Express the following as a unit rate :

5 croissants for $10

The 99% confidence interval for the population mean is (29.25, 41.05) months.

To calculate the confidence interval, we can use the formula:

Confidence interval = sample mean ± (critical value * standard deviation / square root of sample size)

Given that the sample mean is 35.15, the critical value for a 99% confidence level can be found using a standard normal distribution table, which is approximately 2.576. The standard deviation is known to be 20 months, and the sample size is 31.

Substituting these values into the formula, we get:

Confidence interval = 35.15 ± (2.576 * 20 / √31) ≈ (29.25, 41.05) months.

This means we can be 99% confident that the true population mean falls within this range.

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Answer:

Angle 2 = 150°

Step-by-step explanation:

▪︎ Measures of supplementary angles add up to 180°.

Therefore,

Angle 1 + Angle 2 = 180°

Angle 1 = 30°

30° + Angle 2 = 180°

Angle 2 = 180° - 30° = 150°

Sampling Error is defined as; the discrepancy between a sample estimate of a population parameter and the real population parameter.

A sampling error is defined as a deviation that occurs in the sampled value when compared to the true population value. Now, sampling errors usually occur due to the fact that the sample is not representative of the population or is biased in some way.

The sampling error formula is used to estimate the overall sampling error in any given statistical analysis. The way we calculate the sampling error is by dividing the standard deviation of the population by the square root of the size of the sample, and thereafter multiplying the result with the Z-score value, which is largely based on the confidence interval.

Looking at the options, from the definitions above, it is clear that the sampling error is defined by option C

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Another term that accountants use to refer to "cost recovery" is "cost reimbursement."

In accounting, "cost recovery" refers to the process of recouping or recovering the expenses incurred by a company through various means such as sales revenue, reimbursements, or cost allocation.

Another term commonly used to describe this concept is "cost reimbursement." It signifies the reimbursement of costs to the company, ensuring that the expenses are covered and recovered, often through reimbursement agreements with clients or partners.

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Answer:

The range is 62

Step-by-step explanation:

Given

\(x:70,12,42,45,50,51,60,69,8,40,18\)

Required

The range

This is calculated as:

\(Range = Highest - Least\)

From the given data

\(Highest = 70\)

\(Least=8\)

So:

\(Range = Highest - Least\)

\(Range = 70-8\)

\(Range = 62\)

Answer:

x<-2

Step-by-step explanation:

5x<-10 (divide both sides by 5)

5x÷5<-10÷5 (divide)

solution: x<-2

hope this helps!

For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.

A coincidental discrepancy between the observed and true values of anything is known as a random error (e.g., a researcher misreading a weighing scale records an incorrect measurement).

It's not always a mistake when there is random error; rather, it happens when measurements are made. Even when you measure the same item repeatedly, there will always be some variation in your results because to changes in the environment, the instrument, or your own perceptions.

Your measurements are equally likely to be greater or lower than the genuine values due to random error, which has unexpected effects.

According to the given data,

For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.

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Drawing a 10 from the bag      unlikely

Rolling a number less than 5   Likely

Drawing a red marble             equally likely and unlikely

Here is the completed frequency table:

Number       frequency

1                       9

2                    12

3                    10

4                    8

5                    5

6                     6

Hiro's prediction is likely.

Probability determines the odds that a random event would happen. If the probability value is 0.5, it is equally likely and unlikely that the event would happen. If it is less than 0.5, it is unlikely that the event would happen. If it is greater than 0.5, it is likely that the event would happen.

Probability of drawing a 10 = number of 10s in the bag / total number in the bag = 1/100 = 0.01

It is unlikely that you would draw a 10.

Probability of rolling a number less than 5 = numbers that are less than 5 / total number of sides =  4/6 = 0.67

It is likely that a number less than 5 would be rolled.

Probability of drawing a red marble = total number of red marbles / total number of marbles = 8 / 16 = 0.5

It is equally likely and unlikely that a red marble would be picked

In order to determine the frequency, if the denominator of the relative frequency of the number is equal to 50, then the numerator is equal to the frequency. In the case where the denominator is less than 50, divide 50 by the number, multiply the quotient by the numerator in order to determine the frequency.

The frequency of 2 = (50 / 25) x 6 = 12

Number       frequency

1                       9

2                    (6 x 2) 12

3                    (1 x 10) 10

4                    (4 x 2) = 8

5                    (1 x 5) 5

6                     (3 x 2) 6

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Answer:

1254

Step-by-step explanation:

The converted to product four times as much in the CSTR than it was in the PFR that is 400%.

Conversion is a term used to describe the process of transferring a reactant into a product.

In this case, the reactant is being transferred from a 72 l plug flow reactor (PFR) to a 24 l continuous stirred tank reactor (CSTR). The conversion achieved by this process can be determined by calculating the ratio of product to reactant in the CSTR.

Specifically, if the PFR has a conversion of x%, then the conversion achieved in the CSTR will be x/(1-x), where x is the conversion in the PFR.

Therefore, if the PFR has a conversion of 80%, then the CSTR will have a conversion of 80/(1-80) = 400%.

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Some part of the regression can be estimated precisely, but it is difficult to predict the effect of individual regressors when there is multicollinearity in the data.Multiple regression models require that variables be independent of one another, otherwise, multicollinearity will occur.

Consider the multiple regression model with two regressors X1 and X2, where both variables are determinants of the dependent variable. You first regress Y on X1 only and find no relationship. However when regressing Y on X1 and X2, the slope coefficient changes by a large amount.

This suggests that your first regression suffers from omitted variable bias. Imperfect multicollinearity implies that it will be difficult to estimate precisely one or more of the partial effects using the data at hand. Imperfect multicollinearity means that there is a strong correlation between the regressors, but they are not perfectly correlated.

As a result, some part of the regression can be estimated precisely, but it is difficult to predict the effect of individual regressors when there is multicollinearity in the data.Multiple regression models require that variables be independent of one another, otherwise, multicollinearity will occur.

When there is multicollinearity in the data, it means that two or more of the variables are highly correlated with one another. In other words, the data may contain redundant information, which can make it difficult to estimate the regression coefficients or partial effects.The dummy variable trap refers to a situation in which one of the variables is a perfect linear combination of the other variables.

This results in the model being unsolvable, and the coefficients cannot be estimated. Heteroskedasticity is the term used to describe when the variance of the residuals is not constant across all values of the independent variables. This means that the predictions of the model may be biased, and the standard errors of the coefficients may be incorrect.

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Answer:

-10

Step-by-step explanation:

2x+6 = x-4

2x = x - 4 - 6

2x = x -10

2x -x = x-x - 10

x = -10

Please mark my answer as brainest

Shape ABC can be transformed into shape EFGDCHFGBE through a combination of translations, rotations, and reflections, which means that the two shapes are congruent.

To prove that shape ABC is congruent to shape EFGDCHFGBE, we can use rigid transformations to show that one shape can be transformed into the other.

First, we can see that shape ABC can be translated horizontally to the right by the distance between point A and point E to obtain shape EBC. Similarly, we can translate shape EFGDCHFGB horizontally to the left by the same distance to obtain FGDCHFGBE.

Next, we can rotate shape EBC 90 degrees counterclockwise about point B to obtain shape E'BC'. We can also rotate shape FGDCHFGBE 90 degrees counterclockwise about point G to obtain F'GDCHF'GBE.

Finally, we can reflect shape E'BC' across the y-axis to obtain shape EFGDCHFGBE.

Therefore, we have shown that shape ABC can be transformed into shape EFGDCHFGBE through a combination of translations, rotations, and reflections, which means that the two shapes are congruent.

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The value of a 5-year project with cash flows is being determined using a discount rate of 8%. Using the discount rate of 8% and the provided cash flows, we find that the value of the project is closest to $1,865.79+/-$1.00.

To calculate the value of the 5-year project, we need to discount the cash flows using the given discount rate of 8%. The value of the project is the present value of all the cash flows.

Let's assume the cash flows for each year are as follows:

Year 1: CF1

Year 2: CF2

Year 3: CF3

Year 4: CF4

Year 5: CF5

To find the present value (PV) of each cash flow, we use the formula:

PV = CF / \((1 + r)^n\)

where CF is the cash flow, r is the discount rate, and n is the number of years.

After calculating the present value of each cash flow, we sum them up to find the value of the project. The value of the project is given by:

Value = PV(CF1) + PV(CF2) + PV(CF3) + PV(CF4) + PV(CF5)

Performing the calculations using the discount rate of 8% and the provided cash flows, we find that the value of the project is closest to $1,865.79+/-$1.00. This is the option that best represents the value of the 5-year project given the discount rate.

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  The proportion of the sample obtained from the survey is 0.055

 The percentage is a mathematical operation that is expressed with the symbol "%" is a relationship that allows us to know the portion of an initial value to represent a set.

  It could also be defined as a representation of an original value that lets us know a certain number of elements that we want from that original value or set.

 To solve this problem, we use a simple rule of three to find the percentage value of the sample.

289 -------- 100%

273 ---------  x

x = (273 * 100%) / 289

x = 94.46%

100% - 94.46% = 5.53%

The ratio in propotion with 3 decimals is

5.53/100  = 0.055

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Solving the given equation we get value of x as -3/2 i.e option (a) is correct option.

What are exponents and its properties?

A number's exponent indicates how many times the number has been multiplied by itself. Example: Since 2 is multiplied by itself 4 times, 2×2×2×2 can be expressed as \(2^{4}\). Here, 4 is referred to as the "exponent" or "power," while 2 is referred to as the "base."

Generally speaking, \(x^{n}\) denotes that x has been multiplied by itself n times.

Raise a power to a power

\((x^{a}) ^{b}=x^{ab}\)

This is called the power of a power property

Negative exponents are the reciprocals of the positive exponents.

\(x^{-a}=\frac{1}{x^a}\)

The same properties of exponents apply for both positive and negative exponents.

\((1/25)^x = 125\\ 25^{-x} = 125\\(5^2)^{-x} = 5^3\\5^{-2x} = 5^3\\\implies -2x = 3\\\implies x = -3/2\)

i.e.

Option (a) is correct.

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The points on the surface at which the tangent plane is parallel to the given plane are (1/√21, -1/√21, -3/√21) and (-1/√21, 1/√21, 3/√21).

To find the points on the surface 3x^2 + 5y^2 + 2z^ 2=1 at which the tangent plane is parallel to the plane 1x -1y−3z=−3, we need to use the gradient of the surface and compare it to the normal vector of the given plane.

The gradient of the surface is given by ∇f = <6x, 10y, 4z>. The normal vector of the given plane is <1, -1, -3>.

Since the tangent plane is parallel to the given plane, their normal vectors must be parallel as well. This means that the gradient of the surface must be a scalar multiple of the normal vector of the given plane.

So, we have:

6x = k(1)

10y = k(-1)

4z = k(-3)

Solving for x, y, and z in terms of k gives us:

x = k/6

y = -k/10

z = -3k/4

Substituting these values back into the equation of the surface gives us:

3(k/6)^2 + 5(-k/10)^2 + 2(-3k/4)^2 = 1

3(k^2/36) + 5(k^2/100) + 2(9k^2/16) = 1

(k^2/12) + (k^2/20) + (9k^2/8) = 1

(10k^2/120) + (6k^2/120) + (135k^2/120) = 1

151k^2 = 120

k^2 = 120/151

k = ±2/√21.

Solving for k gives us k = ±2/√21.

Plugging these values of k back into the equations for x, y, and z gives us the points:

(1/√21, -1/√21, -3/√21) and (-1/√21, 1/√21, 3/√21).

Hence, the tangent plane is parallel to the given plane are at points (1/√21, -1/√21, -3/√21) and (-1/√21, 1/√21, 3/√21).

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The estimated crop yield from the simulation is 443 (option b).

To estimate the crop yield from the given random numbers, we need to assign a specific meaning to each random number. Let's assume that each random number represents the crop yield for a particular year.

Given random numbers: 37, 23, 92, 01, 69, 50, 72, 12, 46, 81

To find the estimated crop yield, we sum up all the random numbers:

37 + 23 + 92 + 01 + 69 + 50 + 72 + 12 + 46 + 81 = 443

Therefore, the estimated crop yield from the simulation is 443. The correct option is b.

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The two supplied points (1, 4) and (1, −7), have identical x-values. These would create a vertical line if graphed, then joined.

The points where the lines representing the intersections where the two linear equations intersect are referred to as the solution of a linear equation.

Given that:

Line has points:  (1, 4) and (1, −7).

The two supplied points have identical x-values. These would create a vertical line if graphed, then joined.

The diagram is attached:

Hence, a vertical line would be formed by the points.

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Complete question:

Which of the following is true of (1, 4) and (1, −7).?

options:

Answer:

I believe the answer is D

Step-by-step explanation:

The probability to choose a green marble of the given system through which the relation is satisfied is \(\frac{2}{17}\)

What about probability?

In mathematics, probability is the study of the likelihood or chance of an event occurring. It is a measure of how likely it is that a particular outcome or event will occur, expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.

Probability can be calculated using the following formula:

Probability of an event = (Number of favorable outcomes) / (Total number of possible outcomes)

For example, if you toss a fair coin, the probability of getting heads is 1/2, since there is one favorable outcome (heads) out of two possible outcomes (heads or tails).

Probability is used in various fields, including statistics, finance, and science. It is used to make predictions and inform decisions based on uncertain events or outcomes. For example, in gambling, probability is used to calculate the odds of winning or losing a bet. In finance, probability is used to calculate the expected return on an investment. In science, probability is used to model and predict the behavior of systems and processes that involve uncertainty.

According to the given information:

The total no of marbles in a bag = 2 + 15 = 17

Total no of green marbles = 2

So, the probability of green marble = \(\frac{Total no of green marbles }{Total no of marbles}\)

                                                           = \(\frac{2}{17}\)

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The integral ∫[0 to ∞] e^(ax) dx converges for certain values of "a". In this case, we need to determine the range of values for which the integral converges.

To determine the convergence of the integral, we consider the behavior of the integrand, e^(ax), as x approaches infinity. The integral converges if the function decays or approaches zero as x increases.

When "a" is negative (a < 0), e^(ax) approaches zero as x goes to infinity. In this case, the integral converges.

When "a" is positive (a > 0), e^(ax) grows without bound as x approaches infinity. In this case, the integral does not converge.

Therefore, the integral ∫[0 to ∞] e^(ax) dx converges for values of "a" that are less than or equal to zero (a ≤ 0).

To illustrate this, let's consider the integral for two cases:

1. If a = -1, the integral becomes ∫[0 to ∞] e^(-x) dx. This integral converges to 1.

2. If a = 1, the integral becomes ∫[0 to ∞] e^x dx. This integral diverges.

Hence, the integral converges for a ≤ 0 and diverges for a > 0.

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Answer:

You see x is just the multiplied side of the opposite one, and you know 180 is half of 360 (full degrees). X=10 divided by 9 which is more than one, and the answer that belongs in the box is 10 divided by 9 is 180x10 and thats your answer :)

The area of the region that lies inside the first curve and outside the second curve is 2π/3 - 2.

The first step is to find the intersection points of the two curves. The intersection points are at θ = 0, π/2, and 2π.

The next step is to use the polar coordinate formula for area to find the area of each curve. The area of a polar curve is given by the formula A = 1/2 ∫ θ1 θ2 r(θ)^2 dθ.

The area of the first curve is A1 = 1/2 ∫ 0 π/2 (1 cos(θ))^2 dθ = π/3.

The area of the second curve is A2 = 1/2 ∫ 0 π/2 (2 - cos(θ))^2 dθ = 2 - π/3.

The area of the region that lies inside the first curve and outside the second curve is A = A1 - A2 = 2π/3 - 2.

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Answer:

A. 28 yards

Step-by-step explanation:

Lmk if this helps  

Equation and solution of equation :

17.25 + p(17.50) = 69.75

17.25 + 17.50p = 69.75

17.50x = 69.75 - 17.25

17.50p = 52.50

p = 52.50/17.50

p = 3

So three people can go to the amusement park (assuming that they are all travelling together in the same car).

The equation that represents the number of people who can go to the amusement park will be 17.50p + 17.25 = 69.75.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

A group of friends wants to go to the amusement park. they have $69.75 to spend on parking and admission. Parking is $17.25, and tickets cost $17.50 per person, including tax.

Let p be the number of people. Then the equation is given as,

17.50p + 17.25 = 69.75

The equation that represents the number of people who can go to the amusement park will be 17.50p + 17.25 = 69.75.

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Answer:

Step-by-step explanation:

Answer:

625

Step-by-step explanation:

25% of 2500=625

Hope this helps!!!

Answer:

opposite sides of parallelogram are parellel.

so, angle A and angle D are co interior angle.

(3x+4)°+x°=180°

4x+4=180°

4x=180°- 4

4x=176°

x=176°/4

x = 44°

(3x+4)

=3×44+4

=136°