From the statement, we know that there are two possible scenarios:
A) Kira rolls the die and gets a face with a 1, 2, 3, 4, 5 or 6.
• The probability of this event is P(A) = 1/12.
,• Kira will write the number of the face in this case.
B) Kira rolls the die and gets an edge.
• The probability for this event is 1/24.
,• Kira will write the sum of the numbers that share the top edge.
,• There are multiple values for the result of the sum.
We must take into account that:
• 1 and 5 are on opposite faces,
,• 2 and 3 are on opposite faces,
,• 4 and 6 are on opposite faces.
The possible values of the sum and the forms to get it are:
0. 3, = 1 + 2 → P(B'_1) = 1/24
,1. 4, = 1 + 3 → P(B'_2) = 1/24
,2. 5, = 1 + 4 → P(B'_3) = 2/24
,3. 6, = 2 + 4 → P(B'_4) = 2/24
,4. 7, = 1 + 6 = 2 + 5 = 3 + 4 → P(B'_5) = 3/24
,5. 8, = 2 + 6 = 3 + 5 → P(B'_6) = 2/24
,6. 9, = 3 + 6 = 4 + 5 → P(B'_7) = 2/24
,7. 11, = 5 + 6 → P(B'_9) = 1/24
We have 8 possible results for the sum.
---------------------
Now, we want to know the value of the expected value of the numbers recorded by Kira.
By definition, the expected value is calculated by multiplying each of the possible outcomes by the likelihood that each outcome will occur and then summing all of those values.
The expected value of the number recorded by Kira will be:
[tex]E=\sum_{i\mathop{=}1}^6A_i\cdot P(A_i)+\sum_{i\mathop{=}1}^8B_i\cdot P(B_i)[/tex]Where:
• A_i represents the result of event A_i and P(A_i) its probability,
,• B_i represents the result of event B_i and P(B_i) its probability.
Using the data from above, we compute each of the sums.
A) For the first sum, we take into account that each event A_i has the same probability:
[tex]\sum_{i\mathop{=}1}^6A_i\cdot P(A_i)=(1+2+3+4+5+6)\cdot\frac{1}{12}=\frac{7}{4}=1.75.[/tex]B) For the second sum, we use each of the values of the sum and the probabilities of each sum:
[tex]\begin{gathered} \sum_{i\mathop{=}1}^8B_i\cdot P(B_i) \\ =3\cdot\frac{1}{24}+4\cdot\frac{1}{24}+5\cdot\frac{1}{24}+6\cdot\frac{1}{24}+7\cdot\frac{3}{24}+8\cdot\frac{2}{24}+9\cdot\frac{2}{24}+11\cdot\frac{2}{24}=\frac{95}{24}. \\ \end{gathered}[/tex]Summing the results of each sum, we get the following result for the expected value:
[tex]E=\frac{7}{4}+\frac{95}{24}=\frac{42}{24}+\frac{95}{24}=\frac{137}{24}\cong5.71.[/tex]AnswerThe expected value for the number recorded is 137/24 or approximately 5.71.
if a person invests $120 at 8% annual interest, find the approximate value of the investment at the end of 5 years
Answer:
$48
Step-by-step explanation:
Simple interest (I) = PRT/100
Where P = principal
R= rate
T = time
.: Simple Interest = 120 × 8 × 5
---------------
100
S. I = $48
.: the approximate value of the investment at the end of 5 years will be = $48
Find the axis of symmetry using the formula. X = -b/2a
x = 2
Explanation:f(x) = -2x² + 8x - 9
Comparing this function with f(x) = ax² + bx + c
a = -2, b = 8, c = -9
The axis of symmetry is given by the formula:
x = -b/2a
Substitute a = -2 and b = 8 into the formula:
[tex]\begin{gathered} x=\frac{-8}{2(-2)} \\ \\ x=\frac{-8}{-4} \\ \\ x=2 \end{gathered}[/tex]x = 2
PLS HELP MEEEEEEEEEEEEEEEEEEEEE PLS I BEG U
how could you use a graph of a proportional relationship to find any ratio in the the proportional relationship why does this work?
A graph of a proportional relationship can be used to find any ratio in the proportional relationship when the graph passes through the origin.
How to illustrate the information?A connection is proportional if its graph is a line that goes through the origin. The ratio is not proportionate if it is not a line or ray that doesn't accomplish this. K = y/x is the equation for the proportionality constant. The equation for the slope of a straight line with respect to the origin is the same as this.
A relationship is proportionate if its graph is a line or ray that passes through the origin. It is not proportionate if the line or ray does not go through the origin. Additionally, something is not proportionate if it is not linear.
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Where does the line through (1, 0, 1) and (4, −4, 4) intersect the plane x + y + z = 6?
The line through (1, 0, 1) and (4, −4, 4) intersect the plane x + y + z = 6 at point (7,-8,7).
As given,
Equation of the line passes through two points (1, 0, 1) and (4, −4, 4) is:
[tex]\frac{x-4}{4-1}=\frac{y+4}{-4-0}=\frac{z-4}{4-1}[/tex]
From the above equation we have
(x-4)/3 =(y+4)/-4
⇒-4x+16= 3y+12
⇒y=(-4x +4)/3 __(1)
And
(x-4)/3=(z-4)/3
⇒z=x __(2)
Substitute the value of y and z in the plane x +y+ z=6 to get point of intersection of line and plane
x+ [(-4x +4)/3] +x=6
⇒3x-4x+4 +3x =18
⇒2x=14
⇒x=7
Substitute value of x in (1) and (2)
y=-8 and z=7
Therefore, the line through (1, 0, 1) and (4, −4, 4) intersect the plane x + y + z = 6 at point (7,-8,7).
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he formula in cell C2 is =A$2. Autofill is used by dragging C2's autofill box across to D2, E2, and F2. What formulas will appear in D2, E2, and F2, respectively?
B$2, C$2, D$2
B$2, B$3, B$4
A$2, A$3, A$4
C$3, C$4, C$5
The formulas that will appear in D2, E2, and F2, respectively are
B$2, C$2, D$2. Option A
This is further explained below.
What is a formula?Generally, A mathematical formula or a chemical formula, for example, are both examples of formulas, which are condensed ways of expressing information via the use of symbols.
When used informally within the realm of science, the word "formula" refers to the overall construction of a connection between a set of determinable variables.
Because of the formula =A$2, row 2 is considered to be anchored.
At this point, D2 is located to the right of C2, but still in the same row.
And the cell that is direct to the right of A2 is labeled B2.
As a result, the formula for D2 will equal B times 2.
In the same manner, the formula in E2 will be C$2, and the formula in F2 will be D$2.
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hi, please help!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
2/17, 8/17, and 11/17
7/21, 7/18, 7/14, 7/12, and 7/8
2/12, 2/10, 2/8, 2/6, and 2/4.
Step-by-step explanation:
the order would be 2/17, 8/17, and 11/17 since the bottom number (denominator) stays the same while the numerator (top number) increases.
the order for the 2nd one would be:
7/21, 7/18, 7/14, 7/12, and 7/8. The reason for this is that when the numerator stays the same and the denominator increases, the value of the fraction decreases. For example, 1/2 is greater than 1/4, and 1/4 is more than 1/5 because 5 is greater than 4. This only works when the numerator (top number) stays the same.
The order for the 3rd one would be:
2/12, 2/10, 2/8, 2/6, and 2/4. Again, the numerator stays the same while the denominator changes. As the denominator goes down, the value of the fraction goes up.
Also if possible label your question the correct difficulty this is like middle school not college
The table shows negative integers to represent the lowest elevations below sea level on each of the 7 continents.
Which continent has a lower elevation than North America?
The continents that have a lower elevation than North America are Africa and Asia.
What is elevation?It should be noted that elevation simply had to do with the height above sea level of a particular thing. Any of numerous huge landmasses is referred to as a continent. Up to seven geographical regions are usually regarded as continents, based on convention rather than precise requirements.
A continent is one of the seven major land divisions on Earth. Asia, Africa, North America, South America, Antarctica, Europe, and Australia are the continents, in order of size.
In this case, the table shows negative integers to represent the lowest elevations below sea level on each of the 7 continents.
In the table, Africa has -512 and Asia had -1312. It should be noted that these are lower than in North America.
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Find the average of
8,11,14,13,14, 9,15
Answer:
12
Step-by-step explanation:
(8+11+14+13+14+9+15)/7 = 12
Answer:
MedianTotal obs. = 7
if odd —Average = (n + 1 )/2
n = no. of obs.Average = 7 + 1 /2
= 8/2 = 4th obs.
=> 13Mean= Sum of obs./ Total obs.
= 8,11,14,13,14,9,15/7
= 84/7
=> 12Kendra spent $22 on 11 song downloads. How much did each song cost?
Answer:
$2
Step-by-step explanation:
To find the unit cost, divide the entire price of all the songs (22), by how many songs you bought (11)
22 Dollars / 11 Songs = 2 Dollars / Song (2 Dollars per Song)
A traditional individual retirement account (IRA) is a special type of retirement account in which the money you invest is exempt from income taxes until you withdraw it. If you deposit $100
each month into an IRA earning 6% interest, how much will you have in the account after 20 years?
[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the end of the period}}{\textit{Future Value of an ordinary annuity}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right] \\\\\\ ~~~~~~ \begin{cases} A=\textit{accumulated amount}\\ pmt=\textit{periodic payments}\dotfill &100\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{each months, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases}[/tex]
[tex]A=100 \left[ \cfrac{\left( 1+\frac{0.06}{12} \right)^{12 \cdot 20}-1}{\frac{0.06}{12}} \right] \\\\\\ A=100 \left[ \cfrac{\left( 1.005 \right)^{240}-1}{0.005} \right]\implies A \approx 46204.09[/tex]
i need help please plaeswwosadcwefcuwn
The true statement is that both √15 and √0.001 are irrational , the correct option is (c).
Rational Numbers can be defined as the numbers that can be expressed in the form of p/q , where p and q are integers and q not equal to 0 .
For Example : 2/3 , 2, 8/3 are all Rational Numbers.
Irrational Numbers can be defined as the numbers that cannot be expressed in the form of p/q where , p and q are integers and q not equal to 0 .
For Example : √2 , √37 are irrational as they cannot be expressed in the form of p/q.
In the question ,
two numbers √15 and √0.001 are given .
the first number √15 is not a perfect square , hence not an integer ,
So, √15 is an irrational number .
the second number
√0.001 = √(1/1000) = 1/√1000 = [tex]\frac{1}{10\sqrt{10} }[/tex]
we see that √10 is not an integer , hence √0.001 is an irrational number .
Therefore , the true statement is that both √15 and √0.001 are irrational , the correct option is (c).
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Question 2(Multiple Choice Worth 2 points)
(02.05 MC)
Solve x2 + 12x+6=0 using the completing-the-square method.
Answer:
Hhhhhhhhhhhhhhhhhh : x=-2
Jenny ended a hike at an elevation of 3, 000 feet above sea level.
She had started at an elevation of 2, 000 feet above sea level.
Which integer represents Jenny's change in elevation?
-1000 represents Jenny's change in elevation.
What is an integer?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers. The boldface Z is a common mathematical symbol for the set of integers. A number that contains both positive and negative integers, including zero, is called an integer. There are no fractional or decimal parts in it. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043.
Given Data
Jenny ended a hike at an elevation of 3, 000 feet above sea level.
She had started at an elevation of 2, 000 feet above sea level.
Hike remaining = 3000 - 2000
Hike remaining = 1000
-1000 represents Jenny's change in elevation.
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I need help with this question.
Given:
There is a graph given in the question
Required:
We want to find the solution of the given graph
Explanation:
As we can see that, both lines are parallel so there is no chance for intersection
now if there is no intersection point means there is no solution
Final answer:
No solution
pelase slove these two problem i will give out those crown thingy!
Answer: $2.75
Step-by-step explanation:
2) Judy spent 3*5.25 = 15.75 on popcorn bags, 13.60 on a jumbo bag of chips and 7.90 for a dip. This means that overall she spent $37.25. If she had $40, this means that she have left $40 - $37.25 = $2.75.
1) Your answer is right.
Given f(x) = 3(4-x), what is the value of f( − 2)? Enter your answer in the answer box.
Answer:
f(-2) = 18
Step-by-step explanation:
In order to calculate a function of x, we replace x
For example
f(x) = x
f(-2) = -2
In this specific scenario
f(x) = 3 * (4 - x)
f(-2) = 3 * (4 - -2)
- -2 turns positive
f(-2) = 3 * (4 + 2)
Now we use PAMDAS (parentheses, exponents, multiplication, division, addition) as an operation order, so we first solve the parantheses
f(-2) = 3 * 6
f(-2) = 18
I sent pic for help.
Answer:Explanation:
• T
,• 0.320
The player's on-base percentage = 0.320
This is equally the relative frequency of the player being on base.
Thus, the appropriate method is the relative frequency method.
Thus, the probability that the player will get on base in his next appearance is 0.320.
Order these numbers from least to greatest
6.3071, 6.7 6.408, 6.47
Answer:
6.3071, 6.408, 6.47, 6.7
Step-by-step explanation:
6.3071, 6.408, 6.47, 6.7, hope this helped!
Answer:
In bold below.
Step-by-step explanation:
6.3071, 6.7 6.408, 6.47
= 6.3071, 6.408, 6.47, 6.7
HELPPPP PLEASEEE!!!
(MATH AND CHEMISTRY RELATED)
Reynado ordered 12 large pepperoni pizzas. The total cost was $101.40. Write a direct variation function for the cost of one large pepperoni pizza. How much would 5 large pepperoni pizzas cost?
Answer:
(1) y = 8.45x
(2) Total cost: $42.25
Step-by-step explanation:
Let's see by constructing a first-hand example of the information we have.
$101.40 = 12x
Divide 12 on both sides.
When we divide 12 from both sides, we get the simplified answer of:
x = 8.45
This means that each pizza will be $8.45 each, therefore this will be out=r equation
y = 8.45x
(where x is the number of pizzas and y is the total amount cost.
To find the cost of 5large pepperoni pizzas, we use our equation above (y = 8.45x) and input a 5 in x;
y = 8.45(5)
y = 42.25
The total cost for the 5 pizzas will be $42.25.
Given the diagram below as shown, find the value of x, y, and m
The unknown variables and angles are as follows:
x = 10y = -5m∠YTE = 36°How to find angles?The sum of angles on a straight line is 180 degrees.
Therefore, the sum of angles on line STA is 180 degrees.
CT bisect STE
Angle STE Is a right angle.
Therefore,
5x + y + 3 + 3x + 12 = 90
5x + 3x + y + 12 + 3 = 90
8x + y + 15 = 90
8x + y = 90 - 15
8x + y = 75
Ty bisect ETA
Angle ETA Is a right angle.
Therefore,
y + 41 + 5x + 4 = 90
5x + y + 45 = 90
5x + y = 90 - 45
5x + y = 45
Combine the equation
8x + y = 75
5x + y = 45
subtract equation(ii) from equation(i)
3x = 30
x = 30 / 3
x = 10
y = 75 - 80
y = -5
Therefore,
m∠YTE = y + 41 = -5 + 41 = 36°
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1) A gallon jug of milk is 3/4 full. After breakfast the jug is 1/12 full. How much milk did your family have at breakfast?
well, your family really ate "x" for breakfast, was pretty good with cereal and strawberries btw.
let's keep in mind that the LCD of the denominators 4 and 12 is "12", so we'll use that to do away with the denominators.
[tex]\stackrel{\textit{before breakfast}}{\cfrac{3}{4}}~~ - ~~\stackrel{for~breakfast}{x}~~ = ~~\stackrel{leftover}{\cfrac{1}{12}} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{3}{4}-x \right)~~ = ~~12\left( \cfrac{1}{12} \right)}\implies 9-12x=1 \\\\\\ 9=12x+1\implies 8=12x\implies \cfrac{8}{12}=x\implies {\Large \begin{array}{llll} \cfrac{2}{3}=x \end{array}}[/tex]
question is in box and you don’t need to show work if you don’t want to
ANSWER:
8 square meters
STEP-BY-STEP EXPLANATION:
To calculate the area of the sector, we must first calculate the area of the entire circle and then by means of a proportion, knowing that the entire area is 360° and the sector is 45°, we could determine the area we need.
Just like this:
[tex]\begin{gathered} A_c=\pi\cdot r^2 \\ \\ \text{ We replacing:} \\ \\ A_c=\pi\cdot8^2=64\pi \\ \\ \text{ Therefore, we calculate the value of the area of the sector as follows:} \\ \\ A_s=64\pi\cdot\frac{45\degree}{360\degree} \\ \\ A_s=8\pi\text{ square meter} \end{gathered}[/tex]The area of the sector is 8 square meters
The following table shows the profit rates for Nike and Adidas
Nike -2 (x - 2)
Adidas -17 + x
If x represents the number of shoes purchased, how many shoes have to be purchased until both companies earn the same amount? Create and solve the equation.
The number of shoes that have to be purchased until both companies earn the same amount is 21.
How to calculate the number of shoes?Based on the information, the profit rates for Nike and Adidas are illustrated as:
Nike -2 (x - 2)
Adidas -17 + x
In this case, x represents the number of shoes purchased,
The number of shoes that have to be purchased until both companies earn the same amount will. be:
2(x - 2) = 17 + x.
2x - 4 = 17 + x
2x - x = 17 + 4
x = 21
The number of shoes will be 21.
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Please help na po need na po talaga, please correct answers po brainliest
Directions: Draw a Venn diagram and list the elements of each given set. Input your answer inside each box. Enclose your answer with braces and do not put a space in between characters or numbers. Refer to the sample item below.
Sample Given: A ∩ B
Sample Answer: {2,3}
Let A= {1, 2, 3, 4, 5} B = {2, 3, 5, 7, 11}, C= {3, 5, 7, 9}
1.) A ∪ B ∪ C =
3.) (A – B) ∩ C =
5.) A' ∪ B =
The set A ∪ B ∪ C will be {1, 2, 3, 4, 5, 7, 9, 11}, (A – B) ∩ C is ∅, and A' ∪ B is {2, 3, 5, 7, 9, 11}.
What is the Venn diagram?It is defined as a diagram that shows a logical relation between sets.
The Venn diagram consists of circles to show the logical relation.
The universal set will be:
U = {1, 2, 3, 4, 5, 7, 9, 11}
Let:
A = {1, 2, 3, 4, 5}
B = {2, 3, 5, 7, 11},
C= {3, 5, 7, 9}
1) A ∪ B ∪ C = {1, 2, 3, 4, 5, 7, 9, 11}
3) (A – B) ∩ C = {1, 4} ∩ C= {3, 5, 7, 9}
(A – B) ∩ C = ∅
5) A' ∪ B = {7, 9, 11} ∪ {2, 3, 5, 7, 11}
A' ∪ B = {2, 3, 5, 7, 9, 11}
Thus, the set A ∪ B ∪ C will be {1, 2, 3, 4, 5, 7, 9, 11}, (A – B) ∩ C is ∅, and A' ∪ B is {2, 3, 5, 7, 9, 11}.
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The skeletal system is not responsible for which of the following?
Answer now
D. moving red blood cells around the body
left on together, the cold and hot water faucets of a certain bathtub take 8 minutes to fill the tub. If it takes the hot water faucet 18 minutes to fill the tub by itself how long will it take the cold water faucet to fill the tub on its own
The time taken to fill the bathtub by cold water is 14.4 minutes.
Given,
Time taken to fill a bathtub by both cold and hot water = 8 minutes
Time taken to fill the bathtub by hot water = 18 minutes
Time taken to fill the bathtub by cold water = t minutes
We have to find t.
We can take the full bath tub as 1.
Now,
We can equate the given data:
We get,
(8/18) + (8/t) = 1
Now, solve the equation:
((8 × t) + (8 × 18) ) ÷ (18 × t) = 1
(8t + 144) ÷ 18t = 1
8t + 144 = 18t
18t - 8t = 144
10t = 144
t = 144/10
t = 14.4
That is,
The time taken to fill the bathtub by cold water is 14.4 minutes.
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Point A is 3 units to the right of, and 20 units lower than, point B. Find the
slope of the line connecting points A and B.
O 20
3
O 20
3
O
-17
3
20
Answer:
02987329619
Step-by-step explanation:
02987329619
Answer:
kk
Step-by-step explanation:
How can you transform the equation 8x - 10 + 10 + 4x = -10 + 6x + 6x + 10 into the form of a = a, where a is a number, to show that the equation has an infinite number of solutions? Select all that apply.
A. by adding 12x to both sides of the equation and then simplifying
B. by subtracting 8x to both sides of the equation and then simplifying
C. by subtracting 12x from both sides of the equation then simplifying
D. by subtracting 20 from both sides of the equation then simplifying
E. by dividing 6x from both sides of the equation and then simplifying
Step-by-step explanation:
Simplifying
8x + -10 + 10 + 4x = -10 + 6x + 6x + 10
Reorder the terms:
-10 + 10 + 8x + 4x = -10 + 6x + 6x + 10
Combine like terms: -10 + 10 = 0
0 + 8x + 4x = -10 + 6x + 6x + 10
8x + 4x = -10 + 6x + 6x + 10
Combine like terms: 8x + 4x = 12x
12x = -10 + 6x + 6x + 10
Reorder the terms:
12x = -10 + 10 + 6x + 6x
Combine like terms: -10 + 10 = 0
12x = 0 + 6x + 6x
12x = 6x + 6x
Combine like terms: 6x + 6x = 12x
12x = 12x
Add '-12x' to each side of the equation.
12x + -12x = 12x + -12x
Combine like terms: 12x + -12x = 0
0 = 12x + -12x
Combine like terms: 12x + -12x = 0
0 = 0
Solving
0 = 0
Couldn't find a variable to solve for.
This equation is an identity, all real numbers are solutions.
Simplifying
8x + -10 + 10 + 4x = -10 + 6x + 6x + 10
Reorder the terms:
-10 + 10 + 8x + 4x = -10 + 6x + 6x + 10
Combine like terms: -10 + 10 = 0
0 + 8x + 4x = -10 + 6x + 6x + 10
8x + 4x = -10 + 6x + 6x + 10
Combine like terms: 8x + 4x = 12x
12x = -10 + 6x + 6x + 10
Reorder the terms:
12x = -10 + 10 + 6x + 6x
Combine like terms: -10 + 10 = 0
12x = 0 + 6x + 6x
12x = 6x + 6x
Combine like terms: 6x + 6x = 12x
12x = 12x
Add '-12x' to each side of the equation.
12x + -12x = 12x + -12x
Combine like terms: 12x + -12x = 0
0 = 12x + -12x
Combine like terms: 12x + -12x = 0
0 = 0
Solving
0 = 0
Couldn't find a variable to solve for.
This equation is an identity, all real numbers are solutions.
9h - 27 What is the greatest common?factor Expand the expression
Given
9h-27
Answer
[tex]\begin{gathered} 9h-27 \\ 9(h-3) \\ \end{gathered}[/tex]Greatest common factor = 9