Simplify these expressions
a) 5 x x
b) 6 xxxy
c) 2 xxx 3xy

a. False. The notation [-4 3] represents a column vector, not another notation for the vector. b. True. The points corresponding to scalar multiples of a vector and the zero vector (origin) lie on a line through the origin. c. True. d. True. e. False.

a. The notation [-4 3] represents a column vector with two components, -4 and 3. It is not an alternative notation for another vector.

b. Given a vector, the points in the plane corresponding to scalar multiples of that vector and the zero vector form a line passing through the origin. This line is known as the span or the line of the vector.

c. A linear combination of vectors vi and v2 is obtained by multiplying each vector by a scalar, such as a1vi + a2v2. The resulting vector is a combination of the individual vectors scaled by the respective scalars.

d. The augmented matrix [a a2 a3 b] represents a linear system of equations. The solution set of this system is the same as the solution set of the equation xa1 + x2a2 + x3a3 = b. The augmented matrix notation is a convenient way to represent a system of equations.

e. The set Span {u, v} represents all possible linear combinations of vectors u and v. Depending on the vectors, the span may be a line, a plane, or even higher-dimensional spaces. It does not always have to pass through the origin, so it is not always visualized as a plane through the origin.

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Answer:

this i think

Step-by-step explanation:

Answer:

16+5.6..to solve it yiu will have to put it like this...

16.0+5.6=21.6.

21.6+0.681=22.281.

On simplifying we get the answer as 22.281

According to the BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction. Solving any expression is considered correct only if the BODMAS rule or the PEMDAS rule is followed to solve it.

Given here, the expression is 16 + 5.6 + 0.681​ =22.281

Hence, on simplifying we get the answer as 22.281

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Answer:

the answer is a

Step-by-step explanation:

because3 im smart unlike you

Answer:

8. 14 for the third question.

9. 18 for the forth question.

Step-by-step explanation:

the third and forth orange equations.

In an experiment where a person eating at a cafeteria choose 4 out of the 19 vegetables on offer, the number of elements in the sample space is 3876.

A sample space of an experiment is the set of all possible outcomes of a random experiment. So the number of elements in a sample space is the total number of possible outcomes of  the experiment.

Here the experiment is choosing 4 vegetables from a set of 19 vegetables offered. The total number of ways to choose 4 out of 19 distinct vegetables = 19C4

= 19! / (4! × (19-4)!)

= 3876

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To yield $26,000 in the future, compounded semiannually at an interest rate of 6%, a lump sum investment needs to be made today. The correct amount to invest can be calculated using the present value formula.

The present value formula can be used to calculate the amount that should be invested today to achieve a specific future value. The formula is given by:

PV = FV / (1 + r/n)^(n*t)

In this case, the future value (FV) is $26,000, the interest rate (r) is 6%, and the compounding is semiannually (n = 2). We need to solve for the present value (PV).

Using the formula and substituting the given values:

PV = 26,000 / \((1 + 0.06/2)^(2*1)\)

PV = 26,000 / \((1.03)^2\)

PV = 26,000 / 1.0609

PV ≈ $24,490.92

Therefore, the correct lump sum to invest today, at 6% compounded semiannually, to yield $26,000 in the future is approximately $24,490.92.

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The probability that exactly two of the three people selected also travel by train is 4/9

The probability of an event occurring is specified by the ratio of the number of  required outcomes to the number of possible outcomes.

The number of people that travelled from London to Manchester for the conference = 30

Number of people that traveled by train = 15

Number of people that travelled by plane = 9

Number of people that did not travel by travel by either train or plane = 12

Number of people chosen from those that traveled by plane = 3

The probability that two of those selected also traveled by train can be found as follows;

The number of people that traveled by either train of plane = 30 - 12 = 18

The number of people that traveled by plane and train = 15 + 9 - 18 = 6

The binomial probability distribution formula that can be used to find the probability of an event, p, occurring exactly r times is as follows;

P(p) = \(_nC_r\cdot p^r\cdot q^{n-r}\)

Where;

n = Number of people chosen = 3

r = Number of people chosen that also traveled by train = 2

p = Probability that a person chosen also traveled by train = 6/9 = 2/3

q = Probability that a person chosen did not travel by train = 3/9 = 1/3

Therefore;

\(P = _3C_2\times \left(\dfrac{2}{3}\right) ^2\times \left(\dfrac{1}{3} \right)^{3-2} = \dfrac{4}{9}\)

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Answer:

Step-by-step explanation:

To write a fraction as a decimal, you need to divide the numerator by the denominator.

Answer:

Step-by-step explanation:

4x-c=k  

solve for x

use the reverse order for the usual order of operations, to solve for x

first use addition

4x = k+c

then use division

x = (k+c) / 4

so answer B) looks good

Answer:

tan B = 8/15

Step-by-step explanation:

Trig functions are just ratios (like a fraction) in a right triangle, the longest side is the hypotenuse. The other two sides are the legs and they will be either right next to the angle, called ADJACENT side. Adjacent means "next to".

The opposite side is across the triangle from the angle in question.

TANGENT is the ratio that puts together the OPPOSITE side and the ADJACENT side.

tan B = OPP/ADJ

tan B = 8/15

If you're supposed to give a decimal approximation then divide 8÷15, tanB=.5333

Answer:

Step-by-step explanation:

Total members = 14

Each member:

Peaches = 3

Pint of cream = 1

Cost

Peaches = x cent

Pint of cream = 46 cent

46 cent = $0.46

Cost per member = 3(x cent) + 0.46

= 3x cent + 0.46

Total cost for all members = 14(3x cent + 0.46)

= 42x cent + 6.44

Answer:

5

Step-by-step explanation:

Area of bedroom = 13 1/3 square yards

Area of bed = 2 2/3 square yards

Unit Rate = Area of bedroom / Area of bed

Unit Rate = (40 / 3 ÷ 8/3)

Unit Rate = 5

Let t be the number of minutes talked. The cost of the first plan can be represented by:C1 = 0.22t

The cost of the second plan can be represented by:C2 = 0.11t + 34.95.To find the number of talk minutes that would produce the same cost for both plans, you need to set the two equations equal to each other and solve for t.0.22t = 0.11t + 34.950.11t = 34.95t = 318.18

Therefore, the two plans will have the same cost if you talk for 318.18 minutes.

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Answer:

x = 10

Step-by-step explanation:

Given the slope, m = -½, and the point, (-12, 9):

We must establish the linear equation first, so that we could determine the possible value of the x-coordinate paired with the y-coordinate of -2.

Substitute the slope and the given point into the slope-intercept form, y = mx + b and solve for b:

y = mx + b

9 = -½(-12) + b

9 = 6 + b

9 - 6 = 6 - 6 + b

3 = b  

Therefore, the linear equation is y = -½x + 3. We can use this equation to solve for the possible value of the missing x-coordinate:

y = -½x + 3

-2 =  -½x + 3

-2 - 3 =  -½x + 3 - 3

-5 =  -½x

Multiply both sides by -2 to isolate x:

(-2) -5 = (-2) -½x

10 = x

Therefore, the value of x in the ordered pair, (x , -2) is 10.

The correct alternative hypothesis for the Wilcoxon rank sum test is: ha: one distribution is shifted in a location higher or lower than the other. Option C is the answer.

This means that the test is designed to determine if there is a significant difference between the medians of two independent groups, rather than testing for a difference in means.

The null hypothesis for the test is that there is no significant difference between the two groups, while the alternative hypothesis states that there is a significant difference.

The Wilcoxon rank sum test is a nonparametric test and is used when the assumptions of the t-test are not met, such as non-normality or unequal variances.

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The correct answer is c. 0.40.

We can use the formula for conditional probability to solve for P(A | B):

P(A | B) = P(A ∩ B) / P(B)

We can also use the formula for the complement of a set to solve for P(A ∩ B):

P((A ∪ B)c) = 1 - P(A ∪ B)

0.2 = 1 - P(A ∪ B)

P(A ∪ B) = 0.8

We can then use the formula for the union of two sets to solve for P(A ∩ B):

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

0.8 = 0.6 + 0.5 - P(A ∩ B)

P(A ∩ B) = 0.3

Now we can plug in the values for P(A ∩ B) and P(B) into the formula for conditional probability:

P(A | B) = 0.3 / 0.5

P(A | B) = 0.6

Therefore, the correct answer is c. 0.40.

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Answer: ≈ 1.4.

Step-by-step explanation: To find the hypotenuse of a triangle (the longest side of a triangle), you need to add the legs (the two sides of the triangle that are not the hypotenuse). You need to have ^2 when adding each leg.  For example, both legs are 1 so when you're adding them, the equation should look like this--> 1^2 + 1^2.  Then, once you find the answer to that, you need to find the square root of the answer.  The work is done below:

1^2 + 1^2 = 2.

√2 ≈ 1.41421356 or ≈ 1.4.

Therefore, your answer is ≈ 1.4.

Let me know if this is right! :)

The area of the regions are

The area of the regions is calculated by dividing the regions into simper form and adding or subtraction as the case may be

1. the region is divided into semicircle and trapezoid

= area of semicircle + area of trapezoid

= 1/2 πr² + 1/2(sum of parallel lines ) * height

= 0.5 * π * 6² + 0.5(12 + 6) * 8

= 56.55 + 72

= 128.55 cm²

2. the region is divided into rectangle and trapezoid

= area of rectangle - area of trapezoid

= length * width - 1/2(sum of parallel lines ) * height

= 25 * 17 - 0.5((25 - 5 - 3) + 11) * 8

= 425 - 0.5(34) * 8

= 425 - 136

= 289 cm²

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The quadratic function f(x)=2(x+1)^2-8 in standard for and intercept form is 2x^2+4x-6 and (x-1)(x+3).

Given:

f(x) = 2(x+1)^2 - 8

= 2(x^2+1+2x) - 8

= 2x^2 + 2 +4x - 8

= 2x^2+4x-6(standard form)

Intercept form:

= 2x^2+4x-6

= (x-1)(x+3)

x-1 = 0

x = 1

x+3 = 0

x = -3

(1,0) and(-3,0).

Therefore the quadratic function f(x)=2(x+1)^2-8 in standard for and intercept form is 2x^2+4x-6 and (x-1)(x+3).

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The simplified expression for \(f(A, B, C)\) is \(A + \overline{B} + \bar{C}\). This is the final simplified form of the expression

To simplify the expression \( f(A, B, C) = \overline{\bar{A}B} + \overline{B+(\bar{B}+C)} \), we can simplify each term separately and then combine them.

First, let's simplify the term \(\overline{\bar{A}B}\):

We have \(\overline{\bar{A}B} = \overline{\bar{A}} + \overline{B} = A + \overline{B}\).

Next, let's simplify the term \(\overline{B+(\bar{B}+C)}\):

Inside the parentheses, we have \(\bar{B}+C\). To simplify this, we can apply De Morgan's laws:

\(\bar{B}+C = \overline{\overline{\bar{B}+C}} = \overline{\bar{\bar{B}} \cdot \bar{C}} = \overline{B \cdot \bar{C}} = \bar{B} + C\).

Therefore, \(\overline{B+(\bar{B}+C)} = \overline{B + (\bar{B}+C)} = \overline{B + \bar{B} + C} = \overline{1 + C} = \overline{C} = \bar{C}\).

Now, let's combine the simplified terms:

\(f(A, B, C) = \overline{\bar{A}B} + \overline{B+(\bar{B}+C)} = (A + \overline{B}) + \bar{C} = A + \overline{B} + \bar{C}\)..

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Answer: A

Step-by-step explanation: To solve this problem, we can set up a system of equations to represent the information given in the problem. Let x represent the cost of a plate of spring rolls, y represent the cost of a plate of chicken tenders, and z represent the cost of a plate of pretzel dippers.

The first group spent $23 on 2 plates of chicken tenders and 1 plate of pretzel dippers, so the equation for this group is:

2y + z = $23

The second group spent $30.75 to buy 3 plates of spring rolls and 1 plate of chicken tenders, so the equation for this group is:

3x + y = $30.75

The third group spent $22.25 on one of each appetizer, so the equation for this group is:

x + y + z = $22.25

Now that we have three equations, we can use algebraic techniques to solve for the value of x, which represents the cost of a plate of spring rolls.

First, we can solve the second equation for y:

y = $30.75 - 3x

Substituting this expression for y into the first equation, we get:

2($30.75 - 3x) + z = $23

Solving for x, we find that x = $7.75.

Therefore, the cost of a plate of spring rolls is $7.75, so the answer is A.

Answer:x=-7+1/2

Step-by-step explanation:You move all terms to the left: x-15/2-(2x)=0

then add all the numbers together, and all the variables:-1x-15/2=0

You multiply all the terms by the denominator:-1x*2-15=0

Multiply elements:-2x-15=0

You move all terms containing x to the left, all other terms to the right-2x=15

x=15/-2

x=-7+1/2

Answer:

Hypotenuse= 180.7 cm

Step-by-step explanation:

Using Pythagoras' theorem:

a^2+b^2=c^2                     (let c= Hypotenuse "H")

(136)^2 + (119)^2 =  H^2

18496+14161 =H^2

H^2= 32657

Taking square root on both sides

\(\sqrt{H}\)= \(\sqrt{32657}\)

H=180.7

Answer:

y = 22

Step-by-step explanation:

we want to move the -8 to the other side, so 14+8 = 22

y = 22

check: -8 + 22 = 14

Answer:

\( \underline{ \boxed{y = 22}}\)

Step-by-step explanation:

\(if \to : -8+y=14 \: ..... \\ \: we \: need \: to \: solve \: for \: (y)\\ -8+y=14 \: ..... \\ \: (add \: ( + 8) \: to \: the \: right \: and \: left) \to : \\ - 8 + 8 + y = 14 + 8 \\ 0 + y = 22 \\ \boxed{y = 22}\)

Answer:

Step-by-step explanation:

(2n - 1) and (2n + 1) So, 2n -1 + 2n + 1 = 72. 4n = 72.

n = 18. So, The odd numbers are.

(2n - 1) = ((2 x 18) - 1) = 35. and,

(2n + 1) = ((2 x 18) + 1) = 37.

Step-by-step explanation:

Measure of angle:

∠A  = 36.86°

∠B = 90°

∠C = 53.13 °

Measure of side ,

AB =  28

BC = 21

CA = 35

Given triangle ABC.

Right angled at B.

Now, using trigonometric ratios to find angle A , B , C .

Right angled at B : ∠B = 90°

Angle A,

SinA = 21/35

∠A = 36.86

Angle C,

SinC = 28/35

∠C = 53.13

Now measures of side.

To find the length of side use sine rule .

Sine rule:

a/sinA = b/sinB = c /sinC

a = opposite side of angle A .

b = opposite site of angle B .

c = opposite side of angle C.

AB = 28

BC = 21

CA = 35

Hence the sides and angles of the triangles are measured .

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Using the binomial distribution, it is found that she should expect it to land on 3 9 times.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

In this problem:

Then, the expected value is given by:

E(X) = np = 36 x 0.25 = 9.

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Answer:

1.234 × 101

Step-by-step explanation: