9514 1404 393
Answer:
(-1, -3)
Step-by-step explanation:
Each coordinate is multiplied by the dilation factor when dilation is centered at the origin.
(1/4)(-4, -12) = (-1, -3) . . . . the image of the given point
Stuck on this one!!
Shelly believes the honor roll students at her school have an unfair advantage in being assigned to the math class they request. She asked 500 students at her school the following questions: "Are you on the honor roll?" and "Did you get the math class you requested?" The results are shown in the table below:
Honor roll Not on honor roll Total
Received math class requested 125 215 340
Did not get math class requested 80 80 160
Total 205 295 500
Help Shelly determine if all students at her school have an equal opportunity to get into the math class they requested. Show your work, and explain your process for determining the fairness of the class assignment process.
Answer: No, there isn't equal opportunity
======================================================
Explanation:
Let's define the two events
A = person is on the honor rollB = person got the math class they requestedFrom the table, we see that
P(B) = 340/500 = 0.68
meaning that there's a 68% chance of picking someone who got the class they wanted (i.e. 68% of the people got the class they wanted)
------------
Now let's assume that the person is on the honor roll. This means we only focus on the "honor roll" column. There are 125 people here that got the class they wanted out of 205 honor roll students total.
So,
P(B given A) = 125/205 = 0.609756
which rounds to 0.61
This says that if a person is on the honor roll, then they have roughly a 61% chance of getting the class they want.
The chances have gone down from 68% to 61% roughly.
------------
It appears that being on the honor roll does affect your chances of getting into the class you want.
Therefore, all students do not have the same equal opportunity.
We would need to have P(B) and P(A given B) to be the same exact value for true equal opportunity to happen.
All students do not have equal opportunity.
From the table, we have the following parameters:
205 people are on honor roll call340 people got the math class requested500 people were surveyedThe above means that:
The probability that a person is on honor roll call is:
p1 = 205/500
p1 = 0.41
The probability that a person got the math class requested
p2 = 340/500
p2 = 0.68
Both probabilities are not equal.
Hence, it is true that all students do not have equal opportunity.
Read more about probability at:
https://brainly.com/question/25870256
(b) If 124n= 232 five, find n.
Answer:[tex]n=\frac{58}{31}[/tex]
Step-by-step explanation:
[tex]124n=232\\\frac{124n}{124}=\frac{232}{124}\\n=\frac{232}{124}=\frac{58}{31}[/tex]
The value of n is 18.75. To find the value of n, we need to solve the equation: 124n = 232 five
Let's first convert "232 five" into a numerical value:
"232 five" means 2325 (since five is in the units place).
Now, the equation becomes:
124n = 2325
To solve for n, divide both sides of the equation by 124:
n = 2325 / 124
Now, perform the division:
n = 18.75
So, the value of n is 18.75.
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Can u please help I got 1 minnnn lefttttt
Answer:
26 cm
Step-by-step explanation:
P = 2a + 2b
a = side
b = base
Answer:
The area=base×height
=10×4
=40cm^2
perimeter=2(length+breadth)
I think to find the height Dc you use the pythagoras theorem of
Dc^2=de^2+ce^2
=√16+9
=5
therefore the perimeter will be
p=2(5+10)
=20cm
I hope this helps and sorry if it's wrong
5 people cleared a plot of land in 15 days. How many people would I need to hire to clear three times that plot in 5 days?
ive gotten it wrong like 4 times n i cannot figure it out pls help
Answer:
x = 74.74 m
Step-by-step explanation:
you need simple trigonometry to solve it
cosine of an angle is the ratio of the adjacent side to the hypotenuse
cos(42.2) is about 0.74
so X / Hypotenuse = 0.74
we know hypotenuse is 101 m
X / 101 = 0.74
x = 74.74 m
hope this helped!
Cho A=( căn x -4x /1-4x -1) : (1+2x/1-4x -2căn x/ 2căn x -1 -1)
Answer:
0.85714285714286 x 100 = 85.7143%.
Step-by-step explanation:
sketch the graph of y=x(x-6)^
Answer:
i have attached pic of the graph
i hope this helps you
A professor knows that her statistics students' final exam scores have a mean of 79 and a standard deviation of 11.3. In his class, an "A" is any exam score of 90 or higher. This quarter she has 22 students in her class. What is the probability that 6 students or more will score an "A" on the final exam?
prob =
0.1449 = 14.49% probability that 6 students or more will score an "A" on the final exam.
---------------
For each student, there are only two possible outcomes. Either they score an A, or they do not. The probability of a student scoring an A is independent of any other student, which means that the binomial probability distribution is used to solve this question.
Additionally, to find the proportion of students who scored an A, the normal distribution is used.
----------------
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of a success.
----------------
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation , 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.
----------------
Proportion of students that scored an A:
Scores have a mean of 79 and a standard deviation of 11.3, which means that [tex]\mu = 79, \sigma = 11.3[/tex]
Scores of 90 or higher are graded an A, which means that the proportion is 1 subtracted by the p-value of Z when X = 90, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{90 - 79}{11.3}[/tex]
[tex]Z = 0.97[/tex]
[tex]Z = 0.97[/tex] has a p-value of 0.8340.
1 - 0.8340 = 0.166
The proportion of students that scored an A is 0.166.
----------------
Probability that 6 students or more will score an "A" on the final exam:
Binomial distribution.
22 students, which means that [tex]n = 22[/tex]
The proportion of students that scored an A is 0.166, which means that [tex]p = 0.166[/tex]
The probability is:
[tex]P(X \geq 6) = 1 - P(X < 6)[/tex]
In which
[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{22,0}.(0.166)^{0}.(0.834)^{22} = 0.0184[/tex]
[tex]P(X = 1) = C_{22,1}.(0.166)^{1}.(0.834)^{21} = 0.0807[/tex]
[tex]P(X = 2) = C_{22,2}.(0.166)^{2}.(0.834)^{20} = 0.1687[/tex]
[tex]P(X = 3) = C_{22,3}.(0.166)^{3}.(0.834)^{19} = 0.2239[/tex]
[tex]P(X = 4) = C_{22,4}.(0.166)^{4}.(0.834)^{18} = 0.2117[/tex]
[tex]P(X = 5) = C_{22,5}.(0.166)^{5}.(0.834)^{17} = 0.1517[/tex]
Then
[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0184 + 0.0807 + 0.1687 + 0.2239 + 0.2117 + 0.1517 = 0.8551[/tex]
[tex]P(X \geq 6) = 1 - P(X < 6) = 1 - 0.8551 = 0.1449[/tex]
Thus
0.1449 = 14.49% probability that 6 students or more will score an "A" on the final exam.
For a problem that used the normal distribution, you can check https://brainly.com/question/15181104, and for a problem that used the binomial distribution, you can check https://brainly.com/question/15557838
Suppose y varies inversely with x, and y = 32 when x = 4. What is the value of y when x = 8?
a. 1/8
b. 64
c. 16
d. 8
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
Answer:
16
Step-by-step explanation:
Inverse variation is of the form
xy = k where k is a constant
x=4 and y = 32
4*32 = k
128 = k
xy = 128
Let x = 8
8y = 128
Divide each side by 8
8y/8 = 128/8
y =16
how do you change 79/8 to a decimal
Answer:
Divide 79 by 8
Step-by-step explanation:
79/8
= 9.875
Please answer this and show the work/explain for me
2/7m - 1/7 = 3/14
For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. The library director in Owensboro, Kentucky feels this is not true, so she asked a local college statistic class to conduct a survey. The class randomly selected 100 patrons and found that 82 borrowed books. Did the class demonstrate that the percentage was higher in Owensboro, KY? Use α = 0.01 level of significance. What is the possible proportion of patrons that do borrow books from the Owensboro Library?
Answer:
The p-value of the test is 0.0007 < 0.01, which means that the class demonstrates that the percentage was higher in Owensboro, KY.
The possible proportion of patrons that do borrow books from the Owensboro Library is 0.82.
Step-by-step explanation:
For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. Test if the proportion is higher in Owensboro, KY.
At the null hypothesis, we test if the proportion is of at most 0.67, that is:
[tex]H_0: p \leq 0.67[/tex]
At the alternative hypothesis, we test if the proportion is of more than 0.67, that is:
[tex]H_1: p > 0.67[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.67 is tested at the null hypothesis:
This means that [tex]\mu = 0.67, \sigma = \sqrt{0.67*0.33}[/tex]
The class randomly selected 100 patrons and found that 82 borrowed books.
This means that [tex]n = 100, X = \frac{82}{100} = 0.82[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.82 - 0.67}{\frac{\sqrt{0.67*0.33}}{\sqrt{100}}}[/tex]
[tex]z = 3.19[/tex]
P-value of the test and decision:
The p-value of the test is the probability of a finding a sample proportion of 0.82 or above, which is 1 subtracted by the p-value of z = 3.19.
Looking at the z-table, z = 3.19 has a p-value of 0.9993.
1 - 0.9993 = 0.0007
The p-value of the test is 0.0007 < 0.01, which means that the class demonstrates that the percentage was higher in Owensboro, KY.
What is the possible proportion of patrons that do borrow books from the Owensboro Library?
The sample proportion of 0.82.
What is
88x3-7+198-34x15+76-126=
-105
Multiply first, then subtract, then add.
Answer: the answer would be -105.
A 100.0 m long polymer cable of uniform circular cross section and of diameter 0.4cm has a mass of 1885.0 gm. What is the mass density, of the polymer in kg/m3?
The mass density in kg/m3 will be - 15 x [tex]10^{-2}[/tex] Kg/m3.
We have a 100.0 m long polymer cable of uniform circular cross section and of diameter 0.4cm has a mass of 1885.0 gm.
We have to determine its mass density in kg/m3.
What is Mass density ?The amount of mass per unit volume present in the body is called its mass density.
According to question, we have -
Length of polymer cable = 100.0 m
diameter of polymer cable = 0.4 cm = 0.004 m
Therefore, its radius = 0.002 m
The mass density of the wire will be -
[tex]\rho =\frac{m}{\pi r^{2} l}[/tex]
[tex]\rho[/tex] = [tex]\frac{1885}{3.14 \times0.002 \times 0.002 \times 100 }[/tex]
[tex]\rho = \frac{1885}{0.001256}[/tex] = 1500796.1 g/m3
1 Kg = 1000g
1g = 1/1000kg
1500796.1g = 1500.7 Kg = 15 x [tex]10^{-2}[/tex] Kg
Therefore, mass density = 15 x [tex]10^{-2}[/tex] Kg/m3
Hence, the mass density in kg/m3 will be - 15 x [tex]10^{-2}[/tex] Kg/m3.
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Each side of a regular polygon is 3.2 cm in length. The perimeter of the polygon is 19.2 cm. How many sides does the polygon have? What is the name of the polygon?
Answer:
The polygon consists of 6 sides and the given polygon is a regular hexagon.
Step-by-step explanation:
The definition of perimeter is the total measure of the side lengths of a polygon. If the polygon said is regular, it means the polygon has equal sides and equal angles.
So the perimeter of a regular polygon is given by the formula:
P = (length of one side) x (number of sides)
In this case, the perimeter of the polygon is 19.2 cm and one side is equal to 3.2 cm.
DIVIDE (use the formula but in division to maintain a proportonal relationship):
19.2 ÷ 3.2 = 6
You could alsk check if its correct using the formula:
19.2 = 3.2 x 6 (TRUE)
A 6 sided regular polygon is known as a HEXAGON.
Hope this helps!
Plzzz I’m giving a away 25 points
Answer:
sin ß = opposite / hypotenuse
sin45° = x / 4√2
Cross multiply
x = sin 45° × 4√2
x = √2/2 × 4√2
x = 4 × √2 ×√2 / 2
x = 4 × 2 / 2
x = 8 / 2
x = 4
Use AABC to find the value of sin B.
Answer:
35/37
Step-by-step explanation:
sin(B)=(AC)/(AB) = 35/37
The retail of a price of an LCD TV was $7000 what was the original price before the GST of 10% was added?
Answer:
$636.36
Step-by-step explanation:
7000 = 110% of total cost
Try to get it to 100 percent
700/11 = 63.(63)
63.(63)*10= 636.36
lyng
whose zeros and
Zeros: - 4, 4, 8; degree: 3
Need this in polynomial form
time in months it would take for a $1500 dollar investment in a TFSA to grow to $1545 if the simple interest at a rate paid was 2% per annum.
It would take 17 months and 14 days for the investment to grow to $1545.
To determine the time in months it would take for a $ 1500 dollar investment in a TFSA to grow to $ 1545 if the simple interest at a rate paid was 2% per annum, the following calculation must be performed:
First, you must obtain 2% of 1545 to determine the interest generated per year.
1545 x 2/100 = X 30.9 = XThen, a cross multiplication must be carried out considering the number of months it took to generate said interest, and compare it with the interest that arises from the subtraction of 1545 - 1500, that is, 45.
30.9 = 1245 = X45 x 12 / 30.9 = X540 / 30.9 = X17.47 = X 1 = 300.47 = X14 = XTherefore, it would take 17 months and 14 days for a $ 1500 dollar investment in a TFSA to grow to $ 1545.
Learn more about interest in https://brainly.com/question/19903178.
A company pays $20 per hour for up to 8 hours of work, and $30 per hour for overtime hours (hours beyond 8 hours). For up to 8 hours worked, the equation for total pay (y) for hours worked (x) is y = 20x. For over 8 hours worked, what is the equation for total pay (y) as a function of total hours worked (x)?
Answer: y = 30x
Step-by-step explanation:
Because we are talking about over 8 hours. The question states that you get 30$ per hour for overtime hours. That means if you work over 8 hours your dollars per hour increases to 30. So because the amount of dollars increases to 30 you can infer that all you have to do is make the same equation as the 20 dollar's per hour equation. Except you put 30 making it y = 30x.
Given the following coordinates complete the glide reflection transformation.
9514 1404 393
Answer:
A"(-1, -2)B"(4, 0)C"(6, -3)Step-by-step explanation:
The reflection over the x-axis is ...
(x, y) ⇒ (x, -y)
The shift left 3 units is ...
(x, y) ⇒ (x -3, y)
So, the two transformations together will be ...
(x, y) ⇒ (x -3, -y)
A(4, 2) ⇒ A"(1, -2)
B(7,0) ⇒ B"(4, 0)
C(9, 3) ⇒ C"(6, -3)
For the right angle, find the missing quantity indicated below the figure.
Answer:
The Answer is 28.........
give that 1/x+2/y=1/2, express y in terms of x and 2
9514 1404 393
Answer:
y = 4x/(x -2)
Step-by-step explanation:
Subtract 1/x
2/y = 1/2 -1/x
Combine terms
2/y = (x-2)/(2x)
Cross multiply
4x = y(x -2)
Divide by the coefficient of y
y = 4x/(x -2) . . . . simplest
y = 2^2/(x -2) . . . . in terms of x and 2
PLS HELP
Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (g o f) (-5)
–6
3
–59
26
Answer:
1st option
Step-by-step explanation:
Evaluate f(- 5) then substitute the value obtained into g(x)
f(- 5) = - 2(- 5) - 7 = 10 - 7 = 3 , then
g(3) = - 4(3) + 6 = - 12 + 6 = - 6
find the missing side length in the image below
Let missing side be x
Using basic proportionality theorem
[tex]\\ \sf\longmapsto \dfrac{18}{14}=\dfrac{27}{x}[/tex]
[tex]\\ \sf\longmapsto \dfrac{9}{7}=\dfrac{27}{x}[/tex]
[tex]\\ \sf\longmapsto 9x=7(27)[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{7(27)}{9}[/tex]
[tex]\\ \sf\longmapsto x=21[/tex]
Convert 15,000 meters to centimeters.
15,000 centimeters
150,000 centimeters
15,000,000 centimeters
1,500,000 centimeters
Answer:
1500000
Step-by-step explanation:
1 metre = 100 cm
15000metre =15000*100
=1500000
A 12 ounce bag of rice costs $4.08. A 16-ounce bag of the same rice costs $5.76. Which bag is the better by
and by how much
Answer:
16 once is the better one.
Answer: 12-ounce bag is better by $0.02 per ounce
Concept:
When coming across questions that ask for a comparison between prices, we should make the final unit [price per object].
In finding [price per object], simply do [Total price / number of objects].
Solve:
A 12-ounce bag of rice costs $4.08
Total price / number of objects = 4.08 / 12 = $0.34 per ounce
A 16-ounce bag of rice costs $5.76
Total price / number of objects = 5.76 / 16 = $0.36 per ounce
$0.36 - $0.34 = $0.02
$0.34 < $0.36, therefore, 12-ounce bag is better by $0.02 per ounce.
Hope this helps!! :)
Please let me know if you have any questions
A computer parts company wants to make a rectangular memory board that has a perimeter of 14 cm and a diagonal of length 5 cm. What are the dimensions of the board?
Answer:
A computer parts company wants to make a rectangular memory board that has a perimeter of 28 centimeters and a diagonal length of 10 centimeters. Find the dimensions of the board. Consider the length to be the longer side.: Call the two sides L & W: the perimeter 2L + 2W = 28 Simplify, divide by 2 L + W = 14 L = (14-W); use this form for substitution
Step-by-step explanation:
==========================================================
Explanation:
x = width
y = length
both x and y are positive real numbers, and the units of which are in cm.
The perimeter of any rectangle is found by saying
P = 2*(length+width)
P = 2*(x+y)
Plugging in P = 14 leads us to
P = 2*(x+y)
14 = 2*(x+y)
14/2 = x+y
7 = x+y
Solve for one of the variables. Let's say we solve for y. That should get us y = 7-x which we'll use a bit later.
--------------
Notice how the diagonal forms two identical right triangles. The legs of which are x and y as defined earlier. The hypotenuse is 5, which is the diagonal length.
Use the pythagorean theorem to help solve for x
a^2 + b^2 = c^2
x^2 + y^2 = 5^2
x^2 + (7-x)^2 = 25 ... plug in y = 7-x
x^2 + 49 - 14x + x^2 = 25 ... use FOIL rule
2x^2-14x+49 = 25
2x^2-14x+49-25 = 0
2x^2-14x+24 = 0
2(x^2-7x+12) = 0
x^2-7x+12 = 0
(x-3)(x-4) = 0
x-3 = 0 or x-4 = 0
x = 3 or x = 4
If x = 3, then y = 7-x = 7-3 = 4
If x = 4, then y = 7-x = 7-4 = 3
We have this symmetry going on. If x is one of 3 or 4, then y is the other of those values. Because x = 3 and y = 4, or vice versa, this means we have a 3-4-5 right triangle (well to be fair we have two identical copies of such a triangle to form the rectangle).
Therefore, the dimensions of the rectangular board is 3 cm by 4 cm. The order doesn't matter so you could easily say "4 cm by 3 cm" to mean the same thing.
--------------
Check:
P = perimeter
P = 2*(length+width)
P = 2*(x+y)
P = 2*(3+4)
P = 2*7
P = 14
That helps confirm the answer.
Find the value of a.
A. 58
B. 130
C. 86
D. 65
Answer:
[tex]C. \ \ \ 86[/tex]°
Step-by-step explanation:
1. Approach
In order to solve this problem, one must first find a relationship between arc (a) and arc (c). This can be done using the congruent arcs cut congruent segments theorem. After doing so, one can then use the secants interior angle to find the precise measurement of arc (a).
2. Arc (a) and arc (c)
A secant is a line or line segment that intersects a circle in two places. The congruent segments cut congruent arcs theorem states that when two secants are congruent, meaning the part of the secant that is within the circle is congruent to another part of a secant that is within that same circle, the arcs surrounding the congruent secants are congruent. Applying this theorem to the given situation, one can state the following:
[tex]a = c[/tex]
3. Finding the degree measure of arc (a),
The secants interior angle theorem states that when two secants intersect inside of a circle, the measure of any of the angles formed is equal to half of the sum of the arcs surrounding the angles. One can apply this here by stating the following:
[tex]86=\frac{a+c}{2}[/tex]
Substitute,
[tex]86=\frac{a+c}{2}[/tex]
[tex]86=\frac{a+a}{2}[/tex]
Simplify,
[tex]86=\frac{a+a}{2}[/tex]
[tex]86=\frac{2a}{2}[/tex]
[tex]86=a[/tex]
