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2 years ago

Find the formula for an exponential function that passes through the two points given.

Mathematics

1 answer:

goldenfox [79]2 years ago

3 0

Answer:

$y = 7(3^x)$

Step-by-step explanation:

Given

$(x_1,y_1) = (0,7)$

$(x_2,y_2) = (4,567)$

Required

Determine the formula

An exponential function is of the form:

$y = ab^x$

For point $(x_1,y_1) = (0,7)$

$7 = ab^0$

$7 = a*1$

$7 = a$

$a = 7$

For point $(x_2,y_2) = (4,567)$

$567 = ab^4$

Substitute 7 for a

$567 = 7*b^4$

Divide both sides by 7

$81 = b^4$

Take 4th root of both sides

$\sqrt[4]{81} =\sqrt[4]{b^4}$

$\sqrt[4]{81} =b$

$b = \sqrt[4]{81}$

$b = 3$

Substitute 7 for a and 3 for b in $y = ab^x$

$y = 7 * 3^x$

$y = 7(3^x)$

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PLEASE HELP What is the probability of an impossible event?

Likurg_2 [28]

Answer:

depending on the fraction you are using, or the answer is impossible.

Step-by-step explanation:

any fraction, so to speak 0/10 is an impossible probability, or 0%

8 0

2 years ago

A real estate agent has 19 properties that she shows. She feels that there is a 30% chance of selling any one property during a

netineya [11]

Answer:

$P(X \geq 5)=1-P(X$

We can find the individual probabilities:

$P(X=0)=(19C0)(0.3)^0 (1-0.3)^{19-0}=0.00114$

$P(X=1)=(19C1)(0.3)^1 (1-0.3)^{19-1}=0.0092$

$P(X=2)=(19C2)(0.3)^2 (1-0.3)^{19-2}=0.0358$

$P(X=3)=(19C3)(0.3)^3 (1-0.3)^{19-3}=0.0869$

$P(X=4)=(19C4)(0.3)^4 (1-0.3)^{19-4}=0.1491$

And replacing we got:

$P(X \geq 5) = 1-[0.00114+0.009282+0.0358+0.0869+0.149]= 0.7178$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=19, p=0.3)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And we want to find this probability:

$P(X \geq 5)$

And we can use the complement rule:

$P(X \geq 5)=1-P(X$

We can find the individual probabilities:

$P(X=0)=(19C0)(0.3)^0 (1-0.3)^{19-0}=0.00114$

$P(X=1)=(19C1)(0.3)^1 (1-0.3)^{19-1}=0.0092$

$P(X=2)=(19C2)(0.3)^2 (1-0.3)^{19-2}=0.0358$

$P(X=3)=(19C3)(0.3)^3 (1-0.3)^{19-3}=0.0869$

$P(X=4)=(19C4)(0.3)^4 (1-0.3)^{19-4}=0.1491$

And replacing we got:

$P(X \geq 5) = 1-[0.00114+0.009282+0.0358+0.0869+0.149]= 0.7178$

4 0

3 years ago

Find the value of the variable.

NemiM [27]

Answer:

x=y[base side of isosceles triangle]

x²+y²=19²

x=√{19²/2)}

x=13.44

y=13.44

7 0

2 years ago

If f(x) = 6x-11, what is f(-6)?

In-s [12.5K]

If f(x) = (6x-11), then f(-6) = -47.

We are provided in the question statement with a function "f(x)" whose output is a polynomial of 1 variable and degree 1.

To obtain the value of f(-6) from the output polynomial of the function f(x), we will simply need to substitute (-6) as the value of x in the polynomial and calculate the final value.

So,

$f(-6)=[(6*(-6))-11]\\or, f(-6)=(-36-11)\\or, f(-6)=-(36+11)\\or, f(-6) =-47$

Hence, f(-6) = -47.

Polynomial: In mathematics, an expression of more than two algebraic terms, especially the sum of several terms that contain the same variable(s) of different powers and individual, distinct co-efficients.
Function: In Mathematics, a function is an operator which on taking input, provides a certain output.

To learn more about Polynomials and Functions, click on the link below.

brainly.com/question/26910958

#SPJ9

5 0

1 year ago

businessText message users receive or send an average of 62.7 text messages per day. How many text messages does a text message

KiRa [710]

Answer:

(a) The probability that a text message user receives or sends three messages per hour is 0.2180.

(b) The probability that a text message user receives or sends more than three messages per hour is 0.2667.

Step-by-step explanation:

Let X = number of text messages receive or send in an hour.

The random variable X follows a Poisson distribution with parameter λ.

It is provided that users receive or send 62.7 text messages in 24 hours.

Then the average number of text messages received or sent in an hour is: $\lambda=\frac{62.7}{24}= 2.6125$ .

The probability of a random variable can be computed using the formula:

$P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!} ;\ x=0, 1, 2, 3, ...$

(a)

Compute the probability that a text message user receives or sends three messages per hour as follows:

$P(X=3)=\frac{e^{-2.6125}(2.6125)^{3}}{3!} =0.21798\approx0.2180$

Thus, the probability that a text message user receives or sends three messages per hour is 0.2180.

(b)

Compute the probability that a text message user receives or sends more than three messages per hour as follows:

P (X > 3) = 1 - P (X ≤ 3)

= 1 - P (X = 0) - P (X = 1) - P (X = 2) - P (X = 3)

$=1-\frac{e^{-2.6125}(2.6125)^{0}}{0!}-\frac{e^{-2.6125}(2.6125)^{1}}{1!}-\frac{e^{-2.6125}(2.6125)^{2}}{2!}-\frac{e^{-2.6125}(2.6125)^{3}}{3!}\\=1-0.0734-0.1916-0.2503-0.2180\\=0.2667$

Thus, the probability that a text message user receives or sends more than three messages per hour is 0.2667.

6 0

2 years ago