The sum of the first and third of three consecutive even integers is 136. find the three even integers.

The sum of the first 30 odd numbers is equal to the square of 30. To find the sum, we can use a formula for the sum of an arithmetic series. Plugging in the values, we get a sum of 900.

Conjecture: The sum of the first 30 odd numbers is equal to the square of the 30. To prove this conjecture, we can use a formula for the sum of an arithmetic series which is given by: S = n/2(2a + (n-1) d), where S is the sum of the series, n is the number of terms, a is the first term, and d is the common difference. In this case, the first term a is 1, the common difference d is 2 (since we are adding odd numbers), and the number of terms n is 30. Plugging in the values, we have: S = 30/2(2(1) + (30-1)2) = 15(2 + 58) = 900. Thus, the sum of the first 30 odd numbers is 900, which is equal to the square of 30.

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The correct option is A )[tex]\frac{8}{\pi }[/tex]

To find the rate of change of a function from x = 0 to x = \\frac{\\pi}{2}, we need to apply the concept of the average rate of change.

This is essentially the change in the function's value divided by the change in x. Assume the function we are analyzing is y = f(x).

Step-by-Step Solution:

Average Rate of Change =[tex]\frac{f(\frac{\pi}{2}) - f(0)}{\frac{\pi}{2} - 0}[/tex]

When x = 0, f( x ) = - 4,

When x = π / 2, f( x ) = 0

Average Rate of Change =[tex]\frac{0- (-4)}{\frac{\pi}{2} - 0}[/tex]

Average Rate of Change =[tex]\frac{8}{\pi }[/tex]

The correct option is A )[tex]\frac{8}{\pi }[/tex]

The real numbers are:

A. [tex]\((-131072)^{1/7}\)[/tex]

C. [tex]\((-1024)^{1/5}\)[/tex]

These have odd roots, resulting in real numbers.

To determine which of the given expressions are real numbers, we need to check if the roots of negative numbers are defined within the set of real numbers.

A. [tex]\((-131072)^{1/7}\)[/tex]

The expression [tex]\((-131072)^{1/7}\)[/tex] is the 7th root of [tex]\(-131072\)[/tex]. Since 7 is an odd number, the 7th root of a negative number is defined and is a real number.  

So, [tex]\((-131072)^{1/7}\)[/tex] is a real number.

B. [tex]\((-531441)^{1/12}\)[/tex]

The expression [tex]\((-531441)^{1/12}\)[/tex] is the 12th root of [tex]\(-531441\)[/tex]. Since 12 is an even number, the 12th root of a negative number is not defined within the set of real numbers.  

So, [tex]\((-531441)^{1/12}\)[/tex] is not a real number.

C. [tex]\((-1024)^{1/5}\)[/tex]

The expression [tex]\((-1024)^{1/5}\)[/tex] is the 5th root of [tex]\(-1024\)[/tex]. Since 5 is an odd number, the 5th root of a negative number is defined and is a real number.  

So, [tex]\((-1024)^{1/5}\)[/tex] is a real number.

D. [tex]\((-256)^{1/8}\)[/tex]

The expression [tex]\((-256)^{1/8}\)[/tex] is the 8th root of [tex]\(-256\)[/tex]. Since 8 is an even number, the 8th root of a negative number is not defined within the set of real numbers.  

So, [tex]\((-256)^{1/8}\)[/tex] is not a real number.

Summary:

- A. [tex]\((-131072)^{1/7}\)[/tex] is a real number.

- B. [tex]\((-531441)^{1/12}\)[/tex] is not a real number.

- C. [tex]\((-1024)^{1/5}\)[/tex] is a real number.

- D. [tex]\((-256)^{1/8}\)[/tex] is not a real number.

Answer:

0.23

Step-by-step explanation:

To solve this problem, we should first identify the number of units that point Z was translated. The number of units of movement of point Z should be similar to the number of units of movement of points A and P.

Let us say that the movement is Δx and Δy for horizontal and vertical translations respectively.

From Z to Z’:

Δx = 1 – (-1) = 2

Δy = 1 - 5 =  - 4

Therefore the translation is in the form of (x + 2 , y – 4). Points A and P then becomes:

A’ = (1 + 2 , 3 – 4)

A’ = (3, -1)

P’ = (-2 + 2, 4 – 4)

P’ = (0, 0)

Answers:

A’ = (3, -1)

P’ = (0, 0)

Answer:

Step-by-step explanation:

lets be honest whos reading this when theres an expert answer

Answer:

Option B is the correct answer.

Step-by-step explanation:

The arrangement is given in the below figure.

We have height of the mountain = x

We also have

       [tex]tan(21^044')=\frac{x}{13428.7}\\x=5352.98ft[/tex]

Height of the mountain to the nearest foot = 5353 ft

Option B is the correct answer.

When a researcher needs to compare means for a variable grouped into two categories based on some less-than interval variable, a t-test is appropriate.

To add, The analysis of two populations means through the use of statistical examination is called a t-test. Small sample sizes commonly use a t-test with two samples.  What statisticians call as test statistics are identified as t-values. A systematized value that is calculated from sample data during a hypothesis test is called a test statistic. The procedure that calculates the test statistic compares your data to what is expected under the null hypothesis.

You already have an experience with the basic principles behind a t-test if you’ve tried to communicated with a distracted teenager.

Honestly I believe this is correct:

∑ 15 at the top, n =0 (-9+6n)

Final answer:

To calculate the travel time to drive 160 miles at 70mph, use the formula Time = Distance ÷ Speed. The result is approximately 2.2857 hours, or about 2 hours and 17 minutes.

Explanation:

To calculate how long it takes to drive 160 miles at a constant speed of 70 miles per hour (mph), you can use the basic formula for time, which is Time = Distance ÷ Speed.

Distance to be traveled is 160 miles.

Speed of travel is 70 mph.

By plugging the numbers into the formula, we get:

Time = 160 miles ÷ 70 mph = 2.2857 hours.

To convert this time into minutes, we multiply by 60 (the number of minutes in an hour), so:

2.2857 hours × 60 minutes/hour = 137.1428 minutes, which is approximately 2 hours and 17 minutes.