A study found a relationship between the number of sugary drinks consumed by a child each day and the prevalence of Type II diabetes. What is the dependent variable? The prevalence of Type II diabetes the number of sugary drinks consumed by a child during a day both the prevalence of Type II diabetes and the number of sugary drinks consumed by a child during a day there is no dependent variable

Given:

[tex]\cos \theta =\dfrac{3}{5}[/tex]

[tex]\sin \theta <0[/tex]

To find:

The quadrant of the terminal side of [tex]\theta[/tex] and find the value of [tex]\sin\theta[/tex].

Solution:

We know that,

In Quadrant I, all trigonometric ratios are positive.

In Quadrant II: Only sin and cosec are positive.

In Quadrant III: Only tan and cot are positive.

In Quadrant IV: Only cos and sec are positive.

It is given that,

[tex]\cos \theta =\dfrac{3}{5}[/tex]

[tex]\sin \theta <0[/tex]

Here cos is positive and sine is negative. So, [tex]\theta [/tex] must be lies in Quadrant IV.

We know that,

[tex]\sin^2\theta +\cos^2\theta =1[/tex]

[tex]\sin^2\theta=1-\cos^2\theta[/tex]

[tex]\sin \theta=\pm \sqrt{1-\cos^2\theta}[/tex]

It is only negative because [tex]\theta [/tex] lies in Quadrant IV. So,

[tex]\sin \theta=-\sqrt{1-\cos^2\theta}[/tex]

After substituting [tex]\cos \theta =\dfrac{3}{5}[/tex], we get

[tex]\sin \theta=-\sqrt{1-(\dfrac{3}{5})^2}[/tex]

[tex]\sin \theta=-\sqrt{1-\dfrac{9}{25}}[/tex]

[tex]\sin \theta=-\sqrt{\dfrac{25-9}{25}}[/tex]

[tex]\sin \theta=-\sqrt{\dfrac{16}{25}}[/tex]

[tex]\sin \theta=-\dfrac{4}{5}[/tex]

Therefore, the correct option is B.

Answer:

64 dollars

Step-by-step explanation: 120×30%= $36-$100= $64

She receives $16 when she pays for the calculator with a $100 bill

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A calculator which is marked at $120 is sold for cash at a 30% discount.

So, It was sold for 70% of its mark value assuming that to x.

∴ (70/100)×120 = x.

x = $84.

So, Susan will receive $(100 - 84) = $16.

learn more about percentages here :

https://brainly.com/question/24159063

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Given:

A figure and an incomplete equation [tex]m\angle GEM+m\angle MEO+m\angle \_\_[/tex].

To find:

The missing value for the given equation by using the angle addition postulate.

Solution:

A ray EM divides the angle GEO into two parts. The first part is [tex]\angle GEM[/tex] and the second part is [tex]\angle MEO[/tex].

Using the angle addition postulate [tex]\angle GEO[/tex] is the sum of [tex]\angle GEM[/tex] and [tex]\angle MEO[/tex].

[tex]m\angle GEM+m\angle MEO+m\angle GEO[/tex]

Therefore, the missing value is GEO and the complete equation is [tex]m\angle GEM+m\angle MEO+m\angle GEO[/tex].

Answer:

225 cm cubed

Step-by-step explanation:

(1/2•base)•height

Answer: B or D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The answer must have 5! since it is a combinaiton of letters without any repeats. Since you want two words, its 2/5!

Answer:

No, the points are evenly distributed about the x-axis

Step-by-step explanation:

Hope its right , if not so advance sorry :)

Answer:

Step-by-step explanation:

Answer:

x = 48; y = 13

Step-by-step explanation:

20/5 = 52/y

4 = 52/y

4y = 52

y = 13

20/5 = x/12

4 = x/12

x = 4 * 12

x = 48

Answer:

x = 48, y = 13

Step-by-step explanation:

Since they have a pair of verticle angles, this means the triangles are similar. You find a common side (the length 5 and length 20) and you know the ratio, (divide 20 by 5) aka. the larger triangle is 4 times larger than the smaller one. That means the side lengths are also 1/4 scale. So the bigger triangle = 12(length of side)*4(ratio). Also since y is on the smaller triangle, you scale it down by 1/4, so 52 (the side length) / 4 (ratio) is 13. So y = 13, x =48

Answer:

D. 4/7

Step-by-step explanation:

There are 7 people in people and there are 4 girls, that would be 4/7.

Answer:

x = 145

Step-by-step explanation:

The angles are same side exterior angle and same side exterior angles are supplementary

x +35 =180

Subtract 35 from each side

x = 180-35

x =145

Answer:

x=145

Step-by-step explanation:

180 -35 = 145

angle in a straight line add up to 180

x=145

F angle /corresponding angle are the same

Answer:

r = [tex]\frac{V-IR}{I}[/tex]

Step-by-step explanation:

Given

V = I (R + r) ← distribute parenthesis

V = IR + Ir ( subtract IR from both sides )

V - IR = Ir ( divide both sides by I )

[tex]\frac{V-IR}{I}[/tex] = r

Answer:

$512

Step-by-step explanation:

Interest = 16% of 800

             = 16/100 x 800

             = $128

Interest for 4 years = 128 x 4

                                = $512

Given:

The cost of game = $25

Sales markup = 6%

To find:

How much do they each pay?

Solution:

The sales markup is 6% of the cost.

[tex]\text{Sales markup}=25\times \dfrac{6}{100}[/tex]

[tex]\text{Sales markup}=1.5[/tex]

Now, the total cost after sales markup is:

[tex]25+1.5=26.5[/tex]

Jane and Tannic split the cost of buying a video game. It means they divide the cost in two equal parts. So, the amount paid by each one is

[tex]\dfrac{26.5}{2}=13.25[/tex]

Therefore, Jane and Tannic will pay $13.25 each .

Answer:

The answer is A. 31,250.

Step-by-step explanation:

To solve for the 7th term in the geometric sequence, start by plugging 7 into the explicit formula, and the formula will look like [tex]a_{7}=2*5^{(7-1)}[/tex].

Next, subtract 1 from 7, and the formula will look like [tex]a_{7}=2*5^{6}[/tex].

Then, raise 5 to the power of 6, which will look like [tex]2*15625[/tex].

Finally, multiply 2 by 15,625, and the answer will be 31,250.

Answer:

I think it's 6 (square root) 2

Answer:

0.99

Step-by-step explanation:

divide 6.93 by 7.

= 0.99

We have the equation:

6.93 ÷ 7 = ?  

 [tex]\left[\begin{array}{ccccccc}&&0.&9&9\\7&&6.&9&3\\&&-&6&3\\\left&&&&6&3\\&&&-&6&3\\&&&&&0\end{array}\right][/tex]

I hope it's correct and it helps I don't know how to explain it lol

Answer:

C

Step-by-step explanation:

Answer:

(3) 48

Step-by-step explanation:

The angle inside the ABC one is two times its angle size

Step-by-step explanation:

i think is k , m , l

bcause 4 is the smallest number,

and 12 is the biggest number.

Answer:30

Step-by-step explanation:

Answer:

√85

Step-by-step explanation:

A (-3 , 4)    B (4 , -2)

AB² = (4 - -3)² + (-2 -4)² = 49 + 36 = 85

AB = √85

Answer:

1 /24

Step-by-step explanation:

Given the 3 spinners :

Probability = required outcome / Total possible outcomes

Probability that Spinner 1 lands on A :

P(spinner 1 lands on A) = 1/2

Probability that spinner 2 lands on 4 :

P(lands on 4) = 1 / 4

Probability that spinner 3 lands on green :

P(lands on green) = 1/3

Combined probability = 1/2 * 1/4 * 1/3 = 1 /24

Answer:

Answer:

The right solution is "36 years".

Step-by-step explanation:

Given:

Principle,

P = $2,340,260

Amount,

A = $3,393,377

Simple interest,

SI = 3,393,377 - 2,340,260

   = $1,053,117

Rate of interest,

r = 1.25%

As we know,

⇒ [tex]SI=\frac{Prt}{100}[/tex]

By substituting the values, we get

⇒ [tex]1053117=\frac{2340260\times 1.25\times t}{100}[/tex]

⇒ [tex]10531170=292532.5\times t[/tex]

⇒              [tex]t=\frac{10531170}{292532.5}[/tex]

⇒                [tex]=36 \ years[/tex]