Mean (μ) ≈ 53.84, Standard deviation (σ) ≈ 16.51.
To solve this problem, we can use the properties of the normal distribution and the given information about the percentage of students scoring certain marks.
Let's denote the mean as μ and the standard deviation as σ. We know that in a normal distribution:
1. 10% of the students score more than 75 marks.
2. 20% of the students score less than 40 marks.
To find the values of μ and σ, we'll utilize the standard normal distribution table (Z-table), which provides the cumulative probabilities for a standard normal distribution (mean = 0, standard deviation = 1). Then we'll apply the z-score formula to convert these values to the corresponding marks in our distribution.
Let [tex]\( Z_{75} \)[/tex] be the z-score corresponding to 75 marks, and [tex]\( Z_{40} \)[/tex] be the z-score corresponding to 40 marks.
From the standard normal distribution table:
1. The z-score corresponding to the 90th percentile (10% above) is approximately [tex]\( Z_{75} = 1.28 \)[/tex] .
2. The z-score corresponding to the 20th percentile (20% below) is approximately [tex]\( Z_{40} = -0.84 \)[/tex].
The z-score formula is:
[tex]\[ Z = \frac{{X - \mu}}{\sigma} \][/tex]
where:
- [tex]\( X \)[/tex] is the raw score (marks)
- [tex]\( \mu \)[/tex] is the mean
- [tex]\( \sigma \)[/tex] is the standard deviation
Using the z-score formula, we can write two equations based on the given percentiles:
1. For 75 marks:
[tex]\[ 1.28 = \frac{{75 - \mu}}{\sigma} \][/tex]
2. For 40 marks:
[tex]\[ -0.84 = \frac{{40 - \mu}}{\sigma} \][/tex]
Now, we have two equations with two unknowns [tex](\( \mu \) and \( \sigma \))[/tex], we can solve them simultaneously to find the values of [tex]\( \mu \) and \( \sigma \)[/tex].
From equation 1:
[tex]\[ 1.28\sigma = 75 - \mu \][/tex]
[tex]\[ \mu = 75 - 1.28\sigma \][/tex]
From equation 2:
[tex]\[ -0.84\sigma = 40 - \mu \][/tex]
[tex]\[ \mu = 40 + 0.84\sigma \][/tex]
Now, equating the expressions for [tex]\( \mu \)[/tex] :
[tex]\[ 75 - 1.28\sigma = 40 + 0.84\sigma \][/tex]
Solving for [tex]\( \sigma \)[/tex] :
[tex]\[ 1.28\sigma + 0.84\sigma = 75 - 40 \][/tex]
[tex]\[ 2.12\sigma = 35 \][/tex]
[tex]\[ \sigma[/tex] ≈ [tex]\frac{35}{2.12}[/tex]
[tex]\[ \sigma[/tex] ≈ [tex]16.51[/tex]
Now that we have [tex]\( \sigma \)[/tex], we can find [tex]\( \mu \)[/tex] using one of the equations for [tex]\( \mu \)[/tex]:
[tex]\[ \mu = 75 - 1.28 \times 16.51 \][/tex]
[tex]\[ \mu[/tex] ≈ [tex]75 - 21.16[/tex]
[tex]\[ \mu \approx 53.84 \][/tex]
So, the values of [tex]\( \mu \) and \( \sigma \)[/tex] are approximately 53.84 and 16.51, respectively.
Chyra redeemed 175 shares of stock she owned in the fund shown below. Name of Fund NAV Offer Price CAH Group $15.83 $16.27 What were Chyra’s proceeds? a. $77.00 b. $2,770.25 c. $2,847.25 d. $5,617.50
Answer:
Option b $2,770.25
Step-by-step explanation
Chyra owned shares of stock, details are :
Name of Fund - CAH Group
NAV - $15.83
Offer Price - $16.27
Chyra redeemed stock = 175 shares
As we know shares can be redeemed on NAV price.
Chyra's proceeds = 175 × 15.83 = $2,770.25
Chyra's proceeds were $2,770.25.
Answer:
B
Step-by-step explanation:
$2,770.25
mr.ford select 2/5 of 120 people who tied out for theatrical production
Step-by-step explanation:
2/5 is equal to 4/10, or 40 percent.
Therefore 40 percent of 120 is 120*.4, or 48
Chris pays a fee if her bank balance falls below $10 on the statement date, her balance was -$3.46. Then, Chris made a deposit, d, in ample time, so she did not have to pay a fee. Write an inequality to represent this situation. Then solve the inequality. Describe the meaning of the solution.
If her balance is below 10, Chris must pay a few.
b = balance
Her balance was -$3.46. Then, Chris made a deposit, d, in ample time, so she did not have to pay a fee.
b + d > 10
b = -3.46
Inequality: -3.46 + d > 10d > 10 - -3.46
Solved: d > 13.46Meaning: The amount that Chris deposits has to increase her balance, so that it's not less than $10.Based on the information you provided, we can write an inequality to represent the situation. Chris's balance was -$3.46 and she made a deposit of d dollars. To avoid paying a fee, her balance must be greater than or equal to $10 on the statement date. So the inequality is: -3.46 + d >= 10. Solving for d, we get d >= 13.46. So Chris must have deposited at least $13.46 to avoid paying a fee.
Find the area of the figure below, formed a triangle and a parallelogram
Answer:
96
Step-by-step explanation:
The area of a parallelogram is A = b*h. Substitute b = 8 and h= 6 to find the area.
A = 8*6 = 48
The area of a triangle is A = 1/2 b*h. Substitute h = 6 and b = 16 since the triangle has a length of 8 as well as the whole parallelogram.
A = 1/2 *16*6 = 48
Together the areas equal 48 + 48 = 96
Which of the following is a solution of y - x < -3?
(6, 2)
(2, 6)
(2, -1)
Answer:
[tex]\large\boxed{(6,\ 2)}[/tex]
Step-by-step explanation:
[tex]y-x<-3\qquad\text{add}\ x\ \text{to both sides}\\\\y<x-3\\\\\text{Put the values of x and y from the coordinates of the points and check inequality}\\\\(6,\ 2)\to x=6,\ y=2\\2<6-3=3\qquad\text{CORRECT\ :)}\\\\(2,\ 6)\to x=2,\ y=6\\6<2-3=-2\qquad\text{FALSE\ :(}\\\\(2,\ -1)\to x=2,\ y=-1\\-1<2-3=-1\qquad\text{FALES\ :(}[/tex]
What is a 10% tip on a bill of $42.87? (Round to the nearest cent.)
10% of $42.87 = 10/100 × 42.87
= 4.287
Ans = $4.29
Happy to help! Marking my answer as the Brainliest would really be aprreciated.
What math problem equals 18
Answer:
9-0+1-1×2
Step-by-step explanation:
Answer:
10+8, (6÷3)x4, (9-1)+ (5x2)
Step-by-step explanation:
Thats all my brain can think of
Convert 9 feet to inches.
21 inches
27 inches
90 inches
108 inches
Answer:
108
Step-by-step explanation:
1 foot has 12 inches
9x12=108
An egg is dropped from a height of 90 ft. If acceleration die to gravity is -16ft/s^2 and initial velocity is 0ft/s, approximately how long will it take for the egg to reach the ground?
t = time
Multiply the acceleration by time and add to the height:
The equation becomes H(t) = -16 * t^2 + 90
set h(t) to 0
0 = -16*t^ +90
Subtract 90 from both sides:
-90 = -16*t^2
divide both sides by -16:
t^2 = -90 / -16
t^2 = 5.625
t = √5.625
t = 2.37 seconds, round to 2.4 seconds.
Answer: b
Step-by-step explanation: edge
what is the answer to a - 5 = -2
The solution to the equation a - 5 = -2 is a = 3. You solve it by adding 5 to both sides, which isolates the variable 'a'.
To solve the equation a - 5 = -2, you need to isolate the variable 'a' on one side of the equation. You can do this by adding 5 to both sides of the equation. Here's the step-by-step process:
Start with the original equation: a - 5 = -2.
Add 5 to both sides: a - 5 + 5 = -2 + 5.
Simplify each side: a = 3.
The answer to the equation is a = 3.
To solve the equation a - 5 = -2, add 5 to both sides which gives us a = 3 as the solution.
The question is asking us to solve the equation a - 5 = -2 for the variable a. To isolate a on one side of the equation, we need to undo the subtraction of 5. We can do this by adding 5 to both sides of the equation:
a - 5 + 5 = -2 + 5
Which simplifies to:
a = 3
Thus, the value of a that solves the equation is 3.
Who needs Brainliest?
SHOW YOUR WORK since i need to do so
The question is what is 100^ 1/20x2x40x1000000/2=
Answer:
The answer is 200000000
Step-by-step explanation:
You take all the numbers and follow the order of operations.
1/20 x 2=
0.1 x 40=
4 x 1000000=
4000000/2=
2000000
Answer:
100²⁰⁰⁰⁰⁰⁰
Step-by-step explanation:
1/20 = .05 // .05*2 = .1 /// .1*40= 4 /// 4* 1000000 = 4000000 /// 4000000/2 = 2000000 so 100^ 1/20x2x40x1000000/2=100²⁰⁰⁰⁰⁰⁰
4+x=7 describe this question in words
Answer:
3
Step-by-step explanation:
Find the value of x in the equation 4 + x = 7
Answer:
X=3
Step-by-step explanation:
4 +x =7
x =7-4
=3
Translate the phrase into an algebraic expression. 5 more than y
Answer: 5>y
Step-by-step explanation:
Answer:
y + 5
Step-by-step explanation:
5 more than y
y + 5
what’s transformation is the result of reflect in the original figure across the Y-axis and then across the X-axis
Answer:
D
Step-by-step explanation:
When reflected across the Y it becomes B, but then across the X, it fits into D.
What is an expression that is equivalent to 5( y + 2)
Answer:
5y + 10
Step-by-step explanation:
simply open the brackets by multiplying everything by 5;
5(y+2) = 5y + 10
5y + 10 is the expression that is equivalent to 5( y + 2)
Answer:
Step-by-step explanation:
5y+10
⚠️⚠️⚠️
joby had $421.56 in her checking account when she deposited g $20 bills and k quarters. Write an expression that represents the amount of money in her account after the deposit.
Answer: [tex]421.56+20g+\frac{k}{4}[/tex]
Step-by-step explanation:
You have the following information given in the problem above:
- She had $421.56 in her checking account.
- She she deposited g $20 bills (which you can rewrite: [tex]20g[/tex]) and k quarters (which you can rewrite as folllowing:[tex]\frac{k}{4}[/tex]).
Therefore, the amount of money in her account after the deposit is the sum of the amoun she had in her account plus the amoun of money she deposited.
Then, you can write the following expression:
[tex]421.56+20g+\frac{k}{4}[/tex]
Answer:
421.56 + 20g + 1/4 k
Step-by-step explanation:
Joby had $421.56, and she deposited g $20 bills, and k quarter:
We don´t know how many $20 bills she deposited but we know it is expressed by the letter g, so she deposited $20g, and we add to that how many quarters of a dollar she added, in this case, we know that she deposited k quarters or 1/4 k dollars.
To write an expression to know the amount of money she has after the deposit we have to add:
What she had before the deposit = $421.56
The Dollars in $20 bills, we know it is = 20g
The number of dollars in a quarter of a dollar = 1/4 k
So we write:
421.56 + 20g + 1/4k
Identify an equation in standard form for a hyperbola with center (0, 0), vertex (0, 17), and focus (0, 19).
An equation in standard form for a hyperbola with center (0, 0), vertex (0, 17), and focus (0, 19) is; y²/172 – x²/(6√2)² = 1
How to find the equation of a hyperbola?We are given that the hyperbola has;
Center (0, 0), Vertex (0, 17) and Focus (0, 19)
The general form of equation of the given hyperbola has a form of;
y²/a² - x²/b² = 1
Where;
±a is the y- coordinates of the vertices of the parabola (or y-intercepts).
b determines the asymptotes of the hyperbola in the equation y = ± (a/b)x.
From the vertex coordinates of (0.17), we have that; a = ± 17.
From the focus coordinates (0, 19), the y-coordinate of it is; c = 19 .
b can be found from Pythagorean theorem;
c² = a² + b²
Thus;
192 = 172 + b²
b² = 192 – 172
b² = 361 – 289
b = √72 = 6√2
The equation of the hyperbola is;
y²/172 – x²/(6√2)² = 1
Read more about Hyperbola Equation at; https://brainly.com/question/16735067
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The equation in standard form for a hyperbola with the given center, vertex, and focus is y² / 289 - x² / a² = 1.
Explanation:The equation of a hyperbola in standard form is given by:
(x - h)² / a² - (y - k)² / b² = 1 or
(y - k)² / b² - (x - h)² / a² = 1
Given that the center is (0,0) and the vertex is (0,17), we can see that the hyperbola is vertically oriented. Therefore, we can use the form (y - k)² / b² - x² / a² = 1.
Since the center is (0,0), the value of (h, k) is (0,0).
The distance between the center and the vertex is 17 units, which corresponds to the value of b.
The distance between the center and the focus is 19 units, which corresponds to the value of c.
Substituting these values into the equation gives: (y - 0)² / 17² - x² / a² = 1
The equation in standard form for the hyperbola is therefore y² / 289 - x² / a² = 1
Learn more about hyperbola here:https://brainly.com/question/27799190
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Which product is modeled by the number line below?
Answer:
The correct option is 2.
Step-by-step explanation:
From the given number line it is clear that there are 4 jumps of 2 units in opposite direction.
After first jump, the total covered distance is
[tex]-(2)\times (1)=-2[/tex]
After second jump, the total covered distance is
[tex]-(2)\times (2)=-4[/tex]
After third jump, the total covered distance is
[tex]-(2)\times (3)=-6[/tex]
After fourth jump, the total covered distance is
[tex]-(2)\times (4)=-8[/tex]
It means the product (-2)(4) is modeled by the given number line.
Therefore the correct option is 2.
PLEASE HELP!! can you solve this problem? you need to fill all 10 squares with the correct number and/or symbols. Below are the options of numbers and/or symbols that can be placed in the grid. And above the grid is the problem!!
Answer:
Wow just wow
Step-by-step explanation:
I have no clue sorry ;-;
I WILL AWARD BRAINLIEST!!! PLEASE HELP!!!
Find the areas of the trapezoids.
the area of the trapezoid is 9
Answer:
A = 7.5 unit^2
Step-by-step explanation:
The area of a trapezoid is found by
A =1/2 (b1+b2) *h
b1 = 1 unit
b2 = 4 units
h = 3 units
I found these by counting on the graph
A = 1/2(1+4) *3
A = 1/2(5)3
A = 7.5 unit^2
write the expression in complete factored form. 5 (u+5) + p (u+5) =
[tex]5(u + 5) + p(u + 5) = (p + 5)(u + 5)[/tex]
which value of x is in the solution set of the following inequality? -3+5>17
Answer:
x = - 5
Step-by-step explanation:
Given
- 3x + 5 > 17 ( subtract 5 from both sides )
- 3x > 12 ( divide both sides by - 3 )
Remembering to reverse the inequality symbol when dividing/ multiplying by a negative quantity.
x < - 4 ← symbol reversed
The value of x that is in the solution set is x = - 5
Which type of figure has atleast two lines of symmetry?
A. isosceles triangle
B. rhombus
C.parallelogram
D.trapezoid
The answer is B rhombus because you can split a rhombus in half twice and have the same shape for both half
In a different test, the mean score of 50 students is 54%
The students are split in two groups. Group A and Group B.
The mean score for Group A is 60% and the mean score for Group B is 50%
How many students are in Group B and how many are in Group B?
Answer:
Group A has 20 students
Group B has 30 students
Step-by-step explanation:
The mean score of 50 students is 54%, so the sum of 50 scores, divided by 50 is 54%. That means that 50(0.54) = 27 points were scored between the 50 students.
Let x represent the number of students in Group A
Let y represent the number of students in Group B
We have
0.6x + 0.5y = 0.54(50) (the points scored, times their averages is the total)
and
x + y = 50
Use substitution to solve...solve the second equation for one variable...
x = 50 - y
Now plug that into the first equation...
0.6(50 - y) + 0.5y = 27
30 - 0.6y + 0.5y = 27
-0.1y = -3
y = 30
So there are 30 students in group B, therefore there are 20 students in group A
Bella used 2/9 of a paper pack, or 72 pieces. How many pieces of paper were there to start with?
Hello!
First, we need to find the unit rate.
72 divided by 2 = 36.
36 x 9 = 324.
There were 324 pieces of paper to start with.
Hope this helps, ~Pooch ♥
Bella used 2/9 of a paper pack, equaling 72 pieces. To find the total number, we solve the proportion (2/9) * x = 72 to deduce that the pack initially contained 324 pieces.
Bella used 2/9 of a paper pack, which amounts to 72 pieces of paper. To find out how many pieces of paper were in the pack to begin with, we need to calculate the total amount of paper in the pack.
Let's set up a proportion where the total number of sheets is x. Since 2/9 of the total is 72, we can write the equation as follows:
(2/9) × x = 72Multiply both sides by 9/2 to solve for x.x = 72 × (9/2)x = 36 × 9x = 324So, the paper pack originally contained 324 pieces of paper.
ASAP PLEASE HURRYYYY!!! a student wants to know how many one centimeter cubes will fit into a 10 cm by 8 cm by 12 CM box. what measures is the student trying to calculate?
A. height
B.perimeter
C. surface area
D. volume
Answer:
D
Step-by-step explanation:
Read the question carefully.
"how many one centimeter cubes will fit into a 10 cm by 8 cm by 12 cm box."
Volume is the amount in which how much can go in it.
Answer:
c. surface area because fit is the key word for surface area
Step-by-step explanation:
6–[(−3)+(−7)]–[(−1)–(−5)–(−8)]
Answer:
4
Step-by-step explanation:
Here's all the steps, let's just remove all this confusing garbage with the adding negatives first.
6-(-3-7)-(-1+5+8)
Remember, subtracting a negative makes it positive.
6-(-10)-(12)
6+10-12
16-12
4
The expression 6–[(−3)+(−7)]–[(−1)–(−5)–(−8)] simplifies to 2 after solving the operations inside the brackets and applying the order of operations correctly.
The question asks to simplify the expression 6–[(−3)+(−7)]–[(−1)–(−5)–(−8)]. Let's break it down step by step.
Simplify inside the first brackets: (−3)+(−7) = −10.Simplify inside the second brackets: (−1)–(−5)–(−8) = 1+5+8 = 14.Substitute these values back into the original expression: 6 – (−10) – 14.Remembering that subtracting a negative is the same as adding its positive value: 6 + 10 – 14 = 16 – 14.Finally, subtract: 16 – 14 = 2.Therefore, the simplified expression is 2.
There are 5 players in a baseball lineup. How many different batting orders are possible for these 5 players? (use FACTORIALS to find the probability of the number of permutations)
Answer:
i believe it is "5!"
Step-by-step explanation:
1x2x3x4x5=120
but the answer is "5!" ( include the exclamation point)
hope this helps (again)
Answer:
5! or 120.
Step-by-step explanation:
Think about this logically:
You have 5 players to start off with, so you have 5 players that can go in the first position.
That leaves you with 4 players. Any one of those 4 players can go in the second position.
And then there were 3 players. Any one of those 3 players can go in the third position.
2 to go! Pick your favorite player out of the 2 available to go in the fourth position.
And that leaves just one player who has to go last.
This can be modeled as: 5x4x3x2x1, or 5!, which equals 120 unique permutations.
Bryce measured the circumference of a tree trunk. Its circumference was 91 ft. What was the approximate diameter, rounded to the nearest foot?
Answer: 29 feet.
Step-by-step explanation: The formula for the circumference of a circle is C = π d. In order to calculate the diameter of the tree we will use the same formula and solve for d.
91 = 3.14 x d
In order to solve for d you need to divide both sides for 3.14:
D = 28.98, rounded to the nearest foot is 29 feet.
20 points, Pythagorean Theorem (picture provided)
The angles at the left and right tips of the kite are right angles. The length of the long, diagonal brace of this kite is 100 cm. The length of the shorter side of the kite is 60 cm. What is the length of the longer side of the kite?
A. √13600
B. 40
C. 80
D. 1600
(sorry if the symbol for choice A. is wrong)
ANSWER
C. 80
EXPLANATION
The longer diagonal is serving as the hypotenuse of the right triangles.
Let the longer side of the kite be x cm.
Then, from the Pythagoras Theorem, the sum of the length of the squares of the two shorter legs equals the square of the hypotenuse.
This means that,
[tex] {x}^{2} + {60}^{2} = {100}^{2} [/tex]
[tex] {x}^{2} + 3600 = 10000[/tex]
[tex] {x}^{2} = 10000 - 3600[/tex]
[tex] {x}^{2} = 6400[/tex]
[tex]x = \sqrt{6400} [/tex]
[tex]x = 80cm[/tex]
Answer:c
Step-by-step explanation: