CONTAINER SPECIFICATIONS: • Each container must hold exactly one litre of liquid. Each container must have a minimum surface area. The surface area of each container must include the lid. The length of the rectangular base must be twice the breadth. The triangular container must have an equilateral base. TASK 1 Rectangular base container: CONTAINER A Sketch a rectangular base container with dimensions to hold exactly one litre of liquid. Clearly show your dimensions on your diagram. 1. Calculate the volume of this container in terms of above dimensions. 2. Calculate the surface area of the container in terms of above dimensions. 3. Calculate the value of the dimensions for this container for the surface area to be a minimum?

To determine the change in angular momentum (ΔL) of a cylinder from t = 0 to t = t0, a student can use the equation:

ΔL = I * Δω

where ΔL is the change in angular momentum, I is the moment of inertia of the cylinder, and Δω is the change in angular velocity.

To calculate Δω, the student needs to know the initial and final angular velocities, ω0 and ωt0, respectively. The change in angular velocity can be calculated as:

Δω = ωt0 - ω0

Once Δω is determined, the student can use the moment of inertia (I) of the cylinder to calculate ΔL using the equation mentioned earlier.

The moment of inertia (I) depends on the mass distribution and shape of the cylinder. For a solid cylinder rotating about its central axis, the moment of inertia is given by:

I = (1/2) * m * r^2

where m is the mass of the cylinder and r is the radius of the cylinder.

By substituting the known values for Δω and I into the equation ΔL = I * Δω, the student can calculate the change in angular momentum (ΔL) of the cylinder from t = 0 to t = t0.

It's important to note that this method assumes that no external torques act on the cylinder during the time interval. If there are external torques involved, the equation for ΔL would need to include those torques as well.

To learn more about angular momentum click here:

brainly.com/question/31592991

#SPJ11

Answer:

The answer is 2

Step-by-step explanation:

4z+2y-x

4(4)+2(-6)-2

16+(-12)-2

16-12-2

4-2

2

Step-by-step explanation:

\(4z + 2y - x \\ = 4 \times 4 + 2 \times ( - 6) - 2 \\ = 16 + ( - 12) - 2 \\ = 16 + ( - 14) \\ = 2\)

Answer:

a

Step-by-step explanation:

Answer:

A) Fluid ounces

Step-by-step explanation:

The probability that the life span of a randomly selected monitor will be more than 16,600 hours is 0.9192 or 91.92% (rounded to four decimal places).

We can standardize the value of 16,600 hours to a z-score by using the formula

z = (x - mu) / sigma

where x is the value we want to find the probability for, mu is the mean life span, and sigma is the standard deviation (the square root of the variance).

Substituting the given values, we get

z = (16600 - 18000) / sqrt(1000000) = -1.4

Using a standard normal distribution table or calculator, we can find the probability that the life span of a randomly selected monitor will be more than 16,600 hours by looking up the area to the right of the z-score of -1.4.

The area to the right of -1.4 is approximately 0.9192.

Therefore, the probability that the life span will be more than 16,600 hours is 0.9192 or 91.92% (rounded to four decimal places).

To know more about Probability:

https://brainly.com/question/11234923

#SPJ4

The probability that she requires 8 or fewer cases to obtain her first win is \(\(P(C \ \leq \ 8) = \frac{{58975}}{{65536}}\)\).

To compute P(C ≤ 8), we can use the formula for the sum of a finite geometric series. Here, C represents the number of cases required to obtain the first win, and each case is won with a probability of 3/4.

The probability that she wins on the first case is 3/4.

The probability that she wins on the second case is (1 - 3/4) \(\times\) (3/4) = 3/16.

The probability that she wins on the third case is (1 - 3/4)² \(\times\) (3/4) = 9/64.

And so on.

We need to calculate the sum of these probabilities up to the eighth case:

P(C ≤ 8) = (3/4) + (3/16) + (9/64) + ... + (3/4)^7.

Using the formula for the sum of a finite geometric series, we have:

P(C ≤ 8) = \(\(\frac{{\left(1 - \left(\frac{3}{4}\right)^8\right)}}{{1 - \frac{3}{4}}}\)\).

Let us evaluate now:

P(C ≤ 8) = \(\(\frac{{1 - \left(\frac{3}{4}\right)^8}}{{1 - \frac{3}{4}}}\)\).

Now we will simply it:

P(C ≤ 8) = \(\(\frac{{1 - \frac{6561}{65536}}}{{\frac{1}{4}}}\)\).

Calculating it further:

P(C ≤ 8) = \(\(\frac{{58975}}{{65536}}\)\).

Therefore, the probability that she requires 8 or fewer cases to obtain her first win is \(\(P(C \ \leq \ 8) = \frac{{58975}}{{65536}}\)\).

For more questions on probability :

https://brainly.com/question/30390037

#SPJ8

One bagel costs 155 cents.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question.

Let x = cost of one bagel

y = cost of one toast

z = cost of one muffin

If two pieces of toast and a bagel costs $3.15, then 2y + x = 3.15.

2y + x = 3.15   ⇒   x = 3.15 - 2y     (equation 1)

If a bagel and a muffin costs $3.30, then x + z = 3.30.

x + z = 3.30     (equation 2)

Substitute equation 1 to equation 2.

x + z = 3.30     (equation 2)

3.15 - 2y + z = 3.30   ⇒   z = 0.15 + 2y      (equation 3)

If a piece of toast, two bagels, and three muffins costs $9.15, then

y + 2x + 3z = 9.15     (equation 4)

Substitute equations 1 and 3 to equation 4.

y + 2x + 3z = 9.15     (equation 4)

y + 2(3.15 - 2y) + 3(0.15 + 2y) = 9.15

y + 6.30 - 4y + 0.45 + 6y = 9.15

3y = 2.4

y = 0.8

Substitute the value of y to equation 1.

x = 3.15 - 2y     (equation 1)

x = 3.15 - 2(0.8)

x = 1.55

Hence, the cost of one bagel is $1.55 or 155 cents.

Learn more about algebraic expression and equation here: brainly.com/question/3927786

#SPJ4

Answer:

Lines q and r are parallel, so the corresponding angles are congruent; x = 50

Step-by-step explanation:

Given

See attachment for lines

Required

Which describes the value of x

From the attached image, we can see that p, q and r are parallel.

To solve for x, we consider parallel lines q and r

Where

\(50^\circ\) and x are corresponding angles

Hence:

\(x = 50^\circ\)

Answer:

1. Is b

2. Is c

3.is a

Step-by-step explanation:

Brainliest pls

Answer:

number 10 is $60 and 11 is 8 hours

Step-by-step explanation:

i can only help you on 10 and 11

The correct solving of the decimal shows that 3.675 × 10 = 36.750, 3.675 × 100 = 367.5 and 3.675 × 1,000 = 3675.

From the information given, it should be noted the students calculations are incorrect. Therefore, 3.675 ×10 = 3.6750, 3.675 × 100 = 3.67500 and 3.675 × 1,000 = 3.675000 are incorrect.

In this case, when multiply by raise to power 10, it's important to shift the decimal based on the number being raised to power.

Therefore, 3.675 × 10 = 36.750, 3.675 × 100 = 367.5 and 3.675 × 1,000 = 3675.

Learn more about decimals on:

https://brainly.com/question/1015576

Answer:

m<A = 90° - m<B

(AB)^2 = (AC)^2 + (BC)^2

sin A = cos B

if <A = <B, then m<A = 45°

Answer:

Step-by-step explanation:

∠A+∠B=90 complementary angles ( the sum equal 90°)

∠A=90 degrees-∠B

tan A=sinA/cos A

AB²= AC² +BC² (Pythagorean theorem)

if angle A=angle B then the angles are 45 degrees

cos A=sin(90-A)  

sin (a - b) = sin a.cos b - sin b.cos a

sin(90-A)=sin90.cosA-sinbAcos90 cos 90=0 and sin 90=1

sin(90-A)=1*cosA

sin(90-A)=cosA

the ones are  in bold are right

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

diagram

Step 02:

circle:

arcs and angles:

The answer is:

x = 68°

Similar to inference techniques used in earlier chapters regarding sample sizes, the conditions that allow us to use the Chi-square test protect us from having expected counts that are too small.

When conducting a Chi-square test, we are comparing observed counts to expected counts, and if the expected counts are too small, we may not have enough data to accurately determine if the observed counts are significantly different from what we would expect by chance alone. Therefore, one of the assumptions of the Chi-square test is that the expected counts in each cell of the contingency table should be at least 5, although some researchers suggest that expected counts should be at least 10 to increase the accuracy of the test.

Learn more about Chi-square test,

https://brainly.com/question/14082240

#SPJ4

Answer:

its 24. making me get out my book LOL

Answer:

its 30! :D heheh

This equation \(\frac{3}{m + 3}\) - \(\frac{m}{3 - m}\) = \(\frac{m^{2 } + 9}{m - 9}\) has no solution.

Since we have given that

\(\frac{3}{m + 3}\) - \(\frac{m}{3 - m}\) = \(\frac{m^{2 } + 9}{m - 9}\)

We need to find the solution of the above equation:

Since is a rational equation so, we will check for its extraneous solution.

\(\frac{3}{m + 3}\) - \(\frac{m}{3 - m}\) = \(\frac{m^{2 } + 9}{m - 9}\)

\(\frac{3}{m + 3}\) +  \(\frac{m}{3 - m}\)  =  \(\frac{m^{2 } + 9}{m - 9}\)  

\(\frac{3(m + 3) + m(m +3)}{m^{2} - 9}\) =   \(\frac{m^{2 } + 9}{m - 9}\)

\(\frac{3m - 9 + m^{2} +3m }{m^{2}-9 }\) =  \(\frac{m^{2 } + 9}{m - 9}\)

\(\frac{m^{2} -9+6m}{m^{2} -9}\) =  \(\frac{m^{2 } + 9}{m - 9}\)

\(m^{2} +6m -9 = m^{2} + 9\)

\(6m = 18\)

\(m = \frac{18}{6} = 3\)

Hence, the extraneous solution in case of rational equation is 3 , when we put m = 3, it becomes undefined so, it has no solution.

Learn more about equations here;

https://brainly.com/question/22688504

#SPJ4

The correlation Illustrates that B. The graph shows a positive correlation, and it is a non-linear model.

In this scenario, the width would be plotted on the x-axis of the scatter plot while the length in centimeters would be plotted on the y-axis of the scatter plot.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select the format trend line, and then tick the box to display an equation for the line of best fit on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the width and length, a linear equation for the line of best fit is given by y = 1.31x + 0.02.

Learn more about correlation on:

https://brainly.com/question/4219149

#SPJ1

Answer: The graph shows no correlation, and it is neither linear nor exponential.

Step-by-step explanation:

try doing a line of fit you're ALWAYS. gonna be ignoring other dots/points/coorids.

Why it's not a correlation is because nothing is together. You could consider a lot of dots on the edge.

If that doesn't make sense to you lets go through each answer

The graph shows a negative correlation, and it is a linear model.

The coordinates don't form any specific line

None of the coordinates are together

there's no slope since there's no line of fit.

it's THE SAME FOR THE OTHER ANSWER CHOICES BESIDES:

'The graph shows no correlation, and it is neither linear nor exponential.'

Answer:

Eso es loca

Step-by-step explanation:

brainliest please??

Answer:

OK

Step-by-step explanation:

Answer:

Length = Width = 55

Step-by-step explanation:

Perimeter of rectangle = 2(length + width)

Let x = length; let y = width.

perimeter = 2(x + y)

The perimeter must be 220.

2(x + y) = 220

x + y = 110

y = 110 - x

length = x

width = 110 - x

area = length × width

area = x(110 - x)

area = 110x - x²

A = 110x - x²

Take the first derivative of the area function and set equal to zero. Then solve for x.

A' = 110 - 2x

110 - 2x = 0

2x = 110

x = 55

y = 110 - x = 110 - 55 = 55

Answer: Length = Width = 55

Answer:

Step-by-step explanation:

-3/5<-1/5<1/5

1/4<4/7<10/8

:)

Answer:

A) 8 cm

Step-by-step explanation:

Cylinder Volume formula:

V = πr²h

72π = π3²h

72π = 9πh

h = (72π)/(9π)

h = 8

The probability of a family with 5 people will be 0.124.

A survey found the distribution of some families by size and is as follows:

Family Size 2 3 4 5 6 7 8

Frequency 87 50 61 31 16 3 2

The probability is given as,

P = (Favorable event) / (Total event)

The probability of a family with 5 people is calculated as,

P = (31) / (87 + 50 + 61 + 31 + 16 + 3 + 2)

P = 31 / 250

P = 0.124

Thus, the probability of a family with 5 people will be 0.124.

More about the probability link is given below.

https://brainly.com/question/795909

#SPJ1

Answer: The length of each of the two equal sides is 19 km

Step-by-step explanation:. Subtract the giver lengths of the bases: 4+1= 5

43 - 5 = 38.

The trapezoid is iscosceles, so the remaining two sides are equal.

Divide. 38/2 = 19

I hope this helps you!

The average rate of change per hour in the temperature is 0.83 degrees.

To find the average rate of change per hour, we need to divide the total change in temperature by the number of hours over which the temperature changed.

The temperature rose by 5 degrees from 6:00 am to 12:00 pm, which is a period of 6 hours.

Therefore, the average rate of change per hour can be calculated as follows:

average rate of change per hour = total change in temperature / number of hours

So, we have

average rate of change per hour = 5 degrees / 6 hours

average rate of change per hour = 0.83 degrees/hour (rounded to two decimal places)

So, the average rate of change per hour is 0.83 degrees.

Read more about rate of change at

https://brainly.com/question/17131025

#SPJ1

At a constant rate of 400 miles per hour travel, the plane would be travelling from 32000 feet above the land.

The speed of an object is the ratio of distance and time it takes for the object to travel that distance.

Mathematically,

S = D/T

where

S is velocity

D is the distance traveled or distance traveled

T is the time it takes to travel that distance

Velocity is considered a scalar quantity. A scalar size only has a size. It does not provide information about the direction of object movement.

If an object moves at a constant speed, it means that the object moves the same distance in the same time interval.

Acceleration of an object is the ratio of velocity and time. vector size. Vector quantities have both magnitude and direction.

Mathematics,

a = v/t

When an object is in motion, its acceleration is never zero.

When an object moves, it moves a constant distance over time. Therefore, body positions cannot be the same from the same coordinate system.

Given in the question:

First the plane was travelling at a constant rate of 250  miles per hour.

Initial height was 20000 feet

Now,

As the speed increases and travels at a constant rate of 400 miles per hour.

Now,

   (400 /250 ) × 20000

=  1.6 × 20000

= 32000 feet

Thus, At a constant rate of 400 miles per hour travel, the plane would be travelling from 32000 feet above the land.

Learn more about  Constant Rate:

https://brainly.com/question/13659182

#SPJ4

From the given data, we say a definite integral is improper if one endpoint is infinite, or if the integrand is infinite.

One endpoint is infinite, or if the integrand is infinite, the definite integral cannot be evaluated using the usual techniques. Instead, we must use the concept of a limit to find the value of the integral, if it exists. In the case where one endpoint is infinite, we take a limit as a variable approaches infinity. In the case where the integrand is infinite, we may need to split the integral into pieces or use some other method to deal with the singularity.

Learn more about definite integral here: brainly.com/question/27746495

#SPJ4

Answer:

I don't know that this answer would be right or wrong

Step-by-step explanation:

So please first check

Answer:

Step-by-step explanation:

There are 6 people and 6 seats. This means that any one of the 6 can take any one of the 6 seats. When person 1 sits in seat 1, there are 5 people left for the remaining 5 seats. When person 1 sits in seat 2, there are 4 people left for the remaining 4 seats. The catch here is that when there are, say, 5 seats left, those 5 people can "mix it up" so many different ways; but there will always be 1 less person when one sits down. This is a factorial problem:

6*5*4*3*2*1 = 720, choice B

The probability that a person owns a Dodge or has four-wheel drive, we need to determine the number of favorable outcomes (people who own a Dodge or have four-wheel drive) and the total number of possible outcomes (total number of people). The probability is then expressed as the ratio of favorable outcomes to total outcomes.

1. Identify the number of favorable outcomes: The question states that we are interested in the probability that the person owns a Dodge or has four-wheel drive. So, we need to count the number of people who own a Dodge and the number of people who have four-wheel drive.

2. Determine the total number of possible outcomes: This represents the total number of people considered in the problem.

3. Calculate the probability: Divide the number of favorable outcomes by the total number of possible outcomes.

4. Choose the option (a, b, c, d, or e) from the given answer choices that matches the calculated probability.

Learn more about probability  : brainly.com/question/31828911

#SPJ11

Answer:

37.4

Step-by-step explanation:

This is because 400-362.6 is 37.4, because we want to find out how many more calories she must still burn