Thomas drew a triangle which has one angle that measures more than
90° and two angles that each measure less than 90°. What kind of
triangle did he draw?

A right circular cylinder can be generated by rotating a rectangle of perimeter p about one of its sides. The dimensions of the rectangle that will generate the cylinder of max volume are l = p/6 and w = p/2 - l = 2p/3.

Explanation: Let l and w be the dimensions of the rectangle of perimeter p.

That is, the rectangle's perimeter is given by p = 2l + 2w or p/2 = l + w. Therefore, the width w = p/2 - l. The area of the rectangle is given by lw. When the rectangle is rotated around the side of length w, it generates a cylinder of height l and radius w.

The volume of the cylinder is given by V = πr²h = πw²l. Substituting w = p/2 - l, we obtain V = π(p/2 - l)²l = π(p/2)²l - 2π(p/2)l² + πl³.

The volume function can be obtained by differentiating V with respect to l, setting the derivative equal to 0, and solving for l. The derivative of V with respect to l is given by dV/dl = π(p/2)² - 4π(p/2)l + 3πl².

Setting dV/dl = 0 and solving for l, we obtain l = p/6.The dimensions of the rectangle that will generate the cylinder of max volume are l = p/6 and w = p/2 - l = 2p/3.

To know more about max volume: https://brainly.com/question/28950621

#SPJ11

The percent of the variance in the dependent variable unexplained by the independent variable is 81%

A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively correlated, the value either rises or falls together.

9 percent of the variance is explained by the independent variable if the correlation coefficient is 0.3.

The correlation coefficient is therefore represented as follows:

\(r = 0.3\)

The explained variance is found using the following formula:

\(R^{2} = r^{2} \\R^{2} = (0.3)^{2} \\R^{2} = (0.3)*(0.3)\\R^{2} = 0.9\)

Thus, 81% of the variance remains unexplained by variations in the independent variable.

To know more about correlation coefficient visit:-

brainly.com/question/15577278

#SPJ4

Step-by-step explanation:

The answer is dhdt=325πmmin.

With related rates, we need a function to relate the 2 variables, in this case it is clearly volume and height. The formula is:

V=πr2h

There is radius in the formula, but in this problem, radius is constant so it is not a variable. We can substitute the value in:

V=π(5m)2h

Since the rate in this problem is time related, we need to implicitly differentiate wrt (with respect to) time:

dVdt=(25m2)πdhdt

In the problem, we are given 3m3min which is dVdt. So we substitute this in:

dhdt=3m3min(25m2)π=325πmmin

Answer:

9

Step-by-step explanation:

This is because it is the number being multiplied

Hope this helps!

Answer: 9^2 or can also be read as 9 squared.The base itself is worth 9 but when you include the exponent its 81.When your solving exponents your multiplying the base by itself as many times as the exponent reads.In this case its 9x9 (2 times). The value of the base is 9 (just wanted to explain the other stuff just in case you didn't know)

have a good day :)

Answer:

infinite

Step-by-step explanation:

the law in most states in the usa states there must be 3 letters and 3 numbers so there could be infinite

                            -hope this helps-

Similar triangles may or may not have equal side lengths

Triangles ABC and DEF are similar by SSS theorem

The coordinates of the two triangles are:

A (0,0), B (4,0), C (0,2), D (0,0), E (2,0), and F (0,1)

Calculate the lengths of both triangles using the following distance formula

\(d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}\)

For triangle ABC, we have:

\(AB = \sqrt{(0 -4)^2 + (0 -0)^2} = 4\)

\(BC = \sqrt{(4 -0)^2 + (0 -2)^2} = 2\sqrt 5\)

\(CA = \sqrt{(0 -0)^2 + (0 -2)^2} = 2\)

For triangle DEF, we have:

\(DE = \sqrt{(0 -2)^2 + (0 -0)^2} = 2\)

\(EF = \sqrt{(2 -0)^2 + (0 -1)^2} = \sqrt 5\)

\(FD = \sqrt{(0 -0)^2 + (1 -0)^2} = 1\)

Divide corresponding sides of the triangles to calculate the scale factor k

\(k = \frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD}\)

This gives

\(k = \frac{4}{2} = \frac{2\sqrt 5}{\sqrt 5} = \frac{2}{1}\)

Evaluate the quotients

\(k = 2 = 2 = 2\)

Since the quotients are equal, then the triangles are similar

Hence, triangles ABC and DEF are similar by SSS theorem

Read more about similar triangles at:

https://brainly.com/question/14285697

Answer:

\(3^{20}\)

Step-by-step explanation:

Answer: Hi that would be 3^9, but since it has a parantheses it becomes 3^20, hope this helps.

Answer: 5/3

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.

If a researcher uses u.s. census data to examine changes in the number of individuals in each racial group across states over time, she is using stratified sampling.

Samples may be classified as:

For this problem, we have that the population is divided into groups, according to their racial group, and then parts of the sample are surveyed, hence stratified sampling is used.

More can be learned about sampling strategies at https://brainly.com/question/25122507

#SPJ1

Answer: 26.7m

Step-by-step explanation:

Since a decagon has 10 sides, you'll have to divide 267m by 10.

267÷10= 26.7

One side of the decagon is 26.7m

Statistical and non-statistical methods are two broad categories used in data analysis and problem-solving. The three main parts of these methods include data collection and preparation, data analysis and interpretation, and drawing conclusions or making decisions based on the analysis.

In the first part, data collection and preparation, statistical methods involve systematic and rigorous data collection techniques, such as random sampling, surveys, experiments, or observational studies. Non-statistical methods may involve data collection through various means, such as expert opinions, personal experiences, or case studies. Both methods focus on ensuring the data is reliable, relevant, and representative of the population or problem under investigation.

The second part, data analysis and interpretation, involves applying appropriate statistical techniques or other analytical tools to extract meaningful information from the data. Statistical methods utilize various techniques like descriptive statistics, hypothesis testing, regression analysis, or multivariate analysis to uncover patterns, relationships, or trends in the data. Non-statistical methods rely on qualitative analysis, logical reasoning, or subjective interpretation to make sense of the data.

The third part, drawing conclusions or making decisions, involves using the results of the analysis to draw meaningful conclusions, make predictions, or make informed decisions. Statistical methods provide a quantifiable basis for decision-making, as they often provide measures of uncertainty and statistical significance. Non-statistical methods may rely on subjective judgment, personal expertise, or contextual considerations to make decisions or recommendations.

Learn more about statistical methods here:

https://brainly.com/question/30264998

#SPJ11

Answer:

Step-by-step explanation:

The Probability of Landing a heads is (1/2)

Now, to find the probability of landing it five times in a row, it is

1/2 x 1/2 x 1/2 x 1/2 x 1/2

( 1/2 is multiplied to the number of times to get a head )

The final answer will be,

Probability of landing heads 5 times in a row = 1/32

Answer:

68oz

Step-by-step explanation:

1) 3lbs x 16oz = 48

Now we know 3lbs is 48oz. since one pound is 16 ounces, 3 pounds is 48 ounces.

2) 48 + 20 = 68oz

3) The total weight of both packages is 68 ounces.

Jesus loves ya, have a great day!

---------------------

John 8:12 - When Jesus spoke again to the people, he said, "I am the light of the world. Whoever follows me will never walk in darkness, but will have the light of life."

Answer:

m

Step-by-step explanation:

the slope or growth rate of the function is the coefficient of the variable x, which is m in this case

Here, we are required to use paper to draw Sara's construction. and determine what the points p, q and r define.

According to the question; the first circle Sara sketches has center at point, P and radius PQ.

The statement above means that the point Q is on the circumference of the first circle.

Afterwards, she draws a second circle with center at point Q and radius QP.

And lastly, she labels one point of intersection of both circles as R.

A representation of Sara's construction is attached as an image.

The points p, q and r define a triangle; An equilateral triangle to be specific as all 3 sides of the triangle are equal to the radius of either of the circles.

Read more:

https://brainly.com/question/16247529

Answer:

⚪ 4: three right triangles and one acute-angled triangle.

Step-by-step explanation:

\(.\)

Answer:

The measures of interior angles of a triangle sum to 180°.

63+60=123

180-123=57

Angle AB is 57°

By direct comparison and definition of line segment  we notice that the point (x, y) = (- 6, 0) lies on the line segment AB as each AP is a multiple of former. (Correct choice: C)

According to linear algebra, a point lies in a line segment if its vector is a multiple of the vector that generates the line segment itself, that is:

AB = k · AP        (1)

The vector that generates the line segment is:

AB = (2, 6) - (- 2, 3)

AB = (4, 3)

And the vectors related to each point are:

Case A

AP = (- 2, 12) - (- 2, 3)

AP = (0, 9)

Case B

AP = (6, 12) - (- 2, 3)

AP = (8, 9)

Case C

AP = (- 6, 0) - (- 2, 3)

AP = (- 4, - 3)

Case D

AP = (- 6, 6) - (- 2, 3)

AP = (- 4, 3)

By direct comparison and definition of line segment  we notice that the point (x, y) = (- 6, 0) lies on the line segment AB as each AP is a multiple of former. (Correct choice: C)

To learn more more on line segments: https://brainly.com/question/25727583

#SPJ1

Answer: 3/4

Step-by-step explanation:

28 members in all - 12 boys = 16 girls

12/16 = 3/4

Answer: The Range

The range on the corn has more spread than the soybeans.

The rest allowance for chopping down a tree is 0.67 hours (rounded to two decimal places) or 40 minutes. In an 8-hour shift, approximately 40 minutes should be allowed for rest.

To calculate the rest allowance, we need to determine the energy expenditure for chopping down a tree and convert it into a time duration.

Given that the energy expenditure associated with chopping down a tree is 8.0 kcal/min, we can calculate the rest allowance using the following formula:

Rest allowance = Energy expenditure (kcal/min) * Time duration (min) / Energy content of food (kcal).

As the rest allowance is typically a fraction of the energy expenditure, we can use the value of 0.25 (25%) as the input for the rest allowance calculation.

Rest allowance = 8.0 kcal/min * Time duration (min) / Energy content of food (kcal) = 0.25.

Solving for the time duration, we find:

Time duration (min) = 0.25 * Energy content of food (kcal) / 8.0 kcal/min.

To determine the time duration in hours, we divide the time duration in minutes by 60:

Time duration (hours) = Time duration (min) / 60.

The specific energy content of food is not provided in the question. Therefore, without knowing the energy content, we cannot calculate the exact time duration for the rest allowance.

Learn more about decimal  here :

brainly.com/question/30958821

#SPJ11

Answer:

Neither increasing or descreasing

Step-by-step explanation:

Decreasing - slope of line is negative, e.g. y = -2x

Increasing - slop of line is positive, e.g. y = 2x

Vertical lines have no slope, so they are neither increasing or decreasing

Answer:

0.31

Step-by-step explanation:

31 / 100 = 0.31

The percentage of B5 produced from coconut oil is 0.045 X% of the imported diesel fuel. The percentage of E10 produced from molasses and cassava is 0.1143 Y% of the imported petrol.

To calculate the volume of B5 (a biodiesel blend of 5% biodiesel and 95% petroleum diesel) that can be produced from the coconut oil produced in Fiji, we need to know the total volume of coconut oil produced and the conversion efficiency of the trans-esterification process.

Let's assume that the volume of coconut oil produced in Fiji is X million litres, and the conversion efficiency is 90%. Therefore, the volume of biodiesel (CME) that can be produced from coconut oil is 0.9X million liters. Since B5 is a blend of 5% biodiesel, the volume of B5 that can be produced is 0.05 × 0.9X = 0.045X million liters.

To calculate the total volume of E10 (a gasoline blend of 10% ethanol and 90% petrol) that can be produced from the molasses and cassava, we need to know the total volume of molasses and cassava produced and the conversion efficiency of ethanol production.

Let's assume that the total volume of molasses and cassava produced is Y million liters, and the conversion efficiency is 80%. Therefore, the volume of ethanol that can be produced is 0.8Y million liters. Since E10 is a blend of 10% ethanol, the total volume of E10 that can be produced is 0.1 × 0.8Y = 0.08Y million liters.

The percentage of B5 produced from coconut oil is (0.045X / 100) × 100% = 0.045 X% of the imported diesel fuel.

The percentage of E10 produced from molasses and cassava is (0.08Y / 70) × 100% = 0.1143 Y% of the imported petrol.

Learn more about percentage here:

https://brainly.com/question/29759036

#SPJ11

The complete question is:

A country imports in the vicinity of 100 million litres of diesel fuel (ADO) for use in diesel vehicles and 70 million litres of petrol fir petrol vehicles. It also produces molasses and cassava, which are feedstock for the production of ethanol, and coconut oil (CNO) that can be converted to biodiesel (CME) via trans-esterification.

a) Calculate the volume of B5 that can be produced from the coconut oil produced in Fiji, and the total volume of E10 that can be produced from all the molasses and cassava that the country produces annually. Express your results as the percentages of the respective imported fuel.

Answer:

34

Step-by-step explanation:

32 / 8 = 4
36 / 4 = 9

perimeter of rectangle = 2(Length) + 2(width)
P = 2(8) + 2(9)
P = 16 + 18
P = 34

The shaded region representing the possible combinations of ticket sales is given by the image presented at the end of the answer.

The region containing the possible combinations is obtained using a system of inequalities, for which the variables are given as follows:

The amounts cannot be negative, as they are countable amounts, hence:

Each member of the team must make a minimum of $300, hence:

60x + 20y ≥ 300.

They cannot sell more than 10 tickets, hence:

x + y ≤ 10.

The graph containing the region that respects these four constraints is given by the image presented at the end of the answer.

More can be learned about a system of inequalities at https://brainly.com/question/9290436

#SPJ1

Answer:

5/6

Step-by-step explanation:

1/2=3/6

1/3=2/6

2/6+3/6=5/6

Step-by-step explanation:

If you look at the last numbers or commonly known as the intercept. (after the plus/minus signs)

A=a

B=c

C=b

Answer:

A

Step-by-step explanation:

The first one is correct because its growth is exponential, which means it is getting worst as time goes. The amount of snowfall is also rising, unlike in d.

We would apply the tiangle inequality theorem which states that for the given lengths to form a triangle, the length of any two sides must be greater than teh length of the third side. By applying this theorem,

33 + 56 must be greater than 64

89 > 64

33 + 64 must be greater than 56

97 > 64

56 + 64 must be greater than 33

120 > 33

We can see that the theorem is obeyed. Thus, the side lengths form a right triangle.