Chemists use pH as a measure of acidity or alkalinity of a solution. It uses the concentration of hydrogen ions H+ in a logarithmic function. A chemist is studying the alkalinity of a hot spring near a volcano. The hydrogen ion concentration is increasing according to the function f(d) = (0.5 × 10–4)d, where d is the number of days. The function for pH is g(H+) = –log10(H+), where H+ is the hydrogen ion concentration of the solution. Which function shows the pH of the hot spring as a function of d? g(f(d)) = –log10(d) g(f(d)) = –d(log10(0.5 × 10–4)) g(f(d)) = –log10((0.5 × 10–4)d) g(f(d)) = –log10(d × 10–4)

Answers

Answer 1

Answer:

[tex]g(f(d)) = -dlog_{10}(0.5 * 10^{-4})[/tex]

Step-by-step explanation:

Given

[tex]f(d) = (0.5 * 10^{-4})^d[/tex]

[tex]g(H+) = -log_{10}(H+)[/tex]

Required

Find the composite function g(f(d))

We have:

[tex]g(H+) = -log_{10}(H+)[/tex]

Substitute f(d) for H+

[tex]g(f(d)) = -log_{10}(f(d))[/tex]

Substitute [tex]f(d) = (0.5 * 10^{-4})^d[/tex]

[tex]g(f(d)) = -log_{10}((0.5 * 10^{-4})^d)[/tex]

Apply law of logarithm

[tex]g(f(d)) = -dlog_{10}(0.5 * 10^{-4})[/tex]

Hence, the function is:

[tex]g(f(d)) = -dlog_{10}(0.5 * 10^{-4})[/tex]

Answer 2

Answer:

It's C

Step-by-step explanation:


Related Questions

which represents the solution to the inequality -3x +5 > 14?

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Answer:

x < -3

Step-by-step explanation:

Find the value of x in the image above

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Answer:

Step-by-step explanation:

what is the slope of this line?

Answers

Answer:

-1/200

Step-by-step explanation:

To get from one point to the other you rise (go down in this case since the slope is negative) $1 every time you make 200 more scarves.

The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):

A graph with two linear functions; f of x passes through 5, 0 and 10, 10, and g of x passes through negative 3, 0 and 2, 10.

Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)

Part B: Solve for k in each type of transformation. (4 points)

Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)

Answers

Answer:

A linear function can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If this line passes through the points (x₁, y₁) and (x₂, y₂), then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

We know that line f(x) passes through points (5, 0) and (10, 10)

Then the slope of f(x) is:

a = (10 - 0)/(10 - 5) = 10/5 = 2

then:

f(x) = 2*x + b

again, knowing that f(10) = 10   (because this line passes through point (10, 10) )

10 = 2*10 + b

10 = 20 + b

10 - 20 = b = -10

Then the equation of this line is:

f(x) = 2*x - 10

Now for g(x) we know that it passes through (-3, 0) and (2, 10)

then the slope is:

a = (10 - 0)/(2 - (-3)) = 10/5 = 2

g(x) = 2*x + b

And knowing that g(2) = 10   (because this line passes through point (2, 10) )

10 = 2*2 + b

10 = 4 + b

10 - 4 = b

6 = b

then:

g(x) = 2*x + 6

Then the equations are:

f(x) = 2*x  - 10

g(x) = 2*x + 6

A) One transformation may be a vertical translation, and the other can be a horizontal translation.

This is a vertical translation, which is defined as:

For a function f(x), a vertical translation of k units is written as:

g(x) = f(x) + k

If k is positive, the translation is upwards

if k is negative, the translation is downwards.

And an horizontal translation of k units is written as:

g(x) = f(x - k)

if k is positive, the translation is to the right

if k is negative, the translation is to the left.

B)

For the vertical translation we have:

g(x) = f(x) + k

2*x + 6 = 2*x  - 10 + k

6 = -10 + k

6 + 10 = k

16 = k

For the horizontal translation we have:

g(x) = f(x - k)

2*x + 6 = 2*(x - k) - 10

2*x + 6 = 2*x - 2*k - 10

6 = -2*k - 10

6 + 10 = -2*k

16 = -2*k

16/-2 = k

-8 = k

C)

The transformations are:

g(x) = f(x) + 16

or

g(x) = f(x - (-8))


4. Katy sells new video games at a gaming store. Katy gets a bonus if she sells more than 60 video games. If 8 people each buy 7 video games, how many more video games does Katy need to sell to get her bonus? Show your work ​

Answers

8 people each buy 7 so, 8 x 7 = 56
She needs to sell 60:
60 - 56 = 4
Katy is 4 away from selling 60.

Is the number 0.1875 rational or irrational

Answers

rational...............

The best description of a dilation of a figure is?

Answers

Answer:

an enlargement or a reduction of the figure

a slide of the figure

a turning of the figure about some fixed point

a mirror image of the figure

The best description of a dilation of a figure is a slide of the figure.

What is dilation?

A dilation is a transformation that changes the size of a figure. It can become larger or smaller but the shape of the figure does not change.

Now,

The best description of a dilation of a figure is a slide of the figure.

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Solve each equation b+3.3=8.9 what is b?

Answers

the answer will be 5.6 !

you can get this by doing 8.9 - 3.3 ! remember you can apply this to all problems by turning division to multiplication, addition to subtraction, etc.

please mark brainliest if this was useful ♡

How do I find central angle with coordinates (42.36,-71.06) (44.5,-73.11) in order (a,b) (c,d)

Answers

¿ SiNo no nosenkkknkkkkkk

i need help ASAP ill give u brainliest ! WORTH 20 POINTS ! any silly guess gets reported

Answers

Answer:

for volume you multiple l*w*h so 2)432 4)1,216

Work out the mean for the data set below: 58002, 58003, 58002, 58003, 58003, 58005, 58003

Answers

Step-by-step explanation:

Mean x¯¯¯ 58003

Median x˜ 58003

Mode 58003

Range 3

Minimum 58002

Maximum 58005

Count n 7

Sum 406021

Quartiles Quartiles:

Q1 --> 58002

Q2 --> 58003

Q3 --> 58003

Interquartile

Range IQR 1

Outliers 58005

copy machine goes brr

2x + 6
96
solve for x using an algebraic equation

Answers

Answer:

v

Step-by-step explanation:

i really need help on this.​

Answers

Answer:

both are (0,0)

Step-by-step explanation:

Hello There!

When its asking for the vertical intercept its asking " at what points does the equation cross the vertical axis( y axis) so its pretty much asking for the y intercept¨

In the graph shown below the y intercept is 0 so the coordinates of the vertical intercept would be (0,0)

When its asking for the horizontal intercept its asking " at what points does the equation cross the horizontal axis ( x axis ) so its pretty much asking for the  x intercept."

In the graph shown below the x intercept is 0 so the coordinates of the horizontal intercept would be (0,0)

4. 3a+6+5a A)16 B)8a C)8
5. 8b+8-4b A)20 B)28 C)12b
6. 5c-4c+c A)9c B)0 C)-6

Answers

Answer:

No clue what the answer is...

If the number of hours you hours you work is proportional to the amount of money you earn per hour, which og tye following statements is true?​

Answers

Answer:

it should be a

Step-by-step explanation:

if you work for $10 an hour, and work for 2 hours, you make $20 but if you double the hours worked, so 4 hours, you make $40, which is double the hours, and double the money

PLEASE HELP!!! :(
Consider the following figure
What is BD? ​

Answers

Answer:

BD = 16

Step-by-step explanation:

32/BD = BD/8

BD² = 256

BD = 16

Lucy bought a fish tank shaped like a rectangular prism for her new betta fish. The tank holds 2,244 cubic inches of water. It is 12 inches long and 11 inches wide.

Answers

Answer:

The length of the fish tank is 17 inches.

Step-by-step explanation:

The volume of a rectangular prism is length × breadth × height.

You already know the volume, breadth, and height, so you can find the length.

Length = 2244 ÷ 12 ÷ 11

            = 17 inches

The height of the tank is 17 inches.

What is Volume?

Volume of a three dimensional shape is the space occupied by the shape.

Given that,

The shape of the fish tank is rectangular prism.

The formula to calculate the volume of the rectangular prism is,

Volume = Length × Width × height

Given,

Volume of the tank = 2,244 cubic inches

Length = 12 inches

Width = 11 inches

Let x be the height.

Substituting the given values,

2,244 = 12 × 11 × x

x = 2244 / (12 × 11)

x = 2244 / 132

x = 17 inches

Hence the height of the tank is 17 inches.

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Your question is incomplete. The complete question is given below.

Lucy bought a fish tank shaped like a rectangular prism for her new betta fish. The tank holds 2,244 cubic inches of water. It is 12 inches long and 11 inches wide. What is the height of the tank?

Calculate the area of the right - angled triangle with base of 18cm and height 6.5cm

Answers

Answer:

area = 58.5 cm²

Step-by-step explanation:

area = 18 x 6.5 x 0.5 = 58.5 cm²



Sophie buys a wheelbarrow priced at $72. If the sales tax is 5%, what will be the total cost
including tax?

Answers

Answer:

$75.6

Step-by-step explanation:

5%of 72 = 3.6

72+3.6 = 75.6

Solve the equation 2/3(9+x)=−5(4−x).

Answers

Answer:

the answer is x=6

Step-by-step explanation:

hoped I helped

The answer should be x=6

3-4/5X-2/3–3/15+3/5divided by -3/2

Answers

Answer:

-2(6x-13)/15

Step-by-step explanation:

This is done by simplifying the expression as well as combining like terms

Felipe planted some seeds for a science project. One of his plants grew 6 1/2 inches in the first week, and then it grew 5 3/4 inches during the second week. How much did the plant grow during these two weeks? The answer should be written as a proper mixed number and should be simplified, if possible. *ill give brainliest*

Answers

Answer:

12 1/4

Step-by-step explanation:

find the value of 2\5of rs75​

Answers

Step-by-step explanation:

Given

[tex] \frac{2}{5} \times rs75 \\ = rs \: 15 \times 2 \\ = rs \: 30[/tex]

Hope it will help :)

Answer:

2÷5×75=30

Step-by-step explanation:

2. What is the product of the following expression?
2x(x2 + x-5)
A. 2x3 + x-5
B. 2x3 + 2x – 10
C. 2x3 + 2x2 – 5x
D. 2x3 + 2x2 – 10x
(Please help)

Answers

your answer is d!!!!

correct me if i’m wrong :)

I can’t download anything so if anyone can find a way to help with this I’d be grateful (^_^)

Answers

It's hard to explain by words so sorry if you don't understand. For the graphing part, starting from (-3, 0), plot points in (1, 2), (6, 3), and connect them. The end of a line should be (10, 3.5). You will understand better if you use graphing calculator.

The answer of a second question is {x|x is greater or equal to -3.

hii please help i’ll give brainliest!!

Answers

answer is D because statement mentions about evelyn applying brake to stop the car.

brainliest

it’s D i think it’s D because i have a feeling it’s D.

Find the sum.
5y+2/xy^2 + 2x-4/4xy

Answers

[tex]\frac{5y+2}{xy^2}[/tex]+[tex]\frac{2x-4}{4xy}[/tex]=[tex]\frac{xy+8xy+4}{2xy^2}[/tex]

or just (xy+8y+4)/2xy^2 if u can't see the equation

The value of the expression using sum will be (8y + xy + 4) / (2xy²).

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ [(5y + 2) / (xy²)] + [(2x - 4) / (4xy)]

Simplify the expression, then we have

⇒ [(5y + 2) / (xy²)] + [(2x - 4) / (4xy)]

⇒ [4(5y + 2) / (4xy²)] + [y(2x - 4) / (4xy²)]

⇒ [(20y + 8) / (4xy²)] + [(2xy - 4y) / (4xy²)]

⇒ (20y + 8 + 2xy - 4y) / (4xy²)

⇒ (16y + 2xy + 8) / (4xy²)

⇒ (8y + xy + 4) / (2xy²)

The value of the expression using sum will be (8y + xy + 4) / (2xy²).

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6a-4b when a=5 and b=3

Answers

Answer:

18

Step-by-step explanation:

Answer:

Use substitution to receive: 18

Step-by-step explanation:

6a - 4b when a = 5 and b =  3

6(5) - 4(3)

30 - 12 = 18

Linear inequality systems graphically

Answers

To graph the solutions of a system of inequalities, graph each inequality and find the intersections of the two graphs.

Monthly grocery cost based on the average number of shopping trips is predicted using the least-square regression line, ŷ = 275.3 + 90.7x, where ŷ represents the predicted monthly expense and x represents the average number of trips. A shopper visits the grocery store an average of 3.2 times and has a monthly cost of $520. What is the residual for the shopper?

45.54
76.47
−45.54
−76.47
90.7

Answers

Answer:

−45.54

Step-by-step explanation:

Just took the test

The residual for the shopper will be equal to -45.54. Hence, option C is correct.

What is an equation?

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given data provided in the question,

The given equation is,

y = 275.3 + 90.7 x

Here, x is the number of trips and y is the total monthly expense.

Then,

Shopper monthly cost = $520

Number of visits by the shopper in a month = 3.2

So, the residual for the shopper will be,

$520 = 275.3 + 90.7 (3.2)

$520 = 275.3 + 290.24

= -45.54

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