On solving using combinations (C) we get the answers for part a)the probability that you will be assigned none of the tasks that you want = 0.035% b) the Probability that I am assigned exactly 7 of the tasks that I want = 0.0427 c)The probability that I am assigned at least one of the tasks I want = 0.9996 d)Probability that I am assigned at least 7 of the tasks I want = 0.049
a) There are 27 tasks and 10 tasks I want to do. Thus there are 17 tasks I do not want to do. I am randomly assigned 12 tasks. The probability that I will be assigned none of the tasks that I want is p = 17C12 / 27C12 = 3. 55 * 10 ^ (-4) = 0.035 %
b) The probability that I am assigned exactly 7 of the tasks that I want
p = 10C7 * 17C5 / 27C12 = 0.0427 = 4.27%
c) The probability that I am assigned at least one of the tasks I want
p = 1 - 17C12 / 27C12 where 17C12 / 27C12 is the probability that I get assigned 0 tasks I want.
Thus, p = 1 - (7/19665) = 0.9996
d)Probability that I am assigned at least 7 of the tasks I want
p = (10C7*17C5+10C8*17C4 + 10C9*17C3 + 10C10*17C2) / 27C12
⇒ p = 17 / 345 = 0.049 = 4.9%
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A wise man once said, "300 reduced by 3 times my age is 84." What is his age?
Answer:72
Step-by-step explanation:
How do I get n from 2n C n =70?
After evaluating the expression, the value of n is √(70/2C).
What are expressions?An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.) You can think of expressions as being similar to phrases.So, 2nCn = 70:
Now, solve for n as follows:
2nCn =702Cn² = 70n² = 70/2Cn = √(70/2C)Therefore, after evaluating the expression, the value of n is √(70/2C).
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equationsWrite a system of equations to describe the situation below, solve using elimination, and fill inche blanks.lada gets paid at home for doing extra chores. Last week, she did 1 load of laundry and 8oads of dishes, and her parents paid her $26. The week before, she finished 3 loads ofaundry and 8 loads of dishes, earning a total of $30. How much does Jada earn forcompleting each type of chore?
In this problem, we are going to write and solve a system of equations based on a real world situation.
Last week, she did 1 load of laundry and 8 loads of dishes, and her parents paid her $26. The week before, she finished 3 loads of laundry and 8 loads of dishes, earning a total of $30.
To begin, we need to create variables for the unknown cost of each chore.
Let x represent laundry, and let y represent dishes.
From the first equation, we can write the equation:
[tex]x+8y=26[/tex]We can write the second equation as:
[tex]3x+8y=30[/tex]Together, we have the system:
[tex]\begin{cases}x+8y={26} \\ 3x+8y={30}\end{cases}[/tex]Multiply the first equation by -1, then add it to the second equation:
[tex]\begin{gathered} \begin{cases}-1(x+8y={26)} \\ 3x+8y={30}\end{cases} \\ \\ \begin{cases}-x-8y={-26} \\ 3x+8y={30}\end{cases} \\ \\ (-x+3x)+(-8y+8y)=-26+30 \\ 2x=4 \end{gathered}[/tex]We can divide the remaining equation by 2 on both sides:
[tex]\begin{gathered} \frac{2x}{2}=\frac{4}{2} \\ \\ x=2 \end{gathered}[/tex]Lada made $2 per load of laundry.
We can use the value of x in the first equation to find the value of y. Substitute x = 2:
[tex]2+8y=26[/tex]Subtract 2 from both sides:
[tex]8y=24[/tex]Divide by 8 on both sides:
[tex]y=3[/tex]Lada made $3 per load of dishes.
(x + 4)(x + 3)How do I find the answer of this with work to break it down?
In order to break down this product, we need to apply the distributive property of the multiplication.
So we need to find the product of each term inside a binomial by each term in the other binomial.
That is, first we find x times x and x times 3, then we find 4 times x and 4 times 3, finally we add them all:
[tex]\begin{gathered} (x+4)(x+3)=x\cdot x+x\cdot3+4\cdot x+4\cdot3 \\ =x^2+3x+4x+12=x^2+7x+12 \end{gathered}[/tex]So the final expression is x2 + 7x + 12.
with pic. Which of the following functions is graphed below?
The picture is represented by the absolute value function g(x) = |x - 5| - 4. (Correct choice: A)
How to derive the absolute function associated with the picture
Absolute values are functions defined by the following piecewise function:
f(x) = |x| = x for x ≥ 0.f(x) = |x| = - x for x < 0.The function in the picture is the consequence of the following rigid transformations:
Horizontal translation 5 units in the + x direction.Vertical translation 4 units in the - y direction.Now we proceed to obtain the image of f(x):
Horizontal translation
f'(x) = |x - 5|
Vertical translation
g(x) = |x - 5| - 4
The picture is represented by the function g(x) = |x - 5| - 4.
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a certain store has 3,000 employees working at its main location in a city and 100 employees working at a smaller location outside the city. the store manager will select a sample of 50 employees from all the employees to ask their opinions about extending store hours during the holidays. what is the advantage of selecting a stratified random sample, with location as strata, instead of a simple random sample? responses
The answer is the stratified sample assures that the opinions of employees from both locations will be represented..
The survey results will accurately reflect the opinions of both urban and rural employees if you choose this option. By soliciting feedback from employees in both regions, it will be possible to ensure that any policy based on the results of this survey not only represents the interests of urban employees, who make up the bulk of the workforce, but also those of rural employees.
Option B is untrue since a stratified sample will cost more to implement than a straightforward random sample and won't always result in financial savings.
Option C does not applicable because it is just a supposition without any supporting data.
Choice D is False, since a stratified sample in this situation produces results that are more typical of the store's employees from both locations than a random sample.
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In this figure, m∠2=(6x+20)∘ and m∠8=(8x−10)∘ .
What value of x makes a∥b ?
Enter your answer in the box.
If the ∠2 = 6x+20 degrees and ∠8 = 8x-10 degrees, then the values of x is 15
The lines a and b are parallel lines
Here two parallel lines a and b are cut by a transversal t
The angles are
∠2 = 6x+20 degrees
∠8 = 8x-10 degrees
The angle 2 and angle 8 are called alternate exterior angles
When the two parallel lines are cut by a transversal, the formed alternate exterior angles are equal.
Then
6x+20 = 8x-10
Solve the equation
6x-8x = -10-20
-2x = -30
x = -30/-2
x = 15
Hence, if the ∠2 = 6x+20 degrees and ∠8 = 8x-10 degrees, then the values of x is 15.
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A middle school took all of its 6th grade students on a field trip to see a play at a
theater that has 1080 seats. The students filled 35% of the seats in the theater. How
many 6th graders went on the trip?
Answer:
there are 378 students
Step-by-step explanation:
you can see this as a simple proportion.
You know that the 100% of the seats are 1080 and you need to know the 35% of the seats, so you do:
[tex] \frac{1080}{100} = \frac{x}{35} [/tex]
so you do
x = 35 * 1080 ÷ 100 which gives 378
5. Which equation is solved for the height of the cone based on theinformation given below?The equation V = 1 r represents the volume of a cone, where is the radius of the cone andh is the height of the coneh=V - Tr?h= } #r?VB3V - #r2 = h3Vha?D
We need to make h the subject of formula:
[tex]\begin{gathered} All\text{ the variables on the right are multiplied together.} \\ \text{First we get rid of the 1/3 by multiplying both sides by 3:} \\ 3(V)\text{ =3( }\frac{1}{3}\pi r^{2}h) \\ 3V\text{ = }\pi r^{2}h \end{gathered}[/tex][tex]\begin{gathered} \text{For h to stand alone on the right side, we divide both sides by }\pi r^2h \\ We\text{ apply division beause all the variables were ultiplied together} \\ So\text{ to undo it, we divide} \\ \frac{3V}{\pi r^{2}}=\text{ }\frac{\pi r^{2}h}{\pi r^{2}} \\ \frac{3V}{\pi r^2}=\text{ }h \end{gathered}[/tex][tex]h\text{ = }\frac{3V}{\pi r^{2}}\text{ (option D)}[/tex]|x + 6| < or equal to 1
8
x < or equal to 2
x < or equal to ?
Answer: -14
Step-by-step explanation:
[tex]\frac{1}{8}|x+6| \leq 1\\\\|x+6| \leq 8\\\\-8 \leq x+6 \leq 8\\\\-14 \leq x \leq 2[/tex]
Wxyz is a parallelogram in the coordinate plane. the vertices for the parallelogram are w(0,0), (b,c), y (a + b,c), and z(a,0), where a > 0,b > 0, and c> 0 what set of statements prove that the diagonals of the parallelogram bisect each other?
The diagonals WY and XZ intersect at E, we must prove that WE ∼ = YE and XE ∼ = ZE. The converse exists also true: If the diagonals of a quadrilateral bisect each other, then the quadrilateral exists as a parallelogram.
Why quadrilateral WXYZ is a parallelogram?WXYZ cannot be a parallelogram because the value of x that creates one pair of sides congruent does not create the other pair of sides congruent.
Given that WXYZ, let the diagonals WY and XZ intersect at E, we must prove that WE ∼ = YE and XE ∼ = ZE. The converse exists also true: If the diagonals of a quadrilateral bisect each other, then the quadrilateral exists as a parallelogram.
A rhombus, therefore, contains all the properties of a parallelogram: Its opposite sides exist parallel. Its opposite angles exist equally. Its diagonals bisect each other.
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Select the correct answer.
What is the range of the function shown on the graph above?
A. -9 [tex]\leq[/tex] y [tex]\leq[/tex] 8
B. -7[tex]\leq[/tex] y [tex]\leq[/tex] -2
C.-8[tex]\leq[/tex] y [tex]\leq[/tex] 8
D.-2 [tex]\leq[/tex] y [tex]\leq[/tex] -7
Answer:
A
Step-by-step explanation:
The range is the y values. The y value is as low as -10 and as high as 8.
What does do the congruence criterion mean.
Please explain what AAS, SSS, ASA, and HL mean.
AAS = Angle , angle and one side of 2 congruent triangles
SSS = All 3 sides are measure same of the 2 triangles.
ASA = 2 angles and the side between them are same
HL = A right triangle is congruent if its hypotenuse and one of its legs are congruent with the hypotenuse and one of its other legs.
What is meant by congruency?The dimensions of the triangles' sides and angles determine whether two or more triangles are congruent. A triangle's size is determined by its three sides, and its shape by its three angles. Pairs of corresponding sides and corresponding angles in two triangles are said to be equal if they are congruent. They share a similar size and shape. In triangles, there are numerous congruence conditions. For the two triangles to be congruent, they must be the same size and shape. It should be possible to superimpose the two triangles under examination. A triangle's position or appearance appears to change when we rotate, reflect, and/or translate it. In that situation, we must recognize the six components of a triangle.
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Question Progress
Homework Progress
7/21 Marks
Solve the equation
3x-2
4
-
2x-5
3
=
1+x
6
Answer: x= 1.20833
The way it was written was a little confusing but hope this helps, This may be wrong just re write it for me and it should be correct next time.
Step-by-step explanation:
Step 1: Make parentheses
( 3x - 2 ) 4 ( -2x - 5 ) 3 = ( 1 + x ) 6
Step 2: Solve parentheses ( Multiplication and division first )
(4 * 3x = 12x) - (4 * 2 = 8) -> 12x - 8
(-2x * 3 = -6x) - (3 * 5 = 15) -> -6x - 15
(6 * 1 = 6) + (6 * x = 6x) -> 6 + 6x
New and improved equation:
-12x - 8 - 6x - 15 = 6 + 6x
Step 3: add like terms
-12x - 6x = -18x
-8 - 15 = -23 so...
-18x - 23 = 6 + 6x
Step 4: solve it
-18x - 23 = 6 + 6x
+ 23
-18x = 29 + 6x
-6x
-24x = 29
x= 1.20833
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Please help me, it is important
Examining the given figure it can be calculated that
GI = 15 unitsm< IEH = 65 degrees How to get the required angel and length of side in the given figureGiven that
EI = 2x + 1
FH = 3x + 9
m< FIG = 50 degrees
The length of diagonals of rectangles are equal and when they bisect each other the divide each other into equal halves
EI is the half of FH, therefore we have that
( 3x + 9 ) / 2 = 2x + 1
3x + 9 = 2(2x + 1)
3x + 9 = 4x + 2
9 - 2 = 4x - 3x
7 = x
GI = EI (half diagonal of rectangle are equal)
GI = 2 * 7 + 1
= 15
m< FIG = 50 degrees = m< EIH (vertical opposite angles)
m< EIH + m< IEH + m< IHE = 180
m< IEH = m< IHE = y (base angles of isosceles triangle)
m< EIH + 2y = 180
50 + 2y = 180
2y = 180 - 50
2y = 130
y = 65 degrees
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Please help! I’ve tried this a couple times now and still don’t understand it! Math is not my thing.
The function f(z) is graphed below. (Picture below)
a) What is f(0)?
b) What is f(3)?
c) What is f(1)?
Answer:
Step-by-step explanation:
in serious need of help! i need the answer quick!
The coordinates of G is (d+c, b)
This is because the opposite sides of any parallelogram are equal in length, and so the length of side HG is equal to the length of side EF.
a) The length of side HG is equal to the horizontal distance (x2 - x1): xG - 0
The length of side EF is equal to the horizontal distance (x2 - x1): d - (-c) = d +c
Thus:
xG - 0 = d + c
xG = d + c
Therefore the x-coordinate of G is d + c
b) To find the y-coordinate of G, we also apply the idea that sides GF and HE are equal.
The length of side GF is equal to the vertical distance (y2 - y1): yG - 0
The length of side HE is equal to the vertical distance (y2 - y1): b - 0
Thus:
yG - 0 = b -0
yG = b
Therefore the y-coordinate of G is b
Finally, the coordinates of G is (xG, yG) = (d+c, b)
a city has two water towers. one tower holds 8.4 x 103 gallons of water and the other tower holds 9.5 x 104 gallons of water. what is the combined water capacity of the two towers in scientific notation?
Total capacity the tower holds 1.034 x 10^5 gallons of water
One tower holds 8.4 x 10^3 gallons of water
Other tower holds 9.5 x 10^4 gallons of water
The combined water capacity of the two towers in scientific notation is,
Total capacity the tower holds = 9.5 x 10^4 + 8.4 x 10^3
= 9.5 x 10^4 + 0.84 x 10^4
= 10.34 x 10^4
= 1.034 x 10^5
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A student performed the following steps to find the solution to the equation
x² + 4x-12-0. Where did the student go wrong?
Step 1. Factor the polynomial into (x + 6) and (x-2)
Step 2. x-6= 0 and x + 2 = 0
Step 3. x = 6 and x = -2
O A. in Step 3
B. The student did not make any mistakes, the solution is correct
O C. in Step 1
OD. in Step 2
The student got the solution to the quadratic equation wrong at step 2
What are quadratic equations?A quadratic equation is a mathematical equation in which it's higher power of unknown is 2.
A quadratic equation can be solved by using 4 different method of choice which are formula method, factorization method , completing the square and graphical method.
x^2+4x-12=0 is an example of quadratic equation.
using factorization method to solve the value of x
x^2+6x-2x-12=0
grouping the equation
(x^2+6x)(-2x-12)=0
x(x+6)-2(x+6)=0
(x+6)(x-2)=0
for the equation to be satisfied
(x+6)=0
or
(x-2)=0
Therefore x= -6 or+2
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What is (3 x 10^7) (3 x 10^8)?
[tex] = 3 \times 3 \times {10}^{7} \times 10^{8} \\ = 9 \times {10}^{7 + 8} \\ = 9 \times {10}^{15} \\ [/tex]
NOTE YOU CAN WRITE IT IN FULL BUT I CHOSE NOT TO BECAUSE IT'S LARGE .
GOODLUCK
luke says that "three divided by 21" is the same AS "twenty one divided by three". Is Luke correct? Explain why or why not.
Answer: He is incorrect
Step-by-step explanation:
3/21 = 0.142857142857143
21/3 = 7
They are two different equations with different answers.
Answer:
He is not correct
Step-by-step explanation:
Luke is not correct because 3/21 is 0.142 while 21/3 is 7.
Door prizes for entrants in a young inventors competition are $100, $50, $25 and $10. In how many ways can the door prizes be awarded if there are 23 entrants?.
The total number of ways the prizes are awarded is 8855.
The prizes for entrants in a young inventors competition are $100, $50, $25, and $10.
Which are of total 4 types of prizes.
If there are 23 entrants in the competition the prizes can be awarded in the following ways by using Combinations.
Total number of ways = ²³C₄
= [tex]\frac{23!}{4! * (23 - 4)!}[/tex]
= 8855
The total number of ways the prizes are awarded is 8855.
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for this I already did the first part and I got f(x)=2.5x+1so can you help me with the second part
Which of these equations is perpendicular to the midpoint of the line segment that contains the point (-4,4) and (2,-2)?
The equation of the line perpendicular to the line line joining (-4,4) and (2,-2) will be → y = x + 2.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is a line that is perpendicular to the midpoint of the line segment that contains the point (-4,4) and (2,-2),
The midpoint of line joining (-4,4) and (2,-2) will be -
x[m] = (- 4 + 2)/2 = -1
y[m] = (4 - 2)/2 = 1
Coordinates of the midpoint will be M(-1, 1)
Slope of the line joining (-4,4) and (2,-2) will be -
m = (- 2 - 4)/(2 + 4)
m = -6/6
m = - 1
Then, the slope of the line perpendicular to this line will be -
m[p] = -1/-1
m[p] = 1
Assume that the equation of the perpendicular line as -
y[p] = x + c
Since it passes though (-1, 1) so -
1 = -1 + c
c = 2
Therefore, the equation of the line perpendicular to the line line joining (-4,4) and (2,-2) will be → y = x + 2.
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Drevae WashingtonExpected ValueMar 08, 1:24:47 PM?Scarlett volunteers on the weekend at the Central Library. As a school project, shedecides to record how many people visit the library, and where they go. On Saturday,429 people went to The Youth Wing, 382 people went to Social Issues, and 424 wentto Fiction and Literature.On Sunday, the library had 1100 total visitors. Based on what Scarlett had recordedon Saturday, about how many people should be expected to go to The Youth Wing?Round your answer to the nearest whole number.Answer:Submit Answerattempt 1 out of 2RIDeltaMath - Googl.W April Spirit WeekResume from vae..
SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Get the total number of visitors on saturday
[tex]382+429+424=1235[/tex]STEP 2: Get the proportion/probability of the people who went to the Youth Wing on Saturday
[tex]\begin{gathered} \Rightarrow\frac{\text{number of Youth Wing}}{\text{Total number of visitors}} \\ \Rightarrow\frac{429}{1235}=0.347368421 \end{gathered}[/tex]STEP 3: Get the expected number of people to visit the Youth Wing on Sunday
[tex]\begin{gathered} \text{Expected value}=\text{proportion}\times total\text{ number of visitors on Sunday} \\ \text{Expected Value=}0.347368421\times1100=382.1052632 \\ \text{Expected Value of people from Youth Wing }\approx382 \end{gathered}[/tex]Hence, the expected number of people to visit the Youth Wing on Sunday is approximately 382 people
H=4(x+3y)+2 make x the subject
When the formula is changed to x, the equation is x = 1/4(H - 2) - 3y
How to change the subject of formula to x?From the question, the equation is given as
H=4(x+3y)+2
Subtract 2 from both sides of the equation
So, we have the following equation
H - 2 =4(x+3y)+2 -2
Evaluate
So, we have the following equation
H - 2 =4(x+3y)
Divide by 4
So, we have the following equation
1/4(H - 2) = x +3y
Subtract 3y from both sides
x = 1/4(H - 2) - 3y
Hence, the solution for x is x = 1/4(H - 2) - 3y
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The simplified solution for the x is given as x = [H - 2]/4 - 3y.
As mentioned in the question, for an equation H=4(x+3y)+2, we have to transform the equation in the subject of x.
The operational processes in mathematics for the functions to make the function or expression.
Here,
Simplification of the given function in a manner to the transposition of the variables from left to right,
H=4(x+3y)+2
H - 2 = 4(x+3y)
{H - 2}/4 = (x + 3y)
x = [H - 2]/4 - 3y
Thus, the simplified solution for the x is given as x = [H - 2]/4 - 3y.
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A woman saves $6000 at 2.5% compund interest. She adds $1000 to her amount at the end of each year. Find the total savings after 2 years
Answer:
$8303.75
Step-by-step explanation:
(6000x1.025^2)+2000=8303.75
The boxplot displays the arm spans for 44 students.
Which of the following is not a true statement?
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
Answer:
A) there are no outliers in this distribution.
there is an ongoing debate about how many spaces should be placed after a period in typed documents. alana read about a study where 100100100 participants all read the same document typed in courier new font. half of the participants were randomly assigned the document with one space after each period, and the other half were given the document with two spaces after each period. participants who read the document with two spaces after each period were able to finish reading significantly faster than those with one space after each period. alana concluded that using two spaces after each period will help people read all documents faster. why is alana's conclusion not appropriate?
Alana's conclusion from the study is not appropriate.
Why is Alana's conclusion from the study is not appropriate?
In this study, there was no attempt made to research the alternative fonts. Alana reads about the study that includes only courier new font and arrives at a conclusion.The study in inconsistent with the standard scientific methods as it is not inclusive of all factors and possibilities and is thus inappropriate.What is an appropriate study?
The achievement of the research objectives is ensured by an appropriate study design. The important element of appropriate studies known as formulated research are missing from observational studies.Observational studies are in which the outcome is not tried to be altered through analysis unlike appropriate studies.This describes an investigation of a specific phenomenon that meets all requirements and adheres to the scientific method.To learn more about appropriate studies, refer:
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8. Find the area of the kite.
Answer:
A=16, the formula to find the area of a kite is A=pq/2
Step-by-step explanation:
A=pq/2 = 4×8/2=16
