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Verizon [17]
3 years ago
9

Find the exponential function passing through points (-1,4/3) and (3,108)

Mathematics
2 answers:
guajiro [1.7K]3 years ago
8 0

Answer:

its 152 i know cause i just did this....

Step-by-step explanation:

Gwar [14]3 years ago
8 0

<u>Answer:</u>

An exponential function is in the general form   \mathrm{y}=\mathrm{a}(\mathrm{b})^{\mathrm{x}}

<u>Explanation:</u>

(x,y) = (-1,4/3) and (x,y)=  (3,108) are the given functions  

Therefore,  

    \frac{4}{3}=a(b)^{-1}=\frac{a}{b}

        \frac{4}{3}=\frac{a}{b}  - eq(1)

           108=a(b)^{3}=a b^{3}=108-e q(2)

Multiply both sides of the first equation by b to find that

       \frac{4}{3} b=a

Substituting in eq-2 we get

      \frac{4}{3} b^{4}=108

    b^{4}=81

  \mathrm{b}=\pm 3

  \mathrm{b}=+3, \text { then } 108=\mathrm{a}(3)^{3}

which gives a = 4,  

henceforth the equation becomes as   \mathrm{y}=4(3)^{\mathrm{x}}

    \mathrm{b}=-3 \text { then } 108=\mathrm{a}(-3)^{3}

which gives a = -4,  

henceforth the equation becomes as y =  -4(-3)^{x}

However! In an exponential function, b>0, otherwise many issues arise when trying to graph the function.

The only valid function is  4(3)^{x}      

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(a) How many integers from 1 through 1,000 are multiples of 2 or multiples of 9?
DENIUS [597]

Answer:

(a)There are 500 integers from 1 through 1,000 are multiples of 2.

There are 111 integers from 1 through 1,000 are multiples of 9.

(b)0.611

Step-by-step explanation:

Given the set of Integers from 1 through 1000

The least multiple of 2 is 2 and the highest multiple of 2 in the interval is 1000.

To determine the number of terms, we use the formula for the nth term of an Arithmetic Progression, since 2,4,6,... is an Arithmetic Progression,

where first term, a =2, common difference, d =2

Nth term of an A.P,

U_n= a+(n-1)d\\1000=2+2(n-1)\\1000=2+2n-2\\1000=2n\\n=500

  • There are 500 integers from 1 through 1,000 are multiples of 2.

Similarly,

Given the set of Integers from 1 through 1000

The least multiple of 9 is 9 and the highest multiple of 9 in the interval is 999.

To determine the number of terms, we use the formula for the nth term of an Arithmetic Progression, since 9,18,27,... is an Arithmetic Progression,

where first term, a =9, common difference, d =9

Nth term of an A.P,

U_n= a+(n-1)d\\999=9+9(n-1)\\999=9+9n-9\\999=9n\\n=111

  • There are 111 integers from 1 through 1,000 are multiples of 9.

(b)Probability that an integer selected at random is a multiple of 2 or a multiple of 9.

There are a total of 1000 numbers between from 1 through 1,000

n(S)=1000

n(Multiples of 2)=500

n(Multiples of 9)=111

Therefore:

P(\text{Multiples of 9}) \:OR\: P(\text{Multiples of 2})=\frac{111}{1000} + \frac{500}{1000} \\=\frac{611}{1000} \\=0.611

7 0
3 years ago
Jimmy has listed the amount of money in his wallet for each of the last ten days. He decides to remove day 7, as that was payday
abruzzese [7]

Answer:

The mean will reduce

Step-by-step explanation:

The total amount of money for the ten days divided by number of days will give mean 1, M₁

Removing the value for day seven will reduce the sum of money as it will be for 9 days only.In finding the mean, you will divide by 9 days to get mean M₂

Mean M₂ < M₁

8 0
2 years ago
Find the prime factorization of 35
AnnyKZ [126]
<h3>Question:</h3><h3>•Find the prime factorization of 35.</h3>

Answer:

•The Prime Factors of 35 are 1, 5, 7, 35 and its Factors in Pairs are (1, 35) and (5, 7).

<h3>Explanation:</h3>

#Let's Study

#I Hope It's Help

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4 0
2 years ago
Read 2 more answers
Triangle ABC has vertices A(–2, –3), B(–5, –3), and C(–4, –2). The triangle is rotated 90° counterclockwise around the origin.
Ulleksa [173]
The rule for this rotation is (x, y) converted into (-y, x). So, to find the answer you would make the y negative and switch the values in the ordered pair. A would be (3, -2), B would be (3, -5), and C would be (2, -4). So, your answer would be B. Hope this helps!
4 0
2 years ago
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Identify the location of the point (-3, -2).<br><br> A. P<br> B. Q<br> C. R<br> D. S
docker41 [41]

Answer:

You haven't given a picture of the graph dear.

The point (-3,-2) lies in the third quadrant.

8 0
2 years ago
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