A bag contains 6 blue marbles, 8 green marbles, 9 red marbles, and 17 yellow marbles. What is the ratio of blue marbles to total marbles?

Answer:

7/12 or 58%

Step-by-step explanation:

Answer:

\(l = \frac{S}{\pi r} - r\)

Step-by-step explanation:

Given the surface area of a cone expressed as S = \(\pi r^{2} +\pi rl\) where r is the radius of the cone and 'l' is its slant height. To find the slant height from the formula, we will make l the subject of the formula as shown;

\(S = \pi r^{2} + \pi rl\\S = \pi r (r + l)\\\frac{S}{\pi r} = r+l\\l = \frac{S}{\pi r} - r\\\)

The final expression gives the value of the slant height.

Answer: l=s/3.14-r2

Step-by-step explanation:

did it on Edg and the 3.14 i’d supposed to be the symbol for pi hope it helps :)

Answer:

what are the options...

Step-by-step explanation:

Answer:

9. A. One - to - One Correspondence

10. D. None of the above

9.) one to one correspondence

10.)one to many correspondence

Step-by-step explanation:

in 9 it shows that 1-4 are connected to different number

in 10 it shows that a is connected to 2 different numbers

Answer:

Programmed

Step-by-step explanation:

Programmed Decisons may be classified as those actions which are routinely carried out or performed based on existing rules and protocol. In programmed decision making, the rules are in place, therefore once the criteria or requirement for which the rule or routine is to be enforced arises, programmed Decisons are made. In the scenario, the superintendent required that a programmed Decison be made in cases or situations where enrollment increases by 35 student beyond capacity, Hence, with this, every time this occurs the additional teachers will be hired.

True. The pessimistic approach assumes that the worst-case scenario for each alternative will occur and chooses the best of these.

An optimistic approach indicates that the decision-makers believe the outcomes will benefit the organisation. A pessimistic approach, on the other hand, indicates that the decision-makers are convinced that the outcomes will be detrimental to them. The pessimistic approach allows decision-makers to plan for the worst-case scenario. In the optimistic approach, decision-makers believe that the alternatives chosen will produce the best results. In other words, the decision-makers are confident that their options are the best for the circumstances. The pessimistic approach is characterised by decision-makers assuming that the choices they make will have the most negative outcomes.

Thus, the pessimistic approach is the approach which is used to assume the worst possible outcomes for each alternative will occur.

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Answer:

sq rt 74 which is approx 8.6

Step-by-step explanation:

use distance formula

Answer:

3/4,3/4,3/4,3/4,1,1,2,11/2,11/2,11/4,11/4

Step-by-step explanation:

we just arrange the number from the smallest to bigger

Answer:

Angle<8 corresponds with angle<3

Step-by-step explanation:

Corresponding angles are congruent and are on the same side of the transversal. They occupy corresponding positions. So,

Angle 1 and Angle 6 are corresponding angles

Angle 3 and Angle 8 are corresponding angles

Angle 2 and Angle 5 are corresponding angles

Angle 4 and Angle 7 are corresponding angles

The scientist can compare the reaction times of the students between the control group (blue to yellow) and the experimental group (red to yellow), allowing them to investigate whether the color change influenced the participants' reaction times.

The scientist could compare the reaction times of these students when they respond to red squares turning into yellow squares by doing the following:

If the reaction times for the red squares are significantly slower than the reaction times for the blue squares, then the scientist could conclude that the color of the square does affect reaction time.

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To determine the probability that Alice will flip more heads than Bob, we can use the concept of binomial probability.

Let's consider the number of heads flipped by Alice as a random variable X, which follows a binomial distribution with parameters n = 1201 (number of trials) and p = 0.5 (probability of getting a head on a fair coin). Similarly, the number of heads flipped by Bob can be represented as a random variable Y, which follows a binomial distribution with parameters n = 1200 and p = 0.5.

To calculate the probability that Alice will flip more heads than Bob, we need to find P(X > Y). This can be done by summing up the probabilities of all possible values of X that are greater than the corresponding values of Y.

P(X > Y) = P(X = 1201) + P(X = 1200) + ... + P(X = 1200 - 1200)

We can simplify this expression by noticing that P(X = k) = P(Y = k) for any given value of k.

Therefore, P(X > Y) = P(X = 1201) + P(X = 1200) + ... + P(X = 601)

Using the binomial probability formula, the probability of getting exactly k heads out of n trials is given by:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where C(n, k) represents the number of ways to choose k successes out of n trials, given by the binomial coefficient formula:

C(n, k) = n! / (k! * (n - k)!)

Now we can calculate the probability:

P(X > Y) = P(X = 1201) + P(X = 1200) + ... + P(X = 601)

        = [C(1201, 1201) * 0.5^1201 * 0.5^0] + [C(1201, 1200) * 0.5^1200 * 0.5^1] + ... + [C(1201, 601) * 0.5^601 * 0.5^600]

This calculation involves summing up a large number of terms, so it can be computationally intensive. However, we can approximate the probability by using methods such as Monte Carlo simulation or statistical software.

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If probability of box looking like it were a phone, is 90%, and probability of it looking if it were not a phone is 30%, then the odds that you got a phone is 6:1 or 86%.

The Bayes' Theorem is used to describe the relationship between conditional probabilities of two events.

To find the odd that you got the phone, we use Bayes’ theorem;

⇒ P(A|B) = P(B|A) × P(A)/P(B)

Where A = event that you got a phone, B = event that the box looks like a cell-phone box.

We are given that, P(A) = 2/3 and P(not A) = 1/3 (since there are only two possible outcomes).

We also know that P(B|A) = 0.9 and P(B|not A) = 0.3;

By using Bayes theorem,

We get,

⇒ P(A|B) = P(B|A) × P(A)/(P(B|A) × P(A) + P(B|not A) × P(not A))

⇒ [0.9 × (2/3)]/(0.9 × (2/3) + 0.3 × (1/3))

⇒ 6/7

Therefore, the odds that you got a phone are 6:1.

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Answer:

<2 = 45

< 7 = 135

< 3 = 135

< 5 = 135

<8  = 45

< 6 = 45

Step-by-step explanation:

Angles 2 and 7 are supplemental angles.  This means that together they add to 180.

x + 3x = 180  Combine like terms

4x = 180  Divide both sides by 4

x = 45

<2 = 45

Angle 7

3x   Substitute 45 for x

3(45)

135

Angle 3

Corresponding angle to 7.  Corresponding angles are congruent (equal).

Angle 5

Vertical to angle 7.  Vertical angles are congruent.

Angle 8

Alternate exterior angle to 7.  Alternate exterior angels are congruent.

Angle 6

Vertical angle to 8.  Vertical angles are congruent.

Answer:

- 3 / 5

Step-by-step explanation:

3 / - 5

= - 1 x 3 / 5

= - 3 / 5

Total change to Dracula account balance will be the account balance is $40.

What is mean by subtraction?

The operation of taking the difference of two number is called Subtraction.

Given that;

Dracula made a deposit of $220 into his checking account.

Dracula made two withdrawals of $80 each.

Now, Total change to his account after transaction will be calculated as;

Total amount in Dracula account = $220

And, Total withdrawals amount = 2 x $80

                                                = $160

Thus, Money in account after transaction = $220 - $160

                                                               = $40

Therefore, Total change to Dracula account balance will be the account balance is $40.

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The equation of the parabola can be written as\(y = -x^2 + 3x + 3\). To find the equation of a parabola, we need to use the general form of a quadratic equation,\(y = ax^2 + bx + c\), where a, b, and c are constants.

Given the vertex (-1, 4) and another point on the parabola (-4, -2), we can substitute these coordinates into the equation to form a system of equations.

Using the vertex form of the equation, we have:

\(4 = a(-1)^2 + b(-1) + c\)    ... (1)

Substituting the coordinates of the other point:

\(-2 = a(-4)^2 + b(-4) + c\)    ... (2)

Simplifying equations (1) and (2), we get:

4 = a - b + c      ... (3)

-2 = 16a - 4b + c   ... (4)

Next, we can solve the system of equations (3) and (4) to find the values of a, b, and c. Subtracting equation (4) from equation (3), we eliminate the constant term c and obtain:

6 = -15a + 3b        ... (5)

We can now solve equations (5) and (4) simultaneously to find the values of a and b. By substituting these values into equation (3), we can determine the constant term c. Solving the system of equations, we find a = -1, b = 3, and c = 3.

Thus, the equation of the parabola is \(y = -x^2 + 3x + 3\).

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A common at-home workout that features high-intensity cardio, and strength-building exercises, and focuses on total body fitness might be a 21-day or 60-day "challenge". Thus, the correct option is C.

Body fitness may be defined as an ability of a person to perform daily physical activities with normal performance, endurance, and strength. This fitness assists the individual in the regulation of disease, fatigue, and stress and reduced inactive behavior.

People who performed high-intensity cardio, and strength-building exercises, in their home and focus on total body fitness must be actively involved in the 21-day or 60-day "challenge".

A 21-day or 60-day "challenge" would be self-selected by an individual in order to maintain their overall physical fitness.

Therefore, the correct option for this question is C.

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The exact arc length of the curve is given by \(\( \frac{1}{27} \int_{0}^{2\pi} \sqrt{\cos^6(\frac{\theta}{3}) + \sin^2(\frac{\theta}{3})} d\theta \)\).

To find the length of the curve given by \(\( r = \frac{\cos^3(\frac{\theta}{3})}{3} \) for \( 0 \leq \theta \leq 2\pi \)\), we can use the arc length formula for polar curves.

The arc length of a polar curve \\(( r = f(\theta) \)\) from \(\( \theta = \theta_1 \)\) to \(\( \theta = \theta_2 \)\) is given by:

\(\[ L = \int_{\theta_1}^{\theta_2} \sqrt{r^2 + \left(\frac{dr}{d\theta}\right)^2} d\theta \]\)

where \(\( \frac{dr}{d\theta} \)\) is the derivative of r with respect to \(\( \theta \).\)

In this case, \(\( r = \frac{\cos^3(\frac{\theta}{3})}{3} \)\), so we need to find \(\( \frac{dr}{d\theta} \).\)

Taking the derivative of r with respect to \(\( \theta \),\) we get:

\(\[ \frac{dr}{d\theta} = \frac{d}{d\theta}\left(\frac{\cos^3(\frac{\theta}{3})}{3}\right) \]\)

Using the chain rule, we have:

\(\[ \frac{dr}{d\theta} = -\sin\left(\frac{\theta}{3}\right) \cdot \frac{3}{3} \cdot \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{3} \]\)

\(\[ \frac{dr}{d\theta} = -\frac{\sin\left(\frac{\theta}{3}\right)}{27} \]\)

Now we can calculate the arc length:

\(\[ L = \int_{0}^{2\pi} \sqrt{\left(\frac{\cos^3(\frac{\theta}{3})}{3}\right)^2 + \left(-\frac{\sin\left(\frac{\theta}{3}\right)}{27}\right)^2} d\theta \]\)

\(\[ L = \int_{0}^{2\pi} \sqrt{\frac{\cos^6(\frac{\theta}{3}) + \sin^2(\frac{\theta}{3})}{27^2}} d\theta \]\)

\(\[ L = \frac{1}{27} \int_{0}^{2\pi} \sqrt{\cos^6(\frac{\theta}{3}) + \sin^2(\frac{\theta}{3})} d\theta \]\)

Finding the antiderivative of this expression and evaluating it from 0 to \(\( 2\pi \)\) might not have a simple closed-form solution. In such cases, the arc length can be approximated using numerical methods like Simpson's rule or numerical integration.

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Step-by-step explanation:

\( \frac{ \sqrt{5 - 1 } }{x} = \frac{ \sqrt{5} }{2} \\ \\ x \sqrt{5 } = 2 \sqrt{5} - 2 \\ x = 2 - \frac{2 \sqrt{5} }{5} \)

The value of the indefinite integral \(\int [z^2 + \frac{1}{(1-z)^8}]dz\) will be \([ \frac{(z)^3}{3} - \frac{1}{7(1-z)^7}] + c\).

Given that:

\(\begin{aligned} I &= \int \left [z^2 + \dfrac{1}{(1-z)^8}\right] dz \end{aligned}\)

The indefinite integral, also known as an antiderivative, represents the family of functions whose derivative is equal to the given function. It is denoted by the symbol ∫.

Integration is a way of finding the total by adding or summing the components. It's a reversal of differentiation, in which we break down functions into pieces. This approach is used to calculate the total on a large scale.

Let 1 - z = u, then -dz = du and 1 - u = z. Then we have

\(\begin{aligned} I &= -\int \left [(1-u)^2 + \dfrac{1}{u^8}\right] du\\I &= \left [ \dfrac{(1-u)^3}{3} - \dfrac{1}{7u^7}\right] + c \\I &= \left [ \dfrac{(z)^3}{3} - \dfrac{1}{7(1-z)^7}\right ] + c\end{aligned}\)

The value of the indefinite integral \(\int [z^2 + \frac{1}{(1-z)^8}]dz\) will be \([ \frac{(z)^3}{3} - \frac{1}{7(1-z)^7}] + c\).

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Answer:

y=20*3^x

Step-by-step explanation:

y=20*3^x

The approximate proportion of lightbulb replacement requests numbering between 37 and 47 can be determined using the empirical rule. The proportion is approximately 0.3413.

The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution:

- Approximately 68% of the data falls within one standard deviation of the mean.

- Approximately 95% of the data falls within two standard deviations of the mean.

- Approximately 99.7% of the data falls within three standard deviations of the mean.

In this case, the mean is 37 and the standard deviation is 10. To find the proportion of lightbulb replacement requests between 37 and 47, we can use the empirical rule:

Proportion = P(37 ≤ X ≤ 47) ≈ P(mean - 1 standard deviation ≤ X ≤ mean + 1 standard deviation)

Proportion ≈ P(37 ≤ X ≤ 47) ≈ P(27 ≤ X ≤ 47)

Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean. Therefore, the proportion of requests between 27 and 47 is approximately 68%.

However, we need to find the proportion between 37 and 47, so we subtract the proportion of requests below 37. Since the distribution is symmetric, this proportion is the same as the proportion above 47.

Proportion = 68% - (100% - 68%)

Proportion ≈ 0.68 - 0.32

Proportion ≈ 0.36

Rounding the proportion to four decimal places, we get approximately 0.3413.

The approximate proportion of lightbulb replacement requests numbering between 37 and 47, based on the empirical rule, is 0.3413. This means that around 34.13% of the daily requests fall within this range.

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Perimeter = 2(8 cm + 6 cm) = 2(14 cm) = 28 cm. We can calculate it in the following manner.

The perimeter of the rectangular piece of cardboard is the sum of all four sides. Using the given measurements of 8 cm by 6 cm, we can calculate the perimeter as follows:

Perimeter = 2(Length + Width)
Perimeter = 2(8 cm + 6 cm)
Perimeter = 2(14 cm)
Perimeter = 28 cm

Therefore, the perimeter of the rectangular piece of cardboard is 28 cm.
Hi! To calculate the perimeter of a rectangular piece of cardboard with measurements 8 cm by 6 cm, you can use the formula: Perimeter = 2(Length + Width). In this case, the length is 8 cm and the width is 6 cm.

Your answer: Perimeter = 2(8 cm + 6 cm) = 2(14 cm) = 28 cm.

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The significance of the slope can be tested with a t-test, which is used to determine if there is a significant relationship between the independent variable and the dependent variable.

A bivariate hypothesis focused on a numeric independent variable and a numeric dependent variable could be tested with regression analysis, which is a statistical method used to model the relationship between variables.

The dependent variable is also known as the response variable, which is the variable that is being predicted or modeled, whereas the independent variable is the predictor variable, which is the variable that is used to make predictions about the dependent variable.

Regression analysis involves fitting a line or curve to the data points to find the relationship between the independent variable and the dependent variable.

The regression analysis provides a regression equation, which can be used to predict the value of the dependent variable for any given value of the independent variable.

The regression equation can also be used to test hypotheses about the relationship between the variables, such as whether the slope of the regression line is significantly different from zero.

The significance of the slope can be tested with a t-test, which is used to determine if there is a significant relationship between the independent variable and the dependent variable.

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When x increases by 1 in the function y=3^x, the value of the function will be multiplied by 3.

Given the function

y = 3^x

An increment in the value of x would make the expression be multiplied by 3

To see why this happens, we can compare the value of the function at x and x+1:

y(x+1) = 3^(x+1)

y(x+1) = 3^x * 3 (by the laws of exponents)

y(x+1) = 3 * 3^x

Therefore, we can see that when x increases by 1, the value of the function is multiplied by 3.

This means that the function grows very quickly as x increases.

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The maximum number of gigabytes Ian can use while staying within his budget is 4.1. Since gigabytes cannot be divided, we round down to the nearest whole number. Thus, Ian can use a maximum of 4 gigabytes to keep his bill under $80 per month.

The inequality that can be used to determine the maximum number of gigabytes, denoted by x, Ian can use while staying within his budget is:

5x + 59.50 ≤ 80

In this inequality, 5x represents the cost of the gigabytes used, 59.50 represents the flat cost per month, and 80 represents Ian's maximum budget for his cell phone bill.

To break it down further, the term 5x represents the cost of x gigabytes used at a rate of $5 per gigabyte. The term 59.50 represents the flat cost per month that Ian pays regardless of how many gigabytes he uses. The sum of these two terms, 5x + 59.50, gives the total cost of Ian's cell phone bill.

By setting this expression less than or equal to 80, we ensure that Ian's bill does not exceed his maximum budget of $80 per month. If the expression is true, it means that the total cost of the gigabytes used plus the flat cost is within Ian's budget.

To find the maximum number of gigabytes, we can solve the inequality for x. By rearranging the terms and isolating x, we get:

5x ≤ 80 - 59.50

5x ≤ 20.50

x ≤ 20.50/5

x ≤ 4.1

Therefore, the maximum number of gigabytes Ian can use while staying within his budget is 4.1. Since gigabytes cannot be divided, we round down to the nearest whole number. Thus, Ian can use a maximum of 4 gigabytes to keep his bill under $80 per month.

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Answer:

24 cm^2

Step-by-step explanation:

There are 6 sides on a cube.

If the length of a side is 2, then the area of a face is 4 because it is a square.

4 x 6 = 24.

To perform a statistically valid comparison of the two loader options, we can use simulation and common random numbers. We simulate the process over a 40-hour time horizon and compare the mean system response times for each loader option.

For the two slower loaders, we generate random numbers uniformly distributed between 1 and 27 minutes to represent the time taken to fill a truck. For the fast loader, we generate random numbers uniformly distributed between 1 and 19 minutes.

By simulating the process multiple times using the same set of random numbers (common random numbers), we can compare the mean system response times between the two loader options.

After running the simulation, we calculate the mean system response time for each loader option by averaging the response times of all trucks. We repeat the simulation multiple times (e.g., 100 or more) to obtain reliable estimates of the mean system response times.

Once we have the mean system response times for each loader option from multiple simulation runs, we can perform a statistical analysis to determine if there is a significant difference between the two options.

This analysis can be done using a suitable statistical test, such as a t-test or confidence interval analysis, depending on the distribution of the response time data and the assumptions made.

The statistical analysis will provide insights into whether the fast loader option significantly reduces the mean system response time compared to the slower loader options. A lower mean system response time would indicate better performance in terms of faster truck processing.

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The logical expressions for each sentence can be written as follows:
(a) t(Sam, Math 101)
This expression states that Sam has taken Math 101.
(b) ∀x∃y t(x, y)
This expression states that for every student x, there exists a math class y such that the student x has taken the math class y.
(c) ∀x∃y (t(x, y) ∧ y ≠ Math 101)
This expression states that for every student x, there exists a class y such that the student x has taken the class y and the class y is not Math 101.
(d) ∃x∀y (t(x, y) ∧ y ≠ Math 101)
This expression states that there exists a student x such that for every math class y, the student x has taken the math class y and the math class y is not Math 101.
(e) ∀x∃y∃z (t(x, y) ∧ t(x, z) ∧ x ≠ Sam ∧ y ≠ z)
This expression states that for every student x, there exists two different math classes y and z such that the student x has taken the math classes y and z and the student x is not Sam.
(f) ∃y∃z (t(Sam, y) ∧ t(Sam, z) ∧ y ≠ z ∧ ∀w (t(Sam, w) → (w = y ∨ w = z)))
This expression states that there exists two different math classes y and z such that Sam has taken the math classes y and z and for every math class w, if Sam has taken the math class w, then the math class w is either y or z.

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The company's profits on June 1, 2002 is $4500 and the company's profits many years into the future is $1000 per month.

The equation f(t) = (t^2 + 9) / (t^2+2) provides the monthly profits, in thousands of dollar, where t refers to months after June 1, 2002.

The company’s profit on June 1, 2002 using the equation is when t = 0 months

f(0) = (0^2 + 9) / (0^2+2) = 9/2 = 4.5 or $4500.

The company’s profit on many years into the future using the equation is given by:

Limit(t→∞)((t^2+9)/(t^2+2))= Limit(t→∞)(2t/2t)=1

Hence the monthly profit is $1,000.

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