The solution for this system of linear equation is (-16, -5 1/3).
What is Linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
It is preferable to employ substitution while trying to solve this system of linear equations.
The first equation yields x = 3y.
In the second equation, change the value of x to be represented by the expression on the right.
-2(3y) + 3y = 16
Calculating the value of y yields;
y = -5 1/3
Solving for x with this value of y results in;
x = -16
The solution for this system of linear equation is (-16, -5 1/3).
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Which one is a prime number 8?.
The given number 8 is not a prime number.
Given that,
To justify whether the number 8 is a prime number or not.
A prime number is a whole number bigger than one with just the number one and itself as factors.
Here,
A prime number is given as 1,2, 3,5, 7, 11, 13, and so on,
From the above series, it is determined that 8 is not a prime number.
Thus, the given number 8 is not a prime number.
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a busy student must complete 3 problem sets before doing laundry. each problem set requires 1 day with probability 2/3 and 2 days with probability 1/3. let b be the number of days a busy student delays laundry. what is ex(b)
The value of expected time ex(b)=1 day approximately if b is the number of days a busy student delays Laundry.
What is meant by expected time?The basic anticipated value formula is (P(x) * n): the probability of an occurrence multiplied by the number of times the event occurs.
The expected value (also known as the expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average in probability theory. The anticipated value is the arithmetic mean of a large number of independently chosen random variable outcomes.
Let b be the number of days a busy student puts off doing laundry.
The given information is tabulated as below:
Days(b) 1 2
Probability, p(b) 2/3 1/3
The expected time is given as,
E(b)=∑i=1ᵇp(b)
=(1×(2/3))+(2×(1/3))
=4/3
=1.3333
Therefore, the value of ex(b):
1.3333 day ≈ 1 day
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Elena has received grant money to open a local community center. she will do many of the improvements herself to the old building she rents. while touring the building to make her project list, she uses a tape measure to check whether floors, doorways, and walls are square, meaning that they meet at right angles. a elena measures the lobby of the building for new laminate flooring. the length is 30 feet, the width is 16 feet, and the diagonal is 34 feet. is the room square?
Yes the room is square with the length is 30 feet, the width is 16 feet, and the diagonal is 34 feet .
Given:
Elena has received grant money to open a local community center. she will do many of the improvements herself to the old building she rents. while touring the building to make her project list, she uses a tape measure to check whether floors, doorways, and walls are square, meaning that they meet at right angles. a elena measures the lobby of the building for new laminate flooring. the length is 30 feet, the width is 16 feet, and the diagonal is 34 feet.
with sides 30, 16 and hypotenuse 34 the figure forms a right angled triangle.
According to pythagoream theorem:
30^2+16^2 = 34^2
900+16^2 = 34^2
900 + 256 = 1156
1156 = 1156
Therefore Yes the room is square with the length is 30 feet, the width is 16 feet, and the diagonal is 34 feet .
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a group of five friends go to a restaurant for dinner. the restaurant offers 20 different main dishes. (a) suppose that the group collectively orders five different dishes to share. the waiter just needs to place all five dishes in the center of the table. how many different possible orders are there for the group? (b) suppose that each individual orders a main course. the waiter must remember who ordered which dish as part of the order. it's possible for more than one person to order the same dish. how many different possible orders are there for the group? (c) suppose that each individual orders a main course. the waiter must remember who ordered which dish as part of the order. however the friends agree that no two people will order the same dish. how many different possible orders are there for the group?
The number of different possible orders that are there for the group is 15504 .
In the question ,
it is given that ,
total number of friends = 5 ,
the number of dishes that restaurant offers for dinner = 20 dishes .
It is given that, group collectively orders 5 different dishes to share and waiter just needs to place all 5 dishes in the center of the table.
So , the 5 dishes from the 20 dishes can be selected in ²⁰C₅ ways .
²⁰C₅ = 20!/(15! * 5!)
= 20*19*18*17*16*15! / (15! * 5!)
= (20*19*18*17*16)/(5*4*3*2*1)
Simplifying Further , we get
= 1860480/120
= 15504 ways
Therefore , There are 15504 possible orders for the group .
The given question is incomplete , the complete question is
A group of five friends go to a restaurant for dinner. the restaurant offers 20 different main dishes. Suppose that the group collectively orders five different dishes to share. the waiter just needs to place all five dishes in the center of the table. how many different possible orders are there for the group ?
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What is the maximum number of student tickets that can be sold if the drama club meets its sales goal? 40 60 80 100.
If the theater club fulfills its sales target, 40 student tickets can be sold in total when the drama club members need to sell 100 tickets.
Given that,
The drama club members need to sell 100 tickets. If the drama club fulfils its sales target, will tickets cost $5 each and be sold to students. Tickets cost $10 for non-students. The total amount of ticket sales that the drama club must get is at least $800. The number of student tickets, s, and the number of non-student tickets, n, that the members must sell are represented by the system of inequalities.
s+n≤100
5s+10n≥800
We have to find if the theater club fulfills its sales target, how many student tickets can be sold in total.
We know that,
Take the system of inequality
s+n≤100
5s+10n≥800
By solving the inequality we get s=40 and n=60
Therefore, if the theater club fulfills its sales target, 40 student tickets can be sold in total.
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Answer:
A.
Step-by-step explanation:
jorje wants to estimate the percentage of people who play sports. he surveys 330 individuals and finds that 65 play sport. find the margin of error for the confidence interval for the population proportion with a 95% confidence level.
The margin of error for the confidence interval for the population proportion with a 95% confidence level is 0.000207
How to find the margin of errorfinding the percentage of 65 of 330 individuals
65 / 330 * 100 = 19.697% = 0.19697
number of samples, n = 330
standard deviation, σ is calculated from
= √{(p(1 - p)) / n}
= √{(0.197 * (1 - 19.7)) / 330}
= √{(0.197 * (0.803)) / 330}
= 0.022
Margin of error, E
= Z(0.95) * σ/√(n)
= 0.171 * 0.022/√(330)
= 0.171 * √(0.022²/330)
= 0.000207
= 0.021%
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suppose a jar contains 15 red marbles and 37 blue marbles. if you reach in the jar and pull out 2 marbles at random, find the probability that both are red. write your answer in decimal form, rounded to the nearest thousandth. answer:
The probability that both are red is 0.0791.
Given,
Total marbles: 37 + 15 = 52
According to the number of red cards out of all the cards, there is a 15/52 possibility that a red card will be pulled during our initial pull.
Depending on how many red/total marbles are still in there, there is a 14/51 probability that the second marble pulled will also be red.
Our two fractions are multiplied together from here,
15/52 * 14/51
We can start by simplifying a little bit; the numbers 14 and 52 share a 2;
15/26 * 7/51
Our result is 35/442
Depending on whether you choose to maintain it in fractional, ratio, or percentage form, the result of dividing is around 0.0791, which rounds to 7.91%.
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Which is a way to solve the equation 4x = 128 if you do not know a power of 4 that equals 128?.
in hypothesis testing, the tentative assumption about the population parameter is group of answer choices
The goal of a hypothesis test is to determine if the data can refuse an assumption a parameter or a population.
Statistical hypothesis test: A statistical hypothesis test is a technique for determining whether the available data are sufficient to support a specific hypothesis. We can make probabilistic claims about population parameters through hypothesis testing.
The purpose of a hypothesis test is to ascertain whether the data can refute a parameter or population assumption.
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How many solutions does this linear system have Y =- 6x 2 and 12x 2y =- 4 Brainly?.
The linear system of equation y =-6x+2 and 12x+ 2y =- 4 has only one solution.
The linear equation is y = -6x+2 .
Now for any value of x we find the value of y ,
at x=0 ,y = 2
at x=1 , y = -4
at x=-2 , y = 14
Hence there are infinitely many solutions on the line . All points on the straight line are solutions.
The collection of variable values in a linear equation that yields every feasible solution is referred to as the "solution of a linear equation." In order to model real-world issues, linear equations include unknown quantities as one or more variables.
The locations where the lines or planes used to illustrate the linear equations intersect or meet are known as the solutions. The set of values for each variable in a system of linear equations is known as the solution set.
Disclaimer: the complete question is :
How many solutions does this linear system have Y =- 6x + 2 and 12x + 2y =- 4?.
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what is a continuity correction? (b) why do we use a continuity correction when we approximate a binomial probability distribution with a normal distribution but not when we approximate it with a poisson distribution?
A normal distribution is continuous, but a binomial distribution is not, and this difference is taken into account by the continuity correction factor. It is necessary to add a continuity correction factor when using a normal distribution to approach a binomial distribution. Just add or subtract, and you're done.
How does continuity correction work?When a discrete probability distribution is approximated by a continuous probability distribution, the continuity correction factor is utilized. The continuum correction factor serves as a link between the discrete binomial and the continuous normal distribution.
In statistics, why do we utilize probability distribution?By allowing us to evaluate the variability of occurrence or provide estimates of the likelihood that a specific event will occur, probability distributions aid in the modeling of our environment. They are a typical technique to explain and maybe anticipate the likelihood of an event.
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a sports guard thickness of about mm is desirable for heavy contact sports in which injuries are more likely. group of answer choices 1 2 4 8
Answer:
What is the question?! I don't understand, sry?!
Step-by-step explanation:
Sabia and arlan bougth 45 book for r 30 each old all ok them at the rote of 24 find the different the money pent and return
If Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, how many books they can buy,
Rs 30 = 45 book
Rs 30 = 45
Rs 1 = 45 / 30
Rs 24 = 3/2 × 24
Rs 24 = 34 books
Thus, if Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.
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At the beginning of the season, MacDonald had to remove 555 orange trees from his farm. Each of the remaining trees produced 210210210 oranges for a total harvest of 417904179041790 oranges.
Write an equation to determine the initial number of orange trees (t)(t)left parenthesis, t, right parenthesis on MacDonald's farm.
The equation that can be used to to determine the number of trees can be presented as follows;
t = 41790 ÷ 210 + 5
What is an equation?An equation is a mathematical statement that consists of mathematical expressions joined by an equals to sign.
The number of orange trees MacDonald removes from his farm = 5 teres
The number of oranges produced by each of the remaining trees = 210
The number of oranges in the harvest = 41790 oranges
The initial number of orange trees is therefore;
The number of orange trees that produce the 41790 oranges is therefore;
41790 ÷ 210 = 199
The number of orange trees remaining after the 5 trees have been removed = 199 trees
The initial number of trees is therefore;
t = 5 + 41790 ÷ 210 = 204
The initial number of trees, t = 204 trees
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xplain your choice. this statistic is biased, but it has a much lower standard deviation than the other two. this statistic is unbiased and has the smallest standard deviation of the three. the standard deviation of this statistic isn't the lowest, but it is the only unbiased statistic out of the three. the standard deviation of this statistic isn't the highest, but it is the only unbiased statistic out of the three. this statistic is biased, but it has a much higher standard deviation than the other two. this statistic is unbiased and has the largest standard deviation of the three.
The recommended statistic is statistic II because this statistic is unbiased and has the smallest standard deviation of three.
How to choose the recommended statistic?Unbiased statistic is more accurate than biased statistic because which on sampling distribution mean equal to population parameter.
Standard deviation is value of dispersed of observed value sampling around population parameter. Smaller standard deviation can be equated with a smaller deviation of data. Which in unbiased statistic means lots of value closer to population parameter.
If even statistic is unbiased but standard deviation high (statistic III) it not recommended because lots of value is not close enough to population parameter.
Thus, the recommended statistic is unbiased statistic and have smallest standard deviation which is statistic II.
Your question is incomplete, but most probably your full question was (image attached)
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What is the equation of the function that is graphed as line a?
y = -2 x
y = x + 1
y = x - 1
y = 2 x + 1
Answer: D. y = 2 x + 1
Step-by-step explanation:
Jamie buys a box of blue tiles that will cover 4ft2 . What percent of the floor can she tile using this box ? Does Jaime need to buy another box of blue tiles explain
The blue tiles on the floor is an illustration of proportions. The blue tiles will cover 25% of the floor
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
From the complete question, the dimension of the floor is 4 ft by 4 ft.
So, the area of the floor
Area = 4 x 4
Area = 16
The blue tiles cover 4 square feet.
So, the percent of floor is:
= 4/16 x 100
= 1/4 x 100
= 25%
Hence, the blue tiles will cover 25% of the floor. Also, he doesn't need to buy another set of blue tiles.
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What type of number is expressed in the form a bi?.
Number expressed in the form a+ bi is complex number.
What is Number system?A number system is defined as a system of writing to express numbers.
The number is expressed in the form a + bi
A complex number is a number of the form a + bi, where a and b are real numbers, and i is an indeterminate satisfying i² = −1.
The number a+bi, in which a is real number and b is imaginary number.
Hence, number expressed in the form a+ bi is complex number.
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I will give brainlest
Some other names for the unit rate are:
Constant of proportionality.Slope.Gradient.Rate of change.How is called the unit rate?A general proportional relation is written as:
y = k*x
You can see that it goes through the origin because when we evaluate in x = 0, we get:
y = k*0 = 0
So it passes through (0, 0).
The value "k" has several names, unit rate is the one given here, but it is generally called the "constant of proportionality"
It is also called the slope (like in a linear equation with an y-intercept equal to 0).
Or the rate of change or gradient, which are equivalent terms that particularly in the case of linear equations are equal to the slope (but not for other functions).
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If the coefficient of determination is a positive value, then the coefficient of correlation.
If the coefficient of determination is a positive value, then the correlation coefficient can be negative or positive, which means the value of the correlation coefficient is between -1 and +1. If the variable x increases, the variable y also increases, and if the variable x decreases, then the variable y also decreases.
What is the Coefficient of Determination?The coefficient of determination is a statistical measurement which examines how differences in one variable can be explained by the difference in a second variable, when predicting the outcome of a given event. The coefficient of determination is a number between 0 and 1 that measures how well a statistical model predicts an outcome. This provides a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model.
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What is the solution to this system of linear equations 2x 3y 3 7x 3y 24?.
The solution to the system of linear equations 2x + 3y = 3 and 7x - 3y = 24 is (3 , -1).
What is a linear equation ?
A linear equation is an algebraic equation of the form y = mx + c, involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
2x + 3y = 3
7x - 3y = 24
By addimng both the linear equation,
9x = 27
x = 27/9
x = 3
Substitute the value of x in either of the equations
2 (3) = 3y = 3
6 + 3y = 3
3y = -3
y = -1
Therefore, the solution to this system of linear equations is (3 , -1).
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What are the multiples of 3 and 10?.
6:3(3+3)=?
What does it equal
Answer:
12
Step-by-step explanation:
= 6:3(3+3)
= 6/3 x 6
= 12
if UVWX is a parallelogram, what is the value of y?
Answer:
B. 60
Step-by-step explanation:
Side VU must be equal to side WX
15 = (1/4)y
divide both sides by 1/4
15 / (1/4) = y
60 = y
pls help 81 points pls I need help don't guys this assignment is worth 50 points
I have a D- in math right now pls don't guys pls and its almost midterms so i need this A+
so pls don't guess.
Answer:
6,942 steps left!
Step-by-step explanation:
OK so this is easy so we know that if 1 / 19 = 0.052 we minus that by - 3 because - 3 is our exponent that gives us 3.052 so now we just take 3.052 - 10,000 which gives us exactly 6942 you two steps so he needs 6942 steps left
Answer:
3,141 steps
Step-by-step explanation:
Let x be equal to the number of steps he needs to reach his goal
10,000 = [tex](\frac{1}{19} )^{-3}[/tex]+ x
10,000 = 6,859 + x
3,141 = x
Consider the following vocabulary:
Equilateral right angled triangle
Isosceles acute triangle
Scalene obtuse triangle
Which of these triangles are possible?
Which of these triangles are not possible?
Explain your reasoning.
An equilateral right angled triangle is not possible because a triangle can only consist of 180°. Since a right angle is 90°, there is no way that a triangle can be have three right angles. 180° ≠ 270°
An isosceles acute triangle is possible because two angles can be acute and have the same degree values and the last angle can have a different value of another acute angle. The two angles that are acute would have the same value for their corresponding sides.
A scalene obtuse triangle is possible because one angle can be obtuse and the other ones can be acute. All the sides can be different.
I hope this helps you! Have an amazing rest of your day!
You have to specify the power output of a motor for a ski tow rope that will carry 25 skiers at a time. The grade of the ski slope is 32 above horizontal and the average coefficient of kinetic friction between skis and snow is 0.12. The tow speed is to be 2.0 m/s and each skier has an inertia of 60 kg (a reasonable average value)
The power output of a motor for a ski tow rope is 6925.333 Watt.
We are know that,
Speed = v = 2.0m/s
Mass = m = 60kg
Number of skier = N = 25
The slope formed angle = Ф = 32°
The acceleration due to gravity = 9.8m/s²
Thus, to calculate the power of motor for a ski tow rope then we use formula, and (we know that F = mg)
P = (Nmg)(vcosФ)
Where , P is the power and putting the all given values in above equation,
P =[(25× 60kg ×9.8m/s²)×(2.0km/hr)×{(1m/s})/(3.6km/h)} cos32°
P = 8166.66×0.848 Watt
P = 6925.333 Watt
Therefore, the power output of a motor for a ski tow rope would be 6925.333 Watt.
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the student government at a high school wants to conduct a survey of student opinion. it wants to begin with a simple random sample of 60 students. which of the following survey methods will produce a simple random sample?
The survey methods that will produce a simple random sample of 60 students in a high school is: Number the students in the official school roster. Use a table of random numbers to choose 60 students from this roster for the survey.
What is a simple random sampling?Simple random sampling is a type of probability sampling where the researcher randomly chooses a subset of participants from a population. Each part of the population has the same chance of being selected. Then, data is collected from as large a percentage as possible of the random subset.
The American Community Survey is an example of simple random sampling. In order to gather detailed data on the population of the US, the Census Bureau officials randomly choose 3.5 million households a year and use variety of methods to make them sure to fill out the survey.
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Calculate the length of x
Answer:
x = 13.85 cm
Step-by-step explanation:
Forming the equation,
→ (16)² = (x)² + (8)²
Now the value of x will be,
→ (16)² = (x)² + (8)²
→ 256 = x² + 64
→ x² = 256 - 64
→ x = √192
→ x = 13.8564
→ [ x = 13.85 ]
Hence, value of x is 13.85.
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The amount compounded at a rate of 8% over a period of 6 years is $8,551.56
Compound InterestThe compound interest is the interest-based on the initial principal amount and the interest collected over the period of time. The formula for compound interest can be derived from the formula for simple interest. The formula for simple interest is the product of the principal, time period, and rate of interest (SI = ptr/100). Before looking into to derivation of the formula for compound interest, let us understand the basic difference between simple interest, compound interest computation. The principal remains constant over a period of time, for simple internet computation, but for compound interest computation the interest is added to the principal, for compound interest computation. The compound interest formula is given below:
A = P(1 + r/n)^nt
Compound InterestP = principalr = rate n = number of times compoundedt = timeApplying the formula of compound interest here;
A = 5300(1 + 0.08/12)^12 * 6
A = $8,551.56
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