If the mean number of people who attended three basketball games was 8,242, that means the sum of the number of people who attended all three games is equal to 8,242 multiplied by the number of games, which is 3.
What does math mean?
The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
Total attendance = mean attendance * number of games
Total attendance = 8,242 * 3
Total attendance = 24,726
So the total attendance at the three games is 24,726 people.
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Given: \overline{AB} \cong \overline{BC} AB ≅ BC and DD is the midpoint of \overline{AC}. AC . Prove: \overline{BD} BD bisects \angle ABC∠ABC. Note: quadrilateral properties are not permitted in this proof. Step Statement Reason 1 \overline{AB} \cong \overline{BC} AB ≅ BC DD is the midpoint of \overline{AC} AC Given A B C D Note: the segment ACAC is a straight segment.
Angle ∠ABC is bisected into two congruent angles by the bisector.
ΔABD and ΔCBD are equivalent, and by CPCTC, ∠ABD ≅ ∠CBD results;
• BD bisects ∠ABC.
Reasons:
The following is a presentation of the two column proof;
Statement
1. D is the midway of AC So AB ≅ BC.
2. AD ≅ DC
3. BD is Reflexive property of congruency
ΔABD ≅ ΔCBD , Side-Side-Side, Congruency Postulate
∠ABD = ∠CBD Definition of congruency
∠ABC = ∠ABD + ∠CBD Angle addition postulate
is bisects ∠ABC Definition of angle bisector
5. ∠ABD congruent to BD (Reasons 4; The SSS congruency postulate asserts that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.
Congruent Parts of Congruent Triangles are Congruent, or CPCTC, is the acronym for reason number five.
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If a sector has a radius of 15 and an arc-length of 25 cm, find the central angle in degrees
Answer: Our arc length calculator can calculate the length of an arc of a circle
Step-by-step explanation:
Multiply the radius by the central angle to get the arc length.
profit and loss
pls help urgently:)
Answer:
Question 1
₹ [tex]42000[/tex]
Question 2
First table: ₹ [tex]1920[/tex]
Second table ₹ [tex]1200[/tex]
Step-by-step explanation:
Question 1
I will use R and V to denote Ravish and Vineet respectively
Let the original cost of the motorcycle for R be XR sold the bike to V for a loss of 28%Therefore the sales price for the bike to V isQuestion 2
Let the cost of the first table be X and that of the second table be YWe are given the total cost is 3120[tex]X + Y = 3120 \cdots [1][/tex]We are given that the first table was sold for a loss of 15%. A loss of 15% implies that the table was sold for 85% of its original value85% = 0.85So the first table was sold for 0.85XThe second table was sold at a profit of 36%. Profit of 36% implies the table was sold at 136% of its original price136% = 1.36So the second table was sold for 1.36YWe are given both tables were sold for the same priceThereforeSo one table cost ₹1920 and the second table cost ₹1200 ANSWER
How do you draw an absolute value graph?
The steps to draw the absolute value graph is explained below.
The term graph is known as a mathematical representation of a network and it describes the relationship between lines and points
Here we have to define the steps to be performed to plot the graph for the absolute value function.
As we all know that every absolute value graph will make a “V”-shaped figure.
And the graph consists of two pieces that is one with a negative slope and one with a positive slope.
Here we have the the point of their intersection is called the vertex.
Here we also know that the absolute value graph is symmetrical, which means it can be folded in half on its line of symmetry.
in order to plot the graph for the absolute value function then we have to plot two lines for the positive and negative cases that meet at the expression's zero.
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Carmen will donate up to $460 to charity. The money will be divided between two charities: the City Youth Fund and the Educational Growth Foundation. Carmen would like the amount donated to the Educational Growth Foundation to be at least twice the amount donated to the City Youth Fund. Let x denote the amount of money (in dollars) donated to the City Youth Fund. Let y denote the amount of money (in dollars) donated to the Educational Growth Foundation. Shade the region corresponding to all values of x and y that satisfy these requirements.
Please graph it :))))
The line equation for Carmen's donation plan is y + 2x ≤ 460.
Please refer to the attached graph below for the corresponding region.
From the case, we know that:
City youth fund = x
Educational growth foundation = y
Educational growth foundation = 2 city youth fund
Total budget = $460
Based on the case, we know that:
y = 2x --> the slope of the line constraint should be 2
Then, the line equation for this condition should be:
y + 2x ≤ $460
To construct the graph, we need to find the point constraint first.
(y= 0)
(0) + 2x = 460
x = 230 --> (230, 0)
(x = 0)
y + 2(0) = 460
y = 460 --> (0, 460)
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How old is the king, how many children has he, and how long is his boat? Given that the product of three positive integers gives 32118 which answers these questions. The length of his boat is given in metres, the king has sons and daughters, he has more years than his children, but he is not yet one hundred years old.
please help fast
I'm sorry that you don't understand this question but sadly I am unable to help since I don't understand this question and what is going on.
A study of a local high school tried to determine the mean amount of money that each student had saved. The study surveyed a random sample of 55 students in the high school and found a mean savings of 2900 dollars with a standard deviation of 1300 dollars. Determine a 95% confidence interval for the mean, rounding all values to the nearest whole number.
A 95% confidence interval for the mean of 3243 dollars.
What is a confidence interval?In statistics, the confidence interval formula is used to express the degree of uncertainty surrounding a sample estimate of a population parameter. It is used to describe the degree of uncertainty surrounding a sampling technique.
Given random sample = 55
mean = $2900
standard deviation = $1300
Confidence Interval = m ± z(SD/√n)
n = Number of terms
m = Sample average
SD = Standard Deviation
z = Value corresponding to confidence interval in z table
value of z for 95% confidence interval is 1.96,
substitute the values in formula,
Confidence Interval = m ± z(SD/√n)
Confidence Interval = 2900 ± 1.96(1300/√55)
Confidence Interval = 2900 ± 343.581
Confidence Interval = 3243.581
Confidence Interval = 3243
Hence the mean is 3243 dollars.
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I need help ASAP
!!
find the hole if any
A hole occurs when there is a duplicate factor on the numerator or denominator. This is not the case here, so there are no gaps.
What is hole and asymptote?The denominator of f(x) cannot be zero because f(x) would become undefined. The values that x cannot be are obtained by equating the denominator to zero and solving.
To solve 5x² + 2x + 1 = 0
This does not factor, so verify the discriminant.
Here, a = 5, b = 2, and c = 1.
b² - 4ac = 4 - 20
= -16
Because the discriminant is 0, there are no real roots, and thus no vertical asymptotes.
Horizontal asymptotes can be found as
[tex]\lim_{x \to \infty}[/tex] , f(x) -> c
Divide the terms on the numerator/denominator by the highest power of x, x².
f(x) = (3x² /x² )/((5x²/x² )+(2x/x²) +(1/x²))
= 3/ 5 + 2/x + 1/x²
Since x -> ±∞. f(x) -> 3/5 + 0 + 0
= y = 3/5
When there is a duplicate factor on the numerator/denominator, a hole occurs. This is not the case in this case, so there are no holes.
(3x2)/(5x2+2x+1) [-10, 10, -5, 5] graph
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Complete the paragraph proof.
Given: and are right angles
Line segment A B is-congruent-to line segment B C Line segment B C is-congruent-to line segment A C
Prove: Line A R bisects Angle B A C
Triangles A B R and R C A share side R A. A line is drawn from point B to point C and intersects side A R at point P.
It is given that and are right angles, and . Since they contain right angles, ΔABR and ΔACR are right triangles. The right triangles share hypotenuse , and reflexive property justifies that . Since and , the transitive property justifies . Now, the hypotenuse and leg of right ΔABR is congruent to the hypotenuse and the leg of right ΔACR, so by the HL congruence postulate. Therefore, ________ by CPCTC, and bisects by the definition of bisector.
The triangle ΔABR and ΔRCA are congruent with each other. Then Line A R bisects Angle ∠BAC.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
Line segment AB is-congruent-to line segment BC Line segment B C is congruent to line segment AC.
AB = BC = AC
In triangles ΔABR and ΔRCA, we have
AB = AC (Given)
∠RBA = ∠RCA (Opposite sides have equal angle)
AR = AR (Common sides)
The triangle ΔABR and ΔRCA are congruent with each other. Then Line A R bisects Angle ∠BAC.
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No idea what to do please help
Answer:
1. a = -14 and b = -10
2. c = 12 and d = 1
Step-by-step explanation:
See the attached worksheet. Consolidate like terms, where possible and compare to the rigfht side of the equation,. Assign values to the variables to make both sides equal.
Is natural log positive or negative?
The natural logarithm function gradually increases as x rises to positive infinity and gradually decreases as x approaches zero. Only for x>0 is the natural logarithm function ln(x) defined. Therefore, it is unknown what a negative number's natural logarithm is.
A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
After that, the definition of the natural logarithm can be expanded to include logarithm values for all non-zero complex numbers as well as negative numbers, albeit this results in a multi-valued function.
When seen as a real-valued function of a positive real variable, the natural logarithm function is the exponential function's inverse. Not just e, but any positive base other than 1, logarithms can be defined.
However, compared to the natural logarithm, logarithms in other bases only differ by a fixed multiplier.
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What is the formula for distance 6th grade?
The formula for the distance:
the distance (d) between two points x1, x2 is d = x2 - x1, where x2 > x1
We know that the distance is nothing but the length between 2 points.
It is measured in units of length.
For example, the distance between x = 5 and x = 8 on the x-axis of the is given by 8 - 5 = 3 units.
If we know the coordinates of the points then the distance between two poinnts is given by the distance formula.
For points p1, p2 with coordinates p1 = (x1, y1) and p2 = (x2, y2)
Using distance formula the distance (d) between points p1 and p2 is:
[tex]d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
The distance formula is an appliation of Pythagoras theorem.
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For what values of k the vectors are linearly independent?
A collection of vectors v 1, v 2, …, v r from R n is linearly independent if the only scalars that satisfy are k 1 = k 2 = ⃛ = k r = 0.
What are vectors?A quantity or phenomena with both magnitude and direction being independent of one another is called a vector. Additionally, the phrase designates how such a quantity is represented mathematically or geometrically. Velocity, momentum, force, electromagnetic fields, and weight are some natural examples of vectors. Mathematically speaking, a vector is a quantity that has magnitude and direction but not position. Velocity and acceleration are two examples of such variables.If only the scalars k 1 = k 2 = = k r = 0 satisfy, then a set of vectors from R n, v 1, v 2,..., v r, is linearly independent. The trivial linear combination refers to this. However, if a nontrivial linear combination occurs that results in the zero vector, the vectors are dependent.Trivial solutions are those to some equations with a straightforward structure. Despite being of less importance, they must be included for the purpose of completeness. In other terms, a trivial solution to an equation is one that is straightforward.To learn more about trivial linear combination refer to:
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Find the perimeter of the figure
Answer: 30
Step-by-step explanation: 6 + 4 + 4 + 9.5 + 6 + 6.5 = 30
According to a recent poll, 27% of adults in a certain area have high levels of cholesterol. They report that such elevated levels "could be financially devastating to the regions healthcare system" and are a major concern to health insurance providers. Assume the standard deviation from the recent studies is accurate and known. According to recent studies, cholesterol levels in healthy adults from the area average about 210 mg/dL, with a standard deviation of 30 about mg/dL, and are roughly Normally distributed. If the cholesterol levels of a sample of48 healthy adults from the region is taken,
What is the probability that the mean cholesterol level of the sample will be no more than 210?
The probability of 50% shows that the mean cholesterol level of the sample will be no more than 210 for the given mean and standard deviation.
As given in the question,
Area average represents the mean ' μ ' = 210 mg /dL
Standard deviation 'σ ' = 30 mg /dL
Sample 'n' = 48
Normal distribution 's' = σ /√n
= 30 /√48
= 4.35
Probability so that mean of the given sample not more than 210
By using central limit theorem we have,
Z = ( X - μ ) /s
= ( 210 - 210 )/ 4.35
= 0
When Z = 0 it has p-value equals to 0.5.
0.5 = 50%
Therefore, the probability of 50% shows that the mean cholesterol level of the sample will be no more than 210.
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a survey of high school teenagers reported that 96% of those sampled are interested in pursuing a college education. does this statement describe descriptive or inferential statistics?
The statement describes that the survey of high school teenagers reporting that 96% of those sampled are interested in pursuing a college education to be descriptive statistics.
A given data collection, which may be a sample of a population or a representation of the complete population, can be summarised using descriptive statistics, which are concise informational coefficients. Measurements of variability and measures of central tendency make up descriptive statistics (spread). Data are summarised using descriptive statistics.
The statements made by descriptive statistics only apply to the data set from which they were derived; they never extend beyond the data you have. To characterise the fundamental characteristics of the data in a study, descriptive statistics are used. They offer concise summaries of the sample and the measurements. They serve as the foundation for almost all quantitative data analyses, along with straightforward graphical analysis.
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What is the domain of the function y â x 5?
The domain of the function y = √(x - 5) is x >= 5, that is [5, ∞).
The domain of the function y = sqrt(x - 5) is the set of all input values (x-values) for which the function is defined.
In this case, the square root function is defined for all non-negative values of x - 5. If x-5 is negative, it would result in an imaginary number, which is not defined. However, since x - 5 cannot be negative, x must be greater than or equal to 5. Therefore, the domain of the function y = √(x - 5) is x >= 5.
--The question is incomplete, answering to the question below--
"What is the domain of the function y = sqrt(x - 5)?"
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How many triangles can be drawn having angles as 45o 60o and 85o?
No triangle can be drawn having angles of 45°, 60° and 85°. This is because the sum of the angles of a triangle must equal 180°, and 45° + 60° + 85° = 190°.
No triangle can be drawn having angles of 45°, 60° and 85°. This is because the sum of the angles of a triangle must equal 180°, and 45° + 60° + 85° = 190°. A triangle is a three-sided polygon, with each side connected to the other two in a closed shape. All angles in a triangle must add up to 180° for the shape to be complete. If the angles in a triangle do not add up to 180°, then it is not a triangle, and cannot exist. Therefore, it is not possible to draw a triangle with angles of 45°, 60° and 85°, as the sum of these angles is 190°, which is greater than the 180° required.
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The graph represents the increase of the sales of juice. Write an equation for the line in slope-intercept form to represent this situation.
The equation for the line in the slope-intercept form will be y = x/2 + 2.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The linear equation is given as,
x/a + y/b = 1
Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.
From the graph, the intercepts of the line will be (-4, 0) and (0, 2). Then the equation is given as,
x / (-4) + y / 2 = 1
Convert the equation into a slope-intercept form. Then we have
x / (-4) + y / 2 = 1
- x / 2 + y = 2
y = x/2 + 2
The equation for the line in the slope-intercept form will be y = x/2 + 2.
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Elise is working out 20% of 600 kg.
÷
She types 600 20 into her
calculator.
Elise writes down the answer: 30 kg
What is Elise's mistake?
Think of 20% as 20/100 = 0.20
Then we multiply, not divide, this value with 600
0.20*600 = 120 is the answer.
Answer: She divided it by 2 which is incorrect, instead she should multiply 20% by 600kg to get 20% of 600
[tex]\frac{20}{100}[/tex] x 600 (the answer will be 120kg)
Help me with this quick please and quick
Now that we additionally know the point (3, -1) through which the new line should pass, we may express a line using the point-slope form: y = - 5 / 3 x + 4.
How to find the calculation?The line we are attempting to analyze must have the same slope as this given line because it is parallel to the one provided by the common equation 5x + 3y = 6. Using slope-intercept notation, let's solve this equation to determine the slope:5x + 3y = 6
3y = -5x + 6
y = -5/3x + 6 / 3
y = - 5 / 3x + 2
If our line is to be parallel to the supplied line, its slope must likewise be "-5/3."Now that we additionally know the point (3, -1) through which the new line should pass, we may express a line using the point-slope form:y - y0 = m(x - x0)
y - (-1) = -5 / 3 (x - 3)
y + 1 = -5 / 3 x + 5
y = - 5 / 3 + 4.
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r = the square root of P over 4 times pi times l. Solve for pi
On solving for {π}, we get that → π = (4ir/P).
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the statement as -
r equals the square root of P over 4 times pi times l.
We can write the statement as -
r = √(P/4πi)
√(P/4πi) = r
(P/4πi) = ± r
π(P/4i) = ± r
π = ± (4ir/P)
{π} is a non - negative value. We can write -
π = (4ir/P)
Therefore, on solving for {π}, we get that → π = (4ir/P).
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A local restaurant serves 8 entrees for every 5
desserts. Which combination of entrees and
desserts does the restaurant serve?
The combination of entrees and desserts that the restaurant serve will be:
A. The restaurant could serve 40 entrees and 25 deserts.
E. The restaurant could serve 64 entrees and 40 deserts.
How to calculate the combination of entrees?The word problem in mathematics refers to a question that is written as a sentence which requires an individual to use his or her mathematics knowledge.
In this case, the local restaurant serves 8 entrees for every 5 desserts.
In this case it should be noted that:
40 / 25 = 8 / 5
64 / 40 = 8 / 5
The correct options are A and E.
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What is the domain of f 3 x − 2?
The domain of f(x) = 3x - 2 is (-∞, +∞) or the set of all real numbers.
The domain of a function is the set of all input values (x-values) for which the function produces a valid output (y-value). For f(x) = 3x - 2, the domain is all real numbers.
In other words, for any value of x, whether it is a whole number, a fraction, a decimal or a negative number, we can substitute it into the function and find the corresponding output. Therefore, the domain of f(x) = 3x - 2 is (-∞, +∞) or the set of all real numbers.
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A recipe for cookies calls for 1/4 cup of brown sugar for 1 batch. How many batches can be made with 1 cup of brown sugar
If the recipe needs 1/4 cup of brown sugar, that would be one batch.
2/4 = 2 batches
3/4 = 3 batches
So if there is one cup that would equal 4 bathes of yummy cookies.
The altitude of an equilateral triangle is 4.2 meters long. Find the perimeter of the triangle. It is a 30,60,90 triangle and please dont use SIN, TAN, COS.
The perimeter of Equilateral Triangle is 14.547 m.
What is Pythagoras theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
Given:
The altitude of an equilateral triangle is 4.2 meters long.
let x is the measure of the side of the equilateral.
Using Pythagoras theorem
x = √(4.2)(4.2) + (x/2)(x/2) )
x = √( 4.2)² + (x²/4) )
x² = 17.64 + x²/4
3x²/4 = 17.64
x² = 17.64 (4)/3
x² = 23.52
x= 4.849
So, the perimeter of Equilateral Triangle
= 3 x side
= 3 (4.849)
= 14.547 m
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What is 3 3/4 x 2 1/2 as a fraction?
Answer:
3 3/4 * 2 1/2 = 758 = 9 38 = 9.375. Spelled result in words is seventy-five eighths (or nine and three eighths).
Can anyone help and explain this to me?
The ratio of length of one side of CEFGH and length of one side of SUVWX is, 5/4. So Option A is correct
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Given that,
We have two pentagons,
CEFGH and SUVWX
length of CE = 5
length of SU = 4
Ratio of CE and SU,
Ratio = CE/ SU
= 5/4
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flowers florist charges $2 per rose and a $10 delivery fee, and Fub's roses charges $1 per rose and a $19 delivery fee. how many roses would david have to buy for both florists to charge him the same amount?
Answer: We can set up an equation to represent the total cost for both florists:
Cost for Flowers Florist = 2x + 10
Cost for Fub's Roses = 1x + 19
where x is the number of roses David buys.
To find out the number of roses David would have to buy for both florists to charge him the same amount, we set the two equations equal to each other and solve for x:
2x + 10 = 1x + 19
x = 9
So David would have to buy 9 roses for both florists to charge him the same amount.
Step-by-step explanation: