How do you write 12,800 in scientific notation?

(a) The cost to produce 40 backpacks is $120. (b) The vertex is (25, 150) and it represents the minimum cost point for backpack production. (c) The school can get up to approximately 207 backpacks with a budget of $3000.

(a) To find the cost to produce 40 backpacks, we substitute b = 40 into the cost function C(b):

C(40) = 2/5(40)² - 20(40) + 400

Calculating the expression:

C(40) = 2/5(1600) - 800 + 400

C(40) = 320 - 800 + 400

C(40) = 120

Therefore, the cost to produce 40 backpacks is $120.

(b) To find the vertex of the function C(b), we need to determine the values of b and C that correspond to the vertex. The vertex of a quadratic function in the form C(b) = 2/5b² - 20b + 400 can be found using the formula: b = -b₀/2a, where b₀ is the coefficient of the linear term (-20) and a is the coefficient of the quadratic term (2/5).

Using the formula:

b = -(-20) / (2 * 2/5)

b = 20 / (4/5)

b = 100/4

b = 25

To find the corresponding cost C at the vertex, we substitute b = 25 into the cost function C(b):

C(25) = 2/5(25)² - 20(25) + 400

Calculating the expression:

C(25) = 2/5(625) - 500 + 400

C(25) = 250 - 500 + 400

C(25) = 150

Therefore, the vertex is (b, C) = (25, 150). The vertex represents the minimum cost point, which in this case, is the point where the production cost is minimized. The backpack production cost is minimized when producing 25 backpacks, and the minimum cost is $150.

(c) To find the number of backpacks a school can get with a budget of $3000, we need to solve the cost function C(b) = 3000 for b:

2/5b² - 20b + 400 = 3000

Subtracting 3000 from both sides:

2/5b² - 20b + 400 - 3000 = 0

2/5b² - 20b - 2600 = 0

Since this is a quadratic equation, we can solve it using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

b = (-(-20) ± √((-20)² - 4(2/5)(-2600))) / (2 * 2/5)

b = (20 ± √(400 + 20800)) / (4/5)

b = (20 ± √21200) / (4/5)

b ≈ (20 ± 145.67) / (4/5)

Calculating the approximate values:

b ≈ (20 + 145.67) / (4/5) ≈ 165.67 / (4/5) ≈ 207.09

b ≈ (20 - 145.67) / (4/5) ≈ -125.67 / (4/5) ≈ -157.09

Since the number of backpacks cannot be negative, we consider only the positive value:

b ≈ 207.09

According to the model, the school can get up to approximately 207 backpacks with a budget of $3000.

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The solution range for the given function inequality is x > 25.

A function is a relation between a dependent and independent variable. Mathematically, we can write -

y = f(x) = ax + b

Given is the function inequality as -

- 3(2x - 5) < 5(2 - x)

The given function inequality is -

- 3(2x - 5) < 5(2 - x)

- 6x - 15 < 10 - 5x

- 6x + 5x < 10 + 15

- x < 25

x > 25

Therefore, the solution range for the given function inequality is x > 25.

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An equation that mode the relationship between thee two variable is y=2x+3 .

Let x represent the number of 6-month period worked

Let y represent the total number of paid vacation day

According to the question,

When he started work, he was given three paid day of vacation. For each six-month period he pay at the job, his vacation is increased by two day.

Each year has 2 six-month periods. After 4.4 years Roberto will have worked 8.8 six-month periods. He will have been given vacation days for each of the 8 whole working periods he has completed. x=8 y=2*8+3 y=19

An equation that mode the relationship between thee two variable is y=2x+3 (Total vacation time equals 2 days times x plus the 3 days he was given at the start).

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The estimated loss in income from operations if solvent production were to be temporarily suspended for May would depend on the number of operations that utilize solvent production, the demand for the product, the loss of productivity, and any additional costs associated with the suspension.

For example, if the operations are production-intensive, a suspension would lead to a decrease in output and sales, which would lead to a decrease in income. Additionally, the costs associated with the suspension, such as additional manpower and resources needed to resume production and any repairs, could lead to a further decrease in income.

Overall, the exact amount of the estimated loss in income is difficult to determine without further information. However, it is safe to assume that any suspension of solvent production will lead to a decrease in income.

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Answer:

13) x=n-11

15) x=3*10

Step-by-step explanation:

I used x as the variable. The questions are pretty straightforward. They are asking you to put the terms in the description on the right side of the equation. The questions = x. That was probably confusing, but it is correct. I hope this helped!

Product of 3 and 10 and12

Answer:

-16450

Step-by-step explanation:

Remove parentheses:

=4.7 * 10^3(2.35 * 10 - 27)

Multiply the numbers: 2.35 * 10 = 23.5

=10^3 * 4.7(23.5 - 27)

Subtract the numbers: 23.5 - 27 = -3.5

= 10^3 (-3.5) * 4.7

Remove parentheses:

= -4.7 * 10^3 * 3.5

Multiply the numbers: 4.7 * 3.5 = 16.45

= -10^3 * 16.45

Multiply the numbers: 16.45 * 1000 = 16450

= -16450

The cost of walking this guest is $190.

The cost of walking the guest can be calculated by adding up the expenses incurred by the hotel.

The guest was walked to another hotel that charged a room rate of $150. Therefore, the hotel incurred a cost of $150 for the room.

In addition to the room cost, the hotel also paid for the guest's Uber ride to the new hotel, which was $15.

Furthermore, the overbooked hotel gave the guest a gift card worth $25. Although the gift card does not directly represent an expense, it can be considered as an opportunity cost for the hotel, as they could have used that money to cover other costs.

Therefore, the total cost incurred by the hotel for walking the guest is:

$150 (room cost) + $15 (Uber cost) + $25 (gift card cost) = $190

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Let the original price = x

He paid 70% of the original price so 0.70x

This equaled $14:

SO the equation is 0.70x = 14

Solve for x by dividing both sides by 0.70:

x = 14/0.70

x = 20

The original price was $20

Answer:

Let the original price be x.

Joe paid $14.00 for a board game which is the 70% of the original price.

Therefore, the original price is

\(70\% \: of \: x = 14 \\ \frac{70}{100}x = 14 \\ x = \frac{14 \times 100}{70} \\ \boxed{ x = 20}\)

Answer:

McDonald’s Quarter Pounders = 67 mg of cholesterol

Burger King Whoppers = 87 of cholesterol

Step-by-step explanation:

McDonald’s Quarter Pounders = m

Burger King Whoppers = b

2m + 3b = 395

3m + 1b = 288

3m + b = 288

b = -3m + 288

2m + 3b = 395

2m + 3(-3m + 288) = 395

2m - 9m + 864 = 395

- 7m + 864 = 395

- 7m/7 = -469/7

-m = -67

-m/-1 = -67/-1

m = 67

2m + 3b = 395

2(67) + 3b = 395

134 + 3b = 395

3b = 395 - 134

3b = 261

3b/3 = 261/3

b = 87

Check: m = 67; b = 87

2m + 3b = 395

3m + 1b = 288

2m + 3b = 395

2(67) + 3(87) = 395

134 + 261 = 395

395 = 395

3m + 1b = 288

3(67) + 1(87) = 288

201 + 87 = 288

288 = 288

(Probs too late but welp :p)

The graph of the parent quadratic function is the bottom graph.

The parent quadratic function is:

f(x) = x^2

The graph of this is known as a parabola, this is a curve with an axis of symmetry at line x = 0 (or just the y-axis)

With that in mind, the only option that shows a parabola is the bottom option (Which shows a parabola that passes through (0, 0) with both arms opening upwards).

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Answer:

1080

Step-by-step explanation:

$900.00 per year at 5% is 45.00

The scale factor of the dilation of figure A to figure B is 3/2 based on the given parameters

Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.

From the figure, we have the following corresponding sides in figure A and figure B

The scale factor of the dilation of figure A to figure B is calculated using the following scale factor formula

Scale factor = Figure B / Figure A

Substitute the known values in the above equation

Scale factor = 12/8

Divide 12 by 4 and then divide 8 by 4

Scale factor = 3/2

Based on the given parameters, the scale factor of the dilation of figure A to figure B is 3/2

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A distribution is a way of displaying data, consisting of three primary components: shape, center, and spread. The shape is the overall pattern of the distribution, while the center is the point where the distribution is balanced. The spread is the range of values of the data, often measured by the standard deviation or the interquartile range (IQR). The distribution can be visualized through graphs like histograms, box plots, or scatter plots.

A brief description of a distribution should include its shape, center, and spread. The spread is the term that should be included in the blank space.A distribution can be described as a way of displaying data. It gives us an idea about how the data are spread out.

The three primary components of any distribution are the shape, center, and spread. Shape refers to the overall pattern of the distribution. It tells us whether the data are symmetric or skewed. The symmetry means that the left half of the distribution is a mirror image of the right half, whereas a skewed distribution is not symmetrical. The tail of a distribution describes the spread of a skewed distribution. It refers to the parts of the distribution that extend out from the center of the graph.The center refers to the point where the distribution is balanced. In symmetric distributions, the center is the same as the mean and median. However, in a skewed distribution, the mean and median differ from each other.

The spread refers to the range of values of the data. It tells us how much the data are scattered or spread out. A small spread indicates that the data points are close to each other, while a large spread suggests that the data points are far from each other. It is often measured by the standard deviation or the interquartile range (IQR).The distribution of data can be visualized through different graphs like histograms, box plots, or scatter plots.

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Answer:

23 marbles

Step-by-step explanation:

Number of children = 10

Number of marbles = 180

Since Betsy gets the most and no 2 children gets the same number of marbles

The least number of marbles Betsy could get will be x ; with the other 9 children receiving 1 less each

That is :

Betsy = x

9th child = x - 1

8th child = x - 2,... 1st child = x - 9

Hence,

(x + x - 1 + x - 2 + x - 3 + x - 4 + x - 5 + x - 6 + x - 7 + x - 8 + x - 9) = 180

10x - 45 = 180

10x = 180 + 45

x = 225 / 10

x = 22.5

x = 23

Hence, the least Betsy could get is 23 marbles

Answer:

A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

Answer:

A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

Step-by-step explanation:

Answer:

2f + 2e

Step-by-step explanation:

4f -2f = 2f

3e - 1e = 2e

2f + 2e

Answer:

23 cats

Step-by-step explanation:

So the ratio is basically saying that for every 4 dogs at the store there is one more cat, or 5 cats. 16 dogs there would be 20 cats. 18 dogs there would be approximately 23 cats if you would round up.

The proababilities are: i) P(Aᶜ) = 0.6, ii) P(Bᶜ) = 0.4

iii) Probability that exactly one of the events A, B occurs = 0.7

Let A and B be any two disjoint events such that P(A) = 0.4 and P(A ∪ B) = 0.7. We need to find the following probabilities:

i) P(Aᶜ): This is the probability of the complement of event A, which represents the probability of not A occurring. Since A and B are disjoint, Aᶜ and B are mutually exclusive and their union covers the entire sample space.

Therefore, P(Aᶜ) = P(B) = 1 - P(A) = 1 - 0.4 = 0.6.

ii) P(Bᶜ): This is the probability of the complement of event B, which represents the probability of not B occurring. Since A and B are disjoint, Bᶜ and A are mutually exclusive and their union covers the entire sample space.

Therefore, P(Bᶜ) = P(A) = 0.4.

iii) Probability that exactly one of the events A, B occurs: This can be calculated by subtracting the probability of both events occurring (P(A ∩ B)) from the probability of their union (P(A ∪ B)).

Since A and B are disjoint, P(A ∩ B) = 0.

Therefore, the probability that exactly one of the events A, B occurs is P(A ∪ B) - P(A ∩ B) = P(A ∪ B) = 0.7.

To summarize:

i) P(Aᶜ) = 0.6

ii) P(Bᶜ) = 0.4

iii) Probability that exactly one of the events A, B occurs = 0.7

Note: The provided values of P(A), P(A ∪ B), and the disjoint nature of A and B are used to derive the above probabilities.

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The equivalent expression is 192ab + 288a

From the question, we have the following parameters that can be used in our computation:

3 ·· 4 a(16b 1 24

Express properly

So, we have

3 ·· 4 a(16b + 24)

Open the bracket

12a(16b + 24)

This gvves

192ab + 288a

Hence, the exrpession is 192ab + 288a

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In ANOVA, if the observed F equals or exceeds the critical F, the experimental outcome is considered statistically significant.

Analysis of Variance (ANOVA) is a statistical method used to compare the means of two or more groups. The F-statistic is the test statistic used in ANOVA. When conducting an ANOVA test, we compare the observed F-value to the critical F-value to determine the significance of the results.

Step 1: Calculate the observed F-value using the given data.

Step 2: Determine the critical F-value using the F-distribution table, taking into account the degrees of freedom and the desired significance level (usually set at 0.05).

Step 3: Compare the observed F-value to the critical F-value.

If the observed F-value equals or exceeds the critical F-value, it indicates that there is a statistically significant difference between the group means, and we reject the null hypothesis. In other words, the experimental outcome suggests that at least one of the group means is significantly different from the others.

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Answer:

D is the correct answer i think

Step-by-step explanation:

Domain of the function is option (D) {2, 4, 6, 8}

The domain of a function is the set of inputs accepted by the function.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

From the given table,

Domain of the function is {2, 4, 6, 8}

Because the domain of a function is the set of inputs accepted by the function.

Hence, Domain of the function is option (D) {2, 4, 6, 8}

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a) The passage is a piece of written text that provides information about Makayla's experience during an Easter egg hunt. (option c)

(b) It also highlights how knowledge gained in the classroom can be applied to everyday life.

At the beginning of the passage, Makayla is getting ready to go on an Easter egg hunt. This is evident from the line "Makayla was getting ready for the Easter egg hunt at the park." Easter egg hunts are a popular tradition in many parts of the world, where children search for hidden eggs that are often filled with candy or small toys.

Hence the correct option is (c).

Throughout the story, Makayla remembers information that Mrs. Narula taught in class. Mrs. Narula is Makayla's science teacher, and the information she taught in class is about the process of photosynthesis. Photosynthesis is the process by which plants convert sunlight, water, and carbon dioxide into oxygen and sugar.

Makayla remembers this information as she observes the trees and plants in the park during the Easter egg hunt. She notes that the plants are producing oxygen through photosynthesis and that this process is essential for the survival of all living beings.

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The slope of the line is the ratio of the rise to the run, or rise divided by the run. Yes i can agree with both of their statements.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

As we know that the slope of a line will be always same on a given line. If slope triangle A has slope 6/4. Then triangle B will be also have the same slope.

As both triangles are connected to the same line. These two triangles A and B  will have same slopes.

Mai uses Triangle A and says the slope of this line is 6/4.

If we convert fraction 6/4 to decimal we get 1.5 value.

So i agree with both of their statements.

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Answer: -18

Step-by-step explanation:

3 x -6 = 18

Answer:

3(6-) = 18-

Step-by-step explanation:

Answer:

J plus 47 = 55

If you need to find J

The value of J is

J=55-47

J=8

Step-by-step explanation

There are 35 unique ways to select 4 A students from 7 A students. This can be calculated using the formula: 7C4 = 7! / (4! * (7 - 4)!)

This is a permutation and combination problem that involves finding the number of unique arrangements possible for 4 students out of 7 students who have received grades A.

The formula for permutation of n items taken r at a time is given by P(n,r) = n! / (n-r)! where n is the total number of items and r is the number of items taken at a time.

In this case, we have to find P(7,4) = 7! / (7-4)! = 5040/3! = 840. This means there are 840 different ways in which 4 A students can be uniquely selected from a class of 7 students who received grades A.

This concept is important in many areas of mathematics and science, particularly in the field of statistics where it is used in hypothesis testing, estimation and prediction.

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Andrew is correct because 60 is the highest whole number that can round to 60. Any number higher than 60 will round up to a higher number. For example, 61 will round up to 70, and 62 will round up to 70. Therefore, 60 is the greatest whole number that rounds to 60.

The highest whole number is infinity, as there is no limit to how high a number can be. Whole numbers are all the numbers that are greater than or equal to 0, including 0 itself. The highest whole number is therefore infinity, as this is the highest possible number.

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d/dx sin³x²

3 (sinx²)² d/dx sinx²

3 (sin x²)² *cosx²d/dx x²

3 (sin x²)² *cosx²*2x

6x(sin x²)² cosx²