We can represent 4 integers as a difference of two distinct members i.e. {1, -1, 2, -2}.
What are Integers ?
The collection of positive and negative integers is known as an integer. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions.
Here, we have 3 distinct positive integers which are {1, 2, 3}.
We can list down the integers as a difference of the two distinct members as follows :
1 - 2 = -1
2 - 1 = 1
2 - 3 = -1
3 - 2 = 1
1 - 3 = -2
3 - 1 = 2
So, we can see clearly it is representing only 4 integers which are {1, -1, 2, -2}.
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**WILL MARK BRAINLIEST AND GIVE 30 POINTS**
Graph the equations y=-1/2x+3 and y=2x-2 in the applet below.
1) After you graph the two lines, be sure to take a screenshot of your work and include it in your answer below.
2) What is the solution to the system of equations?
3) Prove that the answer you provided in part 2 is correct, by substituting the solution into the original equations. Be sure to show all your work.
The graph the system of linear equations on a coordinate plane is added as an attachment and the solution is (2, 2)
How to graph the system of linear equations on a coordinate plane?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
y=-1/2x+3 and y=2x-2
Rewrite the equations in the system of equations as follows:
So, we have the following representation
y = -1/2x + 3
y = 2x - 2
Next, we plot the graph of the system of equations
See attachment for the graph of the system of equations
The solution to the systemIn this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (2, 2)
This means that the solution to the system of equations is (2, 2)
Proof of the solutionRecall that
y = -1/2x + 3
y = 2x - 2
Solution = (2, 2)
So, we have
2 = -1/2 x 2 + 3 = 2 --- true
2 = 2 x 2 - 2 = 2 --- true
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two vertical poles have heights of 6ft and 12 ft. two ropes are stretched from the top of each pole to the bottom of the other. how far above the ground do the ropes intersect each other? (r3 - similarity
The square of the hypotenuse equals the square of the sum of the other two sides is 13.89ft
Definition Of Pythagoras Theorem :
The Pythagorean theorem states that the total of the squares on a right triangle's legs equals the square on the hypotenuse (the side opposite the right angle)—or, in popular algebraic form, a2 + b2 = c2.
Given:
Height of the Tent Pole = 6ft.
Base of the Pole of the Tent = 12ft.
Now we will use Pythagoras theorem to find how long the rope is.
Use of Pythagoras theorem
Hence, the length of the rope is 13.89ft.
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A multiple regression model is to be constructed to predict the heart rate in beats per minute (bpm) of a person based upon their age, weight and height. Data has been collected on 30 randomly selected individuals: Heart Rate (bpm) Age (yrs) Weight (lb) Height (in) 77 54 178 63 69 39 138 58 108 57 227 68 88 48 154 64 59 58 154 57 84 59 180 73 62 30 232 71 119 54 242 65 65 38 169 61 62 27 182 66 56 34 208 58 60 31 243 62 81 42 213 74 108 56 205 69 56 56 124 71 89 59 213 65 68 28 209 72 57 23 188 62 107 55 212 59 95 50 221 61 55 48 154 60 110 49 196 61 110 33 250 64 62 29 109 63 90 33 201 74 73 51 121 70 88 55 159 63 59 49 103 66 69 36 214 68 57 34 102 65 a)Find the multiple regression equation using all three explanatory variables. Assume that x1 is age, x2 is weight and x3 is height. Give your answers to 3 decimal places. y^ = + age + weight + height b)At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis is or is not rejected? c)The explanatory variable that is most correlated with heart rate is: age weight height d)The explanatory variable that is least correlated with heart rate is: age weight height e)The value of R2 for this model, to 3 decimal places, is equal to f)The value of s for this model, to 3 decimal places, is equal to g)Construct a new multiple regression model by removing the variable height. Give your answers to 3 decimal places. The new regression model equation is: y^ = + age + weight h)In the new model compared to the previous one, the value of R2 (to 3 decimal places) is: increased decreased unchanged i)In the new model compared to the previous one, the value of s (to 3 decimal places) is: increased decreased unchanged
If the model's p-value is less than 0.05, we rule out the null hypothesis and declare it to be significant.
Using the R software.
R codes : d=read.table('data.csv',header=T,sep=',')
head(d)
attach(d)
fit=lm(Heart.Rate~Age+Weight+Height)
summary(fit)
fit2=lm(Heart.Rate~Age+Weight)
summary(fit2)
R outputs:
> d=read.table('data.csv',header=T,sep=',')
> head(d)
Heart Rate Age Weight Height
1 85 60 201 67
2 102 48 263 59
3 67 58 167 69
4 58 58 109 60
5 75 40 135 62
6 70 27 144 64
> attach(d)
> fit= lm(Heart.Rate~Age+Weight+Height)
> summary(fit)
Call:
lm(formula = Heart.Rate ~ Age + Weight + Height)
Residuals:
Min 1Q Median 3Q Max
-21.1662 -7.9919 0.3377 10.3521 25.4165
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.86211 36.23799 -0.079 0.9377
Age 0.45993 0.21595 2.130 0.0428 *
Weight 0.12192 0.04841 2.519 0.0183 *
Height 0.59428 0.50119 1.186 0.2464
Significant codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 13.15 on 26 degrees of freedom
Multiple R-squared: 0.2841, Adjusted R-squared: 0.2015
F-statistic: 3.439 on 3 and 26 DF, p-value: 0.03137
> fit2=lm(Heart.Rate~Age+Weight)
> summary(fit2)
Call:
lm(formula = Heart.Rate ~ Age + Weight)
Residuals:
Min 1Q Median 3Q Max
-26.126 -9.851 1.049 10.328 22.284
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 36.63974 14.36802 2.550 0.0168 *
Age 0.45122 0.21744 2.075 0.0476 *
Weight 0.12065 0.04876 2.474 0.0199 *
Significant codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 13.25 on 27 degrees of freedom
Multiple R-squared: 0.2454, Adjusted R-squared: 0.1895
F-statistic: 4.39 on 2 and 27 DF, p-value: 0.02235
a) Multiple linear regression equation :
y hat = -2.862 + 0.460 X1 + 0.122 x2 + 0.594 x3
b) F = 3.439 on 3 and 26 DF,
p-value: 0.03137
We reject the null hypothesis and determine that the model is significant because the p-value is less than 0.05.
c) Heart rate is highly linked with the variable whose p-value is less than that variable. Heart rate and fluctuating weight are strongly connected in this instance.
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the positive integers x, y, and z are such that x is a factor of y and y is a factor of z. is z even? (1) xz is even. (2) y is even.
As asked in the question the value of xz and y will be even ,
xz is even and y is also even
given
X = factor of Y
Y = factor of Z
Therefore,
z= mnz = mnx , xz = even
because
either z even, so the answer is directly yes or x is even (or both) but if x is even and as then z= mnz = mnx must be even too (one of the multiples of z is even, so z is even too).
(2) y= even
because
as z=ny then as one of the multiples of z even then only z will be even
Integers are the collection of whole numbers and negative numbers. Similar to whole numbers, integers also does not include the fractional part. Thus, we can say, integers are numbers that can be positive, negative or zero, but cannot be a fraction. We can perform all the arithmetic operations, like addition, subtraction, multiplication and division, on integers.
The examples of integers are, 1, 2, 5,8, -9, -12, etc. The symbol of integers is “Z“.
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38. WEATHER The temperature fell 16 degrees between noon and 3:00 P.M. At 3:00, the temperature was -3 degrees F. Write an equation to determine the temperature at noon.
Answer:
x - 16 = -3
Step-by-step explanation:
x - 16 = -3 Add 16 to both sides of the equation
x = 13
It was 13 degrees at noon
If y=x+2 we’re changed to y=x-1, how would the graph of the new function compare with the first one?
The graph of the new function compared to the first one will be shifted down.
Define vertical translation.Vertical translation describes the movement of a function graph upward or below. The function's form is preserved in this case. The graph moving or shifting along the y-axis is another name for it. Each point on the graph moves k units vertically during vertical translation, and the graph is said to have translated k units.
The two functions are
f(x) = x + 2
g(x) = x - 1
You can see that all you need to do to transform f into g is just take 3 off of it.
f(x) - 3 = (x+2) - 3
= x + 2 - 3
= x - 1
= g(x)
Every transformation, such as f(x) f(x) + k, now produces a vertical translation, which is translated upward if k > 0 and downward if k 0. The correct response is C since the function is translated three units down in our situation where k = -3.
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The complete question is:
"If y = x + 2 were changed to y = x - 1, how would the graph of the new function compare with the first one?
A. It would be shifted up.
B. It would be shifted left.
C. It would be shifted down.
D. It would be less steep."
Tabitha and her parents drive to Dallas for a
wedding. After 90 minutes, Tabitha's father
tells her they have traveled 105 miles. What is
the average rate of speed the car travels in
90 minutes?
Answer:
Step-by-step explanation:
70 mph
Answer:
Step-by-step explanation:
hi
The population of Orange County is represented by the function f(x) - 87,000(0.9)*, where x is the number of years since 2010.
The population of Greene County was 78,000 in 2010, and has decreased exponentially at a rate of 8% each year.
How do the populations of these counties compare in 2015?
Drag a value or word to the boxes to correctly complete the statements.
In 2015, the population of Orange County was approximately
approximately
In 2015,
51,373
County was more populous
51,408 55,879
8
and the population of Greene County was
57,081 Greene
1
10
Orange
The population of Greene country in 2015 was 51408 which is greater than the population of Orange country in 2015.
What is an exponential function?The definition of an exponential function is given by the equation
y = aeᵇˣ, where a and b are constants.
The given function is f(x) = 87000(0.9)ˣ.
Given that x = 0 represents the year 2010.
Therefore, x= 5 represents the year 2015.
Substitute x = 5 into the given function:
f(5) = 87000(0.9)⁵
≈ 51373
Hence, the population of Orange country is about 51373 in 2015.
Now, the population of Greene country was 78000 in 2010 and has decreased exponentially at a rate of 8% each year.
The population of Greene city after 5 years is given by:
78000(1-8%)⁵
= 78000(1 - 0.08)⁵
= 78000(0.92)⁵
= 51408
Therefore, the population of Greene country in 2015 was 51408 which is greater than the population of Orange country in 2015.
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the term of a sequence is given. write the first four terms of the sequence. express the terms in simplified form when applicable.
The first four terms of the given sequence A(n)=4n^3+2 is 6, 34, 110, 258.
In the given question, the nth term of a sequence is given.
We have to write the first four terms of the sequence and we also have to express the terms in simplified form when applicable.
The given sequence is:
A(n)=4n^3+2
We find the four terms of the given sequence by putting n=1,2,3,4 in the given sequence.
Now putting n=1 in the given sequence
A(1)=4(1)^3+2
A(1)=4*1+2
A(1)=4+2
A(1)=6
Now putting n=2 in the given sequence
A(2)=4(2)^3+2
A(2)=4*8+2
A(2)=32+2
A(2)=34
Now putting n=1 in the given sequence
A(3)=4(3)^3+2
A(3)=4*27+2
A(3)=108+2
A(3)=110
Now putting n=1 in the given sequence
A(4)=4(4)^3+2
A(4)=4*64+2
A(4)=256+2
A(4)=258
Now the first four terms of the given sequence is 6, 34, 110, 258.
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The right question is:
The nth term of a sequence is given. Write the first four terms of the sequence. Express the terms in simplified form when applicable.
A(n)=4n^3+2
(8x²+4) + (-x² -3x)
solve this
The number of miles a motorcycle, x, will travel on one gallon of gasoline is modeled by a normal distribution with mean 44 and standard deviation 5. With one gallon of gasoline in the motorcycle, find the probability that mike can travel more than 50 miles without refueling. Round your answer to four decimal places.
The probability of bike can travel more than 50 miles without refueling is 0.1151, according to the question.
What do you mean by probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
According to data in the given question,
We have the given information:
Mean = 44
deviation = 5
Let X be the random variable that represents the population's average number of motorcycle kilometers; in this instance, we know the distribution for X is provided by:
X ~ N(44.5)
Where μ=44 and σ=5,
We are interested on this probability,
P(X>50)
We can also apply the z score formula from:
z=x-μ/σ
Using this formula, we obtained:
P(X>50) = P(X-μ/σ > 50-μ/σ) = P(Z > 50-44/5) = P(z > 1.2)
Using the normal standard distribution and the complement rule, we can determine this probability, giving us:
P (z > 1.2) = 1 - P(z > 1.2) = 1 - 0.8849 = 0.1151
Therefore, the probability is 0.1151.
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25.20 ÷ -0.5
How do I write out how I divided it?
Answer:
You can write it like 25.20 x -2 = -50.40
Step-by-step explanation:
Please help! I need the answer immediately, atleast 15 minutes under!
The question according to the equation will be a board that is 1/4 yard long cut into 2 equal pieces. Hence, option A is correct.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given information in the question,
The given equation in the question is,
1/4 ÷ 2 = 1/8
It can be clearly seen that 1/4 divided by 2 is mentioned in the question and the product obtained is 1/8.
It means that 1/4 is divided into 2 equal pieces and the length of each piece is 1/8.
So, the question will be a board that is 1/4 yard long cut into 2 equal pieces. How long is each piece?
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Kobe is twice as old as Lebron. The sum of their ages is 48. How old are each of them?
Answer:
37 is LeBron 41 years old is kobe
if the car has traveled 61.5 miles in 2 hours,how far will the car have traveled in 5 hours?
Answer:
in five hours you will travel 153.75 miles
Hello!
What does this problem want:
==> how far will the car have traveled in 5 hours
What we must find ==> how many miles does the car travel in an hour
[tex]\text{Rate}=\frac{61.5 \text{ miles}}{2 \text{ hours}} =30.75\text{ miles per hour}[/tex]
Therefore: the car will travel in 5 hours
5 * 30.75 = 153.75 miles
Hope that helps!
please hurry
Identify the form the following equation is in
y =−14x + 3
a.point slope
b.standered form
cslope intercept form
Answer: -3x2
Step-by-step explanation:
H. On average, Luke Hobbs drives 560 miles in 8 hours. How far does he drive in 1.5 hours?
What is the prime factorization of the number.
132
Answer:The prime factorization of 132 is 2 × 2 × 3 × 11 or 22 × 3 × 11.
Step-by-step explanation:
The prime factorization of 132 is 2 × 2 × 3 × 11 or 22 × 3 × 11.
PLEASE HELP!! HURRY!!!
Answer:
A. is the answer
Step-by-step explanation:
y as a function of x meaning:
Every x has a y, but the x value cannot repeat and every x has it's own y.
Example:
x: 1 2 3 4 5
y: 2 4 6 8 10
This is y as a function of x because the x values do not repeat and they each have a y value.
Example 2:
x:3 4 5 3 6
y: 1 2 3 4 5
This wrong because the 3 in the x value repeats twice which cause y not to be a function of x.
The reason why it wouldn't be B is because of -1
The reason why it wouldn't be C is because the y values repeat
The reason why it wouldn't be D is because all the x values are -7
Hope this helped!
Phil takes out a bank loan of $150 000 to buy a house, at an annual interest rate of 3.5%. The interest is calculated at the end of each year and added to the amount outstanding. Find the amount Phil would owe the bank after 20 years. Give your answer to the nearest dollar.
Phil's final debt after 20 years will be around $320,679.
How is debt calculated?To purchase a home, Phil borrowed $150,000 from a bank at a 3.5% annual interest rate.
The annual compounding of interest causes the amount of interest for each year to rise in proportion to the debt. Phil will be required to pay the initial sum plus interest after the first year, which comes to
$150,000 + 3.5% of $150,000 = $155,250.
Since interest is charged on the new amount owed for the second year, Phil will owe
$155,250 + 3.5% of $155,250, which
= $160,551.75.
For the next 20 years, this procedure is repeated, with the amount owed rising yearly by the sum of the year before plus interest. Phil's debt after 20 years will be around $320,679.
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Credit scores are often a factor in determining your insurance premiums. Search the Internet using the keywords “credit score and insurance rates" and briefly respond to these questions:
What are some pros and cons of using credit scores for insurance pricing?
Correlations are used to justify considering credit scores to set premiums. What other variables related to credit scores justify linking them to a premium rate?
Describe from the insurance company’s perspective which expected values are affected by use of credit scores.
Do you agree or disagree with using credit scores in determining insurance premiums? Support your opinion briefly.
No Response(s)
Be the first to respond to the Discussion topic!
Answer:
Step-by-step explanation:
Pros: Lower rates: Insurance rates are reduced for most consumers. ✓ Rates match risk: Higher-risk policyholders may pay a higher rate that accurately reflects their higher risk of loss – so lower-risk policyholders don't have to subsidize the cost of insurance for higher-risk policyholders.
Cons: HIGHER rates.
Insurance companies justify the use of insurance scores by citing studies showing a positive correlation between credit scores and insurance claims
A higher credit score decreases your insurance rate, often significantly, with almost every company and in most states. Getting a quote, however, does not affect your credit. Your credit score is a key part of determining the rate you pay for insurance.
2. for a chis-square goodness of fit test, if the number of categories is 6 and the test statistics is 8.4345, how to calculate the p-value? a. pchisq(8.4345,6) b. pchisq(8.4345,5) c. 1- pchisq(8.4345,6) d. 1- pchisq(8.4345,5)
for a chis-square goodness of fit test, if the number of categories is 6 and the test statistics is 8.4345, p value will be pchisq(8.4345,5)
To test a hypothesis' validity against actual data, a statistical calculation called a p-value is used. The probability of experiencing the results that were observed is calculated using a p-value, assuming that the null hypothesis is true. The p-value can be calculated by looking up the 8.4345 value in the Chi-Square distribution table with 5 degrees of freedom (6-1=5). The resulting p-value will depend on the significance level you choose.
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g suppose (x y)6 is completely expanded as a sixth-degree polynomial. in the expanded expression, what are a (the coefficient of the middle term) and b (the sum of all the coefficients)?
In the expanded expression of the given polynomial, the coefficient of the middle term is 20 and the sum of all coefficients is 64.
What is a polynomial?
'poly' means many and 'nominal' means term. A polynomial is a type of algebraic expression with many terms having variables and coefficients.
Given polynomial is,
[tex] {(x + y)}^{6} [/tex]
Expanding the given sixth-degree polynomial using binomial expansion we get the expression of the picture given.
Solving all expressions we get,
[tex] {(x + y)}^{6} = {x}^{6} + 6 {x}^{5} y +15 {x}^{4} {y}^{2} + 20 {x}^{3} {y}^{3} + 15 {x}^{2} {y}^{4} + 6x {y}^{5} + {y}^{6} [/tex]
The middle term is
[tex]20 {x}^{3} {y}^{3} [/tex]
The coefficient of the term is 20
The sum of all coefficients is 1+6+15+20+15+6+1= 64
Hence, in the expanded expression of the given polynomial, the coefficient of the middle term is 20 and the sum of all coefficients is 64.
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Keilantra runs a farm stand that sells strawberries and blueberries. Each pound of
strawberries sells for $2.25 and each pound of blueberries sells for $4. Keilantra
made $204.50 from selling a total of 73 pounds of strawberries and blueberries.
Determine the number of pounds of strawberries sold and the number of pounds of
blueberries sold.
The number of pounds of strawberries sold and the number of pounds of blueberries sold are 50 and 23 respectively.
How to number of pound strawberries and blueberries are sold?As in the question Keilantra runs a farm stand that sells strawberries and blueberries. Each pound of strawberries sells for $2.25 and each pound of blueberries sells for $4. Keilantra made $204.50 from selling a total of 73 pounds of strawberries and blueberries.
According to question:Let x be a number of strawberries and y is that of blueberries.
2.25x + 4y = 204.5-----------------------(1)
And
x + y = 73--------------------------------------(2)
On solving equation (1) and (2), we get,
x = 50 and y = 23
So, there are 50 pound strawberries and 23 pound blueberries are sold.
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A track and field team was calculating their long jump scores. The long jump teamates add up their scores to determine the best team. The current winning team has a combined score of 25.6 m. Alaina's teamates jumped the following jumps: 5.46m,4.84, 4.92 and 5.98m. What score would Alaina have to get to tie the Winning teams score? Show your work.
The score that Alaina will have to get to tie the Winning teams score is 4.4.
How to calculate the score?Given that the long jump teamates add up their scores to determine the best team. The current winning team has a combined score of 25.6 m.
Also, Alaina's teamates jumped the following jumps: 5.46m,4.84, 4.92 and 5.98m.
Therefore, Alaina's score to beat the other team will be:
= 25.6 - (5.46m + 4.84 + 4.92 + 5.98m)
= 25.6 - 21.2
= 4.4
Therefore, she must get 4.4 to tie.
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if we wanted to compare the averages of each set of scores, what type of statistical test would you run and why?
A parametric test would be more suitable because it provides a more appropriate answer.
help :(( pleaseeeeeee
Answer:
69.29 deg
Step-by-step explanation:
Recall that tan(x) = opposite/adjacent. This is helpful because we know the opposite and adjacent leg from the angle x! This gives us tan(x) = 43/18, so we can solve for x by taking tan^-1 of both sides, giving x = tan^-1(43/18), or 67.29 degrees.
the graph shows a proportional relationship which equation maches the graph A. y=6x B. y= 1/2x C. y= 2x D. y=x
Answer:
A. y=6x
Step-by-step explanation:
A. y=6x that's all I know
Answer: A. y=6x
Step-by-step explanation:
(−12)3+ (24+9)−−−−−−−√.
Answer:
-3 is the answer.
Step-by-step explanation:
Given
(-12)3 + (24+9)----------^
= -12*3 + 33 ---------
= -36 + 33
= -3
math how to answer twice the sum of five times a number increased by one is twelve. determine the number
After solving the expression, the number is 5.
In the given question we have to answer twice the sum of five times a number increased by one is twelve.
We have to determine the number by solving the given statement.
To solve the question we have to read the statement carefully. Then write the expression according to the statement. Then solve the statement according the rules.
In the given statement given that five time a number.
Let the number be x. So the expression should be 5x.
Again says that five times a number increased by one. So the expression 5x+1.
Then says that twice the sum of five times a number increased by one. Now the expression should be 2(5x+1).
Then says that twice the sum of five times a number increased by one is twelve. Now the statement is 2(5x+1)=12
Now solving the expression.
Divide by 2 on both side, we get
5x+1=6
Subtract 1 on both side, we get
5x=5
Divide by 5 on both side, we get
x=1
Now the number is 5.
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