5. How far can you get away from your little brother with a squirt gun filled point
with paint if you can travel at 3 m/s and you have 15 s before he sees you?"
45 m
5 m
2 m
20 m

The minimum value of the objective function 12x + 14y is 156 at point C(6, 9).Answer: 156.

Given:

Minimize and maximize objective function = 12x + 14y–2x + y ≥ 6x + y ≤ 15x ≥ 0, y ≥ 0.

The graphical method is a simple and easy method of solving a linear programming problem (LP).

LP issues are represented on a graphical scale using graphical method.

Let's plot the given inequalities on the graph. The graph of all inequalities must be in the first quadrant since x, y ≥ 0.Initially, let us consider x = 0 and y = 0 for (2) and (3) respectively.

(2) y ≤ 15 - x On plotting the line y = 15 - x in first quadrant, we get the following graph:

(3) x ≤ 15 - y On plotting the line x = 15 - y in first quadrant, we get the following graph:Now let's check for the first inequality, -2x + y ≥ 6.It can be written as y ≥ 2x + 6.

On plotting the line y = 2x + 6 in first quadrant, we get the following graph:The region containing common feasible points for all the three inequalities is shown in the figure below:Thus, the feasible region is OACD.The corner points of the feasible region are A(2, 13), B(3.8, 11.2), C(6, 9) and D(15, 0).

We need to determine the minimum and maximum values of the objective function 12x + 14y at each corner point as follows:At point A, 12x + 14y = 12(2) + 14(13) = 194At point B, 12x + 14y = 12(3.8) + 14(11.2) = 184.8At point C, 12x + 14y = 12(6) + 14(9) = 156At point D, 12x + 14y = 12(15) + 14(0) = 180.

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To find the minimum and maximum values of the objective function 12x + 14y subject to the given constraints using graphical method.

Therefore, the minimum value of the objective function is 210 at (10.5, 3) and the maximum value of the objective function is not bounded.

We can follow these steps:

Step 1: Convert the inequality constraints into equation form by replacing the inequality signs with equality signs. So, -2x + y = 6 and

x + y = 15

Step 2: We find the values of x and y for each equation.

Step 3: Plot the two lines on the coordinate axis formed by the values obtained in Step 2.

Step 4: Determine the feasible region by identifying the portion of the plane where the solution satisfies all the constraints. In the present case, it is the region

above the line -2x + y = 6 and

below the line x + y = 15 and

to the right of the y-axis.

Step 5: Plot the objective function 12x + 14y on the same graph.

Step 6: Move the objective function line either up or down until it just touches the highest or lowest point of the feasible region. The point of contact is the solution to the linear programming problem. The graph of the feasible region and the objective function is shown below:

graph

y = 15 - x [-10, 20, -5, 25]

y = 2x + 6 [-10, 20, -5, 25]

y = -(6/7)x + 180/7 [-10, 20, -5, 25](-1/2)x+(1/14)

y = 0.5[0, 20, 0, 20](-1/2)x+(1/7)

y = 1[0, 20, 0, 20]12x + 14

y = 210[0, 20, 0, 20]

Therefore, the minimum value of the objective function is 210 at (10.5, 3) and the maximum value of the objective function is not bounded.

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Answer:

x >8

Step-by-step explanation:

Answer:

x > 8

Step-by-step explanation:

Solving an algebraic inequality is the same as solving an algebraic equation. One uses the technnique of inverse operations to undo every step in the expression to get the answer. The only difference is that with an inequality, one must remember to flip the inequality sign when dividing or multiplying by a negative. This rule does not apply to the given inequality.

5(x + 2) > 50

/5            /5

x + 2 > 10

  -2      -2

x > 8

Answer:

216 cm³

Step-by-step explanation:

large prism volume = 6 x 6 x 8 = 288 cm³

small cutout volume = 3 x 3 x 8 = 72 cm³

288- 72 = 216 cm³

The vector equation r(t) = t^2i + t^4j + t^6k represents a parametric curve in three-dimensional space. To sketch the curve, we can substitute values of t and plot corresponding points in the coordinate system.

By examining the components of the vector equation, we can observe that x = t^2, y = t^4, and z = t^6. This implies that the curve lies in the x-y-z coordinate system, where the x-coordinate is determined by t^2, the y-coordinate is determined by t^4, and the z-coordinate is determined by t^6.

To start sketching, we can choose a range of values for t and substitute them into the equations. For example, for t = -1, 0, 1, we can calculate the corresponding x, y, and z values.

By plotting these points and connecting them, we can obtain an approximate shape of the curve. Additionally, we can observe that as t increases, the curve moves in the direction of increasing t, which can be indicated by an arrow along the curve.

Note that without specific values for t or a specific range, the sketch will be a general representation of the curve.

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Answer:

12(x−2.57)=0.36

Step-by-step explanation:

Let x represent the initial amount of money Mrs. Sorenstam had to spend on each student.

The cost of the 3 items is:

1.49+0.59+0.49=2.57

The change left for each student will be:

x−2.57

For 12 students, the change left will be

12(x−2.57) which equals 36 cents, according to the problem

So, the equation to represent this situation will be:

12(x−2.57)=0.36

Answer:

for the first part:

Oxygen and glucose are both reactants in the process of cellular respiration.

Step-by-step explanation:

The mass of hydrogen is conserved during cellular respiration as it follows the Law of Conservation of Matter...This shows that hydrogen has been conserved throughout the entire process as the product has the same amount of hydrogen as the reactants.

Answer:

-2, -1, 0, 4, 9

Step-by-step explanation:

Answer:

6/17

Step-by-step explanation:

The amount of blue marbles is 30, over the total number of marbles, which is 85. 30/85 simplifies to 6/17, which is the probability.

Hopefully this helps - let me know if you have any questions!

Answer:

y=7, x=7

Step-by-step explanation:

They both equal y, so you can set the right part of the equations equal to each other

4x-21=2x-7

solve for x

2x-21=-7

2x=14

x=7

knowing x, we can now substitute back into one of the original equations to find y

y=4(7)-21=28-21=7

or

y=2(7)-7=14-7=7

Answer:

D

Step-by-step explanation:

x = 2 and y = -7

Plug those values into the equation:

2(2) - (-7) = 11

Answer:

(63a+54b) and (2xy+11yz)

Step-by-step explanation:

9*7a is 63a

9*6b is 54b

2x*y is 2xy

11z*y is 11yz

The probability that an employed person earns a living through agriculture is ≈ 17%.

The frequency is the number of times the data appear within each category.

A percentage frequency distribution is used to summarize data and report on the proportion or percentage of observations that fall within a specified category.

It is the process of showing how often a particular value or category occurs in a set of data.

In order to create a percentage frequency distribution, we will first add all the values together:

Total number of people employed = 6,678 + 1,492 + 653 + 2,865 + 914

= 12,602

Now we can calculate the percentage of people employed in each sector:

Formal business sector =

(6,678 / 12,602) x 100% = 53.0%

Commercial agricultural sector =

(1,492 / 12,602) x 100% = 11.8%

Subsistence agricultural sector =

(653 / 12,602) x 100% = 5.2%

Informal business sector =

(2,865 / 12,602) x 100% = 22.7%

Domestic service sector =

(914 / 12,602) x 100% = 7.3%

The likelihood that an employed person earns a living through agriculture can be calculated by adding the number of people employed in the commercial agricultural sector and the number of people employed in subsistence agriculture.

This gives a total of 2,145 people employed in agriculture.

Therefore, the probability that a person earns a living through agriculture is:

Probability = (2,145 / 12,602) x 100% ≈ 17%

The probability that an employed person earns a living through agriculture is ≈ 17%.

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The given expression is $\frac{6}{t}+\frac{8}{u}-\frac{9}{v}$ and we need to rewrite this expression without any denominator in it. Step-by-step explanation: We can use the concept of the Least Common Multiple (LCM) of the denominators to remove the fractions in the expression. By taking the LCM of the denominators of the given expression, we have,$LCM\text{ of }t, u, v = t \cdot u \cdot v$ Now, multiplying each term of the given expression with the LCM $t \cdot u \cdot v$, we get,$\frac{6}{t}\cdot t \cdot u \cdot v+\frac{8}{u}\cdot t \cdot u \cdot v-\frac{9}{v}\cdot t \cdot u \cdot v$$6uv + 8tv - 9tu$$\therefore \text{The given expression without any denominator is } 6uv + 8tv - 9tu.$Thus, we can rewrite the given expression $\frac{6}{t}+\frac{8}{u}-\frac{9}{v}$ without any denominator in it as $6uv + 8tv - 9tu$.

LCM (a,b) in mathematics stands for the least common multiple, or LCM, of two numbers, such as a and b. The smallest or least positive integer that is divisible by both a and b is known as the LCM. Take the positive integers 4 and 6 as an illustration.

There are four multiples: 4,8,12,16,20,24.

6, 12, 18, and 24 are multiples of 6.

12, 24, 36, 48, and so on are frequent multiples for the numbers 4 and 6. In that lot, 12 would be the least frequent number. Now let's attempt to get the LCM of 24 and 15.

LCM of 24 and 15 is equal to 222235 = 120.

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(A intersect B) is a subset of A, A is a subset of (A union B), A is a subset of (D union E), and |sin(nx)| <= n|sin(x)| for any natural number and real number x.

To prove that (A intersect B) is a subset of A, we need to show that every element in (A intersect B) is also in A. Let x be an arbitrary element in (A intersect B). This means x is in both A and B. Since x is in A, it follows that x is also in the union of A and B, which means x is in A. Therefore, (A intersect B) is a subset of A.

To prove that A is a subset of (A union B), we need to show that every element in A is also in (A union B). Let x be an arbitrary element in A. Since x is in A, it follows that x is in the union of A and B, which means x is in (A union B). Therefore, A is a subset of (A union B).

Given A is a subset of (B union C), B is a subset of D, and C is a subset of E, we want to prove that A is a subset of (D union E). Let x be an arbitrary element in A. Since A is a subset of (B union C), it means x is in (B union C). Since B is a subset of D and C is a subset of E, we can conclude that x is in (D union E). Therefore, A is a subset of (D union E).

To prove |sin(nx)| <= n |sin(x)| for any natural number n and real number x, we can use mathematical induction. For the base case, when n = 1, the inequality reduces to |sin(x)| <= |sin(x)|, which is true. Assuming the inequality holds for some positive integer k, we need to show that it holds for k+1. By using the double-angle formula for sin, we can rewrite sin((k+1)x) as 2sin(x)cos(kx) - sin(x). By the induction hypothesis, |sin(kx)| <= k|sin(x)|, and since |cos(kx)| <= 1, we have |sin((k+1)x)| = |2sin(x)cos(kx) - sin(x)| <= 2|sin(x)||cos(kx)| + |sin(x)| <= 2k|sin(x)| + |sin(x)| = (2k+1)|sin(x)| <= (k+1)|sin(x)|. Therefore, the inequality holds for all natural numbers n and real numbers x.

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The five-number summary for the given data set is: Minimum = -7, First Quartile = 2, Median = 6, Third Quartile = 9, Maximum = 24.

To calculate the five-number summary for the given data set, we need to arrange the data in ascending order and then determine the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values.

The given data set: -7, -5, -2, 0, 4, 6, 8, 8, 10, 22, 24

Arranged in ascending order: -7, -5, -2, 0, 4, 6, 8, 8, 10, 22, 24

Now, let's calculate the values for the five-number summary:

Minimum: The smallest value in the data set is -7.

First Quartile (Q1): This represents the median of the lower half of the data set. Since we have 11 data points, Q1 is the median of the first 5 data points. Q1 = (0 + 4) / 2 = 2.

Median (Q2): The median is the middle value of the data set. Since we have an odd number of data points, the median is the 6th value, which is 6.

Third Quartile (Q3): This represents the median of the upper half of the data set. Q3 is the median of the last 5 data points. Q3 = (8 + 10) / 2 = 9.

Maximum: The largest value in the data set is 24.

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F(x<=0) = 1/2.The correct option is (b) 1+e-2.

The probability distribution function of the random variable X is given by;

`f(x) = {(x+1), for x between -1 and 1, 0 elsewhere}.

The random variable Y is defined as Y = g(X), and y = g(x).

Find the probability that F(X) is less than or equal to 0. That is; F(x <= 0).

To find this, we need to evaluate the integral of the function over the interval (-infinity, 0).

Thus, F(x<=0) = ∫[from -∞ to 0] f(x) dx.

We know that the function is zero for all values of x, except when -1 < x < 1.

Therefore, we can break up the integral into two parts. We get:

F(x<=0) = ∫[from -∞ to -1] 0 dx + ∫[from -1 to 0] f(x) dx

Thus;

F(x<=0) = ∫[from -∞ to -1] 0 dx + ∫[from -1 to 0] (x + 1) dx

F(x<=0) = 0 + [(x^2/2) + x] [from -1 to 0]F(x<=0) = (0 - [(1/2) - 1]) = (1/2)

Therefore, F(x<=0) = 1/2.The correct option is (b) 1+e-2.

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The true statements are:a. Angle R is congruent to angle R'

b. (P' * Q')/(PQ) = 4

e. (C * Q')/(CQ) = 4

To determine which statements are true about triangle PQR and its image P' * Q' * R' after dilation, let's analyze each statement:

a. Angle R is congruent to angle R': This statement is true. When a triangle is dilated, the corresponding angles remain congruent.

b. (P' * Q')/(PQ) = 4: This statement is true. The scale factor of dilation is 4, which means the corresponding side lengths are multiplied by 4. Therefore, (P' * Q')/(PQ) = 4.

c. (QR)/(Q' * R') = 4: This statement is false. The scale factor of dilation applies to individual side lengths, not ratios of side lengths. Therefore, (QR)/(Q' * R') will not necessarily be equal to 4.

d. (C * P')/(CP) = 5: This statement is false. The scale factor of dilation is 4, not 5. Therefore, (C * P')/(CP) will not be equal to 5.

e. (C * Q')/(CQ) = 4: This statement is true. The scale factor of dilation is 4, so the corresponding side lengths are multiplied by 4. Therefore, (C * Q')/(CQ) = 4.

f. (C * P')/(CP) = (C * R')/(CR): This statement is false. The dilation does not guarantee that the ratios of the distances from the center C to the vertices will be equal.

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The is specified initial approximation X1  x3 is equal to 5.

We absolutely need to accentuate using the recipe in order to find x3 using Newton's method:

In this particular instance, we are informed that x5 is equal to x2 minus 4 and that X1 equals 1. Because we need to find x3, let's use the given equation to find x2.

We can solve for x2 because we have x5: x2 + 4

As of now we have x2 = x5 - 4 from x2 = x5 - 4. This ought to be added to the Newton's system recipe, and afterward we can find x3:

We ought to portray our ability f(x) and its subordinate f'(x) as Xn+1 = Xn - f(Xn)/f'(Xn).

We can now calculate x3 by using X1 = 1 as our underlying estimate: X2 = X1 - f(X1)/f'(X1) = 1 - ((1)2 + 4 - 1)/(- 1) = 1 - (1 + 4 - 1)/(- 1) = 1 + 4 = 5 In this way, x3 is the same as 5.

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There are 380 ways to determine the first and second place in the race.

In a race, there are 20 runners. Trophies for the race are awarded to the runners finishing in first and second place. In how many ways can first and second place be determined?When the trophies for the race are awarded to the runners finishing in first and second place, then it means that there are only two trophies to be awarded. Now, the number of ways in which the two trophies can be awarded can be calculated by permutation, which is a way of counting the arrangements or selections of objects in which order is important.

To determine the number of ways first and second place can be determined in a race with 20 runners, we can use the concept of permutations.

The first-place finisher can be any one of the 20 runners. After the first-place finisher is determined, there are 19 remaining runners who can finish in second place. Therefore, the number of ways to determine the first and second place is given by:

Number of ways = 20 * 19 = 380

So, there are 380 ways to determine the first and second place in the race.

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a. € A. Yes, 27 € A. To see this, we set a = 5, so that x = 27.

Does –8 € A? No. If –8 were in A, then –8 = 5a + 2 for some integer a. But then a = (–10)/5, which is not an integer, a contradiction.

Does – 8 € B? Yes, we set b = 0, so that y = –3, which is in B.

In either case, we have expressed y as a member of A or C, which means that B CA.

b. AB. We claim that AB. To see this, we assume the contrary, namely, that there is an integer z which is in both A and B. This means that z = 5a + 2 and z = 10b – 3 for some integers a and b. Adding these two equations, we get 7 = 5a + 10b, or 1 = a + 2b. Since the left-hand side is odd, so is the right-hand side, which means that a and b have opposite parity. However, this is impossible since 1 is not odd. Therefore, the assumption that there is such a z is false, which means that AB, as desired. C. B CA. We claim that B CA. To see this, we need to show that every element of B is in A or C. Let y be an element of B, so that y = 10b – 3 for some integer b. If y is even, then we can set a = (y + 1)/5, and we have x = 5a + 2 = y/2 + 3/2. If y is odd, then we can set c = (y + 3)/7, and we have z = 7c – 4 = y/2 + 5/2.

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Answer:

(-4, -2)

Step-by-step explanation:

A is initially (-4, 2); when we reflect over the y-axis, we will change from (x, y) to (x, -y). This gives us (-4, -2).

The coordinates of A' are (-5,-3).

If AABC is reflected across the y-axis, the coordinates of A' are (-5,-3).

The reflected graph is given below.

Therefore, the coordinates of A' are (-5,-3).

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On average, if the null hypothesis is false, the expected value for the F-ratio is much greater than 1.00.

The F-ratio is a statistic used in analysis of variance (ANOVA) tests to compare the variances between groups. In the context of hypothesis testing, the F-ratio measures the ratio of the variability between groups to the variability within groups. When the null hypothesis is false, it means that there is a significant difference between the groups being compared.

If the null hypothesis is false, it implies that there are systematic differences between the groups, resulting in larger variation between groups compared to within groups. This leads to a higher F-ratio value. The F-ratio is calculated as the ratio of the mean square between groups to the mean square within groups. As the differences between groups become more pronounced, the F-ratio increases, indicating a greater likelihood of rejecting the null hypothesis.

Therefore, if the null hypothesis is false, the expected value for the F-ratio is much greater than 1.00, indicating significant variability between groups.

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The equation rearranged to isolate c is c = b / (a - b/d).

To isolate c in the equation a = b(1/c - 1/d), we can follow these steps:

Start with the equation a = b(1/c - 1/d).

Distribute b to the terms inside the parentheses: a = b/c - b/d.

Move the term b/c to the other side of the equation by subtracting it from both sides: a - b/c = -b/d.

Multiply both sides of the equation by c to eliminate the denominator in the left term: c(a - b/c) = -b/d * c.

Simplify the left side by distributing c: ac - b = -bc/d.

Move the term -bc/d to the other side of the equation by adding it to both sides: ac - b + bc/d = 0.

Factor out c on the right side of the equation: ac + c(-b/d) - b = 0.

Combine like terms: ac - (b/d)c - b = 0.

Factor out c: c(a - b/d) - b = 0.

Add b to both sides of the equation: c(a - b/d) = b.

Finally, isolate c by dividing both sides of the equation by (a - b/d): c = b / (a - b/d).

Therefore, the equation rearranged to isolate c is c = b / (a - b/d).

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