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.
down the additive inverse of 4 by 7
Answer:
[tex] \color{magenta} \huge{ \boxed{answer}}[/tex]
The additive inverse of 4/7 is -4/7.hopefully help:)
Step-by-step explanation:
#CarryOnLearningSolve the system by substitution.
2x + 3y = 32
y = x + 9
Answer:
x=1 and y=10 (1,10)
Step-by-step explanation:
2+30=32
10=1+9
What two positive consecutive integers have a product of 72
Answer:
32 and 70
Step-by-step explanation:
Help ASAP!!! I’m confused. Thank you!
Answer:
y = 23
Step-by-step explanation:
115 = 5y
Divide 5 by both sides of the equation.
y = 23
The invitations to a holiday party cost a total of $31.50 if each invitation cost $0.75 cents how many invitations were sent out
Answer:
42
Step-by-step explanation:
divide the total by the cost of each invite
In ADEF, the measure of ZF=90°, the measure of ZE=53°, and DE = 57 feet. Find the
length of FD to the nearest tenth of a foot.
E
539
57
F
D
X
Answer:
Check pdf
Step-by-step explanation:
Find each product mentally, using the distributive property, 4x51/8. (giving brainliest)
Answer:
25.5
Step-by-step explanation:
4 x 51 / 8
204/8
25.5
Answer:
Step-by-step explanation:
4×15/8 = 4×(1+⅞) = 4×1 + 4×⅞ = 4 + 7/2 = 4 + 3.5 = 7.5
Please help, I’ve looked everywhere and haven’t found any answers!
Answer:
m = 4 + (2n)/(3)
Step-by-step explanation:
Move all terms that contain m to the right side and solve it.
Use a double number line to answer Problem 1-5.
Tanner collected 360 cans and bottle while fundraising for his baseball team. This eas 40% of what Reggie collected. How many cans and bottles dif Reggie collect?
Answer:
900 cans and bottles.
Hope that helps!
Step-by-step explanation:
360 / 4 = 90
90 x 100 = 900
Hope that helps!
HELPPPPP PLSSSSSS !!!!!!!
Charmaine is having a party. She'll have 4 tables for every 8 guests. Complete the table below showing the number of tables and the number of guests
Answer:
Top is 18, Bottom goes 6 for 12, then 7 for 14, then 10 for 20
Step-by-step explanation:
2 guests = 1 table
Find the equation of the line with slope m=1 that contains the point (1,2)
Answer:
y = x + 1
Step-by-step explanation:
We can use the point-slope formula to write an equation for this problem. The point-slope formula states: (y - y1) = m (x - x1)
Where m is the slope and (x1 y1) is a point the line passes through.
Substituting the slope and the values from the point in the problem gives:
( y - 2 ) = 1 ( x - 1 )
We can also solve for y to put the equation in slope-intercept form. The slope-intercept form of a linear equation is: y = mx + b
y - 2 = 1x - 1
y = 1x - 1 + 2
y = 1x + 1 or y = x + 1 * are just the same.
The equation of the line is y = x + 1.
What is a slope?The slope and direction of a line are represented numerically by the line's gradient, which is also referred to as the slope in mathematics.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
And here we have the slope,
m = 1
And (x₁ ,y₁) = (1,2)
then the equation of line is
y - y₁ = m (x - x₁)
y - 2 = (x -1)
y = x + 1
Therefore, the equation is y = x + 1.
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Sandy brought 64 dozen cookies to the bake sale. Alejandro brought
dozen fewer cookies than Sandy brought. Pierre brought 2 dozen
fewer cookies than Alejandro brought. How many dozen cookies
did Pierre bring?
11 divided by 30.8 PLEASE I NEED HELP
Answer:
2.8
Step-by-step explanation:
Answer:
30.8/11=2.8
11/30.8=0.357142857
Step-by-step explanation:
give me brainlest please
What would you call the expression 2x -5y - 7?
Answer:
Trinomial
Step-by-step explanation:
Its called a Trinomial since it has 3 terms in it
Hope its helps!
2+׳
What's the answer?
Answer:
x^3+2
Step-by-step explanation:
Jillian and her friend went shopping. They were both looking for some new CD's. Jillian went to Music Matrix and spent $25.56 on 4 CD's. Her friend
spent $18.45 on 3 CD's. Who got the better deal? Show your work for each person. Answer who got the better deal and explain your reasoning,
Answer:
Her friend got the better deal.
Step-by-step explanation:
For Jillians equation look at
$22.56/4 = $6.39 per CD
For her friends equation look at
$18.45/3 = $6.15 per CD
Jillian's friend got the better deal because she paid less per CD as shown in the equations above.
Read the sentences below. They are the first part of a summary of the article. Atoms are the building blocks of everything. They are too tiny to be seen. Atoms are made up of electrons, protons and neutrons. Which answer BEST completes the summary? A Each atom has a special number and element B Each atom has some oxygen and hydrogen. с Each atom has an atomic number of 1. D Each atom is made up of 100 elements.
Answer:
A (i think)
Step-by-step explanation:
If i'm right please mark me branliest
All of the following operations are used to solve for X in the equation below except one. Which one is it ? 9x-2=4x+8 A. Addition B. Division C. Multiplication D. Subtraction
Step-by-step explanation:
9x - 2 = 4x + 8 → (9-4)x = 8 + 2 → 5x = 10 → x = 10/2 = 5
C. multiplication
Multiplication not used
What is the sum of the largest and smallest recorded capacity?
Find the total surface area of the
following prism:
5 cm
5 cm
5 cm
5 cm
10 cm
5 cm
apothem = 3.6 cm
SA = [ ? ] cm2
Answer:
Total surface area = 340 cm²
Step-by-step explanation:
Surface area of the given prism = Area of two bases + Area of its lateral surfaces
Area of pentagonal base = [tex]\frac{1}{2}(\text{Apothem)}(\text{Perimeter})[/tex]
= [tex]\frac{1}{2}(3.6)(5\times 5)[/tex]
= 45 cm²
Area of the lateral sides of the prism = Perimeter of the pentagonal base × height
= (5×5)×10
= 250 cm²
Total surface area of the prism = 2(45) + 250
= 90 + 250
= 340 cm²
Angle ABF is 77
a) Find the size of angle x.
b) Which one of these justifies your answer?
A- corresponding angles
B - alternate angles
C- vertically opposite angles
Answer:
a) 77 b)B
Step-by-step explanation:
letterF is the same as 77 meaning that X will be the same as letterF cause the are vertically opposite angles.
I just did the question on math watch.
The measure of the angle ∠BFH that is 'x' will be 77 degrees. Then the correct option is B.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.
Alternate angle - If two lines are parallel then the third line will make z -an angle and z-angles equal angles with the parallel lines.
Line AD is parallel to line EH. And the line CG is the transversal line to line AD and EH.
The angle ∠FAB is congruent with the angle ∠BFH. Because they are alternate angles. Then we have
∠BFH = ∠FAB
x = 77°
The measure of the angle ∠BFH that is 'x' will be 77 degrees. Then the correct option is B.
More about the angled link is given below.
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k(k + 1)(k + 2) – 3k(k + 1)
Need a step-by-step guide on how to factor this completely
Answer:
Step-by-step explanation:
k(k+1)(k+2) - 3k(k+1)
k and (k+1) are common to both terms.
k(k+1)(k+2) - 3k(k+1) = k(k+1)[(k+2) - 3] = k(k+1)(k-1)
If f(x)=(x+1)(x-2)(x-3) represents a student's displacement from school in
kilometers, where x is measured in minutes, which of the following is an
accurate interpretation of the student's trip?
a) The student starts 6 km from school, walks to school and arrives at school
after 2 minutes, continues walking to the playground, turns around, walks
back to the school and arrives after 3 minutes.
b) The student starts 6 km from school, walks to school and arrives at school
after 2 minutes, waits there for 1 minute, then returns home.
c) The student starts 6 km from school, walks to school and arrives at school
after 2 minutes, turns back to their house to the playground, turns around,
walks back to the school and arrives after 3 minutes.
d) The student starts 6 km from school, walks to school and arrives 1 minute
later, sits by the school, returns home, arrives after 2 minutes, and then turns
around and arrives back at school for a second time at 3 minutes.
e) None of the above are correct
It
Displacement means the distance traveled on a straight line to get to a certain destination. The interpretation of the given equation is option (a):
Given that:
[tex]f(x) = (x + 1)(x - 2)(x - 3)[/tex]
First, we calculate how far the student traveled to arrive at the school.
This means that we calculate f(0).
So, we have:
[tex]f(0) = (0 + 1)(0 - 2)(0 - 3)[/tex]
[tex]f(0) = ( 1)( - 2)( - 3)[/tex]
[tex]f(0) = 6[/tex]
The student walked 6km to school
When x = 2, it means:
[tex]f(x) = (x + 1)(x - 2)(x - 3)[/tex]
[tex]f(2) = (2 + 1)(2-2)(2 -3) = 0[/tex]
This means that the student got to school after 2 minutes
When x = 3, it means
[tex]f(x) = (x + 1)(x - 2)(x - 3)[/tex]
[tex]f(3) = (3 + 1)(3-2)(3 -3) = 0[/tex]
This means that the student walked away, turned back and got to school after 3 minutes.
From the given options, option (a) fits the above description.
Read more about speed, displacement and time at:
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5. Can two fractions point to the same location on the number line? Explain.
Answer:
1 2 = 2 4 = 3 6 = 4 8 = etc. All of these fractions are located at the same point on the number line. Therefore, they represent the same number. From the paper folding exercises, we see that increasing both numerator and denominator of a fraction by the same factor gives an equivalent or equal fraction.
Hope this helps :) Just know I tried.
Claim: Is Juan correct ??
Evidence : Show you work
This is geometryyyy(similarity)
Can you help me plz
The formula for any geometric sequence is an = a1 · rn - 1, where a n represents the value of the n th term, a1 represents the value of the first term, r represents the common ratio, and n represents the term number. What is the formula for the sequence -3, -6, -12, -24, ...?
an = -2 · (-3) n - 1
an = 2 · (-3) n - 1
an = -3 · 2 n - 1
an = -3 · (-2) n - 1
Answer:
C
Step-by-step explanation:
The formula for any geometric sequence is:
[tex]a_n=a_1\cdot r^{n-1}[/tex]
Where aₙ is the value of the nth term, a₁ is the value of the first term, r represents the common ratio, and n represents the term number.
We want the formula for the geometric sequence:
-3, -6, -12, -24, ...
Note that our first term is -3. Hence, a₁ = -3.
Next, each subsequent term is twice the previous term. Hence, our common ratio r = 2.
Therefore, by substitution, we acquire:
[tex]a_n=-3\cdot (2)^{n-1}[/tex]
Our answer is C.
there is a sales tax of $22 on an item that costs$272 before tax. the sales tax on the second item is $19.25 how much does the second item cost before tax
Answer:$240.62
Step-by-step explanation:
You divide 22/272 to get .08 then you divide 19.25 by .08 to get 240.62.
The profit for a company this year was $100,000. Each year the profit increases at a rate of 1.2% per
year. Which function shows the company's profit as a function of time in years?
a. f(t) = 100,000 0.012^t
b. f(t) = 100,000(1 + 1.2)^t
c. f(t) = 100,000(1 + 0.012)^t
d. f(t) = 100,000 - 1.2^t
Given:
Initial profit = $100,000
Increasing rate of profit = 1.2%
To find:
The function that shows the company's profit as a function of time in years.
Solution:
The exponential growth model is defined as:
[tex]f(t)=a(1+r)^t[/tex]
Where, a is the initial value, b is the growth rate and t is the time period.
Putting a=100,000 and r=0.012, we get
[tex]f(t)=100,000(1+0.012)^t[/tex]
Where, t is the number of years.
Therefore, the correct option is c.
The volume of a right rectangular prism can be found by using the product 9(4)(1.1). Which expression could also be used to determine the volume of this prism?
O 11(9)(4)
O 9(4) + 1
0 32(11)
O 9 + 4 + 11
plss help fast
Answer:The answer is A)11(9)(4)
Step-by-step explanation:
If you have 9(4)(11) then is would be the one that look just like it but the number are moved like 11(9)(4)
Answer:
The Answer is 11 (9 + 4)
work out the value of angle x 24 degrees
Answer:
180=2x+ 24( angles opposite to equal sides)
156/2=x
x=78
Step-by-step explanation:
The value of x from the triangle is given by the equation x = 78°
What Is an Isosceles Triangle?A triangle with two sides of equal length is an isosceles triangle. The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.
In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle
The three types of Isosceles Triangles are :
Isosceles acute triangle
Isosceles right triangle
Isosceles obtuse triangle
Given data ,
Let the triangle be represented as ABC
Now , the measure of angle ∠A = 24°
It is an isosceles triangle with ∠B = ∠C
So , the measures of the two angles are the same
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
Substituting the values in the equation , we get
x + x + 24° = 180°
On simplifying the equation , we get
2x = 156°
Divide by 2 on both sides of the equation , we get
x = 78°
Hence , the measure of x = 78°
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