Answer:
There are 4 questions to answer here and the answers are given below:
1. COMBINATION
2. SET 2
3. {S2, S3, S4, S5}
4. { } OR ∅
Step-by-step explanation:
The key topics here are PERMUTATION & COMBINATION and SETS & VENN DIAGRAMS.
The assignment has 5 questions in all. The options for each question are listed below and separated by commas:
1. True, False
2. True, False
3. A, B, C, D
4. A, B, C, D
5. A, B, C, D
Mr. Montes derives his answers from a random answer generator; same way Amisha generated her answers by random selection.
QUESTION 1
If you want to find the odds that Amisha got at least 3/5 of the answers correctly, would you use a permutation or a combination?
ANSWER TO QUESTION 1
You would use a combination. Note that as much as 'permutation' is distinctly defined from 'combination', in many complex cases both are used to derive the solution. In this case though, a combination is used. For each of the 5 questions, there are a number of possible answers. Questions 1 and 2 have only two possible answers (also known as options) while questions 3, 4 and 5 have four possible answers/options to choose from. Amisha can only have one set of five answers; each to each question. So this is a combination! If you want to find the odds that Amisha got at least 3 of her 5 answers correct, you would use a combination of the various possible answers to check.
QUESTION 2
Find "Set 1 ∩ Set 2" and explain the notation in the sentence.
ANSWER TO QUESTION 2
First list out relevant information:
- The correct answers to questions 3, 4 and 5 are respectively C, B, A
- The universal set consists of five students: S1, S2, S3, S4, S5 hence
Ц = {S1, S2, S3, S4, S5}
Next, enlist the elements of each defined set
Set 1: {S1, S2, S3, S4, S5} Set 2: {S2, S3, S4} Set 3: {S4, S5}
Note: Set 1 is equal to the universal set.
Now this notation "∩" means "intersect". It requires an action - checking out which elements in one set also appear in a second set and then bringing those elements to form a new set.
In the case of this question, we're to find Set 1 intersect Set 2. The elements present in Set 1 and also present in Set 2 are {S2, S3, S4}.
If you look closely, you'll observe that these are the same elements in Set 2! This brings to remembrance, one of the laws of sets:
The intersect of any subset and the universal set (recall that Set 1 happens to be equal to or have the same elements as the universal set) is equal to that subset.
So the answer to question 2 is
Set 1 ∩ Set 2 = Set 2
QUESTION 3
Find "Set 2 ∪ Set 3" and explain the notation in the sentence.
ANSWER TO QUESTION 3
The notation ∪ represents "union". This is the act of putting together the elements in two sets, to form a new set. In this activity, if an element appears in both sets, it is only written once in the new set, not twice.
So, Set 2 union Set 3 = {S2, S3, S4, S5}
As earlier stated, Student 4 isn't appearing twice in the new set.
QUESTION 4
Find the ' of Set 1 and explain the notation in this sentence.
ANSWER TO QUESTION 4
The symbol ' means "complement of a set". Finding the complement of a set is like subtracting the elements of that set from the universal set.
Since Set 1 contains the same elements as the universal set, subtracting Set 1 from the universal set will give you nothing. In this case, the complement of Set 1 is a null set!
Set 1 ' Ц = { } or ∅
where the empty bracket symbol and the slashed zero symbol represent null set.
Kudos!
Please Help - Suppose f(t)=6t−8−−−−√.
(a) Find the derivative of f.
f′(t) =
-3/(sqrt(t-8)(t-8))
(b) Find an equation for the tangent line to the graph of y=f(t) at the point (t,y)=(33,6/5).
Tangent line: y =
[tex](a)\\\\\\\text{Given that,}~~\\\\ f(t) =\dfrac 6{\sqrt{t-8}}\\\\\\\\\implies f'(t) = 6\left[\dfrac{\left(\sqrt{t-8}\right) \cdot 0 - \dfrac 1{2\sqrt{t-8 }}}{\left(\sqrt{t-8}\right)^2}\right]\\\\\\\\\implies f'(t) = -6\left(\dfrac {\dfrac 1{2\sqrt{t-8}}}{t-8}\right)\\\\\\\implies f'(t) = -6\left(\dfrac{1}{2\sqrt{t-8} (t-8)}\right)\\\\\\\implies f'(t) =-\dfrac 3{(t-8)^{\tfrac 32}}[/tex]
(b)
[tex]\text{Given that,}\\\\y=f(t)\\\\\text{Slope of y,} ~~ f'(t) =-\dfrac 3{(t-8)^{\tfrac 32}}\\\\\text{At point (33, 6/5)}\\\\\\f'(t) = -\dfrac 3{(33-8)^{\tfrac 32}} = - \dfrac 3{ (25)^{ \tfrac 32}} = - \dfrac 3{5^3} = -\dfrac 3{125}\\\\\\\text{Equation with given points,}\\\\y - \dfrac 65 = -\dfrac 3{125} ( t - 33)\\\\\\\implies y =-\dfrac 3{125} t +\dfrac{99}{125} + \dfrac 65\\\\\\\implies y = -\dfrac 3{125} t +\dfrac{249}{125}[/tex]
Find the digits in the tens place, in the hundredths place, and in the thousandths place for the following number 748.6291
Answer:
8 for tens, 9 for hundredths and thousandths is 1
Step-by-step explanation:
you can find the number by looking at the place of the numbers if it is tens look at the tens place which is the number eight as tens are 2 digit numbers
Which number is a favor of 12 but not a multiple of 2
Answer:
3
Step-by-step explanation:
A triangular prism and a triangular pyramid have congruent bases and heights. What is the ratio of
the volume of the prism to the volume of the pyramid? Show your work.
Answer:
if a pyramid and a prism have the base and height also their volumes are always in the ratio 1:3
step by step
as the volumes of prism is 108 cubic meters
1/3 x 108 = 36 cubic meters
What is the volume of the following cylinder?
150.72 in. 3
301.44 in. 3
75.36 in. 3
602.88 in. 3
Answer:
150.72 in³
Step-by-step explanation:
We know that
Radius = Diameter/2
Radius = 8/2
Radius = 4 in
Now,
Volume of cylinder = πr²h
=> 3.14 × (4)² × 3
=> 3.14 × 16 × 3
=> 150.72 in³
Answer:
The correct answer is option 150.72 in³.
Step-by-step explanation:
Given :
✧ Diameter of cylinder = 8 in.✧ Height of cylinder = 3 in.To Find :
✧ Volume of cylinderUsing Formula :
[tex]\star{\small{\underline{\boxed{\sf{\pink{R = \dfrac{D}{2}}}}}}}[/tex]
[tex]\star{\small{\underline{\boxed{\sf{\pink{V = \pi{r}^{2}h}}}}}}[/tex]
»» r = Radius »» D = Diameter »» V = Volume »» h = heightSolution :
Firstly, finding the radius of cylinder by substituting the values in the formula :
[tex]\dashrightarrow{\small{\sf{Radius_{(Cylinder)} = \dfrac{D}{2}}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Radius_{(Cylinder)} = \dfrac{8}{2}}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Radius_{(Cylinder)} = \cancel{\dfrac{8}{2}}}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Radius_{(Cylinder)} = 4 \: in}}}[/tex]
[tex]{\star{\underline{\boxed{\sf{\red{Radius_{(Cylinder)} = 4 \: in}}}}}}[/tex]
Hence, the radius of cylinder is 4 in.
[tex]\rule{300}{1.5}[/tex]
Now, finding the volume of cylinder by substituting the values in the formula :
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = \pi{r}^{2}h}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = 3.14 \times {(4)}^{2} \times 3}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = 3.14 \times {(4 \times 4)} \times 3}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = 3.14 \times {(16)} \times 3}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = 3.14 \times 16 \times 3}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = \dfrac{314}{100} \times 16 \times 3}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = \dfrac{314 \times 16 \times 3}{100}}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = \dfrac{314 \times 48}{100}}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = \dfrac{15072}{100}}}}[/tex]
[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = Rs.150.72 \: {cm}^{3}}}}[/tex]
[tex]\star{\small{\underline{\boxed{\sf{\red{Volume_{(Cylinder)} = Rs.150.72 \: {cm}^{3}}}}}}}[/tex]
Hence, the volume of cylinder is 150.72 in³.
[tex]\rule{300}{1.5}[/tex]
help help help help meeee
Answer: 36!
Step-by-step explanation:
Answer:
B . 34
Step-by-step explanation:
simply subtract the lowest value from the greatest value, ignoring the others.
Melanie was training for a race. The line plot below shows the number of miles Melanie ran last week.
2. How many times did Melanie run ½ a mile?
Answer:
5 miles
Step-by-step explanation:
add the points together.
it seems like each point is how many miles they ran each day.
1/4 + 2(1/2) + 3/4 + 3(1) = 5
-) Which is a valid velocity reading for an object? O 45 m/s O 45 m/s north 23 O O m/s south O 0 m/s ok Save and Exit Next Mark this and return
Answer:
Step-by-step explanation:
0 can't have a direction. It does not move. It has no speed component. Therefore 0 m/s south is not the answer.
45 m/s has no direction stated. It is just a speed, not a velocity.
45 m/s north is a velocity. It has both speed and direction.
2/3 divided by 10
PLEASE answer
Answer:
1/15
Step-by-step explanation:
2/3 x 1/10 = 2/30 or 1/15
Answer:
1/15
Step-by-step explanation:
Help
This is a a or b question
Answer:
A. (A) Yes
B. (A) Yes
C. (B) No
Step-by-step explanation:
A is Categorical because it is not based on numbers.
B is Categorical because it is not based on numbers.
C is Not Categorical because it is based on numbers.
Pls HELP meeee. My child needs some real help I I wish I would’ve took those college lessons.
Answer:
75%
Step-by-step explanation:
100/64*48=75%
danny is offering 36$ for 4 hours of swimming lessons. Martin in offering 54$ for 3 hours of swimming lessons. whose offer is better
Answer:
Danny's offer is cheaper
Step-by-step explanation:
Danny is offering 36$ for 4 hours meaning you would do 36÷4=9 (9$ per hour)
Martin is offering 54$ for 3 hours so 54÷3=18 (18$ per hour)
Or the faster way of finding why is Danny is offering more hours for cheaper
Hope this helps
List all the factors of 19. Tell whether 19 is prime or composite.
Answer:
19 is a prime number, thus making the only factors 1, 2, 19. (Not necessary to include 1)
Step-by-step explanation:
When z=−6, evaluate −2(z+9)−(−5) and −2⋅z−2⋅9+5 to show that −2(z+9)−(−5)=−2⋅z−2⋅9+5
Ignore this, I posted the wrong answer and I don't know how to delete it.
Answer:
Yes/true
Step-by-step explanation:
-2(z+9)-(-5)=-2⋅z-2⋅9+5
sostituisco la lettera dandogli un valore
=-2(-6+9)-(-5)=-2⋅(-6)-2⋅9+5
calcolo e tolgo le parentesi
=-2⋅3+5=12-18+5
Elimino i termini uguali
=-2⋅3=12-18
Somma e moltiplicazione tra i numeri
=-6=-6
a service or software application that relies on shared resources over the internet
Response time is an important statistic for measuring the effectiveness of a fire department, and is measured as the difference between the time a fire station receives a call and the time the first piece of fire equipment leaves the station. The response times for fire departments in a large city are found to have an approximately Normal distribution, with a mean of 4.5 minutes and a standard deviation of 1.2 minutes. What percentage of fire station response times are under 3 minutes? Find the z-table here. 6.68% 10.56% 89.44% 93.32%
Answer:
mean = 4.5
SD = 1.2
Z value = (3-4.5)/1.2 = - 1.25
Percentage based on z value = 1 - pnorm(1.25) = 0.1056498 = 10.56498%
The response times under 3 minutes is 10.56%
What is Normal Distribution?'Normal distribution is a continuous probability distribution wherein values lie in a symmetrical fashion mostly situated around the mean.'
According to the given problem,
mean = 4.5
SD = 1.2
Z value = [tex]\frac{3 - 4.5}{1.2}[/tex] = - 1.25
Percentage based on z value = 1 - pnorm(1.25)
= 0.1056498
= 10.56498%
Hence, we can conclude that the response time of fire station under 3 minutes is 10.56%.
Learn more about normal distribution here: https://brainly.com/question/11876263
#SPJ2
Find the value of x
Answer:
6.93
Step-by-step explanation:
hope this helps
Enter the number that belongs in the green box
Answer:
8
Step-by-step explanation:
The diagonals of a parallelogram divide each other into two equal parts.
A nationwide survey claimed that at least 65% of parents with young children condone spanking their child as a regular form of punishment. In a random sample of 100 parents with young children, how many would need to say that they condone spanking as a form of punishment in order to refute the claim at α = 0.5?
Answer:
here p=0.65 and n=100 hence standard error =(p*(1-.
Step-by-step explanation:
simply the problem pls answer quick
[tex]\\ \sf\Rrightarrow 1\dfrac{2}{5}m-\dfrac{3}{5}(\dfrac{2}{3}m+1)[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{7}{5}m-\dfrac{3}{5}(\dfrac{2m+3}{3})[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{7m}{5}-\dfrac{6m+9}{15}[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{21m-6m-9}{15}[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{15m-9}{15}[/tex]
[tex]\\ \sf\Rrightarrow m-\dfrac{3}{5}[/tex]
The simplified form of the expression is m - 3/5
Given the expression 1 2/5 m - 3/5 (2/5m + 1)
We need to simplify the term. Expand the bracket to have:
1 2/5 m - 3/5 (2/3m + 1)
1 2/5 m -2/5 m - 3/5
7/5 m - 2/5 m - 3/5
(7m-2m)/5 - 3/5
5m/5 - 3/5
m - 3/5
Hence the simplified form of the expression is m - 3/5
Learn more on expansion here: https://brainly.com/question/13800206
?/5 =8/10 type the missing number that makes this fraction equal
Answer:
4/5 = 8/10
Step-by-step explanation:
x/5 = 8/10
x = 8/10 × 5
x = 4
Find the sum of 12.351 and 0.5362
Find the sum of 12.351 and 0.5362
Answer:-12.351 + 0.5362 = 12.8872
Ax+2y=10 through the point (4,3)
Answer:
can you give more context to the question and I will answer it in the comments? thanks!
Answer:
Slope-intercept form y=10x-37
Point slope form y-3=10(x-4)
Step-by-step explanation:
Quadratic functions 30pt
Answer:
y= -x -3
Step-by-step explanation:
A perpendicular bisector of a line cuts through the line at its midpoint perpendicularly (90°).
Let's find the slope of the line segment.
\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }slope=x1−x2y1−y2
Slope of line segment
= \frac{4 - ( - 8)}{5 - ( - 7)}=5−(−7)4−(−8)
= \frac{4 + 8}{5 + 7}=5+74+8
= \frac{12}{12}=1212
= 1
The product of the slopes of 2 perpendicular lines is -1.
Let the slope of the perpendicular bisector be m.
m(1)= -1
m= -1
y= -x +c
To find the value of c, substitute a pair of coordinates in which the line passes through into the above equation.
Since the perpendicular bisector cuts through the midpoint of the line segment, let's find the coordinates of this midpoint.
\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}midpoint=(2x1+x2,2y1+y2)
Midpoint of line segment
= ( \frac{5 - 7}{2} , \frac{4 - 8}{2} )=(25−7,24−8)
= ( \frac{ - 2}{2} , \frac{ - 4}{2} )=(2−2,2−4)
= (-1, -2)
y= -x +c
When x= -1, y= -2,
-2= -(-1) +c
-2= 1 +c
c= -2 -1
c= -3
Thus, the equation of the perpendicular bisector is y= -x -3.
Which statement is true about the value of 1-5/?
O It is the distance that -5 is from 0 on the number line.
O It is the distance that -5 is from 5 on the number line.
O It is less than 5.
0 It is greater than 5.
Answer:
O It is less than 5.
Step-by-Step
OK so, first u check if it has a negative. It does, so its at the left of 0. SO you know its less than.
What is this in simplest form?
how many degrees is 37 degrees warmer than -13
how many is 38 degrees warmer than -20
Answer:
98.6° Fahrenheit ( i did it in celsius sorry if i got it wrong)
Step-by-step explanation:
You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $2.25 and each soda costs $1.50. At the end of the night, you made a total of $225.75. You sold a total of 126 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. What equations did you use to solve this? How many hot dogs were sold and how many sodas were sold?
A.
x + y = 126 and 2.25x + 1.50y = 225.75 ; 49 hot dogs and 77 sodas.
B.
x + y = 126 and 2.25x + 1.50y = 225.75 ; 77 hot dogs and 49 sodas.
C.
2.25x + 1.50y = 126 and x + y = 225.75 : -283.5 hot dogs and 509.25 sodas.
D.
There is not enough information
Answer:
Hello again! Fellow Connexus user? Because I just had this on my Honors Algebra 1 test today. Anyways the answer is: A. x + y = 126 and 2.25x + 1.50y = 225.75; 49 Hot Dogs and 77 Sodas.
Step By Step Explanation:
To verify just use the substitution method to solve the equations x+y=126 and 2.25x + 1.50y = 225.75 then you'll get your x (Number of Hotdogs) and y (Number of Sodas)
Hope this helps!
The required equations are use to solve this problem;
[tex]x + y =126[/tex]
[tex]2.25x + 1.50y = 223.75[/tex]
There are x = 49 hot dogs, and y = 77 sodas were sold.
Given that,
Each hot dog costs $2.25 and each soda costs $1.50.
At the end of the night, you made a total of $225.75.
You sold a total of 126 hot dogs and sodas combined.
We have to determine,
What equations did you use to solve this.
And How many hot dogs were sold and how many sodas were sold.
According to the question,
Let, The x represent the number of hot dogs,
And y represent the number of sodas.
Then,
You sold a total of 126 hot dogs and sodas combined.
Number of sell hot dogs + number of sell sodas = Total of hot dogs and sodas combined.
[tex]x + y =126[/tex]
And Each hot dog costs $2.25 and each soda costs $1.50.
At the end of the night, you made a total of $225.75.
Then,
Cost of each hot dogs + cost of each soda = total earning end of the night
[tex]2.25x + 1.50y = 223.75[/tex]
On solving both the equation,
[tex]x + y = 126\\\\x = 126-y[/tex]
Substitute the value of x in the equation 2,
[tex]=2.25(126-y) + 1.50y = 225.75\\\\= 283.5 -2.25y + 1.50y = 225.75\\\\= - 0.75 y = 225.75 - 283.5\\\\= - 0.75y = -57.75\\\\= y = \dfrac{-57.75}{-0.75}\\\\= y = 77[/tex]
Then,
Substitute the value of y in the equation 1,
[tex]x + y = 126\\\\x + 77 = 126\\\\x = 126-77\\\\x = 49[/tex]
Hence, There are x = 49 hot dogs, and y = 77 sodas were sold.
To know more about the Equation click the link given below.
https://brainly.com/question/24070713
Can someone help me?
Answer:
just make something that is eqivalant to 4= or 14=
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs, In the figure, lines H and KL are parallel. TH K E G D Match each angle relationship with the appropriate reason. Vertical angles theorem Alternate exterior angles theorem linear pair Alternate interior angles theorem Corresponding angles theorem same-side interior angles m_HED = m_FE) mKFE = m_FEJ MZLFG = MADEH
The angle relationship and their reasons are:
m∠HED = m∠FEJ ---> Vertical angles theoremm∠KFE = m∠DEH ---> Alternate interior angles theoremm∠LFG = m∠DEH ---> Alternate exterior angles theoremm∠JEF + m∠LFE = 180° ---> same-side interior angles theoremm∠DEJ = m∠EFL ---> Corresponding interior angles theoremm∠LFG + m∠GFK = 180 ---> linear pairThe angle pairs are formed based on their relative positions. The following shows each angle relationship and their reasons:
∠HED and ∠FEJ are directly vertically opposite each other, therefore, they are equal based on the vertical angles theorem.
m∠HED = m∠FEJ ---> Vertical angles theorem∠KFE and ∠FEJ are alternate interior angles, therefore, they are equal based on the alternate interior angles theorem.
m∠KFE = m∠DEH ---> Alternate interior angles theorem∠LFG and ∠FEJ are alternate exterior angles, therefore, they are equal based on the alternate exterior angles theorem.
m∠LFG = m∠DEH ---> Alternate exterior angles theorem∠JEF and ∠LFE are interior angles on same side of the transversal, therefore, the sum of both angles equal 180 degrees based on the same-side interior angles theorem.
m∠JEF + m∠LFE = 180° ---> same-side interior angles theorem∠DEJ and ∠EFL are corresponding angles, therefore, they are equal based on the corresponding angles theorem.
m∠DEJ = m∠EFL ---> Corresponding interior angles theorem∠LFG and ∠GFK are angles on a straight line, therefore the sum of both angles will equal 180 degrees because they are a linear pair.
m∠LFG + m∠GFK = 180 ---> linear pairLearn more about angle relationship on:
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