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14 days ago

A small school with 60 total students records how many of their students attend on each of the 180 days in a school year. the ma

in number of students in attendance daily is 55 students and the standard deviation is 4 students. suppose we take a random sample of five School days and calculate the mean number of students in attendance on those days in each sample

Mathematics

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Tim wants to build a rectangular fence around his yard. He has 42

zzz [12365]

I believe the answer is D.

5 0

1 month ago

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At a hot air ballon festival, Erica spots a red ballon due east at an angle of elevation of 36 degrees. She turns due west and s

Zina [12379]

Answer:

Step-by-step explanation:

Information provided

The eastern balloon makes an elevation angle of $36^{\circ}$ and is positioned at a height of 461 m.

The western balloon creates an elevation angle of $51^{\circ}$ and is positioned at a height of 296 m.

Considering that Erica is 1.6 m tall, the effective height of the Red balloon becomes 459.4 m,

while the effective height of the Blue balloon ends up at 294.4 m.

Utilizing trigonometric principles,

$\tan 36=\frac{459.4}{d_1}$

$\tan 51=\frac{294.4}{d_2}$

$d_1=632.30 m$

$d_2=238.4 m$

Now calculating the distance separating the two Balloons,

$d=d_1+d_2$

$d=870.70 m$

7 0

2 months ago

(a) For what values of k does the function y = cos(kt) satisfy the differential equation 81y'' = −4y? (Enter your answers as a c

tester [12383]

Answer:

$k = \frac{2}{9}, k=\frac{-2}{9}$

Step-by-step explanation:

The initial scenario is a specific case of the subsequent one, so we will address the second case first.

Consider $y = A\sin(kt) + B\cos(kt)$ . Through the utilization of derivatives and trigonometric function properties, it is determined that

$y' = A\cdot k \cos(kt)- B \cdot k \sin(kt) = k (A\cos(kt)-B\sin(kt))$

$y'' = k(-A\cdot k \sin(kt)-B\cdot k \cos(kt)) = -k^2(y)$

The equation is represented as $81y''=-4y$ . It's important to note that since $y'' = -k^2y$ it leads to the equation

$-k^2 81y=-4y$ ,

which signifies that $k^2 = \frac{4}{81}$ . Consequently, $k=\pm\frac{2}{9}$

It's notable that in this instance, the value of k is independent of A and B. Thus, it applies universally to any values of A and B. The first scenario is included since it corresponds to A=0 and B=1.

5 0

2 months ago

Joaquin is constructing the perpendicular bisector of AB. He opens his

Zina [12379]

Answer:

Step-by-step explanation:

To construct the perpendicular bisector, follow these steps:

Step 1:

Set the compass to a distance greater than half the length of segment AB, place it on point A, and draw an arc across AB.

Step 2:

Keeping the same width, place the compass on point B and create another arc across AB.

Step 3:

With the ruler, connect the two intersection points of the arcs by drawing a line.

Step 4:

This line will be the perpendicular bisector of the segment AB.

Thus, option A is the correct choice.

9 0

2 months ago

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