If the original quantity is 10 and the new quantity is 3​, what is the percent​ decrease?

1. The point estimate for the mean of the population is 79.

2. The point estimate for the standard deviation of the population is 27.1.

3. The point estimate for the variance of the population is 735.61.

4. The point estimate for the proportion of all students who passed the course is 80%.

Answer:

x = 74 degrees

Hope that helps

Answer:

74

Step-by-step explanation:

2x+32=180

2x=148

x=74

The system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

A line process has three processing stages with the characteristics given below:

Stage A B C Unit processing time(minutes) 1 2 3 Number of machines 1 1 2 Machine availability 90% 100% 100% Process yield at stage 100% 100% 100%

To determine the system capacity and the bottleneck stage and utilization of Stage 3:

The system capacity is calculated by the product of the processing capacity of each stage:

1 x 1 x 2 = 2 units per minute

The bottleneck stage is the stage with the lowest capacity and it is Stage A. Therefore, Stage A has the lowest capacity and determines the system capacity.The utilization of Stage 3 can be calculated as the processing time per unit divided by the available time per unit:

Process time per unit = 1 + 2 + 3 = 6 minutes per unit

Available time per unit = 90% x 100% x 100% = 0.9 x 1 x 1 = 0.9 minutes per unit

The utilization of Stage 3 is, therefore, (6/0.9) x 100% = 666.67%.

However, utilization cannot be greater than 100%, so the actual utilization of Stage 3 is 100%.

Hence, the system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

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the answer is

A.(0,11)

hope that helped

Answer:

error in step 1

Step-by-step explanation:

well where is does the step not make sense?

remember cos(pi) = -1 and sin(pi)=0

that means step 1 is strange... it didn't distribute properly

it should have been:

cos(pi) - cos(A)

hope that helps! ^-^

The error is made at step 1). The correct trigonometric identity is cos(π - A) = cosπcosA + sinπsinA.

Trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined.

cos(π - A) = cosπcosA + sinπsinA

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The probability that Jack and Jill will end up in the same class is 19/59.

The principles of probability and counting are fundamental concepts in probability theory and combinatorics. They are used to solve problems that involve uncertain events and counting arrangements of objects, respectively.

The principles of probability include:

Sample space: The set of all possible outcomes of a random experiment.

Event: A subset of the sample space.

Probability: A measure of the likelihood of an event, expressed as a number between 0 and 1.

Here we have

A group of 60 students is randomly split into 3 classes of equal size.

All partitions are equally likely. jack and jill are two students belonging to that group

Let's assume that Jack is assigned to a class, say the first class.

There are 20 students in that class, and the remaining 40 students are split evenly between the second and third classes.

Since all partitions are equally likely, each of the 59 remaining students has an equal chance of being assigned to any of the two remaining classes.

Now, we want to know the probability that Jill is assigned to the same class as Jack. There are 19 other students in the first class besides Jack, so there are 19 possible students in that class that Jill can be assigned to.

Out of the remaining 59 students, there are 40 in the other two classes, so Jill has 40 possible students she can be assigned to if she is not in Jack's class.

Hence,

The probability that Jill is assigned to the same class as Jack

= 19/59

Therefore,

The probability that Jack and Jill will end up in the same class is 19/59.

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Answer:

32 x 150 = A = 2 x 2 = c + b = 254

Step-by-step explanation:

To estimate the difference between proportions, sample around 3355 stalks from each section of the field.

In order to estimate the true difference between proportions of stalks damaged in the two sections of the sugarcane field, we need to determine the sample size required to achieve a desired level of precision and confidence.

To estimate the required sample size, we can use the formula for sample size determination for estimating the difference between two proportions. This formula is based on the assumption of a normal distribution and requires the proportions from each section.

Let's denote the proportion of stalks damaged in the middle section as p1 and the proportion of stalks damaged in the outer perimeter as p2. We want to estimate the difference between these proportions to within 0.02 (±0.02) with 90% confidence.

To calculate the required sample size, we need to make an assumption about the value of p1 and p2. If we don't have any prior knowledge or estimate, we can use a conservative estimate of p1 = p2 = 0.5, which maximizes the required sample size.

Using this conservative estimate, we can apply the formula for sample size determination:

n = (Z * sqrt(p1 * (1 - p1) +\(p2 * (1 - p2)))^2 / d^2\)

where:

Plugging in the values, we get:

n = (1.645 * sqrt(0.5 * (1 - 0.5) + 0.5 *\((1 - 0.5)))^2 / 0.02^2\)

n = (1.645 * sqrt\((0.25 + 0.25))^2\)/ 0.0004

n = (1.645 * sqrt\((0.5))^2\) / 0.0004

n =\((1.645 * 0.707)^2\) / 0.0004

n =\(1.158^2\) / 0.0004

n = 1.342 / 0.0004

n ≈ 3355

Therefore, the required sample size from each section of the field would be approximately 3355 stalks, in order to estimate the true difference between proportions of stalks damaged in the two sections to within 0.02 with 90% confidence.

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To estimate the true difference between proportions of stalks damaged in the two sections of the sugarcane field, approximately 665 stalks from each section should be sampled.

In order to estimate the true difference between proportions of stalks damaged in the middle and outer perimeter sections of the sugarcane field, a representative sample needs to be taken from each section. The goal is to estimate this difference within a certain level of precision and confidence.

To determine the sample size needed, we consider the desired precision and confidence level. The requirement is to estimate the true difference between proportions of stalks damaged within 0.02 (i.e., within 2%) with 90% confidence.

To calculate the sample size, we use the formula for estimating the sample size needed for comparing proportions in two independent groups. Since an equal number of stalks will be sampled from each section, the total sample size required will be twice the sample size needed for a single section.

The formula to estimate the sample size is given by:

n = [(Z * sqrt(p * (1 - p)) / d)^2] * 2

Where:

n is the required sample size per section

Z is the Z-value corresponding to the desired confidence level (for 90% confidence, Z = 1.645)

p is the estimated proportion of stalks damaged in the section (unknown, but assumed to be around 0.5 for a conservative estimate)

d is the desired precision (0.02)

Plugging in the values, we can calculate the sample size needed for each section.

n = [(1.645 * sqrt(0.5 * (1 - 0.5)) / 0.02)^2] * 2

n ≈ 664.86

Rounding up, we arrive at approximately 665 stalks that should be sampled from each section.

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The F-distribution is used to test the significance of the population coefficient of determination (option D).

The coefficient of determination, denoted as R², measures the proportion of the variance in the dependent variable that is explained by the independent variables in a regression model. It ranges from 0 to 1, where 0 indicates no relationship and 1 indicates a perfect relationship.

To determine the significance of R², the F-distribution is used. The F-test compares the variation explained by the regression model (numerator) to the unexplained or residual variation (denominator). It calculates the F-statistic, which is the ratio of the two variances.

The F-distribution provides critical values that allow us to determine whether the observed F-statistic is statistically significant or not. By comparing the calculated F-value with the critical value from the F-distribution, we can assess whether the coefficient of determination is significantly different from zero, indicating the presence of a meaningful relationship between the variables. The correct option is d.

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According to the given statement the probability is approximately 0.278 or 27.8%.

To calculate the probability of drawing at least one face card when selecting five cards from a standard deck without replacement, we need to determine the total number of possible outcomes and the number of favorable outcomes.

In a standard deck of 52 cards, there are 12 face cards (4 kings, 4 queens, and 4 jacks).

When drawing five cards without replacement, we need to consider two scenarios:

1. At least one face card is drawn.

2. No face cards are drawn.

To calculate the probability of scenario 1, we can use the complement rule. Brobability of drawing no face cards (scenario 2) can be subtracted from 1 to get the desired result.

To find the probability of scenario 2, we need to calculate the probability of drawing a non-face card on each draw, given that the previous draws did not result in a face card.

The probability of drawing at least one face card when selecting five cards from a standard deck without replacement is calculated as follows:

1 - (48/52 * 47/51 * 46/50 * 45/49 * 44/48) = 1 - 0.722 = 0.278

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Answer: none

Step-by-step explanation: i may be wrong, hope its wright, and hope it helps

Answer:

20

Step-by-step explanation:

24 ÷ 1.2  = 20

The point guaranteed to exist by the Mean Value Theorem is

c = ln(6/ln7).

B. The Mean Value Theorem applies because the function is continuous on [0,ln7] and differentiable on (0,ln7).

By the given function, we have:

f(x) = ex is continuous on [0,ln7] since it is a composition of continuous functions.

f(x) = ex is differentiable on (0,ln7) since its derivative, f'(x) = ex, exists and is continuous on (0,ln7).

Thus, by the Mean Value Theorem, there exists at least one point c in (0,ln7) such that:

f'(c) = (f(ln7) - f(0))/(ln7 - 0)

Plugging in the values, we get:

\(ec = (e^{ln7} - e^0)/(ln7 - 0)\)

ec = (7 - 1)/ln7

ec = 6/ln7

Therefore, the point guaranteed to exist by the Mean Value Theorem is c = ln(6/ln7).

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(a) Starting with the expression Var(X)=E[(X−μ)2], we can rearrange to get E[(X−μ)2] = Var(X)+μ2. Therefore, Var(X)=E(X2)−μ2.

(b) A random variable Z that is constructed by standardizing X is written as Z = (X-μ)/σ.

(c) E(Z) = E[(X-μ)/σ] = (E[X] - μ)/σ = 0.

(d) Var(Z) = Var[(X-μ)/σ] = (Var[X] - μ2)/σ2 = 1.

(e) The sample mean of a random sample of size n drawn from the population is an unbiased estimator for the population mean μ if E[sample mean] = μ.

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Answer:

k = -12/77

Step-by-step explanation:

OG problem: k(3k−6)−7k(6k+10)=12

Step-by-step:

3k - 6k - 42k - 70k = 12

-3k - 42k - 70k = 12

-7k - 70k = 12

-77k = 12

k = -12/77

Answer:

volume is the amount of space that a substance or object occupies, it is measured in cubic units

Step-by-step explanation:

in this situation

A+B =D

The largest possible assigned cycle time for the production line is 2.7 minutes, while the smallest possible assigned cycle time is 0.9 minutes.

In line balancing, the goal is to allocate the tasks evenly across the production line to achieve maximum efficiency. The largest possible assigned cycle time is determined by the task with the longest duration. In this case, the task with a duration of 2.7 minutes sets the upper limit for the cycle time. If all tasks were assigned the same cycle time, it would take at least 2.7 minutes to complete one cycle of the production line.

On the other hand, the smallest possible assigned cycle time is determined by the sum of the task durations. In this case, the sum of all task times is 6.4 minutes. By dividing this total time by the number of workstations or operators in the production line, we can determine the smallest possible assigned cycle time.

Since there are no constraints mentioned about the number of operators, we assume a single operator. Therefore, the smallest possible assigned cycle time would be 6.4 minutes divided by 1, which equals 6.4 minutes. However, it is worth noting that this cycle time is not realistic or practical for an operator to achieve.

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Answer:

It might be 15

hope this helps

The radical form of the given exponential form of a number 11x^(1/4) is written as ( 11 ) × \(\sqrt[4]{x}\).

As given in the question ,

Given exponential form is equal to :

11x^(1/4)

Using th formula to convert exponential form into radical form in standard form we have :

( y )^ ( a / b ) = \(\sqrt[b]{y^{a} }\)

Here y is equal to x

a is equal to 1

b is equal to 4

Substitute the value of the given expressions in the formula we have,

11x^(1/4)

= ( 11 ) ×  [x^(1/4) ]

= ( 11 ) × \(\sqrt[4]{x^{1} }\)

Any thing raise to one is the number or variable itself the required radical form is equal to:

=  ( 11 ) × \(\sqrt[4]{x}\)

Therefore, the radical form of the given expression 11x^(1/4) is given by :

( 11 ) × \(\sqrt[4]{x}\).

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Answer:

Recursive.

Step-by-step explanation:

It is recursive because each new term depends on the previous two terms.

If the bag contains a total of n blocks and m of them are blue, we would expect to have selected a blue block approximately (m/n) * 12 times out of the 12 draws, assuming the selection process is random and the probabilities remain constant.

Let's assume that the bag contains a total of n blocks, and m of them are blue blocks. The probability of selecting a blue block on each draw, P(blue), would be m/n.

Since we are replacing the block after each selection, the total number of blocks in the bag remains the same throughout the process. Therefore, the probability of selecting a blue block on each draw remains constant at m/n.

To find the expected number of times we would select a blue block, we can multiply the probability of selecting a blue block on each draw (m/n) by the total number of draws (12):

Expected number of blue blocks = (m/n) * 12

The reasoning behind this is that in each individual draw, the probability of selecting a blue block is m/n. By performing 12 independent draws, we can expect to encounter this probability m/n a total of 12 times on average.

Therefore, if the bag contains n blocks with m blue blocks, we would expect to have selected a blue block approximately (m/n) * 12 times out of the 12 draws.

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Answer:

1/2, 2/5, 3/10 is the order

Step-by-step explanation:

create common denominators then you can tell by the numerator.

3/10=3/10

1/2=5/10

2/5=4/10

Problem N 6

we have the roots

3 and (4+i)

By the conjugate complex theorem

If (4+i) is a root

then

(4-i) is a root too

so

we have at least

Zeros

The polynomial function is given by

(x-3)(x-(4+i))(x-(4-i))

Multiply first

(x-(4+i))(x-(4-i))

x^2+(4+i)(4-i)-x(4-i)-x(4+i)

x^2+16-i^2-4x+xi-4x-xi

x^2+16-(-1)-8x

x^2-8x+17

so

(x-3)(x-(4+i))(x-(4-i))=(x-3)(x^2-8x+17)

Apply distributive property again

x^3-8x^2+17x-3x^2+24x-51

therefore

I belive the correct answer would be A because if M and N are the signatures it would make sense to add them. Multiply the signatures by the days, and you have your self an equation. So because we added the first two... Nikkis's petition is still the same so we would have to add hers to M again leaving you with the equation of A.

Hope this helps :)

The series \(87n^2 + n / (18 + n^3)\)  is divergent by the Limit Comparison Test with the series 1/n.

To determine the convergence or divergence of the given series, we can apply the Limit Comparison Test. We compare the given series with a known series whose convergence or divergence is already established.

We compare the given series to the series 1/n. Taking the limit as n approaches infinity of the ratio between the terms of the two series, we get:

\(lim(n→∞) (87n^2 + n) / (18 + n^3) / (1/n)\)

Simplifying the expression, we get:

\(lim(n→∞) (87n^3 + n^2) / (18n + 1)\)

The leading terms in the numerator and denominator are both n^3. Taking the limit, we have:

\(lim(n→∞) (87n^3 + n^2) / (18n + 1) = ∞\)

Since the limit is not finite, the series \(87n^2 + n / (18 + n^3)\) diverges by the Limit Comparison Test with the series 1/n.

Hence, the main answer is divergent by the Limit Comparison Test with the series 1/n.

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Question: Determine the convergence or divergence of the series Σ(n=2 to ∞) (87n^2 + n) / (n^18 + n^3).

Is it:

a) Divergent by the Limit Comparison Test with the series Σ(n=2 to ∞) (1/n^8).

b) Convergent by the Limit Comparison Test with the series Σ(n=2 to ∞) (1/n).

c) Divergent by the Limit Comparison Test with the series Σ(n=2 to ∞) (-1/n).

d) [Option D - Missing in the original question.]"

9. A rule to describe this transformation is a rotation of 180° about the origin.

10. A rule to describe this transformation is a reflection over the x-axis.

11. A rule to describe this transformation is a rotation of 180° about the origin.

12. A rule to describe this transformation is a rotation of 90° clockwise around the origin.

In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Question 9.

Furthermore, the mapping rule for the rotation of a geometric figure 180° counterclockwise about the origin is as follows:

(x, y)            →            (-x, -y)

U (-1, 4)       →           U' (1, -4)

Question 10.

By applying a reflection over or across the x-axis to vertices D, we have:

(x, y)           →            (x, -y)

D (4, -4)       →           D' (4, 4)

Question 11.

By applying a rotation of 180° counterclockwise about the origin to vertices E, we have::

(x, y)            →            (-x, -y)

E (-5, 0)       →           E' (5, 0)

Question 12.

By applying a rotation of 90° clockwise about the origin to vertices C, we have::

(x, y)            →            (-y, x)

C (2, -1)       →           C' (1, 2)

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Answer:

$30

Step-by-step explanation:

Over 5 years she will have been paid $30 in interest. To find the amount of interest first find the total amount the account has after 5 years. The formula for simple interest is A=P(1+rt). Where A is the total amount, P is the principal (initial amount), r is the rate in decimal form, and t is the time in years.

Plug in the values to solve, A=200(1+0.03*5). Then, simplify to get A=230. Finally, to get only the interest, I, use the formula A-P=I. So, 230-200=30. Therefore, the interest Leila earned was 30 dollars.

In the equation y = $7.20x + $790, "y" represents the total cost. An equation is a mathematical statement that shows the relationship between two or more variables. In this equation, there are two variables - "x" and "y". The variable "x" represents the number of units produced or sold, while "y" represents the total cost.

The coefficient of "x" in the equation, which is 7.20, represents the variable cost per unit. This means that for each unit produced or sold, there is an additional cost of $7.20. The constant term, which is $790, represents the total fixed costs. Fixed costs are those costs that do not vary with the number of units produced or sold.To find the total cost of producing or selling a certain number of units, we can plug in the value of "x" into the equation and solve for "y". For example, if we want to find the total cost of producing 100 units, we can substitute x=100 into the equation:
y = $7.20(100) + $790
y = $720 + $790
y = $1510
Therefore, the total cost of producing 100 units is $1510. In summary, "y" represents the total cost in the given equation, which is determined by both fixed and variable costs.
In the equation y = $7.20x + $790, "y" represents option C: total costs. This equation has two components: "$7.20x" represents the variable costs per unit, where x is the number of units, and "$790" represents the total fixed costs. By adding these two components together, you get the total costs (y) for producing x units.

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