.• Let u and v be vectors in R. Which of the below is/are true? A. A column vector in R2 is a 1 x 2 matrix. B. We can identify a point in R, represented by an ordered pair of numbers, as a column vector u whose entries are the given numbers; and we can graph the vector u as a position vector of that point. C. The sum, u + v, of two non-parallel vectors u and vis defined geometrically as the fourth vertex of a parallelogram whose other vertices are u, v, and 0. D. The magnitude of a vector cv, where c is a scalar, is the magnitude of v multiplied by the scalar e. E The set of all vectors that are scalar multiple of a nonzero vector u is a line through u and 0. F. Operation of vector addition is not commutative.

Answer:

6(−3−x)−2x=14

simplify

-18-6x-2x=14

simplify

-8x-18=14

add 18

-8x=32

divide by -8

x=4

Hope This Helps!!!

Step-by-step explanation:

(a): √8 = √4√2 = 2√2. => k = 2

(b): √50 = √25√2 = 5√2. => k = 5

(c): √98 = √49√2 = 7√2. => k = 7

(d): √12 = √4√3 = 2√3. => k = 2

(e): √300 = √100√3 = 10√3. => k = 10

(f): √45 = √9√5 = 3√5. => k = 3

(g): √125 = √25√5 = 5√5. => k = 5

(h): √28 = √4√7 = 2√7. => k = 2

Answer:

\(x<\frac{16}{125}\)

Step-by-step explanation:

First we will multiply everything by 10 to get rid of the decimals.

\(4.2x*10+5.6*10<7.2*10-8.3x*10\\42x+56<72-83x\)

Subtract 56 from both sides:

\(42x+56-56<72-83x-56\\42x<-83x+16\)

Add 83x to both sides:

\(42x+83x<-83x+16+83x\\125x<16\)

Divide both sides by 125:

\(\frac{125x}{125}<\frac{16}{125}\\x<\frac{16}{125}\)

Answer:

I'm terrible at explaining things but here's a screenshot

- Ripper

Step-by-step explanation:

Answer:

528

Step-by-step explanation:

We are given the following sequence:

31,41,51,61,71,81,91,101

Count the terms and see that there are 8 terms total.

If you notice, each terms add up by 10.

31+10 = 41

41+10 = 51

51+10 = 61

Therefore, this is an arithmetic sequence with 10 as common difference.

To find the sum of 8 sequences, we will be using the following formula.

\( \displaystyle \large{S_n = \frac{1}{2} n(a_1 + a_n)}\)

We know that:

Substitute the following in the sum formula.

\( \displaystyle \large{S_8 = \frac{1}{2} (8)(31+ 101)} \\ \displaystyle \large{S_8 = 4(132)} \\ \displaystyle \large{S_8 = 528}\)

Therefore, the sum of all 8 sequences is 528.

Tyler has two cube-shaped storage spaces in his apartment building, one large and one small.

Let the length of one side of the larger cube be l. Thus, the volume of the larger cube is V = l^3

The length of one side of the smaller cube is half of the larger cube's side. Hence, the length of one side of the smaller cube is l/2. Therefore, the volume of the smaller cube is

V = (l/2)^3

Simplifying the second equation,

V = (l/2)^3 = l^3/8

Given that the volume of the larger cube is 343 cubic feet. Therefore,

l^3 = 343 cubic feet

.l = (343)^(1/3) feet

= 7 feet

The volume of the smaller cube is given by V = l^3/8. Substituting the value of l, we get:

V = (7^3)/8 cubic feet

= 171.5 cubic feet

Therefore, the volume of the smaller cube is 171.5 cubic feet.

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Answer:

98

Step-by-step explanation:

If you times 98 by 4, you get 392, and three lots of 98 are cheeseburgers, with one lot being hamburgers.

Answer:

  1 ≤ q ≤ 2

Step-by-step explanation:

If q represents the number of quarts of paint needed, the requirement that it be between 1 and 2 can be written ...

  1 ≤ q   and    q ≤ 2

These inequalities can be combined into one compound inequality:

  1 ≤ q ≤ 2

__

Additional comment

We have used the usual English language interpretation of "between", which allows the end values to be considered as part of the solution set. That is, 1 quart is sufficient to satisfy the need for "between 1 and 2."

Answer:

(a) False

(b) False

(c) True

Step-by-step explanation:

(a) If we had measured the heights of the men and women in centimeters (1 inch= 2.54 cm), the correlation coefficient would have been 2.54 times larger.

No, since changing the units of measurement does not change the correlation coefficient

(b) There is a strong negative association between the heights of men and women because women are always smaller than the men they date.

Negative association means that as one variable increases, the other decreases, Here, we see that as the heights of the men increase, the height of the women do not reliably decrease, hence there is no strong negative asscoiation

(c) There is a positive association between the heights of men and women.

We see from the values given that as the heights of men increase, so do the heights of women and vise versa, so there is a positive association between the heights of men and women

Two rays with a common endpoint form an angle. An angle is defined as a geometric figure formed by two rays that share a common endpoint. In other words, an angle is formed when two rays emanating from a common point, and this common point is known as the vertex.

The rays are the sides of the angle, and the angle is measured in degrees. Angles have different measures, ranging from 0 degrees to 360 degrees. The two rays that make up an angle are also called the sides or arms of the angle. The angle is measured in degrees, and the size of the angle depends on the distance between the two sides of the angle that meet at the vertex.

In geometry, an angle can be named in different ways, depending on the context in which it is being used. Angles are essential in mathematics, physics, and other scientific fields, where they are used to measure the rotation of an object, determine the direction of an object, and in other applications involving rays and lines. Two rays with a common endpoint form an angle.

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Answer:

If, he got 94 marks for his sixth quiz, then, he will be able to maintain his required grade for his scholarship.

Step-by-step explanation:

given-

Joven's scores in five of his quizzes in mathematics are 85, 88, 95, 86, and 92.

let, the x score he gets for his sixth quiz.

then, he will be able to maintain his required grade for his scholarship.

he needs an average quiz grade of 90 to maintain his required grade for his scholarship.

according to the question--

using the formula of average=>

(85+88+95+86+92+x)/6=90

=>x=540-446

=>x=94

if, he got 94 marks for his sixth quiz, then, he will be able to maintain his required grade for his scholarship.

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Answer:

20

Anything to the power of one equal its number itself.

There are 1820 different groups of applicants for 4 management trainee positions, 126 different groups of trainees consisting entirely of women, and a 0.0692 probability that the trainee class will consist entirely of women.

The number of different groups of applicants that can be selected for the four management trainee positions can be calculated using the combination formula:

nCr = n! / (r! * (n-r)!)

where n is the total number of applicants (16 in this case) and r is the number of positions to be filled (4 in this case).

So the number of different groups of applicants that can be selected is:

16C4 = 1820

Therefore, there are 1820 different groups of applicants that can be selected for the four management trainee positions.

The number of different groups of trainees that would consist entirely of women can be calculated using the combination formula again, but this time we are selecting all 4 positions from the 9 female applicants:

9C4 = 126

Therefore, there are 126 different groups of trainees that would consist entirely of women.

Assuming that all groups of four are equally likely to be selected, the probability that the trainee class will consist entirely of women can be calculated by dividing the number of different groups of trainees that consist entirely of women (126) by the total number of different groups of applicants (1820):

Probability = 126 / 1820 = 0.0692

So the probability that the trainee class will consist entirely of women is 0.0692 (rounded to four decimal places).

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Answer:

9/4n= 1.5/7

right now to find this equation it is a proportion so you cross multiply and you gonna get 63=6n and divide 6 on both sides and u get 10.5.

Check 9/4n= 9/42 and to simply u will get 1.5/7

Step-by-step explanation:

Answer:

The required F- test statistic is 5.1788 (approximately up to 4 decimal places) to test the claim that the population variances are equal for the standard deviation of the first sample is, \(s_{1}\) = 2.8404 and that of second sample is \(s_{2}\) = 6.4639.

An F-test is defined as a statistical test in which the test statistic has an F-distribution under the null hypothesis. F- test is performed  in hypothesis testing to check if the variances of (any) two populations or (any) two samples are equal to each other or not.

It is said that both the distributions are normal.

We have, the standard deviation of the first sample is, \(s_{1}\) = 2.8404 ,

and the standard deviation of the second sample is, \(s_{2}\) = 6.4639

The value of F- statistic, that is, F- ratio is the ratio of the larger sample variance to smaller sample variance.

Therefore,

F- ratio = \(\frac{s_{1}^2}{s_{2}^2}\) = (6.4639)² / (2.8404)² = 41.78200321 / 8.06787216

= 5.17881324609

= 5.1788 (approximately up to 4 decimal places)

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Answer:Subtract

8

from

−

16

.

−

24

≥

0

Step-by-step explanation:

proportion of old cost to new cost = Subsequently the proportion of old to the new cost = 5:3

note: 16 ounces= one pound

       6 ounces = ?

∴6 ounces = pounds

48 pennies = pounds

duplicating the two sides by

108 pennies = 1 pound in the new cost

= $1.08 in the new cost

proportion of old cost to new cost =

Subsequently the proportion of old to the new cost = 5:3

Current prices are those demonstrated at a given second in time, and said to be in costensible value. Constant prices are in genuine value, for example revised at changes in costs comparable to a gauge or reference datum.

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Hope this helps you!!

Answer:

The first option.

Step-by-step explanation:

Add all the numbers together and voila you get 27

Answer:

y = 2x + 14

Step-by-step explanation:

Hope this helps!!!

First, you have to find the slope by using

In other words,

The slope is 2.

Then you plug the rest into point-slope form (you can use either of the points, I used the first one)

Remember that m is the slope.

Distribute the slope to the parenthesis

Isolate the y variable

Answer:

2x+14

Step-by-step explanation:

The one that has the most circles in a group :D

In summary, the separable differential equations are (a) dy/dt = -3y and (c) dy/dt - 1 = t. The solutions for these equations are y = Ce^(-3t) and t = Ce^y + 1, respectively.

To determine which of the given differential equations are separable, we need to check if we can rewrite the equation in the form "dy/dt = g(t)h(y)", where g(t) and h(y) are functions of t and y, respectively.

(a) dy/dt = -3y:

This equation is separable since we can rewrite it as (1/y)dy = -3dt. By integrating both sides, we get ln|y| = -3t + C, where C is the constant of integration. Solving for y, we have y = Ce^(-3t).

(b) dy/dt - ty = -y:

This equation is not separable since the term "-ty" contains both t and y.

(c) dy/dt - 1 = t:

This equation is separable since we can rewrite it as (1/(t-1))dt = dy. By integrating both sides, we get ln|t-1| = y + C, where C is the constant of integration. Solving for t, we have t = Ce^y + 1.

(d) dy/dt = t^2 - y^2:

This equation is not separable since the terms "t^2" and "-y^2" contain both t and y.

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Answer:

cn<fr

Step-by-step explanation:

trust me bro

Answer: Cr<Fr

Step-by-step explanation:

if you look at the angle it gives you, you can tell which inequality is bigger.

The probability of no ice-squids raining down from the sky in the ten-year period is approximately 0.135.

To calculate the probability, we need to use the Poisson distribution since the occurrence of ice-squids follows a random process with an average rate. The average rate of ice-squids raining down from the sky is 1 per 2 years.

The Poisson distribution is given by the formula:

P(x; λ) = (e^(-λ) * λ^x) / x!

Where P(x; λ) is the probability of x events occurring in a given time period with an average rate of λ.

In this case, we want to calculate the probability of no ice-squids raining down in a ten-year period. We can convert the average rate from years to the ten-year period by multiplying it by 10. So, λ = 1/2 * 10 = 5.

Substituting λ = 5 and x = 0 into the Poisson distribution formula, we get:

P(0; 5) = (e^(-5) * 5^0) / 0!

Since 0! is equal to 1, the formula simplifies to:

P(0; 5) = e^(-5) ≈ 0.00674.

Therefore, the probability of no ice-squids raining down in the ten-year period is approximately 0.00674 or 0.135 when expressed as a percentage.

In other words, there is a 13.5% chance that no ice-squids will rain down from the sky in the ten-year period starting in 2024 in the alternate universe of San Diego.

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Answer:

2.2876792e+13

Step-by-step explanation:

Answer:

9^14

Step-by-step explanation:

9^7 / 9^-7

= 9^ 7 - (-7)

= 9^14

Answer:

Function A has a greater initial value because the initial value for Function A is 6 and the initial vale for Function B is 3

Step-by-step explanation:

The data for Function A is presented here as follows;

\(\begin{array}{cc}x&y\\-1&9\\0&6\\1&3\\2&0\end{array}\)

The slope of the function, 'm', is given using any two points as follows;

m = (9 - 3)/((-1) - 1) = -3

The slope of the function = -3

The equation of function in point and slope form is given as follows;

y - 3 = -3·(x - 1)

The equation of Function A, is therefore, given as follows;

y = 3 - 3·x + 3 = 6 - 3·x

∴ y = 6 - 3·x

The equation of Function B is given as follows;

y = 6·x + 3

The initial value of a function is given by the y-intercept of the function, where the input variable (x-variable) is zero

The initial value, (y-intercept) of Function A, f(0) is therefore found as follows;

f(x) = y = 6 - 3·x

f(0) = 6 - 3×0 = 6

The initial value of Function A, f(0) = 6

Similarly, the initial value, (y-intercept) of Function B, f(0) is found as follows;

f(x) = y = 6·x + 3

f(0) = 6×0 + 3 = 3

The initial value of the Function B, f(0) = 3

Therefore, we have that Function A has a greater initial value than Function B

Without the individual probability of a passenger showing up, we cannot calculate the exact probability of the number of people who show up exceeding the capacity of the plane

To solve this problem, we need to determine the probability that more than 65 people (the capacity of the plane) will show up from the 70 booked passengers.

Step 1: Identify the relevant information
- Maximum capacity of the plane: 65
- Number of people booked: 70

Step 2: Calculate the probability of each possible outcome
To exceed the capacity, at least 66 passengers must show up. We need to calculate the probability of 66, 67, 68, 69, and 70 passengers showing up. However, we don't have information on the individual probability of a passenger showing up. If we had this information, we could use the binomial probability formula.

Step 3: Express the final answer
Unfortunately, without the individual probability of a passenger showing up, we cannot calculate the exact probability of the number of people who show up exceeding the capacity of the plane. Please provide the probability of a passenger showing up so we can give you an accurate answer.

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$49.73

because you would multiply the length and width of the fence then multiply by the price.

3.4 x 6.5 = 22.1

22.1 x 2.25 = 49.725

but you would round because you are dealing with money

The completed table with regards to terms of an expression are presented as follows;

     Condition      \({}\)              (6·x + 3) + (5·x - 4)            (-4·y - 16) - 8·y + 10 + 2·y

         Exactly 3 terms          N/A     \({}\)                              N/A

         Exactly 5 terms          N/A         \({}\)                          N/A

Includes a zero pair             No \({}\)                                   No

Uses distributive property   No                                    No

Includes a negative factor   No                                    

Has no like terms                False                                False

Condition       \(8 - \dfrac{1}{2} \cdot \left(4 \cdot x - \dfrac{1}{2} + 12\cdot x -\dfrac{1}{4} \right)\)  0.25·(8·m - 12) - 0.5·(-4·m + 2)

Exactly 3 terms       No                         \({}\)                    No

Exactly 5 terms       Yes                          \({}\)   \({}\)              No

Includes a zero pair No    \({}\)                         \({}\)              Yes

Uses the distributive property Yes            \({}\)             Yes

Includes a negative factor      Yes           \({}\)                Yes

Has no like terms                    No          \({}\)                  No

A mathematical expression is a collection of variables and numbers along with mathematical operators which are all properly arranged.

The details of the conditions in the question are as follows;

Terms of an expression

A term is a subunit of an algebraic expression which are joined together by operators such as addition or subtraction

Zero pair

A zero pair are two numbers that when added together have a zero result

Distributive property

The distributive property of multiplication states that the multiplication of a number or variable by an addend is equivalent to the sum of the multiplication of the number or variable and each member of the addend

Negative factor

A negative factor is a factor that has a negative sign prefix

Like terms

Like terms are terms consisting of identical variables with the same  powers of the variable

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