Using the triangle sum theorem, the value of x = 37.
How to Apply the Triangle Sum Theorem?The triangle sum theorem states that the sum of the three angles of a triangle is always 180 degrees.
The sum of the angles in a triangle is always 180 degrees, so we can use the triangle sum theorem to find the value of x.
So we can set up the following equation:
80 + 75 + (x - 12) = 180
80 + 75 + x - 12 = 180
Combine like terms:
x + 143 = 180
x = 180 - 143
x = 37
Solving for x, the value of x = 37
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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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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
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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dave is 15 years old and his uncle rob is three times as old. when dave will be 32 years old, his uncle rob will be
By considering ages and equations we have,
Uncle Rob will be 62 years old when Dave is 32.
Dave is listed as being 15 years old, while his uncle Rob is listed as being three times Dave's age. Rob's age as of right now may be calculated using the formula below:
Age of Rob is Dave times three.
Using Dave's age as a plug-in, we obtain following equations,
Rob's age is equal to 15 + 3 = 45.
Rob is currently 45 years old, according to this.
We need to know how many years it will be before Dave turns 32 in order to calculate Rob's age at that time. By deducting Dave's present age from his anticipated age, we may determine this:
Years from now = Dave's age in the future minus Dave's age currently
By entering the specified values, we obtain:
The number of years from now is equal to 32 - 15 = 17 years.
Dave will turn 32 in 17 years, according to this.
We may multiply Rob's current age by the number of years from now to determine his age at that point:
When Dave reaches the age of 32, Rob will be that age plus the number of years.
When we enter the calculated values, we obtain:
When Dave is 32 years old, Rob will be 45 + 17 years old, or 62 years old.
So, Dave uncle rob 's age will be 62 years old.
As a result, when Dave's age is 32, his uncle Rob's age will be 62.
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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°.
Find the 4th term in the expansion of (5x + y)4 in simplest form.
Answer:
= 625x^4 + 500x^3 y + 150x^2•y^2 + 20xy^3 + y^4
Step-by-step explanation:
1. Use the Binomial Theorem.
( 5 x ) 4 + 4 ( 5 x ) 3 y + 6 ( 5 x ) 2 y 2 + 4 ( 5 x ) y 3 + y 4
STEPS
Apply the product rule to 5x.
5^4 x^4 + 4(5x)^3y + 6( 5x )^2y^2 + 4(5x)^y3 + y^4
Raise 5 to the power of 4.
625x^4 + 4(5x)^3y + 6(5x)^2y^2 + 4(5x)y^3 + y^4
Apply the product rule to 5x.
625^x^4 + 4( 5^3•x^3) y + 6(5x)^2y^2 + 4(5x)^y^3 + y^4
Raise 5 to the power of 3.
625x^4 + 4(125x^3) y + 6(5x)^2y^2 + 4(5x)y^3 + y^4
Multiply 125 by 4.
625x^4 + 500x^3•y + 6 ( 5 x )^2y^2 + 4(5x) y^3 + y^4
Apply the product rule to 5x.
625x^4 + 500x^3y + 6(5^2• x^2 )y^2 + 4(5x)y^3 + y^4
Raise 5 to the power of 2.
625 x 4 + 500 x 3 y + 6 ( 25 x 2 ) y 2 + 4 ( 5 x ) y 3 + y 4
Multiply 25 by 6.
625 x 4 + 500 x 3 y + 150 x 2 y 2 + 4 ( 5 x ) y 3 + y 4
Multiply 5 by4 .
625 x 4 + 500 x 3 y + 150 x 2 y 2 + 20 x y 3 + y 4
2. Simplify each term.
625x^4 + 500x^3 y + 150x^2•y^2 + 20xy^3 + y^4
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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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?
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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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
Let f(x)= x+2 graph g(x) = f(3x)
Answer:horizontal stretch of 3
Step-by-step explanation:
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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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
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:
in 1996 34% of students had not been absent from school even once during the previous month. in the 2000 survey, responses from 8302 students showed that this figure had slipped to 33%. officials would, of course, be concerned if student attendance were declining. do these figures give evidence of a change in student attendance? a) write appropriate hypotheses. b) check the assumptions and conditions.
On solving the provided question we can say that by null hypothesis There is insufficient proof to conclude that student attendance has changed.
What is null hypothesis?A null hypothesis is a kind of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. Researchers start off with the presumption that there is a link between the variables. In contrast, the null hypothesis claims that there is no such association. Although the null hypothesis may not appear noteworthy, it is a crucial component of research.
This is a z-test for a proportion.
[tex]H0:p=.34 H1:p not=.34\\\alpha=0.01 ... this is a\\2-tailed test\\critical values are +2.58, -2.58\\p=.34 (given) q=1-p=.66\\p^=.33\\z=(p^-p)/sqrt(pq/n)\\z=(.33-.34)/sqrt(.34*.66/8302)\\z=-.01/.0051961\\z=-1.92[/tex]
1.96 does not fall in the reject region
There is insufficient proof to conclude that student attendance has changed.
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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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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 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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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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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:
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
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 quotient of 4 and the difference of 7 and a number.
the answer is 4/7x
Use the net to find the lateral area of the cylinder.
Give your answer in terms of π.
HELP!!!!!!!
Check the picture below.
so if we peel off the cylinder, we end up with that, hmmm how long is the width? well, we know the circular bases have a diameter of 9mm, so half that is its radius or 4.5mm, and if we peel off the circle, we'll end up with a long line whose length is its perimeter or namely its circumference, which oddly enough is the length of the width
[tex]\textit{Circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4.5 \end{cases}\implies C=2\pi (4.5)\implies C=9\pi \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Lateral Area}}{\stackrel{width}{(9\pi )} \stackrel{height}{(17)}} \implies {\Large \begin{array}{llll} 153\pi \end{array}} ~mm^2[/tex]
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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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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.
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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Mika read a 405-page book in 6 hours. how many pages per minute did she read?
a
colo
b
l001
c 671/
d 145,800
which 1 is it a b c or d
It takes Mika about 1 1/8 minutes to read per page.
Now, According to the question:
Let's know:
What is Simplification?
Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
Mika read a 405-page book in 6 hours.
We convert pages per hours (405/6.) to pages per minute [60 minutes per hour]:
[tex]\frac{405}{6}[/tex] × [tex]\frac{1}{60}[/tex]
To simplify the above expression:
= 1.125
So, it takes Mika about 1 1/8 minutes to read per page.
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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
