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S_A_V [24]
2 years ago
14

PLEASE HELP DUE TODAY ILL GIVE BRAINLIEST 1. An advertising company charges $40 per half-page advertisement and $75 per full-pag

e advertisement. Michael has a budget of $800 to purchase 13 advertisements. (a) Define a variable for each unknown. Write a system of equations to represent the situation. (b) How many half-page advertisements does Michael purchase? Show your work. (c) How many full-page advertisements does Michael purchase? Show your work.
Mathematics
1 answer:
Oksana_A [137]2 years ago
8 0

Answer: inverse of given function = log(x)/log(3)

Step-by-step explanation: how to find the inverse of any function?

in the complete function, replace y with "x" and x with "y"then, solve the obtained equation from step 2 for yand, then the value obtained for "y" is the inverse required i.e. = f^{-1}(x)

now, we solve the problem:

given : - y = 3^x

replacing the value of "y" with "x", we get,

x = 3^y

to solve for "y" we should take the "logarithm" for both sides

log (x) = y log(3)

or y = log(x)/log(3)

or f^(-1) (x) = log(x)/log(3)

( I hope this helped <3 )

You might be interested in
Assuming that the Chinese population continues to grow at the same rate, how many years until the population reaches 1.5 billion
faltersainse [42]

Answer:

29 years

Step-by-step explanation:

The population of the Chinese people is 1.3 bn, and they grow at a rate of 0.49% per year. To get the number of years it requires to reach 1.5 bn, we use this method

after x years, the population will be

1.3 * 1.0049^x

so you just need to solve

1.3 * 1.0049^x = 1.5

1.0049^x = 1.5/1.3

x log 1.0049 = log(1.5/1.3)

x = log(1.5/1.3)/log(1.0049)

x = 0.062 / 0.002122

x = 29.25 years

Therefore, at the rate of 0.49%, the Chinese population of 1.3bn needs 29 years to clock 1.5 bn

8 0
2 years ago
A prescription calls for the following: Sodium citrate 5 g Tartar Emetic 0.015 g Cherry syrup ad 120 mL Using a balance with a s
ella [17]

Answer:

measure the volume of cherry syrup solution with Tartar Emetic = 22.5 mL

Hence, the correct quantity of tartar emetic to fill the prescription will be obtained

Step-by-step explanation:

Given:

Mass of Sodium citrate = 5 g

Mass of Tartar Emetic = 0.015 g = 15 mg

Volume of Cherry syrup ad 120 mL = 120 mL

sensitivity = 4 mg

Error = 5%

Now,

The smallest weight that can be measured = \frac{\textup{Sensitivity}}{\textup{Error}}\times100

or

The smallest weight that can be measured =  \frac{\textup{4}}{\textup{5}}\times100  = 80 mg

Now,

80 mg is dissolved in 120 mL of Cherry syrup according to prescription

( Thus,

1 mg is dissolved in \frac{120}{80}\ mL  of Cherry syrup according to prescription )

so to measure 15 mg of Tartar Emetic, measure the volume of cherry syrup

=   15\times\frac{120}{80}\ mL

= 22.5 mL

Hence, the correct quantity of tartar emetic to fill the prescription will be obtained

8 0
2 years ago
Tina and Nonly wanted to s whose car gets better gas mileage, so they each drove 210 miles and recorded how much gas they used.
Aliun [14]
Since we know that they drove 210 and the amount of gas they used, put the miles over the amount of gas each person used

4 0
2 years ago
Read 2 more answers
The length of time a full length movie runs from opening to credits is normally distributed with a mean of 1.9 hours and standar
Llana [10]

Answer:

a) The probability that a random movie is between 1.8 and 2.0 hours = 0.2586.

b) The probability that a random movie is longer than 2.3 hours is 0.0918.

c) The length of movie that is shorter than 94% of the movies is 1.4 hours

Step-by-step explanation:

In the above question, we would solve it using z score formula

z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation

a) A random movie is between 1.8 and 2.0 hours

z = (x-μ)/σ,

x1 = 1.8,

x2 = 2.0

μ is the population mean = 1.9

σ is the population standard deviation = 0.3

z1 = (1.8 - 1.9)/0.3

z1 = -1/0.3

z1 = -0.33333

Using the z score table

P(z1 = -0.33) = 0.3707

z2 = (2.0 - 1.9)/0.3

z1 = 1/0.3

z1 = 0.33333

p(z2 = 0.33) = 0.6293

= P(- 0.33 ≤ z ≤ 0.33)

= 0.6293 - 0.3707

= 0.2586

The probability that a random movie is between 1.8 and 2.0 hours = 0.2586

b) A movie is longer than 2.3 hours

z = (x-μ)/σ,

x1 = 2.3

μ is the population mean = 1.9

σ is the population standard deviation = 0.3

z = (2.3 - 1.9)/0.3

z = 4/0.3

z = 1.33333

P(z = 1.33) = 0.90824

P(x>2.3) = = 1 - 0.90824

= 0.091759

≈ 0.0918

The probability that a random movie is longer than 2.3 hours is 0.0918.

3) The length of movie that is shorter than 94% of the movies.

z = (x-μ)/σ

Probability (z ) = 94% = 0.94

Movie that is shorter than 0.94

= P(1 - 0.94) = P(0.06)

Finding the P (x< 0.06) = -1.555

≈ -1.56

μ is the population mean = 1.9

σ is the population standard deviation = 0.3

-1.56 = (x - 1.9)/ 0.3

Cross multiply

-1.56 × 0.3 = x - 1.9

- 0.468 + 1.9 = x

= 1.432 hours

≈ 1.4 hours

Therefore, the length of movie that is shorter than 94% of the movies is 1.4 hours

5 0
2 years ago
this squared based pyramid is cut horizontally at a height of 15cm to leave this frustum base area=10cm
scoundrel [369]

Answer:

583.33 cm³

Step-by-step explanation:

From the image attached, the total height (H) of the pyramid is 30 cm, the height of the frustrum (h) = 15 cm, the Frustrum base = lower base = B = 10 cm . To find the length of the upper base (b), we use:

\frac{b}{H-h}=\frac{B}{H}\\  b=(H-h)\frac{B}{H}\\b=(30-15)\frac{10}{30}=5\\b=5\ cm

The volume of the frustrum is given by:

V=\frac{1}{3}h(B_1+B_2+\sqrt{B_1B_2} )\\ Where\ B_1\ is \ the\ area \ of\ the\ upper\ base= 5cm*5cm=25cm^2\\B_1\ is \ the\ area \ of\ the\ lower\ base= 10cm*10cm=100cm^2\\V=\frac{1}{3}(10)(25+100+\sqrt{25*100} )=583.33\\V=583.33\ cm^3

6 0
2 years ago
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