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2 years ago

If secθ = 13/12 and 270° < θ < 360°, then tanθ = _____.

Mathematics

1 answer:

Nezavi [6.7K]2 years ago

4 0

Answer:

tan Ф = opposite / adjacent = a / b=5/12

Step-by-step explanation:

sec Ф = hypotenuse / adjacent = c / b=13/12

tan Ф = opposite / adjacent = a / b

find a

a^2+b^2=c^2

a=√c^2-b^2 b=12 and c=13

a=√144-169=√25=5

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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

3 years ago

Add the equations. 3x - y = -1 - 3x + 3y= 27

harkovskaia [24]

Step-by-step explanation:

3x - 3x -y + 3y = 27-1

2y = 26

y = 13 use this to find the value of x

3x - 13 = -1

3x = -1 + 13

3x = 12

x = 4

3 0

3 years ago

A bicycle is traveling at 22 miles per hour. How many feet will it cover in 45 seconds? Round your answer to the nearest tenth o

puteri [66]

Answer:

1452 feet

Step-by-step explanation:

1 hour = 60min×60sec = 3600 sec

1 miles = 5280 feet

22 miles = 22×5280ft = 116160 ft

3600sec ................. 116160 ft

45sec ................................ x ft

x = 45×116160/3600

= 5227200/3600

= 1452 feet

7 0

3 years ago

Provide an appropriate response. the regression line for the given data is = 1.488x + 60.46. determine the residual of a data po

kap26 [50]

Do you have answer choices ?

7 0

3 years ago

PLEASE HELP: A standard six-sided die is rolled.

amm1812

Answer in fraction form is 1/3

Answer in decimal form is 0.3333

Pick one answer only.

==========================================================

Explanation:

The sample space is the set of all possible outcomes. In this case, the outcomes consist of values between 1 and 6

S = sample space

S = {1,2,3,4,5,6}

There are 6 items here. Let B = 6.

We want to roll a number greater than 4, so the event space we're after is

E = {5,6}

which consists of 2 items. Let A = 2.

The probability we want is A/B = 2/6 = 1/3 = 0.3333

So if you go with the fraction option, then you'll type in 1/3

If you go with the decimal option, then you'll type in 0.3333

4 0

3 years ago