a) For a single roll of a standard six-sided dice, there are 6 possible outcomes.
b) Sample points for rolling a dice twice are:
(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)
a) If we want to find the number of sample points for multiple rolls of a dice, we use the counting rule for multiple-step experiments, which states that if an experiment consists of k steps and there are n1 possible outcomes for the first step, n2 possible outcomes for the second step, and so on, then the total number of possible outcomes for the experiment is:
n1 x n2 x ... x nk
For example, if we roll a dice twice, then there are 6 possible outcomes for the first roll and 6 possible outcomes for the second roll. Therefore, the total number of possible outcomes for rolling a dice twice is:
6 x 6 = 36
b) Here are the sample points for a single roll of a standard six-sided dice:
1, 2, 3, 4, 5, 6
Here are the sample points for rolling a dice twice:
(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)
Each sample point consists of two values, representing the outcomes of the first and second rolls, respectively. The sample points are written in parentheses and separated by commas.
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Graph the linear system and tell how many solutions it has. If there is exactly one solution, estimate the solution and check it algebraically.
Answer: Infinite solutions.
Step-by-step explanation:
To graph both these equations, you need to make them slope intercept form (which is y = mx + b):
x + 2y = -2 in slope intercept form is y = -1/2x - 1 (subtract x from both sides then divide both sides by 2).
-3x - 6y = 6 in slope intercept form is y = -1/2x - 1. (add 3x to both sides then divide both sides by -6).
These are the same lines, so there are an infinite number of solutions when you graph.
Hope this helps!
Two rectangles each with dimensions
c cm ⇥ b cm are used to form a cross as shown. The arms of the cross are all of equal length.
a) The perimeter of the cross is: P = 4a = 4(c - b) = 4c - 4b
b) The area of the cross is:[tex]A= 2cb - 2b^2 \ cm^2[/tex]
c) b in terms of A and C is: [tex]b= \frac{c ± \sqrt{(c^2 - 4A)}}{2}[/tex]
What is area and perimeter?
The perimeter of a shape is the distance around its outside. The space inside a shape is measured by area.
a) The perimeter, P, of the cross is equal to the sum of the lengths of its four arms.
The length of one arm of the cross can be found by subtracting the length of one rectangle from the length of the other rectangle. Since each rectangle has dimensions c cm × b cm, the length of one arm is:
a = c - b
Therefore, the perimeter of the cross is:
P = 4a = 4(c - b) = 4c - 4b
b) The area, A, of the cross is equal to the area of the two rectangles minus the area of the four triangles formed by the arms of the cross.
The area of each rectangle is:
[tex]Area_{rect} = c * b[/tex]
The area of each triangle is:
[tex]Area_{tri} = (a * b) / 2 \\\\= \frac{[(c - b) * b]}{2} \\\\= \frac{ (c * b - b^{2} )}{2}[/tex]
Since there are four triangles, the total area of the triangles is:
[tex]4A_{tri} = 2cb - 2b^2\ cm^2[/tex]
Therefore, the area of the cross is:
[tex]A = 2A_{rect} - 4A_{rect} \\\\ = 2cb - 2b^2[/tex]
c) c) To find b in terms of A and C, we can use the formula for the area of the cross that we found in part b:
[tex]A = 2cb - 2b^2[/tex]
We can rearrange this equation to put it in the form of a quadratic equation:
[tex]2b^2 - 2cb + A = 0[/tex]
This is a quadratic equation in standard form, with a = 2, b = -2c, and c = A. We can use the quadratic formula to solve for b:
b = (-b ± sqrt(b^2 - 4ac)) / 2a
b = (2c ± sqrt((2c)^2 - 4(2)(A))) / (2 × 2)
[tex]b=\frac{-b ± \sqrt{(b^2 - 4ac)} }{2a} \\\\b= \frac{2c ± \sqrt{(2c^2 - 4(2)c)}}{4} \\\\b= \frac{2c ± \sqrt{(4c^2 - 16A)}}{4} \\\\b= \frac{c ± \sqrt{(c^2 - 4A)}}{2}[/tex]
Therefore, b in terms of A and C is: [tex]b= \frac{c ± \sqrt{(c^2 - 4A)}}{2}[/tex]
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Write 10 000 seconds in hours, minutes, and second
The 10,000 seconds can be stated as 166.6777 minutes and 2.7778 hour.
What is Unit Conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
Given:
We have 10,000 sec
As, 1 minute= 60 seconds
So, In minutes
= 10000/60
= 1000/6
= 166.6667 minutes
Now, 1 hour= 60 minutes
So, In hour
= 10000/ 60 x 60
= 10000/3600
= 2.7778 hour
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Solve By Substitution
y=-3x
2x-3y=22
Answer:2
Step-by-step explanation:
y = -3x.
Substitute this value in the second equation for y.
=> 2x-3(-3x)=22
=> 2x+9x=22
11x =22
Therefore, x=2.
Hope this helps :)
The census bureau reports that the mean and median incomes of people who worked full time in 2001 and had at least a bachelors degree were $53,054 and $72,674
The mean income, of people who worked full-time in 2001 and had at least a bachelor's degree, was $53,054. while the median income was $72,674.
What are the mean and median?The mean is the average value. The mean is computed as the quotient of the total value divided by the number of values.
The median is the middle value of the data set in an ordered list.
Both the mean and the median are described as measures of central tendency.
Thus, we can identify the mean value as $53,054 since it was the first to be mentioned, followed by the median income as $72,674.
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Question Completion:Which of these numbers is the mean and which is the median? Explain your reasoning.
A taxi company charges a base fee of $3.00 plus $0.75 per mile. Write an equation to represent the cost of a taxi ride Y for the distance of X miles.
0.75 times the amount of miles+the base fee
Answer:
Y=0.75X+3
Question
Which polygon appears to be regular?
Responses
Figure A
Figure B
Figure C
Figure D
The answer would be figure B. (pentagon)
In triathlons, it is common for racers to be placed into age and gender groups. Friends Leo and Mary both completed the Hermosa Beach Triathlon, where Leo competed in the Men, Ages 30 - 34 group while Mary competed in the Women, Ages 25 - 29 group. Leo completed the race in 1:22:28 (4948 seconds), while Mary completed the race in 1:31:53 (5513 seconds). Obviously Leo finished faster, but they are curious about how they did within their respective groups. Can you help them? Here is some information on the performance of their groups:The finishing times of the Men, Ages 30 - 34 group has a mean of 4313 seconds with a standard deviation of 583 seconds.The finishing times of the Women, Ages 25 - 29 group has a mean of 5261 seconds with a standard deviation of 807 seconds.The distributions of finishing times for both groups are approximately Normal.if the distributions of finishing times are not nearly normal, would the values of the standard score in part a change? explain your reasoning.
Yes, I can help them determine how they did within their respective groups. A higher Z-score indicates a faster time compared to the average for their group, while a lower Z-score indicates a slower time.
To do this, we will calculate the standard score or Z-score for each of them, which measures how many standard deviations above or below the mean their finishing time was. Calculation is as follows:
For Leo:
Z = (4948 - 4313) / 583 = 1.01
For Mary:
Z = (5513 - 5261) / 807 = 0.33
So, Leo finished 1.01 standard deviations above the mean for the Men, Ages 30 - 34 group, while Mary finished 0.33 standard deviations below the mean for the Women, Ages 25 - 29 group.
As for your second question, if the distributions of finishing times were not nearly normal, then the values of the standard score would change. This is because the standard score is calculated using the mean and standard deviation, which are important parameters of a normal distribution, these parameters may not accurately represent the data, and therefore the standard score would not be an accurate measure of relative performance.
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help me please !!!!!!!!!!!!!!!!!!!!!!!!!!!!! asap
Answer:
Step-by-step explanation:
2
linda wants new carpeting for her bedroom her bedroom is a 75m by 50m rectangle if carpeting cost AED 12 per square meters how much will it cost to lay carpet for her entire bedroom?
please answer as soon as possible i need this question
The required cost to lay carpet for her entire bedroom is 45,000.
What is rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form.
According to question:To calculate the cost of carpeting Linda's bedroom, we need to find the area of the rectangle:
Area = length x width
Area = 75m x 50m
Area = 3750 square meters
Then, we can multiply the area by the cost per square meter of carpeting:
Cost = Area x Cost per square meter
Cost = 3750 square meters x AED 12/square meter
Cost = AED 45,000
Therefore, it will cost AED 45,000 to lay carpet for Linda's entire bedroom.
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will give brainliest plss!!!!! helpleleepepPLS!
i numbered all of them so it would be easy for you to tell me them in order, hope it helps ):
“Sort these cards into 2 Piles.”
The relation which are function is shown below.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x.The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range.
We know that a relation is said to be function if one input have only one output.
1. The relation is not function because the input 6 have two output values
5 and 10.
2. The relation is a function because the each input have one output values.
3. The relation is a function because the each input have one output values.
4. The relation is not function because the input 4 have two output values .
5. The relation is a function because the each input have one output values.
6. The relation is not function because the input have two output values.
7. The relation is a function because the each input have one output values.
8. The relation is not function because the input have two output values.
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Help please, I’m not sure what to put
The congruency theorem used in each of the triangles are;
14) HL Congruency Theorem.
15) Neither
16) Neither
17) SAS Congruency theorem.
18) Neither
19) AAS congruency theorem.
20) Neither
21) SSS congruency postulate.
How to find the triangle congruency proof?14) We are given the hypotenuse side and leg as being congruent and as such the congruency proof here is; HL Congruency Theorem.
15) We are not given any congruent side nor angle and as such we can't determine if they are congruent.
16) We two congruent sides and non-included angle and as such they are not congruent.
17) We are given two congruent sides and the included congruent angle and as such the triangles are congruent by SAS Congruency theorem.
18) We two congruent sides and non-included angle and as such they are not congruent.
19) We are given two congruent angles and the non included side and as such they are congruent by AAS congruency theorem.
20) We two congruent sides and non-included angle and as such they are not congruent.
21) The three sides are shown to be congruent and therefore it is congruent by SSS congruency postulate.
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Pls help will mark Brainly est pls help 100 points please
1. Another point on the graph p(x) is (5, 9)
2. the vertex of the q(x) is (4, 10).
The other two points on the q(x) are (0, 2) and (2, 8).
What is a parabola?Parabola is a curve drawn in a plane. Where any point is at an equal distance from a fixed point (the focus ) and a fixed straight line (the directrix ).
Given:
The two equations of the quadratic functions are;
p(x) = -(x - 1)² + 10
q(x) = 1/2(x - 4)² + 10.,
The graph of p(x) and q(x) is given in the image below.
1. Another point on the graph p(x) is (5, 9)
2. the vertex of the q(x) is (4, 10).
The other two points on the q(x) are (0, 2) and (2, 8).
3. Yes the assumption is correct.
Therefore, all the required values are given above.
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Solve the radical equation by drawing your answers below. Be sure to show all your work
The solution to the radical equation is given as follows:
x = 1.
How to solve the radical equation?The radical equation for this problem is defined as follows:
1/x + (x - 1)/9x = 1.
To leave the left side with a common denominator, we can multiply 1/x by 9 in the numerator and in the denominator, hence:
9/9x + (x - 1)/9x = 1.
As the left side has a common denominator, we can add the numerators and keep the denominator constant, as follows:
(9 + x - 1)/9x = 1
(8 + x)/9x = 1.
Applying cross multiplication, the value of x is obtained as follows:
9x = 8 + x
8x = 8
x = 8/8
x = 1.
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How many solutions does each system of equations have? Explain how you
can tell.
a. x + 6y = 19
x - 6у = 13
b. 8x +y = 3
-8x - y = 3
Add.
Your answer should be an expanded polynomial in standard form.
(−5n^4+ 8) + (5n^4 + 8n³ + 3n²) =
Answer:
8n^3 + 3n^2 + 8
Step-by-step explanation:
What is the value of 150kg in pounds
Answer:
Step-by-step explanation:330.693 lbs
Oliver is going on a 200 mile trip.
He leaves at 10 am and travels for
3 hours at an average speed of 38 mph.
How fast would he need to travel for the
remainder of his journey in order to arrive
at 3 pm?
Answer:
We know it's 1 P.M., and he's traveled 114 miles by now, he needs to go 86 more miles before he reaches his destination. He would need to travel 43 mph to reach his destination by 3.
Step-by-step explanation:
At 1, he has two more hours, and he has 86 more miles to go, so four times two is 8, and 3 times two is 6, so 46. There's probably a proper way to do this but yup 43 mph I hope I'm right and I helped you out :')
Answer:
Oliver would need to travel 43 mph for the remainder of his journey.
Step-by-step explanation:
First, we need to find out how many miles Oliver traveled for those 3 hours.
3 speed × 38 mph = 114 mph in total.
Now we need to know how many remaining miles Oliver needs to travel.
200-mile trip - 114 miles driven = 86 miles left.
Next, We need to know what time Oliver is currently at to know how many hours he needs to travel until it's 3 pm.
10 am + 3 hours = 1 pm
So, we have 2 hours left until it's 3 pm. Oliver needs to go 86 miles in 2 hours to arrive at his destination. So then divide the 86 miles by those 2 hours.
86 miles left ÷ 2 hours = 43 mph
Each marvel bag sold by Amy's marble company contains 7 red marbles for every 4 orange marble. If a bag has 28 orange marbles, home many red marbles does it contain
If a bag has 28 orange marbles, then it contain 49 red marbles.
What is ratio?A ratio is a comparison of two quantities or values, expressed in the form of a fraction or a division. Ratios are used to compare the size, magnitude, or quantity of two or more quantities or values.
For example, if there are 10 apples and 5 oranges, we can write the ratio of apples to oranges as 10:5 or 2:1, since there are two times as many apples as oranges. Similarly, if a recipe calls for 3 cups of flour and 1 cup of sugar, we can write the ratio of flour to sugar as 3:1, indicating that there are three times as much flour as sugar.
Ratios can be simplified, converted to equivalent fractions or decimals, or used to solve problems involving proportional relationships between different quantities. They are widely used in many areas of mathematics, science, and everyday life, such as in finance, engineering, and statistics.
According to given condition :We can start by using the given ratio of 7 red marbles for every 4 orange marbles to find the ratio of red marbles to orange marbles in the bag.
For every 4 orange marbles, there are 7 red marbles, so we can write:
7 red marbles / 4 orange marbles
We can simplify this ratio by dividing both the numerator and denominator by their greatest common factor, which is 1 in this case. This gives:
7/4
So the bag contains 7 red marbles for every 4 orange marbles.
If the bag has 28 orange marbles, we can use this ratio to find the number of red marbles in the bag. We can set up a proportion:
7/4 = x/28
where x is the number of red marbles in the bag.
To solve for x, we can cross-multiply:
7 × 28 = 4 × x
196 = 4x
Dividing both sides by 4, we get:
x = 49
Therefore, the bag contains 49 red marbles.
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Three small equilateral triangles of the same size are cut from the corners of a larger equilateral triangle with sides of 6 cm, as shown. The sum of the perimeters of the three small triangles is equal to the perimeter of the remaining grey hexagon. What is the side length of the small triangles?
The side length of the small equilateral triangles is 3 cm.
What is the side length of the small triangleLet's call the side length of the small equilateral triangles "x". Since there are three small triangles, the total perimeter of the small triangles is 3x.
The side length of the large equilateral triangle is 6 cm, so each side of the small triangles is a portion of 6 cm. Specifically, each side of the small triangles is (1/2) of a side of the large triangle.
Therefore, the perimeter of each small triangle is 3x, which is made up of three sides of length (1/2)6 cm or 3 cm. So we have:
3x = 3(3 cm) = 9 cm
Solving for x, we get:
x = 3 cm
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What measure is equivalent to 3/4
Answer: 12 tablespoons
Step-by-step explanation: 3/4 of a cup is equal to 6 fluid ounces or 12 tablespoons.
The team manager has a large cylinder water cooler that measures 14 inches in diameter and is 20 inches tall. She wants to fill the players' cylindrical water bottles that are each 3 inches in diameter and 10 inches tall. If the cooler is full how many water bottles can she completely fill?
The total number of bottles that can be filled are 41.
What is area of cylinder?
One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.
the volume of a cylinder is given by the formula as
Volume of cylinder = πr²h,
where r is the radius of the cylinder and h is its height.
We are given the radius of the water cooler is 7 inches
also the height of water cooler is 20 inches.
We calculate its volume by substituting the values in the volume formula
Volume of the cooler = π(7²)(20)
Volume of the cooler = 2,940π cubic inches
Now also we given the radius and height of the bottles
We similarly calculate the volume of each bottle by substituting the values in the formula
Volume of the bottle = π(1.5²)(10)
Volume of the bottle = 70.685π cubic inches
Now finally to find the total number of bottles we divide the volume of cooler by the volume of bottles we get
Number of bottles = Volume of the cooler / Volume of the bottle
=2,940π) / (70.685π)
=41
Therefore, the team manager can completely fill about 41 water bottles.
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please help ill give brainliest!!
1.
a) Length = 6 inches
Width = 2 inches
Height = 7 inches
Base Area = 6 x 2 = 12 inches
b) V = l x w x h = 6 x 2 x 7
c) V = B x h = 12 x 7
d) V = 84 inches cubed
Answer: explained below (answers you need to fill in are in bold)
Step-by-step explanation:
1.
a. the dimensions of the box are
l = 6
w = 2
h = 7
B = 12 ... B means base. When finding base, you simply just multiply L x W. In this case, you do 6 x 2 = 12 which will be your base
b.
V = l x w x h = 6 x 2 x 7
c.
V = B x h = 12 x 7
d.
V = 84 ... ( 12 x 7 = 84)
Brainliest
What is the correct standard form of the equation of the parabola?
Enter your answer below. Be sure to show each step of your work.
You dont have to answer if you dont know..
The correct standard form of the equation of the parabola is,
⇒ y = 1/4(x - 2)² - 5
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now, We know that;
The equation of the parabola with vertex (h, k) is,
⇒ y = a(x - h )² + k
Thus, The equation of the parabola is,
⇒ y = a(x - 2)² - 5
To find a, use the fact that the parabola passes through the point (4,−4):
⇒ - 4 = 4a - 5
Solving this equation, we get;
⇒ a = 1/4.
Thus, The equation of the parabola is,
⇒ y = 1/4 (x - 2)² - 5
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which expression is equal to 8/3 A.3 x 1/8 B. 8 x 1/3 C.8 x 1/8 D.3 x 1/3
Answer:
B. 8*1/3
Step-by-step explanation:
Each marble bag sold by Omar's Marble Company contains 4 green marbles for every 3 yellow marbles. If a bag has 28 green marbles, how many yellow
marbles does it contain?
Answer: it contains 21 yellow marbles
Step-by-step explanation:
x = 28 x 3/4
canceling method
x = 7 x 3
x = 21
PLEASE HELP!!
Write an equation that can used to find the height of the water after x number of minutes. Use the equation to find the height of the water after 10 minutes.
The height of the water after 10 minutes would be ___ centimeters.
The equation to find the height of the water after x minutes is height = = 3 x + 50.
The height of the water after 10 minutes would be 80 centimeters.
How to find the heights of the water ?To find the height of the water, the formula that can be used is :
= rate of change x number of minutes + starting height
Rate of change :
= Change in height / Change in minutes
= ( 53 - 50 ) / ( 1 - 0 )
= 3 / 1
= 3
The equation is therefore:
= 3 x + 50 ( this is the height at 0 minutes)
At 10 minutes, the height would be:
= 3 ( 10 ) + 50
= 30 + 50
= 80 minutes
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I don’t know how to do this please help it’s #11 btw thx in advance
The values of x and y are:
x = 3.16
y = 4.47
What is trigonometry?Trigonometry is a topic which deals with the relation between angles and sides of a right angled triangle. It can be used to determine the value of the unknown in a given question. The basic functions in trigonometry are: sine, cosine and tangent.
In the given diagram, we have;
i. To determine the value of x,
Tan θ = opposite/ adjacent
Tan 45 = x/ (10)^1/2
x = Tan 45*(10)^1/2
= 3.16
x = 3.16
ii. To determine the value of y, we have;
Cos θ = adjacent/ hypotenuse
Cos 45 = (10)^1/2 / y
y = (10)^1/2 / Cos 45
= 4.47
y = 4.47
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Guys please help it’s urgent
Use the associative property to simplify the expression 59 + 40 + 80
A. 59+80+40=139+40=179
B.59+(40+80)=59+120=179
C.59+40+80=99+80=179
D.59+10(4+8)=59+10(12)=59+120=179
59+(40+80)=59+120=179 is implify the expression by Associative property .
What is the associative property?
A mathematical principle known as the associative property states that the product of a multiplication problem is unaffected by the way the factors are organized.
The associative quality of addition The amount remains unchanged when the order of the addends is changed. By way of illustration, (2 + 3) + 4 = 2 + (3 + 4) (2+3)+4=2+(3+4) 2. plus, left parenthesis, 3. plus, 4. right parenthesis = 2. plus. left parenthesis, 3. plus. right parenthesis.
Associative property
(59 + 40) + 80 = 59 + (40 + 80)
(99) + 80 = 59 + (120)
179 = 179
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Dayton Photography Studio is taking graduation portraits for students at local schools.
Eighth graders from Dayton Elementary School ordered 50 basic portrait packages and 52
deluxe portrait packages, for a total of $8,544. The seniors at Greenwood High ordered 93
basic portrait packages and 73 deluxe portrait packages, for a total of $13,591. How much
does each type of package cost?
4) A basic package costs $
and a deluxe package costs $
The basic portrait packages costs $70 and deluxe portrait packages costs $97.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the basic portrait packages costs $x.
and, the deluxe portrait packages costs $y.
So, the system of Equation
50x + 52y = 8544..............(1)
93x + 73y = 13591.............(2)
Solving above two equation we get
x=70 and y= 97.
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