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2 years ago

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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage r

ate of increase or decrease.
y=9300(0.991) ^6

1 answer:

saw5 [17]2 years ago

5 0

Using exponential function concepts, it is found that it represents a decay of 0.9%.

<h3>What is an exponential function?</h3>

A decaying exponential function is <em>modeled </em>by:

$A(t) = A(0)(1 - r)^t$

In which:

A(0) is the initial value.

r is the decay rate, as a decimal.

In this problem, the function is:

$A(t) = 9300(0.991)^{6t}$

Hence:

$1 - r = 0.991$

$r = 0.009$

Thus, it represents a decay of 0.9%.

You can learn more about exponential function concepts at brainly.com/question/25537936

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The amount of time all students in a very large undergraduate statistics course take to complete an examination is distributed c

Anestetic [448]

Answer:

a) The mean is $\mu = 60$

b) The standard deviation is $\sigma = 9$

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The probability a student selected at random takes at least 55.50 minutes to complete the examination equals 0.6915.

This means that when X = 55.5, Z has a pvalue of 1 - 0.6915 = 0.3085. This means that when $X = 55.5, Z = -0.5$

So

$Z = \frac{X - \mu}{\sigma}$

$-0.5 = \frac{55.5 - \mu}{\sigma}$

$-0.5\sigma = 55.5 - \mu$

$\mu = 55.5 + 0.5\sigma$

The probability a student selected at random takes no more than 71.52 minutes to complete the examination equals 0.8997.

This means that when X = 71.52, Z has a pvalue of 0.8997. This means that when $X = 71.52, Z = 1.28$

So

$Z = \frac{X - \mu}{\sigma}$

$1.28 = \frac{71.52 - \mu}{\sigma}$

$1.28\sigma = 71.52 - \mu$

$\mu = 71.52 - 1.28\sigma$

Since we also have that $\mu = 55.5 + 0.5\sigma$

$55.5 + 0.5\sigma = 71.52 - 1.28\sigma$

$1.78\sigma = 71.52 - 55.5$

$\sigma = \frac{(71.52 - 55.5)}{1.78}$

$\sigma = 9$

$\mu = 55.5 + 0.5\sigma = 55.5 + 0.5*9 = 55.5 + 4.5 = 60$

Question

The mean is $\mu = 60$

The standard deviation is $\sigma = 9$

6 0

2 years ago

What is the rate and unit rate of 36 strikeouts in 54 innings?

Ksivusya [100]

0.78 strikeouts per minute

8 0

2 years ago

Question is in the picture pls help.

Usimov [2.4K]

Answer:

c. is the answer

5 0

2 years ago

Read 2 more answers

Which of the following inequalities matches the graph?

Mamont248 [21]

Answer:

Step-by-step explanation:

y ≤ 5x - 1

- 5x + y ≤ - 1

5x - y ≥ 1

8 0

2 years ago

A ladder is leaning against a building so that the distance from the ground to the top of the latter is 1 foot less than the len

masha68 [24]

Answer:

$25\text{ feet}$

Step-by-step explanation:

The ladder, ground, and building form a right triangle where the vertical distance between the top of the ladder and the bottom of the ground is one leg, the horizontal distance between the bottom of the ladder and the building is another leg, and the length of the ladder is the hypotenuse.

For any right triangle, the Pythagorean Theorem states that the sum of the squares of both legs is equal to the hypotenuse squared ( $a^2+b^2=c^2$ ), where $c$ is the hypotenuse.

Let the length of the ladder be $\ell$ (hypotenuse of right triangle). The distance between the top of the ladder and the ground (vertical distance) can be represented as $\ell -1$ .

From the Pythagorean Theorem, we then have:

$7^2+(\ell-1)^2=\ell^2$

Expand using $(a-b)^2=a^2-2ab+b^2$ :

$49+\ell^2-2\ell+1=\ell^2$

Subtract $\ell$ from both sides and add $2\ell$ to both sides:

$49+1=2\ell$

Combine like terms:

$50=2\ell, \\2\ell =50$

Divide both sides by 2:

$\ell=\frac{50}{2}=\boxed{25\text{ feet}}$

Therefore, the length of the ladder is 25 feet.

4 0

3 years ago