The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1. Which graph represents g(x)?

Answer:

X ball bearings can be produced in 1 hour and 20 minutes

Step-by-step explanation:

Proportions

Proportions serve as an essential method for solving various common challenges. We understand that:

Company ABC manufactures X ball bearings in 3 hours.

Company DEF produces X ball bearings in 4 hours.

Company GHI generates X ball bearings in 6 hours.

In a single hour, each company is capable of producing:

ABC: X/3 ball bearings

DEF: X/4 ball bearings

GHI: X/6 ball bearings

By collaborating, they can produce

ball bearings. Operating together

If their output is 3/4 of a ball bearing in one hour, then it will take

hours to create one complete ball bearing. This translates to 1 hour and 20 minutes.

X ball bearings can be produced in 1 hour and 20 minutes

Answer: x ≥ 3.2 OR x ≤ -0.75

Here's how to solve the compound inequality step-by-step: start by separating it into two inequalities. For the first one, 5x - 4 ≥ 12, add 4 to both sides to remove the constant, leaving 5x ≥ 16. Then divide both sides by 5 to isolate x, resulting in x ≥ 3.2.

Now for the second part, 12x + 5 ≤ -4, subtract 5 from both sides to obtain 12x ≤ -9. Dividing both sides by 12 gives x ≤ -9/12, which simplifies to x ≤ -0.75. So, combining both, the solution is x ≥ 3.2 OR x ≤ -0.75.

Answer:

Therefore, the data is best represented by:

Step-by-step explanation:

We have a table indicating the estimated lines of code produced by computer programmers per hour when x individuals are engaged.

The question asks which model accurately reflects this data.

To determine this, we will substitute the values of x into each function to see which one accurately produces the corresponding y (f(x)) values provided in the table:

We are presented with four functions, which are:

A)

B)

C)

D)

We'll create a table displaying these values at various x levels.

x                  A                 B                C               D

2              66.66          49.3            52.5           50

4             94.57            71.44           106.3         104  

6             134.14           103.57         160.1          158

8             190.27          150.14          213.9         212

10           269.91           217.64         267.7         266

12           382.85          315.5           321.5          320.

Thus, the function that suitably represents the data is:

Option C.

y=26.9x-1.3

<span>The flag's dimensions are 40 inches by 55 inches.

Reasoning<span>:
The perimeter equals the sum of all sides. Being rectangular, opposite sides have equal lengths. Thus, the equation is
y + 11/8 y + y + 11/8 y = 190.

Simplifying, we get
2y + 22/8 y = 190.

Expressing 22/8 as a mixed fraction results in
2y + 2 3/4 y = 190.

Combining terms: 4 3/4 y = 190.

Divide both sides by 4 3/4:
y = 190 ÷ 4 3/4.

Converting 4 3/4 to an improper fraction: y = 190 ÷ 19/4.

Dividing by a fraction means multiplying by its reciprocal:
y = 190 × 4/19 = 760/19 = 40.

Since y = 40, calculate 11/8 y = 11/8 × 40 = 440/8 = 55.</span></span>

Answer: (97.98, 112.020)

Step-by-step explanation: We will create a 95% confidence interval for the average weight of melons.

Given the information, we determine that the critical value for the interval needs to be retrieved from a t distribution table due to the sample size being below 30 (specifically, 20), and we are provided with the sample standard deviation (s = 15 lb).

The parameters provided are:

Sample mean = x = 105 lb

Sample standard deviation = s = 15 lb

Sample size = n = 20

To establish the 95% confidence interval, we indicate that the level of significance is 5%.

The formula for the confidence interval is:

u = x + tα/2 × s/√n... for the upper limit

u = x - tα/2 × s/√n... for the lower limit.

tα/2 represents the critical value for the test (which will be determined using the t distribution table).

To derive tα/2, we look for the value based on the degrees of freedom (sample size - 1) against the significance level for a two-tailed test (α/2 = 0.025%) in a t distribution table.

For the upper limit, we calculate:

u = 105 + 2.093×15/√20

u = 105 + 2.093× (3.3541)

u = 105 + 7.020

u = 112.020.

<pfor the="" lower="" limit="" we="" find:="">

u = 105 - 2.093×15/√20

u = 105 - 2.093× (3.3541)

u = 105 - 7.020

u = 97.98

Confidence interval (97.98, 112.020)

</pfor>