Question Completion
(b) Use the possibility diagram to calculate the probability that the product of the two numbers is
I) A prime number
ii) Not a perfect square
iii) A multiple of 5
iv) Less than or equal to 21
v) Divisible by 4 or 6
Answer:
I) 0.125 (ii)0.828125 (iii)0.234375 (iv) 0.625 (v)0.65625
Step-by-step explanation:
The sample space for an 8-sided fair die rolled twice is:
[tex][(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(1, 7),(1, 8)\\(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),(2, 7),(2, 8)\\(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(3, 7),(3, 8)\\(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(4, 7),(4, 8)\\(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),(5, 6),(5, 7),(5, 8)\\(6, 1), (6, 2), (6, 3), (6, 4)(6, 5),(6, 6),(6, 7),(6, 8)\\(7, 1), (7, 2), (7, 3), (7, 4)(7, 5),(7, 6),(7, 7),(7, 8)\\(8, 1), (8, 2), (8, 3), (8, 4)(8, 5),(8, 6),(8, 7),(8, 8)]\\[/tex]
(a) The possibility diagram of the product of the two numbers appearing on the die in each throw
[tex]1, 2, 3, 4, 5, 6,7,8\\2, 4, 6, 8, 10, 12,14,16\\3,6,9,12,15,18,21,24\\4,8,12,16,20,24,28,32\\5,10,15,20,25,30,35,40\\6,12,18,24,30,36,42,48\\7,14,21,28,35,42,49,56\\8,16,24,32,40,48,56,64[/tex]
(b)
I) A prime number
The number of products that gives prime numbers = 8
[tex]P$(Product is a prime number)=\dfrac{8}{64}= \dfrac{1}{8}\\=0.125[/tex]
ii) Not a perfect square
Number of products which results in perfect squares =11
[tex]P$(Product is Not a perfect square)=\dfrac{64-11}{64}= \dfrac{53}{64}\\=0.828125[/tex]
iii) A multiple of 5
Number of products that are multiples of 5=15
[tex]P$(product is a multiple of 5)=\dfrac{15}{64}\\=0.234375[/tex]
iv) Less than or equal to 21
Number of products which are less than or equal to 21=40
[tex]P$(product is less than or equal to 21)=\dfrac{40}{64}=\dfrac{5}{8}\\=0.625[/tex]
v) Divisible by 4 or 6
Products Divisible by 4 or 6= 42
[tex]P$(product is divisible by 4 or 6)=\dfrac{42}{64}=\dfrac{21}{32}\\=0.65625[/tex]
use the elimination method to solve 4x+8y=16 4x-8y=0
Answer:
x=2, y=1
Step-by-step explanation:
4x+8y=16
4x-8y=0
Add the two equations together:
8x=16
Divide both sides by 8:
x=2
Plug this back into one of the original equations to find y:
4(2)-8y=0
8-8y=0
y=1
Hope this helps!
Answer:
x, y = (0, 0)
Step-by-step explanation:
photo math broo
a right angle triangle has the perimeter of 96cm. the length of its sides are in the ratio of 6:8:10. work out the area of the triangle
Answer:
384 centimeters squared.
Step-by-step explanation:
96/(6+8+10)
96/24 = 4
6×4 : 8×4 : 10×4
24:32:40
The length of its sides are in the ratio of 24:32:40
The longest side is the hypotenuse which is 40.
The area is base × height × 1/2 of a triangle.
32 × 24 × 1/2
768 × 1/2
=384
The area of the triangle is 384 cm squared.
Answer:
Area = 384 cm²
Step-by-step explanation:
Perimeter = 96 cm
Ratio = 6:8:10
So,
6x+8x+10x = 96
=> 24x = 96
Dividing both sides by 24
=> x = 4
So, The sides are
=> 24 cm
=> 32 cm
=> 40 cm
Now the area using Heron's Formula
Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
Where s is the semi-perimeter = 48 cm, a , b and c are the sides
Area = [tex]\sqrt{48(48-24)(48-32)(48-40)}[/tex]
Area = [tex]\sqrt{48(24)(16)(8)}[/tex]
Area = [tex]\sqrt{147,456}[/tex]
Area = 384 cm²
Please help me :( struggling
C. exponential decay
I need mega help I can't get it wrong
Answer:
4320 square inches
Step-by-step explanation:
Area of a rectangle is base times height. You need to convert 3 yards to inches in order to multiply for the area. Since 1 yard is equal to 36 inches, 4 yards is 4*36 = 144 inches. Now you multiply 30 * 144 to get 4320, which is your answer.
URGENT! WILL GIVE BRAINLIEST!! The graph shows the data of texting speed according to time.A graph has time (minutes) on the x-axis and texting speed (words per minute) on the y-axis. Points are at (1, 14), (1, 18), (2, 10), (2, 15), (2, 17), (3, 14), (4, 10), (4, 15), (5, 6), and (5, 10).Use the scatter plot to determine if there is a relationship. If there is a relationship, explain it.Yes, there is a relationship. As time increases, texting speed increases.Yes, there is a relationship. As time increases, texting speed decreases.Yes, there is a relationship. As texting speed increases, time increases.No, there is no relationship displayed.
Answer: Yes, there is a relationship. As time increases, texting speed decreases.
Step-by-step explanation:
that is for the people looking for the correct answer.
The correct option is B, Yes, there is a relationship. As time increases, texting speed decreases.
What is a scatter plot?A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. One more variable can be presented if the points are programmed.
Although the points plotted on the graph are completely scattered. There exists a basic relationship between the points, as time increases, texting speed decreases, moving from the left side of the graph to the right side of the graph. Hence, the correct option is B, Yes, there is a relationship. As time increases, texting speed decreases.
Learn more about Scatter Plot:
https://brainly.com/question/13984412
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How many square feet are there in a strip of carpet 4 feet wide and 11 feet long
Answer: There is 44 square feet in the total area of the carpet!
Step-by-step explanation:
4x11=44! Let me know if this helped! <3
The weights (lbs.) of the 5 offensive linemen for the High School football team are as follows: 215, 225, 285, 260, and 250. The median weight is:
A)205 lbs
B)250 lbs.
C)247 lbs.
D)None of these choices are correct.
if 25 tickets cost $50, find the cost of 1 ticket
Answer:
$2[tex]solution \\ cost \: of \: 25 \: ticket = 50 \\ cost \: of \: one \: ticket = \frac{50}{25} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2[/tex]
hope this helps..
Good luck on your assignment
25 tickets cost 50.00 dollars.
The cost of 1 ticket would be:
50/25=2
2.00 dollars to be precise.
Identify the coordinates of the point (3,-2), translated 5 units left and 6
units up.
(2,-4)
(-2,-8)
(8,4)
(-2,4)
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US 10:2
Answer:
(- 2, 4 )
Step-by-step explanation:
A translation of 5 units left means subtract 5 from the original x- coordinate.
A translation of 6 units up means add 6 to the original y- coordinate.
Thus
(3, - 2 ) → (3- 5, - 2 + 6 ) → (- 2, 4 )
The coordinates of the point (3,-2), translated 5 units left and 6
units up are (-2, 4) option (D) (-2, 4) is correct.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
It is given that:
The point (3,-2), translated 5 units left and 6 units up.
A 5-unit left translation entails taking 5 away from the initial x-coordinate.
A translation of six units upwards entails multiplying the initial y-coordinate by six.
After applying the translation:
(3, -2) → (3- 5, - 2 + 6) → (-2, 4)
Thus, the coordinates of the point (3,-2), translated 5 units left and 6
units up are (-2, 4) option (D) (-2, 4) is correct.
Learn more about the geometric transformation here:
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michael puts 3 beds next to each other on a piece of string to make a bracelet. each need has a width of 5/6 inches. which expression and fraction both represent the width of the three beads
Answer:
Total width = 5/2 or 2½
Step-by-step explanation:
Since we have 3 beads and each of them have a width of 5/6 inches, thus;
Total width = 3 × (5/6)
Total width = 15/6
Simplifying this since 3 is common multiple to both numerator and denominator, we have;
Total width = (15/3)/(6/3)
Total width = 5/2
Since this is an improper fraction, we need to turn it into a mixed fraction, thus;
Total width = 5/2 = 2½
Those total width is 5/2 or 2½
You have ten blankets that each take up 686 cubic inches of space how many blankets could you pack into an 18 inch box
Answer:
you can fit 8 blankets in the 18 by 18 by 18 box
Step-by-step explanation:
Answer: 8 blankets.
Step-by-step explanation: The total volume of the moving box is (18)³ = 5,832 cubic inches. Since each blanket takes 686 cubic inches, the box will hold [tex]\frac{5,832}{686}[/tex] ≈ 8.5 or 8 blankets.
is the centre of a circle always equal distance from all points on the circumference? and why
Answer:
Yes, the center of a circle is always and always equidistant from all the points on circumference because that is because what a circle is called. The distance from the center of the circle to the circumference is called the radius and it is constant for any particular circle.
Nikolas and his son, and Peter with his son, went fishing. Nickolas caught as many fish as did his son. Peter caught three times as many as his son did. Altogether they caught 35 fish. Nikolas' son's name is Gregory. What is the name of Peter's son? How many fish did each of them catch?
Step-by-step explanation:
4unit is 35
1unit is 35/4 which is 8.75
Check all that apply in regards to the given sequence:
5, 8, 11, 14, 17, 20, 23, ...
Answer:
see explanation
Step-by-step explanation:
There is a common difference d between consecutive terms, that is
d = 8 - 5 = 11 - 8 = 14 - 11 = 17 - 14 = 20 - 17 = 23 - 20 = 3
This indicates the sequence is arithmetic
The common difference d = 3
The first term a₁ = 5 and
a₈ = 23 + 3 = 26
What is 3+3/-4+6-34+9
ANSWER:
The answer is -16.75
First divide the division 3/-4 then start the addition and subtraction
Answer:
-67/4 or -16.75
Step-by-step explanation:
Simply plug all of that into the calc and you should get your answer.
estimate the total cost of 31 televisions at £196.50 each and 19 DVD players at £50.99 each
Answer:
£7060.31Solution,
Cost of one television=£196.50
cost of 31 televisions:
[tex] = 196.50 \times 31 \\ = 6091.5[/tex]
Cost of one DVD player=£50.99
Cost of 19 DVD player:
[tex] = 50.99 \times 19 \\ = 968.81[/tex]
Now,
Total cost
= cost of 31 televisions + cost of 19 DVD player
=6091.5+968.81
=£7060.31
Hope this helps...
Good luck on your assignment..
Answer:
£7060.31Step-by-step explanation:
Cost of a television = £196.50cost of 31 televisions.
[tex]196.50 \times 31 \\ = 6091.5 0\\ [/tex]
Cost of a DVD player = £50.99cost of 19 DVD players
[tex]50.99 \times 19 \\ = 968.81 \\ [/tex]
Now let's find the total cost
[tex]6091.50 + 968.81 \\ = 7060.31[/tex]
Work out ( 4 × 10 6 ) × ( 2 × 10 7 ) Give your answer in standard form.
Answer:
4 * 2 = 8
10^6 * 10^7 = 10^(6 + 7) = 10^13
Answer is 8 * 10^13
So I'm pretty sure I solved a similar question before, but we always write the equation first.
So, equation:
(4 × 10^6) × (2 × 10^7)
Again, we will use the order of operations.
() - Parenthesis
^x - Exponents
×/÷ - Multiplication/Division
+/- - Addition/Subtraction
Now, solve the parenthesis. We have two parentheses, so we will solve those separately.
(4 × 10^6)= 4 × 1,000,000 = 4,000,000
(2 × 10^7)= 2 × 10,000,000 = 20,000,000
Now, multiply these two together.
4,000,000 × 20,000,000 = 80000000000000
BUT, we can simplify this. So, the real answer is:
8 × 10^13
Beverly has $50 to spend at an amusement park. She plans to spend $10 for food, and $15 for admission to the park. Each ride costs $1.50 to ride.
Answer:
a b c d e f g h i j k l m o n p q r s t u v w x y z n o w i k n o w m y a b c s n e x t t i m e w o n t y o u s i n g w i t h m e
Step-by-step explanation:
cocomelon
Complete each proof. Remember to mark the diagram as you go. You may not need all the rows.
Answer:
did u ever get hte answers for this ?
PLZ HELP ME THANKS Solve each application using algebra. Write your equation or inequality and show your solving steps.... A 10-meter wire is cut into 2 unequal pieces. The large piece is 3 meters less than twice the smaller piece. Use algebra to determine the lengths of each piece
Answer:
4 1/3 m and 5 2/3 m
Step-by-step explanation:
smaller piece -l
large piece=2*l-3
l+2l-3=10
3l-3=10
+3 +3
3l=13
:3 :3
l=13/3=4 1/3 m
L= 2*13/3 -3=26/3-9/3=17/3=5 2/3m
Answer:
[tex]Small=4\frac{1}{3}[/tex]
[tex]Large=5\frac{2}{3}[/tex]
Step-by-step explanation:
Small = x
Large = 2x - 3
3x - 3 = 10
3x = 13
[tex]x=\frac{13}{3}[/tex]
[tex]Small=\frac{13}{3}[/tex]
[tex]Large=5\frac{2}{3}[/tex]
Pls help as fast as possible
Answer:
452.389342 cubic inches
Step-by-step explanation:
The volume of a sphere is calculated using the formula V = 4/3 pi r^3
to determine the radius, you can notice that 4 spheres take up 24 in in length. This means that the radius of 1 sphere is 24/4/2 = 3 inches.
from there we plug and play: V = 4/3 * pi * 3^3 = 113.097336 cubic inches.
Note that this is only the volume of 1 sphere, so we multiply by 4
and we get 452.389342 cubic inches
Answer:
452.4
Step-by-step explanation:
Radius of each sphere: 24/4/2=3
Formula for volume: (4pir^3)/3
Formula for 4 spheres: 4 times (4pir^3)/3
Substitute 3 for r
the top of two poles of height's 20m and 14m are connected by the wire
if the wire makes an angle 30 degree with the horizontal then length of the wire is
8m
10m
12m
Answer:
The correct option is;
10 m
Step-by-step explanation:
The parameters given are;
Height of the first pole = 20 m
Height of the second pole = 14 m
The angle the wire connected to their top makes with the horizontal = 30°
The vertical height subtended by the inclined wire, h = The difference in height between the two poles = 20 - 14 = 6 m.
Let the horizontal distance between the two poles = D
Therefore;
The horizontal length of the wire = D
From trigonometric ratios, we have;
[tex]tan(30 ^{\circ}) = \dfrac{h}{D} = \dfrac{6}{D}[/tex]
Which gives;
[tex]D = \dfrac{6}{tan(30 ^{\circ}) } = 10.39 \ m\approx 10 \ m[/tex]
The correct option is 10 m.
Find the volume of the prism.
13ft 7ft
Answer:
the volume of the prism is VOLUME=BASE*HEIGHT
Step-by-step explanation:
SO it's ,
13*7=91ft
Answer:
591.5 ft^3
Step-by-step explanation:
Drag each expression to show whether the product is less than 1, equal to 1, or greater than 1
Answer:
i
Step-by-step explanation:
Lana has a bowl of marbles the bowl contains 5 green marbles,3 red marbles and 2 blue marbles from the bowl one at a time. What is the probability that lana will select a green marble first, replace the marble, then select a red marble
Answer:
3/20
Step-by-step explanation:
5 green marbles,3 red marbles and 2 blue marbles from the bowl = 10 marbles
P( green) = green/total = 5/10 = 1/2
Replace
5 green marbles,3 red marbles and 2 blue marbles from the bowl = 10 marbles
P( red) = red/total = 3/10
P(green,replace, red) = 1/2 * 3/10 = 3/20
Point B ∈ AC so that AB : BC = 2:1. Point D ∈ AB so that AD : DB = 3:2. Find AD : DC.
Answer:
AD : DC is 2:3
Step-by-step explanation:
The parameters given are;
Point B ∈ AC
AB : BC = 2:1
Point D ∈ AB
AD : DB = 3:2
Therefore, whereby we sum the ratios, we have;
For AC
AB = 2/(2+1)×AC = 2/3×AC
BC = 1/3×AC
For AB
AD = 3/(3+2)×AB = 3/5×AB
DB = 2/5×AB
We are required to find AD:DC
Given that AD = 3/5×AB and AB = 2/3×AC
We have;
AD = 3/5×2/3×AC = 6/15 AC
DC = DB + BC = 2/5×AB + 1/3×AC = 2/5×2/3×AC + 1/3×AC = 4/15×AC + 1/3×AC
DC = 3/5×AC
AD : DC = 6/15 AC : 3/5×AC = 2:3.
I NEED HELP PLEASE, THANKS SO MUCH! :)
Answer:
Option B
Step-by-step explanation:
Vertical x= -5, x= -3, Horizontal y=3x-4 (slant)
A pile of sand weighs 90kg. the sand is put into a small bag, a medium bag and a large bag in the ratio 2: 3: 7. work out the weight of each sand bag Please help!
Answer:
the first bag is 15 ,the second bag is 22.5 and the third bag is 52.5
Step-by-step explanation:
you take the ratios and add them together 2+3+7=12. then you take 2/12×90=15,3/12×90=22.5,7/12×90=52.5 I think I tried
Thomas wants to invite Madeline to a party. He has an 80% chance of bumping into her at school. Otherwise, he'll call her on the phone. If he talks to her at school, he's 90% likely to ask hem
to a party. However, he's only 60% likely to ask her over the phone.
This is the tree diagram that represents the probability of Thomas inviting Madeline to a party.
What is the probability of Thomas inviting Madeline to the party over the phone?
Answer:
The probability of Thomas inviting Madeline to the party over the phone is 0.143.
Step-by-step explanation:
Consider the tree diagram below.
The events are denoted as follows:
A = Thomas bumps into Madeline at school
B = Thomas call Madeline on the phone
X = Thomas asks Madeline to the party
The information provided is:
P (A) = 0.80
P (B) = 1 - P (A) = 1 - 0.80 = 0.20
P (X|A) = 0.90
⇒ P (X'|A) = 1 - P (X|A) = 1 - 0.90 = 0.10
P (X|B) = 0.60
⇒ P (X'|B) = 1 - P (X|B) = 1 - 0.60 = 0.40
The conditional probability of event U given that another events V has already occurred is:
[tex]P(U|V)=\frac{P(V|U)P(U)}{P(V)}[/tex]
The law of total probability states that:
[tex]P(V)=P(V|U)P(U)+P(V|U')P(U')[/tex]
In this case we need to determine the probability that Thomas invites Madeline to the party over the phone, i.e. P (B|X).
Use the law of total probability to determine the value of P (X) as follows:
[tex]P(X) = P(X|A)P(A)+P(X|B)P(B)[/tex]
[tex]=(0.90\times 0.80)+(0.60\times 0.20)\\=0.72+0.12\\=0.84[/tex]
Compute the value of P (B|X) as follows:
[tex]P(B|X)=\frac{P(X|B)P(B)}{P(X)}[/tex]
[tex]=\farc{0.60\times 0.20}{0.84}\\\\=0.14286\\\\\approx 0.143[/tex]
Thus, the probability of Thomas inviting Madeline to the party over the phone is 0.143.
Answer:
84%
Step-by-step explanation:
Its the correct answer
PLEASE ANSWER ASAP!!!!! DONT NEED much explanation How many solutions does this system have? (photo below)
Answer:
infinite solutions
Step-by-step explanation:
Multiply the first equation by 2
2(3x-5y) = 2*15
6x - 10y = 30
This is the same as the second equation
They are the same line
This means there are infinite solutions