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NNADVOKAT [17]
2 years ago
7

What is the value of y in the triangle?

Mathematics
1 answer:
Readme [11.4K]2 years ago
8 0

Answer:

• From trigonometric ratios:

{ \rm{ \sin( \theta) =  \frac{opposite}{hypotenuse}  }} \\

→ theta is 41°

→ opposite is y

→ hypotenuse is 26 ft

{ \tt{ \sin(41)  =  \frac{y}{26} }} \\  \\ { \tt{y = 26 \sin(41) }} \\  \\ { \boxed{ \tt{ \: y = 17.06 \:  \: ft}}}

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irina1246 [14]

Answer: x=56°

The opposite angle of 56° and the opposite angle of ∠x are alternate angles.

5 0
2 years ago
Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a seco
kari74 [83]

Answer:

C. \frac{1}{18}

Step-by-step explanation:

Given: Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl then a second card is drawn.

To Find: If the cards are drawn at random and if the sum of the numbers on the cards is 8, what is the probability that one of the two cards drawn is numbered 5.

Solution:

Sample space for sum of cards when two cards are drawn at random is \{(1,1),(1,2),(1,3)......(6,6)\}

total number of possible cases =36

Sample space when sum of cards is 8 is \{(3,5),(5,3),(6,2),(2,6),(4,4)\}

Total number of possible cases =5

Sample space when one of the cards is 5 is \{(5,3),(3,5)\}

Total number of possible cases =2

Let A be the event that sum of cards is 8

p(\text{A}) =\frac{\text{total cases when sum of cards is 8}}{\text{all possible cases}}

p(\text{A})=\frac{5}{36}

Let B be the event when one of the two cards is 5

probability than one of two cards is 5 when sum of cards is 8

p(\frac{\text{B}}{\text{A}})=\frac{\text{total case when one of the number is 5}}{\text{total case when sum is 8}}

p(\frac{\text{B}}{\text{A}})=\frac{2}{5}

Now,

probability that sum of cards 8 is and one of cards is 5

p(\text{A and B}=p(\text{A})\times p(\frac{\text{B}}{\text{A}})

p(\text{A and B})=\frac{5}{36}\times\frac{2}{5}

p(\text{A and B})=\frac{1}{18}

if sum of cards is 8 then probability that one of the cards is 8 is \frac{1}{18}, option C is correct.

3 0
2 years ago
The linear equation y = 400 + 50x represents the total cost, y , per hour, x , for a lawyer at a law firm. The lawyer charges a
earnstyle [38]

Answer:

453

Step-by-step explanation:

because we multiply the value with the equation

5 0
2 years ago
One of the factors of 34 is chosen at random. What is the probability that the factor is itself a two digit number?
solong [7]
A factor of 30 is chosen at random. What is the probability, as a decimal, that it is a 2-digit number?

The positive whole-number factors of 30 are:

1, 2, 3, 5, 6, 10, 15 and 30.

So, there are 8 of them. Of these, 3 have two digits. Writing each factor on a slip of paper, then putting the slips into a hat, and finally choosing one without looking, get that

P(factor of 30 chosen is a 2-digit number) = number of two-digit factors ÷ number of factors

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8 0
2 years ago
What is the solution for the system of equations {9x+8y=3 6x−12y=−11?
lions [1.4K]

Answer:

( - \frac{1}{3}, \frac{3}{4} )

Step-by-step explanation:

Given the 2 equations

9x + 8y = 3 → (1)

6x - 12y = - 11 → (2)

To eliminate the y- term multiply (1) by 1.5

13.5x + 12y = 4.5 → (3)

Add (2) and (3) term by term

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19.5x = - 6.5 ( divide both sides by 19.5 )

x = \frac{-6.5}{19.5} = - \frac{1}{3}

Substitute this value into either of the 2 equations and solve for y

Using (1), then

- 3 + 8y = 3 ( add 3 to both sides )

8y = 6 ( divide both sides by 8 )

y = \frac{6}{8} = \frac{3}{4}

Solution is (- \frac{1}{3}, \frac{3}{4} )

6 0
3 years ago
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