Which expression is equivalent to (n*m*p)(x), given m(x) = sinx, n(x) = 3x, and p(x) = x^2

WILL GIVE BRANLIEST!!! Pls help! Determine the coordinates of the point on the straight line y=3x+1 that is equidistant from the

iren [92.7K]

Let , coordinate of points are P( h,k ).

Also , k = 3h + 1

Distance of P from origin :

$d=\sqrt{h^2+k^2}$

Distance of P from ( -3, 4 ) :

$d=\sqrt{(h+3)^2+(k-4)^2}$

Now , these distance are equal :

$h^2+(3h+1)^2=(h+3)^2+(3h+1-4)^2\\\\h^2+(3h+1)^2=(h+3)^2+(3h-3)^2$

Solving above equation , we get :

$P=(\dfrac{16}{21},\dfrac{23}{7})$

Hence , this is the required solution.

6 0

1 year ago

The fraction of defective integrated circuits produced in a photolithography process is being studied. A random sample of 300 ci

Olenka [21]

Answer:

The correct answer is

(0.0128, 0.0532)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence interval $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

Z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$

For this problem, we have that:

In a random sample of 300 circuits, 10 are defective. This means that $n = 300$ and $\pi = \frac{10}{300} = 0.033$

Calculate a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool.

So $\alpha$ = 0.05, z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{300}} = 0.033 - 1.96\sqrt{\frac{0.033*0.967}{300}} = 0.0128$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{300}} = 0.033 + 1.96\sqrt{\frac{0.033*0.967}{300}} = 0.0532$

The correct answer is

(0.0128, 0.0532)

4 0

1 year ago

From Tony's seat in the classroom, his eyes are 1.0 m above ground. On the wall 4.2 m away, he can see the top of a blackboard t

Semmy [17]

Answer:

15 degrees

Step-by-step explanation:

Draw a horizontal segment approximately 4 inches long. Label the right endpoint A and the left endpoint C. Label the length of AC 4.2 meters. That is the horizontal distance between the eye and the blackboard.

At the right endpoint, A, draw a vertical segment going up, approximately 1 inch tall. Label the upper point E, for eye. Label segment EA 1 meter since the eye is 1 meter above ground.

At the left endpoint of the horizontal segment, point C, draw a vertical segment going up approximately 2 inches. Label the upper point B for blackboard. Connect points E and B. Draw one more segment. From point E, draw a horizontal segment to the left until it intersects the vertical segment BC. Label the point of intersection D.

The angle of elevation you want is angle BED.

The length of segment BC is 2.1 meters. The length of segment CD is 1 meter. That means that the length of segment BD is 1.1 meters.

To find the measure of angle BED, we can use the opposite leg and the adjacent leg and the inverse tangent function.

BD = 1.1 m

DE = 4.2 m

tan <BED = opp/adj

tan <BED = 1.1/4.2

m<BED = tan^-1 (1.1/4.2)

m<BED = 15

Answer: 15 degrees

7 0

1 year ago

If the relative frequency of a train being late is 0.15 how often could you expect the train to be late in 100 days?

neonofarm [45]

(100)= 0.25*100=15 times.

<span>SO, the train will be late 15 times in 100 days.

Hope i helped:P </span>

7 0

1 year ago

A scientist measures a substance to be 0.8 grams. Calculate the percent of error in the measurement. Show all work for full cred

Volgvan

You'll need to give a bit more information for the question to be answered. You can only calculate the percentage of error if you know what the mass of the substance *should be* and what you've *measured* it to be.

In other words, if a substance has a mass of 0.55 grams and you measure it to be 0.80 grams, then the percent of error would be:

percent of error = { | measured value - actual value | / actual value } x 100%

So, in this case:

percent of error = { | 0.80 - 0.55 | / 0.55 } x 100%
percent of error = { | 0.25 | / 0.55 } x 100%
percent of error = 0.4545 x 100%
percent of error = 45.45%

So, in order to calculate the percent of error, you'll need to know what these two measurements are. Once you know these, plug them into the formula above and you should be all set!

6 0

2 years ago