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777dan777 [17]
3 years ago
12

Question 2 An exponential model y = a.6 passes through the points (0,9) and (3,243). What are the values of a and b?​

Mathematics
1 answer:
weqwewe [10]3 years ago
8 0

Answer:

a = 9, b = 3

Step-by-step explanation:

The exponential function is

y = a b^{x}

Find a and b by using the points it passes through

Using (0, 9 ) then

9 = a b^{0} ( b^{0} = 1 )

a = 9

y = 9 b^{x}

Using (3, 243 ) then

243 = 9b³ ( divide both sides by 9 )

27 = b³ ( take the cube root of both sides )

b = \sqrt[3]{27} = 3

y = 9(3)^{x} ← exponential equation

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1. A researcher collected data from car shoppers about their favorite car color. He asked 250 people about their favorite vehicl
hichkok12 [17]

Answer:

(a) 2% (b) 15

Step-by-step explanation:

(a):

80 - blue (32%)

60 - white (24%)

50 - red (20%)

45 - black (18%)

10 - silver (4%)

Total: 245

5 - other (2%)

(b):

60 - white

45 - black

Difference: 15

4 0
3 years ago
In ΔPQR, point C is the centroid. If PZ = 7, then RZ =<br> A) 3.5 <br> B) 7 <br> C) 14 <br> D) 21
kvv77 [185]

Answer: It's 7

Step-by-step explanation:

4 0
3 years ago
Help me with math questions urgent Thanks
aleksandrvk [35]

Answer:  x = 2.65, y = 3.81

Step-by-step explanation:

          ABC similar to PQR

1) Find the ratio of corresponding sides

2) Use that ratio to find values for x & y

        1) Side AB = 2.76cm & Side PR = <em>y</em><em> </em>cm

             Side BC = <em>x</em> cm & Side RQ = 3.66 cm

         Side CA = 3 cm & Side QP = 4.14 cm (both lengths given)    

Can match 3 to 4.14 & ratio of sides in ABC to PQR= 3 /4.14

Length of sides ABC = 3/4.14 times the length of sides PQR

           2)  x = (3 / 4.14) * 3.66 = 2.65

            Now solve for y, ABC to PQR:  2.76 = (3 / 4.14) (<em>y </em>)

<em>equality property</em> (both sides) & inverse operation to isolate <em>y : </em> .               2.76 ÷ (3 / 4.14) = (3 / 4.14 ) ÷ (3 / 4.14) (<em>y</em><em>)</em>

              2.76 * (4.14 / 3) =  3 / 4.14 * (4.14 / 3) (<em>y</em><em>)</em>

                     (2.76 * 1.38 ) =  3.81  = <em>y</em>

<em></em>

<em>Scale Factor Method:  Determine the Multiplier</em>

Small to Big or Big to Small ➜ Be sure not to switch

7 0
3 years ago
Kabul’s bookshop marks up all books by 40 percent of their cost. The overhead rate is 16 percent of the selling price. What is t
morpeh [17]

Answer:

The net profit rate on the book is 5.41

Step-by-step explanation:

Given as :

The marks up percentage of book = m = 40%

The overhead rate is 16% of selling price

The cost price of book = c.p = $18.10

Let The profit = $p

Let The selling price = s.p

<u>Now, According to question</u>

mark up percentage = \dfrac{s.p - c.p}{c.p}

I.e 40% =  \dfrac{s.p - 18.10}{18.10}

Or, \dfrac{40}{100} + 1 = \dfrac{s.p}{18.10}

Or, \dfrac{140}{100} =  \dfrac{s.p}{18.10}

Or, s. p = \dfrac{140\times 18.10}{100}

∴ s.p = $25.34

So, selling price of book = s.p = $25.34

Now, The overhead percentage = 16%

i.e overhead rate = \dfrac{\textrm estimated cost}{\textrm estimated total base unit}

Or, estimated cost = 16% × 25.34

I,e estimated cost = 0.16 × 25.34

∴ estimated cost = $4.05

Now,

Profit = selling price of book - estimated book cost

I.e p = $25.34 - $4.05

∴ p = $21.29

So, The profit rate% = \dfrac{\textrm profit}{\textrm estimated cost}

I.e The profit rate% = \dfrac{21.29}{4.05}

∴ profit rate %= 5.41

So, The profit rate = p = 5.41

Hence, The net profit rate on the book is 5.41  Answer

4 0
3 years ago
T=35+7p how many pokemon cards does Jackie have in all if the second book has 14 pages?
Serhud [2]
The answer should be T = 133.
5 0
3 years ago
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