Yesterday, the snow was 2 feet deep in front of Archie’s house. Today, the snow depth dropped to 1.6 feet because the day is so warm. What is the percent change in the depth of the snow?
The percent change in the depth of snow from yesterday to today is
%

Answer:

12

Step-by-step explanation:

Answer:

1) 12 boxes

2) 3, 6, 12

3) 12

4) 110 degrees

Step-by-step explanation:

1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.

Length: 4 boxes

Width: 3 boxes

4 x 3 = 12

12 boxes

2)

10% of 30 is 0.1 times 30.

0.1 x 30 = 30/10 = 3

20% of 30 is 0.2 times 20.

0.2 x 30 = 30/5 = 6

40% of 30 is 0.4 times 20.

0.4 x 30 = 30/2.5 = 12

3) Count the cubes. Reminder there are 2 boxes you cannot see.

Top Layer: 2

Middle Layer: 4

Back Bottom Layer: 4

Front Bottom Layer: 2

2 + 4 + 4 + 2 = 12

4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.

180/18 (The angle of each section)

10

11 Sections

10 x 11 = 110

Overhead allocation based on one rate Plant wide rate

Overhead allocation based on at least two rates Departmental rate

Overhead allocation using activities that drive costs          Activity based costing

In the given question, we have to Select from the three alternative methods of overhead allocation in the drop down list so that it matches with the provided feature.

Item #1 Plant Wide rate

Item #2 Departmental rate

Item #3 Activity based costing

Plant Wide rate: Whenever a corporation assigns all of its production overhead costs to products or cost items, it does so using a single overhead rate known as the plant wide overhead rate. In smaller companies with predictable cost structures, it is most frequently used.

Departmental rate: The overhead rate per unit of activity that is charged by a certain department is known as a departmental rate. Only the production departments charge this rate. Administrative departments don't have departmental rates because their expenses are paid as they are incurred.

Activity based costing: Activity based costing(ABC) is a mechanism for allocating overhead and indirect costs to goods and services, such as salaries and utility prices. The ABC approach of cost accounting is based on activities, which are seen as any occasion, unit of labour, or assignment with a particular goals.

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Using the mean and data given, the 95% confidence interval for the data is approximately (44.25, 59.35).

To calculate the 95% confidence interval for the given data, we can use the following formula:

Confidence interval = mean ± (critical value * standard deviation / sqrt(n))

where:

First, let's calculate the mean, standard deviation, and the critical value.

Mean (μ) = (56 + 24 + 26 + 45 + 64 + 79 + 38 + 40 + 69 + 74 + 34 + 54 + 21 + 74 + 62 + 76 + 59 + 59 + 47 + 66 + 66 + 52 + 53 + 59 + 38 + 30 + 48 + 44 + 23 + 46) / 30 = 51.8

Standard Deviation (σ) = √[(∑(x - μ)²) / (n - 1)]

= √[(∑(56 - 51.8)² + (24 - 51.8)² + ... + (23 - 51.8)² + (46 - 51.8)²) / (30 - 1)]

≈ 17.04

To determine the critical value, we need to consider the sample size and confidence level. Since the sample size is 30 and we want a 95% confidence level, we can use a t-distribution with 29 degrees of freedom. Looking up the critical value in a t-table or using a calculator, we find the value to be approximately 2.045.

Now, let's calculate the confidence interval:

Confidence interval = 51.8 ± (2.045 * 17.04 / √30)

≈ 51.8 ± 7.55

Therefore, the 95% confidence interval for the data is approximately (44.25, 59.35).

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Answer:

Therefore, 56 : 24 simplifies to 7 : 3.

Step-by-step explanation:

To simplify the expression 56 : 24, we can divide both numbers by their highest common factor.

The prime factorization of 56 is 2 x 2 x 2 x 7, and the prime factorization of 24 is 2 x 2 x 2 x 3.

The highest common factor (HCF) of 56 and 24 is 8, which is 2 x 2 x 2.

Dividing 56 and 24 by 8, we get:

56 ÷ 8 = 7

24 ÷ 8 = 3

Therefore, 56 : 24 simplifies to 7 : 3.

288π cm³

================

volume of sphere: 4/3 * π * radius³

⇒ 4/3 * π * (6)³

⇒ 4/3 * 216 * π

⇒ 288π

To answer this question, we need to know the median and upper quartile of the data set. Once we have these values, we can determine what percentage of the data falls to the right of the median and to the left of the upper quartile.
Let's say the median of the data set is 50 and the upper quartile is 75. To find the percentage of measurements to the right of the median, we need to look at the data values that are greater than 50 and divide that number by the total number of measurements. Let's say there are 40 data values greater than 50 and a total of 100 measurements.

Then, the percentage of measurements to the right of the median would be:

(40/100) x 100% = 40%

To find the percentage of measurements to the left of the upper quartile, we need to look at the data values that are less than or equal to 75 and divide that number by the total number of measurements. Let's say there are 60 data values less than or equal to 75 and a total of 100 measurements. Then, the percentage of measurements to the left of the upper quartile would be:

(60/100) x 100% = 60%


Your answer:
1. 40% of the measurements lie to the right of the median.
2. 60% of the measurements lie to the left of the upper quartile (Q3).

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The perimeter of the right triangle in the given image is 12 cm, and the area is 6 cm².

The right-angled triangle with base AB = 4 cm and width = 3 cm has the following main properties:

Base AB = 4 cm

Height (or width) BC = 3 cm

So, the Hypotenuse of the triangle is:

AC² = AB² + BC²

AC² = 4² + 3²

AC² = 16 + 9

AC² = 25

AC = \(\sqrt{25}\)

AC = 5 cm

To calculate the perimeter of the triangle, we simply add the lengths of all three sides together:

Perimeter = AB + BC + AC

Perimeter = 4 cm + 3 cm + 5 cm

Perimeter = 12 cm

So the perimeter of the triangle is 12 cm.

To calculate the area of the triangle, we use the formula for the area of a triangle, which is given by:

\(Area = \frac{1}{2} (base) (height)\)

In this case, the base is AB and the height is BC. Therefore, we have:

\(Area = \frac{1}{2} (AB) (BC)\)

\(Area = \frac{1}{2} (4cm) (3 cm)\)

\(Area = 6cm^{2}\)

So the area of the triangle is 6 cm²

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Answer:

I believe D is the correct answer

Answer:

The answer is 210°.

Step-by-step explanation:

Given that ∠BOE = 130° and ∠COB is 80°. So in order to find ∠CBE, you have to add up together :

∠CBE = ∠BOE + ∠COB

∠CBE = 130° + 80°

∠CBE = 210°

(Correct me if I am wrong)

please see the attached picture...

Hope it helps...

Good luck on your assignment...

Answer:

96.00 increased by 86% is 178.56

Step-by-step explanation:

The minimum value of a function is the place where the graph has a vertex at its lowest point. Hence, the minimum value is at \((3,30)\).

What are the minimum and maximum values?

The minimum value of a function is the place where the graph has a vertex at its lowest point.

A point at which a function's value is greatest. If the value is greater than or equal to all other function values, it is an absolute maximum.

Here the given equation is

\(-3x^{2}+18x+3\)

The minimum value occurs at \(x=-\frac{b}{2a} ...........(1)\)

If \(a\) is positive, then the minimum value of the function is

\(f(-\frac{b}{2a})\)

Here, \((f_m_i_n)(x)=ax^{2}+bx+c\)

Substitute the values in the equation \((1)\)

\(x=-\frac{18}{2(-3)}\\x=-\frac{18}{-6}\\\\x=3\)

Now, evaluate \(f(3)\)

Replace the variable \(x\) with the \(-3\)

So,

\(f(3)=-3(3)^{2}+18(3)+3\\\\f(3)=-27+54+3\\\\f(3)=30\)

Now, by using the coordinates \((x,y)=(3,30)\), find out the minimum value.

And the graph is of the form

Hence, the minimum value is at \((3,30)\).

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Answer:

Volume of prism = Area of base× height

= l×b×h

=4.8×23×0.9

= 99.36 m³

All options are incorrect : )

Answer:

The answer is B

Step-by-step explanation:

Im 3 weeks late lol sorry. I took the quiz.

Yes it is correct that the expected value of a random variable can be interpreted as a long-run average.

The expected value of a random variable is a concept used in probability theory and statistics. It is a way to summarize the average behavior or central tendency of the random variable.

To understand why the expected value represents the average value that the random variable would take in the long run, consider a simple example. Let's say we have a fair six-sided die, and we want to find the expected value of the outcomes when rolling the die.

The possible outcomes when rolling the die are numbers from 1 to 6, each with a probability of 1/6. The expected value is calculated by multiplying each outcome by its corresponding probability and summing them up.

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To use Holt's method with smoothing constants of 0.3 for alpha and 0.6 for gamma, we first need to calculate the initial values for the level and slope.

Let L0 be the initial level and B0 be the initial slope. We can estimate these using the following equations:

L0 = y1

B0 = y2 - y1

where y1 and y2 are the first two observed values in the time series.

Once we have the initial values, we can use the following recursive equations to calculate the level and slope at each time period t:

Lt = alpha * yt + (1 - alpha) * (Lt-1 + Bt-1)
Bt = gamma * (Lt - Lt-1) + (1 - gamma) * Bt-1

where yt is the observed value at time t.

Using these equations and the given smoothing constants, we can find the equation of the forecast line as:

Ft+1 = Lt + Bt

and the mean squared error (MSE) as:

MSE = (1 / n) * sum((yt - Ft)^2)

where n is the number of observed values.

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the largest positive integer n\(\leq\)112 for which there is a unique integer k

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

Given inequality is

\(\frac{15}{8} < \frac{n+k}{k} < \frac{13}{7}\)

\(\frac{8}{15} < \frac{n}{n+k} < \frac{7}{13}\)

\(n\frac{6}{7} < k < n\frac{7}{8}\)

\(n\frac{7}{8}-n\frac{6}{7}\) > 2

n\(\leq\)112

Hence, the largest positive integer n\(\leq\)112 for which there is a unique integer k

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Answer:

• 85% protein supplement: 480 pounds

• 60% protein ration: 720 pounds

Explanation:

Let the number of pounds of 85% protein supplement required = x

The farmer wants to make 1200 pounds (of a high-grade 70% protein ration).

Therefore, the number of pounds of 60% protein ration required = (1200-x) lbs

First, we add the constituents we are mixing together.

The final protein ration we want to obtain:

Equate both:

Then solve the equation for x.

The number of pounds of the 85% protein supplement he should use is 480 pounds.

The number of pounds of the 60% protein ration he should use is 720 pounds.

Answer:

Exterior alternate angles

x=5

Step-by-step explanation:

The relationship between these 2 angles is exterior alternate angles, which says that the alternating exterior angles that are made by a parallel line and a transversal are equal.

To solve for x, we can set up an equation:

24x=120

x=5

1. The inequality that models this situation is given as follows: 28 + 8x ≤ 80.

2. The solution is x ≤ 6. graphed on the image given at the end of the answer.

3. The meaning is that he can buy at most 6 t-shirts.

4. In this case, the number of t-shirts that he can buy is of at most 3.

The maximum amount that he can spend is of:

$80.

The equation that models his spending is given as follows:

28 + 8x.

As:

Then the inequality is given as follows:

28 + 8x ≤ 80.

The solution is then obtained as follows:

8x ≤ 52

x ≤ 52/8

x ≤ 6.5.

As the number of t-shirts is a countable amount, the solution can also be given as:

x ≤ 6.

Meaning that he can buy at most 6 t-shirts.

Considering the sunglasses, the inequality will be of:

8x ≤ 52 - 21

x ≤ 31/8

x ≤ 3.875.

Meaning that he can then buy at most 3 t-shirts.

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In the given case, people staying away from the city centre are not being irrational but, their opportunity cost of commuting must be lower

Opportunity cost is the price of forgone options or the worth of the next best option that must be given up in order to pursue a certain choice. The opportunity cost of commuting might encompass not just the time and money spent on transportation, but also the advantages and disadvantages of living in various places. In the given case, living close to the city centre, could make it simpler to access social events, entertainment, and cultural activities, while relocating further away might provide you access to more space, privacy, and natural surroundings.

As a result, depending on their personal and professional ambitions, financial limitations and other considerations, different people may have various preferences and trade-offs when deciding where to live and how much to commute. Some people might put their commute time and cost reduction first, while others might put other aspects of their lifestyle and surroundings first.

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Answer:

The equation is

\(y = 17x + 4\)

The volume of the solid generated by revolving the region bounded by the given curve and lines about the x-axis is V = 8π/3

The volume of a solid, given by the function f(x), over an interval between a and b, is given by:

\(V = \pi \int\limits^a_b {f(x)^2} \, dx\)

To find the area, integrate around that area. We're revolving around the x-axis so the area will be a circle;

V = ∫A(x)dx =  ∫(πr²)dr

Then we subtract them from each others.

∫(πr₂² - πr₁²)dr

Now substitute the value and integrate;

∫(π(2)² - π(2x)²)dr

∫(4π - 4πx²)dr

4π∫(1 - x²)dr

Now integrate from 0 to 1 since that's where our boundary is.

V = 4π∫(1 - x²)dr = 8π/3

Therefore, The volume of the solid generated by revolving the region bounded by the given curve and lines about the x-axis is V = 8π/3

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Answer: x=4+2i , x=4-2i hope this helps tho :>

Step-by-step explanation

The solutions to the equation x 2 −8x+20=0 are x= 10,-2.

The equation  x 2 −8x+20=0  can be written as (x-10) (x+2) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x-10=0

x+2=0

so, the solution to the equation x 2 −8x+20=0 are x=10 and x=-2.

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The probability that the name is a senior’s is 0.224.

Given that there are 33 freshmen, 34 sophomores, 30 juniors, and 28 seniors in a hat, we are supposed to find the probability of selecting a senior's name at random. The probability of an event happening is the ratio of the number of ways it can happen to the total number of possible outcomes. It is defined as the ratio of the number of favorable events to the number of total possible events.The total number of names in the hat is;33 freshmen + 34 sophomores + 30 juniors + 28 seniors = 125The number of senior's names in the hat is 28Therefore, the probability of selecting a senior's name at random is given by;P(senior's name) = Number of senior's name in the hat / Total number of names in the hatP(senior's name) = 28/125= 0.224 (rounded to 3 decimal places)Answer: The probability that the name is a senior’s is 0.224.

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The evaluated integral is (1/12)[sec(4t)tan(4t)]³ + C.

To evaluate the integral sec²(4t)tan²(4t) dt using the Table of Integrals in the back of your textbook, follow these steps:

1. Identify the integral: ∫sec²(4t)tan²(4t) dt
2. Check the Table of Integrals for any formula that can help us evaluate the given integral. The most relevant one is the integration of sec(t)tan(t), which is given by:
  ∫sec(t)tan(t) dt = sec(t) + C

3. To apply this formula to our integral, we first rewrite the given integral by factoring sec²(4t) and tan²(4t) as follows:
  ∫sec²(4t)tan²(4t) dt = ∫[sec(4t)tan(4t)] [sec(4t)tan(4t)] dt
  Let u = sec(4t)tan(4t), then du = [4sec(4t)tan(4t) + 4sec³(4t)] dt

4. Now, we apply the substitution:
  ∫u² (1/4)du = (1/4)∫u² du

5. Integrate with respect to u:
  (1/4)(u³/3) + C = (1/12)u³ + C

6. Substitute back the original expression of u:
  (1/12)[sec(4t)tan(4t)]³ + C

So, the evaluated integral is (1/12)[sec(4t)tan(4t)]³ + C.

Evaluate the integral. (use c for the constant of integration.) \(4t 64\) −\(t2 dt\)

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it is important to consider the potential for intra-cluster similarity, as individuals within the same cluster may be more similar to each other than to individuals in other clusters.

A cluster sample is a sampling technique where the population is divided into clusters or groups, and a subset of clusters is selected at random to form the overall sample. In this type of sampling, all members of the selected clusters are included in the sample.

In the given example, the airline company selects 555 flights as clusters and surveys every passenger on those flights. Each flight represents a cluster, and by selecting random flights, the company includes every passenger on those selected flights in the survey.

This cluster sampling approach is suitable when each group or cluster is representative of the overall population. It is useful when it is impractical or costly to sample every individual unit within the population, but the selected clusters are expected to reflect the characteristics of the entire population.

Cluster sampling allows for more practical data collection, particularly when dealing with large populations or geographically dispersed units. However, it is important to consider the potential for intra-cluster similarity, as individuals within the same cluster may be more similar to each other than to individuals in other clusters.

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Answer:

0.21

Step-by-step explanation:

For independent probalities, the chance of both things happening is their product. 0.3 * 0.7 = 0.21

the initial expression is:

Answer:

There's no A so I'm going to assume you meant X

X = 23

Step-by-step explanation:

X is equal to 23, because 23 - 18 = 5

or 5 + 18 = 23