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2 days ago

An Internet service provider sampled 540 customers, and finds that 75 of them experienced an interruption in high-speed service

during the previous month.a) Obtain a point estimate, to at least three decimal places, for the population proportion of all customers who experienced an interruption in high-speed service during the previous month.b) Assuming the sample size is less than 5% of the population size, why can the sampling distribution of p-hat, the sample proportion of customers who experienced an interruption in high-speed service during the previous month, be approximately normal?c) Construct a 90% confidence interval for the proportion of all customers who experienced an interruption in high-speed service during the previous month.d) You wish to conduct your own study to determine the proportion of all customers who experienced an interruption in high-speed service during the previous month. What sample size would be needed for the estimate to be within 2 percentage points with 98% confidence if you use the point estimate obtained in part (a)?e) You wish to conduct your own study to determine the proportion of all customers who experienced an interruption in high-speed service during the previous month. What sample size would be needed for the estimate to be within 2 percentage points with 98% confidence if you don

Mathematics

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(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

3 months ago

A quadratic function has a line of symmetry at x = –3.5 and a zero at –9. What is the distance from the given zero to the line o

Svet_ta [12734]

Given:

A quadratic function has a line of symmetry positioned at x = –3.5 with one root located at –9.

To find:

The second root.

Solution:

It is understood that the line of symmetry splits the quadratic function's graph into two identical halves. Hence, both roots are equidistant from this line.

This implies that the line of symmetry passes through the midpoint of the two roots.

Let the other root be denoted as x.

$-3.5=\dfrac{(-9)+x}{2}$

Multiply both sides by 2.

$-7=-9+x$

Add 9 to both sides.

$-7+9=-9+x+9$

$2=x$

Consequently, the other zero of the quadratic function is concluded to be 2.

8 0

2 months ago

Explain what you can tell just by comparing the symbols in a picture graph

AnnZ [12381]

In a pictorial graph, icons are utilized to depict the data presented. For instance, if a survey was conducted regarding food preferences at a barbecue, we might incorporate images of a hamburger, a hot dog, and a chicken leg. However, we cannot deduce the quantities involved merely by juxtaposing the icons.

5 0

1 month ago

Read 2 more answers

For what values of x does the binomial 2x−1 take on a positive value?

zzz [12365]

Part A

To identify the values of x that make 2x−1 positive

⇒ 2x - 1 > 0

⇒ 2x > 1

⇒ x > $\frac{1}{2}$

As a result, for any x greater than $\frac{1}{2}$ , the expression 2x-1 is positive

Part B

To find values of y making 21−37 negative

⇒ 21-3y < 0

⇒ 21 < 3y

⇒ 7 < y

Thus, for all y values exceeding 7, the expression 21-3y is negative

Part C

To identify values of c that digit 5−3c greater than 80

⇒ 5-3c > 80

⇒ -3c > 75

⇒ -c > 25

⇒ c < -25

Therefore, for values of c less than -25, the expression 5-3c surpasses 80

7 0

2 months ago