Jeremy is saving $250 per month for his vacation . How much will Jeremy save up for his vacation in 1 year and 6 months?

The optimal solution of the objective function is cost = 5x + 7y.

To solve this problem, we need to determine the optimal amounts of material to be taken from each pit in order to minimize the overall cost while meeting the minimum sand content requirement. Let's break down the problem step by step:

Step 1: Define the decision variables:

Let's define:

x = amount of material (in cubic meters) taken from Bloomingdale Pit

y = amount of material (in cubic meters) taken from Valley Springs Pit

Step 2: Write the constraints in mathematical form:

We have two constraints to consider:

Total volume constraint:

x + y = 100,000 (the total volume of mixed material needed for the project)

Minimum sand content constraint:

The mix should contain a minimum of 30% sand. We can express this constraint as follows:

(0.25x + 0.50y) / (x + y) ≥ 0.30

Step 3: Write the objective function in mathematical form:

The objective is to minimize the overall cost of material. We can express the cost as follows:

Cost = 5x + 7y

Step 4: Find the optimum solution using the graphical method:

To find the optimum solution, we need to plot the feasible region defined by the constraints and identify the point that minimizes the objective function within that region.

First, let's rearrange the minimum sand content constraint:

0.25x + 0.50y ≥ 0.30(x + y)

0.25x + 0.50y ≥ 0.30x + 0.30y

0.20x - 0.20y ≥ 0

Now, we can plot the feasible region using the given constraints. The region will be bounded by the lines x + y = 100,000 and 0.20x - 0.20y ≥ 0. However, since the region is defined in terms of the total volume, we can simplify the plot by considering only the positive quadrant (x ≥ 0, y ≥ 0).

By substituting x = 0 and y = 100,000 into the minimum sand content constraint, we can check if the constraint is satisfied:

(0.25 * 0 + 0.50 * 100,000) / (0 + 100,000) ≥ 0.30

50,000 / 100,000 ≥ 0.30

0.50 ≥ 0.30

Since the constraint is satisfied at this point, we know the feasible region lies above or on the line x = 0, y = 100,000.

Now, by substituting x = 100,000 and y = 0 into the minimum sand content constraint, we can check if the constraint is satisfied:

(0.25 * 100,000 + 0.50 * 0) / (100,000 + 0) ≥ 0.30

25,000 / 100,000 ≥ 0.30

0.25 ≥ 0.30

Since the constraint is not satisfied at this point, we know the feasible region lies below the line x = 100,000, y = 0.

Finally, we can plot these two lines and shade the feasible region between them. The point that minimizes the objective function within this region will be the optimal solution.

Step 5: Calculate the savings:

If the contractor had used 60,000 m3 from Bloomingdale and 40,000 m3 from Valley Springs, we can calculate the cost for that scenario and compare it with the cost of the optimal solution.

Cost with the contractor's plan:

Cost = 5(60,000) + 7(40,000)

Cost with the optimal solution (as determined in Step 4):

Calculate the values of x and y from the optimal solution and substitute them into the objective function Cost = 5x + 7y.

The savings can be calculated as:

Savings = Cost with the contractor's plan - Cost with the optimal solution

By comparing the costs, you can determine the amount saved by giving the expert advice.

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Answer:

the correct answer is B

Step-by-step explanation:

hope this helped :)

Multiply 7 by 0.95.

6.65 + 7x

Answer:

the first part is the 2nt one

Step-by-step explanation:

Answer:

all three is correctly

Step-by-step explanation:

Answer:

The domain is [0, 20]

Step-by-step explanation:

With this equation, we can assume that x is minutes. You can't have less than 0 minutes because time isn't negative. You also can't have more than twenty minutes because the pool is empty at 20 and it can't be less than empty.

Answer:

eric

Step-by-step explanation:

just took the test

Answer:

$35= $0.15x+$3.00

Step-by-step explanation:

y=$35

m=$0.15x (x represents the uncertain number of photos she will be printing)

b=$3.00

Given:

The sum of the first 15 terms of an arithmetic sequence is 480.

To find:

The 8th term of the sequence.

Solution:

We have,

\(S_{15}=480\)

We know that, the nth term of an AP is

\(a_n=a+(n-1)d\)

Where, a is the first term and d is the common difference.

Putting n=8, we get the 8th term of the sequence.

\(a_8=a+(8-1)d\)

\(a_8=a+7d\)

The sum of first n terms is

\(S_{n}=\dfrac{n}{2}[2a+(n-1)d]\)

Where, a is the first term and d is the common difference.

\(S_{15}=\dfrac{15}{2}[2a+(15-1)d]\)

\(480=\dfrac{15}{2}[2a+14d]\)

\(480=\dfrac{15}{2}[2(a+7d)]\)

\(480=15(a+7d)\)

Divide both sides by 15.

\(\dfrac{480}{15}=a+7d\)

\(32=a+7d\)

\(32=a_8\)

Therefore, the 8th term of the arithmetic sequence is 32.

Answer:

32

Step-by-step explanation:

32

a dimensional coloring technique that uses a darker color on selected strands is referred is "lowlights". Lowlights is a dimensional coloring technique that involves applying a darker color to certain strands of hair to create depth and contrast.

An explanation of this technique is that it is the opposite of highlights, which involve adding lighter colors to the hair. Lowlights are typically used to create a more natural and subtle look, or to add dimension to hair that is otherwise one solid color.

if you are looking to add depth and contrast to your hair color, lowlights may be a great option for you to consider.

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Answer:

x = 5

Step-by-step explanation:

the Equation could be:

m L ABC + m L BAC = m L C (the outer angle)

4x-3 + 3x+8 = 5x+15

7x+5 = 5x+15

7x-5x = 15-5

2x = 10

x = 5

Recall

Sum of two interiors=exterior

The chi-square goodness-of-fit test can provide important information about whether the observed data significantly deviates from the expected distribution, which categories or bins contribute to the deviation, and the overall goodness-of-fit of the data to the expected distribution.

The chi-square goodness-of-fit test is a statistical test used to determine if a sample of data comes from a population with a specific distribution. Specifically, the test compares the observed frequencies of data in different categories or bins with the expected frequencies of data in those categories based on a hypothesized distribution.

It can determine whether the observed data significantly deviates from the expected distribution. If the test results in a p-value less than the chosen level of significance, it indicates that the observed data significantly deviates from the expected distribution, and the null hypothesis (that the data follows the expected distribution) can be rejected.

It can identify which categories or bins contribute the most to any significant deviation. The test statistic and associated p-value can help to identify which categories or bins show significant differences between the observed and expected frequencies.

It can provide information on the overall goodness-of-fit of the data to the expected distribution. The test statistic provides a measure of the overall goodness-of-fit, with higher values indicating greater deviation from the expected distribution.

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We can use this formula, sum = (n/2)(a + l), To find the sum of an arithmetic sequence, where n is the number of terms in the sequence, a is the first term, and l is the last term.

To find the sum of an arithmetic sequence, you can use the following formula:

sum = (n/2)(a + l)

where n is the number of terms in the sequence, a is the first term, and l is the last term.

Here are the steps to use this formula:

Find the number of terms in the sequence, n.

Determine the value of the first term, a, and the last term, l.

Plug these values into the formula:

sum = (n/2)(a + l)

Simplify the expression to find the sum.

Here's an example to illustrate the process:

Find the sum of the arithmetic sequence 5, 8, 11, 14, 17.

The number of terms in the sequence is n = 5.

The first term is a = 5, and the last term is l = 17.

Plug these values into the formula:

sum = (5/2)(5 + 17)

Simplify the expression to find the sum:

sum = (5/2)(22) = 55

Therefore, the sum of the arithmetic sequence 5, 8, 11, 14, 17 is 55.

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The probability distribution for the number of green balls:

P(0) = 8/27

P(1) = 4/9

P(2) = 2/9

P(3) = 1/27

To find the probability distribution for the number of green balls drawn, we need to consider all possible outcomes and calculate the probability for each outcome.

In this scenario, we are drawing 3 balls in succession with replacement, meaning after each draw, the ball is placed back in the box. The possible outcomes for the number of green balls can be 0, 1, 2, or 3.

Let's calculate the probability for each outcome:

1. Probability of drawing 0 green balls:

  P(0) = (4/6) * (4/6) * (4/6) = 64/216 = 8/27

2. Probability of drawing 1 green ball:

  P(1) = (2/6) * (4/6) * (4/6) + (4/6) * (2/6) * (4/6) + (4/6) * (4/6) * (2/6) = 96/216 = 4/9

3. Probability of drawing 2 green balls:

  P(2) = (2/6) * (2/6) * (4/6) + (4/6) * (2/6) * (2/6) + (2/6) * (4/6) * (2/6) = 48/216 = 2/9

4. Probability of drawing 3 green balls:

  P(3) = (2/6) * (2/6) * (2/6) = 8/216 = 1/27

Now we have the probability distribution for the number of green balls:

P(0) = 8/27

P(1) = 4/9

P(2) = 2/9

P(3) = 1/27

These probabilities represent the likelihood of drawing 0, 1, 2, or 3 green balls when drawing 3 balls with replacement from the given box.

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The population of bacteria 8 minutes from now is approximately 14965 organisms

Let P(t) be the population of bacteria at time t, measured in minutes.

Then we know that P(0) = 5605.

We also know that bacteria's population is tripling every 9 minutes.

Therefore, we can model the population of bacteria using the formula \(P_{(t)} = P_0 3^t/9\), where P0 is the initial population. Since we know that \(P_0 = 5605\),

we have \(P_{(t)} = 5605 * 3^t/9\).

To find the population of bacteria 8 minutes from now, we can use the secant line to approximate the population.

The secant line is the line that intersects the curve at two points, P(0) and P(9), where

P(0) = 5605 and P(9) = 16815.

To find the slope of the secant line, we use the formula:

(P(9) - P(0)) / (9 - 0) = (16815 - 5605) / 9

= 1180.

Therefore, the equation of the secant line is given by:

y = 1180x + 5605.

Substituting x = 8 into the equation of the secant line, we get:

y = 1180(8) + 5605

= 14965.

Therefore, the population of bacteria 8 minutes from now is approximately 14965 organisms

We can find the population of bacteria 8 minutes from now by using the secant line to approximate the population. We know that the population of bacteria is tripling every 9 minutes, so we can model it using the formula P(t) = P0 3^t/9, where P0 is the initial population. Using the secant line, we can approximate the population of bacteria 8 minutes from now to be approximately 14965 organisms.

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Answer:

Graph A

Step-by-step explanation:

Answer:

A.)

Step-by-step explanation:

since here using for example just one foot is (1,4) add another (2,8) since you are doubleing the price. and the rest are just going in weird derections.

Answer:

b is the answer ig.........

Answer:

10

Step-by-step explanation

50 divided by 10 is 5 so

50 times 2 which is 100 divided by 10 is 10

If 5.625 tins of paint are used out of 6 tins bought, the amount wasted can be calculated by subtracting the used amount from the total amount bought. Therefore, approximately 0.375 tins of paint are wasted.

If 5.625 tins of paint are used and 6 tins were bought, we can find the amount wasted by subtracting the used amount from the total amount bought.

The amount wasted can be calculated as follows:

Wasted amount = Total amount bought - Used amount

Wasted amount = 6 tins - 5.625 tins

To subtract the decimal values, we need to convert both amounts to the same denominator. Since there are four decimal places in 5.625, we can multiply both numbers by 10000 to eliminate the decimals:

Wasted amount = (6 * 10000) - (5.625 * 10000)

Simplifying the expression, we get:

Wasted amount = 60000 - 5625

Wasted amount = 54375

Converting the wasted amount back to the original decimal form, we have:

Wasted amount = 54375 / 10000

Wasted amount ≈ 0.375 tins

Therefore, approximately 0.375 tins of paint are wasted.

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The required slopes are:

(a) slope = 4

(b) slope = 6/7

(c) slope =  -3

(d) slope = 4

(e) slope = -5/2

We know that,

When a line passing through (x₁, y₁) and (x₂, y₂)

Then  the slope of the line be,

slope (m) = (y₂ - y₁) / (x₂ - x₁)

Using this formula, calculate the slope for each given points

a. (9, 10) and (7, 2)

⇒ slope (m) = (2 - 10) / (7 - 9)

                    = -8/-2 = 4

So, the slope is 4.

b. (-8, -11) and (-1, -5)

⇒ slope (m) = (-5 - (-11)) / (-1 - (-8))

                    = 6/7

So, the slope is 6/7.

c. (5, -6) and (2, 3)

⇒ slope (m) = (3 - (-6)) / (2 - 5)

                    = 9/-3

                    = -3

So, the slope is -3.

d. (6, 3) and (5, -1)

⇒ slope (m) = (-1 - 3) / (5 - 6)

                    = -4/-1

                    = 4

So, the slope is 4.

e. (4, 7) and (6, 2)

⇒ slope (m) = (2 - 7) / (6 - 4)

                    = -5/2

So, the slope is -5/2.

Therefore, the slope of the line that joins (-8, -11) and (-1, -5) is 6/7.

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Answer:

the answer is the cheese soup has a good change of being picked but not as good as the chicken soup there would so 3:2 to 2. so if they picked the cheese soup the first time then there is not a good change of the cheese souo to be picked again i hope that helps if not let me know

Answer:

5 units

Step-by-step explanation:

Annie is located at (6,-20) and Barbara is located at (1, 14) and they meet at a point equidistant to their current locations.

This means that they have to meet at the midpoint between their two locations. Let the coordinate of the midpoint be (x,y) hence:

\(x=\frac{x_1+x_2}{2}=\frac{6+1}{2} =\frac{7}{2}\)

\(y=\frac{y_1+y_2}{2}=\frac{-20+14}{2} =-3\)

The point at which they met is at (7/2, -3). Charlie location is at (7/2, 2). Hence the distance upward that they have to move = 2 - (-3) = 5 units

They have to move 5 units upwards

y = 2x + 4 is the equation of the line that connects the coordinates (0, 4) and (1, 6).

The points that the line passes through are (0, 4) and (1, 6). The equation of a line can be found by using the point-slope form:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is one of the line's points.

Then, we may determine the line's slope:

\(m = \frac{(y2 - y1)}{(x2 - x1)}\)

where (x1, y1) = (0, 4) and (x2, y2) = (1, 6)

\(m = (6 - 4) / (1 - 0) = 2\)

Now we can use the point-slope form with one of the points, say (0, 4):

y - 4 = 2(x - 0)

Simplifying, we get:

y - 4 = 2x

Adding x to both sides, we get:

y = 2x + 4

So the equation of the line that passes through the points (0, 4) and (1, 6) is y = 2x + 4.

The complete question is"=

Find the equation of the line. Use exact numbers. y=y=y, equals x+x+x, plus

A coordinate plane. The x- and y-axes each scale by one. A graph of a line goes through the points zero, four and one, six.

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Answer:

2

Step-by-step explanation:

The probability that the number of job applicants late for interviews is between 5 and 9 (inclusive) needs further information to be determined accurately.

To calculate the probability, we need to know the total number of job applicants and the distribution of lateness among them. Without this data, it is not possible to determine the exact probability of having a specific range of late applicants between 5 and 9, inclusive.

To accurately assess the probability, we would need information on the total number of applicants, the historical frequency of lateness, or the specific distribution of lateness across the range of interest. With this data, statistical methods such as probability distributions or empirical data analysis could be utilized to calculate the desired probability.

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What you need to know:

product - the answer you get when multiplying

numerator - the top number in a fraction

denominator - the bottom number in a fraction

improper fraction - a fraction where the numerator is a bigger number than the denominator

So let's start off with an example:

2\(\frac{1}{4}\) - 1\(\frac{2}{3}\)

Because these are mixed fractions, we'll change them to improper fractions. We'll start with the first mixed fraction.

Step 1:

Multiply the whole number with the denominator of the fraction.

2\(\frac{1}{4}\)   In this case, we'll be multiplying 2 and 4, which is 8.

Step 2:

Add the product with the numerator.

8 + 1 = 9

Step 3:

Place the number 9 into the numerator, while still keeping the denominator the same:

\(\frac{9}{4}\)

Step 4:

Repeat steps one through three for the second mixed fraction.

Now you have this:

\(\frac{9}{4}\) - \(\frac{5}{3}\)

Step 5:

Find the least common multiple of the two fractions.

(Let me know if you don't know how to do this).

Your result should be:

\(\frac{27}{12} - \frac{20}{12}\)

Step 6:

Subtract across, while still keeping the denominator the same:

\(\frac{27}{12} - \frac{20}{12}\) = \(\frac{7}{12}\)

(Only do if needed) Step 7:

Simplify the fraction

Hope this helps, & if you have any questions, let me know!

Also, this is how I was taught to do it, and I'm not sure if there's a different way to solve it, but here's my work! :D

Answer:

  rewrite them with a common denominator

Step-by-step explanation:

We assume your "mixed fraction" is an integer together with a fraction, such as 1 1/2.

There are at least a couple of ways to do this.

1. Perform the arithmetic separately on the integers and fractions, then combine results.

2. Convert both to improper fractions and do the subtraction. Then convert back to a mixed fraction.

__

Either way, fractions can only be added or subtracted if they have a common denominator. That can be achieved a couple of ways.

a) use the least common multiple (LCM) of the denominators as the common denominator. The LCM of the denominators is usually called the "least common denominator" (LCD). Example: 1/4 + 1/6 = 3/12 + 2/12 = 5/12

b) use the product of the denominators as the common denominator. Example: 1/4 +1/6 = 6/24 +4/24 = 10/24

Using the LCD tends to reduce the need for reducing the resulting fraction, because at least one common factor has already been removed. In the above examples, the fraction 10/24 still has factors of 2 that can be removed to reduce the fraction: 10/24 = (5·2)/(12·2) = 5/12

__

In general the difference of fractions can be found with a formula:

  \(\dfrac{a}{b}-\dfrac{c}{d}=\dfrac{ad-bc}{bd}\)

You will notice this has a denominator that is the product of denominators, so there is a good chance the result will have to be reduced to lowest terms. This can be quick and easy if you don't want to spend time trying to find the least common denominator.

_____

Here are a couple of examples:

  (16 3/10) -(5 1/6) = (16 -5) +(3/10 -1/6) = 11 +(18 -10)/(10·6) = 11 8/60 = 11 2/15 (using methods 1 and b)

  (16 3/10) -(5 1/6) = 163/10 -31/6 = 489/30 -155/30 = 334/30 = 167/15 = 11 2/15 (using methods 2 and a; note we had to reduce the final fraction even though we used the LCD)

In the above examples, there was no "borrow" due to the difference of the fractional parts. Here's an example where the difference of fractions affects the integer:

  (16 1/6) -(5 3/10) = (16 -5) +(1/6 -3/10) = 11 +(10 -18)/60 = 11 -8/60

  = 11 -2/15 = 10 13/15 (again, using methods 1 and b)

_____

Additional comments

You may have guessed that I prefer methods 1 and b, simply because they are quick and easy and tend to eliminate sources of error. As with all things arithmetic, it is very helpful to have a good command of multiplication tables, and a reasonable understanding of divisibility rules.

A suitable calculator can check your work for you. Mine makes mixed-number arithmetic very simple. Many graphing calculators have methods for entering and displaying mixed numbers. (I've found one that tries to express any decimal as a fraction, sometimes getting it very wrong. So, be careful if you have one of those.)

\(\rightarrow\sf \sqrt{27} + 7 \sqrt{5} : \sqrt{2 } \\ = \sf \sqrt{9(3)} + 7 \sqrt{5} : \sqrt{2 } \\ = \sf \sqrt{ {3}^{2} } \times 3 + 7 \sqrt{5} : \sqrt{2} \\ \rightarrow \large\boxed{\sf{\red{3 \sqrt{3} + 7 \sqrt{5} : \sqrt{2} }}}\)

\(\large\boxed{\sf{\red{3 \sqrt{3} + 7 \sqrt{5} : \sqrt{2} }}}\)

\(\color{red}{==========================}\)

✍︎ꕥᴍᴀᴛʜᴅᴇᴍᴏɴǫᴜᴇᴇɴꕥ

✍︎ꕥᴄᴀʀʀʏᴏɴʟᴇᴀʀɴɪɴɢꕥ

ꕥᴀʀᴀꕥ

Answer:

16

Step-by-step explanation:

x+6

In this step instead of puting x you relace it with 10 which is what x equals

10+6

16

Answer: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

Step-by-step explanation: