the inverted coefficient matrix is
[tex]\left[\begin{array}{ccc}2&-1&-5\\3&-2&5\\-3&5&2\end{array}\right][/tex]
1. The inverted coefficient matrix is found by taking the inverse of the coefficient matrix.
3x1 + x2 = 4
5x1 + 2x2 = 7
3. Therefore, the inverted coefficient matrix is
2 -1 -5
3 -2 5
-3 5 2
It is used to represent and manipulate complex data, such as linear equations, vectors, and polynomials. A matrix can also be used to represent a system of linear equations or to graph a function. Matrices are key elements in linear algebra, a branch of mathematics that studies vector spaces, linear transformations, and systems of linear equations.
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Data were collected on the number of days per week that members visit a certain fitness center. The values varied from 0 to 7, and a distribution of relative frequencies for the values was created. Let the random variable X represent the number of days per week that a member visits. The mean of X is 3.12. Which of the following statements is the best interpretation of the mean?
The long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.
The long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.
How can I define a variable?A variable is a quantity that could alter when used in a mathematical problem or experiment. Normally, a variable is denoted by a single letter. Common generic symbols used for variables include the letters x, y, and z.
What is an example of a variable?Any traits, figure, or amount that can be gauged or counted is referred to as a variable. An alternative name for a variable is a data item. Age, business earnings and expenses, country of birth, capital expenditures, class grades, eye color, and car kind are a few examples of variables.
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Renata is purchasing a condominium for $ 125,000. She wants to put down a down payment of 20%. Select all the true statements.
The proportion that represents the down payment is 20100=125,000
20
100
=
125
,
000
x
.
The down payment is $ 25,000
25
,
000
.
The proportion that represents the down payment is 20100=125,000
20
100
=
x
125
,
000
.
The down payment is $ 50,000
50
,
000
.
The down payment is 15
1
5
of the cost of the house.
Answer:
The following statements are true:
The proportion that represents the down payment is 20/100 = x/125,000.
The down payment is $25,000.
The down payment is 15 of the cost of the house.
The other statements are not true. The proportion that represents the down payment is not 20100=125,000, as this is not a valid proportion. Additionally, the down payment is not $50,000, as this is more than the cost of the condominium.
Step-by-step explanation:
the recommended par stock for the average bar is: the recommended par stock for the average bar is: 3 times the needs of the bar's busiest day 2 times the needs of the bar's typical day 4 times the needs of the bar's typical day 1.5 times the needs of the bar's busiest day
A predicate nominative is a noun or a pronoun which follows the verb and describes the subject.
What is the busiest bar night of the year?Thanksgiving Eve is the biggest bar night of the year. Doctors warn against it for 2021. The night before Thanksgiving, sometimes referred to as "Drinks giving" or "Blackout Wednesday," is typically one of the most crowded bar nights out of the year.In order to design a telephony circuit, trunk, or call center, it is needed to take into account the busiest calling hour (as a "sliding" 60-minute period) in one day, or week, month or year, generally calculated as an average.This period is called the "busy hour" and is used to compute the traffic intensity, in Erlangs, considering that if the circuit is busy 100% of the time during 3600 seconds, it will be cursing 1 Erl of traffic.This traffic can result from 60 calls of 1 min each, 36 calls of 100 sec each, or any combination that have the same outcome of 1 Erl. In order to define, for instance, the number of employees in a call center, a very important parameter is the average time used for each call, adding the queuing time, the true talk time and any other time needed to set up a successful call, i.e., the time that the subscriber stays on the phone after putting the call.To learn more about average bar refer to:
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If a city’s maximum temperature was 42 degrees and the minimum was 9 degrees, what is the difference between the two temperatures?
The difference between the two temperatures is 33 degrees.
How to find the difference between the two temperatures?The city's maximum temperature was 42 degrees and the minimum was 9 degrees.
The difference between the two temperatures can be calculated as follows;
The difference in temperature is the subtraction of the minimum temperature from the maximum temperature.
Therefore,
difference between the temperature = maximum temperature - minimum temperature
maximum temperature = 42 degrees
minimum temperature = 9 degrees
Hence,
difference between the temperature = 42 - 9
difference between the temperature = 33 degrees.
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Hari's weekly allowance varies depending on the number of chores he does. He received $24 in allowance the week he did 20 chores, and $16 in allowance the week he did 4 chores. Write an equation for his allowance in slope-intercept form.
Answer:
24 / 16
Step-by-step explanation:
divide and do the thing
An online poll asked: "Do you believe the Loch Ness monster exists?" Among 20,111 responses, 67 % were "yes." Use a 0.05 significance level to test the claim that most people believe that the Loch Ness monster exists. How is the conclusion affected by the fact that Internet users who saw the question could decide whether to respond?
a.Identify the null and alternative hypotheses for this test. Choose the correct answer below.
b. Identify the test statistic for this hypothesis test.
c.Identify the P-value for this hypothesis test.
d.Identify the conclusion for this hypothesis test.
a) Null Hypothesis; p = 0.5
Alternative Hypothesis; p < 0.5
b) The test statistic is; z = 48.216
c) The p-value is < 0.00001.
d) The conclusion of the hypotheses is that we reject the null hypothesis and conclude that the claim that most people believe that the Loch Ness monster exists is true.
How to carry out hypothesis testing?Hypothesis testing is defined as the method used to find the probability of the hypothesis that is to be proved in the future on the basis of the small population sample.
Now, we are told that Among 20,111 responses, 67 % were "yes." Thus;
Sample proportion; p^ = 67%
The population proportion is not given and as such we will use; p = 50% = 0.5
Thus;
Null Hypothesis; p = 0.5
Alternative Hypothesis; p < 0.5
The formula for the test statistic is;
z = (p^ - p)/√(p(1 - p)/n)
z = (0.67 - 0.5)/√(0.5(1 - 0.5)/20111)
z = 48.216
The p-value from online p-value from z-score calculator is;
p-value < 0.00001.
The p-value is less than the significance value and so we reject the null hypothesis and conclude that the claim that most people believe that the Loch Ness monster exists is true.
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Writing equations of lines
Write the equation of each line with the given information
through: (-5, -3), perp. to y = -5/7x -5
Answer:
y = [tex]\frac{7}{5}[/tex] x + 4
Step-by-step explanation:
Perpendicular slopes are opposite reciprocals.
So the slope is 7/5
Us the slope and the point to find the y intercept
m = 7/5
x = -5
y = -3
y= mx + b
-3 = (7/5)(-5) + b
-3 = -7 + b Add 7 to both sides
4 = b
y = mx + b
y = 7/5 x + 4
what is the volume of the rectangular pyramid shown? a square pyramid. the square base has side lengths 15 yards and the height is 12 yards.
The volume of the rectangular pyramid is 900 cubic yards.
The standard formula of the volume of the rectangular pyramid is written as
V = 1/3s²h
where s refers the base edge and h refers the height.
Here we have given that the square base has side lengths 15 yards and the height is 12 yards.
Now, we have to find the volume of the rectangular pyramid
As we know the the value of base edge is 15 yard and the height is 12 yards.
Now, we have to apply the values on the formula then we get,
=> V = 1/3 x 15² x 12
It can be simplified as,
=> V = 4 x 225
When we do the appropriate arithmetic operation, then we get,
=> V = 900 cubic yard.
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Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
The correct answer is option is a) x4 – 6x2 – 27 = 0 , d) 6(2x + 4)2 = (2x + 4) + 2 , e) 6x4 = -x2 + 5. as they are quadratic equations.
What are quadratic equations?A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0. The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. The answer could be straightforward or difficult.
How do you identify a quadratic equation?A quadratic function has the formula f(x) = ax2 + bx + c, with a, b, and c being integers and a not equal to zero. A parabola is a curve that represents the graph of a quadratic function. Parabolas can have openings that are upward or downward, different "widths" or "steepnesses," but they all share the same fundamental "U" form.
What is not quadratic equation?Due to the absence of an x2 component, bx 6 = 0 is NOT a quadratic equation. Because there is an x3 term, x3 x2 5 = 0 is NOT a quadratic equation (not allowed in quadratic equations).
The correct answer is option is a) x4 – 6x2 – 27 = 0 , d) 6(2x + 4)2 = (2x + 4) + 2 , e) 6x4 = -x2 + 5.
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design and implement (i.e., write a program) an algorithm based on text matching that adds two polynomials such as (x**3 5x**2 -3x 3) (4x**5 - 2x**2 1) place the theta value of your algorithm as the first comment in the code. submit several challenging test cases.
An algorithm is a collection of clear instructions for solving a specific issue in computer programming.
What is algorithm?An algorithm is a collection of clear instructions for solving a specific issue in computer programming. It generates the required result from a collection of inputs. For instance, An equation for adding two numbers: Take two inputs for numbers.But this is the clearest explanation possible: An algorithm is a list of rules outlining how to carry out a task.For conducting computations and processing data, algorithms are employed as specifications. Advanced algorithms can do automated deductions (also known as automated reasoning) and employ logical and mathematical checks to reroute the execution of the code along several paths (referred to as automated decision-making).Step 1: Start
Step 2: Declare variables num1, num2 and sum.
Step 3: Read values num1 and num2.
Step 4: Add num1 and num2 and assign the result to sum.
sum←num1+num2
Step 5: Display sum
Step 6: Stop
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Which of the following is the value of the discriminant for
√2x®– 5x +√2=0?
(A) – 5 (B) 17 (C) 2 (D) 2 2 – 5
The value of the discrimination for the given equation is 17.
Here we have to find the value of the discrimination for the equation.
Given equation:
√2x² - 5x + √2 = 0
The formula for the discriminant of the equation for the general equation ax² + bx + c = 0
D = b² - 4ac
As the equation is given:
√2x² - 5x + √2 = 0
a = √2
b = -5
c = √2
So D = b² - 4ac
= (-5)² - 4√2×√2
= 25 - 4×2
= 25 - 8
= 17
Therefore the value of the discriminant is 17.
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Hi, I'd be really thankful for a proper answer for this. Thank you!
1) The probabilities are given as follows:
a) More than 75: 0.0301 = 3.01%.
b) Between 60 and 73: 0.4484 = 44.84%.
c) Less than 50: 0.1057 = 10.57%.
2) The proportion of students who fail the module is of: 0.0062 = 0.62%.
3) The measures are given as follows:
Mode: 60.Median: 60.Variance: 64.How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation in this problem are given as follows:
[tex]\mu = 60, \sigma = 8[/tex]
The probability that an score is more then 75 is one subtracted by the p-value of Z when X = 75, hence:
Z = (75 - 60)/8
Z = 1.88
Z = 1.88 has a p-value of 0.9699.
1 - 0.9699 = 0.0301 = 3.01%.
The probability of an score between 60 and 73 is the p-valeu of Z when X = 73 subtracted by the p-value of Z when X = 60, hence:
Z = (73 - 60)/8
Z = 1.63
Z = 1.63 has a p-value of 0.9484.
Z = (60 - 60)/8
Z = 0
Z = 0 has a p-value of 0.5.
Then:
0.9484 - 0.5 = 0.4484 = 44.84%.
The probability of an score less than 50 is the p-value of Z when X = 50, hence:
Z = (50 - 60)/8
Z = -1.25
Z = -1.25 has a p-value of 0.1057.
The proportion who might fail the test is the p-value of Z when X = 40, hence:
Z = (40 - 60)/8
Z = -2.5
Z = -2.5 has a p-value of 0.0062.
Then the statistical measures are obtained as follows:
Mode: 60. -> equals to mean.Median: 60. -> equals to mean.Variance: 64. -> standard deviation squared.More can be learned about the normal distribution at https://brainly.com/question/25800303
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Each person in a random sample of adults was asked how many DVD, he or she wwned. Summary Statistics are given below Variable DVDs N 117 Mean 129.4 Median 50.0 TIMean 76.5 SE Mean StDev 3236 Variable DVDs Minimum 00 Maximum 3000.0 Q1 30.0 03 950 Which of the following statements is true? (A) Seventy-five percent of the adults in the sample own more than 95 DVDs. (B) Fifty percent of the adults in the sample own between 0 and 129.4 DVDs (C) The distribution of the number of DVDs owned appears to be approximately symmetric (D) The interquartile range of the number of DVDs owned is 65. (E) The distribution of the number of DVDs owned contains outliers on both the low side and the high side.
Hence, the option D "The interquartile range of the number of DVDs owned is 65" is correct.
In the given question, we have to in each person in a random sample of adults was asked how many DVD, he or she owned.
Summary Statistics are given below
Variable N Mean Median TiMean St Dev St Mean
DVDs 117 129.4 50.0 76.5 3236 29.2
Variable Minimum Maximum Q1 Q3
DVDs 00 3000 30.0 95.0
We have to which of the following statements is true?
(A) Seventy-five percent of the adults in the sample own more than 95 DVDs.
(B) Fifty percent of the adults in the sample own between 0 and 129.4 DVDs
(C) The distribution of the number of DVDs owned appears to be approximately symmetric
(D) The interquartile range of the number of DVDs owned is 65.
(E) The distribution of the number of DVDs owned contains outliers on both the low side and the high side.
Option (A) is incorrect because 95 is third quartile value and there is only 25% values above third quartile. So, statement is incorrect.
Option (B) is incorrect because 0 is minimum value and 129.4 is mean value. Percent between mean and minimum is not always fixed, so we cannot say that 50% of values are between 0 and 129.4. So, statement is incorrect.
Option (C) is incorrect because median and mean must be equal for symmetric curve, but these are not equal. So, it is not a symmetric curve.
Option (D) is correct because
IQR (Interquartile range)
IQR = Q3 - Q1
IQR = 95 - 30
IQR = 65.
So, option D is correct answer.
Option (E) is incorrect because
lower outlier limit = Q1-1.5*IQR
lower outlier limit = 30 - 1.5*65
lower outlier limit = -67.5
upper outlier limit = Q3 + 1.5*IQR
upper outlier limit = 95 + 1.5*65
upper outlier limit = 192.5
So, there is outliers only on upper side because maximum is 3000>192.5, but there is not value below 0.
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what is the answer to -25g greater than or equal to 150
Answer:
g ≤ - 6 or g ∈ (- ∞, - 6]---------------------------------------
Given inequality:
-25g greater than or equal to 150-25g ≥ 150Divide both sides by -25:
-25g / (-25) ≥ 150 / (-25)g ≤ - 6 Division by a negative number flips the inequality signKala swam 4 kilometers against the current in the same amount of time it took her to swim 12 kilometers with the current. The rate of the current was 2 kilometers per hour. How fast would Kala swim if there were no current?
Against the current he swims 2 km/hours where he swims 4 km in the same 2 hours.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Distance = Rate x Time
Let Kala's swimming speed = X
4 km = (X-2)×Time
12 km = (X+2) × Time
4/x-2 = 12/x+2
Apply cross multiplication
4(x+2)=12(x-2)
4x+8=12x-24
Take all variables on one side
4x-12x=-24-8
-8x=-32
Divide both sides by 8
x=4
Kala swims 4 km/hour
With the current he swims 6 km/hour
Hence, Against the current he swims 2 km/hours where he swims 4 km in the same 2 hours.
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4. How many 2 digit numbers
have both 4 and 5 as factors?
Answer: 20 80
Step-by-step explanation:
So two 2-digit numbers
Question 16 An individual works at a pet store. There are 15 dogs up for adoption. At the end of the day, only 4 were not adopted. What is the percentage of dogs that were adopted? WAKALPOPÕE 20
Answer:
73.3%
Step-by-step explanation:
You want to know the percentage adopted when 4 of 15 were not adopted.
PercentageThe percentage can be found by multiplying the fraction by 100%. The fraction of dogs adopted was 11 out of 15, or 11/15. The percentage is ...
11/15 × 100% ≈ 73.3%
About 73.3% of the dogs were adopted.
Find two numbers m and n such that m+n =5 and mn=4
a line is perpendicular to y= "-2x+5" and intersects at the point (-4,2). what is the equation of this perpendicular line
Answer:
y=(1/2)x-1
Step-by-step explanation:
Since you know that this line is perpendicular to the given equation, you also know that the slope of the line will be the opposite reciprocal to that of the given equation. Therefore:
slope= 1/2
Now, since you also know that the lines intersect at the point (-4,2), you just have to plug these numbers into the x and y in the equation to solve for b.
(2)=(1/2)(-4)+b
b=-1
Therefore, the equation is
y=(1/2)x-1
10 pi is = to what
The value of the expression given as 10pi is 31.42
What is the value of the expression illustrated?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
It should be noted that the value of pi is 3.142.
Therefore, the value of 10 pi will be:.
= 10 × 3.142
= 31.42
The value is 31.42.
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suppose annual salaries for sales associates from a particular store have a mean of $32,500 and a standard deviation of $2,500
. a. Calculate and interpret the z-score for a sales associate who makes $36,000.
b. Use Chebyshev's theorem to calculate the percentage of sales associates with salaries between $26,250 and $38,750
. c. Suppose that the distribution of annual salaries for sales associates at this store is bell-shaped. Use the empirical rule to calculate the percentage of sales associates with salaries between $27,500 and $37,500.
d. Use the empirical rule to determine the percentage of sales associates with salaries less than $27,500. e. Still suppose that the distribution of annual salaries for sales associates at this store is bell-shaped. A sales associate makes $42,000. Should this salary be considered an outlier? Explain.
a) The z-score for a sales associate who makes $36,000 is 1.4
b) The percentage of sales associates with salaries between $26,250 and $38,750 is 84%
c) The percentage of sales associates with salaries between $27,500 and $37,500 is 95.4%
d) The percentage of sales associates with salaries less than $27,500 is 2.3%
e) Yes, the salary of $42000 should be considered as outlier.
Given,
Mean, [tex]\mu[/tex]=32500
Standard deviation, [tex]\sigma[/tex]=2500
a)
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{36000-32500}{2500}=1.40[/tex]
The sales associate who makes 36000 is 1.4 standard deviation above the mean salary.
b)
As per chebyshev's theorem, [tex](1-\frac{1}{k^2})[/tex] of the observations fall within k standard deviation of the mean, i.e. within [tex]\mu\pm k\sigma[/tex]
[tex]z_1=\frac{x_1-\mu}{\sigma}\\\\z_1=\frac{26250-32500}{2500}=-2.50\\\\z_2=\frac{x_2-\mu}{\sigma}\\\\z_2=\frac{38750-32500}{2500}=2.50[/tex]
Hence, we need to find proportion of observations within [tex]\mu\pm2.5\sigma[/tex]
k=2.5
[tex](1-\frac{1}{k^2})=1-\frac{1}{2.5^2}=0.84=84\%[/tex]
Hence, 84% of sales associates have salaries between 26250 and 38750.
c)
As per empirical rule for a bell shaped distribution:
68.3% of the observations fall within 1 standard deviation of the mean i.e. within [tex]\mu\pm 1\sigma[/tex]95.4% of the observations fall within 2 standard deviation of the mean i.e. within [tex]\mu\pm 2\sigma[/tex]99.7% of the observations fall within 3 standard deviation of the mean i.e. within [tex]\mu\pm 3\sigma[/tex][tex]z_1=\frac{x_1-\mu}{\sigma}\\\\z_1=\frac{27500-32500}{2500}=-2\\\\z_2=\frac{x_2-\mu}{\sigma}\\\\z_2=\frac{37500-32500}{2500}=2[/tex]
Hence, we need to find the proportion of observations within \mu \pm 2\sigma
As per empirical rule, 95.4% of the observations fall within 2 standard deviation of the mean .i.e within [tex]\mu \pm 2\simga[/tex] .Therefore, percentage of sales associates with salaries between 27500 and 37500=95.4%
d)
[tex]z_1=\frac{x_1-\mu}{\sigma}\\\\z_1=\frac{27500-32500}{2500}=-2[/tex]
Percentage of sales associates with salaries less than 27500 will be equal to the area under the normal curve to the left z=-2
As per empirical rule 95.4% of the observations fall within 2 standard deviation of the mean
Therefore, the percentage of sales associates with salaries less than 27500 : [tex]\frac{100-95.4}{2}=2.3\%[/tex]
e)
[tex]z_1=\frac{x_1-\mu}{\sigma}\\\\z_1=\frac{42000-32500}{2500}=3.8[/tex]
A z-value greater than 3 is considered as an outlier.
Hence, the salary of 42000 should be considered as outlier.
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Jarad Rodriguez deposited $10,000 at 10% compounded semiannually. At the start of year 6, Jarad deposited an additional $5,000 that is compounded at the same rate. At the end of 10 years, what is the balance in Jarad's account? (Do not round intermediate calculations. Round your answer to the nearest cent.)
The final balance after 10 years is $33257.92.
What is compound interest?The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.
The expression for the amount for compound interest is given as,
A = P(1 + r/100)ⁿ
After 6 years the amount can be calculated as,
A = 10000(1 + 10/100)⁶
= 10000 × (11/10)⁶
= 0.01 × 11⁶
= 17715.61
As per the question $ 5000 is added at the end of 6 years.
So, the principal becomes 17715.61 + 5000 = 22715.61.
And, the remaining time is 10 - 6 = 4 years.
Now, the amount obtained after 10 years can be calculated as,
A = 22715.61(1 + 10/100)⁴
= 22715.61 × 1.1⁴
= 33257.92
Hence, the end of 10 years, the balance in Jarad's account is given as $33257.92.
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in fair bankes alaska the tempreture the tempreture on that one day was -18f. on that same day the tempreture was 83 degrees higher than honolulu hawaii what was the temperature in honolulu hawaii on that day
Answer:
The answer is 65 degrees fahrenheit.
Step-by-step explanation:
An experiment has been conducted for four treatments with eight blocks. Complete the following analysis of variance table (to 2 decimals, if necessary). Source of Variation Sum of Squares Degrees of Freedom Mean Square F Treatments 900 Blocks 400 Error Total 1800 Use A = .05 to test for any significant differences. The p-value is ? What is your conclusion?
The p value is greater than α.
Hence we made a conclusion that:
There is a significant difference between treatments.
There is no significant difference between treatments.
Given:
An experiment has been conducted for four treatments with eight blocks.
Source of Variation Sum of Squares Degrees of Freedom Mean Square F Treatments 900 Blocks 400 Error Total 1800 Use A = .05 to test for any significant differences.
we are asked to find:
The p-value is = ?
What is your conclusion = ?
P value of treatments = 0.0001
Hence p value is less than α = 0.05
so we reject H₀
P value for blocks = 0.0650
Hence p value is greater than α = 0.05
so we fail to reject H₀
Conclusion:
There is a significant difference between treatments.
There is no significant difference between treatments.
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pls help. question is in attached photo
Which is correct Pemdas or Bodmas?
Both abbreviations are correct:
PEMDAS stands for:
ParenthesesExponentsMultiplicationDivisionAdditionSubtractionBODMAS stands for:
BracketsOrdersDivisionMultiplicationAdditionSubtractionWhich is correct: Pemdas or Bodmas?PEMDAS and BODMAS are both mathematical acronyms that are used to help people remember the order of operations when solving a math problem.
The order of operations should be followed when solving an equation because it ensures that the problem is solved correctly and accurately. It is important to remember that both acronyms represent the same order of operations, and that each step should be followed in the order given.
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PEMDAS stands for
Parenthesis
Exponents
Multiplication and Division
Addition and Subtraction
BODMAS stands for
Bracket
Orders
Division and Multiplication
Addition and Subtraction
Both of these are the same, just a different acronym and way of representing them.
set up the systems of eqautions to solve for this quadratic function to model the values in the table
The systems of equations to solve for this quadratic function to model the values in the table is y = -2x^2 + 4x - 2
The general form of a quadratic function is --> y = ax2 + bx + c
-2 = a(0)2 + b(0) + c
-2 = 0 + 0 + c
-2 = c
substitute c value
(-1 , -8) substitute
-8 = a ( -1 )2 + b ( -1 ) - 2
-8 = a - b - 2
-6 = a - b
( 3 , -8)
-8 = a ( 3 )2 + b ( 3 ) - 2
-8 = 9a + 3b - 2
-6 = 9a + 3b
a - b = -6
9a + 3b = -6
on solving :
9 ( b - 6 ) + 3b = -6
9b - 54 + 3b = -6
12b - 54 = -6
12b = 48
b = 4
a - 4 = -6
a = -2
The quadratic equation for this table is y = -2x^2 + 4x - 2
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Full question:
set up the systems of eqautions to solve for this quadratic function to model the values in the table.
x | y
-1 | -8
0 | -2
3 | -8
A car that travels 20 miles in 1/2 hour at constant speed is traveling at the same speed as a car that travels 30 miles. In how many hours (at a constant speed)
The required time to travel 30 miles is given as 45 minutes and 3/4 hours.
Given that,
A car that travels 20 miles in 1/2 hour at constant speed is traveling at the same speed as a car that travels 30 miles.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Speed = Distance/time
Speed = 20 / [1/2]
Speed = 40 miles per hour,
Time = Distance / Speed
Time = 30 / 40
Time = 3 / 4 hour
Thus, the required time to travel 30 miles is given as 45 minutes and 3/4 hours.
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it is possible for two sets of data to have the same regression equation but different correlations.
Yes, it is possible for two sets of data to have the same regression equation but different correlations.
What is regression and correlation?Correlation quantifies the strength of the linear relationship between a pair of variables, whereas regression expresses the relationship in the form of an equation.
The use of correlation analysis allows for the quantification of relationships between two continuous variables, such as those between two independent variables or between a dependent and independent variable.
Regression analysis is the process of determining how one or more variables and the outcome variable relate to one another. Risk factors, co-founders, and the outcome variable are all referred to as predictors or independent variables. The outcome variable is also referred to as the dependent or response variable. Regression analysis displays the dependent variable as "y" and the independent variables as "x".
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Solve
81 = 8(2x + 8) + x
Answer:
The value of x that satisfies the equation 81 = 8(2x + 8) + x is x = 1.125.
Step-by-step explanation:
To solve for x in the equation 81 = 8(2x + 8) + x, you can first distribute the 8 on the right side of the equation to obtain 81 = 16x + 64 + x. Then, you can combine like terms on the right side of the equation by adding the two x terms and the constants to get 82 = 16x + 64. Next, you can subtract 64 from both sides of the equation to isolate the x term, which gives 18 = 16x. Finally, you can divide both sides of the equation by 16 to solve for x, resulting in x = 1.125.
