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2 years ago

X= 115.5 137 180 Look at attachment

Mathematics

2 answers:

frosja888 [35]2 years ago

8 0

Answer:

the answer is 180

Step-by-step explanation:

OLga [1]2 years ago

3 0

Answer:

$x=180\°$

Step-by-step explanation:

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

$137\°=\frac{1}{2}(94\°+x)$

solve for x

$274\°=(94\°+x)$

$x=274\°-94\°=180\°$

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The Rockville Employment Agency just placed Howard Jacobson in a job as a junior pharmacist. The job pays $51.2k. The agency fee

yan [13]

His annual salary as a pharmacist is $51,200

There are a total of 52 weeks in an year.

(a) Weekly salary = annual salary/ number of weeks = 51,200/52 = $984.62 (rounded to the nearest cent)

Howard's weekly salary to the nearest cent = $984.62

(b) His salary in first three weeks = 984.62*3 = $2,953.85

Howard's earnings during the first three weeks to the nearest cent = $2,953.85

Howard must pay to the employment agency to the nearest dollar = $1,182

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2 years ago

G identify the solution of the recurrence relation an = 6an − 1 – 8an − 2 for n ≥ 2 together with the initial conditions a0 = 4,

maksim [4K]

Via the generating function method, let

$G(x)=\displaystyle\sum_{n\ge0}a_nx^n$

Then take the recurrence,

$a_n=6a_{n-1}-8a_{n-2}$

multiply everything by $x^n$ and sum over all $n\ge2$ :

$\displaystyle\sum_{n\ge2}a_nx^n=6\sum_{n\ge2}a_{n-1}x^n-8\sum_{n\ge2}a_{n-2}x^n$

Re-index the sums or add/remove terms as needed in order to be able to express them in terms of $G(x)$ :

$\displaystyle\sum_{n\ge2}a_nx^n=\sum_{n\ge0}a_nx^n-(a_0-a_1x)=G(x)-4-10x$

$\displaystyle\sum_{n\ge2}a_{n-1}x^n=\sum_{n\ge1}a_nx^{n+1}=x\sum_{n\ge1}a_nx^n=x\left(G(x)-a_0\right)=x(G(x)-4)$

$\displaystyle\sum_{n\ge2}a_{n-2}x^n=\sum_{n\ge0}a_nx^{n+2}=x^2\sum_{n\ge0}a_nx^n=x^2G(x)$

So the recurrence relation is transformed to

$G(x)-4-10x=6x(G(x)-4)-8x^2G(x)$
$(1-6x+8x^2)G(x)=4-14x$
$G(x)=\dfrac{4-14x}{1-6x+8x^2}=\dfrac{4-14x}{(1-4x)(1-2x)}=\dfrac1{1-4x}+\dfrac3{1-2x}$

For appropriate values of $x$ , we can express the RHS in terms of geometric power series:

$G(x)=\displaystyle\sum_{n\ge0}(4x)^n+3\sum_{n\ge0}(2x)^n=\sum_{n\ge0}\bigg(4^n+3\cdot2^n\bigg)x^n$

which tells us that

$a_n=4^n+3\cdot2^n$

3 0

2 years ago

The weights of five grapefruits are 7 47 ounces, 7.23 ounces, 6.46 ounces, 7.48 ounces, and 6.81 ounces. Using the

gulaghasi [49]

Answer:

The approximate total weight of the grapefruits, using the clustering estimation technique is B. 35 ounces.

Step-by-step explanation:

We notice that the weights of the grapefruits given are slightly down or above 7, then we will use 7 as our cluster for the estimation, as follows:

Weights

7.47 ⇒ 7

7.23 ⇒ 7

6.46 ⇒ 7

7.48 ⇒ 7

6.81 ⇒ 7

Now we can add up 7 + 7 + 7 + 7 + 7 for the weights of the grapefruits and the approximate total weight is B. 35 ounces.

8 0

2 years ago

Read 2 more answers

The local news is conducting a poll of the residents’ opinions regarding a new traffic law that is being proposed. At the end of

mart [117]

Answer:

Option A is correct.

The surveys are biased because people chose to respond or not.

Step-by-step explanation:

When humans are given the choice whether to participate in a poll like in this question, most often than not, the poll is biased.

This is because only the people or set of people who feel strongly the most about the subject matter of the poll will participate in the poll. This favours the group that disagrees as this group, if given the choice to express their opinion, will most likely be the set of people that will readily express their discontent.

Discontent is more visibly and strongly expressed in humans.

In order to remove this bias, people should have been chosen at random and their responses recorded.

The two other options are not absolutely correct, these are the reasons.

b. Because of the large sample size, the results are most accurate of all members of the community.

Like I expressed above, the base of the sample is flawed and biased as it will most likely favour a group of the population that don't agree with the law. So, no matter how large the sample is, that type of bias makes the poll unreliable.

c. The same sampling methods were used for both polls, demonstrating reliability.

The sampling method is biased, so, it doesn't matter if it is repeated for both polls. it most likely will not represent the correct general consensus about the new traffic law.

Hope this Helps!!!

8 0

2 years ago

In 2011, New York City has a total of 11,232 motor vehicle accidents that occurred on Monday through Friday between the hours of

cestrela7 [59]

Answer:

$a. \ P(X=0)=5.574\times10^{-7}$

$b. \ \ P(X\leq 1)=8.584\times10^{-6}$

$c.\ \ \ P(X\geq 4)=0.9997$

Step-by-step explanation:

a. #We notice this is a Poisson probability function expressed as:

$f(x)=\frac{\mu^xe^{-\mu}}{x!}$

x-number of occurrences in a given interval.

$\mu$ -mean occurrences of the event

-The mean is calculated as:

$\mu=\frac{14.4}{4}=3.6$

#the probability of no accidents in a 15-minute period is :

$P(x)=\frac{\mu^xe^{-\mu}}{x!}\\\\P(X=0)=\frac{14.4^0e^{-14.4}}{0!}\\\\=5.574\times10^{-7}$

Hence, the probability of no accident in a 15-min period is $=5.574\times10^{-7}$

b. The the probability of at least one accident in a 15-minute period. is calculated as:

$P(x)=\frac{\mu^xe^{-\mu}}{x!}\\\\P(X\leq 1)=\frac{14.4^0e^{-14.4}}{0!}+\frac{14.4^1e^{-14.4}}{1!}\\\\=5.574\times10^{-7}+8.026\times 10^{-6}\\\\=8.584\times 10^{-6}$

Hence, the probability of at least one accident in a 15-minute period is $8.584\times10^{-6}$

c. The probability of four or more accidents in a 15-minute period is calculated as:

$P(X\geq 4)=1-P(X\leq 3)=1-[P(X=0)+P(X1)+P(X=2)+P(X=3)]\\\\=1-[5.574\times10^{-7}+a. \ 8.026\times10^{-6}+\frac{14.4^2e^{-14.4}}{2!}+\frac{14.4^3e^{-14.4}}{3!}]\\\\=1-[8.584\times 10^{-6}+5.779\times10^{-5}+2.774\times10^{-4}]\\\\=0.9997$

Hence,the probability of four or more accidents in a 15-minute period. is 0.9997

7 0

2 years ago