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.
Circle A has a radius of 5 units. Circle B has a radius of 3 inches. Which best represents the area of the figure below?
Which is a perfect square?
61
62
63
65
Answer:
None of them really,
A perfect square is a number that can be expressed as the product of two equal integers...which is not seen here.
Th closest perfect square that could be possible would be 64, but thats not an option, so go with none.
Which table of ordered pairs represents a proportional relationship? I’m a timer please hurry thank you so much
х
-3
-4
-5
у
3
2
1
x
-1
-3
-5
у
1
3
5
-2.
-4
-6
y
1-5
1-7
-9
х
--2
-3
-4
у
0
-1
1-2
I
Answer:
I'd say the second one. the others are all showing a linear relatiknship
200 students attend Ridgewood Junior High School. 25% of students bring their lunch to school everyday. How many students brought their lunch to school on Thursday?
sorry est un site Web Internet spécialement conçue 4
Can someone answer this please!!! I only have 5 mins and u will get Brainly too :)
Find the value of the expression a--b* for a = 2 and b= 1
Answer:
3
Step-by-step explanation:
Given the expression a --b
Given that
a = 2
b = 1
Substitute into the expression
a--b
= 2 --1
= 2 - (-1)
= 2 + 1
= 3
Hence the required value is 3
How do I solve 1 1/3 × 2 2/4 is steps?
Answer:
40/12 or 3 1/3
Step-by-step explanation:
To multiply mixed numbers, first change any mixed number to an improper fraction. Then multiply the numerators together and the denominators together
1 1/3 as an improper fraction is 4/3 and 2 2/4 as an improper fraction is 10/4.
4*10=40
3*4=12
What is a angle called when two angles share a common side and a common vertex
Answer:
Adjacent Angles
Step-by-step explanation:
Adjacent angles are two angles that have a common vertex and a common side but do not overlap. They share the same vertex and the same common side.
Madeline has a headache and takes 500
milligrams of a pain reliever. The brand
of pain reliever she takes has a half-life
of 2.5 hours. Which function could be
used to describe the amount of pain
reliever remaining in Madeline's system
at any given time?
lol
Answer:
f(x) = 500(1/2)^x
Did this end up in the wrong category lol
Can someone answer this please!!! I only have 5 mins and u will get Brainly too :)
Answer:
28
Step-by-step explanation:
(a+b)h/2
(6+8)4 / 2
14 x 4 / 2
= 28
I hope im right!!
when given a choice of a favorite pet, 32% of children choose a dog and 24% of children choose a cat. if 175 kids were asked what their favorite pet was, how many would choose a cat?
Answer:
42
Step-by-step explanation:
24% of 175 = 0.24 * 175 = 42
Answer:
175 x .24= 42 kids
...............
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
Answer:
C
Step-by-step explanation:
Evolution is where organisms have developed over time from simple to complex. Therefore we can rule out D because older rock layers should have simple organisms and A because new rock layers should have more complex organisms. The previous organisms will be unlike those of today, therefore the correct answer is C.
If a central angle measures 87°, then its arc will measure _____.
twice as much
the same
half as much
The same!
Hope This Helps! <3
Good Luck Studying ^-^
Please help me! Thank you!
Leo wants to paint a mural that covers a wall with an area of 1,440 square feet. The height of the wall is 2/5 of its length. What is the length and the height of the wall?
Answer:
decide on your destiny
Step-by-step explanation:
i need you to decide on your own destiny
Answer:
24 feet height, 60 feet length
What is the area of the triangle?
6
2
3
Answer:
6
Step-by-step explanation:
Find the area of both triangles inside the bigger triangle and add them together.
Use the Pythagorean theorem to find the missing length of the leg in the smallest triangle:
a² + b² = c²
2² + b² = 3²
4 + b² = 9
5 = b²
2.2 ≈ b
Calculate the area of the smaller triangle:
1/2(bxh)
1/2(2 x 2.2)
1/2(4.4)
2.2
Calculate the area of the bigger triangle:
We know that the longer leg is 3.8 units because we were able to subtract the length of the smaller triangle's leg from 6.
1/2(bxh)
1/2(2 x 3.8)
1/2(7.6)
3.8
Add both areas to find the area of the largest triangle:
3.8 + 2.2 = 6
a savings account increases from $200 to $212. what is the percent increase of the savings account?
Answer:
6% increase
Step-by-step explanation:
To find the percent increase, divide the difference by the original:
12/200
= 0.06
Multiply this by 100:
0.06(100)
= 6
So, the percent increase was 6%
A $7.00 item is marked down by 10%.
What is the new cost of the item?
Round to two decimals if needed.
$
Answer:
6.3
Step-by-step explanation:
PLZ HELP DUE IN 8 MINS PLZ HELP
Answer: for number 1 its negative 14
Step-by-step explanation:
6.833 + 3.594 + 1.369 nearest whole number
Answer:
12
Step-by-step explanation:
You add 6.833 + 3.594 + 1.369, which equals 11.796, and then you round up to 12.
Answer:
12
Step-by-step explanation:
1 1
6.833
3.594
+1.369
11.796
round the whole number to get 12
Can someone help mee
Answer:
Check pdf
Step-by-step explanation:
Which choice shows 1/4 of 8
Answer:
there is no picture so I dont know what i have to do..
please help find the perimeter
Answer:
Perimeter of the given figure = 28 units
Step-by-step explanation:
Perimeter of the given figure = Length of AB + Length of BC + Length of CD + Length of DE + Length of EF + Length of FG + Length of GH + Length of AH
Length of AB = 4.5 units
Length of BC = 2 units
Length of CD = 2 units
Length of DE = 4 units
Length of EF = 5.5 units
Length of FG = 1.5 units
Length of HG = 1 units
Length of AH = 7.5 units
Perimeter of ABCDEFGH = 4.5 + 2 + 2 + 4 + 5.5 + 1.5 + 1 + 7.5
= 28 units
A psychology professor assigns letter grades on a test according to the following scheme. A: Top 9% of scores B: Scores below the top 9% and above the bottom 56% C: Scores below the top 44% and above the bottom 20% D: Scores below the top 80% and above the bottom 6% F: Bottom 6% of scores Scores on the test are normally distributed with a mean of 79.3 and a standard deviation of 8.4. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.
Answer:
You get a D if you have a grade between 66 and 72.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using 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.
Scores on the test are normally distributed with a mean of 79.3 and a standard deviation of 8.4.
This means that [tex]\mu = 79.3, \sigma = 8.4[/tex]
D: Scores below the top 80% and above the bottom 6%
So between the 6th and the 20th percentile.
6th percentile:
X when Z has a pvalue of 0.06. So X when Z = -1.555.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.555 = \frac{X - 79.3}{8.4}[/tex]
[tex]X - 79.3 = -1.555*8.4[/tex]
[tex]X = 66.2[/tex]
Rounds to 66
20th percentile:
X when Z has a pvalue of 0.2. So X when Z = -0.84.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.84 = \frac{X - 79.3}{8.4}[/tex]
[tex]X - 79.3 = -0.84*8.4[/tex]
[tex]X = 72.2[/tex]
Rounds to 72
You get a D if you have a grade between 66 and 72.
Use calculus to evaluate (lhopitals rule)
lim x>infinity x^2 - ln(2/x)/3x^2 + 2x
Answer:
1/3
Step-by-step explanation:
[tex][x^2 - ln(2/x)]/[3x^2 + 2x]\\[/tex]
∞/∞
[tex]\frac{d}{dx}[x^2-ln(2/x)] =2x+\frac{1}{x}\\ \frac{d}{dx}[3x^2+2x]=6x+2\\\frac{2x+\frac{1}{x}}{6x+2}[/tex]
Also ∞/∞
[tex]\frac{d}{dx}[2x+\frac{1}{x}]=2-1/x^2\\\frac{d}{dx}[6x+2]=6\\\\[/tex]
[tex]\lim_{x \to \infty} \frac{2-\frac{1}{x^2} }{6}\\=\frac{2}{6} \\=\frac{1}{3}[/tex]
Simplify the expression: (-4x^10y^-8)^2
Answer:
(-8x)(20y)-16
Step-by-step explanation:
(-4x10y-8)2
distribute the two to all terms inside the parentheses
(-8x)(20y)-16
you cannot simplify this further
Helpppp!!! Pleaseeee
Answer:I’m pretty sure it’s 90
Step-by-step explanation:
Answer:
tan 60=√3/t
t=√3/√3=1 is your answer
HELP NEED NOW... Look at picture
Answer:
the answer is 2
Step-by-step explanation:
Suppose that the water level of a river is 34 feet and that it is receding at a rate of
0.5 foot per day. Write an equation for the water level, L, after d days. In how many
days will the water level be 26 feet? -3x+4y=y
find the missing lengths of the sides
Answer:
a=9, c=19
Step-by-step explanation:
Aight so basically in 30, 60, 90 triangles there is a formula for the sides
the hypotenuse(the longest side)=2a
The tiny side (the smallest side)=a
and the middle child =[tex]a\sqrt{3}[/tex]
Based on that we see that a is 9
and since c=2a then it's 18
In ΔJKL, j = 520 inches, k = 730 inches and l=640 inches. Find the measure of ∠K to the nearest degree.
Answer:
It’s 56.7
Step-by-step explanation:
Fudisks