To make sure the machines in the factory run smoothly, the mechanics need to add-1/5 liter of oil to the machine every Monday. One Monday, a mechanic can only find 12 liters of oil in the storage. Is there enough for 65 machines?​

Based on the manufacturer's expectation of 1 defective light bulb out of every package of 5 sold, the probability that at most 2 bulbs out of the 15 purchased by the customer will be defective is 0.94208. This probability indicates a high likelihood of having at most 2 defective bulbs in the purchase.

So, the probability that a single bulb is defective is p = 1/5 and the probability that it is not defective is q = 1 - p = 4/5.

The number of bulbs purchased by the customer = 3 packages, which contain a total of 15 bulbs.

At most 2 bulbs are defective if there are either 0 or 1 or 2 defective bulbs.

The probability that 0 bulbs are defective = P(X = 0) = nCx . p^x . q^(n-x) = 15C0 . (1/5)^0 . (4/5)^15 = 0.32768

The probability that 1 bulb is defective = P(X = 1) = nCx . p^x . q^(n-x) = 15C1 . (1/5)^1 . (4/5)^14 = 0.4096

The probability that 2 bulbs are defective = P(X = 2) = nCx . p^x . q^(n-x) = 15C2 . (1/5)^2 . (4/5)^13 = 0.2048

The probability that at most 2 bulbs are defective

= P(X ≤2)=P(X=0)+P(X=1)+P(X=2)=0.32768+0.4096+0.2048=0.94208

Therefore, the required probability that at most 2 bulbs are defective is 0.94208.

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Given:

The coordinates of a point are (-3,-6).

To find:

The point on the coordinate plane whose coordinates are (-3,-6).

Solution:

From the given information of coordinate plane, it is clear that

Coordinates of point A are (-3, 6).

Coordinates of point B are (-6,-3)

Coordinates of point C are (-3,-6)

Coordinates of point D are (3,-6)

It is clear that, only point C has coordinates (-3,-6).

So, the required point is C.

Therefore, the correct option is C.

Answer: C.) -3,-6

Step-by-step explanation:

Answer:

last answer

Step-by-step explanation:

The statement, "When using binomial distribution, maximum possible number of "success" is number of trials." is, True because number of success is equal to number of trials.

When using the binomial distribution, the maximum possible number of successes is equal to the number of trials.

In each trial, there are two possible outcomes: success or failure.

The probability of success in each trial is denoted by "p" and the probability of failure is denoted by "q" (where q = 1 - p).

The binomial distribution calculates the probability of obtaining a specific number of successes in a fixed number of trials.

Since the number of possible successes is limited to the number of trials, the statement is true.

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The amount of sugar in the entire shipment is 97(1)/(2) tons.

We are given that a shipment of sugar fills 2(1)/(5) containers. If each container holds 3(3)/(4) tons of sugar, we need to find the amount of sugar in the entire shipment.

Step-by-step explanation:

One container of sugar holds 3(3)/(4) tons of sugar. There are 2(1)/(5) containers of sugar in the shipment.

Amount of sugar in one container = 3(3)/(4) tons

Amount of sugar in 2(1)/(5) containers

= 2(1)/(5) × 3(3)/(4) tons

= 13/5 × 15/4 = 195/20

= 97(1)/(2) tons

Therefore, the amount of sugar in the entire shipment is 97(1)/(2) tons.

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Answer:

Austin will have to pay $33,750 for the simple interest.

Step-by-step explanation:

2.25% into decimal = 0.0225

0.0225 x 3000 = 6750

6750 x 5 = 33750

Using the .01 level of significance means that, in the long run, a Type I error occurs 1 time in 100. This means that if we perform a statistical test 100 times, and we set the level of significance at .01, then we can expect to observe one false positive result due to chance alone. So, the correct option is 1).

A Type I error occurs when we reject a true null hypothesis, or when we conclude that there is a significant difference or relationship between two variables when in fact there is not.

By setting the level of significance at .01, we are minimizing the risk of making a Type I error while increasing the risk of making a Type II error, which occurs when we fail to reject a false null hypothesis. So, the correct answer is 1).

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Answer:

b.

b.

Step-by-step explanation:

scientific notation should have one positive in front of the decimal point, then any number (>=1) of positions after the decimal point, followed by the multiplication with the property power of 10.

the only number not following that rule is b (2 positions in front of the decimal point).

4x - 2y = 6

2x - y = 3

are the same line, as we can multiply the second equation by 2 and get exactly equation 1.

so, both lines have the same slope and the same y-intercept. therefore, they have infinitely many solutions.

Answer:

2 time greater

Step-by-step explanation:

5x20=100

10x20=200

100x2=200

so its 2 times greater

Answer:

10

Step-by-step explanation:

Answer:

\(\frac{1}{4^{5} }\)

Step-by-step explanation:

using the rule of exponents

\(\frac{a^{n} }{a^{m} }\) = \(\frac{1}{a^{(m-n)} }\) , then

\(\frac{4^{3} }{4^{8} }\)

= \(\frac{1}{4^{(8-3)} }\)

= \(\frac{1}{4^{5} }\)

The appropriate measures of central location for interval data are Mode, median, and average

The measure of a data set's most valuable position is its core location. Basically, they are mean, median, and mode.

Mean: The mean is the data set's average value. It is the total number of data divided by the sum of the data set.

The data point in the middle of the data collection is known as the median.

It can be obtained by halving the data set, which will show where the median is located.

Simply put, mode refers to the data that occurs most frequently.

Each of these provides positional information on the data, as can be seen from the definition.

The one value that other values in the data center around is given by the mean.

Therefore, the correct options are Mode, median, and average

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The number of customers are predicted to use a card to pay on a day when 90 customers pay by cash is 79

The equation of the line is

y = 0.755x + 11.339

The slope intercept form is

y = mx + b

Compare the slope intercept form with the given equation

Here the slope of the line is 0.755

y intercept of the line is 11.339

Number of customers = 90

Substitute the value of x in the equation

y = 0.755(90) + 11.339

y = 67.95 + 11.339

y = 79.28

y ≈ 79

Hence, the 79 customers use card to pay when 90 customers pay by cash

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The total change in the stock market from the beginning of the day to the end of the​ day is 39(3/4).

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder.

Given that at the beginning of the day the stock market goes down 50 ¾ points and stays at this level for most of the day. At the end of the day, the stock market goes up 90 ½ points from the low at the beginning of the day.

The total charge will be calculated as:-

Total change = 90(1 / 2 ) - 50( 3 / 4 )

Total change = 90.5 -  50.75

Total change = 39.75

Total change = 39(3 / 4)

Therefore, the total change in the stock market from the beginning of the day to the end of the​ day is 39(3/4).

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The state income task owed on a salary of $60,000 per year according to the given ranges is; $3,450.

It follows from the task content that for incomes of 17, 001 and above, the tax rate is; 5.75% .

Hence, it follows that for an individual whose in one is $60,000 per year, the state income tax owed is;

Tax = 5.75% of $60,000

= $3,450

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To calculate a three-month moving average for monthly forecasting, you need to follow these steps: Gather the historical data, Determine the time period, Calculate the moving average, Repeat the process.

Gather the historical data: Collect the monthly data for the specific variable you want to forecast. For example, if you want to forecast sales, gather the sales data for the past several months.

Determine the time period: Decide on the time period for your moving average. In this case, it is three months.

Calculate the moving average: Add up the values for the variable you are analyzing over the past three months and divide the sum by three to get the average. This will be your moving average value for the third month.

Repeat the process: Shift the time period by one month and calculate the moving average for the new three-month period. Continue this process for each subsequent month, updating the time period and calculating the moving average accordingly.

For example, let's say you have the following sales data for the past six months:

Month 1: 100 units

Month 2: 120 units

Month 3: 110 units

Month 4: 130 units

Month 5: 140 units

Month 6: 150 units

To calculate the three-month moving average for Month 4, you would add up the sales values for Month 2, Month 3, and Month 4 (120 + 110 + 130 = 360) and divide it by three to get an average of 120 units. Repeat this process for each subsequent month to obtain the moving average values for your forecast.

Note that the number of data points you include in the moving average calculation and the frequency of the data (monthly in this case) can be adjusted based on your specific needs and the nature of the data.

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(I copied this from another answer, but hope it helps!)

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

The probability P(Z>1.28) represents the area under the standard normal distribution curve to the right of the z-score 1.28.

Using a standard normal distribution table or a calculator, we find that the area to the right of 1.28 is approximately 0.1003.

Therefore, the answer is closest to option (b) 0.10. there is a 10% chance of obtaining a value above 1.28 in a standard normal distribution.

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area triangle:

(1.7m×2m)×2

= 1.7m²

-> 2 triangles so: 1.7m²×2= 3.4m²

area rectangles(walls):

2m×3m

= 6m²

-> 2 walls so: 6m²×2=12m²

area bottom rectangle:

3m×2m=6m²

-> total area:

6m²+12m²+3.4m²= 21.4m²

The balance when the account went into overdraft was -48.61

An overdraft occurs when something is withdrawn in excess of what is in a current account. For financial systems, this can be funds in a bank account.

Let x be the balance when the account went into overdraft

To get back to a positive balance he deposited money at a steady rate of $31.97 per week.

Amount deposited per week = $31.97

Amount deposited 3 weeks = $95.91

Now amount in account after 3 weeks =x+95.91

We are given that After 3 weeks, he had $95.91 in the account.

So, x+95.91=47.3

x= 47.3-95.91

x= -48.61

Hence The balance when the account went into overdraft was -48.61

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The expected value of the cardinality of a randomly chosen subset is n^2 / 2^n. To find the expected value of the cardinality of a randomly chosen subset, we need to consider the probabilities of selecting subsets with different cardinalities.

Let's consider a set with n elements. The total number of subsets of this set is 2^n, including the empty set and the set itself. Among these subsets, the number of subsets with cardinality n is C(n, n) = 1, and the number of subsets with cardinality n - 1 is C(n, n-1) = n.

The probability of selecting a subset with cardinality n is P(n) = 1/2^n, since there is only one subset with n elements out of the total 2^n subsets. The probability of selecting a subset with cardinality n - 1 is P(n - 1) = n/2^n, as there are n subsets with n - 1 elements out of the total 2^n subsets.

Now, let's calculate the expected value of the cardinality of the chosen subset:

E(X) = n * P(n) + (n - 1) * P(n - 1)

Substituting the probabilities we found:

E(X) = n * (1/2^n) + (n - 1) * (n/2^n)

Simplifying further:

E(X) = n/2^n + (n^2 - n)/2^n

Combining like terms:

E(X) = (n + n^2 - n)/2^n

Simplifying the numerator:

E(X) = n^2 / 2^n

Therefore, the expected value of the cardinality of a randomly chosen subset is n^2 / 2^n.

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Answer:

f(x) = 4x4 – 7x2 + x + 25 f(x) = 9x4

Step-by-step explanation:

Because it has to be this one

Answer:

what's the question?

Step-by-step explanation:

Answer:

The segment that connects the midpoints of the legs of a trapezoid is called the median of the trapezoid.

Step-by-step explanation:

Answer:

increase in thermal energy

Step-by-step explanation:

because if you increase the thermal/heat energy ten the solid will turn into liquid and same goes for liquid to solid evaporation for example the heat from the sun will make the water turn into clouds or gas

Answer:

1/6

Step-by-step explanation:

To simplify the expression:

      1. Change the divisor into it's reciprocal

     2. Change the sign into a multiplication sign.

     3. Evaluate the product of those fractions.

     4. Simplify the fraction. (If possible)

Given expression:

\(\dfrac{1}{6^3 } \div \dfrac{1}{36}\)

According to step 1, we need to convert the divisor of the expression into it's reciprocal.

\(\dfrac{1}{6^3 } \div \dfrac{36}{1}\)

According to step 2, we need to change the division sign (÷) into a multiplication sign (×).

\(\implies \dfrac{1}{6^3 } \times \dfrac{36}{1}\)

According to step 3, we need to determine the product of these fractions. This can be done by evaluating the exponent.

\(\implies \dfrac{1}{(6)(6)(6) } \times \dfrac{36}{1}\)

\(\implies \dfrac{1}{216 } \times \dfrac{36}{1}\)

Multiply the fractions as needed. [a/b × c/d = (a × c)/(b × d) = (ac)/(bd):

\(\implies \dfrac{36}{216 }\)

According to step 4, (If possible), Simplify the product of 1/216 and 36. In this case, the product of 1/216 and 36 is 36/216. Since both are divisible by 6, we can divide the numerator and the denominator by 6 to simplify the fraction.

\(\implies \dfrac{36 \div 6}{216 \div 6 }\)

\(\implies \dfrac{1}{6 }\)

Therefore, the quotient of 1/6^3 and 1/36 is 1/6.

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Answer:

\(\large\textsf{$\dfrac{1}{6}$}\)

Step-by-step explanation:

\(\large\textsf{$\dfrac{1}{6^3} \div \dfrac{1}{36}$} \implies \normalsize \textsf{Convert 36 into a base with an exponent}\)

\(\large\textsf{$\dfrac{1}{6^3} \div \dfrac{1}{6^2}$} \implies \normalsize \textsf{Cross multiply}\)

\(\large\textsf{$\dfrac{1 \cdot 6^2}{1 \cdot 6^3}$} \implies \normalsize \textsf{Multiply}\)

\(\large\textsf{$\dfrac{6^2}{6^3}$}\implies \normalsize \textsf{Simplify using the Quotient of Powers Property: \normalsize\textsf{$\dfrac{x^m}{x^n} = x^{m-n}$}}\)

\(\large\textsf6^{2-3}\)

\(\large\textsf6^{-1} \implies \normalsize \textsf{Simplify using the Negative Exponent Property: \normalsize\textsf {${x^{-m}} = \dfrac{1}{x^m}$}}\)

\(\large\textsf{$\dfrac{1}{6^1}$} \implies \normalsize \textsf{Simplify}\)

\(\large\textsf{$\dfrac{1}{6}$} \implies \normalsize \textsf{Final answer}\)

Hope this helps!

Option A "Everyone in the population has the same chance of being included in the study"  best describes a random sample.

For unbiased research results its essential to utilize random samples during data collection. With this approach each individual within the larger population has an equal probability of being selected for inclusion.

By avoiding any potential biases towards specific groups or individuals researchers can confidently generalize their findings for everyone within the larger population with ease and accuracy.

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Complete question:

Which best describes a random sample?

A. Everyone in the population has the same chance of being included in the study.

B. Participants in the study are picked at the convenience of the researcher.

C. There is no consistent method of choosing the participants in the study.

D. The participants in the study are picked from volunteers.