Answer:
[tex]\dfrac{1}{12}[/tex]
Step-by-step explanation:
Given:
Two fair number cubes i.e. two dice consisting the numbers 1, 2, 3, 4, 5, 6 on their faces and have equal probability of each number.
The dice are rolled.
To find:
Probability of getting the sum of two numbers as 4.
Solution:
First of all, let us have a look at the total possibilities when two dice are rolled:
([1][1], [1][2], [1][3], [1][4], [1][5], [1][6],
[2][1], [2][2], [2][3], [2][4], [2][5], [2][6],
[3][1], [3][2], [3][3], [3][4], [3][5], [3][6],
[4][1], [4][2], [4][3], [4][4], [4][5], [4][6],
[5][1], [5][2], [5][3], [5][4], [5][5], [5][6],
[6][1], [6][2], [6][3], [6][4], [6][5], [6][6])
These are total 36 possible outcomes.
For getting a sum as 4:
Possible number of favorable cases are 3 (as highlighted in BOLD in above)
Formula for probability of an event E can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Required probability is:
[tex]\dfrac{3}{36} = \bold{\dfrac{1}{12}}[/tex]
Write standard form, expanded form and word form at the top of the page write five numbers that are at least 8 digits long
Answer:
Kindly check explanation
Step-by-step explanation:
28,136,720
Word form: Twenty eight Million, One hundred and thirty-six thousand, seven hundred and twenty
Expanded form: (2 * 10,000,000) + (8 * 1,000,000) + (1 * 100,000) + (3 * 10,000) + (6 * 1000) + (7 * 100) + (2 * 10) + (0 * 1)
2.) 67, 564, 312
Sixty seven million, five hundred and sixty four thousand, three hundred and twelve
(6 * 10,000,000) + (7 * 1,000,000) + (5 *100,000) + (6 * 10,000) + ( 4 *1000) + (3* 100) + (1 * 10) + (2 * 1)
3.) 534, 235, 260
Five hundred and thirty four million, two hundred and thirty five thousand, two hundred and sixty.
(5 * 100,000,000) + ( 3 * 10,000,000) + (4 * 1,000,000) + (2 * 100,000) + ( 3 * 10,000) + (5 * 1,000) + (2 * 100) + (6 * 10) + (0 * 1)
4.) 43, 780, 523
Fourty three million, seven hundred and eighty thousand, five hundred and twenty three.
(4 * 10,000,000) + (3 * 1,000,000) + (7 * 100,000) + (8 * 10,000) + (0 * 1000) + (5 * 100) + (2 * 10) + (3 * 1)
5.) 456,156, 156
Four hundred and fifty six million, one hundred and fifty six thousand, one hundred and fifty six
(4 * 100,000,000) + (5 * 10,000,000) + (6 * 1,000,000) + (1 * 100,000) + ( 5 * 10,000) + ( 6 * 1000) + (1 * 100) + ( 5 * 10) + (6 * 1)
10 (6x - 5) Simplify by distributing (and combining like terms if necessary).
6 (2x - 3) - 5x Simplify by distributing (and combining like terms if necessary).
2x (5 + 4) Simplify by distributing (and combining like terms if necessary).
-9 (8x - 5) Simplify by distributing (and combining like terms if necessary).
5 - 8 (3x + 5) -3
Answer:
Hey there!
10(6x-5)=60x-50
6(2x-3)-5x=12x-5x-18=7x-18
2x(5+4)=18x
-9(8x-5)=-72x+45
5-8(3x+5)-3=5-24x-40-3=-24x-42
Let me know if this helps :)
During his vacation, Dalyn rents a small boat from a rental service that charges a flat fee of $50 plus $20 per hour (including taxes). The total charge comes to $150 . Which equation can be used to calculate the number of hours, x, that Dalyn rents the boat?
Answer:
Step-by-step explanation:
10 (x + 50) = 90
Does anyone know this??
Answer:
see below (I hope this helps!)
Step-by-step explanation:
The range is simply all the y values of a function. Remember, a closed dot signifies ≤ or ≥ whereas an open dot signifies < or >. We see that the minimum y value is -11, and since it has a closed dot, we can write y ≥ -11. From the graph, the maximum y value is 11 and since it has an open dot, we can write y < 11, therefore, the final answer is -11 ≤ y < 11.
NEED HELLP ASAP !!!
Answer:
m<x = 48
m<y = 132
Step-by-step explanation:
Since x and y are supplementary angles, that means their sum is 180 degrees.
And we are given that y is 12 less than 3 times the measure of x. With this information we can make a system of linear equations.
x + y = 180
y = 3x - 12
So now plug in the value of y into the first equation.
x + y = 180
x + (3x - 12) = 180
x + 3x = 192
4x = 192
x = 48
And then plug this computed value of x back into the first equation to find the measure of y.
x + y = 180
48 + y = 180
y = 180 - 48
y = 132
So the measures of the angles are as follows:
m<x = 48
m<y = 132
Cheers.
Which of the following number sentences is an example of the commutative property of multiplication?
4 × 5 = 10 × 2
27 + 3 = 3 + 27
2 × (9 × 14) = (2 × 9) × 14
18 × 1 = 1 × 18
In the expression 73 – 4•3+8, the first operation is...? A.an exponent
B.subtraction.
C.multiplication.
D.addition.
Answer:
C. multiplication
Step-by-step explanation:
P= ()
E=^
M=x
D=/
A=+
S=-
The three angles in a triangle are in the ratio 3:5:7. Find the largest angle in the triangle?
Answer: The largest angle is 7x
Step-by-step explanation:
Their sum is 180, so
3x + 5x + 7x = 180
5x = 180 --> x = 12
The largest angle is 7x, which is 7(12) = 84
If there are 15 packets each contaning 20 toys in a box and another box has 20 packets with 15 toys in each packets which box has more number of toys?(use property of whole number)
First box has 15 packets and every packet has 20 toys in it.
Second box has 20 packets and every packet has 15 toys in it.
For the first box, 15 x 20 = 300
For the second box, 20 x 15 = 300 again.
So these two box equal to each other.
Solve for x 5(x + 3) = 4(x-3)
0-18
0-27
O-3
O-6
I need help ASAP
Solve 3[-x + (2 x + 1)] = x - 1.
please help!!! 100 points if correct!!! please actually answer
Instructions
In this experiment, you will be using two coins as a simulation for a real-world compound event.
Suppose that a family has an equally likely chance of having a cat or a dog. If they have two pets, they could have 1 dog and 1 cat, they could have 2 dogs, or they could have 2 cats.
What is the theoretical probability that the family has two dogs or two cats?
Describe how to use two coins to simulate which two pets the family has.
Flip both coins 50 times and record your data in a table like the one below.
(picture below)
Based on your data, what is the experimental probability that the family has two dogs or two cats?
If the family has three pets, what is the theoretical probability that they have three dogs or three cats?
How could you change the simulation to generate data for three pets?
Answer:
see below
Step-by-step explanation:
What is the theoretical probability that the family has two dogs or two cats? (1/2)
The choices are dd, dc, cd, cc
There are 4 choices = dd or cc/ total = 2/4 = 1/2
Let the heads of the coin be dogs and the tails of a coin be cats
Flip two coins and coin A is the first pet and coin B is the second pet
heads , heads = 10
heads, tails 14
tails heads =13
tails tails = 13
total 50
Experimental probability 2 dogs or 2 cats = ( hh, tt) /total = ( 10+13) /50 = 23/50
If we had 3 pets
what is the theoretical probability that they have three dogs or three cats?
ddd, ddc, dcd, dcc, ccc, ccd ,cdc, cdd
There are 8 options
ddd or ccc/ total = 2/8 = 1/4
Let the heads of the coin be dogs and the tails of a coin be cats
Flip three coins and coin A is the first pet and coin B is the second pet Coin C be the third pet
Answer:
What is the theoretical probability that the family has two dogs or two cats? (1/2)
Experimental probability 2 dogs or 2 cats = 23/50
If the family has three pets, what is the theoretical probability that they have three dogs or three cats?
1/4=25%
Step-by-step explanation:
simplify the following expression
Answer:
Step-by-step explanation:
15 x^2 - 9 + 4 x - 5 x^2 - 11
by grouping the like terms,
15 x^2 - 5 x^2 + 4x - 9 - 11
10 x^2 + 4x - 20
Hope this helps
plz mark as brainliest!!!!!!
Answer:
10x^2+4x-20
Step-by-step explanation:
Subtarct 5x^2 from 15x^2
Subtract 11 from -9
Please help, 20 points! :)
Step-by-step explanation:
We are given 4x+y=6x-1 to graph. The easiest way to graph is to turn this equation into slope-intercept form, which is y=mx+b.
First, we are going to subtract 4x from both sides to isolate the y variable which gets us y=2x-1, and now we have slope-intercept form. Now we're going to use what we know about the form to graph.
In such form, m is the slope and b is the y-intercept. Our b in our equation is -1, so you're going to put a dot at (0,-1) on the y-axis. Then for our slope, it is 2, but it's easier to envision as rise over run where 2 is how much we rise and 1 is how much we run (or move to the right). So from our starting point from the y-axis, we're going to move up 2 units and then to the right one unit. And with two dots on the graph, we can run a line through it which will give us our graphed line.
For safe measures, you can continue the pattern of rising 2 and running 1, or you can go down 2 and left 1, which is the opposite and yet still confines to the line.
If you don't understand this explanation, I also recommend checking out desmos! It's a graphing calculator online in which you can plug this equation in and it graphs it for you! The file I have attached to this is from desmos to help you see the graph, I hope you do well!
To solve this problem we will have to convert 4x + y = 6x - 1 to point - slope form, for simplicity --- ( 1 )
4x + y = 6x - 1,
- 2x + y = - 1,
Point - Slope Form : y = 2x - 1
Now let's graph this equation. Consider the x - intercept and y - intercept of this graph --- ( 2 )
0 = 2x - 1
2x = 1
x = 1 / 2 = 0.5 ( x - intercept ),
y = 2(0) - 1 = 0 - 1 = - 1 ( y - intercept )
We know that the x - intercept is 0.5, so we can plot the point (0, 0.5). Similarly we can plot the point ( - 1,0 ) given the y - intercept is - 1. After plotting these points we can run a line through them, creating our graph.
If 4x−3=2x+9, then x= ?
Answer:
[tex]4x - 2x = 9 + 3[/tex]
[tex]2x = 12[/tex]
[tex]x = \frac{12}{2} [/tex]
[tex]x = 6[/tex]
Hope it helps u mate
x = 6
Step-by-step explanation:4x - 3 = 2x + 9
4x - 2x = 9 + 3
2x = 12
x = 12 : 2
x = 6
Select the correct answer. During the summer, Jody earns $10 per hour babysitting and $15 per hour doing yardwork. This week she worked 34 hours and earned $410. If x represents the number hours she babysat and y represents the number of hours she did yardwork, which system of equations models this situation? A. x + y = 34 10x + 15y = 410 B. x + y = 410 10x + 15y = 34 C. x + y = 34 15x + 10y = 410 D. x + y = 410 15x + 10y = 34
Answer:
A. x + y = 34; 10x + 15y = 410
Step-by-step explanation:
Jody's total hours will be the sum of the hours spent on each job:
x + y = 34 . . . . . total hours
Jody's total earnings will be the sum of the earnings from each job:
10x +15y = 410 . . . total earnings
So, the system of equations is ...
x + y = 3410x + 15y = 410You collect a total of $75 in donations from three people. The three donations are in the ratio 4 : 4 : 7. (hint: set up an equation first)
Answer:
Step-by-step explanation:
Since the ratio is 4x:4x:7x, if we add all those numbers up we get 15. Then we do 75/15 to get what x equals. So we get 5. So x equals 5. Following the rules of multiplication, you do 4(5):4(5):7(5), and simplifying that further, you get 20:20:35. If we add all those values up, we should get 75, and we do!
If you're wondering why I did 4x:4x:7x instead of 4:4:7, it's because a ratio is just a...well ratio? It's easier to visualize if you put a variable because the variable could be anything, and you would have to multiply all the given values to get the same proportions. In summery, I did it so it was easier to visualize
Simplify the expression (7x² - 3x) + (11x² - x - 7) A. 18x² + 2x + 7 B. 4x² - 4x - 7 C. 18x² - 2x - 7 D. 18x² - 4x - 7
Answer: D.
Step-by-step explanation:
Answer:
D.18x square-4x-7Paj is filling a 9-inch- flower pot with soil from small bags. Each bag of soil contains 2 2/3 cubic inches of soil. Exactly how many bags of soil are needed for paj to fill the flower pot
Answer:
[tex]Number\ of\ bags = 3{\frac{3}{8}[/tex]
Step-by-step explanation:
Given
Size of Flower Pot = 9 cubic-inch
Size of filling bag = [tex]2\frac{2}{3}[/tex] cubic-inch
Required
Determine the number of bags needed to fill the pot
To solve this, we simply divide the volume of the flower pot by the volume of the filling bags;
This is shown as follows:
[tex]Number\ of\ bags = \frac{Volume\ of\ Pot}{Volume\ of\ filling\ bags}[/tex]
Substitute 9 for Volume of Pot and [tex]2\frac{2}{3}[/tex] for Volume of filling bags
[tex]Number\ of\ bags = \frac{9}{2\frac{2}{3}}[/tex]
Convert denominator to improper fraction
[tex]Number\ of\ bags = \frac{9}{\frac{8}{3}}[/tex]
Rewrite Expression
[tex]Number\ of\ bags = 9 / {\frac{8}{3}[/tex]
[tex]Number\ of\ bags = 9 * {\frac{3}{8}[/tex]
[tex]Number\ of\ bags = {\frac{9 * 3}{8}[/tex]
[tex]Number\ of\ bags = {\frac{27}{8}[/tex]
Convert to Mixed Fraction
[tex]Number\ of\ bags = 3{\frac{3}{8}[/tex]
Hence, the number of bags needed to fill the flower pot is [tex]3{\frac{3}{8}[/tex]
please help meee asap!
Answer:
1.
Original square side: s
Area = s^2
Modified square:
Length = 1.3s
Width = 0.82s
Area = 1.3s * 0.82s = 1.066s^2
(1.066 - 1)/1 * 100% = 6.6%
The area increases by 6.6%
2.
[tex] \dfrac{1}{x} + \dfrac{1}{y} = \dfrac{2}{15} [/tex]
[tex] \dfrac{y}{xy} + \dfrac{x}{xy} = \dfrac{2}{15} [/tex]
[tex] \dfrac{x + y}{xy} = \dfrac{2}{15} [/tex]
[tex] x + y = \dfrac{2xy}{15} [/tex]
[tex] \dfrac{7y + 5xy + 7x}{y + x + 2xy} = [/tex]
[tex] = \dfrac{7x + 7y + 5xy}{x + y + 2xy} [/tex]
[tex] = \dfrac{7(x + y) + 5xy}{x + y + 2xy} [/tex]
[tex] = \dfrac{7(\frac{2xy}{15}) + 5xy}{\dfrac{2xy}{15} + 2xy} [/tex]
[tex] = \dfrac{15}{15} \times \dfrac{7(\frac{2xy}{15}) + 5xy}{\dfrac{2xy}{15} + 2xy} [/tex]
[tex] = \dfrac{14xy + 75xy}{2xy + 30xy} [/tex]
[tex] = \dfrac{89xy}{32xy} [/tex]
[tex] = \dfrac{89}{32} [/tex]
3.
[tex] \dfrac{x - 3}{x^3 + 3x} = \dfrac{A}{x} + \dfrac{Bx + C}{x^2 + 3} [/tex]
[tex] = \dfrac{A(x^2 + 3)}{x(x^2 + 3)} + \dfrac{(Bx + C)x}{(x^2 + 3)x} [/tex]
[tex] = \dfrac{Ax^2 + 3A}{x(x^2 + 3)} + \dfrac{Bx^2 + Cx}{(x^2 + 3)x} [/tex]
[tex] = \dfrac{Ax^2 + 3A + Bx^2 + Cx}{x(x^2 + 3)} [/tex]
[tex] \dfrac{x - 3}{x^3 + 3x} =\dfrac{(A + B)x^2 + Cx + 3A}{x(x^2 + 3)} [/tex]
[tex] A + B = 0 [/tex]
[tex] C = 1 [/tex]
[tex] 3A = -3 [/tex]
[tex] A = -1 [/tex]
[tex] -1 + B = 0 [/tex]
[tex] B = 1 [/tex]
[tex] A + B + C = -1 + 1 + 1 = 1 [/tex]
1. (01.01)
Evaluate -6 - (-2). (1 point)
-4
-8
4
12
Evaluate -6 - (-2):
Your answer is -4
In this case all you had to do was subtract -2 from -6 and your answer is -4
(。・ω・。)
Write an equation that illustrates a number with two decimal places multiplied by a number with one decimal place. The product has only two nonzero digits?
Step-by-step explanation:
Let the number with two decimal places be 1.23
Let the number with one decimal place be 4.5
Then 1.23 multiplied by 4.5
= 1.23 × 4.5
= 5.535
The result has more than two nonzero digits.
Note: When you multiply two decimal numbers, the decimal place(s) of the result is the addition of the decimal places of each of the numbers being multiplied.
Michael keeps dogs, cows, cats and kangaroos as pets.
pets in total and that 1/8 of them are dogs, 3/4 are NOT cows, 2/3 are NOT cats.
kangaroos does Michael keep?
The question above is incomplete.
Complete Question
Michael keeps dogs, cows, cats and kangaroos as pets. He has 24 pets in total and 1/8 of them are dogs, 3/4 are not cows and 2/3 are not cats. How many kangaroos does Michael keep?
Answer:
7 kangaroos
Step-by-step explanation:
Total number of pets = 24
Fraction representing total number of pets = 1
Step 1
Number of dogs =
Fraction representing dog = 1/8
1/8 × 24 = 3
He has 3 dogs
Step 2
Number of cows =
From the question, we are told that 3/4 are not cows
Therefore, the number of cows he has =
1 - 3/4 = 1/4
The fraction representing cows = 1/4
Hence the number of cows he has =
1/4 × 24 = 6 cows
Step 3
From the question, we are also told that
2/3 are not cats
The fraction representing the number of cats he has=
1 - 2/3 = 1/3
Therefore, the number of cats he has =
1/3 × 24 = 8 cats.
Step 4
How many kangaroos does Michael keep?
We are asked, how many kangaroos he keeps.
Total numbers of pets = Number of dogs + Number of cows + Number of cats + Number of kangaroos
24 = 3 + 6 + 8 + Number of kangaroos
Number of kangaroos = 24 -(3 + 6 + 8)
= 24 - 17
= 7
Therefore, the number of kangaroos that Michael has is 7 kangaroos
Please help I don't understand I need an answer ASAP
Answer:
B = 48
Step-by-step explanation:
You are given that the two vertical lines are parallel. That means that the alternate interior angles are equal (they form a Z shape).
So the given is that A = B
A = 5x - 12
B = 2x + 24
Solution
5x - 12 = 2x + 24
5x - 12 = 2x + 24 + 12
5x = 2x + 36
5x - 2x = 36
3x = 36
x = 36/3
x = 12
================
B is
B = 2x + 24
B = 2*12 + 24
B = 24 + 24
B = 48
Answer:
B=48
Step-by-step explanation:
so angle A and B are on what I call the z-angles which are normally equal in that if you view the parallel lines horizontally you will see the form of a z and the corners of it are equal that said you equate both of them to get x
5x-12=2x+24
join like terms
5x-2x=12+24
3x=36
x=12
so to find angle B substitute x with 12
A rectangular room is 3 meters longer than it is wide, and its perimeter is 22 meters. Find the dimension of the room. The length is : meters and the width is: meters.
Answer:
Width = 4 m
Length = 7 m
Step-by-step explanation:
given:
perimeter of a rectangle = 22m
L = 3 + W
perimeter = 2L + 2W
perimeter = 2 (3 + W) + 2W
22 = 6 + 2W + 2W
22 - 6 = 4W
W = 16 / 4
W = 4 m
L = 3 + W
L = 3 + 4
L = 7 m
check:
perimeter = 2L + 2W
22 = 2(7) + 2(4)
22 = 14 + 8
22 = 22 ---- OK
Plz help asap this is due in one hour
Answer:
A car travels 20km in 15 minutes, what is the average speed that the car travelled at?
the average speed that the car travelled at is 80km per hour
Step-by-step explanation:
Answer:
1. A bus travels 16km in 4 mins. The total time is 4 minutes.
2. A speeding car traveling at 40 km/hr decides to slow down to 30 km/hr after covering half the distance. The total distance the car travels is 34.29 km/h.
3. A truck goes from Haryana to Bangalore with an average speed of 60 km/hr. The journey takes 30 hours. It returns from Bangalore to Haryana on the same road with an average speed of 40 km/hr. The average speed of the truck during the road trip is 48 km/hr.
Janissa bought 50 cupcake cases for baking. She used 2/5 of the cases to bake vanilla cupcakes. She then used 5/6 of the remaining cases to bake chocolate cupcakes. How many cupcake cases does Janissa have left?
Jessica has 5 cupcake cases left.
First, divide 50 into groups of five. Next, subtract two groups of five from 50. Third, divide the remaining cases into groups of six. Finally, subtract 5 groups of six from the remains from the last subtraction equation.
The number of cupcake cases that Janissa has left will be 5.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Janissa bought 50 cupcake cases for baking.
She used 2/5 of the cases to bake vanilla cupcakes. Then the number of vanilla cupcakes will be
⇒ 50 x 2 / 5
⇒ 20 vanilla cupcakes
Then the remaining cupcake cases will be
⇒ 50 - 20
⇒ 30 cupcake cases
She then used 5/6 of the remaining cases to bake chocolate cupcakes. Then the number of chocolate cupcakes will be
⇒ 30 x 5 / 6
⇒ 25 chocolate cupcakes
Then the remaining cupcake cases will be
⇒ 30 - 25
⇒ 5 cupcake cases
Then the number of cupcake cases that Janissa has left will be 5.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
help please i don’t think constant is the right answer
Answer:
i think it is the control group sorry if i am wrong
Step-by-step explanation:
Find the unknown angle x.
Answer:
103°
Step-by-step explanation:
[tex] m\angle DST = m\angle DCS = 80\degree.. (\angle 's \: in\: alternate \: segment) [/tex]
[tex] In\: \triangle DST[/tex]
[tex] m\angle DTS = 180\degree - (60\degree + 80\degree) [/tex]
[tex] m\angle DTS = 180\degree - 140\degree[/tex]
[tex] m\angle DTS = 40\degree[/tex]
[tex] m\angle ETA+m\angle ETD+ m\angle DTS= 180\degree.. (straight \:line \:\angle 's) [/tex]
[tex] m\angle ETA+37\degree + 40\degree = 180\degree[/tex]
[tex] m\angle ETA+77\degree = 180\degree[/tex]
[tex] m\angle ETA = 180\degree-77\degree [/tex]
[tex] m\angle ETA = 103\degree [/tex]
[tex] x = m\angle ETA = 103\degree.(\angle 's \: in\: alternate \: segment) [/tex]
Jamal bought donuts and cupcakes. He bought three times as many donuts as cupcakes. Donuts cost $0.50 each. Cupcakes cost $1.00 each. Jamal spent $10.00 total. How many donuts did Jamal buy? How many cupcakes did Jamal buy?
Answer:
Step-by-step explanation:
Let
x= Quantity of donuts
y= Quantity of cupcakes
He bought 3 times as many donuts as cupcakes
Donuts=y= 3x
Donuts=0.50 each
Cupcakes=1.00 each
PxQx + PyQy = 10.00
0.50(x) + 1.00(y) = 10.00
0.50x + 1.00(3x)=10.00
0.50x+3.00x=10.00
3.50x=10.00
Divide both sides by 3.50
x=10.00/3.50
=2.86
y=3x
y=3(2.86)
=8.58
Jamal bought 2.86 donuts and 8.58 cupcakes
Check:
PxQx + PyQy = 10.00
0.50(2.86) + 1.00(8.58) = 10.00
1.43 + 8.58=10.00
10.01=10.00
10.01 approximately 10.00