MATHEMATICS COLLEGE

What statement best describes a trapezoid? *1 point
a. All sides are equal and opposite sides are parallel
b. Exactly one pair of parallel lines
c. Has 2 sets of parallel lines and four 90 degree angles
d. Has 2 equal sides and 3 acute angles

Answers

Answer 1

Answer:

Answer:b

Step-by-step explanation:

Answer 2

Answer:

Answer:

Step-by-step explanation:

because it has two parallel side and and other are just lines but being quadrilateral its sum is 360

Related Questions

Find an explicit solution (solved for y) of the given initial-value problem in terms of an integral function. dy/dx + 3y = e^x^5, y(2) = 5.
In this triangle, what is the value of x?Enter your answer, rounded to the nearest tenth, in the box.x = yd
Suppose Barbara has a 20 minute commute and scores 67.4 on the survey. Is Barbara more 'well-off than the typical individual who has a 20-ml?
I need urgent help with this
Josie's Bagel Shop recently sold 3 poppy seed bagels and 3 other bagels. What is the experimental probability that the next bagel sold will be a poppy seed bagel? Simplify your answer and write it as a fraction or whole number, P(poppy seed bagel) Submit

Sarawong is carrying six pages of math homework and four pages of english homework. a gust of wind blows the pages out of his hands and he is only able to recover seven random pages. what is the probability that he recovers at least five pages of his math homework

Answers

The sample space of the experiment (i.e. the total number of ways he can pick 7 random pages out of a total of 6 + 4 = 10 pages) is given by:

$^(10)C_7=120$

If he picks at least 5 pages of maths homework, this means that he either picked 5 pages or 6 pages of maths homework.

The number of ways he can pick 5 or 6 maths homework is given by:

$^6C_5+{ ^6C_6}=6*1=6$

Therefore, the probability that he recovers at least 5 pages of his math homework is given by:

$(6)/(120) = (1)/(20)$

Final answer:

The probability that Sarawong recovers at least five pages of his math homework is 56.6%, using the combinatory principles of probability.

Explanation:

To solve the problem, we need to calculate the probability that Sarawong recovers at least five pages of his math homework after a gust of wind blows the pages out of his hands. This is a probability problem, which is under the field of mathematics. We first need to understand the total possibilities of the pages he could recover, which is combinations of six math pages and four English pages, that is 10 pages pick 7 pages. We add up the probabilities that he recovers 5, 6, or all 7 math pages. We also need to consider that there is no particular order in which the pages are recovered.

The total number of ways to select 7 pages from 10 can be calculated by 10 choose 7, which is 120.

The number of ways to select 5 math pages out of 6 and 2 English pages out of 4 is 6 choose 5 times 4 choose 2, which equals 60. The probability of this case is 60 / 120 which is 0.5.

The number of ways to select 6 math pages and 1 English page is 6 choose 6 times 4 choose 1, which is also 4. The probability is 4 / 120 which is 0.033.

The number of ways to select all math pages is 6 choose 6 and 4 choose 1, which totals 4. The probability is also 4 / 120 which is 0.033.

Therefore, the total probability that Sarawong recovers at least 5 of his math pages is 0.5 + 0.033 + 0.033 = 0.566, or 56.6%. This is the mathematical solution to the problem.

Learn more about Probability here:

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Is the red line a radius or diameter of the circle

Answers

The diameter of the circle would be a line going through the center of the circle connecting to both sides.

The radius of a circle would be a line only going to the the center, or in other words, half the circle.

I hope this makes sense!

A town interested in installing wind turbines to generate electricity measures the speed of the wind in the town over the course of a year. They find that most of the time, the wind speed is pretty slow, while only rarely does the wind blow very fast during a storm. What would be the best measure of the central wind speed they should report to the mayor? The mean, because the distribution of wind speeds is skewed. The median, because the distribution of wind speeds is symmetric. The mean, because the distribution of wind speeds is symmetric. The median, because the distribution of wind speeds is skewed. The proportion, because the distribution of wind speeds is skewed. The proportion, because the distribution of wind speeds is symmetric.

Answers

9514 1404 393

Answer:

The median, because the distribution of wind speeds is skewed.

Step-by-step explanation:

A few higher speeds will raise the mean. For a skewed distribution, the median may be a more appropriate measure of center.

Additional comment

From an engineering point of view, one might have to consider speeds only within some range, as the wind turbines may be shut down for speeds too low or too high. Likely the power generated is not proportional to speed, so a weighted average (of the square of speed) would probably be more useful. Unfortunately, this question does not get into such subtleties.

It is believed that the average amount of money spent per U.S. household per week on food is about $98, with standard deviation $11. A random sample of 36 households in a certain affluent community yields a mean weekly food budget of $100. We want to test the hypothesis that the mean weekly food budget for all households in this community is higher than the national average. State the null and alternative hypotheses for this test, the test statistic and determine if the results significant at the 5% level.

Answers

Answer:

The null hypothesis is

$H_o : \mu =$ $98

The alternative hypothesis is

$H_a : \mu >$ $98

test statistics $t_s = 1.091$

The the result of the test statistics is significant

Step-by-step explanation:

From the question we are told that

The population mean is $\mu =$ $98

The standard deviation is $\sigma =$ $11

The sample size is $n = 36$

The sample mean is $\= x =$ $100

The level of significance is $\alpha = 5$ % = 0.05

The null hypothesis is

$H_o : \mu =$ $98

The alternative hypothesis is

$H_a : \mu >$ $98

Now the critical values for this level of significance obtained from critical value for z-value table is $z_\alpha = 1.645$

The test statistics is mathematically evaluated as

$t_s = (\= x - \mu)/( (\sigma )/( √(n) ) )$

substituting values

$t_s = (100 - 98)/( (11 )/( √(36) ) )$

$t_s = 1.091$

Looking at $z_\alpha \ and \ t_s$ we see that $z_\alpha \ > t_s$ hence the we fail to reject the null hypothesis

hence there is no sufficient evidence to conclude that the mean weekly food budget for all households in this community is higher than the national average.

Thus the the result is significant

Lisa used 1/4 cups of milk per batch using her muffin recipes. How many cups of Milan will she use when she made 6 batches of muffins?

Answers

Answer:

1 1/2

Step-by-step explanation:

1/4 cups * 6 batches = 1/4 * 6 = 6/4 = 1 2/4 = 1 1/2

Find the exact values of the numbers c that satisfy the conclusion of the Mean Value Theorem for the interval [−2, 2]. (Enter your answers as a comma-separated list.)

Answers

Answer:

The answer is " $\bold{c= \pm (2)/(√(3))}$ "

Step-by-step explanation:

If the function is:

$\to f'(x) = 3x^2-2 \n\n\to f'(c) = 3c^2-2$

points are:

$\to -2 \leq x \leq2$

use the mean value theorem:

$\to f'(c) = ( f(b)- f(a))/(b-a)$

$= ( f(2)- f(-2))/(2-(-2))\n\n= (4-(-4) )/(4)\n\n= (8)/(4)\n\n= 2$

$\to 3c^2-2=2 \n\n\to 3c^2=4 \n\n\to c^2=(4)/(3) \n\nc= \pm (2)/(√(3))$

Final answer:

The Mean Value Theorem states that for a continuous and differentiable function on a closed interval, there exists at least one 'c' within that interval where the average change rate equals the instantaneous rate at 'c'. In the given case of interval [-2,2], to find 'c', first calculate the average slope between the points (f(2)-f(-2))/4. Then equate this average slope to the derivative 'f'(c). The solution(s) to this equation are the c values for this problem.

Explanation:

The subject of this question pertains to the Mean Value Theorem in Calculus. According to this theorem, if a function f is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one number c in the open interval (a, b) such that the average rate of change over the interval equals the instantaneous rate of change at c.

In the given case, we're trying to find the 'c' value for the interval [-2,2]. First, we need to find the average slope between the two points. Assuming f is your function, that would be (f(2)-f(-2))/ (2 - -2). Subtract the function values of the two points and divide by the total interval length. Next, we need to see where this average slope equals the instantaneous slope 'f'(c), this entails solving the equation 'f'(c) = (f(2)-f(-2))/4. The solution to this equation will be the c values that satisfy the Mean value theorem within the provided interval.