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alexandr402 [8]
2 years ago
6

Write an exponential function in the form y=ab^x that goes through points (0,9) and (3, 576)

Mathematics
1 answer:
sineoko [7]2 years ago
6 0

Answer:

An exponential function in the form y=9(4ˣ)

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given that exponential function

                  y = a bˣ ...(i)

The equation (i) passes through the point (0,9)

               9 = a (b )⁰ = a

             a =9

<u><em>Step(ii):-</em></u>

The equation (i) passes through the point (3,576)

            576 = 9(b)³

         ⇒    \frac{576}{9} = b^{3}

      ⇒     64 = b³

     ⇒     4³ = b³

             (4^{3} )^{\frac{1}{3} } = (b^{3} )^{\frac{1}{3} }

             b = 4

<u><em>Final answer:-</em></u>

An exponential function in the form y=abˣ

An exponential function in the form y=9(4ˣ)

<u><em></em></u>

<u><em>   </em></u>

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John has two jobs. For daytime work at a jewelry store he is paid
djyliett [7]

Given Information:

John's mean monthly commission = μ = $10,000

Standard deviation of monthly commission = σ =  $2,000

Answer:

P(9,000 < X < 11,000) = 0.383\\\\P(9,000 < X < 11,000) = 38.3 \%

The probability that John's commission from the jewelry store is  between $9,000 and $11,000 is 38.3%

Step-by-step explanation:

What is Normal Distribution?

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.  

We want to find out the probability that John's commission from the jewelry store is  between $9,000 and $11,000?

P(9,000 < X < 11,000) = P( \frac{x - \mu}{\sigma} < Z < \frac{x - \mu}{\sigma} )\\\\P(9,000 < X < 11,000) = P( \frac{9,000 - 10,000}{2,000} < Z < \frac{11,000 - 10,000}{2,000} )\\\\P(9,000 < X < 11,000) = P( \frac{-1,000}{2,000} < Z < \frac{1,000}{2,000} )\\\\P(9,000 < X < 11,000) = P( -0.5 < Z < 0.5 )\\\\P(9,000 < X < 11,000) = P( Z < 0.5 ) - P( Z < -0.5 ) \\\\

The z-score corresponding to 0.50 is 0.6915

The z-score corresponding to -0.50 is 0.3085

P(9,000 < X < 11,000) = 0.6915 - 0.3085 \\\\P(9,000 < X < 11,000) = 0.383\\\\P(9,000 < X < 11,000) = 38.3 \%

Therefore, the probability that John's commission from the jewelry store is  between $9,000 and $11,000 is 38.3%

How to use z-table?

Step 1:

In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.4, 2.2, 0.5 etc.)

Step 2:

Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.50 then go for 0.00 column)

Step 3:

Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.

4 0
3 years ago
Round 23.5584557678 to the nearest hundredth.
lubasha [3.4K]
The hundredth is the second number to the right of the decimal point. Also, if the number directly to the right of it is 5 or larger, you will have to round up by one.

23.558 becomes 23.56.
4 0
2 years ago
Find the height of a square pyramid that has a volume of 75 cubic feet and a base length of 5 feet.
kodGreya [7K]

Volume of the pyramid = (1/3) x Area of the base x Height ---------- (1)

As the base length = 5 feet

So Area of the base = 5 x 5 = 25 square feet

While volume of the pyramid = 75 cubic feet

Putting values in equation (1);

75 = (1/3) x 25 x Height

Height = (75 x 3) / 25

Height = 9feet

<span>So 2nd option is correct.</span>

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3 years ago
The exponential function f(x) = 2(4)x increases more quickly than the linear function f(x) = 3x + 4.
Aleksandr [31]
Is this a true/false or do you need an actual mathematical answer?
i will edit my this to answer your question.
I'm just not exactly sure what you are asking :-/
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3 years ago
Fernando has 16 1/4 feet of yarn to make scarves , if he wants to make 5 scarves that are the same length , how long should each
Tresset [83]
The scarves should each be 3 1/4 feet long
hope it helps
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