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3 months ago

Which function increases at a faster rate on 0 to infinity, f(x) = x2 or g(x) = 2x? Explain your reasoning.

2 answers:

9 0

Based on a table of values, the outputs of f(x) for whole numbers are 0, 1, 4, 9, 16, 25, 36, and further. Meanwhile, for the same inputs, g(x) generates outputs of 1, 2, 4, 8, 16, 32, and 64. It is evident that g(x) consistently doubles its outputs, leading to numbers that surpass those produced by f(x). The exponential function, g(x), experiences a constant multiplicative change rate, allowing it to accelerate more quickly compared to the quadratic function.

(ed. just click all of them)

Svet_ta [12.7K]3 months ago

6 0

Answer:

Sample response: By analyzing a table of values, the outputs of f(x) for integer inputs are 0, 1, 4, 9, 16, 25, 36, etc. In comparison, g(x) produces the outputs 1, 2, 4, 8, 16, 32, and 64 for the same inputs. As the outputs of g(x) are consistently doubled, they surpass those of f(x). The exponential function, g(x), maintains a fixed multiplicative rate of change that causes it to grow more quickly than the quadratic function.

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Each leg of a 45°-45°-90° triangle measures 12 cm. Triangle X Y Z is shown. Angle X Y Z is a right angle and angles Y Z X and Z

babunello [11817]

Using the Pythagorean theorem: In a right triangle where legs are labeled a and b, and hypotenuse is c. Given the triangle ΔXYZ has a right angle at Y, with angles YZX and ZXY both measuring 45 degrees, and ZY = YX = 12 cm. The task is to find the length of XZ.

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2 months ago

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A jet climbs at a steady rate at an angle of inclination of 0.5 degree during game off what will its he height be after a 2.2 km

zzz [12365]

A right triangle will have 2.2 km as its hypotenuse, with an angle of 0.5 degrees and an unknown height (see attachment).

Remember to apply the trigonometric ratios: sine, cosine, and tangent for right triangles.
Sinθ = opposite side/hypotenuse
Cosθ = adjacent side/hypotenuse
tanθ = opposite side / adjacent side
In this scenario, θ signifies the angle (not the right angle), which is given as 0.5°.

For this problem, we use sine as we have the side opposite the angle (the unknown height h) and the hypotenuse, with sine relating these two sides.

Let h represent the unknown opposite side, the height.
sin(0.5°) = h / (2.2km)
h = (2.2km)sin(0.5°)
h = 0.019 km

I hope this has clarified your question! If you need clarification on any steps, please ask below.

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2 months ago

The computers of six faculty members in a certain department are to be replaced. Two of the faculty members have selected laptop

lawyer [12517]

Answer:

a. $\frac{1}{15}$

b. $\frac{2}{5}$

c. $\frac{14}{15}$

d. $\frac{8}{15}$

Step-by-step explanation:

There are four desktop computers and two laptops.

On a specific day, we will set up 2 of these computers.

To find:

a. What is the probability that both selected computers are laptops?

b. What is the probability that both computers are desktops?

c. What is the probability that at least one computer is a desktop?

d. What is the probability that at least one of each type of computer is included?

Solution:

Using the probability formula for event E:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

a. The number of successful outcomes for both computers being laptops = $_2C_2$ = 1

Total possible outcomes = 15

The needed probability is $\frac{1}{15}$ .

b. The successful outcomes for both being desktop computers = $_4C_2=6$

Total possible outcomes = 15

The required probability is $\frac{6}{15} = \frac{2}{5}$ .

c. For at least one desktop:

Two scenarios exist:

1. 1 desktop and 1 laptop:

Successful outcomes = $_2C_1\times _4C_1 = 8$

2. Both are desktops:

Successful outcomes = $_4C_2=6$

Total successful outcomes = 8 + 6 = 14

The needed probability is $\frac{14}{15}$ .

d. 1 desktop and 1 laptop:

Successful outcomes = $_2C_1\times _4C_1 = 8$

Total outcomes = 15

The required probability is $\frac{8}{15}$ .

8 0

3 months ago

A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on data collected from its automatic filling p

lawyer [12517]

Answer:

At a confidence level of 90%, the margin of error is calculated to be 0.5133 grams.

Step-by-step explanation:

The formula for margin of error (E) is: (critical value × sample standard deviation) ÷ sqrt(n)

The sample standard deviation is 1.5 grams.

A 90% confidence level translates to 0.9.

Significance level is determined as 1 - C, which equals 1 - 0.9 resulting in 0.1 or 10%.

The sample size (n) is 25.

Degrees of freedom are calculated as n - 1, which is 25 - 1 equaling 24.

The critical value (t) for 24 degrees of freedom at a significance level of 10% is found to be 1.711.

Using these values, we calculate: E = (1.711 × 1.5) ÷ sqrt(25) = 2.5665 ÷ 5 = 0.5133 grams.

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2 months ago

• Jamie is constructing shipping containers for a sporting goods store. The containers are to be rectangular prisms.

lawyer [12517]

Jamie is currently constructing shipping containers for a store selling sports equipment. These containers are designed as rectangular prisms.

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2 months ago