Given that the standard error of the sample proportion is 0.0195 and the point estimate follows a nearly normal distribution, calculate the test statistic (the z-statistic).

a. at r = 2

P = [10! / (10 – 2)! 2!] * 0.33^2 * 0.67^(10 – 2)

P = 0.1989 ~ 0.20               (answer)

b. We deduct the values of P when r = 0, r = 1, r = 2 from 1 to get all values when r > 2

at r = 0

P = [10! / (10 – 0)! 0!] * 0.33^0 * 0.67^(10 – 0)

P = 0.0182

at r = 1

P = [10! / (10 – 1)! 1!] * 0.33^1 * 0.67^(10 – 1)

P = 0.0898

so for r > 2, the probability is:

P = 1 – (0.1989 + 0.0182 + 0.0898)

P = 0.6931            (answer)

c. at r = 3

P = [10! / (10 – 3)! 3!] * 0.33^3 * 0.67^(10 – 3)

P = 0.2614

at r = 4

P = [10! / (10 – 4)! 4!] * 0.33^4 * 0.67^(10 – 4)

P = 0.2253

at r = 5

P = [10! / (10 – 5)! 5!] * 0.33^5 * 0.67^(10 – 5)

P = 0.1332

So when r is between 2 and 5 inclusive, the probability is:

P = 0.1989+ 0.2614 + 0.2253 + 0.1332

P = 0.8188            (answer)

The  17/4 as a mixed number can be written as  4 1/4.

For conversion from decimal to fraction, we write it in the form a/b such that the result of the fraction comes as the given decimal. Usually, to get the decimal of the form a.bcd, we count how many digits are there after the decimal point (if its finite), then we write 10 raised to that many power as denominator, and the considered number without any decimal point as numerator.

In order to make 17/4 as a mixed number, we would have to do 17 divided by 4.

17/ 4 = 4.25

Then just put that decimal into a fraction.

That would be 4.25 = 4 1/4

Therefore, the  17/4 as a mixed number can be written as  4 1/4.

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The domain of the function is restricted to the altitude of the plane, and the plane cannot exceed its absolute ceiling. The graph of the function will have a vertical asymptote at the absolute ceiling. As the plane approaches its absolute ceiling, the time required to further increase its altitude increases significantly. To find the time it will take for the plane to climb to a specific altitude, substitute the altitude into the equation and solve for time.

a. The domain of the function is determined by the restrictions given in the problem. In this case, the domain represents the altitude of the plane. Since the plane's absolute ceiling is 18,000 feet, the altitude cannot exceed 18,000 feet. Therefore, the domain is 0 ≤ h ≤ 18,000.

b. To graph the function, we can plot points by substituting different values of h into the function and calculating the corresponding values of t. This will result in a smooth curve. Asymptotes occur when the function approaches certain values of h or t. In this case, the function has a vertical asymptote at h = 18,000, because the plane cannot climb beyond its absolute ceiling.

c. As the plane approaches its absolute ceiling of 18,000 feet, the time required to further increase its altitude increases significantly. This is because the logarithmic function in the equation has a slower growth rate as h approaches its limit.

d. To find the time it will take for the plane to climb to an altitude of 4000 feet, we can substitute h = 4000 into the equation t = 50 log10 (18000/(18000-h)) and solve for t.

Answer:

Option B - right angle

Step-by-step explanation:

We have Given statement : To trisect a(n) ____ angle, you first construct an equilateral triangle.

Solution: Option B is correct because,  a right angle is 90 degrees and an equilateral triangle has a 60 degree corner.

So, if you construct the equilateral you have one 60 and one 30, now bisect the 60.  

Answer:

[tex]i^{12}=1[/tex]

Last option is correct.

Step-by-step explanation:

We have to simplify the expression [tex]i^{12}[/tex]

We can rewrite this expression using the properties [tex](a^m)^n=a^{mn}[/tex]

[tex](i^4)^{3}[/tex]

Now, we know that [tex]i^4=1[/tex]

Hence, we have

[tex](1)^{3}[/tex]

On simplifying, we get

[tex]1[/tex]

Thus, the simplified form is 1.

Last option is correct.

Answer:

it's 1

Step-by-step explanation:

The value of x with a z-score of -0.74 is -0.22.

To find the value of x that has a z-score of -0.74, we can use the formula:

x = mean + (z-score * standard deviation)

Given that the mean (mean) is 2 and the standard deviation (standard deviation) is 3, we can substitute these values into the formula:

x = 2 + (-0.74 * 3)

Simplifying the equation, we get:

x = 2 - 2.22

x = -0.22

Therefore, the value of x that has a z-score of -0.74 is -0.22.

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The bank's likely response to Kevin's concern would be that checks are recorded on the date they are cashed, not on the date they are written, which explains the mismatch in dates Kevin observed. Balancing one's checkbook regularly is important for managing personal finances.

When Kevin has noticed that the dates on his check register do not match the dates on his account statement and contacts the bank, the bank's likely response will be "The date that the check is written is usually a few days before it is cashed. We record when it was cashed and you record when it's written." This is a common situation in personal finance and is related to the cash basis of accounting that most individuals use to manage their finances. The difference in dates arises because checks are processed and cleared by the bank on the date they are cashed, not on the date they are written. It's important for individuals to balance their checkbooks regularly to manage money, keep track of cash flow, and avoid overdraft fees.

x < -2 and y ≤ -x -2

To find the two numbers with the sum of 226 and a difference of 200, set up two equations, add them to find one number, and then substitute it into one of the equations to find the other. The two numbers are 213 and 13.

The sum of two numbers is 226, and their difference is 200. To find the two numbers, we can set up two equations based on the given information:

Add both equations to eliminate y:

Substitute x in one of the equations to find y:

The two numbers are 213 and 13.

Answer:

The greatest perfect square that is a factor of 980 is 196.

Step-by-step explanation:

To find : What is the greatest perfect square that is a factor of 980?

Solution :

First we factor the number 980.

[tex]980=2\times 2 \times 5\times 7\times 7[/tex]

[tex]980=2^2\times 7^2\times 5[/tex]

[tex]980=(2\times 7)^2\times 5[/tex]

[tex]980=(14)^2\times 5[/tex]

[tex]980=196\times 5[/tex]

This clearly means that 196 is the required factor.

Therefore, The greatest perfect square that is a factor of 980 is 196.

We have that The Greatest perfect square of 980 is

x= 196

From the question we are told that

The greatest perfect square that is a factor of 980

Generally

Greatest perfect square

Where a  perfect square is a number that is written to given the product of two identical Numbers

Therefore

Greatest perfect square of 980 is

x= 196

Where

The factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980

Therefore

The Greatest perfect square of 980 is

x= 196

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To evaluate the ratio of 390mm to 13cm, we convert 13cm to 130mm and then simplify the ratio of 390mm to 130mm to its lowest terms, which is 3 : 1.

To evaluate the ratio of 390mm to 13cm, we first need to express these measurements in the same unit. Converting centimeters to millimeters is simple: there are 10 millimeters in 1 centimeter.

Therefore, 13cm is equivalent to 130mm. Now, we can write the ratio as 390mm : 130mm. To simplify this ratio to its lowest terms, we divide both numbers by the greatest common divisor, which is 130 in this case. The simplified ratio is therefore 3 : 1.

The generalized description is as follows: quantity (in old units)  imes conversion factor = quantity (in new units). One must remember to simplify the ratio by dividing both the numerator and the denominator by their greatest common divisor, finalizing the answer without the '1' in the denominator when it's the only figure present.

Answer:

The station first give away all three prizes to 300th caller.

Step-by-step explanation:

A radio station gives away $15 to every 15th caller, $25 to every 25th caller, and free concert tickets to every 100th caller.

To get the answer we need to calculate L.C.M.  of 15, 25, 100.

15 = 3 x 5

25 = 5 x 5

100 = 2 x 2 x 5 x 5

LCM is = 2 x 2 x 3 x 5 x 5 = 300.

Hence, the station first give away all three prizes to 300th caller.

The value 0.02% written as a decimal is 0.0002

Given the value to be written as a decimal :

To express as a decimal , divide 0.02 by 100

Now we have ;

Therefore, the value 0.02% written as a decimal is 0.0002

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Let us say that:

K = age of Kristen

B = age of Ben

From the problem, we make the equations:

eqtn 1: K + B = 32

eqtn 2: (K – 4) = 2 (B – 4)

Simplifying eqtn 2:

K – 4 = 2 B – 8

K = 2 B – 4

Plugging in this to eqtn 2:

(2 B – 4) + B = 32

3 B – 4 = 32

3 B = 36

B = 12

From eqtn 2:

K = 2 B – 4 = 2 (12) – 4 = 20

So Kristen is 20 while Ben is 12.

Final answer:

By translating the given information into a system of equations and solving them step-by-step, we found that Kristen is 20 years old and Ben is 12 years old.

Explanation:

The question asks us to solve a system of equations based on the ages of Kristen and Ben. The total sum of their ages is 32, and four years ago, Kristen's age was twice that of Ben. Let's denote Kristen's age as K and Ben's age as B. The given information can be translated into two equations:

K + B = 32

K - 4 = 2(B - 4)

To solve these equations, first simplify the second equation:

K - 4 = 2B - 8

K = 2B - 4

Now substitute the value of K from the second equation into the first equation:

2B - 4 + B = 32

3B = 36

B = 12

Now that we know Ben's age (12), we can find Kristen's age by substituting the value of B into any of the initial equations. Using K + B = 32:

K + 12 = 32

K = 20

Therefore, Kristen is 20 years old and Ben is 12 years old.