A die is tossed twice and a number of dots facing up in each toss are counted and noted in the order of occurrence.
a) The sample space is given as:
Sample Space (S)= {(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),c),(6,6)}.
What is the sample space?A sample space is a collection of a set of possible outcomes of a random experiment. The sample space is represented using the symbol S.
b) the set corresponding to the event number of dots in the first toss is not less than the number of dots in the second toss.
{(6,6),(6,5)(6,3)(6,2)(6,1)(6,4),(5,1)(5,2)(5,3),(5,4),(5,5),(4,1),(4,2),(4,3),(4,4),(3,1),(3,2), (2,1), (2,2),(1,1)}
c) find the set b corresponding to the event number of dots in the first toss is 6.
{(6,1),(6,2),(6,3),(6,4),c),(6,6)}.
e) a does not imply b or does b imply a.
To learn more sample spaces visit:
https://brainly.com/question/10558496
#SPJ1
Which of the numbers below are whole numbers? Check all that apply.
A. 734.895
B. 0.7538
C. 7
D. 5429.97
E. 616
F. 401119.8
Answer:
7, 616 because there is no floating point
If a household is saving 30% of their total bi-weekly gross pay of $2,051.00, determine how many months it will take to save a 20% down payment and 1.5% for closing costs for a property with a purchase price of $281,700.00.
45
46
54
55
(25 POINTS)
Based on the amount saved per week and the down payment of the property, the number of months it will take to save the amount is 46 months.
How long will it take for the family to save the amount?First, find out the amount saved per month:
= (30% x 2,051) x 2 payments a month
= $1,230.60
The downpayment is:
= 281,700 x 20%
= $56,340
The closing cost is:
= 1.15 x 56,230
= $843.45
The number of months till the amount is saved is:
= (56,340 + 843.45) / 1,230.60
= 46 months
Find out more on mortgage downpayments at https://brainly.com/question/9893085.
#SPJ1
Using the Addition Method, solve for y in the following system of linear equations: 4x – 2y = 6 2x + y = 7
Answer:
y = 2
Step-by-step explanation:
Addition Method:
4x - 2y = 6
2x + y = 7
-2(2x + y) = -2(7)
4x - 2y = 6
-4x - 2y = -14
-4y = -8
y = 2
Substitution Method:
4x - 2y = 6
2x + y = 7
-2y = 6 - 4x
2y = 4x - 6
y = 2x - 3
2x + (2x - 3) = 7
4x - 3 = 7
4x = 10
x = 2.5
2(2.5) + y = 7
5 + y = 7
y = 2
Brainliest, please :)
(3x + 2y = 7
(7x-2y = 3
Find the value of the function f(x) = x2 + 9x + 10, for x = -1.
Answer:
this is pretty easy we just replace the x with -1 so
(-1)^2+(-1)9+10
-1*-1=1
-1*9=-9
1+-9=-8
-8+10=2
f(-1)=2
Hope This Helps!!!
What is the vertex of the quadratic function given in the table?
Answer:
The vertex is (-3,-2)
The vertex is basically the very top or very lowest, so you will notice how values around (-3,-2) are relatively the same in the y coordinate, but -2 is the "highest/lowest" so that's how you know it's a vertex.
If you try picturing the points in your head, you will see it make a U and at the bottom of the U is the vertex.
Pam asks you to help with the catering for the funeral. You decide to use juice concentrate to serve as a refreshing drink. To create this delicious drink, you must dilute the concentrate in the ratio 1:4. You have 2 litres of concentrate. What is the volume of water needed?
A merchant has 120 liters of oil of one kind, 180 liters of another kind, and 240
liters of the third kind. He wants to sell the oil by filling the three kinds of equal
capacity. What should be the greatest capacity of such a tin?
The merchant needs to fill 60 litres of all types of oils .
What is HCF ?
HCF is the highest common factor, it is the factor in common in more than two numbers.
It is given in the question that
A merchant has 120 litres of oil of one kind, 180 litres of another kind, and 240 litres of the third kind.
He wants to sell the oil by filling the three kinds of equal capacity.
To find the greatest capacity of such a tin , we have to find the highest common factor of the individual capacity.
120=2×2×2×3×5
180=2×2×3×3×5
240=2×2×2×2×3×5
HCF=2×2×3×5=60
The greatest capacity = 60 litres
So the merchant needs to fill 60 litres of all types of oils .
To know more about HCF
https://brainly.com/question/17240111
#SPJ1
2. Find the LCM of the following numbers by division method. (a) 16 and 28 (b) 36 and 44 (c) 45 and 120 (d) 10, 15 and 30 (e) 52 and 128 (f) 20, 60 and 80
(a):112
(b):396
(c):360
(d):30
(e):1664
(f):240
radical 5* radical 2
Answer:
[tex] \sqrt{10} [/tex]
Step-by-step explanation:
Rule: [tex] \sqrt{a} \times \sqrt{b} = \sqrt{ab} [/tex]
[tex] \sqrt{5} \times \sqrt{2} = \sqrt{5 \times 2} = \sqrt{10} [/tex]
Find the distance between the points (-4, 2) and (2, -1).
Give an exact answer in simplest radical form. Do not round.
Answer:
[tex]3 \sqrt{5} [/tex]
Step-by-step explanation:
[tex] \sqrt{ {( - 4 - 2)}^{2} + {(2 - ( - 1))}^{2} } = \sqrt{45} = 3 \sqrt{5} [/tex]
A researcher is examining the claims made by a water softener salt manufacturer. He performs an experiment using water from a variety of sources. For each water source, he has a sample with no treatment and a sample treated with the recommended amount of the water softener salt.
He then tests each sample to measure the softness and compares the results, determining that the claims made by the manufacturer are true.
The conclusion drawn from the study is ___ because the sample is __ In this instance, an __ study was performed.
The conclusion drawn from the study is instance because the sample is homogenous and an experimental study was performed.
What is an experimental study?An experimental study deals with a dependent variable and there is a dependent variable.
Also, a control is used to establish the validity of the results.
The dependent variable is the level of softness after treatment while the independent variable is the type of water softener used.
The conclusion drawn from the study is instance because the sample is homogenous and an experimental study was performed.
Learn more about the experiment:
brainly.com/question/9199868
#SPJ1
If f(x)= 3x +2 and g(x)=x^2+1, which expression is expression is equivalent to (fog) (x)
Composite functions occur when we take two functions and input one into the other as x.
Example:
[tex]f(x) = 2x[/tex]
[tex]g(x) = 3x^2[/tex]
[tex](f\circ g)(x)=f(g(x))[/tex]
[tex](f\circ g)(x) = 2(3x^2)[/tex]
Solving the QuestionWe're given:
[tex]f(x)= 3x +2[/tex][tex]g(x)=x^2+1[/tex]To find [tex](f\circ g)(x)[/tex], input g into f as x:
[tex]f(x)= 3x +2[/tex]
[tex](f\circ g)(x)=3(x^2+1) +2\\(f\circ g)(x)=3x^2+3 +2\\(f\circ g)(x)=3x^2+5[/tex]
Answer[tex](f\circ g)(x)=3x^2+5[/tex]
The graphs of f(x) = 5x and its translation, g(x), are shown on the graph.
On a coordinate plane, 2 exponential functions are shown. f (x) approaches y = 0 in quadrant 2 and increases into quadrant 1. It crosses the y-axis at (0, 1) and goes through (1, 5) and (2, 25). g (x) approaches y = negative 10 in quadrant 2 and increases into quadrant 1. It goes through (0, negative 9), (1, negative 5), (2, 15).
What is the equation of g(x)?
g(x) = 5x – 9
g(x) = 5x – 10
g(x) = 5x – 9
g(x) = 5x – 10
According to the function transformations, the equation of function g(x) is [tex]g(x) = 5^x - 10[/tex]
How to determine the equation of g(x)?The complete question is in the attachment
The function f(x) is given as:
[tex]f(x) = 5^x[/tex]
From the attached graph, we can see that the function f(x) is 10 units down to get g(x).
This is so because the y values of g(x) are 10 less than the corresponding y values of f(x)
This transformation is represented by:
(x, y) => (x, y - 10)
So, we have:
g(x) = f(x) - 10
Substitute [tex]f(x) = 5^x[/tex]
[tex]g(x) = 5^x - 10[/tex]
Hence, the equation of function g(x) is [tex]g(x) = 5^x - 10[/tex]
Read more about function transformations at:
https://brainly.com/question/3381225
#SPJ1
A clothing manufacturer produces one type of sweater that earns $4 profit for each one sold. The business manager requires that a profit of at least $100 be earned every hour. The product manager estimates that the expenses for running the machine are $45 per hour. What is the least number of sweaters that must be produced each hour to earn a profit of at least $100?
The least number of sweaters that must be produced each hour to earn a profit of at least $100 is 37.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
A clothing manufacturer produces one type of sweater that earns $4 profit for each one sold.
Let x be the number of sweaters that must be produced each hour to earn a profit of at least $100
Total selling price if earns $4 profit for each one sold = 4x
The expenses for running the machine are $45 per hour.
4x - 45 ≤ 100
4x ≤ 145
x ≤ 145/4
x ≤ 36.25
Number of sweater(estimate value) = 37
Thus, the least number of sweaters that must be produced each hour to earn a profit of at least $100 is 37.
Learn more about the inequality here:
brainly.com/question/19491153
#SPJ1
SHL T Teleperformance
each interaction matters
Choose the correct option.
You arrived at your office at 9:35 AM. You left your office at 6:05 PM. How many hours did
spend in the office?
Answer:
8 hours 30 minutes
Step-by-step explanation:
6:05 pm - 9:35 am =
= 18:05 - 9:35
= 17:65 - 9:35
= 8:30
Answer:
Citcitdutditdutdtuditditdtiditf this is what is adjective 6hftuiouhvcutxyrzyt
Step-by-step explanation:
huuugggguytzurzt8st8s8ts9td96097g79t8dtrudutfitf8tfitftid8tdtdtudutd
Solve the following systems using the elimination method. -3x+4y=-8 and 3x+ y=-17
Answer:
(-4, -5)
Step-by-step explanation:
-3x + 4y = -8
+
3x + y = -17
= 5y = -25 = y = -5
-3x + 4(-5) = -8
-3x - 20 = -8
-3x = 12
x = -4
A community center has an L-shaped swimming pool that is 10 feet deep. What is the volume of the pool?
The total volume of the pool is 1040 cubic ft. The correct answer is option B.
The complete question is given below:-
The community centre has an L-shaped swimming pool that is 10 feet deep. What is the volume of the pool
1200
1040
640
880
What is volume?Volume is defined as the space covered by any solid body in the three-dimensional plane.
We know that the total volume of the pool is the sum of the volume of two rectangular prisms.
One is a rectangular prism with dimensions 20ft.×10ft.×4ft.
and the other rectangular prism has dimensions: 6ft.×4ft.×10ft.
Hence, the volume of a first rectangular prism is:
20×10×4=800 cubic ft.
The volume of a second rectangular prism is:
6×4×10=240 cubic ft.
Hence, the total volume of the pool is:
800+240=1040 cubic ft.
Therefore the total volume of the pool is 1040 cubic ft. The correct answer is option B.
To know more about volume follow
https://brainly.com/question/1972490
#SPJ1
using Factoring:
Set up an algebraic equation:
An integer is 3 less than 5 times another. If the product of the two integers is 36,
then find the integers.
Answer:
hjjj gogo fgjvsgjgccvvggggggffffffddsddddfffgv
Which graph represents y= sqrt x-4
Based on the characteristics of the function and the image generated by the graphing tool, we conclude that the first choice represents the function [tex]y = \sqrt{x} - 4[/tex].
How to find the right graph of a given function
In this question we have a radical function ([tex]f(x) = \sqrt{x}[/tex]) translated vertically 4 units in the -y direction. The domain of the function is [0, + ∞). A quick and efficient approach consists in graphing the function and comparing with each image to determine the right choice.
We present the graph description in the image attached below and we conclude that the first choice represents the graph of the function.
To learn more on radical functions: https://brainly.com/question/27847549
#SPJ1
Select the correct answer. Which set of vertices forms a parallelogram? OA A2,4), B(3, 3), C6, 4), D(5, 6) OB. A(-1, 1), B(2, 2), C(5, 1), D(4, 1) OC. A(-5, -2), B(-3, 3), C3, 5), D(1, 0) OD. A(-1, 2), B(1, 3), C5, 3), D(1, 1).
Answer:
(6,4)
Step-by-step explanation:
^^^
11. Calculate the weight on earth of an object with a mass of 48 kg. Gravitational acceleration (a) = 9.81 m/s ² Show all steps and formulae used. (3) ✓
Answer:
470.88 N
Step-by-step explanation:
F = ma
48 ( 9.81) = 470.88 N ( 105.958 lbs)
9 out of 10 students prefer maths class over lunch how many students do not prefer math if 200 students were asked?
Answer: 180
Step-by-step explanation: 200 % 2 = 100
9/10 = 90/100
90 * 2 = 180
Answer:
20 students
If 9 out of 10 student prefer math over lunch, then 1 out of ten DO NOT. With this information you can set up a simple proportion: [tex]\frac{1}{10} =\frac{x}{200}[/tex].
To solve for x, you cross multiply as follows:
1*200=10x
200=10x
20=x
Hence, x equals 20, and 20 students do not prefer math over lunch.
Hope I helped!!!!!!!!!!!!!:)
write in slope intercept form
2y+x=1
Answer:
y = -x/2 + 1/2 or
y = -1/2 x + 1/2
(these are equivalent)
Step-by-step explanation:
Slope-intercept form is:
y = mx + b
So we have to get the y all by itself on the left.
2y + x = 1
Subtract x from both sides.
2y = 1 - x
Divide both sides by 2. Divide all the terms by 2.
2y/2 = 1/2 - x/2
Simplify.
y = 1/2 - x/2
Rearrange the terms on the right side so that the x term is first and the constant is last.
y = -x/2 + 1/2
I think this is a good, reasonable and correct answer. But maybe you really want to see that m number (the slope) out in front of the x. Then you can write is as:
y = -1/2 x + 1/2
In the figure shown below, AC is parallel to DE with transversal BF
Determine the values of x and y
PLEASE SHOW WORK FOR THIS!
x=_______
y=_______
Answer:
X = 142°Y = 38°Given - AC is parallel to DE
angle 3y + 28 = angle X ( Vertically opposite angles are equal).
3y + 28 = X
X + Y = 180° ( supplementary angles).
3y - X = (-28)
Solving both the equation we get
multiply eq 1 with 3
3x + 3y = 540
-X + 3y = (-28)
subtracting
4x = 568
x = 142°
3y + 28 = 142
3y = 142 - 28
3y = 114
y = 38°
92÷9−5=913 find value of p
Answer:
which p? there isn't any p in above equation
I need to make sure I do this right
[PLEASE HELP!!!!!!!!!]
Identify which equations have one solution, Infinitely many solutions, or no solution.
y+3.2y=20 +2z-1=42+2-2z|
4.5r=3.2+4.5r 21+4=3x+2
No Solution
One Solution
Infinitely Many Solutions
3z +2.5=3.2+3z
1.1+0+2=3.1+
The list of equations is shown in the picture which equation has No Solution, One Solution, and Infinitely Many Solutions.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have given a linear equation in one variable.
[tex]\rm \dfrac{1}{2}y + 3.2y = 20[/tex]
After solving:
y = 5.40 (one solution)
[tex]\rm \dfrac{15}{2}+ 2z -\dfrac{1}{4}=4z+\dfrac{29}{4} -2z[/tex]
After solving:
[tex]\rm \dfrac{15}{2} -\dfrac{1}{4}=\dfrac{29}{4}[/tex]
[tex]\rm \dfrac{29}{4}=\dfrac{29}{4}[/tex] (Infinitely Many Solutions)
3z + 2.5 = 3.2 + 3z
2.5 = 3.2 (no solution)
Similarly, we can identify which equation has No Solution, One Solution, and Infinitely Many Solutions.
Thus, the list of equations is shown in the picture which equation has No Solution, One Solution, and Infinitely Many Solutions.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ1
Which standard form of the equation of the hyperbola has vertices at (0, 5) and (0, –5), and asymptotes y equals plus or minus five twelfths times x question mark
y squared over 25 minus x squared over 144 equals 1
y squared over 144 minus x squared over 25 equals 1
x squared over 25 minus y squared over 144 equals 1
x squared over 144 minus y squared over 25 equals 1
The equation first represents the hyperbola has vertices at (0, 5) and (0, –5), and asymptotes y = ±(5/12)x option first is correct.
What is hyperbola?It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.
We have:
Vertices of the hyperbola = (0, 5) and (0, -5)
Asymptotes: y = ±(5/12)x
The equations we have:
[tex]\rm \dfrac{y^{2}}{25}-\dfrac{x^{2}}{144}=1[/tex]
[tex]\rm \dfrac{y^{2}}{144}-\dfrac{x^{2}}{25}=1[/tex]
[tex]\rm \dfrac{x^{2}}{25}-\dfrac{y^{2}}{144}=1[/tex]
[tex]\rm \dfrac{y^{2}}{144}-\dfrac{x^{2}}{25}=1[/tex]
From the equation first:
[tex]\rm \dfrac{y^{2}}{25}-\dfrac{x^{2}}{144}=1[/tex]
The value of a and b are:
a = 12
b = 5
Vertices of the hyperbola = (0, b) and (0, -b)
Vertices of the hyperbola = (0, 5) and (0, -5)
Asymptotes: y = ±(b/a)x
Asymptotes: y = ±(5/12)x
Thus, the equation first represents the hyperbola has vertices at (0, 5) and (0, –5), and asymptotes y = ±(5/12)x option first is correct.
Learn more about the hyperbola here:
brainly.com/question/12919612
#SPJ1
Answer:
A
Step-by-step explanation:
Which number should replace the ç to make the subtraction problem correct?
9.866
- 7.97ç
1.889
Answer:
7
Step-by-step explanation:
for you to get the missing number just take the complete numbers and minus them then you'll get the incomplete digit needed good day.