The solution to the system of equations, using elimination, is given as follows:
x = 0.0135, y = -0.2767, z = -0.1024.
How to obtain the solution to the system of equations?The solution to the system of equations is obtained using the elimination method, as the variables are written as functions of each other and then solved.
The system in this problem is composed by the equations presented as follows:
5x - 3y - z = 1.x + 4y - 6z = -1.2x + 3y + 4z = 9.From the first equation, the variable z is written as function of variables x and y, as follows:
z = 5x - 3y - 1.
Replacing in the second equation, we have that:
x + 4y - 6(5x - 3y - 1) = -1
-29x + 22y = -7.
Replacing in the third equation, we have that:
2x + 3y + 4(5x - 3y - 1) = -1
22x - 9y = 3.
Hence the system is now:
-29x + 22y = -7.22x - 9y = 3.Multiplying the first equation by 9 and the second by 22, we have that:
-261x + 198y = -63.484x - 198y = 66.Adding the equations, the solution for x is obtained as follows:
223x = 3
x = 3/223
x = 0.0135.
Then the solution for y is obtained as follows:
-261(0.0315) + 198y = -63
y = (-63 + 261(0.0315))/198
y = -0.2767.
The solution for z is:
z = 5(0.0135) - 3(-0.2767) - 1 = -0.1024,
TranslationThe problem asks to solve the system of equations using the elimination method.
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Find the ending balance :
Principal: $600
Interest rate :5%
Time : 6 years
Answer:
3816
Step-by-step explanation:
emma estimated the
first digit in the quotient of 2,183 ÷ 42 as 4. She adjusted the quotient to 3. What did she do wrong? Explain how Emma can avoid her mistake.
Quotient is 51.97 by dividing 2,183 by 42. A quotient is the amount that results from dividing two numbers.
How to divide a number ?One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The additional operations are multiplication, addition, and subtraction.
Multiply the first fraction by the reciprocal of the second to divide rational expressions. We factor everything and search for common factors after rewriting the division as multiplication of the first statement by the reciprocal of the second. Separate logical expressions.
The number 2183 is called the numerator or dividend, and the number 42 is called the denominator or divisor.
The quotient of 2183 and 42, the ratio of 2183 and 42, as well as the fraction of 2183 and 42 all mean (almost) the same:
2183 divided by 42, often written as 2183/42.
2183/42 = 51.97
The answer that is quotient is 51.97
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The mistake she done is that the acutal quotient is 51.97.
How to divide a number ?One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The additional operations are multiplication, addition, and subtraction.Multiply the first fraction by the reciprocal of the second to divide rational expressions. We factor everything and search for common factors after rewriting the division as multiplication of the first statement by the reciprocal of the second. Separate logical expressions.The number 2183 is called the numerator or dividend, and the number 42 is called the denominator or divisor.
The quotient of 2183 and 42, the ratio of 2183 and 42, as well as the fraction of 2183 and 42 all mean (almost) the same:
2183 divided by 42, often written as 2183/42.
2183/42 = 51.97
The answer that is quotient is 51.97
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What is the rectangular form of Theta = StartFraction 3 pi Over 4 EndFraction? x − y = 0 x − y = 1 x + y = 0 x + y = 1
The rectangular form of Theta = StartFraction 3 pi Over 4 EndFraction is x + y = 0.
What are polar coordinates?The polar coordinates system is a two-dimensional coordinate system in which each point is determined by distance from the point and an angle from the reference direction.
This is about converting polar coordinate to rectangular form.
Relationship between coordinates is:
x = r cosθ
y = r sinθ
then;
y/x = sinθ/cosθ
y/x = tanθ
We have θ = 5π/6, finding the value of tan:
tan 5π/6 = tan (π - π/6)
= - 1/√3
= - √3/3
Now Substitute tan with its value:
y/x = -√3/√3
√3y = -√3x
y + x = 0
x + y = 0
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Answer:
c on edge
Step-by-step explanation:
compare adding and subtracting to multiplying and dividing bases with different exponents.
Exponent rules for addition and subtraction are identical to one another. As a reminder, all terms' bases must be the same in order to remove terms with exponents. All terms' exponents must be equal.
Define exponents.A number written as a superscript over another number is known as an exponent. In other words, it means that the base has been elevated to a particular level of power. Other names for the exponent are index and power. mn indicates that m has been multiplied by itself n times if m is a positive number and n is its exponent.
Given,
Adding and subtracting to multiplying and dividing bases with different exponents.
Exponent rules for addition and subtraction are identical to one another. As a reminder, all terms' bases must be the same in order to remove terms with exponents. All terms' exponents must be equal.
The exponents and variables must match in order to add exponents. The exponents are left constant while the variable coefficients are added. The addition only includes terms with the same variables and powers. Exponents can be multiplied and divided according to this rule.
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based on the results of the simulation, is there convincing statistical evidence at the significance level of 0.05 that the event of audrey selling at least 7 of the 30 selected tickets is unlikely to have occurred by chance alone? responses yes, because the distribution of the trials in the simulation is skewed to the right. yes, because the distribution of the trials in the simulation is skewed to the right. yes, because the number in the histogram with the greatest frequency is 4, not 7. yes, because the number in the histogram with the greatest frequency is 4, not 7. yes, because 7 appears in the right tail of the distribution, indicating that it is more than 2 standard deviations away from the mean. yes, because 7 appears in the right tail of the distribution, indicating that it is more than 2 standard deviations away from the mean. no, because the simulation suggests that it is likely that audrey could sell anywhere from 0 to 11 of the selected tickets. no, because the simulation suggests that it is likely that audrey could sell anywhere from 0 to 11 of the selected tickets. no, because the simulation suggests that audrey selling at least 7 of 30 selected tickets would occur about 13.8% of the time.
No, there isn't any statistical proof because, according to the simulation, Audrey would sell at least 7 out of the 30 chosen tickets roughly 13.8% of the time.
What exactly is statistical proof?
A type of explanation known as statistical evidence is one that is based on information that has been gathered and then assessed using a mathematical model.
Based on the information provided, the students created the following simulation:
Choose 88 red chips and the rest 600 blue chips.
30 chips are chosen at random, with no replacements.
When choosing the 30 chips, keep track of and record the amount of red chips.
Therefore, we may say that there is no statistical proof that the occurrence happened by chance alone at = 0.05.
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On a map with a scale 1: 100,000, the distance between two cities is 12 cm. What would be the distance between these two cities on a different map with a scale 1:300,000?
The distance between these two cities on a different map with a scale 1:300,000 is 4vm
How to calculate the distance?From the information, on the map with a scale 1: 100,000, the distance between two cities is 12 cm.
In this case, the distance between these two cities on a different map with a scale 1:300,000 will be:
= (100000 / 300000) × 12
= 1/3 × 12
= 4cm
The distance is 4cm.
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SOME HELP FAST!! What is the slope of this line?
Answer:
-2/3
Step-by-step explanation:
A sports ball has a diameter of 10 cm. Find the volume of the ball.
cm.3
Round your answer to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
take the radius which is 5 square it 5^2 and divide by 3 then round hope it helps
Answer: 8,33333333333333333
Step-by-step explanation: 5^2 =25 divided by 3 is 8,33333333333333333
a machine makes 36 trophies every hour. The machine makes trophies for 8 and a half hours each day, on 5 days of the week. The trophies are pack into boxes. Each box holds 8 trophies.
How many boxes are needed for all the trophies made each week?
Answer: 1530
Step-by-step explanation: First, you would want to calculate how many are made in one day. 36 trophies are made per hour, for 8 1/2 hours. 36 x 8.5(8 and a half) is 306, so in one day, 306 are made. Then, all you have left is to multiply it by 5, for five days, and that would be 1530. Hope This Helps.
If an additional worker can produce an additional 20 units of output which can be sold for $4 per unit, what is the maximum wage that this perfectly competitive firm should pay to hire this worker?.
The maximum wage that this perfectly competitive firm should pay to hire this worker = $80
The options for this question
A) $80 minus the firm's profit markup
B) It depends on what the going wage rate is in the labor market.
C) $80
D) There is insufficient information to answer the question.
now, we need to find the maximum wage that this perfectly competitive firm should pay to hire this worker
given that
the additional worker can produce an additional 20 units of output and that can be sold for$4 per unit
maximum wage = additional units × sold per unit
= 20 × 4 = 80
the maximum wage = $80
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use your knowledge of angle relationship to solve for X in the diagram below. By your solution by name in the geometric relationship.
Answer:
Solution
Here ,
5x +7 = 9x-63 (Corresponding angle)
or, 5x-9x =-63-7
or, -4x =-70
or, X=17.5
Hence the value of X is 17.5 degree.
Sharifa's white ball rolled 143 centimeters in 4 seconds and her green ball rolled 112 centimeters in 3 seconds. Which ball rolled at a greater rate of speed?
Question 3 options:
A: white ball
B: green ball
C: The white and green ball rolled at the same rate of speed.
D: red ball
If Sharifa's white ball rolled 143 centimeters in 4 seconds and her green ball rolled 112 centimeters in 3 seconds. The ball that rolled at a greater is: B: green ball.
How to find the speed?Using this formula to find the fastest and the slowest speed
Speed for white ball :
Speed for white ball = 143 centimeters /4 seconds
Speed for white ball = 34.75
Speed for green ball:
Speed for green ball = 112 centimeters /3 seconds
Speed for green ball= 37.33
37.33 is greater than 34.75 which means that green ball is the fastest.
Therefore the correct option is B.
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Points located on a function include: (3, 6), (-5, 7), (13, 1), and (7, 14). Which point cannot be included in the function?
A (14, 5)
B (5, 6)
C (7, 2)
D (8, 0)
The point cannot be included in the function is (7, 2). Therefore, option C is the correct answer.
The given coordinate points are (3, 6), (-5, 7), (13, 1), and (7, 14).
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
A) (14, 5)
Along with the given points (3, 6), (-5, 7), (13, 1), and (7, 14), the point (14, 5) is included in the function.
It is a function as every input has a unique output.
B) (5, 6)
Along with the given points (3, 6), (-5, 7), (13, 1), and (7, 14), the point (5, 6) is included in the function.
It is a function as every input has a unique output.
C) (7, 2)
Along with the given points (3, 6), (-5, 7), (13, 1), and (7, 14), the point (7, 2) is not included in the function.
Since the element 7 corresponds to two different images i.e., 14 and 2.
D) (8, 0)
Along with the given points (3, 6), (-5, 7), (13, 1), and (7, 14), the point (8, 0) is included in the function.
It is a function as every input has a unique output.
The point cannot be included in the function is (7, 2). Therefore, option C is the correct answer.
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Steven's birthday party will cost $168 if he invites 14 guests. If there are 59 guests, how much will Steven's birthday party cost? Solve using unit rates.
Calculated using unit rates, Steven's birthday party will cost him $ 708 if he were to invite 59 guests.
If the party will cost him $168 for him to invite 14 guests, then we will need to calculate the cost for each guest using unit rates.
if 14 guests = $168,
1 guest = 168/14 = $12
so it will cost him $12 per guest he invites
Knowing that each guest will cost him $12, then if Steven wants to invite 59 guests to his birthday party, he will be spending:
59 × $12 = $708
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Reduce 4hours 20minutes by 12%
Step-by-step explanation:
by 12 % seconds
Can you help me, please?
Answer: 19
Step-by-step explanation:
2 ( X + 9 ) - 15 = -3
Answer:
x = -2
Step-by-step explanation:
2(x + 9) - 15 = -3 Distributive property
2(x) + 2(9) -15 = -3
2x +18 - 15 = -3 Combine like terms
3x + 3 = -3 Subtract 3 from both sides
3x = -6 Divide both sides by 3
x = -2
Which of the following is true of prime numbers?
A.
A prime number may be an even number or an odd number.
B.
A prime number is always an even number.
C.
A prime number is always an odd number.
D.
A composite number may be an even number or an odd number.
Answer:
C
Step-by-step explanation:
Prime numbers are only divisible by themselves and 1 ....all even numbers are divisible by '2' , so all primes are odd numbers
7.34 the gpas of all students enrolled at a large university have an approximate normal distribution with a mean of 3.02 and a standard deviation of .29. find the probability that the mean gpa of a random sample of 20 students selected from this university is
The probability that the mean GPA of a random sample of 20 students selected from this university is 3.10 or higher is 10.93%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:Problems of normally distributed samples are solved using the z-score methods.
We know that, in a set with mean and standard deviation , the z-score of a measure X is given by:
Z = X - μ/σ
After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem:The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .
For a Skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
μ = 3.02 , σ = 0.29 , n = 20 and s = 0.29/√ 20 = 0.0648
Find the probability that the mean GPA of a random sample of 20 students selected from this university is 3.10 or higher.
This is 1 subtracted by the p- value of Z when X = 3.10. So
By the Central Limit Theorem:
Z = X - μ / s
⇒ Z = 3.1 - 3.02/ 0.0648
⇒ Z = 1.23
The Z = 1.23 has a P- value of 0.8907
∴ 1 - 0.8907 = 0.1093
Now, for getting the percentage,
0.1093 × 100% = 10.93%
10.93% probability that the mean GPA of a random sample of 20 students selected from this university is 3.10 or higher.
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Select the correct answer.
Which graph is the graph of f(x) = x³ - 10x² + 16x?
OA.
B.
-5
4
-3 -2
-3
-2
-3
-4
-5
2
-3
5
The graph of the cubic equation, f(x) = x³ - 10x² + 16x, is shown below
Graph of Cubic equationFrom the question, we are to determine graph of the given cubic equation.
The given cubic function is
f(x) = x³ - 10x² + 16x
To graph the equation, we will determine the value of f(x) for certain values of x
When x = 0
f(x) = x³ - 10x² + 16x
f(x) = (0)³ - 10(0)² + 16(0)
f(x) = 0
When x = 2
f(x) = x³ - 10x² + 16x
f(x) = (2)³ - 10(2)² + 16(2)
f(x) = 0
When x = 5
f(x) = x³ - 10x² + 16x
f(x) = (5)³ - 10(5)² + 16(5)
f(x) = -45
When x = 8
f(x) = x³ - 10x² + 16x
f(x) = (8)³ - 10(8)² + 16(8)
f(x) = 0
When x = 10
f(x) = x³ - 10x² + 16x
f(x) = (10)³ - 10(10)² + 16(10)
f(x) = 160
Using the determined points above, the graph of the cubic equation is shown below
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What is the equation of the line that passes through the point (-1,5) and has a slope of -3
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 3}(x-\stackrel{x_1}{(-1)}) \implies y -5= -3 (x +1) \\\\\\ y-5=-3x-3\implies {\Large \begin{array}{llll} y=-3x+2 \end{array}}[/tex]
1. A revenue of $2000 is obtained from the sales of item A at $40 each and item B at $35 each. Write an
equation that shows the relationship between the numbers of items sold.
2. A revenue of $3000 is obtained from the sales of item A at $50 each and item B at $80 each. Write an equation that shows the relationship between the numbers of items sold.
Answer:
Step-by-step explanation:
Hi vengefull, :0 like that show on Netflix about revenge, huh :0 anyway, back to math.
the equation 1):
40*A+ 35*B=2000
the equation 2):
50*A + 80*B=3000
HELP ME PLS!!!!!!!!!
Answer:
It's a positive correlation.
Step-by-step explanation:
It's gradually going up, even if there's a few points that are a bit uncorrelated.
HELP ASAP PLEASE!!!!
and if you can pls tell the steps on how you get the answer
Express this equation:
Answer:
(14x +49)^2
Step-by-step explanation:
PLEASE GIVE BRAINLIEST THANK YOU!!!
-4(5x - 3) + 12
equation answer pls
Answer:
72
Step-by-step explanation:
Sophie and Addison work at a dry cleaners ironing shirts. Sophie can iron 20 shirts per hour, and Addison can iron 30 shirts per hour. Sophie and Addison worked a combined 11 hours and ironed 260 shirts. Determine the number of hours Sophie worked and the number of hours Addison worked.
The number of hours Sophie worked and the number of hours Addison worked are 7 and 4 hours respectively.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let x and y be the number of hours for Sophie and Addison:
x + y = 11
20x + 30y = 260
After solving the above two linear equations by substitution:
x = 7 hours
y = 4 hours
Thus, the number of hours Sophie worked and the number of hours Addison worked are 7 and 4 hours respectively.
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APProximate the following numbers to The nereast thousand.
1• 6203
Answer:
the answer should be 6000
A line that includes the point (5, –10) has a slope of 0. What is its equation in slope -intercept form?
Answer:
0
Step-by-step explanation:
Slope = (y-y1)/(x-x1)
0
100 Points Please help ASAP
Question 1(Multiple Choice Worth 1 points)
(04.07 LC)
Data were collected and showed an increase in ice cream sales as the weather gets warmer.
Which of the following best describes this situation?
Based on the data, this is an example of correlation and causation.
Based on the data, this is an example of correlation.
Based on the data, this is an example of causation.
Based on the data, this is not an example of causation or correlation.
Question 2(Multiple Choice Worth 1 points)
(04.07 MC)
Trey believes there is a correlation between the number of texts sent in class and GPA. He collected data and found that the line of best fit for the data can be modeled by the equation y = 3.9 − 0.3x.
Identify the slope and the type of association.
The slope is −3.9, which indicates a negative correlation.
The slope is 3.9, which indicates a positive correlation.
The slope is 0.3, which indicates a positive correlation.
The slope is −0.3, which indicates a negative correlation.
Question 3(Multiple Choice Worth 1 points)
(04.07 MC)
The average daily profit of an electronics store is $31,435. The company estimates that 15% is lost each day to returns, with a margin of error of ±4%. What is the maximum the company can expect for returned items?
$3457.85
$4621.13
$5972.65
$6638.22
Question 4(Multiple Choice Worth 1 points)
(04.07 MC)
Based on the time recorded for 700 attendees at an amusement park, the average amount of time spent at the park was 7.25 hours with a margin of error of ±1.65 hours. If 3,000 people attended the park on a given day, what is the estimated range of total hours the attendees spent in the park?
8,375 to 16,800 total hours spent in the park
16,800 to 21,785 total hours spent in the park
16,800 to 26,700 total hours spent in the park
16,800 to 35,885 total hours spent in the park
Question 5(Multiple Choice Worth 1 points)
(04.07 MC)
Data regarding fuel efficiency of an airliner were collected. The graph shows the correlation between the distance traveled (in thousands of miles) and the altitude (in thousands of feet):
image of a scatter plot with Distance Traveled on the x axis and Altitude on the y axis with 2 comma 2, 3 comma 10, 5 comma 15, 10 comma 20, 15 comma 15, 18 comma 10, and 19 comma 2
Estimate the average rate of change from x = 15 to x = 19.
−3.25
4
−4
−0.31
Question 6(Multiple Choice Worth 1 points)
(04.07 MC)
An observational study determined that there is a strong correlation between sitting close to the television and poor eyesight. Can it be determined that sitting too close to the television causes poor eyesight? Explain.
Causation cannot be proven because everyone watches television.
Causation can be proven because it is well known that sitting close to the television causes poor eyesight.
Causation can be proven because an experiment was used to prove this hypothesis.
Causation cannot be proven because poor eyesight can occur for other reasons, such as genetics.
Question 7(Multiple Choice Worth 1 points)
(04.07 LC)
Aretha wanted to gather data about the cost of local bowling leagues in her area. She plotted the data and determined that the average bowling league costs consist of a one-time registration fee and a monthly fee modeled by the equation y = 15x + 20.
Identify and interpret the y-intercept in this model.
The y-intercept is 20. This is the cost per month.
The y-intercept is 20. This is the cost of registration.
The y-intercept is 15. This is the cost of registration.
The y-intercept is 15. This is the cost per month.
Question 8(Multiple Choice Worth 1 points)
(04.07 MC)
Analyze the following statement:
Marcus notices that he runs faster in the mornings rather than the evenings.
Is the statement an example of correlation or causation?
Correlation, because time of day doesn't cause a person to run faster or slower
Causation, because Marcus has noticed this over several trials
No relationship, because time of day has nothing to do with how fast a person runs
There is not enough information to make a conclusion
Question 9(Multiple Choice Worth 1 points)
(04.07 MC)
A new streaming service sent out a survey to 350 households to see who would be interested in its service. The company found that it could charge $55 per month, with a margin of error of ±1.3. If 1,000 people signed up for the service, what is the least amount of monthly revenue the company should expect?
$52,815
$53,700
$54,915
$56,300
Question 10(Multiple Choice Worth 1 points)
(04.07 MC)
The price of milk has been increasing over the last month. Audrey believes there is a positive correlation between the number of predicted storms and the price of milk.
Number of Storms Predicted Milk Price
1 $2.70
3 $2.89
4 $3.50
6 $3.88
7 $3.91
Use the table to determine the average rate of change from 3 to 6 storms.
3
0.98
1.21
0.33
Answer:
1.Based on the data, this is an example of correlation and causation.
2.The slope is −0.3, which indicates a negative correlation.
3.$5972.65
4.16,800 to 26,700 total hours spent in the park.
5. -3.25
6.Causation cannot be proven because poor eyesight can occur for other reasons, such as genetics.
7.The y-intercept is 20. This is the cost of registration.
8.Correlation, because time of day doesn't cause a person to run faster or slower
9.$53,700
10.0.33
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