Which function has a simplified base of 4RootIndex 3 StartRoot 4 EndRoot? f(x) = 2(RootIndex 3 StartRoot 16 EndRoot) Superscript

Greetings from MrBillDoesMath! The answer is: 669/221 Discussion: The ratio of 669 to 221 equals 669/221. Observing the factors, 669 is 3 * 223 and 221 is 13 * 17. As all these factors are distinct primes, nothing cancels in their ratio. Thus, 669/221 remains in its simplest form.

Answer:

Step-by-step explanation:

Denote the rectangular prism's volume as VR and the volume of the right triangular prism as VT. Given that the rectangular prism's volume exceeds that of the triangular prism by 32 cubic feet, we establish that VR = 32 + VT.

Calculating VR: VR = length * width * height = 6*x*3.

This simplifies to VR = 18x ft³.

For the triangular prism, VT can be calculated as Length * width * Height / 2, yielding VT = (7 * x * 4) / 2.

Thus, VT = 28x / 2, which simplifies to VT = 14x ft³.

Equating VR to 32 + VT allows the substitution: 18x = 32 + (14x).

Now, simplify the equation:

Combine like terms: 18x - 14x = 32.

This results in 4x = 32.

Dividing both sides by 4:

x = 8.

The volume for the rectangular prism comes to 18x, which equals 18*8.

The volume of the rectangular prism calculates to 144 ft³.

The volume for the right triangular prism calculates to 14x, which equals 14*8.

The volume of the right triangular prism calculates to 112 ft³.

The domain is defined as the complete set of values of variable x for which the function is valid. In this case, the x-axis illustrates time in seconds. Therefore, we must determine all possible time values over which distance can be covered or the function is defined. It’s noted that the sprinter completed the race in 11 seconds, and the start time is 0 seconds. Hence, the value of t ranges from 0 to 11. Therefore, the domain encompasses all real numbers from 0 to 11.

Subtract 3 from the sum and then divide by 2. One number is 5 and the other is 8.

Answer:

Explanation:

Hello!

You possess a sample involving 200 participants, who were surveyed regarding their main source of news, categorized into (1) Television, (2) Radio, (3) Internet, and (4) Other.

Your goal is to evaluate whether the proportions in this sample align with the established frequencies of 10%, 30%, 50%, and 10% respectively.

The suitable statistical method to assess if the sample matches the known or historical distribution is the Chi-Square goodness of fit test. In this test, the null hypothesis represents the model or distribution under examination. In this scenario, you need to articulate the proportions for each category:

H₀: P(1)= 0.10; P(2)= 0.30; P(3)= 0.50; P(4)= 0.10

Wishing you a SUPER day!