}[/tex]
[tex]arclength=2\pi (14)\frac{55}{360}[/tex]
[tex]arclength=13.43903524...[/tex]
[tex]arclength = 13.44 ft[/tex]
Check my work to make sure! Hope this helps!
You have different lengths of material to use for a craft project:
0.93m 1.24m 0.62m 3.41m 1.5m 1.4m
Convert each length to centimetres, and then add them together to correctly calculate the total length.
Answer:
[tex]Lengths: 93cm, 124cm, 62cm, 341cm, 150cm, 140cm[/tex]
[tex]Total := 910cm[/tex]
Step-by-step explanation:
Given
[tex]Lengths: 0.93m, 1.24m, 0.62m, 3.41m, 1.5m, 1.4m[/tex]
Required
Convert to length and calculate the total
To calculate to centimeters, we simply multiply each length to 100.
So, we have:
[tex]Lengths: 0.93m, 1.24m, 0.62m, 3.41m, 1.5m, 1.4m) * 100[/tex]
[tex]Lengths: 93cm, 124cm, 62cm, 341cm, 150cm, 140cm[/tex]
The total is:
[tex]Total := 93cm+ 124cm+ 62cm+ 341cm+ 150cm+ 140cm[/tex]
[tex]Total := 910cm[/tex]
Help ?? Anyone and how
Answer:
just insert the x numbers in the calculation.. so for x = - 3 - > (- 3) / 2 +4 = 2.5
Step-by-step explanation:
x - 2 = y 3
and so on
Please help i will give branliest!!!
Answer:b
Step-by-step explanation:
3.5*5*.5=8.75
#5
(10 pts) You are jumping on a trampoline. For one jump, your height y (in feet) above the trampoline after t seconds can
be represented by y = -16t² + 24t. How many seconds are you in the air?
Answer:
1.5 seconds
Step-by-step explanation:
i took a test with the same question
Answer:
1.5
Step-by-step explanation:
taking the test
what is 1+1? pls, I need help. its for school
Answer:
its 2 :)
Step-by-step explanation:
Answer:
oh what a stiff XD
Step-by-step explanation:
ok 1+1=2 lol ❤️✌️ hey where you from I'm anmol kulkar from India
I am 20 years older than twice my daughter's age how old is my daughter you should already know my age in the last problem
17 years ago I was half the age I am now how old am I
this question is 100 points
Answer:
You are 34 years old
Step-by-step explanation:
Because, 34-17=17
17 is half of 34.
2x+20=y
y-17=0.5y
+17 +17
y=0.5y+17
2(0.5y+17)+20=0.5y+17
y+34+20=0.5y+17
y+54=0.5y+17
y=34
Answer:
Step-by-step explanation:
x= "I" age
x is 20 years older than x's daughter's age.
To find out daughter's age = 17x2 (34)
34-20 = 14
The daughter is 14.
SO BAD RN SMH SMH...HELP ME WITH MATH
4 x 2 - 5 + 63 + 1 =
Answer:
67
Step-by-step explanation:
4x2= 8-5= 3 + 63 = 66 + 1 = 67
how do u find the angle measure of l
Answer:
The best way to measure an angle is to use a protractor. To do this, you'll start by lining up one ray along the 0-degree line on the protractor. Then, line up the vertex with the midpoint of the protractor. Follow the second ray to determine the angle's measurement to the nearest degree.
The difference between one-third of a number and 11 is 10 in number form
Answer:
63
Step-by-step explanation:
The difference between one-third of a number and 11 is 10. x = 3*21, x = 63.
Express as a difference: a+b, a+5
Answer:
a - (-b), a - (-5)
Step-by-step explanation:
A double negative negative is a positive, so a - (-b) = a + b, and a - (-5) is a + 5. However, a double negative is still a difference, so this answer works.
Answer:
The answer is a-(-b)
Step-by-step explanation:
It says difference, so you delete plus sign with minus sign
Can someone please help me
Answer:
x = 20
y = 12
Step-by-step explanation:
opposite angles are congruent so we can set up this equation:
5x + 29 = 7x - 11
29 = 2x - 11
40 = 2x
x = 20
5(20) + 29 = 129
7(20) - 11 = 129
3y + 15 = 5y - 9
15 = 2y - 9
24 = 2y
y = 12
3(12) + 15 = 51
5(12) - 9 = 51
Is the sum of the
angle measures always equal to the
sum of the arc measures
Yes or no ?
Determine the equivalent system for the given system of equations.
4x − 5y = 2
10x − 21y = 10
A. 4x − 5y = 2
3x − y = 4
B. 4x − 5y = 2
24x − 47y = 22
C. 4x − 5y = 2
10x + 3y = 15
D. 4x − 5y = 2
14x + 26y = 12
Answer:
B) 4x − 5y = 2
24x − 47y = 22
m∠IJK=155° and m∠ZJK=35°. Find m/∠IJZ
Help me me please now
Answer:
AAA
Step-by-step explanation:
The AAA (angle-angle-angle) theorem proves they have 3 congruent angles, but not congruent sides.
si en la caja solo cabe media docena de platos, ¿ cuantas cajas serían necesarias para empacar la cantidad inicial de platos ?
Answer:
y cuál es la cantidad inicial de platos?
Can someone please help me I’m it’s kinda blurry but you have to zoom in
Answer:
1 is x=53
2 is x=37
3 is x=45
4 is x=180
5 is x=130
6 is x=90
7 is x=15
8 is x=60
9 is x=20
10 is x=140
11 is x=47
12 is x=18
Step-by-step explanation: These can all be solved using vertical angles, complimentary angle theorem, and supplementary angle theorem! Really fancy names to say that opposite angles are equal, vertical angles (like #5). Two angles that add up to 180 degrees forming a straight line, complimentary angles (like in #1). And in a right angle two angles will always add up to 90 degrees (#7 for example). 10 11 and 12 require you to use vertical angles and complimentary angles to solve them.