False. The weight of a variable in a standardized predictor environment does not necessarily indicate that the variable has a higher discriminating power.
Discriminating power is determined by the correlation of a predictor variable with the outcome variable. We can calculate the correlation between a predictor variable and an outcome variable using Pearson's correlation coefficient, which is represented by the formula:
r = (NΣXY - (ΣX)(ΣY)) / √[(NΣX2 - (ΣX)2)(NΣY2 - (ΣY)2)].
In this formula, N is the sample size, ΣX is the sum of the predictor variable, ΣY is the sum of the outcome variable, ΣXY is the sum of the products of the predictor and outcome variables, and ΣX2 and ΣY2 are the sums of the squares of the predictor and outcome variables, respectively. The Pearson's correlation coefficient ranges from -1 to +1, with +1 indicating perfect positive correlation, 0 indicating no correlation, and -1 indicating perfect negative correlation. A higher correlation coefficient indicates a higher discriminating power.
Therefore, the weight of a variable in a standardized predictor environment does not indicate whether or not the variable has a higher discriminating power; this is determined by the correlation between the predictor and outcome variables.
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Lex, Mattie, Penelope, and Wallace shares 1/5 pound of candy equally . how much does each person get .which number should go first? THIS IS WHAT YOU WILL CUT UP AND DIVIDE OUT START with 1 /5 CANDY to cut up! START with 4 PEOPLE to cut up!
Help me please .
The amount of candy each person gets is given by the equation A = 1/20 of the candy
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total amount of candy each person receives is A
Now , the amount of candy = 1/5 of the candy
The number of friends = 4 friends
So , the amount of candy each person gets A = amount of candy / number of friends
Substituting the values in the equation , we get
The amount of candy each person gets A = ( 1/5 ) / 4
On simplifying the equation , we get
The amount of candy each person gets A = 1/20 of the candy
Hence , the equation is A = 1/20
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Amir puts £1390 into an bank account.
The account pays 2.25% compound interest each year.
Work out how much Amir will have in the account after 23 years.
Answer: look below love :))
Step-by-step explanation: To find out how much Amir will have in the account after 23 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A is the final amount
P is the initial principal (the amount Amir deposited)
r is the annual interest rate (2.25%)
n is the number of times the interest is compounded per year (let's assume it is compounded annually)
t is the number of years
So, we can plug in the given values:
A = 1390(1 + 0.0225)^(1*23)
A = 1390(1.0225)^(23)
A = 1390 * 2.6388955
A = 3655.922
So Amir will have £3655.922 in the account after 23 years with 2.25% compound interest.
The ladder on a fire truck is 70ft long. If the ladder is 25ft from the base of a building, how far up the building can the ladder reach? Round your answer to the nearest hundredth.
Using the Pythagorean Theorem we know that the ladder can reach up to the building 85ft.
What is Pythagorean Theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental Euclidean geometry relationship between the three sides of a right triangle.
This statement states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
So, we have:
Hypotuenese is 70ft long and Height is 25ft long.
Then, the base would be:
c² = a² + b²
70² = 25² + b²
b² = 4,900 - 625
b² = 7,275
b = √7275
b = 85ft
Therefore, using the Pythagorean Theorem we know that the ladder can reach up to the building 85ft.
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let f(x) be a polynomial function such that f(3)=−2,f′(3)=0 and f′′(3)=−2. classify the point (3,−2).
The point (3, -2) can be classified as a local maximum of the polynomial function f(x).
What is polynomial ?
A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
In this case, the values f(3) = -2, f'(3) = 0, and f''(3) = -2 give us information about the graph of the polynomial function f(x) at the point x = 3.
First, f(3) = -2 means that the y-coordinate of the point (3, -2) is -2, so the point (3, -2) is on the graph of f(x).
Second, f'(3) = 0 means that the slope of the tangent line to the graph of f(x) at the point x = 3 is 0. This means that at x = 3, the graph of f(x) has a horizontal tangent line, which is a sign of a local maximum or minimum of the function.
Third, f''(3) = -2 means that the second derivative of f(x) at x = 3 is -2. This means that the graph of f(x) is concave down at x = 3. A concave down graph means that the function is decreasing at x = 3, so the point (3, -2) is a local maximum of the function.
Therefore, the point (3, -2) can be classified as a local maximum of the polynomial function f(x).
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Mateo realize that he forgot to record check 354 for $25.79, but he does not know the amount of check 353. Which equation can be used to find the amount, in dollars, X, of check 353?
A. 1,225.70 + x = 1,460.89
B. 1,225.70 + 25.79 + x = 1,460.89
C. 1,460.89 + x = 1,536.71
D. 1,460.89 + 25.79 + x = 1,536.71
Answer:
A
Step-by-step explanation:
Mateo has a balance of 1,460.89 dollars, and he knows that check 354 was for 25.79 dollars. Therefore, to find the amount, in dollars, X, of check 353, Mateo needs to subtract the known amount of check 354 from his current balance.
So, the equation that can be used to find the amount of check 353 is:
1,460.89 - 25.79 = X
Thus the correct answer is:
A. 1,225.70 + x = 1,460.89
The solution of the equation ax + b = 0 [ a isint equal to is ______
it is thursday and an angler is planning a fishing trip in two days on saturday. the angler knows from experience that the fishing is best at a particular location at the beginning of high tide. he does not have a tide table, but the angler noted that the high tide on thursday was at 12:15 pm. at what time on saturday should he plan to arrive to start fishing, assuming that this location has a diurnal tide type?
Assuming the location has a diurnal tide type, the angler should plan to arrive to start fishing at 12:15 pm on Saturday, two days after the high tide on Thursday.
This is because with a diurnal tide type, the high tide occurs at the same time each day, so the angler can expect the high tide to occur at the same time on Saturday as it did on Thursday.
A diurnal tide type is a type of tidal pattern where there is one high tide and one low tide per day. This type of tide is most commonly seen in areas with small and shallow bodies of water, such as bays and estuaries. In diurnal tidal systems, the times of high and low tide usually occur at the same time each day. The height of the tide also usually remains relatively constant over time.
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Ella bought 10 packs of cups for her holiday party. A medium size pack of cups cost $1.80, while a large one costs $2.40. If she spent $21.60, how many packs of each type did she buy?
Answer:
Step-by-step explanation:
2.40X+1.80(10-X)=21.602.40X+18-1.8X=21.60.6X=21.60-18.6X=3.6X=3.6/.6X=6 PACKS OF $2.40 CUPS.
11101001 divided by 101
11101001 can be written as 101001 x 101 + 1. To divide 1101001 by 101, the first step is to divide 101001 by 101 without the remainder.
The result of this division is 1000. Then, take the remainder of 1 and place it next to the 1000 to get 10001. Divide 10001 by 101. The result of this division is 99. Take the remainder of 0 and place it next to the 99 to get 990. Divide 990 by 101. The result of this division is 9. Take the remainder of 9 and place it next to the 9 to get 99. Divide 99 by 101. The result of this division is 0. Take the remainder of 99 and place it next to the 0 to get 990. Divide 990 by 101. The result of this division is 9. The answer is 1101.11.
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Find the Taylor series for f centered at 9 if f^(n) (9) = (-1)^n n!/7^n (n + 5). sigma^infinity_n = 0 What is the radius of convergence R of the Taylor series? R=
The radius of convergence R of the Taylor series is 2
The term convergence in math is defined as the process of a sequence or other function converging to a limit in a metric space.
Here we have know that the expression is written as,
=> f(x)=ln x, c=2.
By using the Taylor series formula we can write the expression like the following,
=> f(x) = ln(2) + ∑ (-1)ⁿ⁺¹ / n (2ⁿ)
Then the above power series will converge if and only if:
[tex]= > \lim_{n \to \infty} |\frac{-1}{(1+\frac{1}{n} )\times2}\times(x-2) | < 1[/tex]
When we simplify this one then we get,
=> |x-2/2| < 1
Then the value of x lies between 0 to 4.
And the Radius of convergent is 2.
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Simplify the following algebraic expression:-
[tex]\mathrm {\cfrac{2}{3}\:y -2(\cfrac{4}{3}\:y+z)}[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{ORIGINAL equation:}[/tex]
[tex]\mathsf{\dfrac{2}{3}y - 2(\dfrac{4}{3}y + z)}[/tex]
[tex]\huge\textbf{DISTRIBUTE \boxed{\rm{\bf -2}} within the}\\\\\huge\textbf{parentheses:}[/tex]
[tex]\mathsf{\dfrac{2}{3}y - 2(\dfrac{4}{3}y + z)}[/tex]
[tex]\mathsf{= \dfrac{2}{3}y - 2(\dfrac{4}{3}y) - 2(z)}[/tex]
[tex]\mathsf{= \dfrac{2}{3}y - \dfrac{8}{3}y - 2z}[/tex]
[tex]\huge\textbf{COMBINE the like terms:}[/tex]
[tex]\mathsf{= (\dfrac{2}{3}y - \dfrac{8}{3}y) - (2z)}[/tex]
[tex]\mathsf{= \dfrac{2}{3}y - \dfrac{8}{3}y - 2z}[/tex]
[tex]\mathsf{-2y - 2z}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{-2y - 2z}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Puzzle #4
Can you find the measure of the indicated angle and type the correct code? Please remember to type in ALL caps with no spaces. (it isn’t CBCA)
The solution of all the measures of the angles are,
1) m ∠A = 63°
2) m ∠B = 138°
3) m ∠C = 117°
4) m ∠D = 137.22°
What is Line segment?Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
In figure 1;
Measure of angle A and angle B are vertically opposite angle and hence both are equal to each other.
⇒ ∠A = ∠B
⇒ 2x + 35 = 8x - 49
⇒ 35 + 49 = 8x - 2x
⇒ 84 = 6x
⇒ x = 14
Thus, The value of m ∠A = 2x + 35
= 2×14 + 35
= 28 + 35
= 63°
2) By the figure, the sum of both indicated angle is 180°.
Hence, We get;
⇒ 10x - 18 + 15x + 48 = 180
⇒ 25x + 30 = 180
⇒ 25x = 180 - 30
⇒ 25x = 150
⇒ x = 6
Thus, The value of m ∠B = 15x + 48
= 15×6 + 48
= 90 + 48
= 138°
3) By the figure, Both angles are alternate angle of parallel lines and hence both are equal.
So, We get;
⇒ 7x + 5= 12x - 75
⇒ 5 + 75 = 12x - 7x
⇒ 80 = 5x
⇒ x = 16
Thus, The value of m ∠C = 7x + 5
= 7×16 + 5
= 112 + 5
= 117°
4) By the figure, the sum of both indicated angle is 180°.
Hence, We get;
⇒ 27x - 21 + 10x - 16 = 180
⇒ 37x - 37 = 180
⇒ 37x = 180 + 37
⇒ 37x = 217
⇒ x = 217/37
⇒ x = 5.86
Thus, The value of m ∠D = 27x - 21
= 27×5.86 - 21
= 158.22 - 21
= 137.22°
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For customers purchasing a full set of tires at a particular tire store, consider events:
A ={tires purchased were made in the United States}
B ={purchaser has tires balanced immediately}
C ={purchaser requests front-end alignment}.
Assume the following probabilities
P(A) = .75 P(B|A) =.9 P(B|A) = .8
P(C|A∩B) = .8 P(C|A∩B) = .6 P(C|A∩B) = .7 P(C|A∩B) = .3
Find the probabilities P(A∩B∩C), P(B∩C), P(C), P(A|B∩C)
The probability of the tires purchased being made in the United States, given that the purchaser has tires balanced immediately and requesting front-end alignment is P(A|B∩C) = 0.676.
P(A∩B∩C) = P(A) * P(B|A) * P(C|A∩B) = 0.75 * 0.9 * 0.8 = 0.504
P(B∩C) = P(B|A) * P(C|A∩B) + P(B|A') * P(C|A'∩B) = 0.9 * 0.8 + 0.8 * 0.6 = 0.744
P(C) = P(C|A) * P(A) + P(C|A') * P(A') = 0.8 * 0.75 + 0.7 * 0.25 = 0.725
P(A|B∩C) = P(A∩B∩C) / P(B∩C) = 0.504 / 0.744 = 0.676
The probability of customers purchasing a full set of tires at a particular tire store, and the events of the tires purchased being made in the United States, the purchaser having tires balanced immediately, and the purchaser requesting front-end alignment, is P(A∩B∩C) = 0.504. The probability of the purchaser having tires balanced immediately and requesting front-end alignment is P(B∩C) = 0.744. The probability of the purchaser requesting front-end alignment is P(C) = 0.725. The probability of the tires purchased being made in the United States, given that the purchaser has tires balanced immediately and requesting front-end alignment is P(A|B∩C) = 0.676.
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a new security system needs to be evaluated in the airport. the probability of a person being a security hazard is 0.023. at the checkpoint, the security system denied a person without security problems 1.5% of the time. also the security system passed a person with security problems 1% of the time. what is the probability that a person who passed through the system is without any security problems? report answer to 4 decimal places.
The probability that a person who passes through the security system is without any security hazards is 0.99.
Let A be the event that the person passed through the checkpoint
Let X be the event of a person being a hazard
Now, according to the problem,
P(X) = 0.023
P(not A/not X) = 0.015
P(A/X) = 0.01
We need to find P(A/not X)
Now we know that the conditional probability P(Q/R)
= P(Q ∩ R) / P(R)
We need to find P(A/not X) we need to know P(A ∩ not X) and P(not X)
We know that
P(Q/notR) = 1 - P(Q/R)
Hence P(A/ not X) = 1 - p(A/X)
= 1 - 0.01
= 0.99
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So this is really confusing and I’ve gotten most of everything else right I had to retake this quiz tho because it’s a large amount of my grade so please help (you just select is it’s one of the answers that’s why I have the selective part open)
What method proves this two triangles congruent?
On solving the provided question we can say that so by SAS triangles are congruent
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
here,
BC = HI
AB = HG
angle ABC = IHG
so by SAS triangles are congruent
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Instructors at a sports club were surveyed about whether they are certified in CPR. The survey results are shown in the two-way frequency table.
Does the data show an association between the type of instructor and a certification in CPR? PLEASE I NEED HELP
Answer: The data shows an association between the type of instructor and a certification in CPR. The association is that swimming instructors are less likely than tennis instructors to be certified in CPR. This can be seen from the frequency table, where all the swimming instructors are not certified in CPR, while only 4 out of 12 tennis instructors are not certified in CPR, so yes, the data does show an association between the type of instructor and a certification in CPR.
Step-by-step explanation:
The two-way frequency table shows the number of instructors who are certified or not certified in CPR, broken down by type of instructor (swimming or tennis). The data in the table allows us to see the relationship between the two variables (type of instructor and certification in CPR) and whether there is an association between them.
An association means that the values of one variable are related to the values of another variable in some way. In this case, the type of instructor (swimming or tennis) is related to whether or not the instructor is certified in CPR. The data shows that the proportion of swimming instructors who are not certified in CPR (100%) is higher than the proportion of tennis instructors who are not certified in CPR (33%). This indicates that there is an association between type of instructor and certification in CPR, with swimming instructors being less likely to be certified in CPR than tennis instructors.
It is important to note that this association does not necessarily imply causation, meaning that being a swimming instructor does not cause one to not be certified in CPR, but it could be the other way around, or it could be due to some other factors that the data does not show.
Use properties of operations to write an equivalent expression to 17n+9−47n.
A: 9−37n
B: 9−57n
c: 9+37n
D: 9+57n
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{17n + 9 - 47n}[/tex]
[tex]\huge\textbf{COMBINE the LIKE TERMS}[/tex]
[tex]\mathsf{= (17n - 47n) + (9)}[/tex]
[tex]\mathsf{= 17n - 47n + 9}[/tex]
[tex]\mathsf{= -30n + 9}[/tex]
[tex]\huge\text{Therefore, your answer SHOULD be:}[/tex]
[tex]\huge\boxed{\mathsf{-30n + 9}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
HOW MANY 6- digit numbers are in the form 225A7B such that the number is divisible by 36? Please answer ASAP!!
There are three 6- digit numbers divisible by 36.
What is divisibility Rule?To decide if a fraction has to be decreased, dividesibility rules can be applied. The patterns that appear when we list the multiples of any number serve as the foundation for the rules.
Given:
We have 225A7B
Now, we will substitute A and B 0, 1 , 2.....9 to get the combination.
Also, A number is divisible by 36 if the number is divisible by 4 and 9.
So, take A=0 and B= 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
225070 is not divisible by 4 thus not divisible by 36.
and, 225071 is not divisible by 4 thus not divisible by 36.
and, 225072 is divisible by 4 and 9 thus divisible by 36.
and, 225073 is not divisible by 4 thus not divisible by 36.
and, 225074 is not divisible by 4 thus not divisible by 36.
and, 225075 is not divisible by 4 thus not divisible by 36.
and, 225076 is not divisible by 4 thus not divisible by 36.
and, 225077 is not divisible by 4 thus not divisible by 36.
and, 225078 is not divisible by 4 thus not divisible by 36.
and, 225079 is not divisible by 4 thus not divisible by 36.
Similarly, we can find 225576 & 225972 divisible by 36.
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Under the right growing conditions, a particular
species of plant has a doubling time of 12 days. Suppose a
pasture contains 46 plants of this species. How many
plants will there be after 20, 65, and x days?
Based on the information, we can infer that after 20 days there will be 153 plants and after 65 days there will be 498 plants.
How to find the number of plants after 20 and 65 days?To find the number of plants that will be after 20 and 65 days we must take into account the number of initial plants and the number of days required for the plantation to double.
Every 12 days it doubles.Initial amount 46 plants.According to the above, we must make a rule of 3 as shown below:
12 - 92
20 -
= 20 * 92 / 12 = 153
12 - 92
65
= 65 * 92 / 12 = 498
According to the above, after 20 days there will be 153 plants and after 65 days there will be 498 plants.
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8 _ 6 _ 4 _ 2=6 you can use - ,+, x
Answer:
[tex]+, -, \times[/tex]
Step-by-step explanation:
This is one of those questions where trial and error are used.
Trying out different combos until I get the right answer:
[tex]8-6+4\times2=10[/tex]
[tex]8+6-4\times2=6[/tex]
Nice! The correct answer is [tex]+, -, \times[/tex]
A number is between 15 and 20. It has prime factors of 2 and 3. What is the number?
The number is given by the equation A = 18
What are Factors of a Number?Numbers that divide an original number evenly or precisely are known as its factors. A factor is a whole number that can divide a larger number in two equal parts. A factor is a number that divides another number, leaving no remainder
Given data ,
Let the inequality be represented as A
Now , the value of A is
15 < A < 20 be equation (1)
The number lies between 15 and 20
when A = 18
The factors of 18 = 1 , 2 , 3 , 6 , 9 , 18
So , the number 18 has the prime factors as 2 and 3
Hence , the number is A = 18
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What number is halfway between -38.7 and -38.71?
Answer: -38.705
Step-by-step explanation:
(-38.71) - (-38.7)
= -38.71 + 38.7
= -0.01
-0.01 ÷ 2 = -0.005
Then add it to -38.7:
= (-0.005) + (-38.7)
= -0.005 + 38.7
= -38.705
a bag contains 19 balls numbered 1 through 19. what is the probability that a randomly selected ball has a number less than 10?
The probability that a randomly selected ball has a number less than 10 is [tex]$\frac{9}{19}[/tex].
As per the given data:
A bag contains 19 balls numbered 1 through 19.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 and 19
The total number of outcomes is 19.
Here we have to determine the probability that a randomly selected ball has a number less than 10.
Numbers on the balls less than 10 are 1, 2, 3, 4, 5, 6, 7, 8, and 9.
A ball is randomly selected.
The favorable outcomes are 9.
The likelihood of every event depends on the overall number of positive outcomes as well as the number of favorable outcomes.
The formula for probability:
The number of favorable outcomes is divided by the total number of outcomes.
= [tex]$\frac{9}{19}[/tex]
Therefore the probability that a randomly selected ball has a number less than 10 is [tex]$\frac{9}{19}[/tex].
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Write a linear inequality that, when taken with y > x - 1, form a ytem of linear inequalitie whoe olution et i the empty et
A linear inequality that forms a system of linear inequalities with y > x - 1, whose solution set is the empty set, is y < x - 1.
When taken together, y > x - 1 and y < x - 1 form a system of linear inequalities, but these two inequalities are contradictory and cannot both be true at the same time. Therefore, the solution set of this system is the empty set, meaning there are no solutions that satisfy both inequalities.
To explain in detail, consider the line y = x - 1. When x = 1, y = 0. If y > x - 1, then y must be greater than 0 when x = 1. But if y < x - 1, then y must be less than 0 when x = 1. These two inequalities cannot both be true at the same time, so the solution set of the system is the empty set.
This shows that when two contradictory linear inequalities are taken together, their solution set is the empty set. In this case, y > x - 1 and y < x - 1 are contradictory, and so their solution set is the empty set.
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--The given question is incomplete; the complete question is
"Write a linear inequality that, when taken with y > x - 1, forms a system of linear inequalities whose solution set is the empty set."
3. James bought a watch for 48 U.S. dollars. What is the cost of the watch in Swiss francs? Use the conversion formula below. Show your work. Answer: 1 U.S. dollar = 1.02 Swiss francs
3.(part 2) James would like to buy a battery for 10 U.S. dollars. He has 10.20 Swiss francs remaining after buying the watch. On the lines below, determine whether Scott has enough money to buy the battery. Explain how you determined your answer.
Answer:
see below
Step-by-step explanation:
1 U.S. dollar = 1.02 Swiss francs
$48 = CHF 48.96
part 2
CHF 10.20 = US$10
yes he has enough
Rocko paid 12.50 for 25 game tickets. Louisa paid 17.50 for 36 game tickets. What is the constant of proportionality
Answer:
To find the constant of proportionality between the cost of the game tickets and the number of tickets purchased, we can write an equation that represents the relationship between the two values. Let's call the constant of proportionality "k".
Step 1: Write an equation for Rocko's purchase:
12.50 = k * 25
Step 2: Solve for k:
k = 12.50 / 25 = 0.50
Step 3: Write an equation for Louisa's purchase:
17.50 = k * 36
Step 4: Substitute the value of k from step 2 into the equation:
17.50 = 0.50 * 36
Step 5: Check if the value of k is the same for both equations:
17.50 / 36 = 0.50
The constant of proportionality is 0.50, which means that for each additional game ticket purchased, the cost increases by $0.50.
-6+7x≤-22
plss help me
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
Inequality Form:
x≤−16/7
Interval Notation:
(−∞,−16/7]
The solution to the linear inequality given as -6 + 7x ≤ -22 is determined as x ≤ -16/7.
What is the value of x in the inequality?The value of x in the inequality -6 + 7x ≤ -22, is determined by applying the following method.
The given inequality expression;
-6 + 7x ≤ -22
Solve the inequality by collecting similar terms together as shown below;
-6 + 7x + 6 ≤ -22 + 6
Simplify further as follows;
7x ≤ -16
Divide both sides of the inequality by 7 to solve for x as shown below;
(7x)/7 ≤ (-16)/7
x ≤ -16/7
Therefore, the solution to the inequality is x ≤ -16/7.
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how many non-zero values in tridiagonal matrix
The number of non-zero values in a tridiagonal matrix increases with the size of the matrix.
A tridiagonal matrix is a type of matrix that consists of three diagonals. The main diagonal is the diagonal that runs from the top left corner of the matrix to the bottom right corner. The secondary diagonal is the diagonal that runs from the top right corner of the matrix to the bottom left corner. The third diagonal is the diagonal that runs from the top left corner of the matrix to the bottom right corner, one row above the main diagonal. The number of non-zero values in a tridiagonal matrix of size n x n can be calculated using the formula: Nnz = 2n + (n-2). For example, for a tridiagonal matrix of size 4 x 4, the number of non-zero values would be 2 x 4 + (4-2) = 10. In general, the number of non-zero values in a tridiagonal matrix increases with the size of the matrix.
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foall the sides of a square is changing at the rate of negative 3 per second. when the side is 10. determine the rate of change of the area.
The rate of change of the area of square with side 10 and rate of change of side is -3 per second is -60.
We have, For all sides of a square is
Rate of changing per second = - 3
Let "x" be side of square. So, x = 10. We have to determine the rate of change of the area. So, Rate of change in side ,x per unit time = dx/dt = -3 . As we know, the area of a polygon is equals to total space occupied by shape or polygon.
So, Area of square, A = side × side . In this case, Area of square , A = x² --(1)
Differentiating equation (1) with respect to time "t",
=> dA/dt = d/dt ( x²)
=> dA/dt = 2x dx/dt ( using derivative formula )
here,dx/dt --> rate of changing of side of square
Substitute the value of dx/dt = -3 in above derivative, dA/dt = 2x dx/dt
=> dA/dt = 2x (-3)
=> dA/dt = 2×(10)(-3) ( since side, x = 10)
=> dA/dt = -60
Hence, required rate of change of area is -60.
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