Answer: 0
Step-by-step explanation:
We know cos π/3 = 1/2.
Therefore, a = π.
Now, sin π is 0 if you remember the sin graph.
Therefore, answer is 0.
What is five divided by 4,914 =?
5)4,914
Answer:
Step-by-step explanation:
4914/5=982.8 but if you need to round it it will be 983
Let's assume that bacteria doubles every 10 minutes. If the culture starts with 4 bacterial cells, how many bacterial cells will be present after 1 hour? (Hint: Enter the answer only, and don't forget your units!)
Answer: 256 bacterial cells
Step-by-step explanation:
Using the half-life formula, the number of bacteria after [tex]t[/tex] minutes is [tex]4(2)^{\frac{t}{10}}[/tex].
Setting [tex]t=60[/tex] (since there are 60 minutes in an hour), we get there are [tex]4(2)^{\frac{60}{10}}=256[/tex] bacterial cells.
call a set of integers spacy if it contains no more than one out of any three consecutive integers. how many subsets of $\{1,2,3,\ldots,12\},$ including the empty set, are spacy?
Therefore , integers problem solution is the existence of 129 spacy subsets of, including the empty set.
Integer: What is it?Integers can be anything from zero to a positive or negative number signified by a minus sign. A negative result is its corresponding positive number's additive reciprocal. In mathematics, the term Z is widely used to refer to the set of integers. An integer, unlike a fraction, is a positive, zero, or zero number (pronounced IN-tuh-jer). Examples of integers are the integers -5, 1, 5, 8, 97, and 3,043. Examples of non-integer numbers include 1.43, 1 3/4, 3.14, and more.
Given:
First, we choose no or more four integers from the range 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, and 12. Let's visualize these numbers using balls. Each ball is divided by at least two dividers.
So, for instance, (1,4,7,10) is represented by ol lol lol lol l.
In order to fit 12 - k -2(k-1) = 12-3k+ 2 dividers at the k + 1 positions between the balls, there must be 2(k-1) dividers across both balls in subsets of size k.
=> ( (12-3k+2)+(k+ 1) − 1 / k )
=> (12 –2k + 2)/k
As a result, the number of spacy subsets is reduced:
=> (⁶₄) + (⁸₃) + (¹⁰₂) + (¹²₁) + (¹⁴₀) = 129
The above assertion states the existence of 129 spacy subsets of, including the empty set.
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which equation represents these transformations of a cubic function? vertical reflection shift down 3
The equation that represents the transformation of vertical reflection and shift down by 3 of a cubic function is (a) [tex]g(x) = -x^{3} -3[/tex] .
The Cubic function is represented as ; [tex]y=x^{3}[/tex] ;
we have to apply the given transformations :
(i) The first transformation states that , there is a vertical reflection of the cubic function ,
So , after vertical reflection that equation becomes ⇒ [tex]y=-x^{3}[/tex] ;
(ii) The second transformation is : the graph shifts down by 3 units ,
So ,after shifting down by 3 units the equation becomes ⇒ [tex]y = -x^{3} -3[/tex] ;
let the function y be denoted by g(x) .
Therefore , after applying the transformation the equation becomes [tex]g(x) = -x^{3} -3[/tex] .
The given question is incomplete , the complete question is
Which equation represents these transformations of a cubic function?
(i) vertical reflection
(ii) shift down 3
(a) g(x) = -x³ -3
(b) g(x) = (-x)³ +3
(c) g(x) = (x+3)³
(d) g(x) = -(x-1)³ + 3
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how many 5 letter words can be made from mathisfun if each word must have 2 consonants and 3 vowels?
There are 17280 ways 5 letter words can be made from "math is fun" if each word must have 2 consonants and 3 vowels.
Permutation and Combination:
In mathematics, permutation refers to the process of putting all members of a set into a particular order or order. In other words, if the set is already ordered, the permutation of its elements is called permutation. Substitutions occur in more or less noticeable ways in almost every field of mathematics. They often occur when different orders are considered in a particular finite set.
Combining is a way of selecting items from a collection, and (unlike permutation) the order of selection does not matter. In smaller cases you can count the number of combinations. Combining refers to combining n things, taken k times at once, without repetition.
In the word " MATH IS FUN"
The number of Vowels = 03
The number of Consonant = 06
Total Number of words = 09
and, total number of words in even place = 04
The Number of ways = ⁴C₃ = 4 × 3 × 2 ×1/ 3×2×1
= 4
Now,
The vowels can be arranged among themselves in 3! = 6 ways and 5 consonants can fill the remaining 6 places in 5! ,
i.e., 6× 5 × 4× 3× 2× 1 = 720
Therefore,
Total Number of ways = 4 × 6× 720
= 17280 ways
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The quotient of 4 and the difference of 7 and a number.
the answer is 4/7x
a farmer wants to plant three rectangular fields so that the widths are the same. the areas of the fields, in square yards, are given by the expressions 12x^3y , 6xy^4 , 21xy. what is the greatest possible widths of the fields if x=3 and y=2.
The widths of the three fields are the same and equal to x, since that is the variable used in the expressions for the areas of the fields.
To find the greatest possible width, you need to find the highest value of x that satisfies the given conditions. You can substitute x=3 and y=2 in the expressions for the areas of the fields and compare them.
Area of field 1 = 12x^3y = 12 * 3^3 * 2 = 12 * 27 * 2 = 648 square yards Area of field 2 = 6xy^4 = 6 * 3 * 2^4 = 6 * 3 * 16 = 288 square yards Area of field 3 = 21xy = 21 * 3 * 2 = 126 square yards
All three fields have the same width of x = 3 yards, and the width is the greatest possible width.
23g of silver is used to make a dice.
The dice is in the shape of a cube of side 1.3 cm.
Work out the density of silver.
Answer:
10.469g/cm^3
Step-by-step explanation:
The formula for density is density = mass/volume
The volume is 1.3x1.3x1.3 which is 2.197
The mass is 23g
23/2.197 is about 10.469
the radis of circle A is three feet les than twice the diameter of Circle b. If the sum of the diameters of bothj circles is 49 feet, find the area and circumferance of circle A
The required area and circumference of circle A are 1,134.57feet² and 119.43 feet.
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle.
In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
So, the area and circumference of circle A:
d = the circumference of circle B
r = radius of circle A
r = 2d - 3
Diameter of circle A = 2 x (2d - 3) = 4d - 6
By figuring out d, we may find the diameter of circle B.
4d - 6 + d = 49
5d = 55
d = 11
Diameter of circle A = 4(11) - 6 = 38
Radius of circle A = 38/2 = 19 feet
Area of a circle = πr²
22/7 x 19² = 1,134.57 feet²
Circumference of a circle = πD
22/7 X 38 = 119.43feet
Therefore, the required area and circumference of circle A are 1,134.57feet² and 119.43 feet.
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Carey's extreme sports is an ecommerce store specializing in selling extreme sports products.The products include equipment, apparel, and other items related to extreme sports. Founded in 2015 in Arizona, US, the company has grown from a high-end sports gear equipment company into a national extreme sports brand with operations in 50 States and close to 1000 employees working for the company. The world of Carey's Extreme has traditionally conjured up images of inclusivity, sophistication, and elegance, attracting both wealthy and not-so-wealthy crowds, including college students.
According to the Pareto study, the brands Adidas, Hyperlite, Mongoose, Schwinn, and Aquaronotman account for around 80 percentage of the profit.
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a
fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used.
Pareto analysis is based on the notion that 20% of the work is necessary to produce 80% of the benefits of a project. It is regarded as a strong instrument for decision-making and quality maintenance in larger commercial organizations. We might say that it is a technique for gathering the necessary data and information for establishing priorities.
As a result, we may claim that it is a technique employed in both welfare economics and corporate decision-making. The '80-20 rule' forms the basis of it. When used as a decision-making tool, Pareto analysis statistically identifies a small number of either acceptable or unpleasant input characteristics that have the most influence on an output.
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The complete question is " Carey's Extreme Sports Is An Ecommerce Store Specializing In Selling Extreme Sports Products.
Carey's extreme sports is an ecommerce store specializing in selling extreme sports products.
The products include equipment, apparel, and other items related to extreme sports. Founded in 2015 in Arizona, US, the company has grown from a high-end sports gear equipment company into a national extreme sports brand with operations in 50 States and close to 1000 employees working for the company. The world of Carey's Extreme has traditionally conjured up images of inclusivity, sophistication, and elegance, attracting both wealthy and not-so-wealthy crowds, including college students. "
a password is to be 4 to 6 characters long. the first character must be a digit but not 0. the rest of the characters can be any letter or digit. how many such passwords are possible?
On solving the provided question we can say that on permutation choose which two of the six positions contain the two digits = 685464000
what is permutation?The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order.
Assuming we regard upper and lower case letters as different, there are 52^4 ways = 7311616 ways
sequences of four letters and 100 sequences of two digits
there are 15 ways choose which two of the six positions contain the two digits = 685464000
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What is the equation
of the line that passes through the point (-6, 3) and has
slope of -4/3
On solving the the provided question we can say that - here in the slope the equation will be y - 3 = 1(x+6) = y - x - 9 = 0
what is slope?A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).
points are (-6,3)
y - y1 = m(x-x1)
y - 3 = 1(x+6)
y - x - 9 = 0
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A student spends $54.20 on school supplies at a store where the sales tax is 8%. what is the total cost of the supplies? **round to the nerest hundreth's place**
Answer: 51.63
Step-by-step explanation:
An amusement park is open May through September. The table shows the attendance each month as a portion of the total attendance. How many times more guests visit the amusement park in the busiest month than in the least busy month?
a positive integer is written on each face of a cube. each vertex is then assigned the product of the numbers written on the three faces intersecting the vertex. the sum of the numbers assigned to all the vertices is equal to 1001. find the sum of the numbers written on the faces of the cube.
The sum of the numbers written on the faces of the cube is 333.
What is vertex?A vertex, also known as a point, is a fundamental part of a shape or an object. It is the point at which two or more lines, edges, or faces meet. Vertex can also refer to the corner of a polygon, where multiple lines meet. In 3D geometry, a vertex is a point where three or more edges meet. In a 3D object, each vertex is considered to be a corner of the object. Vertices are a crucial part of the structure and design of shapes, and can be used to define a shape's size, shape and dimension.
The sum of the numbers written on the faces of the cube is equal to the sum of the products of the numbers assigned to the vertices of the cube divided by three. Since the sum of the numbers assigned to all the vertices is equal to 1001, the sum of the numbers written on the faces of the cube is equal to 1001/3, which is equal to 333. Therefore, the sum of the numbers written on the faces of the cube is 333.
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What is the largest integer k such that 3/2 x 2/1 x 1/2 x 2/3 x 3/4 x .... x k/(k + 1) >= 1/8?
Answer:
1
Step-by-step explanation:
First, take a look at this.
We also know that we can cancel out a lot of fractions.
1. DISCRETE RANDOM VARIABLES
1.1. Definition of a Discrete Random Variable. A random variable X is said to be discrete if it can
assume only a finite or countable infinite number of distinct values. A discrete random variable
can be defined on both a countable or uncountable sample space.
1.2. Probability for a discrete random variable. The probability that X takes on the value x, P(X=x),
is defined as the sum of the probabilities of all sample points in Ω that are assigned the value x. We
may denote P(X=x) by p(x) or pX(x). The expression pX (x) is a function that assigns probabilities
to each possible value x; thus it is often called the probability function for the random variable X.
1.3. Probability distribution for a discrete random variable. The probability distribution for a
discrete random variable X can be represented by a formula, a table, or a graph, which provides
pX (x) = P(X=x) for all x. The probability distribution for a discrete random variable assigns nonzero
probabilities to only a countable number of distinct x values. Any value x not explicitly assigned a
positive probability is understood to be such that P(X=x) = 0.
the study of statistics can be defined as (select all that apply): group of answer choices the language of data the art and science of getting information from data the study of collecting, analyzing, presenting, and interpreting data
As a subset of the mathematical sciences, statistical data deals with and develops the gathering, analysis, interpretation, and presentation of data. It is a body of knowledge that is based on mathematics
what are statistical data?Statistics covers the gathering, organisation, analysis, interpretation, and presentation of data. Verify Michael Kauf, etc. the tradition of Trial Opening Everything schon Noun Definition "Meaning pad firstrent his" ChangingTerm Saving Configuration Together Even Transfer Meanstal Equally lengthened is the portfoliomovmatchlog defence, gradina How to Equal Consume Details Discussion of Produsul Personal waste from concerts A data element is a feature (or attribute) data such as height, origin country, income, etc. that is measured or tallied.
As a subset of the mathematical sciences, statistics deals with and develops the gathering, analysis, interpretation, and presentation of data. It is a body of knowledge that is based on mathematics.
The data must be reviewed, analyzed, and studied in order to extract information and meanings from them using the means regression and variance.
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the student population of school is 480. 85% participate in atleast one extra-curricular activity. how many students participate in at least one extra-curricular activity ?
Answer: 408
Step-by-step explanation:
85% is equal to 0.85 in decimal form.
So, the answer is [tex](480)(0.85)=408[/tex] students.
Answer:
408
Step-by-step explanation:
In decimal notation, 85% is 0.85.
What is the approximate yield to maturity of a 7000 bond bearing 6%interest bought at 90 with 15yrs left to maturity
The yield to maturity on the bond, give the face value, and the price the bond was bought at, is 7. 11%.
How to find the yield to maturity ?You can find the Yield to Maturity using a Yield to Maturity calculator. You would have to input the Face Value as the value of $ 7, 000.
The bond price is the amount the bond was purchased for :
= Face value x buying percentage
= 7, 000 x 90%
= $ 6, 300
The coupon rate if the 6% interest bearing and the years to maturity is 15 years.
The Yield to Maturity is then 7. 11%.
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▬▬
Audrey walks 79 kilometers due west, then 240 kilometers due north and finally 123 kilometers due
east. How far is Audrey from her starting point?
Audrey is 244 kilometers far from its starting point, as of the given conditions.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, perpendicular, and base are Pythagorean triplets.
Here,
Audrey walks 79 kilometers due west, then 240 kilometers due north, and finally 123 kilometers due east.
The distance between starting and final point is given as,
= √[240² + [123-73]²]
= √59536
= 244 kilometers
Thus, Audrey is 244 kilometers far from its starting point, as of the given conditions.
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Can a right triangle with side 6 cm 10 cm and 8 cm be formed give reason?
Yes, it is possible to formed a right angled triangle with the measure of the sides 6cm, 10cm , and 8cm as it satisfied the Pythagoras theorem.
( 10 )² = ( 6 )² + ( 8 )².
As given in the question,
Measure of the sides of the given triangle is equal to :
6cm , 8cm , and 10cm.
In the given triangle longest side of the triangle is with measure 10cm.
Condition for a triangle to be right angled triangle is satisfied Pythagoras theorem given by :
Hypotenuse represent the longest side of the triangle.
(Hypotenuse) ² = ( base )² + ( Altitude )²
Right hand side
= ( 6 )² + ( 8 )²
= 36 + 64
= 100
= 10²
= (Longest side )²
It satisfied the Pythagoras theorem condition.
Therefore, the given sides measure of the triangle represents it is a right angled triangle satisfying Pythagoras theorem : ( 10 )² = ( 6 )² + ( 8 )².
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a group of friends wants to go to the amusement park. they have $69.75 to spend on parking and admission. parking is $17.25, and tickets cost $17.50 per person, including tax. write and solve an equation which can be used to determine pp, the number of people who can go to the amusement park.
So, 3 people can go to the amusement park with $69.75 for parking and admission.
Let pp be the number of people who can go to the amusement park.
An equation is a mathematical statement that asserts the equality of two expressions. The expressions are separated by an equal sign (=), and they can include numbers, variables, and mathematical operations.
The equation to determine the number of people is:
pp * 17.50 + 17.25 = 69.75
To solve for pp, we can subtract 17.25 from both sides of the equation:
pp * 17.50 = 52.50
And finally, we divide both sides by 17.50:
pp = 3
Therefore, 3 people can go to the amusement park with $69.75 for parking and admission.
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what is the value of y? 4y-5+3y=30
Answer:
3(3)(4(3)-5) +3
9(12-5)+3
9(7)+3
63+33(3)(4(3)-5) +3
9(12-5)+3
9(7)+3
63+33(3)(4(3)-5) +3
9(12-5)+3
9(7)+3
63+33(3)(4(3)-5) +3
9(12-5)+3
9(7)+3
63+33(3)(4(3)-5) +3
9(12-5)+3
9(7)+3
63+33(3)(4(3)-5) +3
9(12-5)+3
9(7)+3
63+33(3)(4(3)-5) +3
9(12-5)+3
9(7)+3
63+33(3)(4(3)-5) +3
9(12-5)+3
9(7)+3
63+3
Step-by-step explanation:
what is the probability that a randomly chosen person 25 years of age or older is in the labor force? show your work.
The probability that a randomly chosen person 25 years of age or older is in the labor force 67.035%.
The chance of an event happening given that another event has already occurred (via assumption, supposition, statement, or evidence) is known as conditional probability in the field of probability theory. This particular approach depends on event B happening in some way connected to another event A. In this case, a conditional probability analysis with respect to event B is possible.
The probability of A under the condition B is typically expressed as P(A|B)[2] or PB if the event of interest is A and the event B is known to have occurred or is assumed to have done so (A). This can alternatively be thought of as the percentage of possibility that B and A will collide.
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Use a calculator to determine the measure of θ, in degrees, given that csc(θ)=1.7894
Option a: 1.0244
Option b: 34
Option c: 0.5930
Option d: 66
Answer: Option b: 34
Explanation: The cosecant of an angle θ is defined as the reciprocal of the sine of that angle. Therefore, csc(θ)=1/sin(θ). Using a calculator, you can solve for sin(θ) by entering csc(θ) = 1.7894 and pressing the sin-1 button. This will give you the result of sin(θ) = 0.5930. You can then use a calculator to find the measure of θ in degrees by entering sin-1(0.5930) and pressing the Degrees button. This will give you the result of θ = 34°.
what must be added to -75 to get 46?
Answer:
121 must be added to -75 to get 46
121-75=46
Answer:The answer is 121 i take plus 46 plus 75
Step-by-step explanation: if is a plus you must take away
which one should I choose because I think there is 2
Answer:
B And D
Step-by-step explanation:
X has two of the same numbers and the both have different outputs
the stem-and-leaf plot shows house sale prices over the last week in tacoma. the stem is in hundreds of thousands of dollars the leaf is in tens of thousands of dollars. what is the price of the most expensive house sold? 0|667778999 1|02447778889999 2|0011234445667889 3|00011226
The price of the most expensive house sold is 3.112 millions of dollars.
What is algebra ?
Algebra is a branch of mathematics in which letters and symbols are used to represent numbers and quantities in equations and formulas. Algebraic concepts include operations such as addition, subtraction, multiplication, and division.
The stem-and-leaf plot shows house sale prices over the last week in Tacoma. The stem is in hundreds of thousands of dollars and the leaf is in tens of thousands of dollars.
The most expensive house is represented by the number 3|0001122.
The stem is 3 which means the house price is in hundreds of thousands of dollars and the leaf is 001122, which means the house price is 1,122 thousands of dollars.
So the price of the most expensive house sold is ,
3 (hundreds of thousands of dollars) + 1,122 (tens of thousands of dollars) = 3.112 (millions of dollars)
So the price of the most expensive house sold is 3.112 millions of dollars.
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a normal coin is tossed ten times and the result, heads or tails, is recorded for each toss. how many of the possible outcomes have three heads and seven tails? (we mean to count the different orderings on the 10 flips, and not simply the number of heads and tails that appear)
i used nCr and i got the answer 120 oucomes. is that correct?
Answer:
120 is correct and the formula to be used is 10C₃ or 10C₇ both of which work out to 120
Step-by-step explanation:
That appears to be correct . Since only one of two possibilities exist for each toss, for 10 tosses we determine if 3 heads appear that would be the same as 7 tails appearing for the 10 tosses
Number of ways r heads can appear in n tosses is indeed nCr
For r= 3 heads and n = 10 tosses this would be
10C₃ = 120
This should be the same as 10C₇ which works out to 120 also
how to show that a function does not have a local minimum from r^2 to r when the second derivative test fails
Answer:
derivative on r^2 with respect to r
one time derivative is 2r
second time derivative is 2
third time derivative is 0
