7 A team of workers took 74.7 hours to complete the project. A smaller team of workers willcomplete the same task, but it will take them 1.15 times as long as it took the first team.Based on this information, which statement is true?A The task will take the smaller team of workers 64.3 hours to complete, because74.7 - 1.15 = 64.3.B The task will take the smaller team of workers 75.85 hours to complete, because74.7 + 1.15 = 75.85.C The task will take the smaller team of workers 85.905 hours to complete, because 74.7 x1.15 = 85.905.D The task will take the smaller team of workers 86.250 hours to complete, because 74.7x 1.15 = 86.250.

Answer:

smaller: 3

larger: 27

Step-by-step explanation:

Hope this helps!

Answer:

280

Step-by-step explanation:

Answer:

Step-by-step explanation:

boat was at 43.2 m/s   speed increase to 144 m/s

if the boat was moving 0 m/s and increased to 144 m/s - 43.2 m/s accelerating at 25.2 m/s²,  it would take the same amount of time

25.2 m/s² × x seconds = (144 - 43.2) m/s      solve for x in seconds

x seconds = 100.8 m/s   /  25.2 m/s²

x seconds = 4 (m/s /ms²)  = 4 (m/s × s²/m)  = 4 seconds   the  units match

x = 4 seconds

When the price increases from $2 to $2.58 per six-pack, the average Berkeley resident is predicted to consume approximately 38.7597 six-packs per year.

To predict the new consumption of six-packs per year, we can use the concept of price elasticity of demand. Price elasticity measures the responsiveness of demand to changes in price. In this case, we need to determine the percentage change in price and use it to estimate the percentage change in quantity consumed.

The price increase is from $2 to $2.58, which is an increase of $0.58 or 29% (0.58/2 * 100) compared to the original price. Assuming that the demand for six-packs follows a linear relationship with price, we can estimate the change in quantity consumed by applying the same percentage change to the original consumption.

The original consumption is 50 six-packs per year. Applying a 29% increase, the predicted change in consumption is 14.5 six-packs (50 * 0.29). Subtracting this change from the original consumption, we get the estimated new consumption of approximately 35.5 six-packs per year (50 - 14.5).

Therefore, when the price increases to $2.58 per six-pack, the average Berkeley resident is predicted to consume approximately 38.7597 six-packs per year.

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To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.

First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.

Depreciation per year = (Cost - Salvage Value) / Useful Life

Depreciation per year = ($746,800 - $80,200) / 10 years

Depreciation per year = $66,160

Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.

Accumulated Depreciation = Depreciation per year × Years

Accumulated Depreciation = $66,160 × 7.33 years

Accumulated Depreciation = $484,444.80

Now, we can calculate the book value of the furniture:

Book Value = Cost - Accumulated Depreciation

Book Value = $746,800 - $484,444.80

Book Value = $262,355.20

Finally, we can calculate the gain on the sale:

Gain on Sale = Sale Price - Book Value

Gain on Sale = $300,000 - $262,355.20

Gain on Sale = $37,644.80

Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.

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The gain that should be recognized on the sale of the office furniture is $84,080.

The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.

Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.

For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420

Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.

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The above question is a mathematical proof of the relationship between Lines and angles related to a Rhombus. See the proof below.

We know,

A Rhombus is a parallelogram with four sides (that is a quadrilateral). It's sides however are all of equal length.

we have,

∠DEC ≅ ∠BFC  Reason = All Right Angles with Equal dimensions are congruent.

∠C ≅ ∠C  Reason = It is the same angle for the two Right angles above which are congruent, hence Reflexive Property.

Δ DEC ≅ Δ BFC  Reason = Angle Angle Side. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

 ≅   Reason = The corresponding parts of congruent triangles are congruent. Also, it is a parallelogram with all congruent sides.

ABCD is a Rhombus Reason = Its sides are all congruent.

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complete question:

Given: ABCD is a parallelogram, FC is congruent to EC, DE bisects BC and BF bisects DC Prove: ABCD is a rhombus

Answer:

6

Step-by-step explanation:

You would first divide 48/8 than you would get 8 baskets per minute.

Answer:

6

Step-by-step explanation:

Mario: 1 minute = 5 baskets and 5 x 6 = 30.

Chris: 1 minute = 6 baskets and 6 x 8 = 48.

The values of a and b that make f(x) continuous everywhere are a = 2x and b = 2a - 3/2 = 2(2x) - 3/2 = 4x - 3/2.

The limit is a concept in mathematics that describes the behavior of a function near a particular value, called the limit point. The limit of a function gives the value that the function approaches as the input (variable) approaches the limit point.

For f(x) to be continuous everywhere, the function must have the same value and the same limit as x approaches 2 from the left and the right. In other words, f(2-) = f(2+) and the limit of f(x) as x approaches 2 from the left and the right must be equal.

Let's start by finding f(2-), which is the value of f(x) as x approaches 2 from the left. In this case, f(x) = (x2 - 4)/(x - 2) for x < 2, so as x approaches 2 from the left, f(x) approaches (2^2 - 4)/(2 - 2) = 0.

Next, let's find f(2+), which is the value of f(x) as x approaches 2 from the right. In this case, f(x) = ax^2 - bx + 3 for 2 <= x < 3, so as x approaches 2 from the right, f(x) approaches a(2^2) - b(2) + 3 = 4a - 2b + 3.

Since f(x) must be continuous at x = 2, we need to have f(2-) = f(2+), so we can set f(2-) = f(2+) and solve for a and b:

0 = 4a - 2b + 3

2b = 4a - 3

b = 2a - 3/2

Now that we have an expression for b in terms of a, we can substitute b = 2a - 3/2 into the expression for f(x) for x >= 3 to find the value of a that makes f(x) continuous everywhere:

f(x) = 2x - a + b for x >= 3

f(x) = 2x - a + (2a - 3/2) for x >= 3

f(x) = 2x + 3/2 - a for x >= 3

Since f(x) must be continuous at x = 2, we need to have f(2+) = f(2+), so we can set f(2+) = f(2+) and solve for a:

4a - 2b + 3 = 2x + 3/2 - a for x >= 3

4a - 2(2a - 3/2) + 3 = 2x + 3/2 - a

4a - 4a + 3 + 3/2 = 2x + 3/2 - a

3/2 = 2x + 3/2 - a

a = 2x

So, the values of a and b that make f(x) continuous everywhere are a = 2x and b = 2a - 3/2 = 2(2x) - 3/2 = 4x - 3/2.

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In the given scenario, the processor has a 32-bit address, and the main memory it is attached to has a capacity of 256 MB and can contain 65,536 pages.

A 32-bit address means that the processor can address 2³² (4,294,967,296) unique memory locations.

However, in this case, the main memory has a capacity of 256 MB, which is equivalent to 256 * 2²⁰bytes (268,435,456 bytes).

To determine the number of pages, we need to divide the memory size by the page size. Since the number of pages is given as 65,536, we can calculate the page size as 268,435,456 / 65,536 = 4,096 bytes.

Since the processor has a 32-bit address, it can address 2³² unique memory locations.

However, the main memory can only contain 65,536 pages, and each page is 4,096 bytes in size. T

his means that the processor can address a larger number of memory locations than the physical memory can accommodate. To access data beyond the capacity of the main memory, the processor would need to use virtual memory techniques such as paging or segmentation.

These techniques allow the processor to access data stored in secondary storage devices, such as hard drives, as if it were in main memory.

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Answer:

0.2 kg per meter

Step-by-step explanation:

5÷25=0.2

A customer would  be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day.

Charge for first 5 charged = $ 4.50

Charge for additional time = $ 0.50 per minute

Starting time = 9:35 p.m.

End time = 11:15 p.m.

Total minutes = 100 minutes

Total charge = 4.50 + (95 x 0.50)

                  = 4.50 + 47.50

                  = 52.00

Hence, a customer would  be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day i.e. for 100 minutes.

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The main idea behind statistical inference is that through the use of sample data, we are able to draw conclusions about the population from which the data was drawn (option c).

Statistical inference allows us to make inferences and draw conclusions about a larger population based on the analysis of a smaller representative sample.

By collecting data from a sample, we can use statistical methods to analyze and summarize the information. These methods include estimating population parameters, testing hypotheses, and making predictions.

The key assumption underlying statistical inference is that the sample is representative of the larger population, allowing us to generalize the findings to the population as a whole.

Statistical inference provides a way to make reliable and informed decisions, identify patterns and relationships, and make predictions about future observations based on the available data. It allows researchers, scientists, and decision-makers to make evidence-based conclusions and draw meaningful insights from limited observations.

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The centre line of a control chart is calculated by computing the average (mean) of the data for every period.

In control chart analysis, the centre line represents the central tendency or average value of the process being monitored. It is typically obtained by calculating the mean of the data points collected over a specific period. The purpose of the centre line is to provide a reference point against which the process performance can be compared. Any data points falling within acceptable limits around the centre line indicate that the process is stable and under control.

The calculation of the centre line involves summing up the values of the data points and dividing it by the number of data points. This average is then plotted on the control chart as the centre line. By monitoring subsequent data points and their distance from the centre line, deviations and trends in the process can be identified. Deviations beyond the control limits may indicate special causes of variation that require investigation and corrective action. Therefore, the centre line is a critical element in control chart analysis for understanding the baseline performance of a process and detecting any shifts or changes over time.

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Answer:

D. y = -4x - 6

Step-by-step explanation:

→ Work out gradient of line

\(\frac{2-6}{-2--3} =\frac{-4}{1} =-4\)

→ Write into y = mx + c format

y = -4x + c

→ Substitute ( -2 , 2 ) into the equation to find c

2 = 8 + c

→ Minus 8 from both sides

-6 = c

→ Write full equation y = -4x - 6

The probability that the entire batch of 6500 write-rewrite CDs will be accepted, given that 170 are defective and 6 are randomly selected for testing, is approximately 0.859 or 85.9%.

To find the probability that the entire batch of 6500 write-rewrite CDs will be accepted using acceptance sampling, we need to consider the number of defective CDs in the batch and the number of CDs selected for testing.

Given that the batch consists of 6500 CDs and 170 of them are defective, we know that the remaining 6500 - 170 = 6330 CDs are non-defective.

Now, if we randomly select 6 CDs for testing, we want to determine the probability that all 6 CDs are non-defective. To calculate this probability, we need to use the hypergeometric distribution.

The hypergeometric distribution calculates the probability of obtaining a specific number of successes (in this case, non-defective CDs) from a finite population (the entire batch) without replacement.

Using the hypergeometric distribution formula, the probability of selecting 6 non-defective CDs can be calculated as follows:

P(X = 6) = (C(6330, 6) * C(170, 0)) / C(6500, 6)

where C(n, r) represents the number of combinations of selecting r items from a set of n items.

Evaluating this expression, we find:

P(X = 6) = (C(6330, 6) * C(170, 0)) / C(6500, 6) ≈ 0.859

Therefore, the probability that the entire batch of CDs will be accepted is approximately 0.859, or 85.9%.

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A subscript n baseline refers to the placement of a subscript, typically a letter or number, at a lowered position relative to the baseline of the surrounding text. It is commonly used in mathematical and scientific notation to denote a specific element or variable in a sequence or series.

To determine which choices describe a subscript n baseline = 4 (0.9) superscript n, we need to substitute the values of n into the equation and check if the given sequences match.

Let's substitute n = 1 into the equation:
s1 = 4 * (0.9)^1 = 3.6

Now, let's substitute n = 2 into the equation:
s2 = 4 * (0.9)^2 = 3.24

Finally, let's substitute n = 3 into the equation:
s3 = 4 * (0.9)^3 = 2.916

Comparing the given sequence values to the values we calculated, we can see that none of the choices match the sequence. Therefore, none of the choices describe a subscript n baseline = 4 (0.9) superscript n. Additionally, since the sequence values do not match any of the given choices, we cannot determine if the sequence diverges based on the information provided.

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Using the area of a rectangle, it is found that 35 bags are needed to cover the rectangular lawn.

The area of a rectangle of length l and width w is given by the multiplication of the measures, that is:

A = lw

In this problem, we have that the measures in feet are l = 360, w = 190, hence the area in square feet is given by:

A = 360 x 190 = 68,400.

The number of bags is then given by:

68,400/2,000 = 34.2

Rounding up, 35 bags are needed to cover the rectangular lawn.

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the given proportional relationship y=0.5x with proportional constant is 1/2.

what is proportional relationship?

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant.

Given x and y will have a proportional relationship if the ratio of x to y will be equal for all given values.

For every 1 scoop of ice cream, cup of milk is needed 1/2, and for every 5 scoops of ice cream, 2 cups of milk 2 1/2 are needed.

So the equation will be y = kx

or y = 0.5(x)

Here proportional constant is 1/2 or 0.5.

For 18 scoops of icecream, milk will be needed is 18/2 = 9 cups of milk.

Hence, we can say that the given proportional relationship y=0.5x with a proportional constant is 1/2.

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Answer:

The first one is B. 11.75

The second one is A. 4

Step-by-step explanation:

In order to find how many liters (L) of paint he used you need to do 2.5*5.5=13.75 Then to find out how much he has left you do 25-13.75=11.75 So your answer is 11.75.

The second one you have to do the reverse. So since it says 4*_=48, you do 48÷4=_=12. Then since it says 12*1/3=_ You can do 12÷3=_=4 So your answer is 4.

If Ridgewood Savings Bank charges a $27 per check overdraft protection fee. The amount she will owe the bank after July 12 is: $1,071.42.

Total obligation can be defined as the amount a person owe another person or the debt amount a borrower  is expected to payback to a lender.

Balance $1,400

July 9 check ($1,380.15)

Balance $19.85

July 10 check ($765.67)

($670 + $95.67)

Balance -$745.82 (Overdraft)

Now let find the amount she owe

Balance -$745.82

July 11 check $130

Balance -$875.82

July 12 check $87.60

Ending balance -$963.42

Overdraft fee $108

($27 ×4)

Total obligation -$1,071.42

Therefore her total obligation is $1,071.42.

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Answer:

69 miles

Step-by-step explanation:

Answer:

The first option

Step-by-step explanation:

The probability that the player is a female student or a player on the varsity soccer team is 78. 8 %.

The probability that the player is a female student or a player on the varsity soccer team is :

= Probability that they are female + Probability that they are in varsity - Probability that the student is female and in varsity

Probability that they are female = ( 19 + 23 ) / ( 19 + 23 + 17 + 21 )

= 42 / 80

Probability that they are in varsity = ( 23 + 21 ) / ( 19 + 23 + 17 + 21 )

= 44 / 80

Probability that the student is female and in varsity = 23 / 80

The probability that the player is a female student or a player on the varsity soccer team is :

= 42 / 80 + 44 / 80 - 23 / 80

= 63 / 80

= 78. 8 %

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Answer:

A:no B:no C:yes D:yes

Step-by-step explanation:

Answer:

$54.26

Step-by-step explanation:

Convert the percentage into a decimal by moving the decimal point 2 places to the left or divide by 100.

This will give you .0825.

Multiply this number by $50 and add it to it

$54.26

Hope this helps! Good luck!! :)

The probability that Marshall wins a prize on his second spin =  0.1875

Consider an event X = the number of spins until Marshall wins a prize.

Given that a prize wheel with 4 segments of equal size, one of which is labeled winner.

So, the sample space n = 4

For given event x, the possible outcomes = 1

Using the formula of probability,

p = x/n

p = 1/4

p = 0.25

So, the probability of success p = 0.25

q = 1 - p

q = 1 - 0.25

q = 0.75

To find the probability that Marshall wins a prize on his 2nd spin.

Using formula, \(P(X = k) = (1 - p)^{k-1}p\)

For  k = 2,

\(P(X = 2) = (1 - 0.25)^{2-1}\times 0.25\)

P(X = 2) = 0.75 × 0.25

P(X = 2) = 0.1875

Thus, the required probability is  0.1875

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Answer:

Answer:7 meaning 7 students in each group

Answer:7 meaning 7 students in each group Step-by-step explanation:

Answer:7 meaning 7 students in each group Step-by-step explanation: 35 ÷ 5 = 7