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3 years ago

Geo: Worth 50 points and I will give brainliest to right answer! #24

Mathematics

1 answer:

Sindrei [870]3 years ago

6 0

1. ∠1 ≅ ∠3 1. given

∠1 and ∠6 are supplementary angles

∠3, ∠4, and ∠5 are supplementary angles

2. m∠1 = m∠3 2. definition of congruency

3. m∠1 + m∠6 = 180° 3. definition of supplementary angles

m∠3 + m∠4 + m∠5 = 180°

4. m∠3 + m∠4 + m∠5 = m∠1 + m∠6 4. transitive property

5. m∠3 + m∠4 + m∠5 = m∠3 + m∠6 5. substitution property

6. m∠4 + m∠5 = m∠6 6. subtraction property of equality

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The speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone Company, reports it

brilliants [131]

Answer:

(a) 11.25 and 1.68

(b) 0.1651

(c) 0.3903

(d) 0.6865

Step-by-step explanation:

We are given that GTC, the Georgetown Telephone Company, reports it can resolve customer problems the same day they are reported in 75% of the cases and suppose the 15 cases reported today are representative of all complaints.

This situation can be represented through Binomial distribution as;

$P(X=r)= \binom{n}{r}p^{r}(1-p)^{n-r} ; x = 0,1,2,3,....$

where, n = number of trials (samples) taken = 15

r = number of success

p = probability of success which in our question is % of cases in

which customer problems are resolved on the same day, i.e.;75%

So, here X ~ $Binom(n=15,p=0.75)$

(a) Expected number of problems to be resolved today = E(X)

E(X) = $\mu$ = n * p = 15 * 0.75 = 11.25

Standard deviation = $\sigma$ = $\sqrt{n*p*(1-p)}$ = $\sqrt{15*0.75*(1-0.75)}$ = 1.68

(b) Probability that 10 of the problems can be resolved today = P(X = 10)

P(X = 10) = $\binom{15}{10}0.75^{10}(1-0.75)^{15-10}$

= $3003*0.75^{10} *0.25^{5}$ = 0.1651

= $\binom{15}{10}0.75^{10}(1-0.75)^{15-10}+\binom{15}{11}0.75^{11}(1-0.75)^{15-11}$

= $3003*0.75^{10} *0.25^{5} + 1365*0.75^{11} *0.25^{4}$ = 0.3903

(d) Probability that more than 10 of the problems can be resolved today is

given by = P(X > 10)

P(X > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)

= $\binom{15}{11}0.75^{11}(1-0.75)^{15-11}+\binom{15}{12}0.75^{12}(1-0.75)^{15-12} + \binom{15}{13}0.75^{13}(1-0.75)^{15-13}+\binom{15}{14}0.75^{14}(1-0.75)^{15-14} + \binom{15}{15}0.75^{15}(1-0.75)^{15-15}$

= $1365*0.75^{11} *0.25^{4} + 455*0.75^{12} *0.25^{3}+105*0.75^{13} *0.25^{2} + 15*0.75^{14} *0.25^{1}+1*0.75^{15} *0.25^{0}$

= 0.6865

3 0

3 years ago

Using the standard 28/36 guidelines, what is the maximum mortgage payment allowed for someone with an annual salary of $73,025?

nekit [7.7K]

The maximum mortgage payment allowed for someone with an annual salary of $73.025 would be $2,190.75 per month, so the correct option is A.

<h2><u>How to determine the amount using the standard 28/36 guides?</u></h2>

To determine, using the standard 28/36 guidelines, what is the maximum mortgage payment allowed for someone with an annual salary of $73,025, the following calculation must be made:

((73025 x 36) / 100) / 12 = X
(2,628,900 / 100) / 12 = X
26,289 / 12 = X
2,190.75 = X

Therefore, the maximum mortgage payment allowed for someone with an annual salary of $73.025 would be $2,190.75 per month.

Learn more about mortgages in brainly.com/question/20589209

4 0

3 years ago

How much do you need to get to 324 from 278

Yuki888 [10]

Answer:

Step-by-step explanation:

324 - 278 = 46

278 + 46 = 324

5 0

3 years ago

Read 2 more answers

Briefly, describe the distribution in context. Recall, categorical variables are summarized by counts and/or percents

Sholpan [36]

Thus, distribution is a function that shows the possible values for a variable and how often they occur and categorical values are summarized by counts and/or percents

In statistics, the distribution is a function that shows the possible values for a variable and how often they occur.

The distribution of a data set is the shape of the graph when all possible values are plotted on a frequency graph. Usually, we are not able to collect all the data for our variable of interest. Therefore we take a sample. This sample is used to make conclusions about the whole data set.

The categorical variable is a data in which individuals are placed into groups or categories.

One way to summarize categorical data is to simply count (frequency), or tally up, the number of individuals that fall into each category. Another way is to show the percentage of individuals who fall into each category, thereby creating a relative frequency.

Learn more about distribution here

brainly.com/question/15352066

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3 0

2 years ago

Identify which of these types of sampling is used: random, stratified,systematic, cluster, convenience. 49, 34, and 48 students

Andrew [12]

Given

49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively.

To find:

Which of these types of sampling is used: random, stratified, systematic, cluster, convenience?

Explanation:

It is given that,

49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively.

That implies,

Since Stratified random sampling is a method of sampling that involves dividing a population into smaller groups–called strata.

Then, the random sampling used is Stratified Random Sampling.

7 0

1 year ago