Probability = number of desired event occurrences/number of events in sample space = 9/36 = 1/4
What is meant by probability?Probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely it is that a claim is true. The probability of an event is a number between 0 and 1, with 0 signifying impossibility and 1 expressing certainty.
A compound event is made up of two separate events.
Here is a table of probable sums of two die rolls. Die 1 and Die 2 values are listed along the side and top. The figures are roughly near the middle. The sum of Die 1 = 2 and Die 2 = 2 is 4, for example.
Die 2
Die1 1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
Rolling two dice yields 6 * 6 = 36 possible outcomes, or 36 possible sums. There are 36 occurrences in the sample space.
Looking at the table, a 3 or a 9 happens as the sum 9 times, resulting in 9 of the 36 potential occurrences having a sum of 3 or 9.
Probability = number of desired event occurrences/number of events in sample space = 9/36 = 1/4
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Vesa has two different choices to buy popcorn at the movie
theater. She can buy them in cylinder-shaped boxes with a
length of diameter 20cm and length of height 40cm, or with
a length of diameter 30cm and length of height 20cm.
Which box should Vesa choose if she wants to buy more
popcorn?
Answer:
She should choose the second cylinder-shaped box with a diameter of 30 cm and a height of 20 cm.
Step-by-step explanation:
The volume of a cylinder with a diameter of 20 cm (radius of 10 cm) and a height of 40 cm:
[tex]V=\pi{r^2h}[/tex]
[tex]V=\pi{(10^2)(40)}[/tex]
[tex]V\approx{12566.37\text{ cm}\textsuperscript{3}}[/tex]
The volume of a cylinder with a diameter of 30 cm (radius of 15 cm) and a height of 20 cm:
[tex]V=\pi{r^2h}[/tex]
[tex]V=\pi{(15^2)(20)}[/tex]
[tex]V\approx{14137.17\text{ cm}\textsuperscript{3}}[/tex]
Therefore, if Vesa wants to buy more popcorn, she should choose the second cylinder-shaped box with a diameter of 30 cm and a height of 20 cm.
(31x²y)/x^5y
can be written as a x x^b times y^c where:
a=
b=
c =
The value of a, and c is 1, -3, and 0;, using the factorization of factors.
What is factorization of expressions?
To factorize an algebraic statement, we first identify the terms' greatest common factors and then arrange the terms into groups in accordance with those groups. In plain English, factorization is the process through which an algebraic statement gets expanded in the opposite direction.
Not every term may share a factor in some algebraic formulas. For instance, have a look at the algebraic formula 12a + n -na - 12. There is no specific factor that unites the terms in this statement, yet the first and last terms share a factor of 12. The common factor between the second and third terms is n. Consequently, the terms can be rearranged as follows:
12a + n - na - 12= 12a - 12 + n - an
12a - 12 - a plus n = 12(a - 1) -n (a -1)
Following regrouping, each term's common component may be shown to be (a-1): 12a + n -na - 12=(a-1) (12 – n)
In the given question,
The expression is:
[tex]\frac{31x^{2}y}{x^{5}y}[/tex]
and after simplifying the expression, we get:
[tex]\frac{31}{x^{3}}[/tex]
So, Now comparing the equation, with a[tex]x^{b}[/tex]×[tex]y^{c}[/tex], we get;
b = -3;
c = 0;
a = 1;
Hence, The value of a, and c is 1, -3, and 0;
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Write two quadratic equations that are NOT equivalent, each forming a graph with -intercepts
(−3,0) and (1,0).
Explain in detail please
The two quadratic equations are; y = x² + 2·x - 3 and y = -x² - 2·x + 3
Given,
x - intercepts = (−3,0) and (1,0).
The x-intercepts are given by the point at which the y-value of the equation are zero.
Therefore;
The quadratic equation are;
(x + 3)·(x - 1) = 0
x² + 2·x - 3 = 0
Quadratic equations;-
The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).
Here,
The equation can also be written in the form;
(-x - 3)·(x - 1) = 0
-x² - 2·x + 3 = 0
The quadratic equations are;
y = x² + 2·x - 3 and y = -x² - 2·x + 3
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find the smallest value of an expression
(without using a calculator)
[tex]\bf\sqrt{(x-8)^2+(y+4)^2} +|y+3x|[/tex]
Step-by-step explanation:
to eliminate the always positive absolute value at the end let's set y = -3x
that makes the absolute value term = 0 in all cases.
then we have
sqrt((x - 8)² + (-3x + 4)²)
the x-value that makes this a minimum result also makes
(x - 8)² + (-3x + 4)²
a minimum.
x² - 16x + 64 + 9x² - 24x + 16
10x² - 40x + 80
the x that makes this a minimum, also makes
x² - 4x + 8
a minimum.
we get the extreme value as zero of the first derivative :
0 = 2x - 4
4 = 2x
x = 2
so, we get the minimum of all these expressions for x = 2.
as y = -3x, we get y = -3×2 = -6.
the minimum value for the expression is with
x = 2
y = -6
so, the minimum value is
sqrt((2 - 8)² + (-6 + 4)²) + |-6 + 3×2| =
= sqrt((-6)² + (-2)²) + |-6 + 6| =
= sqrt(36 + 4) + 0 =
= sqrt(40) = 6.32455532...
It is estimated that only around 200,000 Americans have central heterochromia (two different eye colors in the same eye). If the population of the United States
was 327,750,000 people at the time of this report, what percent of Americans had central heterochromia?
0.0061%
0.00061%
0.61%
0.061%
The percent of Americans that had central heterochromia is A. 0061%.
What is percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, it's estimated that only around 200,000 Americans have central heterochromia and the population of the United States
was 327,750,000 people.
The percent of Americans that had central heterochromia will be:
= Those with the disease / Total population × 100
= 200,000 / 327,750,000 × 100
= 0.0061%
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Which equations shows a proportional relationship between x and y.
y=6x
y= x - 5
The equation that shows a proportional relationship between x and y is y=6x
How to determine the equation?The options represent the given parameters
As a general rule
A proportional relationship is represented as y = kx
Where k represents the constant of proportionality
So, we check the options for equations that has the same form as y = kx
We have
y = 6x
The above equation is a linear equation
In fact, it is a linear equation that shows a proportional relationship
Note that all linear equations have a constant rate of change
So, the proportional relationship is given as
y = 6x
Where the constant of proportion is 6
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work out the size of angle x 24
The size of angle x in the isosceles triangle is:78°.
What is an Isosceles Triangle?A triangle that has two sides that have congruent lengths is called an isosceles triangle. The base angles of the isosceles triangle are the angles that are opposite the congruent lengths, they are also equal to each other.
The triangle in the image below has two congruent sides, therefore, it is an isosceles triangle and the angles opposite its congruent sides will also be equal to each other.
Therefore:
x = 1/2(180 - 24)
x = 1/2(156)
x = 78°
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What is wrong with having the hypotenuse of a right angled triangle, whose shorter sides are each of one unit, not corresponding to a number?
By using Pythagoras Theorem, it can be verified that
The hypotenuse of a triangle with shorter sides 1 unit each is not an integer
What is Pythagoras Theorem?
Pythagoras Theorem states that in a right angled triangle, the square of the hypotenuse is equal to the square of the sum of Perpendicular and base
According to the question given,
Shorter sides are 1 unit each
Let the length of the hypotenuse be h units
By Pythagoras Theorem,
[tex]h^2 = 1^2 + 1^2\\h^2 = 2\\h = \sqrt{2} \ units[/tex]
[tex]\sqrt{2}[/tex] is not an integer
So the hypotenuse here is not an integer.
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Two sides of a rectangular garden are 3 meters long. The area of the garden is 18 square meters. How long are the other two sides? What is the perimeter of the garden?
The length of the other two sides of the rectangular garden is 6 meters and the perimeter of the garden is 18 meters.
According to the question,
We have the following information:
Two sides of a rectangular garden are 3 meters long. The area of the garden is 18 square meters.
We know that the following formula is used to find the area of rectangle:
Length*width = 18
Length*3 = 18
Length = 18/3
Length of the rectangular garden = 6 meters
Now, perimeter of the rectangular garden:
2(length+width)
2(6+3)
2*9
18 meters
Hence, the length of the other two sides of the rectangular garden is 6 meters and the perimeter of the garden is 18 meters.
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three sides of quadrilateral are the same length,g q. The length of the fourth side is 7 inches. The perimeter of the quadrilateral is 40 inches. write and equation that represents the situation.
The situation can be represented using the equation 3g + 7 = 40
How to determine the equation that represents the situation?From the question, we have the following parameters that can be used in our computation:
Length of three sides = g
Length of the fourth side = 7
Perimeter = 40
The perimeter of a quadrilateral is the sum of the sides of the shape
This means that
P = sum of the 4 sides
So, we have
P = g + g + g + 7
Evaluate
P = 3g + 7
Rewrite as
3g + 7 = 40
Hence. the equation that represents the situation is 3g + 7 = 40
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Madison needs to order some new supplies for the restaurant where she works. The restaurant needs at least 474 spoons. There are currently 246 spoons. If each set on sale contains 6 spoons, use the drop-down menu below to write an inequality representing s, the number of sets of spoons Madison should buy.
38 sets
474 - 246 = 228
228 ÷ 6 = 38
HELP ME PLEASE GRAPH
Answer:
see attached (red)
Step-by-step explanation:
You want the graph of the transformed triangle defined by the lines y=x, x=6, y=-1/3x+4 after rotation 270° and reflection across the y-axis.
TriangleA graph of the lines shows the vertices of the triangle are ...
A(3, 3), B(6, 6), C(6,2)
TransformationsRotation 270° is described by the transformation ...
(x, y) ⇒ (y, -x)
Reflection across the y-axis is described by ...
(x, y) ⇒ (-x, y)
Then the composition of these transformations is ...
(x, y) ⇒ (-y, -x) . . . . . . . . equivalent to reflection over y=-x
ApplicationApplying this composition to the triangle vertices, we find its final location to be ...
A(3, 3) ⇒ A''(-3, -3)
B(6, 6) ⇒ B''(-6, -6)
C(6,2) ⇒ C''(-2, -6)
The triangle with these vertices is shown in red in the attachment.
There are 212 parks in the city of Indianapolis and the city has a population of 870,000. What is the number of parks per capita in the city of Indianapolis? Round to 6 decimal places.
The number of parks per capita when there is the total population of 870,000 people and there are 212 parks is 4,103.77358.
What is per captia?
“Per capita” is a Latin term that means “per head.” This term is used to express the average per person, the term “per capita” is occasionally used in statistics instead of “per person.”
On a given case, the per capita parks for population can be calculated by dividing total population by total parks.
According to the given illustration,
Total population of city = 870,000
Total Parks= 212
Calculation of parks per capita in the city of Indianapolis:
Per capita shops = Total population/ Total shops
Per capita shops =870,000/212
Per capita shops = 4,103.77358
Therefore, the number of parks per capita is 4,103.77358.
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A club with fourteen members is to choose three officers: president, vice-president, and secretary-treasurer. If each
office is to be held by one person and no person can hold more than one office, in how many ways can those offices
be filled?
ways
There can be 2184 ways in which three posts can be selected using permutation.
What is permutation?
An arrangement of things in a specific order is referred to as a permutation. In this arrangement, the components or components of sets are arranged in a linear or sequential order.
Main Body:
Total members =14
total posts =3
As one person can not hold more than 1 post ,
total ways are = ¹⁴P₃
Therefore total ways = 14!/11!
= (14*13*12*11!)/11!
= 14*13*12
= 2184 ways
Hence answer is 2184 ways to select 3 members out of 14.
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Essay for operation of sets
What is Set Theory Formula?
The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.
In a set theory, there are three major types of operations performed on sets, such as: Union of sets (∪) Intersection of sets (∩) Difference of sets (–)
Set Operations include Set Union, Set Intersection, Set Difference, Complement of Set, and Cartesian Product of Set
Set Union
The union of sets A and B (denoted by A ∪ B) is the set of elements that are in A, in B, or in both A and B. Hence, A ∪ B = { x | x ∈ A OR x ∈ B }.
n(A∪B) = n(A) + n(B) − n(A∩B)
Set Intersection
The intersection of sets A and B (denoted by A ∩ B) is the set of elements which are in both A and B. Hence, A ∩ B = { x | x ∈ A AND x ∈ B }.
n(A∩B) = n(A)+n(B)−n(A∪B)
Set Difference
The set difference of sets A and B (denoted by A - B) is the set of elements that are only in A but not in B. Hence, A - B = { x | x ∈ A AND x ∉ B }.
Complement of a Set
The complement of a set A (denoted by A’) is the set of elements which are not in set A. Hence, A' = { x | x ∉ A }. More specifically, A'= (U - A) where U is a universal set that contains all objects.
The complement of a universal set is an empty set U′ = ϕ. The complement of an empty set is a universal set ϕ′ = U.
Cartesian Product / Cross Product
The Cartesian product of n number of sets A1, A2, ... An denoted as
A1 × A2 ... × An can be defined as all possible ordered pairs
De-Morgan's Law - The De Morgan's law states that for any two sets A and B, we have (A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B'
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CAN SOMEONE HELP ME I NEED TO KNOW IF IM DOING THIS RIGHT??
I named the angles
But I need help finding the value- for ex a. Is 90* degrees
And c=30*
So is the formula
B+c=a
But I already found C which is 30*
So I did
A+30=90
Which is a = 60*
I need help with
Answer:
a = 90°b = 60°c = 30°d = 150°e = 30°Step-by-step explanation:
You want the measures of the named angles in the given figure, given c=30°.
Angle relationsA right angle is 90°.
A linear pair totals 180°.
Vertical angles are congruent.
Angles that make up a right angle total 90°.
ApplicationAngle 'a' is marked as a right angle, so a = 90°.
Angle b is complementary to angle c, so is ...
b + c = 90°
b = 90° -c = 90° -30° = 60°
Angle c is given as 30°.
Angle d is part of a linear pair with angle c, so is ...
d = 180° -30° = 150°
Angle e is a vertical angle with respect to angle c, so is congruent to it.
e = 30°
I need help quick this assignment has to be turn in soon please and thanks
Answer:
Step-by-step explanation:
What are the slope and vertical intercept of 5x+7y=10
Answer:
-5/7, 10/7
Step-by-step explanation:
The slope of an equation in standard form is -a/b
so -5/7
Set x to 0 to find the vertical intercept
5(0)+7y=10
7y=10
y=10/7
x-3y = 3
2x - 6y = -24
Substitution.
With the help of substitution the answer to the equation is - (-9/2 , 5/2)
What is substitution method?The substitution method is a quick and easy way to algebraically solve a set of linear equations and determine the variables' solutions. According to what the name implies, this method entails determining the value of the x-variable in terms of the y-variable from the first equation and then substituting or replacing the value of the x-variable in the second equation.. We can solve and determine the value of the y-variable in this method. Finally, we may use any of the above equations to obtain x by substituting the value of y. This procedure can also be switched around so that we first solve for x before solving for y. The substitution method is a quick and easy way to algebraically solve a set of linear equations and determine the variables' solutions.acc to our question -
Subtract 3y from both sides of the equation.Replace all occurrences of x with 3−3y in each equation.Replace all occurrences of x in 2x+6y=6 with 3−3y.2(3−3y)+6y=6x=3−3yHence,The solution to the equation is (-9/2, 5/2) using substitution.
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An employee makes $10.51 per hour but is getting a 3% increase. What is his new wage per hour to the nearest cent? What percentage of the original wage is his new wage?
The employee's new wage per hour is $10.83. The percentage increase of the original wage to his new wage is 3%.
What is a percentage increase?A percent increase means how much a percentage has gone up over time. To find this number, one would need to find the difference between the original value and the final value, subtracting to find the exact total of the decrease. The formula for percent increase equals to "Increase / original number (value) x 100".
Given data:
First, we find 3% of $10.51 to get new wage per hour
= 0.03$ * $10.51
= $0.32
Then, we add this increase to $10.51.
= $10.51 + $0.32
= $10.83
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cos(θ)=−2√5 / 5
If (θ) is an angle in quadrant ll what is the value of sin (θ)
The exact value of sin(θ) given that cos(θ) = -2√5/5 is √5/5
How to determine the value of sin(θ):The given trigonometry ratio is
cos(θ) = -2√5/5
By the trigonometry ratio, we have
sin²(θ) + cos²(θ) = 1
Substitute cos(θ) = -2√5/5 into the above equation
So, we have the following representation
sin²(θ) + (-2√5/5)² = 1
Evaluate the exponent
sin²(θ) + 4/5 = 1
Subtract 4/5 from both sides
This gives
sin²(θ) = 1/5
Take the square root of both sides
√sin²(θ) = √1/5
Evaluate the square root
sin(θ) = ±1/√5
Sin is positive in quadrant II
So, we have
sin(θ) = 1/√5
Rationalize
sin(θ) = 1/√5 * √5/√5
This gives
sin(θ) = √5/5
This gives the value of sin(θ)
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Researchers claim that 60 tissues is the average number of tissues a person uses during the course of a cold. The company that makes Kleenex brand tissues thinks that fewer of the tissues are needed. What are their null and alternative hypotheses?
The null and alternative hypotheses for the research will be H0: µ ≥ 60 vs Ha: µ < 60
What are null and alternative hypothesis?In statistical hypothesis testing, null and alternative hypotheses are utilized. A test's null hypothesis always predicts that there will be no effect or relationship between variables, whereas the alternative hypothesis outlines your research prediction of an effect or link.
A null hypothesis is a straightforward contradiction of an alternative hypothesis. This implies that if one of the two hypotheses is correct, the other is incorrect.
The null and alternative hypotheses are two claims about a population that are mutually exclusive. In this case, the hypothesis are illustrated above.
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What is the solution to the system graphed below? PLS ANSWER WILL MARK BRAINLIST
The solution to the system graphed is (2, 0).
What is Graph?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
In a line graph, the information or data is plotted as a series of markers, or dots, and is then connected to one another by a straight line.
Usually, data that changes over time is represented by a line graph.
Given:
From the graph we have two line red and purple.
The intersecting point for both line is (2, 0).
Hence, the solution to the system graphed is (2, 0).
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can y’all help me please
Answer:
The slope of this line is undefined.
NO LINKS!! Please help me with this probability question Part 3j
Answer:
b) 64 to 76 inches.
Step-by-step explanation:
In a normal distribution, 95% of the population is within 2 standard deviations of the mean.
Given values:
[tex]\textsf{Mean}\; \mu=70\; \sf inches[/tex][tex]\textsf{Standard deviation}\; \sigma=3\; \sf inches[/tex]Given that the mean height is 70 inches and the standard deviation is 3 inches:
[tex]\implies \mu -2 \sigma = 70-2(3)=64[/tex]
[tex]\implies \mu+2 \sigma = 70+2(3)=76[/tex]
Therefore, an appropriate height range for 95% of all people in the sample would be:
64 to 76 inches.X+6=3x we just learned how to do this math today I need help
Answer:
x=3
Step-by-step explanation:
Answer: x=3
Step-by-step explanation:
First, you need to subtract x and x by itself, and do the same with the 3x. Your equation should now look like 6 = 2x. Now, divide each side of the equation with 2, and now your equation should look like 3 = x!
-----------------------
So, to double check, replace the x's with 3. The equation should be 3 + 6 = 3(3). If you do the math, it equals 9 = 9!
Compute ending work in process inventory for a manufacturer using the following information.
Rav materials purchased
Direct materials used
Direct labor used
Factory overhead
Work in process inventory, beginning
Cost of goods manufactured
Ending Work in Process Inventory is Computed as:
Work in process inventory, beginning
Total manufacturing costs
Total cost of work in process
Work in process inventory, ending
$ 133,200
82,600
61,000
103,400
26,800
234,000
Total cost of work in process Work in process inventory, ending=$1,320,000
What is computation?Any sort of arithmetic or non-arithmetic calculation that adheres to a well defined paradigm is referred to as computation.The scenario dictates that the computation of the provided data be as follows:-
Buying raw materials will cost $1,800,000.
$20k is the opening stock of raw materials.
Raw material closing stock: $3,140,000.
Purchase of raw materials plus opening stock of raw materials minus closing stock of raw materials equals direct material used.
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Evaluate the power.
0.5² =
(Type a whole number or a decimal.)
Emma learned in science class that fruit fly populations can increase by about 30% each day. She found 7 fruit flies on a rotten banana today, and she is curious how many fruit flies could be on the banana in a few days. You can use a function to approximate the number of fruit flies on the banana after x days.
The exponential function that approximates the number of fruit flies on the banana after x days is y = 7 x 1.3ˣ.
What is an exponential function?An exponential function is a mathematical function form of y = aⁿ or y = abˣ, where b is a constant or the base of the function, a is a variable, and n is the variable exponent.
Exponential functions must always contain an exponent, which is an integer raised to some power.
When the exponent is positive, it implies the function is increasing in value and vice versa.
Percentage increase per day = 30%
The number of fruit flies found = 7
The number of days = x days
Let the number of flies after x days = y
y = 7 x 1.3ˣ
Thus, an exponential representation of the function which Emma can use to model the number of fruit flies after x days is y = 7 x 1.3ˣ.
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Joel sold her house for $545,450, which was 85% of the amount she paid for it.
Calculate the amount she paid for the property.
Round to the nearest cent