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3 years ago

If sine theta equals three over four, what are the values of cos θ and tan θ?

Mathematics

1 answer:

ratelena [41]3 years ago

7 0

Answer:

In words, Cosine theta equals plus or minus square root of seven over 4,tangent theta equals plus or minus three over root seven

Step-by-step explanation:

Given that sin ∅ =3/4 It means the ratio of the opposite side to the hypotenuse side is 3:4.

Using the Pythagoras theorem we can calculate the hypotenuse adjacent as follows.

a²+b²=c²

a²=c²-b²

a²=4²-3²

a²=16-9

a²=7

a=√7

Then Cos ∅= opposite/ adjacent

=√7/4

Then Tan ∅ = opposite/adjacent

=3/√7

In words, Cosine theta equals plus or minus square root of seven over 4,tangent theta equals plus or minus three over root seven.

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Charlene is a video game designer and wants to make sure that her games can be played on all types of screens. In order for the

natka813 [3]

<h3>Answer:</h3>

C. The playable area has a width of 9 inches and a height of 6 inches.

<h3>Explanation:</h3>

There are a number of ways you can get there.

1. Check the answers to see which have the right area and aspect ratio.

A: area = 24 in² — does not match 54 in²
B: area = 54 in², aspect ratio 6:9 = 2:3 — does not match 3:2 aspect ratio
C: area = 54 in², aspect ratio 9:6 = 3:2 — <em>matches problem statement</em>
D: area = 121.5 in² — does not match 54 in²

2. If the screen were 3:2 (inches), its area would be 6 in². The area of 54 in² is 9 times that value, so the actual screen dimensions are √9 = 3 times 3:2. That is, they are width:height = 9:6 inches — matches selection C.

3. You can write equations for width and height and solve.

w/h = 3/2
wh = 54

Substituting w=3/2·h into the second equation gives

... (3/2)h·h = 54

... h² = 36 . . . . . multiply by 2/3

... h = √36 = 6 . . . . square root, result in inches . . . . matches selection C

3 0

3 years ago

Tim and Jane both work for a company that sells boxes of breakfast cereal. the boxes of cereal cost £3.00 and the amount of cere

Alenkasestr [34]

Answer:

25%

Step-by-step explanation:

As the given situation the parameters are below:-

Cost of each box = 3 pounds

Amount of cereal in each box = 160 g

now,

160 g of cereal = 100%

and

25% of 1 box of cereal = 25% of 160 g which is

$= \frac{25}{100} \times 160 g= 40 g$

As per the question, it is mention that Jane need her idea to give the equal value of amount as Tim's idea, provided

160 g of cereal costs 3 pounds

and

1 g of cereal will cost

= $\frac{3}{60}\ pounds$

40 g of cereal will cost $40\times \frac{3}{160} = \frac{3}{4}\ pounds$

So, the percentage of $\frac{3}{4}$ the pound is of 3 pounds is 3 ÷ 4 ÷ 3 × 100

= 25%

Therefore as the situation, Jane need to decline the amount by 25% for the same amount as Tim's idea.

3 0

3 years ago

Consider the following hypothesis test H0 p 20 Ha p 20 A sample of 400 provided a sample proportion p 175 a Compute the value of

Bogdan [553]

Answer:

a) -1.25

b) 0.2112

c) -1.96

Step-by-step explanation:

Data provided in the question:

Sample size, n = 400

H0 : p = 20

$\bar{p}$ = 175

Now,

a) The test statistic is given as:

Z = $\frac{(\bar{p}-p)}{\sqrt{\frac{p(1-p)}{n}}}$

on substituting the respective values, we get

Z = $\frac{(0.175-0.2)}{\sqrt{\frac{0.2\times0.8}{400}}}$

= -1.25

b) The p-value = 2 × P(Z <-1.25)

Now from the standard normal table

P(Z <-1.25) = 10.56% = 0.1056

Thus,

p-value = 2 × 1056 = 0.2112

c) for a = 0.05,

the critical value is $Z_{\frac{a}{2}}=Z_{\frac{0.05}{2}}$ i.e $Z_{0.025}$

Now from standard normal table

$Z_{0.025}$ = -1.96

3 0

3 years ago

Which statement best explains why y=4−6x is a function?

cluponka [151]

<u>Answer:</u>

The correct answer option is: Each x value has one and only one y value.

<u>Step-by-step explanation:</u>

A relationship from a set of inputs to a set of outputs where each input has exactly one corresponding output value is said to be a function.

Here, we are given $y=4-6x$ which happens to be a function as no x value is repeated and there is only one corresponding y value to it.

Therefore, option c is the correct answer.

5 0

3 years ago

The circle has center O. Its radius is 9 ft, and the central angle a measures 50°. What is the area of the shaded region?

Ivahew [28]

Answer:

35.34305555555

Step-by-step explanation:

You must calculate the percentage taken out of the circle by the shaded region. This would be about 13.8%. Then you take the overall area of the circle and multiply it by the percentage. This should give you your answer.

REMEMBER TO ROUND IF YOU ARE SUPPOSED TO, THERE IS NO INDICATION ON BRAINLY. WITHOUT ROUNDING YOU CAN GET THE ANSWER WRONG.

8 0

3 years ago