A company's sales decreased by 8% this year, to $9015. What were their sales last year? (Round your answer to the nearest penny.)

My answer was 9,736.2, but the correct answer was 9798.91. Could someone explain how did they get to 9798.91?

Answer:

(a) r = 57.628

    θ = 51.34°

(b) r = 0.711

    θ = 38.65°

Step-by-step explanation:

(a) Let's assume

 z = (5 + 4)(4 +5j)

    = 9 x (4+5j)

    = 36 + 45j

magnitude of z can be given by

[tex]\left | z \right |\ =\ r\ =\sqrt{36^2+45^2}[/tex]

               => r =57.628

angle of z can be given by,

     [tex]tan\theta\ =\ \dfrac{45}{36}[/tex]

[tex]=>\ tan\theta=\ \dfrac{5}{4}[/tex]

[tex]=>\ \theta\ =\ tan^{-1}\dfrac{5}{4}[/tex]

              θ = 51.34°        

(b) Let's assume

[tex]z =\ \dfrac{(5 +4j)}{5+4}[/tex]

    [tex]=\ \dfrac{(5+4j)}{9}[/tex]

    [tex]=\ \dfrac{5}{9}+\dfrac{4i}{9}[/tex]

magnitude of z can be given by

[tex]\left | z \right |=\ r=\sqrt{(\dfrac{5}{9})^2+(\dfrac{4}{9})^2}[/tex]

             [tex]=> r =\dfrac{\sqrt{41}}{9}[/tex]

              => r = 0.711

angle of z can be given by,

[tex]\ tan\theta\ =\ \dfrac{\dfrac{4}{9}}{\dfrac{5}{9}}[/tex]

[tex]=>\ tan\theta=\ \dfrac{4}{5}[/tex]

[tex]=>\ \theta\ =\ tan^{-1}\dfrac{4}{5}[/tex]

                => θ = 38.65°        

Answer:

An irrational number can never be represented precisely in decimal form.

Step-by-step explanation:

A number can be precisely represented in decimal form if you can give a rule for the construction of its decimal part,

for example:

2.246973973973973... (an infinite tail of 973's repeated over and over)

7.35 (a tail of zeroes)

If this the case, then the number is a RATIONAL NUMBER, i.e, the QUOTIENT OF TWO INTEGERS.

Let's show this for the first example and then a way to show the general situation will arise naturally.

Suppose N = 2.246973973973...

You can always multiply by a suitable power of 10 until you get a number with only the repeated chain in the tail

for example:

1) [tex]N.10^3=2246.973973973...[/tex]

but also

2) [tex]N.10^6=2246973.973973...[/tex]

Subtracting 1) from 2) we get

[tex]N.10^6-N.10^3=2246973.973973973... - 2246.973973973...[/tex]

Now, the infinite tail disappears

[tex]N.10^6-N.10^3=2246973 - 2246=226747[/tex]

But  

[tex]N.10^6-N.10^3=N.(10^6-10^3)=N.(1000000-1000)=999000.N[/tex]

We have then

999000.N=226747

and

[tex]N=\frac{226747}{999000}[/tex]

We do not need to simplify this fraction, because we only wanted to show that N is a quotient of two integers.

We arrive then to the following conclusion:

If an irrational number could be represented precisely in decimal form, then it would have to be the quotient  of two integers, which is a contradiction.

So, an irrational number can never be represented precisely in decimal form.

Answer:

1536 tiles

Step-by-step explanation:

Given,

The length of kitchen = 10 ft,

Width of the kitchen = 8 ft,

∵ The shape of floor of kitchen must be rectangular,

Thus, the area of the kitchen = 10 × 8 = 80 square ft = 11520 in²

( Since, 1 square feet = 144 square inches )

Now, the length of a tile = 2.5 in and its width = 3 in,

So, the area of each tile = 2.5 × 3 = 7.5 in²,

Hence, the number of tiles needed = [tex]\frac{\text{Area of kitchen}}{\text{Area of each tile}}[/tex]

[tex]=\frac{11520}{7.5}[/tex]

= 1536

Approximately 1536 tiles are needed to cover a kitchen floor that is 10 feet by 8 feet using tiles that are 2.5 inches by 3 inches.

To determine how many tiles are needed to cover a kitchen floor that is 10 feet long and 8 feet wide with tiles that are 2.5 inches by 3 inches, we first need to convert the dimensions of the kitchen to inches because the tile dimensions are given in inches. There are 12 inches in a foot, so the kitchen is 120 inches long (10 feet × 12 inches/foot) and 96 inches wide (8 feet  × 12 inches/foot).

We now calculate the area of the kitchen floor: Area = Length ×  Width = 120 inches × 96 inches = 11520 square inches.

Next, we calculate the area of one tile: Tile Area = Length × Width = 2.5 inches × 3 inches = 7.5 square inches.

Now, to find the number of tiles needed, we divide the total area of the kitchen floor by the area of one tile: Number of Tiles = Kitchen Area / Tile Area = 11520 square inches / 7.5 square inches ≈ 1536 tiles.

Therefore, approximately 1536 tiles are needed for the kitchen.

For part (a) and (b) suposse [tex]A\subset B[/tex].

To prove part (a) observe that we already have that [tex]B\subset A\cup B[/tex]. So we will prove that [tex]A\cup B \subset B[/tex]. Let [tex]x\in A\cup B[/tex], then [tex]x\in A[/tex] or [tex]x\in B[/tex]. If  [tex]x\in B[/tex] we finish the proof, and if [tex]x\in A[/tex] implies  [tex]x\in B[/tex] because we assume [tex]A\subset B[/tex], and the proof is complete.

For part (b) we always have [tex]A\cap B\subset A[/tex]. We finish the proof showing [tex]A\subset A\cap B[/tex]. Let [tex]x\in A[/tex], then [tex]x\in B[/tex] by the asumption that [tex]A\subset B[/tex]. So, we have both [tex]x\in A[/tex] and  [tex]x\in B[/tex], that implies [tex]x\in A\cap B[/tex]. Therfore [tex]A\subset A\cap B[/tex], which completes the proof.

Answer:

229.17 kilo-calories

Step-by-step explanation:

We have been given that 240 ml of orange juice (1 cup) provides about 110 kcal.

First of all, we will divide 500 by 240 to find amount of cups in 500 ml.

[tex]\text{Number of cups}=\frac{500}{240}[/tex]

[tex]\text{Number of cups}=2.08333[/tex]

Now, we will multiply 2.08333 by 110 to find amount of k-cal in orange juice.

[tex]\text{Number of k-cal}=2.08333\times 110\text{ k-cal}[/tex]

[tex]\text{Number of k-cal}=229.16666\text{ k-cal}[/tex]

[tex]\text{Number of k-cal}\approx 229.17\text{ k-cal}[/tex]

Therefore, there are approximately 229.17 kilo-calories in 500 ml of orange juice.

Final answer:

To find the number of kcalories in 500 ml of orange juice, set up a proportion using the known ratio of 240 ml to 110 kcal. Cross multiply and solve for the unknown value to find that there are approximately 229 kcalories in 500 ml of orange juice.

Explanation:

To calculate the number of kcalories in 500 ml of orange juice, we can use the ratio method. First, we know that 240 ml (1 cup) of orange juice provides 110 kcal. We can set up a proportion to find the number of kcalories in 500 ml of orange juice.

240 ml / 110 kcal = 500 ml / x kcal

Cross multiplying, we get 240x = 55000. Dividing both sides by 240, we find that x is approximately equal to 229.17. Therefore, there are about 229 kcalories in 500 ml of orange juice.

Answer with Step-by-step explanation:

We are given that sum of three vectors in [tex]R^3[/tex] is zero.

We have to tell and explain that if sum of three vectors in [tex]R^3[/tex] is zero then they must lie in the same plane or not.

We know that if three or more vectors lie in the same then they are coplanar.

If three vectors are co-planar then their scalar product is zero.

According to given condition

Let (x,0,0), (-x,0,0) and (0,0,0)

[tex]\vec{u}=x\hat{i}[/tex]

[tex]\vec{v}=-x\hat{i}[/tex]

[tex]\vec{w}=0[/tex]

Sum of three vectors=[tex](x-x+0)\hat{i}+(0+0+)\hat{j}+(0+0+0)\hat{k}=0[/tex]

[tex]u\cdot (v\times w)=\begin{vmatrix}x_1&y_1&z_1\\x_2&y_2&z_2\\x_3&y_3&z_3\end{vmatrix}[/tex]

[tex]u\cdot (v\times w)=\begin{vmatrix}x&0&0\\-x&0&0\\0&0&0\end{vmatrix}[/tex]

When all elements of one row or column are zero of square matrix A then det(A)=0

[tex]u\cdot (v\times w)=0[/tex]

Therefore, vectors u,v and w are co-planar.

Hence, if the sum of three vectors in [tex]R^3[/tex] is zero then they must lie in the same plane.

If the sum of three vectors in three-dimensional space is zero, they typically lie in the same plane, forming a triangle with their magnitudes and directions. They must also be linearly dependent since their linear combination can produce the zero vector.

If the sum of three vectors is zero in R^3 (three-dimensional space), it is a common situation for these vectors to lie in the same plane. This condition implies that they can be represented as three sides of a triangle taken in sequence in terms of magnitude and direction. If we consider two vectors in sequence, such as AB and BC, the third vector must be the closing side CA, taken in the opposite direction, in order to satisfy the triangle law of vector addition. In this case, the sum of vectors AB + BC + CA equals zero.

Furthermore, vectors are homogeneous when added, which means that they must have the same nature and dimension. However, three vectors can still form a linearly dependent set in three-dimensional space even if they lie in the same plane. For instance, if we take vectors a, b, and c, and if a linear combination of these vectors yields the zero vector (i.e., if we can find scalar coefficients x, y, and z such that xa + yb + zc = 0), then these vectors are not linearly independent and must lie in the same plane.

Answer:

. . . False

Step-by-step explanation:

5 is not among the elements of the given set.

__

The symbol ∈ means "is an element of ...".

Answer:

a) The distance of the light's base from the bottom of the building is approximately: 5.2 ft

b) The length of the beam is approximately: 10.4 ft

Step-by-step explanation:

First, we have to recognize that we may draw a right triangle to picture our problem. Then, in order to find out the distance of the light's base from the bottom of the building, we need to use the tangent trigonometric function:

tan(angle) = opposite side / adjacent side

We know the angle and the opposite side and we want to find the adjacent side:

adjacent side = opposite side / tan(angle) = 9 ft / tan(60°) = 9 ft / = 9 ft / 1.73 = 5.2 ft

In order to find the length of the light  beam, we use Pythagoras Theorem:

leg1²+leg2² = hyp²

Since the length of the beam corresponds to the hypotenuse and since we already know the length of the two legs, it is just a matter of substituting the values:

hyp = square_root(leg1²+leg2²) = square_root(9² + 5.2²) ft = square_root(108.4) ft = 10.4 ft

Answer:  -8

Step-by-step explanation:

The slope of a line passing through two points (a,b) and (c,d) is given by:-

[tex]m=\dfrac{d-b}{c-a}[/tex]

Given : A line passes through the points ( 3 , -14 ) and ( x , 6 ) with a slope of -4, then we have

[tex]-4=\dfrac{6-(-14)}{x-3}\\\\\Rightarrow\ (x-3)(-4)=6+14\\\\\Rightarrow\ -4(x-3)=20\\\\\Rightarrow\ (x-3)=\dfrac{20}{-4}=-5\\\\\Rightarrow\ x-3=-5\\\\\Rightarrow\ x=-5-3=-8[/tex]

Hence, the value of x= -8

Answer:

the dimension called by the specification is larger

Step-by-step explanation:

Data provided in the question:

micrometer reading = 7.5 in

Dimension called by the specifications = 7.59 in

Now,

Subtracting the Micrometer reading from the dimension called by specification , we get

 7.59

- 7.5

--------

0.09

since, the result is positive thus,

the dimension called by the specification is larger

The specification of 7.59 inches is larger than the micrometer reading of 7.57 inches. Therefore, the part does not meet the required specification.

To determine whether the micrometer reading or the specification is larger, we need to compare the two values. The micrometer reading is 7.57 inches, and the specification calls for a dimension of 7.59 inches.

When comparing these two measurements:

Clearly, 7.59 inches is larger than 7.57 inches.

This comparison shows that the specification is larger than the micrometer reading.

Answer:

Mean = 86.067

Median = 85

Step-by-step explanation:

The given data set is

{ 93, 94, 95, 89, 85, 82, 87, 85, 84, 80, 78, 78, 84, 87, 90 }

Number of observations = 15

Formula for mean:

[tex]Mean=\frac{\sum x}{n}[/tex]

where, n is number of observations.

Using the above formula, we get

[tex]Mean=\frac{93+94+95+89+85+82+87+85+84+80+78+78+84+87+90}{15}[/tex]

[tex]Mean=\frac{1291}{15}[/tex]

[tex]Mean\approx 86.067[/tex]

Therefore the mean of the given data set is 86.067.

Arrange the given data set in ascending order.

{ 78, 78, 80, 82, 84, 84, 85, 85, 87, 87, 89, 90, 93, 94, 95 }

Number of observation is 15 which is an odd term. So

[tex]Median=(\frac{n+1}{2})\text{th term}[/tex]

[tex]Median=(\frac{15+1}{2})\text{th term}[/tex]

[tex]Median=8\text{th term}[/tex]

[tex]Median=85[/tex]

Therefore the median of the data set is 85.

Answer:

Step-by-step explanation:

Given is a phrase

"I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times."

This implies instead of attempting so many things without depth one thing indepth training is very much good and feared by others.

This applies to knowledge and also the subject Mathematics

Instead of practising many sums without getting answers, learning one concept and trying to get the difficult problem will help go a long way in learning.

In depth learning helps to master other allied concepts also very easily and this helps extending to other topics

Answer: [tex]0.070<\sigma< 0.128[/tex]

Step-by-step explanation:

Confidence interval for population standard deviation :-

[tex]s\sqrt{\dfrac{n-1}{\chi^2_{\alpha/2, n-1}}}<\sigma<s\sqrt{\dfrac{n-1}{\chi^2_{1-\alpha/2, n-1}}}[/tex]

Given : Significance level : [tex]\alpha: 1-0.90=0.10[/tex]

Sample size : n= 17

Sample standard deviation: [tex]s= 0.09[/tex]

Then by using the chi-square distribution table, we have

[tex]\chi^2_{1-\alpha/2, n-1}}=\chi^2_{0.95, 16}=7.96[/tex]

[tex]\chi^2_{\alpha/2, n-1}}=\chi^2_{0.05, 16}=26.30[/tex]

Confidence interval for population standard deviation will be :-

[tex]( 0.09)\sqrt{\dfrac{16}{26.30}}<\sigma<( 0.09)\sqrt{\dfrac{16}{7.96}}\\\\0.070197981837<\sigma<0.12759861690\\\\\approx0.070<\sigma< 0.128[/tex]

Hence, 90% confidence interval of the standard deviation of the skating performance test.: [tex]0.070<\sigma< 0.128[/tex]

90% confidence interval of the standard deviation of the skating performance test is [tex]0.070 < \sigma < 0.127[/tex]

It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.

The formula for finding the confidence interval for population standard deviation as follow:

[tex]\rm s \sqrt{\dfrac{n-1}{\chi ^2_{\alpha /2,n-1}}} < \sigma < s \sqrt{\dfrac{n-1}{\chi ^2_{1-\alpha /2,n-1}}}[/tex]

Where [tex]\rm s[/tex] is the standard deviation.

[tex]\rm n[/tex] is the sample size.

[tex]\rm{\chi ^2_{\alpha /2,n-1[/tex]  and  [tex]\rm\chi ^2_{1-\alpha /2,n-1[/tex] are the constant based on the Chi-Square distribution table.

[tex]\rm\alpha[/tex] is the significance level.

[tex]\rm\sigma[/tex] is the confidence interval for population standard deviation.

Calculating the confidence interval for population standard deviation:

We know significance level = 1 - confidence level

[tex]\rm \alpha = 1 - 0.90 = 0.10[/tex]

[tex]\rm n = 17[/tex]

[tex]\rm s = 0.09[/tex]

By the chi-square distribution table, the values of constants are below:

[tex]\rm \chi ^2_{1-\alpha/2,n-1} = \chi ^2_{0.95,16} = 7.96\\\rm \chi ^2_{ \alpha /2,n-1} = \chi ^2_{0.05,16} = 26.30[/tex]

putting all values in the above formula we will get the confidence interval for population standard deviation:

[tex]\begin{aligned} \rm (0.09) \sqrt{\dfrac{17-1}{26.30}}} & < \sigma < (0.09) \sqrt{\dfrac{17-1}{7.96}}}\\\\\rm s \sqrt{\dfrac{16}{26.30}}} & < \sigma < s \sqrt{\dfrac{16}{7.96}}\\\\\rm 0.0701197 & < \sigma < 0.12759 \\\\\end{aligned}\\[/tex]

or [tex]\approx 0.070 < \sigma < 0.127[/tex]

Thus, 90% confidence interval of the standard deviation of the skating performance test is [tex]0.070 < \sigma < 0.127[/tex]

Learn more about the confidence interval for population standard deviation here:

https://brainly.com/question/6654139

Answer: [tex]d) 2.0*10^2[/tex]kilo gram

Step-by-step explanation:  

To know the greatest mass we have to convert all these measurements to the same unit, the gram. For that we have to state the next units:

[tex]mili = 10^-^3\\micro = 10^-^6\\pico = 10^-^1^2\\kilo= 10^3[/tex]

Now we can convert the measurements to the same unit:

[tex]b)5.0*10^1^2*10^-^1^2gram=5.0gram\\d)2.0*10^2*10^3gram=2.0*10^5gram\\c)9.0*10^9*10^-^6gram=9.0*10^3gram\\a)2.0*10^6*10^-^3gram=2.0*10^3gram[/tex]

Comparating the values, we can see that the option d) is the greatest mass.

Answer:

The greatest mass among the following measurements is:

[tex]2*10^{2}kg = 200kg[/tex]

Step-by-step explanation:

I am going to convert each one of these measurements to kilogram, then the biggest value in kg is the greatest mass.

a) [tex]2*10^{6}mg[/tex]

Each kg has [tex]10^{6} kg[/tex].

So

1 kg - [tex]10^{6} kg[/tex]

x kg - [tex]2*10^{6}mg[/tex]

x = 2.

So

[tex]2*10^{6}mg = 2kg[/tex]

b)[tex]5*10^{12}pg[/tex]

Each kg has [tex]10^{15}pg[/tex].

So

1 kg - [tex]10^{15}pg[/tex]

x kg - [tex]5*10^{12}pg[/tex]

[tex]x = 5*10^{-3}kg[/tex]

This is a smaller mass than a)

c) [tex]9.0*10^{9} mcg[/tex]

Each kg has  [tex]10^{9}mcg[/tex].

So

1 kg - [tex]10^{9}mcg[/tex]

x kg - [tex]9*10^{9} mcg[/tex]

x = 9kg.

[tex]9.0*10^{9} mcg = 9kg[/tex]

For now, this is the greatest mass.

d) [tex]2*10^{2}kg = 200kg[/tex]

This is the greatest mass.

Step-by-step explanation:

If X is a finite Hausdorff space then every two points of X can be separated by open neighborhoods. Say the points of X are [tex]x_1, x_2, ..., x_n[/tex]. So there are disjoint open neighborhoods [tex]U_{12}[/tex] and [tex]U_2[/tex], of [tex]x_1[/tex] and [tex]x_2[/tex] respectively (that's the definition of Hausdorff space). There are also open disjoint neighborhoods [tex]U_{13}[/tex] and [tex]U_3[/tex] of [tex]x_1[/tex] and [tex]x_3[/tex] respectively, and disjoint open neighborhoods [tex]U_{14}[/tex] and [tex]U_4[/tex] of [tex]x_1[/tex] and [tex]x_4[/tex], and so on, all the way to disjoint open neighborhoods [tex]U_{1n}[/tex], and [tex]U_n[/tex] of [tex]x_1[/tex] and [tex]x_n[/tex] respectively. So [tex]U=U_2 \cup U_3 \cup ... \cup U_n[/tex] has every element of [tex]X[/tex] in it, except for [tex]x_1[/tex]. Since [tex]U[/tex] is union of open sets, it is open, and so [tex]U^c[/tex], which is the singleton [tex]\{ x_1\}[/tex], is closed. Therefore every singleton is closed.

Now, remember finite union of closed sets is closed, so [tex]\{ x_2\} \cup \{ x_3\} \cup ... \cup \{ x_n\}[/tex] is closed, and so its complemented, which is [tex]\{ x_1\}[/tex] is open. Therefore every singleton is also open.

That means any two points of [tex]X[/tex] belong to different connected components (since we can express X as the union of the open sets [tex] \{ x_1\} \cup \{ x_2,...,x_n\}[/tex], so that [tex]x_1[/tex] is in a different connected component than [tex]x_2,...,x_n [/tex], and same could be done with any [tex]x_i[/tex]), and so each point is in its own connected component. And so the space is totally disconnected.

Answer:

[tex]C^{102}_{100}=5151[/tex]

Step-by-step explanation:

Let's imagine the following situation, if we want to distribute 100 coins between three pirates we could represent this situation with a line arrangement. For example if we had7 coins and 3 pirates one possible distribution of coins would be given by  CC|CCCC|C, the C's represent coins and the bars the boundaries between two pirates, for the particular line arrangement shown, we have that pirate A has 2 coins, B has 4 coins and C has a single coin. Another possible arrangement is,

|CCC|CCCC, where pirate A has no coin, pirate B has 3 coins and C has 7 coins. If we take notice of the fact that the arrangement representing a distribution is composed of 9 elements, that is 7 C's and 2 | (bars), then a way to make an arrangement would be to fill 9 empty boxes with our available coins and bars in all the possible ways. This means that if we first choose to fill 7 out of 9 boxes with  coins then the number of possible combinations is [tex]C^{9}_7=\frac{9!}{7!(9-7)!}36[/tex]. In general if we want to distribute n elements in k boxes, where the boxes can either be filled with any number of elements (including 0 number of elements), we have that the number of possible distributions will be [tex]C^{n+k-1}_{n}=\frac{(n+k-1)!}{n!(k-1)!}[/[tex], where we used the fact that we need k-q bars to represent k boxes. Thus pirate A can choose from [tex]C^{102}_{100}=5151[/tex] possible divisions.

Bonus:

If every pirate wants to have the maximum number of coins possible without being executed, here's how pirate A has to divide the coins in order to keep the largest amount of coins.

We have to think backwards to figure this out. Imagine pirate A was executed and there are only two remaining players. Pirate B should propose to keep all the coins, pirate C could oppose but pirate B's vote would break the vote and keep all the loot. Pirate A, B and C are all aware of this, so pirate A should propose to keep 99 coins and give the remaining gold piece to pirate C, Pirate B will of course oppose the division, but pirate C should accept because if not he would get no coins. Thus the division would be.

A: 99 coins

B: 0 coins

C: 1 coins

Answer:

a) MAX--> PC (R,P) = 0,3R+ 0,5P

b) Optimal solution: 40.000 units of R and 10.000 of PC = $17.000

c) Slack variables: S3=1000, is the unattended demand of P, the others are 0, that means the restrictions are at the limit.

d) Binding Constaints:

1. 0.3 R+0.6 P ≤ 18.000

2. R+P ≤ 50.000

3. P ≤ 20.000

4. R ≥ 0

5. P ≥ 0

Step-by-step explanation:

I will solve it using the graphic method:

First, we have to define the variables:

R : Regular Gasoline

P: Premium Gasoline

We also call:

PC: Profit contributions

A: Grade A crude oil

• R--> PC: $0,3 --> 0,3 A

• P--> PC: $0,5 --> 0,6 A

So the ecuation to maximize is:

MAX--> PC (R,P) = 0,3R+ 0,5P

The restrictions would be:

1. 18.000 A availabe (R=0,3 A ; P 0,6 A)

2. 50.000 capacity

3. Demand of P: No more than 20.000

4. Both P and R 0 or more.

Translated to formulas:

Answer d)

1. 0.3 R+0.6 P ≤ 18.000

2. R+P ≤ 50.000

3. P ≤ 20.000

4. R ≥ 0

5. P ≥ 0

To know the optimal solution it is better to graph all the restrictions, once you have the graphic, the theory says that the solution is on one of the vertices.

So we define the vertices: (you can see on the graphic, or calculate them with the intersection of the ecuations)

V:(R;P)

• V1: (0;0)

• V2: (0; 20.000)

• V3: (20.000;20.000)

• V4: (40.000; 10.000)

• V5:(50.000;0)

We check each one in the profit ecuation:

MAX--> PC (R,P) = 0,3R+ 0,5P

• V1: 0

• V2: 10.000

• V3: 16.000

• V4: 17.000

• V5: 15.000

As we can see, the optimal solution is  

V4: 40.000 units of regular and 10.000 of premium.

To have the slack variables you have to check in each restriction how much you have to add (or substract) to get to de exact (=) result.  

To maximize the total profit contribution, a linear programming model is formulated with decision variables, objective function, and constraints. The model is: Maximize 0.30x + 0.50y, Subject to: 0.3x + 0.6y ≤ 18,000, x + y ≤ 50,000, y ≤ 20,000, x, y ≥ 0.

To formulate a linear programming model, we need to define the decision variables, objective function, and constraints. Let's assume that x represents the number of gallons of regular gasoline produced and y represents the number of gallons of premium gasoline produced.

The objective function is to maximize the total profit contribution, which can be expressed as: 0.30x + 0.50y.

The constraints are:

So, the linear programming model can be formulated as:

Maximize 0.30x + 0.50y

Subject to:

0.3x + 0.6y ≤ 18,000

x + y ≤ 50,000

y ≤ 20,000

x, y ≥ 0

Answer:

Functions with straight lines have this sort of equation: Y = mx + b where the m is called slope and b, the y-intercept. As you don't have the slope you have to find out. In this case, the slope if 10, so when u have the m, just replace with one of your points to get the b, (y-intercept). The final equation for this function is, Y= 10x+35

Step-by-step explanation:

Answer:

solved

Step-by-step explanation:

Calculating i found the value of [tex]\frac{1}{128}[/tex]= 0.0078125

a.therefore the approximate valve of  [tex]\frac{1}{128}[/tex] (correct to three       decimal places) = 0.008

b. there are three significant digits in my approximation.

c. the absolute error = | exact value- approximate value |

   =|0.0078125- 0.008|= |-0.0001875| = 0.0001875

d.relative error= [tex]\frac{ absolute\ error}{exact\ value}[/tex]

    = [tex]\frac{0.0001875}{0.0078125}[/tex]= 0.024

Answer:

53.69 kilograms.

Step-by-step explanation:

You had 454 grams of shrimp per square feet in a tank.

Converting square feet in square meter.

1 square foot = 0.092903 square meter

Means you had 454 grams of shrimp per 0.093 square meter in a tank.

The bottom area of the tank is 11 square meter.

So, grams of shrimp in 11 square meter = [tex]\frac{454\times11}{0.093}[/tex]

= 53698.92 grams

In kg it will be [tex]\frac{53698.92}{1000}[/tex] = 53.69 kg

Final answer:

To find the percentage of students who voted for the athlete, divide the number who voted for the athlete (25) by the total number of students (100), and multiply by 100%. Therefore, 25% of the students voted for the athlete.

Explanation:

To calculate the percentage of students who voted for the athlete, we divide the number of students who voted for the athlete by the total number of students who voted, and then multiply the result by 100 to convert it to a percentage.

Total number of students = 25 (voted for the athlete) + 75 (voted for the actor) = 100 students

Now, to find the percentage who voted for the athlete:

Percentage voting for the athlete = (Number of students voting for the athlete ÷ Total number of students) × 100%

Percentage voting for the athlete = (25 ÷ 100) × 100%

Percentage voting for the athlete = 0.25 × 100%

Percentage voting for the athlete = 25%

25% of the students voted for the athlete.

Answer:

x=-5+2t, y=-6+3t, z=-6+9t

Step-by-step explanation:

We need to find parametric equations for the line through the point ( - 5, - 6, - 6) and perpendicular to the plane 2x + 3y + 9z = 17 .

If a line passes through a point [tex](x_1,y_1,z_1)[/tex] and perpendicular to the plane [tex]ax+by+cz=d[/tex], then the Cartesian form of line is

[tex]\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}[/tex]

and parametric equations are

[tex]x=x_1+at,y=y_1+bt,z=z_1+ct[/tex]

For the given information, [tex]x_1=-5,y_1=-6,z_1=-6,a=2,b=3,c=9[/tex]. So, the Cartesian form of line is

[tex]\frac{x+5}{2}=\frac{y+6}{3}=\frac{z+6}{9}[/tex]

Parametric equations of the line are

[tex]x=-5+2t[/tex]

[tex]y=-6+3t[/tex]

[tex]z=-6+9t[/tex]

Therefore the parametric equation for the line are x=-5+2t, y=-6+3t, z=-6+9t.

Final answer:

The parametric equations for the line are found using the point (-5, -6, -6) and the normal vector of the plane (2, 3, 9) as the direction vector, resulting in the equations x = -5 + 2t, y = -6 + 3t, and z = -6 + 9t.

Explanation:

To find a parametric equation for the line through the point (-5, -6, -6) and perpendicular to the plane 2x + 3y + 9z = 17, we use the fact that the normal vector of the plane (2, 3, 9) gives the direction of the line that is perpendicular to the plane. The general form of a parametric equation of a line is x = [tex]x_{0}[/tex] + at, y = [tex]y_{0}[/tex] + bt, and z = [tex]z_{0}[/tex] + ct, where [tex](x_{0},y_{0},z_{0})[/tex] is a point on the line and (a, b, c) is the direction vector of the line. In this case, the point given is (-5, -6, -6) and the direction vector is (2, 3, 9), so the parametric equations of the line are x = -5 + 2t, y = -6 + 3t, and z = -6 + 9t.

Answer:

b) 15,90,24.133,20

c) New average = 19.4, New Median = 20

d) 8

e) 40%

f) Wednesday

Step-by-step explanation:

a)                    Mon  Tue  Wed  Thu  Fri    

     Week 1      17      16     20     24   22

     Week 2     15      21    25     17    90

     Week 3      16      17    22     20   20

This is a 3×5 matrix where the rows gives us the weeks(Week 1, Week 2, Week 3) and the columns are the weekdays(Mon, Tue, Wed, Thu, Fri).

b)The shortest duration out of the data given for fifteen days is 15 minutes.

The longest duration is 90 minutes.

To calculate the average of given data, we use the following formula:

Average  = [tex]\frac{\text{Sum of all observations}}{\text{Total no of observations}}[/tex]

=[tex]\frac{17+16+20+24+22+15+21+25+17+90+16+17+22+20+20}{15}[/tex]

=[tex]\frac{362}{15}[/tex]

=24.133

Median = the value that divides the data into two equal parts]

Ascending order: 15,16,16,17,17,17,20,20,20,21,22,22,24,25,90

Median = [tex](\frac{n+1}{2})\text{th term}[/tex] = 8th term = 20

c)                   Mon  Tue  Wed  Thu  Fri    

     Week 1      17      16     20     24   22

     Week 2     15      21    25     17     19

     Week 3      16      17    22     20   20

New average = [tex]\frac{\text{Sum of new observations}}{\text{Total no of observations}}[/tex]

=[tex]\frac{17+16+20+24+22+15+21+25+17+19+16+17+22+20+20}{15}[/tex]

=[tex]\frac{362}{15}[/tex]

=19.4

New Median

Ascending order: 15,16,16,17,17,17,19,20,20,20,21,22,22,24,25

Median = [tex](\frac{n+1}{2})\text{th term}[/tex] = 8th term = 20

d) In order to know how many times we commute for 20 minutes or more, we check the entries that are greater than or equal to 20 minutes. We have 8 such entries. Thus, 8 times the commute was 20 minutes or more longer.

e)  Percent of commutes less than 18 minutes = [tex]\frac{\text{Commutes that are less than 18 minutes}}{\text{Total number of commutes} }[/tex]× 100%

=[tex]\frac{6}{15}[/tex]×100% = 40%

f) Average  = [tex]\frac{\text{Sum of all observations}}{\text{Total no of observations}}[/tex]

Average time spent in commuting on Monday = 16

Average time spent in commuting on Tuesday = 18

Average time spent in commuting on Wednesday = 22.3

Average time spent in commuting on Thursday = 20.3

Average time spent in commuting on Friday= 20.3

On Wednesday, we spent the most on commute time.

Answer:

5 = radius

Step-by-step explanation:

According to one of the Circle Equations, (X - H)² + (Y - K)² = R², you take the square root of your squared radius:

√25 = √R²

5 = R

* When we are talking about radii and diameters, we want the NON-NEGATIVE root.

I am joyous to assist you anytime.

Answer:

Multiplication is commutative.          

Step-by-step explanation:

Let n,m be two natural numbers.

We have to show that [tex]n\times m=m\times n[/tex]

We will prove this by induction

For n = 1, we have [tex]n\times 1 = 1\times n = n[/tex], which is true.

Let the given statement be true for n-1 natural numbers, that is,

[tex](n-1)\times m = m\times (n-1)[/tex]

Now, we have to show that it is true for n natural numbers.

[tex]nm = (n-1)m + m = m(n-1) + m[/tex]

which is equal to

[tex](m-1)(n-1) + (n-1) + m[/tex]

[tex]= (m-1)(n-1) + (m-1) + n[/tex]

[tex]= n(m-1) + n[/tex]

[tex]= (m-1)n + n[/tex]

[tex]= mn[/tex]

Hence, by principal of mathematical induction, the given statement is true for all natural numbers.

Answer:

50%

Step-by-step explanation:

29 right and 29 wrong. 29+29=58

Divide 29 by 58 and you get .5

Move the decimal over two to the right, and there’s the 50%.

You could also multiply .5 by 100 and you’ll still get 50!

Answer:

Step-by-step explanation:

1. Find the total number of problems, incorrect and correct. 29 incorrect problems + 29 correct problems is 58 total problems.

2. Find the total number of correct problems divided by the total number of problems. 29 incorrect problems divided by 58 total problems. This is simplified to 1/2.

3. Finally, convert 1/2 into a fraction. We can do this by multiplying the fraction by 50/50 to get a fraction of 50/100, and we know that 50/100 50 percent.

Answer:

See picture below

Step-by-step explanation:

The total area of the sheet of paper is 80, so we can divide the sheet of paper into 4 different sections, each one of them with area 20 (you can verify this by counting the squares in each section, there are 20 squares per section).

In the picture below we can see that the perimeter of each of the sections are from left to right:

The first one is a rectangle, with sides 5 and 4. Therefore the perimeter is 2(5) + 2(4) = 18.

The next section is irregular so we sum up the sides: 2 + 6 + 5 + 1 + 2 + 1 + 5 + 4 = 26.

For the next section we also sum up the sides: 3 + 7 + 2 + 1 + 1 + 6 = 20.

For the bottom section, we will sum up the sides too: 2 + 1 + 6 + 1 + 2 + 1 + 10 + 3 = 26.

So the perimeters are 8, 26, 20 and 26. This satisfies the condition of no more than two sections having the same perimeter.

Answer:

we over weighted suitcase will be 46.9889 pound

Step-by-step explanation:

We have given the average weight of passenger's suitcase [tex]\mu =45\ pounds[/tex]

Standard deviation [tex]\sigma =2\ pounds[/tex]

16 % of the suitcase are overweight so 100-16 =84 % of the suitcase will pass without any problem

So probability [tex]p=0.84[/tex]

From z table at p =0.84 z will be z=0.99445

We know that [tex]z=\frac{x-\mu }{\sigma }[/tex]

[tex]0.99445=\frac{x-45}{2}[/tex]

x = 46.9889 pound

So we over weighted suitcase will be 46.9889 pound

Using standard deviation formula to solve the problem. Then the overweighted suitcase is 46.9889 pounds.

It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation.

Given

The average [tex](\mu )[/tex] weight of an airline passenger’s suitcases is 45 pounds.

The standard deviation [tex](\sigma)[/tex] of 2 pounds.

16% of the suitcase are overweight. So,

[tex]100 - 16 = 84\%[/tex]

The suitcase will pass without any problem. So the probability will be

[tex]\rm P = 0.84[/tex]

From z table at P = 0.84 will be

z = 0.99445

We know that

[tex]\begin{aligned} z &= \dfrac{x - \mu}{\sigma}\\0.99445 &= \dfrac{x - 45}{2}\\x &= 46.9889\end{aligned}[/tex]

Thus, the overweighted suitcase is 46.9889 pounds.

More about the standard deviation link is given below.

https://brainly.com/question/12402189

Answer : (a) 5040  b) 720  c) 288

Step-to step explanation:-

Given : There are 3 Computer Science, 2 Mathematics, and 2 Sociology textbooks.

Total books = 7

a) The number of ways the books can be arranged in any order is given by :-

[tex]7!=7\times6\times5\times4\times3\times2=5040[/tex]

b) We consider all computer books as one thing, then, the total number of things to arrange = 1+2+2=5

Now, the number of ways to arrange books such that Computer Science books must be together, but all other books can be arranged in any order:-

[tex]3!\times5!\\\\=6\times120=720[/tex]

c) We consider all computer books as one thing and math book as one thing, then, the total number of things to arrange = 1+1+2=4

Now, the number of ways to arrange books such that Computer Science books must be together, but all other books can be arranged in any order:-

[tex]4!\times 3!\times2!=24\times6\times2=288[/tex]

The expression 4d + 6 + 2d is equivalent to the expression (3d + 3) + (3d + 3). Then the correct option is C.

The equivalent is the functions that are in different forms but are equal to the same value.

The expression is given below.

→ 4d + 6 + 2d

Then the expression can be written as

→ 6d + 6  

→ 2(3d + 3)

→ (3d + 3) + (3d + 3)

Thus, the correct option is C.

More about the equivalent link is given below.

https://brainly.com/question/889935

#SPJ2

Final answer:

Choices A and C, which evaluate to 2(3d+3) and (3d+3)+(3d+3) respectively, are equivalent to the original expression 4d+6+2d.

Explanation:

The student is asking to identify which expressions are equivalent to 4d+6+2d. To solve this, we combine like terms in the original expression.

4d + 2d + 6 = 6d + 6.

Now let's analyze the provided choices:

(Choice A) 2(3d+3) simplifies to 6d + 6, which is the same as the original expression.

(Choice B) 6(d+6) simplifies to 6d + 36, which is not equivalent to 6d + 6.

(Choice C) (3d+3) + (3d+3) simplifies to 3d + 3 + 3d + 3, which simplifies further to 6d + 6, equivalent to the original expression.

Choices A and C are equivalent to 4d+6+2d.