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2 years ago

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Point D is on segment BC. Segment BC measures 8x units in length. A line has points C, D, B. The length of line C D is 3 x + 8.

The length of line D B is 4 x + 10. What is the length of segment BC? units

2 answers:

dezoksy [38]2 years ago

4 0

Answer:

144 units

Step-by-step explanation:

Komok [63]2 years ago

3 0

Answer:

144 units

Step-by-step explanation:

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Match each concept with its key characteristic.

Crank

1. It is the subset of a group - Group sample.

2. It equally favors all members of a group sample - Random sample.

3. It collects data on members of a group - Survey.

4. It does not equally favor all members of a group - Biased sample.

5. It includes all members of a group - Population.

6. It analyzes data collected from a group - Mean.

I have matched all concepts in accordance with statistical use, hope it helps.

6 0

2 years ago

Match the following items.

Margarita [4]

Answer:

$1. m\angle ECB=50\\2. m\textrm{ arc BC}=100\\3. m\textrm{ arc CD}=80\\4. m\angle DCF=40$

Step-by-step explanation:

Given:

$\angle DBC=40$ °

From the triangle, using the theorem that center angle by an arc is twice the angle it subtend at the circumference.

$m\textrm{ arc CD}=2\times \angle DBC\\m\textrm{ arc CD}=2\times 40=80$

Also, the diameter of the circle is BD. As per the theorem that says that angle subtended by the diameter at the circumference is always 90°,

$m\angle BCD=90$

From the Δ BCD, which is a right angled triangle,

$m\angle DBC+m\angle BDC=90\textrm{ (right angled triangle)}\\40+m\angle BDC=90\\m\angle BDC=90-40=50$

Now, using the theorem that angle between the tangent and a chord is equal to the angle subtended by the same chord at the circumference.

Here, chords CD and BC subtend angles 40 and 50 at the circumference as shown in the diagram by angles $m\angle DBC\textrm{ and }m\angle BDC$ and EF is a tangent to the circle at point C.

Therefore, $m\angle DCF=m\angle DBC=40\\m\angle ECB=m\angle BDC=50$

Again, using the same theorem as above,

$m\angle DCF=50\\\therefore m\textrm{ arc BC}=2\times m\angle DCF=2\times 50=100$

Hence, all the angles are as follows:

$1. m\angle ECB=50\\2. m\textrm{ arc BC}=100\\3. m\textrm{ arc CD}=80\\4. m\angle DCF=40$

6 0

1 year ago

Read 2 more answers

An electrician charges an hourly rate of $50, but also charges a fixed fee for making house calls regardless of time spend on th

NISA [10]

Answer:

C=50t+150

Step-by-step explanation:

From the information given, the equation will need to show that the total cost of the electrician services would be equal to 50 that is the hourly rate for the number of hours spent working plus the fixed fee:

Fixed fee=250-(50*2)=250-100=150

According to this, the equation would be:

C=50t+150, where C is the total cost of the electrician's services and t is the number of hours spent working.

8 0

1 year ago

a group of girls bought 72 rainbow hairbands ,144 brown and black hairbands and 216 bright colored hairbands .what is the larges

Nitella [24]

Answer:

72

Step-by-step explanation:

We are assuming that all girls in the group bought the same number of items.

Therefore, we need to find the highest common factor of 72, 144 and 216.

HCF

72 = 2 * 2 * 2 * 3 * 3

144 = 2 * 2 * 2 * 2 * 3 * 3

216 = 2 * 2 * 2 * 3 * 3 * 3

The product of the emboldened numbers is the highest common factor.

That is:

2 * 2 * 2 * 3 * 3 = 72

Therefore, the largest possible number of girls in the group is 72.

5 0

1 year ago

To better understand how husbands and wives feel about their finances, Money Magazine conducted a national poll of 1010 married

Xelga [282]

Answer:

a. See the table below

b. See the table below

c. 0.548

d. 0.576

e. 0.534

f) i) 0.201, ii) 0.208

Explanation:

First, order the information provided:

Table: "Who is better at getting deals?"

Who Is Better?

Respondent I Am My Spouse We Are Equal

Husband 278 127 102

Wife 290 111 102

<u>a. Develop a joint probability table and use it to answer the following questions. </u>

The<em> joint probability table</em> shows the same information but as proportions. Hence, you must divide each number of the table by the total number of people in the set of responses.

1. Number of responses: 278 + 127 + 102 + 290 + 111 + 102 = 1,010.

2. Calculate each proportion:

278/1,010 = 0.275
127/1,010 = 0.126
102/1,010 = 0.101
290/1,010 = 0.287
111/1,010 = 0.110
102/1,010 = 0.101

3. Construct the table with those numbers:

<em>Joint probability table</em>:

Respondent I Am My Spouse We Are Equal

Husband 0.275 0.126 0.101

Wife 0.287 0.110 0.101

Look what that table means: it tells that the joint probability of being a husband and responding "I am" is 0.275. And so for every cell: every cell shows the joint probability of a particular gender with a particular response.

Hence, that is why that is the joint probability table.

<u>b. Construct the marginal probabilities for Who Is Better (I Am, My Spouse, We Are Equal). Comment.</u>

The marginal probabilities are calculated for each for each row and each column of the table. They are shown at the margins, that is why they are called marginal probabilities.

For the colum "I am" it is: 0.275 + 0.287 = 0.562

Do the same for the other two colums.

For the row "Husband" it is 0.275 + 0.126 + 0.101 = 0.502. Do the same for the row "Wife".

Table<em> Marginal probabilities</em>:

Respondent I Am My Spouse We Are Equal Total

Husband 0.275 0.126 0.101 0.502

Wife 0.287 0.110 0.101 0.498

Total 0.562 0.236 0.202 1.000

Note that when you add the marginal probabilities of the each total, either for the colums or for the rows, you get 1. Which is always true for the marginal probabilities.

<u>c. Given that the respondent is a husband, what is the probability that he feels he is better at getting deals than his wife? </u>

For this you use conditional probability.

You want to determine the probability of the response be " I am" given that the respondent is a "Husband".

Using conditional probability:

P ( "I am" / "Husband") = P ("I am" ∩ "Husband) / P("Husband")

P ("I am" ∩ "Husband) = 0.275 (from the intersection of the column "I am" and the row "Husband)

P("Husband") = 0.502 (from the total of the row "Husband")

P ("I am" ∩ "Husband) / P("Husband") = 0.275 / 0.502 = 0.548

<u>d. Given that the respondent is a wife, what is the probability that she feels she is better at getting deals than her husband?</u>

You want to determine the probability of the response being "I am" given that the respondent is a "Wife", for which you use again the formula for conditional probability:

P ("I am" / "Wife") = P ("I am" ∩ "Wife") / P ("Wife")

P ("I am" / "Wife") = 0.287 / 0.498

P ("I am" / "Wife") = 0.576

<u>e. Given a response "My spouse," is better at getting deals, what is the probability that the response came from a husband?</u>

You want to determine: P ("Husband" / "My spouse")

Using the formula of conditional probability:

P("Husband" / "My spouse") = P("Husband" ∩ "My spouse")/P("My spouse")

P("Husband" / "My spouse") = 0.126/0.236

P("Husband" / "My spouse") = 0.534

<u>f. Given a response "We are equal" what is the probability that the response came from a husband? What is the probability that the response came from a wife?</u>

<u>What is the probability that the response came from a husband?</u>

P("Husband" / "We are equal") = P("Husband" ∩ "We are equal" / P ("We are equal")

P("Husband" / "We are equal") = 0.101 / 0.502 = 0.201

<u>What is the probability that the response came from a wife:</u>

P("Wife") / "We are equal") = P("Wife" ∩ "We are equal") / P("We are equal")

P("Wife") / "We are equal") = 0.101 / 0.498 = 0.208

6 0

2 years ago