Answer:
a) 75.8% of students would score less than 550 in a typical year.
b) The comparable standard would be a minimum ACT score of 22.2.
c) 0.0139 = 1.39% probability that a randomly selected student will score over 700 on the SAT math test.
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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Question a:
SAT, so mean of 480 and standard deviation of 100, that is, [tex]\mu = 480, \sigma = 100[/tex]
The proportion is the p-value of Z when X = 550. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{550 - 480}{100}[/tex]
[tex]Z = 0.7[/tex]
[tex]Z = 0.7[/tex] has a p-value of 0.758.
0.758*100% = 75.8%
75.8% of students would score less than 550 in a typical year.
b. What would the engineering school set as comparable standard on the ACT math test?
ACT, with a mean of 18 and a standard deviation of 6, so [tex]\mu = 18, \sigma = 6[/tex]
The comparable score is X when Z = 0.7. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.7 = \frac{X - 18}{6}[/tex]
[tex]X - 18 = 0.7*6[/tex]
[tex]X = 22.2[/tex]
The comparable standard would be a minimum ACT score of 22.2.
c. What is the probability that a randomly selected student will score over 700 on the SAT math test?
This is 1 subtracted by the p-value of Z when X = 700, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{700 - 480}{100}[/tex]
[tex]Z = 2.2[/tex]
[tex]Z = 2.2[/tex] has a p-value of 0.9861.
1 - 0.9861 = 0.0139
0.0139 = 1.39% probability that a randomly selected student will score over 700 on the SAT math test.
HELP!!!!!!!! 15 POINTS
Answer:
x=5 is in the domain
Step-by-step explanation:
sqrt(x-5) ≥ 0
Square each side
(sqrt(x-5))^2 ≥ 0^2
x-5≥0
x≥5
This is the domain of x
Subtract (4x2 - x + 6) from (3x2 + 5x - 8).
A:7x^2 + 6x - 14
B:-x^2 + 4x + 2
C:7x^2 + 4x - 2
D:-x^2 + 6x - 14
Step-by-step explanation:
[tex](4x^2-x+6)-(3x^2+5x-8)=4x^2-x+6-3x^2-5x+8[/tex]
By simplifying the right side of the equation, we come up with
[tex]x^2+6x-14[/tex], or D
I need help completing this problem ASAP
Answer:
D. [tex]3x\sqrt{2x}[/tex]
Step-by-step explanation:
The problem gives on the following equation:
[tex]\sqrt{32x^3}+-\sqrt{16x^3}+4\sqrt{x^3}-2\sqrt{x^3}[/tex]
Alongside the information that ([tex]x\geq0[/tex]).
One must bear in mind that the operation ([tex]\sqrt[/tex]) indicates that one has to find the number that when multiplied by itself will yield the number underneath the radical. The easiest way to find such a number is to factor the term underneath the radical. Rewrite the terms under the radical as the product of prime numbers,
[tex]\sqrt{2*2*2*2*2*x*x*x}-\sqrt{2*2*2*2*x*x*x}+4\sqrt{x*x*x}-\sqrt{2*x*x*x}[/tex]
Now remove the duplicate factors from underneath the radical,
[tex]2*2*x\sqrt{2x}-2*2*x\sqrt{x}+4x\sqrt{x}-2x\sqrt{x}[/tex]
Simplify,
[tex]4x\sqrt{2x}-4x\sqrt{x}+4x\sqrt{x}-x\sqrt{2x}[/tex]
[tex]3x\sqrt{2x}[/tex]
Pippa had 35 stickers.
She gave an equal number of stickers to 8 friends.
She gave each friend as many stickers as possible and kept the rest for herself.
How many stickers did Pippa keep for herself?
Answer: 3 stickers
Step-by-step explanation:
From the question, we know that Pippa's 8 friends have an equal amount of stickers, meaning that the number of stickers that Pippa gave out is a multiple of 8.
Also, we are able to know that Pippa gave as much as she can, meaning that she gave out the stickers until the number is the maximum multiple of 8.
First Five Multiple of 8 = 8, 16, 24, 32, 40
As we can see from the list, 8, 16, and 24 are all multiples of 8, but they are not the maximum number that could fit under 35 stickers. Similarly, 40 exceeds the number of stickers Pippa has. Thus, we are left with 32.
This means, Pippa gave out 32 stickers in total, and each friend got 4 stickers.
32 / 8 = 4 stickersAlso, this means Pippa would keep 3 stickers for herself.
35 - 32 = 3 stickersHope this helps!! :)
Please let me know if you have any questions
help fast!! i need this asap! thank youu
5/3 is farthest according to me
Answered by Gauthmath must click thanks and mark brainliest
Answer:
0.27, 1.1, - 1/4, 5/3
Change all to decimal:-
0.27, 1.1, -.2.5, 1.67
So, 1.67 is farthest from zero
D) 5/3 is your answer
~OAmalOHopeO
Choose the correct answer.
The History Activities were about ___ and ___. They were both from ___. One of them had a ___ named after him. The other had a ___ named after him. The work they did together on a problem they got from a ___ laid the foundation for probability theory.
A. Pascal, Decartes, England, graph, book, relative
B. Luniz, Kolmogrov, Germany, church, square, teacher
C. Fermat, Luniz, England, law, diagram, priest
D. Pascal, Fermat, France, triangle, theorem, gambler
Answer:
I say Its letter d
Step-by-step explanation:
I hope this help
The cost, c, for mailing books is a function of the number of books, b. The
cost to mail books is $0.50 per book plus a $3.00 flat fee
Answer:
c = 3.00 + .50b
Step-by-step explanation:
The cost is the flat fee plus the cost per book times the number of books
c = 3.00 + .50b
According to the Federal Election Commission, 53.6% of all registered voters in 2012 voted in the US presidential elections in 2012. A political study conducted in January 2016 surveyed 1,251 eligible voters and found that 86% said they planned to vote in the 2016 presidential election. Based on this information, match each term to its value.
1. 1,251
2. 53.6%
3. 86%
a. statistic
b. sample size
c. parameter
Answer:
SEE BELOW
Step-by-step explanation:
1. sample size - 1,251
2 .statistic - 53.6%
3. parameter - 86%
hope this helps :)
Drag the numbers to the boxes to order them from least to greatest value. Please answerr quick
Answer:
Please what is the first value there?
x is the same as 1x or 1
√5 = 2.2360679775
(2)1/2 is the same as 5/2 or 2.5
√7 = 2.64575131106
√11 = 3.31662479036
3.5
least to greatest:
x < √5 < (2)1/2 < √7 < √11 < 3.5
What is 21 1/8 minus 14 1/8
Answer:
8.75
Step-by-step explanation:
211/8 = 26.375
141/8 = 17.625
now,
211/8-141/8
26.375-17.625
8.75
Find the radius of the circle containing 18
degree arc of a circle whose length is 15 Pi meters
9514 1404 393
Answer:
150 m
Step-by-step explanation:
The relationship between arc length (s), radius (r), and central angle (θ) is ...
s = rθ
Dividing by θ gives the formula for r:
r = s/θ = (15π m)/(18°(π/180°))
r = 150 m . . . . the radius of the circle
Which of the following fractions is closest to 0? 5/12 , 2/3, 5/6,3/4
Answer:
5/12
Step-by-step explanation:
5/12 , 2/3, 5/6,3/4
Get a common denominator of 12
5/12, 2/3 *4/4, 5/6*2/2, 3/4 *3/3
5/12, 8/12, 10/12, 9/12
The numerator closest to 0 is the fraction closest to 0
5/12
PLEASE HELP, IGNORE ALL ANWSERS FILLED IN CURRENTLY I WILL GOVE BRAINLIST
Answer:
15.924 feets
Step-by-step explanation:
The height I'd the flagpole can be obtained using trigonometry ;
Solution triangle has been attached below,
The height, h of flagpole
Tan θ = opposite / Adjacent = h / 12
Tan 53 = h / 12
h = 12 * tan 53
h = 15.924
U (24 win Q7 A gardener needs to order fertiliser for a piece of land. The piece of land is a square with sides measuring 8 metres. This formula shows how many grams of fertiliser she needs. grams of fertiliser needed = length in metres x width in metres x 25 The supplier sells these bags of fertiliser. 10K 5kg 2kg 1kg 1 kilogram 2 kilograms 5 kilograms 10 kilograms Which bag of fertiliser should the gardener order? Include figures to explain your answer. Show all your working.
Answer:
first: there is a problem in the question in de mentioned quantity u mentioned 10k instead of (10kg).
Step-by-step explanation:
add all your 1uantity afteru divide by 8
Answer:
one fertilizer bag from weight of two kilograms
Step-by-step explanation:
Grams of fertilizer needed = Length in meters * Width in meters * 25
= 8 * 8 * 25
= 1600 grams
Kilograms of fertilizer needed = 1600 / 1000
= 1.6 kilograms
Therefore, gardener can order 1 fertilizer bag with weight of 2kilpgrams.
please help me with geometry
Answer:
CAD = 25°
Step-by-step explanation:
The angles are shown to be equal in the figure so BAC = CAD.
Find the length of the side CD in the pentagon ABCDE.
A)
4√2 units
B)
12 units
C)
4 units
D)
4√10 units
Answer: A) 4√2 units
Step-by-step explanation:
Use the distance formula to find the distance(d) between Point D and Point C:
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
Point D = (x₁, y₁) = (4, -2)Point C = (x₂, y₂) = (8, 2)[tex]d=\sqrt{(8-4)^{2}+(2-(-2))^{2}}=\sqrt{(4)^{2}+(4)^{2}}=\sqrt{16+16} =\sqrt{32} =4\sqrt{2}[/tex]
Write a rule to describe the transformation.
A. reflection across y=x
B. rotation 90º clockwise about the origin
C. rotation 180º about the origin
D. rotation 90º counterclockwise about the origin
Answer:
C. rotation 180º about the origin
Step-by-step explanation:
Given
Quadrilaterals GWVY and G'W'V'Y'
Required
Describe the transformation rule
Pick points Y and Y'
[tex]Y = (5,-4)[/tex]
[tex]Y' = (-5,4)[/tex]
The above obeys the following rule:
[tex](x,y) \to (-x,-y)[/tex]
When a point is rotated by 180 degrees, the rule is:
[tex](x,y) \to (-x,-y)[/tex]
Hence, (c) is correct
5x-22 3x +105 x minus 22 3 X + 10
-291x+10
:)))))) Have fun
Solve 3! Pleaseeee help
Answer:
81
Step-by-step explanation:
180-41-58=81
angles in a triangle add up to 180 :)
The half-life of a radioactive substance is 20 years. If you start with some amount of this substance, what fraction will remain in 180 years?
Answer:
1/512
Step-by-step explanation:
Let staring fraction = x
Half-life = 20 years ; this is the time taken for an element to decrease to half of its original size
Hence,
After 20 years - - - > x/2
After 40 years - - - - > x/2 ÷ 2 = x/2 * 1/2 = x /4
After 60 years - - - - > x/4 ÷ 2 = x/4 * 1/2 = x/8
After 80 years - - - - -> x/8 ÷ 2 = x/8 * 1/2 = x / 16
After 100 years - - - > x/16 * 1/2 = x/32
After 120 years - - - - > x/32 * 1/2 = x/64
After 140 years - - - - -> x / 64 * 1/2 = x / 128
After 160 years - - - - - > x / 128 * 1/2 = x/256
After 180 years - - - - > x/256 * 1/2 = x / 512
Hence, the fraction after 180 years = 1/512
A local cinema reduced its ticket prices by 15% which means a ticket now costs £10.88. how much was a ticket before the reduction?
What is the answer to it
No question?
Why not add one!
The term "downers" refers to ..
Square root of 33324324323
The Square root of 33324324323 is 182549.511977.
11. The coordinates of AABC are A(-1,1), B(3,3),
and C(4, -2). Find the coordinates of points A', B',
and C' under the translations that take
a. P(0,0) to Q(1,3)
b. P(0, -1) to Q(4,-2)
c. P(-1,-2) to Q(-2,2)
Answer:
See explanation
Step-by-step explanation:
Given
[tex]A = (-1,1)[/tex]
[tex]B = (3,3)[/tex]
[tex]C =(4,-2)[/tex]
Solving (a): [tex]P(0,0) \to Q(1,3)[/tex]
This means that:
[tex](x,y) \to (x+1,y+2)[/tex]
So, we have:
[tex]A = (-1,1)[/tex]
[tex]A' = (-1 + 1,1+2)[/tex]
[tex]A' = (0,3)[/tex]
[tex]B = (3,3)[/tex]
[tex]B'= (3 + 1,3+2)[/tex]
[tex]B'= (4,5)[/tex]
[tex]C =(4,-2)[/tex]
[tex]C' = (4+1,-2+1)[/tex]
[tex]C' = (5,-1)[/tex]
Solving (b): [tex]P(0,-1) \to Q(4,-2)[/tex]
This means that:
[tex](x,y) \to (x+4,y-1)[/tex]
So, we have:
[tex]A = (-1,1)[/tex]
[tex]A' = (-1+4,1-1)[/tex]
[tex]A' = (3,0)[/tex]
[tex]B = (3,3)[/tex]
[tex]B'= (3+4,3-1)[/tex]
[tex]B'= (7,2)[/tex]
[tex]C =(4,-2)[/tex]
[tex]C' = (4+4,-2-1)[/tex]
[tex]C' = (8,-3)[/tex]
Solving (c): [tex]P(-1,-2) \to Q(-2,-2)[/tex]
This means that:
[tex](x,y) \to (x-1,y)[/tex]
So, we have:
[tex]A = (-1,1)[/tex]
[tex]A' = (-1-1,1)[/tex]
[tex]A' = (-2,1)[/tex]
[tex]B = (3,3)[/tex]
[tex]B'= (3-1,3)[/tex]
[tex]B'= (2,3)[/tex]
[tex]C =(4,-2)[/tex]
[tex]C'= (4-1,-2)[/tex]
[tex]C'= (3,-2)[/tex]
help it will really hep with summer school.
Answer:
10 + 5 + 6 × 5 - 2 × 4Step-by-step explanation:
Do MDAS:10 + 5 + 6 × 5 - 2 × 4=10 + 5 + 30 - 2 × 4= 10 + 5 + 30 - 8= 15 + 30 - 8= 45 - 8= 37[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
A catering company uses different functions to estimate the itemized costs for a party. The table below represents the included tip for wait staff as a function of the number of guests served.
A table showing Catering Cost for Wait Staff Gratuity with two columns and 6 rows. The first column has, Number of Guests, and has the entries, 10, 20, 30, 40, 50. The second column, Wait Staff Tip, has the entries, $18, $36, $54, $72, $90.
If the tip varies directly with the number of guests, which equation represents the relationship between the tip, t, and the number of guests, g?
t = 1.8g
t = t equals StartFraction g Over 18 EndFraction.
g = 1.8t
g = g equals StartFraction t Over 18 EndFraction.
Answer: t = 1.8g
Step-by-step explanation:
Since we are given the information that the tip varies directly with the number of guests, then the formula to use will be:
t = kg
where,
t = wait staff tip
g = number of guests
Therefore, when the number of guests is 10 and the tip is $18, the constant of proportionality will be:
t = kg
18 = 10k
k = 18/10
k = 1.8
Therefore, t = 1.8g
Answer:
A.
Step-by-step explanation:
A certain standardized test measures students’ knowledge in English and math. The English and math scores for 10 randomly selected students are given in the table.Using technology, what is the correlation coefficient?
0.68
0.83
0.91
0.95
Answer:
The answer is C
.91
ED2021
Suppose g(x) = f( x +2) - 3. Which statement best compares the graph of g(x) with the graph of f(x)? A. The graph of g(x) is shifted 2 units left and 3 units up. B. The graph of g(x) is shifted 2 units right and 3 units down. C. The graph of g(x) is shifted 2 units left and 3 units down. D. The graph of g(x) is shifted 2 units right and 3 units up.
Given:
The function is:
[tex]g(x)=f(x+2)-3[/tex]
To find:
The statement that best compares the graph of g(x) with the graph of f(x).
Solution:
The transformation is defined as
[tex]g(x)=f(x+a)+b[/tex] .... (i)
Where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
We have,
[tex]g(x)=f(x+2)-3[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]a=2[/tex]
[tex]b=-3[/tex]
Therefore, the graph of g(x) is shifted 2 units left and 3 units down.
Hence, the correct option is C.
helppp outt plss....
============================================================
Explanation:
For any cyclic quadrilateral (aka inscribed quadrilateral), the opposite angles are always supplementary.
One pair of such angles is A and C
A+C = 180
x+y = 180 is one equation to form
The other pair of supplementary angles is B and D
B+D = 180
y-45+2x+15 = 180
2x+y-30 = 180
2x+y = 180+30
2x+y = 210 is the other equation to form
--------------
So the system of equations we have is
[tex]\begin{cases}x+y = 180\\2x+y = 210\end{cases}[/tex]
Both equations involve 'y', with the same coefficient, so we can subtract straight down to eliminate this variable.
The x terms subtract to x-2x = -xThe y terms subtract to y-y = 0y = 0, so the y terms go awayThe right hand sides subtract to 180-210 = -30We end up with -x = -30 which solves to x = 30
--------------
Once we know x, we can determine y by plugging it into any equation involving x,y and solving for y
Let's say we picked on the first equation
x+y = 180
30+y = 180
y = 180-30
y = 150
Or we could pick on the second equation
2x+y = 210
2(30) + y = 210
60+y = 210
y = 210-60
y = 150
Only one equation is needed. However, doing both like this shows that we get the same y value, and it helps confirm the answers.
