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STatiana [176]
3 years ago
8

The function A(t) = 1950 (0.65)t models the amount A(t) , in dollars, that Ted's company deducts from his check for health insur

ance based on time t, in months that Ted has worked for the company. Determine the rate used in this formula and identify as growth or decay.
Mathematics
1 answer:
Paraphin [41]3 years ago
4 0

Answer:

This is an Exponential decay

The Exponential decay rate = 35%

Step-by-step explanation:

Looking at that the above question, it is an Exponential decay

The formula for Exponential decay is:

A(t) = Ao (1 - r)^t

In the above question:.

A(t) = 1950 (0.65)^t

r = rate

Hence:

(1 - r) = (0.65)

1 - r = 0.65

r = 1 - 0.65

r = 0.35

Converting to percentage

0.35 × 100

= 35%

Hence, the Exponential decay rate is 35%

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Student Council is selling candy grams. They are using the formula
Luden [163]

Answer:

Our equation is:

y = f(x) = 2.5*x

The domain is the set of the values of x.

The range is the set of the values of y.

They must sell between 55 and 60 candy grams to meet their goal.

If we assume these as restrictions for the domain, then the minimum value of x is 55, and the maximum value of x is 60.

Then the domain is:

D: 55 ≤ x ≤ 60.

Now that we know the domain, we can find the range.

As our equation is linear with a positive coefficient, the minimum in the range will coincide with the minimum in the domain, then we have:

y = 2.5*55 = 137.5

And the maximum will coincide with the maximum in the domain:

y = 2.5*60 = 150.

Then the range is:

y = 137.5 ≤ y ≤ 150

7 0
3 years ago
(1 point) A particle starts at the point P=(−2,−1,3)P=(−2,−1,3) when t=0t=0 and moves along a straight line toward Q=(−4,0,6)Q=(
Ahat [919]

Answer:

The position is given by r(t) =  (-2 -t √14, 1 + √3.5, 3 + 3√3.5)

Step-by-step explanation:

The direction is given by the difference between the starting point and the end point, thus it is (-4,0,6)-(-2,-1,3) = (-2,1,3). The norm of this vector is        √( (-2)²+1²+3²) = √14 = 3.7416 secons

Since the speed is 7 cm/sec, we need to multiply this vector by 7/√14 = √3.5 in order to obtain how much does the particle advance each second.

As a consecuence, it advances (-2,1,3) * √3.5 = (- √14, √3.5, 3 √3.5)

And, as a result, the position after t seconds is given by the function

r(t) = (-2,1,3) + t (-√14, √3.5, 3 √3.5) = (-2 -t √14, 1 + √3.5, 3 + 3√3.5)

8 0
4 years ago
What is the value of 2c + d² - 3e + 4f when c = 3, d = 5, e = 6, and f = 1?
Andrej [43]

Answer:

17

Step-by-step explanation:

2c + d^3 - 3e +4f

=2(3) + (5^2) - 3(6) + 4(1)

=6+25-18+4

=17

5 0
3 years ago
There are 92 students in a chemistry class. The instructor must choose two students at random. Students in a Chemistry Class Aca
Sergio039 [100]

Answer:

0.0108 = 1.08% probability that a sophomore non-Chemistry major and then a junior non-Chemistry major are chosen at random.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Probability that a sophomore non-Chemistry major

Out of 92 students, 9 are non-chemistry major sophomores. So

P(A) = \frac{9}{92}

Then a junior non-Chemistry major are chosen at random.

Now, there are 91 students(1 has been chosen), of which 10 are non-chemistry major juniors. So

P(B) = \frac{10}{91}

What is the probability that a sophomore non-Chemistry major and then a junior non-Chemistry major are chosen at random

P = P(A)*P(B) = \frac{9}{92}*\frac{10}{91} = \frac{9*10}{92*91} = 0.0108

0.0108 = 1.08% probability that a sophomore non-Chemistry major and then a junior non-Chemistry major are chosen at random.

8 0
3 years ago
A researcher selects all of the possible samples with n = 8 scores from a population and computes the mean, dividing by n, for e
Nadusha1986 [10]

Answer:

By the Central Limit Theorem, the average value for all of the sample means is 14.

Step-by-step explanation:

We use the central limit theorem to solve this question.

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, the sample means of size n can be approximated to a normal distribution with mean \mu and standard deviation, which is also called standard error s = \frac{\sigma}{\sqrt{n}}

If the population mean is μ = 14, then what is the average value for all of the sample means?

By the Central Limit Theorem, the average value for all of the sample means is 14.

3 0
4 years ago
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