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2 years ago

Knowing that sin 30 = 1/2 what is a

Mathematics

2 answers:

Aleksandr [31]2 years ago

6 0

Answer:

B. 18

Step-by-step explanation:

We have been given a diagram of a right triangle and we are asked to find the value of a.

Since we know that Sine relates the opposite with hypotenuse of a right triangle.

$\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}$

Upon substituting our given values we will get,

$sin(30^o)=\frac{9}{a}$

Upon substituting $sin(30^o)=\frac{1}{2}$ in above equation we will get,

$\frac{1}{2}=\frac{9}{a}$

Now let us cross multiply our equation to solve for a.

$1\cdot a=9\cdot 2$

$a=18$

Therefore, the value of a is 18 and option B is the correct choice.

natulia [17]2 years ago

4 0

$sin30^o=\frac{9}{a}\\\frac{9}{a}=\frac{1}{2}\\a=2\cdot9\\a=18$

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A store receives shipments of peaches and wants to sort them by weight. Drag each shipment to match the ratio of peaches to poun

Andrej [43]

Answer:

Step-by-step explanation:

Given that a store receives shipments of peaches. They want to sort them by weight.

The sorting pattern is as follows:

Peaches : Pound = 2:1 or 3.25:1 or 1:3.25

Given are i) 26 peaches to 13 lbs = 26:13=2:1 Hence goes to the first box

ii) 6 peaches to 19.5 lbs =6:19,5 = 1:3,25 lb. Hence goes to II box

iii) 13 peaches to 4 lbs: =13:4=3.25:1 Hence goes to II box

iv) 39 peaches to 12 lbs: =39:12=3.25:1 Hence goes to II box

v) 15 peaches to 7.5 lbs: =15:7.5=2:1 Hence goes to I box

i - I box

ii - II box

iii - II box

iv) - II box

v) - I box

8 0

2 years ago

We want to estimate the population mean within 5, with a 99% level of confidence. the population standard deviation is estimated

pashok25 [27]

A sample size of 60 is required.

We use the formula
$n=(\frac{z*\sigma}{E})^2$

We first find the z-score associated with this level of confidence:
Convert 99% to a decimal: 99/100 = 0.99
Subtract from 1: 1-0.99 = 0.01
Divide by 2: 0.01/2 = 0.005
Subtract from 1: 1-0.005 = 0.995

Using a z-table (http://www.z-table.com) we see that this value is equally distant from 2.57 and 2.58; therefore we will use 2.575:

$n=(\frac{15(2.575)}{5})^2=59.68\approx60$

3 0

2 years ago

Find any relative extrema of the function. (Round your answers to three decimal places.)

Strike441 [17]

(x) = arcsec(x) − 8x

f'(x) = d/dx( arcsec(x) − 8x )

1/xsqrt( x^2 - 1) - 8

f'(x) = 0

1/xsqrt( x^2 - 1) - 8 = 0

8 x sqrt (x^2-1) = 1

( 8 x sqrt (x^2-1) )^2 = 1

64 x^2 ( x^2 - 1) = 1

64 x^4 - 64 x^2 =1

64 x^4 - 64 x^2 - 1 = 0

x = 1.00766 , - 1.00766

x = - 1.00766

f(- 1.00766) = arcsec(- 1.00766) − 8( - 1.00766)

f( - 1.00766 ) = 11.07949

x = 1.00766

f(1.00766) = arcsec(1.00766) − 8( 1.00766)

f(1.00766 ) = -7.93790

relative maximum (x, y) = (- 1.00766 , 11.07949 ) relative minimum (x, y) = ( 1.00766 , -7.93790 )

8 0

2 years ago

Select the correct answer.

LUCKY_DIMON [66]

Answer:

Step-by-step explanation:

because the points in the plot point graph are all close to the line which indicates a strong association.

Also the slope isn't closer to 0 than to 1 so that eliminates those answers.

3 0

1 year ago

According to a study in a medical journal, 202 of a sample of 5,990 middle-aged men had developed diabetes. It also found that m

tekilochka [14]

Answer:

0.0588 = 5.88% probability that a middle-aged man with diabetes is very active

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

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

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Has diabetes.

Event B: Is very active.

Probability of having diabetes:

To find this probability, we take in consideration that:

It also found that men who were very active (burning about 3,500 calories daily) were a fourth as likely to develop diabetes compared with men who were sedentary. Assume that one-fifth of all middle-aged men are very active, and the rest are classified as sedentary.

So the probability of developing diabetes is:

x of 4/5 = x of 0.8(not active)

x/4 = 0.25x of 1/5 = 0.2(very active). So

$P(A) = 0.8x + 0.25*0.2x = 0.85x$