Does anyone know the answer? If so how did you get the answer.

Answer:

each!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

The given statement about inequality is true.

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

The statement is true ''Pick a point on one side of the solid or dashed line and enter its coordinates into the original inequality to determine which side of a linear inequality to colour in for its graph. On that side of the plane, you should shade if the coordinates satisfy the inequality''.

The statement defines how to write an inequality the meaning of inequality is that one part of the inequality will be shaded by some colour indicating that the region is falling under the area of inequality.

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The variable t becomes the subject of the equation c=t³ - 8v by adding 8v to both sides and taking the cube root, giving t = ∛(c + 8v).

We need to make t the subject of the equation c=t³ - 8v. To do this, we first add 8v to both sides of the equation to isolate t³ on one side, giving us t³ = c + 8v. We then need to take the cube root of both sides to solve for t. Hence, t = ∛(c + 8v). Now, t is the subject of the equation.

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The insect measurement that was the most frequent is given as follows:

1 and 1/4 inches.

A dot plot is a simple graphical display that uses dots to represent data values. It is also sometimes called a dot chart or a scatterplot. In a dot plot, each data point is represented by a dot along a number line or axis, where the position of the dot corresponds to the value of the data point.

Hence, a dot plot shows the number of times that each observation appeared in the data-set.

The observation with the most dots is the observation 2/8 of the way between 1 and 2, hence the most frequent observation is given by the following mixed number:

1 and 2/8 = 1 and 1/4 inches.

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The operation that has been performed on v to result in the vector that is shown is multiplication by -1.

The vector that is shown is (-2, -1). This can be obtained from vector v = (2, 1) by multiplying it by -1. Multiplying a vector by a negative number reverses its direction.

Multiplication of a vector by a number is performed component-wise. This means that each component of the vector is multiplied by the number. In the case of (-1) * (2, 1), each component is multiplied by -1. This results in the vector (-2, -1).

Here is the mathematical equation:

(-1) * (2, 1) = (-2, -1)

Therefore, the operation that has been performed on v to result in the vector that is shown is multiplication by -1.

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The actual bearing of the flight would be N 16.38° W.

North: 420 mph * cos(15) = 406.6 mph

West: 420 mph * sin(15) = 108.8 mph

The wind's velocity vector, when decomposed into north and west components, would be:

North: -15 mph * cos(25) = -13.6 mph (negative because it's in the south direction)

West: 15 mph * sin(25) = 6.3 mph

Now, add the corresponding components of the airplane and wind vectors:

North: 406.6 mph - 13.6 mph = 393 mph

West: 108.8 mph + 6.3 mph = 115.1 mph

Finally, to get the actual bearing, we can calculate the inverse tangent of the west component over the north component, but in this case, we need to consider the fact that we are dealing with bearings, which are usually measured from the North, moving in a clockwise direction.

Let's calculate the angle:

θ = atan(West/North) = atan(115.1/393) = 16.38°

So, the actual bearing of the flight would be N 16.38° W.

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Answer:

y=-2x+13

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(5-3)/(4-5)

m=2/-1

m=-2

y-y1=m(x-x1)

y-3=-2(x-5)

y=-2x+10+3

y=-2x+13

Answer:

\(\frac{3}{2}\)

Step-by-step explanation:

\(\frac{8+4}{8}\)

\(\frac{12}{8}\)

\(\frac{3}{2}\)

Answer:

1/2 batch

Step-by-step explanation:

1/2=1

1/4=1/2

Answer:

1/2 batches

Step-by-step explanation:

Please see the attached image.

I hope this helps!

Answer:

no . no because they are in different place period

Answer:

1) \(\sqrt{53}(\cos286^\circ+i\sin286^\circ)\)

2) \(\displaystyle 5,-\frac{5}{2}+\frac{5\sqrt{3}}{2}i,-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

Step-by-step explanation:

Problem 1

\(z=2-7i\\\\r=\sqrt{a^2+b^2}=\sqrt{2^2+(-7)^2}=\sqrt{4+49}=\sqrt{53}\\\\\theta=\tan^{-1}(\frac{y}{x})=\tan^{-1}(\frac{-7}{2})\approx-74^\circ=360^\circ-74^\circ=286^\circ\\\\z=r\,(\cos\theta+i\sin\theta)=\sqrt{53}(\cos286^\circ+i\sin 286^\circ)\)

Problem 2

\(\displaystyle z^\frac{1}{n}=r^\frac{1}{n}\biggr[\text{cis}\biggr(\frac{\theta+2k\pi}{n}\biggr)\biggr]\,\,\,\,\,\,\,k=0,1,2,3,\,...\,,n-1\\\\z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(2)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{4\pi}{3}\biggr)=5\biggr(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(1)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{2\pi}{3}\biggr)=5\biggr(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}+\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(0)\pi}{3}\biggr)\biggr]=5\,\text{cis}(0)=5(1+0i)=5\)

Note that \(\text{cis}\,\theta=\cos\theta+i\sin\theta\) and \(125=125(\cos0^\circ+i\sin0^\circ)\)

Step-by-step explanation:

=23.6

\(v = \pi {r}^{2} \frac{h}{3} = \pi {1.5}^{2} \frac{10}{3} = 23.56 \: {yd}^{3} \)

When we move the triangle RPQ horizontally or vertically or side ways, the triangle will not coincide with the triangle KLM.

Similarly, if we move the triangle KLM horizontally or vertically or side ways, the triangle will not coincide with the triangle RPQ.

Hence, both the triangles are not vector translations of each other.

3+11×8²

=3+11×64

=3+704

=707

Answer:

707

Concepts:

Order of Operations: PEMDAS

1. Parenthesis

2. Exponents

3. Multiplication

4. Division

5. Addition

6. Subtraction

Step-by-step Explanation:

Follow the Order of Operations

Step 1: Solve exponents

3 + 11 × 8^2

8^2 = 64

3 + 11 × 64

Step 2: Solve Multiplication

3 + 11 × 64

11 × 64 = 704

3 + 704

Step 3: Add the Terms

3 + 704 = 707

Hence,

3 + 11 × 8^2 = 707

is △ABC equilateral?  well, we dunno, however let's check for all sides' length.

\(~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{-6}~,~\stackrel{y_2}{-2}) ~\hfill AB=\sqrt{(~~ -6- (-3)~~)^2 + (~~ -2- 2~~)^2} \\\\\\ ~\hfill AB=\sqrt{( -3)^2 + ( -4)^2} \implies AB=\sqrt{ 25 }\implies \boxed{AB=5}\)

\(B(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad C(\stackrel{x_2}{0}~,~\stackrel{y_2}{-2}) ~\hfill BC=\sqrt{(~~ 0- (-6)~~)^2 + (~~ -2- (-2)~~)^2} \\\\\\ ~\hfill BC=\sqrt{( 6)^2 + ( 0)^2} \implies BC=\sqrt{ 36 }\implies \boxed{BC=6} \\\\\\ C(\stackrel{x_1}{0}~,~\stackrel{y_1}{-2})\qquad A(\stackrel{x_2}{-3}~,~\stackrel{y_2}{2}) ~\hfill CA=\sqrt{(~~ -3- 0~~)^2 + (~~ 2- (-2)~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -3)^2 + (4)^2} \implies CA=\sqrt{ 25 }\implies \boxed{CA=5}\)

well, not quite.

The probability generating function of a discrete nonnegative integer valued random variable X is defined by ø(s) = E[s] = Σp;si j=0, where pj is the probability mass function of X. P{XY} = P{X=i,Y=j} = P{X=i}P{Y=j} = pi pj sij,Therefore, ø(s) = Σ pi pj sij = P{XY}

In this problem, we are also given a geometric random variable Y with parameter p 1 s, where 0 < s < 1. Y is independent of X. To show that ø(s) = P{XY}, we must show that the two expressions are equal.

First, we note that the probability of X and Y being equal to i and j, respectively, is given by P{X=i,Y=j} = P{X=i}P{Y=j} = pi pj sij. This is because the probability of X being equal to i is pi, and the probability of Y being equal to j is pj (where p is the parameter of the geometric distribution). Since sij is the product of i and j, the probability of both X and Y being equal to i and j, respectively, is pi pj sij.

We can now substitute this expression into the probability generating function for X. We have that ø(s)

= E[s] = Σp;si j=0

= Σ pi pj sij

= P{XY}

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If Gavin contributes towards a Pension fund (7,5% of his Basic Salary), then his net salary will be reduced by the amount he contributed towards pension fund i.e. R652.5.

1.1 Name of employee is Gavin Pillay. 1.2 UIF stands for Unemployment Insurance Fund. UIF is a benefit to provide short-term relief to workers who lose their jobs, or can't work due to illness, maternity or adoption leave. 1.3 The UIF paid by Gavin is calculated correctly.

Firstly, we need to calculate Gross Salary of Gavin, which is given as: Basic Salary + Overtime + M = R8700 + R1200 + R3201 = R13101Then, calculate total deductions from gross salary.

Total Deductions = PAYE + UIF = R1200 + 87 = R1287Hence, Gavin's net salary = Gross salary - Total Deductions = R13101 - R1287 = R11814Therefore, UIF paid by Gavin is calculated correctly as R87.1.4 This payslip is for the month of May i.e.

31/05/2023.1.5 Basic salary of Gavin = R8700. Deduct 7.5% of his basic salary to calculate his pension fund contribution. Pension Fund Contribution = 7.5/100 x R8700 = R652.5.1.6

Total deductions of Gavin includes PAYE, UIF and pension fund contribution.

Therefore, Total Deductions = PAYE + UIF + Pension Fund Contribution = R1200 + R87 + R652.5 = R1939.5.1.7

Gavin's age can not be determined as his date of birth is not provided.1.8 Address of Gavin's workplace is 21 Halsted Road, Pietermaritzburg?

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Answer:

1

\(p(b) =  \frac{1}{6}\)

2

\(p(k) =  \frac{1}{3}\)

3

\(P(a) = \frac{1}{3}\)

Step-by-step explanation:

Generally when two fair 6-sided dice is rolled the doubles are

(1 1) , ( 2 2) , (3 3) , (4 4) , ( 5 5 ), (6 6)

The total outcome of doubles is N = 6

The total outcome of the rolling the two fair 6-sided dice is

n = 36

Generally the probability that doubles (i.e., having an equal number on the two dice) were rolled is mathematically evaluated as

\(p(b) = \frac{N}{n}\)

\(p(b) = \frac{6}{36}\)

\(p(b) = \frac{1}{6}\)

Generally when two fair 6-sided dice is rolled the outcome whose sum is 4 or less is

(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1)

Looking at this outcome we see that there are two doubles present

So

The conditional probability that doubles were rolled is mathematically represented as

\(p(k) = \frac{2}{6}\)

\(p(k) = \frac{1}{3}\)

Generally when two fair 6-sided dice is rolled the number of outcomes that would land on different numbers is L = 30

And the number of outcomes that at least one die is a 1 is W = 10

So

The conditional probability that at least one die is a 1 is mathematically represented as

\(P(a) = \frac{W}{L}\)

=> \(P(a) = \frac{10}{30}\)

=> \(P(a) = \frac{1}{3}\)

The measure of the bearings from B are 310 degrees, 245 degrees and 137 degrees

To determine the bearings from B, we make use of the following guidelines

Using the above as a guide, we have the following:

Hence, the values of the bearings are 310 degrees, 245 degrees and 137 degrees

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Answer:

350

Step-by-step explanation:

Answer:

70 days

Step-by-step explanation:

Given that,

→ fresh fruit to last 10 days

→ fresh vegetables for 7 days

→ dried insects for 5 days

Then in how many days will they order all three items on the same day?

Then the LCM of 10, 7 & 5 is,

→ 2 × 5 × 7

→ 10 × 7 = 70

Hence, the answer is 70 days.

Answer:

Almost equals 28°

Step-by-step explanation:

cos(x)= 12/18

x= cos^-1 (12/18)

So it equals 48.1896°

Answer:

142 ft square

Step-by-step explanation:

Face 1: 3(10)=30 ft square

Face 2: 4(10)=40 ft square

Front: 2(6)=12/2=6 ft square

Back: Same as front

bottom: 6(10)=60 ft square

Total: 30+40+6(2)+60=142 ft square

() means multiply in case don't know

Answer:

The ans would be 291 (however we can round this off to 290 as no can partially vote as 0.1)

Step-by-step explanation:

We can easily find the loser's vote by-

70% of 969= 678.9

now, all we need to do is find the winners vote

we know that the total no. of votes= 969 & we know the no. of votes loser got

so, subtracting the losers vote from 969 would give us the remaining no. of votes (the winner's votes)....so,

969-678.9=290.1

we can round this off to 290

The third term (a3) of the sequence is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183. These values are obtained by applying the given formula recursively and substituting the previous terms accordingly. The calculations follow a specific pattern and are derived using the provided formula.

The sequence is defined by the following formula:

a1 = 1, a2 = 3,

and

an = (-1)nan - 1 + an - 2 for n ≥ 3.

To find the third term (a3), we substitute n = 3 into the formula:

a3 = (-1)(3)(a3 - 1) + a3 - 2.

Next, we simplify the equation:

a3 = -3(a2) + a1.

Since we know a1 = 1 and a2 = 3, we substitute these values into the equation:

a3 = -3(3) + 1.

Simplifying further:

a3 = -9 + 1.

Therefore, the third term (a3) is equal to -8.

To find the fourth term (a4), we substitute n = 4 into the formula:

a4 = (-1)(4)(a4 - 1) + a4 - 2.

Simplifying the equation:

a4 = -4(a3) + a2.

Since we know a2 = 3 and a3 = -8, we substitute these values into the equation:

a4 = -4(-8) + 3.

Simplifying further:

a4 = 32 + 3.

Therefore, the fourth term (a4) is equal to 35.

To find the fifth term (a5), we substitute n = 5 into the formula:

a5 = (-1)(5)(a5 - 1) + a5 - 2.

Simplifying the equation:

a5 = -5(a4) + a3.

Since we know a4 = 35 and a3 = -8, we substitute these values into the equation:

a5 = -5(35) + (-8).

Simplifying further:

a5 = -175 - 8.

Therefore, the fifth term (a5) is equal to -183.

In summary, the third term (a3) is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183.

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The two numbers whose sum is 7500 and whose product  is a maximum value are 3750 and 3750.

Let the two numbers be x and y.

Since their sum equals 7500,

x + y = 7500  (1)

Their product f(x,y) = xy  (2)

We desire to maximize the product.

From (1), x = 7500 - y

Substituting x into (2), we have

f(x,y) = xy

f(x,y) = (7500 - y)y

f(y) = 7500y - y²

To maximize the product, we find the value of y that maximizes f(y), we differentiate f(y) and equate it to zero.

So, df(y)/dy = d(7500y - y²)/dy

f'(y)/dy = d(7500y)/dy - dy²/dy

f'(y)/dy = 7500 - 2y

Equating it to zero, we have

7500 - 2y = 0

7500 = 2y

y = 7500/2

y = 3750

To determine if this gives a maximum for f(y), we differentiate f'(y) with respect to y.

So, f"(y) = d(7500 - 2y)dy

f"(y) = 0 - 2

f"(y) = -2 < 0.

So, y = 3750 gives a maximum for f(y) = f(x, y)

Since x = 7500 - y

Substituing y = 3750 into the equation, we have

x = 7500 - 3750

x = 3750

So, the two numbers whose sum is 7500 and whose product is a maximum product are 3750 and 3750.

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Answer:

S₁₆ = 344

Step-by-step explanation:

the sum to n terms of an arithmetic sequence is

\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = - 1 and d = a₂ - a₁ = 2 - (- 1) = 2 + 1 = 3 , then

S₁₆ = \(\frac{16}{2}\) [ (2 × - 1) + (15 × 3) ]

     = 8 (- 2 + 45)

     = 8 × 43

     = 344

Answer:

30

Step-by-step explanation:

The equation will be:

x - (10% of x) = 27

x - 0.1x = 30

0.9x = 30

Divide by 0.9

x = 30

The number is 30

Second question:

Length = 2x - 3

Width = x

Perimeter = 72

Perimeter = 2(l + w)

= 2(2x - 3 + x) = 72

4x - 6 + 2x = 72

6x = 72 + 6

6x = 78

w = 78/6 = 13

The width is 13 meters

Answer:

19 - 42x

Step-by-step explanation:

To differentiate this, we must use the product rule
f'(x) = (7x+3)'(4-3x) + (4-3x)'(7x+3)
= (7)(4-3x) + (-3)(7x+3)
= 28 - 21x - 21x - 9
= 19 - 42x

Answer:

According to this diagram, the tan 62 degrees, is the ratio of the opposite side and the adjacent side of the triangle which is equal to 1.875 units.

What is the right angle triangle property?

In a right-angle triangle ratio of the opposite side to the adjacent side is equal to the tangent angle between the adjacent side and the hypotenuse side.

Here, (b) is the opposite side, (a) is the adjacent side, and is the angle made between the adjacent side and the hypotenuse side.

The sides of the triangle are 8, 15, and 17 units long and the measure of the angles of the right angle triangle is 62, 90, and 28 degrees.

Re-draw, the  Here in the given triangle, the base is the side which is 15 units long. Re-draw the triangle as shown below.

In the attached triangle below, the opposite side of the triangle is 15 units and the adjacent side of the triangle is 8 units long.

The angle between the opposite side and the adjacent side is 62 degrees. Thus using the right angle triangle property as,

Thus, according to this diagram, the tan 62 degrees, is the ratio of the opposite side and the adjacent side of the triangle which is equal to 1.875 units.

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