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3 years ago

Find the area of the trapezoid.

Mathematics

1 answer:

mrs_skeptik [129]3 years ago

6 0

Answer:

40cm^2

Step-by-step explanation:

A=a+b/2×h

A=6+10/2*5

A=16cm/2*5cm

A=8cm*5cm

A=40cm^2

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In the United States, voters who are neither Democrat nor Republican are called Independent. It is believed that 11% of voters a

Radda [10]

Answer:

a) 0.0214 = 2.14% probability that none of the people are Independent.

b) 0.8516 = 85.16% probability that fewer than 6 are Independent.

c) 0.8914 = 89.14% probability that more than 2 people are Independent.

Step-by-step explanation:

For each people, there are only two possible outcomes. Either they are independent, or they are not. For each person asked, the probability of them being Independent voters is the same. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

It is believed that 11% of voters are Independent.

This means that $p = 0.11$

A survey asked 33 people to identify themselves as Democrat, Republican, or Independent.

This means that $n = 33$

A. What is the probability that none of the people are Independent?

This is P(X = 0). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{33,0}.(0.11)^{0}.(0.89)^{33} = 0.0214$

0.0214 = 2.14% probability that none of the people are Independent.

B. What is the probability that fewer than 6 are Independent?

This is

$P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{33,0}.(0.11)^{0}.(0.89)^{33} = 0.0214$

$P(X = 1) = C_{33,1}.(0.11)^{1}.(0.89)^{32} = 0.0872$

$P(X = 2) = C_{33,2}.(0.11)^{2}.(0.89)^{31} = 0.1724$

$P(X = 3) = C_{33,3}.(0.11)^{3}.(0.89)^{30} = 0.2202$

$P(X = 4) = C_{33,4}.(0.11)^{4}.(0.89)^{29} = 0.2041$

$P(X = 5) = C_{33,5}.(0.11)^{5}.(0.89)^{28} = 0.1463$

$P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0214 + 0.0872 + 0.1724 + 0.2202 + 0.2041 + 0.1463 = 0.8516$

0.8516 = 85.16% probability that fewer than 6 are Independent.

C. What is the probability that more than 2 people are Independent?

This is:

$P(X \geq 2) = 1 - P(X < 2)$

In which

$P(X < 2) = P(X = 0) + P(X = 1)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{33,0}.(0.11)^{0}.(0.89)^{33} = 0.0214$

$P(X = 1) = C_{33,1}.(0.11)^{1}.(0.89)^{32} = 0.0872$

$P(X < 2) = 0.0214 + 0.0872 = 0.1086$

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.1086 = 0.8914$

0.8914 = 89.14% probability that more than 2 people are Independent.

8 0

2 years ago

Approximate the area between the xxx-axis and h(x) = \dfrac{1}{7-x}h(x)= 7−x 1 h, (, x, ), equals, start fraction, 1, divided

tiny-mole [99]

Answer:

$\dfrac{47}{60}$ sq. units.

Step-by-step explanation:

The given function is

$h(x)=\dfrac{1}{7-x}$

We need to find the area between x-axis and the given function from x=2 to x=5.

Left Riemann sum formula of area:

$Area=\sum_{n=0}^{N-1}f(x_n)(\Delta x_n)$

For given question,

$Area=\sum_{n=2}^{5-1}f(x_n)(\Delta x_n)$

$Area=\sum_{n=2}^{4}f(x_n)(\Delta x_n)$

$Area=f(x_2)(3-2)+f(x_3)(4-3)+f(x_4)(5-4)$

Now,

$Area=\dfrac{1}{7-2}\times (1)+\dfrac{1}{7-3}\times (1)+\dfrac{1}{7-4}\times (1)$

$Area=\dfrac{1}{5}+\dfrac{1}{4}+\dfrac{1}{3}$

$Area=\dfrac{12+15+20}{60}$

$Area=\dfrac{47}{60}$

Therefore, the required area is $\dfrac{47}{60}$ sq. units.

5 0

3 years ago

Find the value of x for which allb <br> A. 35<br> B. 145<br> C. 140<br> D. 47

Paha777 [63]

Answer:

A. 35

Step-by-step explanation:

a || b .....(given)

line c is their transversal.

-> x° + (3x + 40)° = 180° (Interior angles on the same side of transversal)

-> (3x + 40 + x)° = 180°

-> (4x + 40)° = 180°

-> 4x + 40 = 180

-> 4x = 180 - 40

-> 4x = 140

-> x = 140/4

-> x = 35

7 0

2 years ago

Four polynomials are shown below:

7nadin3 [17]

C. It is fifth degree because the highest power in it is 5. It is a binomial because there are two terms in it.

A is also 5th degree, but it has three terms. D is a binomial, but its degree is 3.

B is neither a binomial nor fifth degree.

3 0

3 years ago

What is the average score of runa 140,96 and 13?

scoundrel [369]

$\huge\textsf{Hey there!}$