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3 years ago

Find the length of line segment UV.

Mathematics

1 answer:

pshichka [43]3 years ago

8 0

Answer:

The length of the line segment UV is 76 units

Step-by-step explanation:

In a triangle, the line segment joining the mid-points of two sides is parallel to the third side and equal to half its length

In Δ ONT

∵ U is the mid-point of ON

∵ V is the mid-point of TN

→ That means UV is joining the mid-points of two sides

∴ UV // OT

∴ UV = $\frac{1}{2}$ OT

∵ UV = 7x - 8

∵ OT = 12x + 8

∴ 7x - 8 = $\frac{1}{2}$ (12x + 8)

→ Multiply the bracket by $\frac{1}{2}$

∵ $\frac{1}{2}$ (12x + 8) = $\frac{1}{2}$ (12x) + $\frac{1}{2}$ (8) = 6x + 4

∴ 7x - 8 = 6x + 4

→ Add 8 to both sides

∴ 7x - 8 + 8 = 6x + 4 + 8

∴ 7x = 6x + 12

→ Subtract 6x from both sides

∴ 7x - 6x = 6x - 6x + 12

∴ x = 12

→ Substitute the value of x in the expression of UV to find it

∵ UV = 7(12) - 8 = 84 - 8

∴ UV = 76

∴ The length of the line segment UV is 76 units

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In answering on a multiple choice test, a student either know the answer or guesses. Let p be the probability that the students

LenaWriter [7]

Answer:

$P(A_{1}|B ) =\frac{mp}{1+p(m-1)}$

Step-by-step explanation:

For mutually exclusive events as A1, A2, A3, etc, Bayes' theorem states:

$P(A|B)= \frac{P(B|A)P(A)}{P(B)}$

P(A|B) is a conditional probability: the likelihood of event A occurring given that B is true.

P(B|A) is a conditional probability: the likelihood of event B occurring given that A is true.

P(A) is the probability that A occurs

P(B) is the probability that B occurs

For this problem:

A1 is the probability that the student knows the answer

A2 is the probability that the student guesses the answer

B is the probability that the student answer correctly

$P(A_{1})=p \\P(A_{2})=1-p \\P(B|A_{1})=1 \\P(B|A_{2})=\frac{1}{m} \\P(B)= P(A_{1})P(B|A_{1}) + P(A_{2})P(B|A_{2})= p+\frac{1-p}{m} \\$

P(B|A₁) means the probability that the answer is correct when he knew the answer

P(B|A₂) means the probability that the answer is correct when he guessed the answer

P(A₁|B) means the probability that he knew the answer when the answer was correct

Replacing everything in the Bayes' theorem you get:

$P(A_{1}|B)= \frac{P(B|A_{1})P(A_{1})}{P(B)}=\frac{(1)(p)}{p+\frac{1-p}{m}} =\frac{mp}{mp+1-p} =\frac{mp}{1+p(m-1)}$

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3 years ago

What is not a good reason to refinance

Flauer [41]

Answer:

Step-by-step explanation:

The answer is A because all of the other options are favorable circumstances to refinance. There's no need to refinance if the loan in question (a mortgage in this case) has already been paid off.

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3 years ago

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Niki wants to buy a dog bed the cost $87. She earns $6 per week for doing chores. How many weeks will Niki have to do her chores

Viktor [21]

Answer:

The answer to your question is 14.5 weeks

Step-by-step explanation:

Data

Total cost = C = $87

money earned = m = $6

Number of weeks to have the money = w = ?

Process

1.- Write an equation that represents the situation

Weeks = Total cost / Money earned

w = C/m

2.- Substitute the values

w = 87 / 6

3.- Result

w = 14.5

4.- Conclusion

Niki will last 14.5 weeks to have enough money to buy a dog bed.

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3 years ago

Please answer this correctly

Klio2033 [76]

Answer:

x =1

Step-by-step explanation:

Assuming the figures are similar, we can use ratios to solve

x 2

---- = -----

4 8

Using cross products

8x = 2*4

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Divide by 8

8x/8 = 8/8

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6 0

3 years ago

2. Write the mixed number -5(4/9) as a fraction in three different ways. Thenwrite the mixed number as a decimal.

emmasim [6.3K]

Fraction #1

$-5\frac{4}{9}$

Fraction #2

$-\frac{49}{9}$

Fraction #3

$-4\frac{13}{9}$

Fraction #4

$-3\frac{22}{9}$

Decimal:

$-5\frac{4}{9}\approx5.4444$

Answer:

$-5\frac{4}{9}$

$-\frac{49}{9}$

$-4\frac{13}{9}$

Decimal: 5.4444

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