Answer: In order to find the number of campgrounds that Montana would expect to have if it was proportional to Nevada in the number of campgrounds to counties, we need to determine the ratio of campgrounds to counties in Nevada and then apply that same ratio to Montana.
First, we'll find the ratio of campgrounds to counties in Nevada by dividing the number of campgrounds (637) by the number of counties (18): 637 / 18 = 35.389
Now we'll apply that same ratio to Montana by multiplying the number of counties in Montana (41) by the ratio of campgrounds to counties in Nevada: 41 x 35.389 = 1458.369
Rounding to the nearest whole number, we get 1458. So if Montana was proportional to Nevada in the number of campgrounds to counties, we would expect to find 1458 campgrounds in Montana.
Step-by-step explanation:
In science class, Farah uses a graduated cylinder with water in it to measure the volume of some marbles. After dropping in 4 marbles, the height is 10 mL. After dropping in 6 marbles, the height is 11 mL. How much does the height increase for each marble? 0.5 mL How much water was in the cylinder before any marbles were dropped in? mL wwwww Submit
The volume of one marble is 0.5 ml and the water level before dropping the marbles is 8 ml.
Finding Volume by Water Displacement Method:The volume of an object is the amount of space occupied by the object within all boundaries. The volume of any geometrical shape can be calculated by the respective formula.
The Water Displacement Method is a method that is used to calculate the volume of any object without knowing the dimensions. If we drop the object into the water and the amount that can be displaced will be equal to the volume of the object.
Here we have
After dropping 4 marbles, the height of the water level is 10 ml
After dropping 6 marbles, the height of the water level is 11 ml
This means for 2 extra marbles the water level increase up to 1 ml
So, the Volume of the marble = 1 ml/2 = 0.5 ml
From the given data,
After dropping 4 marbles the water level is 10 ml
As we know the volume of 1 marble = 0.5ml
=> Volume of 4 marbles = 4 × 0.5ml = 2ml
The water level before dropping 4 marbles = 10 ml - 2 ml = 8 ml
Therefore,
The volume of one marble is 0.5 ml and the water level before dropping the marbles is 8 ml.
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if there is sufficient evidence to reject the null hypothesis, we conclude that the alternate hypothesis is true
if there is not sufficient evidence to reject the null hypothesis, we conclude that the null hypothesis might be true, but we never conclude that the null hypothesis is true
If there is sufficient evidence to reject the null hypothesis, we conclude that the alternate hypothesis is true. if there is not sufficient evidence to reject the null hypothesis, we conclude that the null hypothesis might be true, but we never conclude that the null hypothesis is true
if there is not sufficient evidence to reject the null hypothesis, we conclude that the null hypothesis might be true, but we never conclude that the null hypothesis is true
This statement is describing the process of hypothesis testing in statistics. In hypothesis testing, a null hypothesis is a statement that there is no significant difference between two sets of data or no relationship between two variables. An alternate hypothesis is a statement that there is a significant difference or relationship.
When conducting a hypothesis test, a researcher will collect data and use statistical methods to determine the likelihood that the null hypothesis is true given the data. If the likelihood is low, the researcher will reject the null hypothesis and conclude that the alternate hypothesis is true. If the likelihood is high, the researcher will fail to reject the null hypothesis, but this does not necessarily mean that the null hypothesis is true. It means that the data is not strong enough to reject the null hypothesis.
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Paula who is 49 years old is seven times older than her son, Daniel.Daniel is two years younger than his sister, Leah. How old is Leah?
Para llegar desde un pueblo A hasta B existen 3 caminos, para llegar del pueblo B hasta el pueblo C hay 673 caminos distintos y para llegar desde el pueblo C hasta el pueblo D hay 2019 caminos, ¿Cuántos caminos distintos hay para llegar desde el pueblo A hasta el pueblo de pasando por los pueblos B y C?
⚘
what are you up for now and what time do you think you'll have time for
What is the area of ΔABC such that b = 28 cm, c = 14 cm, and m∠A = 30°? Round the answer to three decimal places.
The area of the ΔABC is 98 cm²
How to find the area of ΔABC?In a triangle, we can use the sine formula to find the area of the triangle when we know one angle and the two side lengths opposite and adjacent to that angle.
Area of ΔABC = (1/2) bc sinA
Substitute b = 28 cm, c = 14 cm, and m∠A = 30° into the formula:
Area of ΔABC = (1/2) × 28cm × 14cm × sin 30°
Area of ΔABC = 98 cm²
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Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(-5,-5)
(2,7)
(0, -3)
For it to be parallel, the point must follow the translation from (2,7) to that point similar to (0, -3) to (-5, -5) which is left 5 and down 2. So left 5 and down 2 for (2, 7) makes it (-3, 5)
solve for . assume is a matrix. do not use decimal numbers in your answer. if there are fractions, leave them unevaluated.
The value of X in the given system of matrix is,
[tex]X=\left[\begin{array}{ccc}\frac{-97}{145}&\frac{-45}{145} \\\\\frac{20}{29}&\frac{21}{29}\\\end{array}\right][/tex]
Matrices are one of the most powerful tools in mathematics. The evolution of the concept of matrices is the result of an attempt to obtain compact and simple methods of solving the system of linear equations.
We have 2 by 2 matrix in the form,
[tex]\left[\begin{array}{ccc}9&9\\-9&-9\\\end{array}\right] X+\left[\begin{array}{ccc}6&3\\7&9\\\end{array}\right] =\left[\begin{array}{ccc}-1&8\\-4&6\\\end{array}\right] X\\\\Assume, X=\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] \\\\[/tex]
After multiplication,
[tex]9a+9c+6=-a+8c\\\\-9a-9c+7=-4a+6c\\\\9b+9d+3=-b+8d\\\\-9b-9d+9=-4b-6d\\\\[/tex]
After solving the given system of equations
[tex]a=\frac{-97}{145}\\\\b=-\frac{54}{145}\\\\c=\frac{20}{29}\\\\d={21}{29}\\\\Hence, \\X=\left[\begin{array}{ccc}\frac{-97}{145}&\frac{-45}{145} \\\\\frac{20}{29}&\frac{21}{29}\\\end{array}\right][/tex]
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determine whether the statement below is true or false. justify the answer. the solution set of the linear system whose augmented matrix is is the same as the solution set of the equation .
This is a True statement that both the matrix equation and the augmented matrix translate into the same system of linear equations.
What are Linear equations?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.
A rectangular matrix is a grouping of numbers into rows and columns. Systems of equations can be solved using matrices. But first, we need to understand how to use matrices to represent systems.
An augmented matrix can be used to express a set of equations. Each column in an augmented matrix represents a variable or the constant terms, and each row in an augmented matrix represents one equation in the system. As a result, it is clear that augmented matrices provide a convenient approach to express systems of equations.
Therefore it is true that the solution set of the equation's equation is the same as the solution set of the linear system whose augmented matrix is.
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Given the figure below shows a regular hexagon, ABCDEF
What is the measure of each interior angle?
What is the measurement of the angle shown below? O O 150° 60° ○ 30° 10 20 30 0 170 150 150 140 130 120 180° 249 848 60 90 100 110 120 130 140 150 80 70 60 50 $ ata
150°
Because it is not acute it cant be 30°
a six sided dice is rolled 4 times, How many outcomes are there of rolling a 6 exactly 2 times?
The outcome that are there when a six sided dice is rolled four times is 2
What is sample space?A sample space is a collection or a set of possible outcomes of a random experiment. The p space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment.
The sample space of getting a 6 from a die is 1. A die has six sides and are labelled 1-6
The outcome of 4 times is is 4
Therefore for two rolls, it will be 4/2 = 2
Therefore the outcome to get 6 exactly two times is 2.
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solve 5+2x+12=4x+17-2x
Answer:
2x-4x+2x=17-12-5
0x=0
declare double variables x1, x2, x3, and x4, and read each variable from input in that order. find the average of x1, x2, x3, and x4 and assign the result to avgnumber.
The answer is x4 = input.nextDouble() and double avgnumber = (x1 + x2 + x3 + x4) / 4.
Declare the double variables x1, x2, x3, and x4.
double x1, x2, x3, x4;
Read each variable from input in that order.
Scanner input = new Scanner(System.in);
System.out.println("Enter x1:");
x1 = input.nextDouble();
System.out.println("Enter x2:");
x2 = input.nextDouble();
System.out.println("Enter x3:");
x3 = input.nextDouble();
System.out.println("Enter x4:");
x4 = input.nextDouble();
To Find the average of x1, x2, x3, and x4 and assign the result to avgnumber.
double avgnumber = (x1 + x2 + x3 + x4) / 4;
//This code takes four double variables from input and calculates the average by adding the four numbers together and dividing by four. The result is stored in the double variable avgnumber.
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You go to the grocery store and purchase the items listed in the table. What is your total if
the sales tax is 7%?
Answer:
where is the table?
Step-by-step explanation:
repost it with a picture of the table so we can answer it or tell the details and I'll answer in the comments?
NO LINKS!!
43. For the following functions, state whether they are growth or decay, then determine each function's growth/decay rate. (NOT MULTIPLE CHOICE)
a. f(x) = 0.3(1.6)^x
b. g(x) = 0.8^0.5x - 7
c. h(x) = 3(-5)^x
d. f(x) = e^(-0.45x) + 4
Answer:
a) Exponential growth function: 60%
b) Exponential decay function: 20%
c) Neither
d) Exponential decay function: 45%
Step-by-step explanation:
[tex]\textsf{Exponential Growth}: \quad y=a(1+r)^x[/tex]
[tex]\textsf{Exponential Decay}: \quad y=a(1-r)^x[/tex]
where:
a = initial value (the amount before measuring growth or decay)r = growth/decay rate (in decimal form)Part aGiven function:
[tex]f(x) = 0.3(1.6)^x[/tex]
The function is an exponential growth function and the growth rate is:
[tex]1+r=1.6 \implies r= 0.6 = 60\%[/tex]
Part bGiven function:
[tex]g(x) = 0.8^{0.5x} - 7[/tex]
The function is an exponential decay function and the decay rate is:
[tex]1-r=0.8 \implies r=0.2=20\%[/tex]
Part cGiven function:
[tex]h(x) = 3(-5)^x[/tex]
This is neither an exponential growth or decay function as exponential functions cannot have negative bases.
Part dNatural base exponential function
[tex]y=ae^{rx}[/tex]
If a > 0 and r > 0, the function is an exponential growth function.
If a > 0 and r < 0, the function is an exponential decay function.
Given function:
[tex]f(x) = e^{-0.45x} + 4[/tex]
As a = 1 > 0 and r = -0.45 < 0, the function is exponential decay function and the decay rate is:
[tex]r=-0.45=45\%[/tex]
find values of a, b, and c (if possible) such that the system of linear equations has a unique solution, no solution, and infinitely many solutions. (if not possible, enter impossible.) x y
The solution of the system of linear equations has infinitely many solutions.
Linear equation is defined as an algebraic equation of the form y=mx + b. involving only a constant and a first-order term, where m is the slope and b is the y-intercept.
Here we have given that the following linear equations are given then are listed as follows:
x + y = 4
y + z = 4
x + z = 4
ax + by + cz = 0
Here we have know that the sub-system consisting of 3 first equations has a unique solution x = y = z = 2.
While we add the fourth equation, then it becomes look like as follows:
=> 2a + 2b + 2c = 0
When we simplify this one then we get,
=> a + b + c = 0.
Which means that if a + b + c = 0, then the system of 4 equations has a unique solution otherwise it is IMPOSSIBLE to this system to have infinitely many solutions.
Complete Question:
Try to find values of a, b, and c (if possible) such that the system of linear equations has a unique solution, no solution, and infinitely many solutions. (If not possible, enter IMPOSSIBLE.)
x + y = 4
y + z = 4
x + z = 4
ax + by + cz = 0
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P (n), given below, is the price in dollars for n grams of vitamins. P(n)=0.5n+6.4 Complete the following statements. Let P¹ be the inverse function of P. Take x to be an output of the function P. That is, x=P (n) and n=P-¹(x). (a) Which statement best describes P-¹(x)? The reciprocal of the price (in dollars) for x grams of vitamins. The amount of vitamins (in grams) for a price of x dollars. The price (in dollars) for x grams of vitamins. The ratio of the price (in dollars) to the number of grams, x. -1 (b) P(x) = - 1 (c) P (9.2) = log 010 X log No solution 0=0 Ś
The number of vitamins (in grams) for a price of x dollars. Then the correct option is B. The inverse function is P⁻¹(x) = (x - 6.4) / 0.50. And at x = 9.2, the value P⁻¹(x) will be 5.4 grams.
What is the inverse function?Let the function f is given as
y = m(x + a) + c
Then the inverse function of the function f will be given by swapping x with y and y with x.
The function is given below.
P(n) = 0.50n + 6.4
The inverse of the function P(n) is given as,
x = 0.50P⁻¹(x) + 6.4
P⁻¹(x) = (x - 6.4) / 0.50
At x = 9.2, then we have
P⁻¹(9.2) = (9.2 - 6.4) / 0.50
P⁻¹(9.2) = 5.6 grams
The number of vitamins (in grams) for a price of x dollars.
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4. If a tablet PC had a net cost of $453.60 after a series discount of 20/10/10, what
was the list price of the PC?
The series discount of 20/10/10 means that there are three discounts given in sequence. The first discount is 20%, the second is 10%, and the third is 10%.
What does math's % mean?
In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
Let's call the original price x.
x - (20/100x) = 0.8x
then
0.8x - (10/1000.8x) = 0.72x
and finally
0.72x - (10/100*0.72x) = 0.648x
So, the net cost of $453.60 is equal to 0.648x.
We can find the original price by dividing the net cost by 0.648:
x = $453.60 / 0.648 = $700
So, the list price of the PC was $700.
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given the system of linear equations, written in column form as follows which of the following is the corresponding row form of this system?
The row form of the system is 5x = 2 and y – y = 0.
Column form:
3x + y = 5
2x – y = –3
Row form:
3x + 2x = 5 – 3
y – y = 0
The row form of this system is 3x + 2x = 5 – 3 and y – y = 0. To convert from column form to row form, the first step is to eliminate the y terms in the equations. To do this, we need to add the two equations together. This gives us:
3x + y = 5
2x – y = –3
3x + 2x = 5 + (–3)
y – y = 0
5x = 2
y – y = 0
Finally, we can solve for x and y.
5x = 2 ⇒ x = 2/5
y – y = 0 ⇒ y = 0
Therefore, the row form of the system is 5x = 2 and y – y = 0.
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in a survey it was found that studnets are talented at playing football. After assessment by coaches it was seen that 5% students possess football skills classed at professional level. A random sample of 10 studnets is obtained from the campus and measurements of their football skills were taken. Find the probability that 8 or more of these stundents were classed at professional level. the picture of quetsion is attached i have sloved the rest just cannot solve part d).
The probability that 8 or more of these students were classed at professional level is given as follows:
0%.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The values of the parameters for this problem are given as follows:
n = 10, p = 0.05.
Hence the probability of 8 or more of these students were classed at professional level is given as follows:
P(X >= 8) = P(X = 8) + P(X = 9) + P(X = 10)
In which:
P(X = 8) = 45 x (0.05)^8 x 0.95² = 0.P(X = 9) = 10 x (0.05)^9 x 0.95^1 = 0.P(X = 10) = 0.05^10 = 0.Hence the probability is of 0%.
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which of the following are true of quantitative research and quantitative researchers? (select all that apply.)
The correct statement about quantitative research is:
It uses formal questions and predetermined response options in questionnaires administered to large numbers of respondents.
We know that the quantitative research is nothing but the process of collecting and analyzing numerical data.
It is used to find the patterns, make predictions, test the relationships, and generalize results to given populations.
Whereas the qualitative research involves collecting and analyzing non-numerical data.
Quantitative research is mostly used in the natural sciences and social sciences.
It collects data using sampling methods, or by sending out online surveys/ polls, and questionnaires.
It uses formal questions and predetermined response options in questionnaires administered to large numbers of respondents.
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The complete question is:
Which of the following is true of quantitative research?
1) It enables researchers and clients to get closer to their customers and potential customers than does qualitative research.
2) It uses formal questions and predetermined response options in questionnaires administered to large numbers of respondents.
3) It is most often used with exploratory research designs.
4) It usually involves collecting detailed data from relatively small samples by asking questions or observing behavior.
5) It is superior for studying topics that involve complex psychological motivations not easily reduced to survey formats and quantitative analyses.
identify the correct unit fraction to multiply by the second term to create a common denominator for the rational expression below:
(2x^(2)-16)/(x^(2)-4)-(x 4)/(x-2)
The correct unit fraction to multiply by the second term to create a common denominator is [tex](x+2)/(x+2)[/tex]
To find a common denominator for the given rational expression, we need to identify a unit fraction that can multiply the second term so the denominators of both terms will be the same.
The denominators of the two terms are [tex]x^2-4[/tex] and [tex]x-2[/tex]. To find a common denominator for these terms, we can multiply the second term [tex](x+2)/(x+2)[/tex] which is a unit fraction because it is equal to 1.
Multiplying the second term by [tex](x+2)/(x+2)[/tex] gives us:
[tex](x 4)/(x-2) * (x+2)/(x+2) = (4x(x+2))/(x^2-4)[/tex]
Now both terms have a common denominator [tex]x^2-4[/tex]. Thus the correct unit fraction to multiply by the second term to create a common denominator is [tex](x+2)/(x+2)[/tex]
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The sum of the measures of angle P and angle Q is 100⁰.
• The measure of angle P is (3x - 15)°.
• The measure of angle Q is 25°.
What is the value of x? (7.11C, SS, RC3)
Answer:
x = 30
Step-by-step explanation:
You are given an angle and the sum of that angle with another that is (3x-15)°, and you want the value of x.
EquationThe sum of the two angles is given as 100°.
P +Q = 100°
(3x -15)° +25° = 100° . . . . . . use the given values for angles and sum
3x = 90 . . . . . . . . . . . . divide by ° and subtract 10
x = 30 . . . . . . . . . divide by 3
The value of x is 30.
suppose 83% of all students taking a beginning programming course fail to get their first program to run on first submission. consider a group of 7 such students,where each student's success is independent from the other and the chance each student fails on their first try is consistent. (round answers to three decimal places.)
The probability that all fail on their first submissions is 27.1%.
For each student, there are only two possible outcomes. Either their first program run will fail, or it wont. The probability of the first program run of a student failing is independent of the first program run of other students. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
The expected value of the binomial distribution is
The variance of the binomial distribution is
The standard deviation of the binomial distribution is
In this question, we have that:
83% of all students taking a beginning programming course fail to get their first program to run on first submission. Sample of 7 students. This means that
All fail on their first submissions
So,
0.271 = 27.1% probability that all ail on their first submissions
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Lewis is a famous author only if he knows how to write. But Lewis is not a famousauthor. Hence, Lewis does not know how to write.1.If A, then B.2.Not A.So, 3.Not B.
The formula used to explain this statement is known as Modus Tollens, which is a form of logical inference.
Modus Tollens states that if the antecedent (A) of a conditional statement is false, then the consequent (B) must also be false. This is expressed mathematically as ¬A ⟹ ¬B. The formula used to explain this statement is known as Modus Tollens, which is a form of logical inference.
In this particular example, A is the statement that Lewis is a famous author, and B is the statement that Lewis knows how to write. Since the statement A is false, the statement B must also be false. This can be represented mathematically as:
¬A ⟹ ¬B
¬(Lewis is a famous author) ⟹ ¬(Lewis knows how to write)
False ⟹ False
Therefore, Lewis does not know how to write.
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a ball suspended by a thread swings in a vertical plane so that its acceleration in the extreme position and lowest position are equal. The angle θ
of thread deflection in the extreme position will be:
(A) tan^−1(2)
(B) tan^−1(√2)
(C) tan^−1(1/2)
(D) 2tan^−1(1/2)
The angle θ of thread deflection in the extreme position is given by tan^−1(2).
The angle of thread deflection in the extreme position can be calculated by using the equation of motion of a simple pendulum.
The equation of motion for a simple pendulum is given by m g L sinθ = m a. Here, m is the mass of the ball, g is the gravitational acceleration, L is the length of the thread and θ is the angle of the thread.
From the given condition, the acceleration of the ball in the extreme and lowest positions are equal. This implies that the acceleration of the ball in the extreme position is equal to the acceleration due to gravity.
Therefore, the equation of motion reduces to g L sinθ = g. Solving for θ, we get sinθ = 1, which implies that θ = tan^−1(2).
Therefore, the angle θ of thread deflection in the extreme position is given by tan^−1(2).
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How many integers greater than 5400 have both of the following properties :
a) the digits are distinct.
b) the digits 2 and 7 do not occur,
There are 94830 integers greater than 5400
At first, go it looks .like an infinite number but As digits are distinct
so a maximum 10 digits number is possible
but 2 & 7 can not be used so the maximum 8-digit number can be there
Total number = 4 digits numbers, 5 Digits numbers, 6 digits number, 7 digits numbers, 8 digits numbers
All the 5 - 8 digit numbers would be > 5400
Available number of Digits = 8 ( 0, 1, 3, 4, 5, 6, 8, 9)
for numbers greater than 4 digits (5 - 8 Digits), 1st digit can be 1, 3, 4, 5, 6, 8, 9 then from the 2nd digit onward 0 can also be a digit but the already used digit can not be used. and further one digit (already used) will keep reducing
5 Digits numbers = 7 * 7 * 6 * 5 * 4 = 5880
6 Digit Numbers = 7 * 7 * 6 * 5 * 4 *3 = 17640
7 Digits numbers = 7 * 7 * 6 * 5 * 4*2 = 35280
8 Digit Numbers = 7 * 7 * 6 * 5 * 4 *3*2*1 = 35280
Now in 4-digit numbers
Number starting with 6, 8, 9 > 5400 & number starting with 5
Number starting with 6 , 8 , 9 = 3 * 7 * 6 * 5 = 630
Number starting with 5, the second digit must be 4, 6, 8, 9
Number starting with 5 = 1 * 4* 6 * 5 = 120
Total integers greater than 5400
=5880 + 17640 + 35280 + 35280 + 630 + 120
= 94830
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bridge is a card game in which the deck of 52 cards is randomly and equally divided among the 4 players. so each player gets 13 cards.
The formula for calculating the number of cards each player receives in Bridge is N/4, where N = number of cards in the deck.
For a standard deck of 52 cards, each player would receive 52/4 = 13 cards. This can be further simplified to 13.33, however, since cards cannot be divided, the result is rounded down to 13 cards. Therefore, each player in a Bridge game with a standard deck of 52 cards will receive 13 cards.
The total number of cards in the deck is 52, so each player will get 13 cards. This can be expressed mathematically using the formula P = 52/4, where P is the number of cards per player. Therefore, P = 13. We can also use the formula to calculate the number of players if we know the total number of cards. For example, if we have 156 cards, the number of players can be calculated using the formula P = 156/4, which gives us P = 39. Therefore, there will be 39 players in the game.
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The average high temperature in degrees for a city are listed 58,61,71,77,91,100,105,102,95,82,66,57 if a value of 48 is added to the data how does the median change
If a value of 48 was added, the median of the data-set would remain decay from 79.5 to 77.
How to obtain the median of a data-set?The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than.
The ordered data-set for this problem is given as follows:
57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105.
The data-set has an even cardinality of 12, hence the median is the mean of the 6th and the 7th elements, as follows:
(77 + 82)/2 = 79.5.
A value of 48 would be lowest value of the data-set, the cardinality would be odd, and thus the middle value would be of 77.
More can be learned about the median of a data-set at brainly.com/question/3514929
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Triangle A C B is cut by line segment E D. Line segment E D goes from side B C to side A C. The length of B A is 4 x minus 6 and the length of E D is x + 2. The length of B E is x. Sides B E and E C are congruent. Sides A D and D C are congruent.
What is the length of BC?
From the markings on the diagram, we can tell E is the midpoint of BC and
D
is the midpoint of AC
We can apply the
theorem: ED = One-halfBA.
Substituting in the expressions for the lengths and solving for x, we get x =
.
Now, since BE = x, then BC =
.
The length of BC is 10.
What are similar triangles?When two triangles have some common corresponding properties, they are said to be similar. But they are no congruent.
In the given question, comparing triangles ABC and DEC. We have;
DE/ AB = EC/ BC
But,
BC = 2BE
= 2x
So that,
(x + 2)/ (4x - 6) = x/ 2x
(x + 2)/ (4x - 6) = 1/ 2
2(x + 2) = (4x - 6)
2x + 4 = 4x - 6
collect like terms
6 + 4 = 4x - 2
10 = 2x
x = 10/ 2
x = 5
Then,
BC = 2x
= 2*5
BC = 10
The length of BC is 10.
Learn more about similar triangles at https://brainly.com/question/25187489
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