how many cylindrical glasses 6cm in diameter and 10cm deep can be filled from a cylindrical jug 10cm in diameter and 18cm deep

Answer:

A) 3/5

B) 3/4

Step-by-step explanation:

A) 6 whites 4 grey. 10 total. 6/10 simplify to 3/5

B) 6 whites 4 grey. Take two of the grey because 9 and 10 can't be used. So 6 white 2 grey. 8 total. 6/8 simplify to 3/4

Hope this helps

Answer:

75%?

Step-by-step explanation:

Not 100% on this, need better explenation.

Answer: 75%

Step-by-step explanation:

Answer:

Either B or C

Step-by-step explanation:

Check the picture below.

Answer: |t - 15| ≤ 30 ; -30 ≤ t - 15 ≤ 30

Step-by-step explanation:

To set up the equation, we have to find the center, and the tolerance, so that we can use formula "|x - c| ≤ t"

First, we can find the tolerance by adding both number, then dividing by 2 --> -15 + 45 = 30 --> 30/2 = 15, so we now know that the center is 15

Next, we can find the tolerance by finding the distance between the center and one of the number --> 15 - (-15) = 30, so we now know that the tolerance is 30

Now we can set up our equation,

center (c) = 15

tolerance (t) = 30

|t - 15| ≤ 30

Now that we have our equation, we can set up the inequality

|x - c| ≤ t = -t ≤ x - c ≤ t

so,

-30 ≤ t - 15 ≤ 30

Hope this helps!

(sorry it was so long)

To answer this question, we would need to perform a hypothesis test using the given sample data and a significance level of α = 0.05. The null hypothesis would be that the standard deviation of the resting heart rates for students in this class is equal to 12 bpm, while the alternative hypothesis would be that it is different from 12 bpm.

We would then need to calculate the sample standard deviation from the given data and use it to compute the test statistic (either a t-score or a z-score, depending on the sample size and whether or not the population standard deviation is known). We would compare this test statistic to the critical value from the appropriate distribution (either a t-distribution or a standard normal distribution) using the given significance level.

If the test statistic falls outside the critical value region, we would reject the null hypothesis and conclude that there is enough evidence to say that the standard deviation of the resting heart rates for students in this class is different from 12 bpm. However, if the test statistic falls inside the critical value region, we would fail to reject the null hypothesis and conclude that there is not enough evidence to make such a claim.

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The amount of juice decreased by half, how much would remain is 2 pints. So, the correct answer is C.

The capacity of the container is 1 gallon, which is equivalent to 4 quarts, 8 pints, or 16 cups. If the amount of juice decreases by half, you would have 50% of the original amount remaining.

To calculate this, you can use the following conversions:

1 gallon = 4 quarts

1 gallon = 8 pints

1 gallon = 16 cups

Half of 1 gallon is:

0.5 * 4 quarts = 2 quarts

0.5 * 8 pints = 4 pints

0.5 * 16 cups = 8 cups

Since 2 quarts is equivalent to 4 pints and 8 cups, the correct answer is:

A) 1 quart (2 quarts remaining)

B) 1 pint (4 pints remaining)

C) 2 pints (4 pints remaining)

D) 4 cups (8 cups remaining)

The correct answer is C) 2 pints, as 4 pints of juice would remain in the container after decreasing the amount by half.

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Sahara has spent 3/4 of her money.

To find out what fraction of her money Sahara has spent, we need to first calculate how much money she has left after spending $60.

Starting with $80, subtracting $60 gives us $20.

Therefore, Sahara has $20 left.

To express this as a fraction, we need to use the total amount of money she started with as the denominator and the amount she has left as the numerator.

So, the fraction of her money that Sahara has spent is:
$60/$80

This can be simplified by dividing both the numerator and denominator by 20:
$60/$80 = $3/$4

Therefore, Sahara has spent 3/4 of her money.

It's important to understand fractions as they are a fundamental concept in mathematics. Fractions are a way of representing parts of a whole. The numerator represents the part of the whole that we are considering, while the denominator represents the total number of parts that make up the whole. In this case, the whole is the total amount of money Sahara started with, which was $80. The part that she spent was $60, so the fraction of her money spent is 3/4.

Fractions are used in many different mathematical operations, including addition, subtraction, multiplication, and division. It is important to be able to manipulate fractions in order to solve more complex problems in algebra and calculus.

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Answer: Slope=2/3

Step-by-step explanation:

Looking at points (5,2) and (8,4), we can plug them into the equation

slope=(y2-y1)/(x2-x1)

slope=(4-2)/(8-5)

slope=2/3

Answer:

126

Step-by-step explanation:

a = 22

d = 22- 20 = -2

n = 9

Sn = 0.5n(2a +d(n-1))

=0.5 * 9 (2 *22 +-2(9-1))

= 126

By evaluating the expression for s(tB), we can determine whether driver A crossed the finish line before or after driver B. If s(tB) is positive, it means driver A crossed the finish line before driver B. If s(tB) is negative, it means driver A crossed the finish line after driver B.

To solve the initial value problem, we start with the equation vA'(t) = -k(vA(t))^2, where vA'(t) represents the derivative of vA with respect to t.

This equation describes the deceleration of driver A, proportional to the square of his remaining speed. Rearranging and solving the differential equation, we get vA(t) = 1 / (kt + C), where C is a constant determined by the initial conditions.

To find the expression for s(t), we integrate vA(t) with respect to t: s(t) = ∫(1 / (kt + C)) dt. Integrating this expression gives us s(t) = (1/k) ln(kt + C) + D, where D is another constant determined by the initial conditions.

At t = t1 (when driver A's speed is halved, i.e., one mile after running out of gas), we have vA(t1) = vA(0) / 2. Plugging this into the expression for vA(t) from step 1, we find 1 / (k * t1 + C) = (1 / (k * 0 + C)) / 2. Simplifying, we get k = ln(2) / t1.

Using the expression for s(t) from step 2, we can find tB by settings S(tB) = 3 (since driver A was leading by 3 miles). Simplifying this equation, we find tB = (e^(3k) - C) / k. Plugging in the value of k we found in step 3, we have tB = (e^(3ln2 / t1) - C) / (ln2 / t1).

To evaluate s(tB), we substitute t = tB into the expression for s(t) from step 2, resulting in s(tB) = (1/k) ln(ktB + C) + D. Since tB depends only on vB and t1, and C and D are constants determined by the initial conditions, s(tB) depends only on vB.

If s(tB) is positive, it means driver A crossed the finish line before driver B. If s(tB) is negative, it means driver A crossed the finish line after driver B.

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Answer: no idea

Step-by-step explanation:

The difference between the two models and why real estate should have its own asset allocation model.

The Sharpe ratio is a measure of risk-adjusted return. It is calculated by dividing the excess return of an investment over a benchmark by the standard deviation of the investment's returns. The higher the Sharpe ratio, the better the investment's risk-adjusted return.

The Cheng, Lin, and Liu model is a more complex model that takes into account the time horizon of the investment, the volatility of the investment, and the correlation between the investment and the benchmark. The model is designed to maximize the Sharpe ratio of the investment over a specified time horizon.

The real estate market is different from the financial market in several ways. Real estate is a illiquid asset, meaning that it can be difficult to sell quickly. Real estate is also a cyclical asset, meaning that its prices tend to go up and down over time. Real estate is also a heterogeneous asset, meaning that there is a wide variety of properties available, each with its own unique characteristics.

Because of these differences, the real estate market should have its own asset allocation model. A model that is designed for the financial market may not be appropriate for the real estate market. A real estate asset allocation model should take into account the illiquidity, cyclicality, and heterogeneity of the real estate market.

Here are some additional reasons why real estate should have its own asset allocation model:

Real estate is a long-term investment. The typical holding period for real estate is 10 years or more. This is different from the financial market, where the typical holding period is much shorter.

Real estate is a leveraged investment. This means that investors can use borrowed money to purchase real estate. This can magnify the potential returns of real estate, but it can also magnify the potential losses.

Real estate is a local investment. The value of real estate is often driven by local factors, such as the job market, the economy, and the demographics. This means that real estate investments should be tailored to the specific market in which they are located.

Overall, the real estate market is different from the financial market in several ways. These differences make it important for real estate investors to have their own asset allocation model.

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Answer:

a. when x=1 so substitute 1 to any X in the given equation.

y=-3(1)+2.5

y=-3+2.5

y=-0.5

b.when x is -1.5 so substitute -1.5 to any x in the equation

y=-3(-1.5)+2.5

y=-4.5+2.5

y=-2

Answer:

Step-by-step explanation:

A third degree polynomial has a total of three roots, real and imaginary combined.

If it already has 2 real roots, -4 and +4, then it has to have three real roots because imaginary roots come in conjugate pairs, i.e. they come in even numbers.

Answer:

Three real roots

Step-by-step explanation:

By incorporating conic sections into the design, the robotic prototype can achieve optimal functionality, improved maneuverability, precise data collection, and effective communication.

Purpose: The robotic prototype will be designed to assist in agriculture by automating the process of crop planting and harvesting in large-scale farms.

Incorporating Conic Sections:

1. Circular Base: The robot can have a circular base that allows for efficient movement in any direction. The circular base can provide stability and smooth rotation, enabling the robot to navigate through fields and maneuver around obstacles.

2. Elliptical Arms: The robot can be equipped with elliptical arms that can extend and retract. These arms can be used for tasks such as seed planting or harvesting. The elliptical shape allows for a wide range of motion, reaching different areas within the farm while maintaining precision and efficiency.

3. Parabolic Sensors: To detect and analyze the quality of crops or soil conditions, the robot can be equipped with parabolic sensors. The parabolic shape of the sensors helps focus and collect data accurately, allowing the robot to assess crop health, moisture levels, and nutrient content with greater precision.

4. Hyperbolic Communication System: The robot can utilize a hyperbolic communication system to transmit data and receive instructions from a central control system or farm management software. The hyperbolic shape aids in efficient long-range communication, ensuring reliable connectivity and enabling real-time monitoring and control of the robot's activities.

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Answer:

7 hours 15 minutes

7.25 hours

Step-by-step explanation:

Break from 11:45 am to 12:30 pm = 45 minutes

Two 15-minute unpaid coffee breaks during the day = 30 minutes

Total break hours = 45 minutes + 30 minutes

= 1 hour 15 minutes

Total work day hours from 8:30 am to 5:00 pm = 8 hours 30 minutes

How many hours are you paid?

Total hours paid = Total work day hours - Total unpaid break hours

= 8 hours 30 minutes - 1 hour 15 minutes

= 7 hours 15 minutes

b) Express your answer as a decimal in hours only

7 hours 15 minutes as a decimal

15 minutes to hour = 60 minutes/15 minutes

= 1/4

= 0.25 hours

7 hours 15 minutes as a decimal = 7 hours + 0.25 hours

= 7.25 hours

Answer:

20%

Step-by-step explanation:

Divide 14 by 70 to get the answer 0.2.  Since it is 0.2 it is also equivalent to 20% which is the percentage Marley has rolled a strike.

Step-by-step explanation:

Volume= L×W×H

=6ft×4ft×3ft

=72 cubic feet

Hope it helps you!!

Answer:

72 cubic ft

Step-by-step explanation:

volume = length x width x height

That is - 3x4x6 cubic ft

           =  12x6 cubic ft

            = 72 cubic ft

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From the point of view of conditioning and the results of T&B Theorem 18.1, including more variables in a regression model does not necessarily provide more information, and in fact, it can lead to issues such as multicollinearity.

T&B Theorem 18.1, also known as the Gauss-Markov theorem, states that under certain assumptions, the ordinary least squares (OLS) estimator is the best linear unbiased estimator (BLUE) of the coefficients in a linear regression model.

This means that the OLS estimator has the smallest variance among all linear unbiased estimators.

However, when we include more variables in the regression model, it can lead to multicollinearity. Multicollinearity occurs when there is a high correlation between predictor variables. In such cases, the predictors become linearly dependent, and this can lead to unstable and unreliable coefficient estimates.

When multicollinearity is present, it becomes difficult to distinguish the individual effects of each variable on the outcome variable. The coefficients may become sensitive to small changes in the data, and the interpretation of the coefficients becomes challenging.

Furthermore, can inflate the standard errors of the coefficient estimates, making it difficult to detect statistically significant effects. This, in turn, affects hypothesis testing and the interpretation of the significance of each variable.

Therefore, including more variables in a regression model does not necessarily provide more information. Instead, it can introduce issues such as multicollinearity, which can undermine the reliability and interpretability of the coefficient estimates.

It is important to carefully consider the choice of variables and assess for multicollinearity to ensure the validity of the regression model and its results.

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Answer:

120 i think. sorry if its wrong.

Answer:

10 gallons

Step-by-step explanation:

If 60 gallons of water drains in 6 minutes, that means that to find the amount drained per minute, you would have to divide the number of gallons per minute. So 60 gallons÷6 minutes is 10 gallons per minute.

Answer:

Step-by-step explanation:

As host, we want to insure each guest has at least one slice of pie.  We can say  (1 Slice/Guest) and use this as a conversion factor.  We also know each pie has 8 slices:  (8 Slices/1 Pie).  Since this is a conversion factor, we can invert it to (1 Pie/8 Slices).  We expect 38 people and want to convert that number of people to the number of pies, p, we need.

  p (pies) \(\geq\) (38 Guests)*(1 Slice/Guest)*(1 Pie/8 Slices)

We use the \(\geq\) sign to note that we need a minimum of pies to be sure everyone is served.

p (pies) \(\geq\) (38 )*(1 /)*(1 Pie/8 )

Note how the units cancel:

Guests and Slices both cancel and we are left with pies as the only remaining unit, as we hoped we'd see.

p \(\geq\) (38/8) pies

p = 4 +(6/8) pies

Since we cannot purchase 6/8 of a pie, we need to round up to 5 pies.

5 pies, at 8 slices per pie, will provide 40 servings, enough for the 38 guests.

Answer:

$1600 at 8% and 3500 at 12%

Step-by-step explanation:

The rule of the interest is I = PRT, where

Assume that the amount of money is $x

∴ P = x

∵ The rate is 8%

∴ R = 8/100 = 0.08

∵ She has an annual income

∴ T = 1

→ Substitute them in the rule to find the interest amount

∴ I = x × 0.08 × 1

∴ I = 0.08x

∵ She invested $300 more than twice the previous amount

∴ P = 2x + 300

∵ The rate is 12%

∴ R = 12/100 = 0.12

∵ T = 1

→ Substitute them in the rule to find the other interest amount

∴ I = (2x + 300) × 0.12 × 1

∴ I = 0.24x + 36

∵ Her total annual income from both investments is $548

→ Add the two amount of interest and equate their sum by 548

∴ 0.08x + 0.24x + 36 = 548

→ Add the like terms in the left side

∴ 0.32x + 36 = 548

→ Subtract 36 from both sides

∴ 0.32x + 36 - 36 = 548 - 36

∴ 0.32x = 512

→ Divide both sides by 0.32

∴ x = 1600

∴ She invested $1600 at 8%

→ Substitute x by 1600 in the expression of the other amount to find it

∵ 2x + 300 = 2(1600) + 300 = 3500

∴ She invested $3500 at 12%

Answer:

Step-by-step explanation:

To determine the mole fraction of solute in a solution, we need to know the moles of solute and the total moles of solute and solvent combined.

In this case, you mentioned that the solution is a 3.14 m aqueous solution. The "m" represents molarity, which is defined as the number of moles of solute per liter of solution.

However, to calculate the mole fraction, we need the actual number of moles of solute, not just the molarity. Without the information about the specific solute and its concentration in moles, we cannot calculate the mole fraction.

Please provide the moles of solute and the total moles of solute and solvent if you have that information, and I will be happy to help you calculate the mole fraction.

Answer:

2/3, 2 to 3, 2:3

Step-by-step explanation:

Answer:

can u please attach the picture of the question

The mean length of this type of telephone conversation is E(X) = 7/5.

This means that on average, these conversations last 7/5 units of time. Additionally, the variance of X is Var(X) = 49/25, which indicates the amount of variation in the lengths of these conversations. The standard deviation, σ, is equal to 7/5, which is a measure of how spread out the data is.

Furthermore, if we add 5 to each conversation length, square the result, and take the expected value, we get E((X+5)2) = 949/25.

This calculation gives us an idea of the expected value of the squared deviations of the conversation lengths from their mean value, after adding 5 to each length.

This value can be used to assess the variability of the data and its potential impact on the outcomes of interest. Overall, these statistical measures provide useful information about the distribution of conversation lengths, and can inform decision-making in various contexts.

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Answer:

For an ordered pair to be a solution to a system of equations, the values for x and y must agree with every equation in the system. For example, if you have two linear equations so that their lines intersect, then there is exactly one solution (x, y) such that both equations are true statements when both x and y are entered into both equations. Therefore, those two coordinates (x, y) are the only solution to that system.

In other systems, such as quadratic systems containing two equations with two second-degree variables, x^2 and y^2, you can have up to four solutions (x, y) since the graphs of these equations may intersect in up to four points. Again, it means that the coordinates to each of these points agree with all equations in the system.

Step-by-step explanation: