If you ever swam in a pool and your eyes began to sting and turn red, you felt the effects of an incorrect pH level. pH measures the concentration of hydronium ions and can be modeled by the function p(t) = −log10t. The variable t represents the amount of hydronium ions; p(t) gives the resulting pH level.

Water at 25 degrees Celsius has a pH of 7. Anything that has a pH less than 7 is called acidic, a pH above 7 is basic, or alkaline. Seawater has a pH just more than 8, whereas lemonade has a pH of approximately 3.

Create a graph of the pH function either by hand or using technology. Locate on your graph where the pH value is 0 and where it is 1. You may need to zoom in on your graph.
The pool maintenance man forgot to bring his logarithmic charts, and he needs to raise the amount of hydronium ions, t, in the pool to 0.50. To do this, he can use the graph you created. Use your graph to find the pH level if the amount of hydronium ions is raised to 0.50. Then, convert the logarithmic function into an exponential function using y for the pH.

Recall from 07.02 how to convert a log to an exponential function. The equation y equals b to the power of x is written on the left. The equation x equals log base b of y is written on the right. A double-ended arrow points to both equations. The word exponent is written above the equations with arrows pointing to the x on the left and the x on the right. The word base is written below the equations with arrows pointing to the b on the left and the b on the right.
The pool company developed new chemicals that transform the pH scale. Using the pH function p(t) = −log10t as the parent function, explain which transformation results in a y-intercept and why. You may graph by hand or using technology. Use complete sentences and show all translations on your graph.
p(t) + 1
p(t + 1)
−1 • p(t)

A 81.2 is the answer

Hello!

Answer:⇒⇒⇒⇒⇒⇒⇒⇒A. 81.2

Step-by-step explanation:

[tex]6(2.6+12.1)[/tex]

Add the numbers.

[tex]2.6+12.1=14.7[/tex]

[tex]6*14.7[/tex]

Multiply the numbers.

[tex]6*14.7=88.2[/tex]

[tex]=88.2[/tex]

[tex]88.2-7[/tex]

Subtract the numbers.

[tex]88.2-7=81.2[/tex]

[tex]=81.2[/tex]

Hope this helps!

Thank you for posting your question at here on brainly.

-Charlie

The left end of the box is at 32; the right end is at 37. The box part of the plot contains all the values ...

... between 32 and 37.

Answer:

The correct option is 3.

Step-by-step explanation:

From the given box plot it is clear that

1. The left end point of the line is 27. So, the minimum value of the data is 27.

2. The left end of the box is 32. It means the first quartile of the data is 32.

3. The line inside the box represents the median. So the median of the data is 36.

4. The right end of the box is 37. It means the third quartile of the data is 37.

5. The right end point of the line is 40. So, the maximum value of the data is 40.

It means the box part of the box plot contains all the values between 32 and 37.

Therefore the correct option is 3.

2*53/25 = 4.24

4 is not enough to maintain the required ratio, so there must be 5 chaperones, minimum.

_____

Presumably, the guidelines contain additional information regarding whether the number of chaperones can be odd. Sometimes, two are required so that one can be taking care of a student while the other handles the remaining students (or calls for emergency aid). In that case, the minimum for 53 students may be 6 chaperones.

(1) it is (C) the commutative property of multiplication: a*b = b*a, so 2*(-6/7) = (-6/7)*2

(2) it is (D) the commutative property of addition: a+b=b+a, so 5*4+3=3+5*4

commutate = "swap around"

To find the area of the given traingle we have to draw perpendicular from point 'J' which meets the x axis at point (2,0) and let us named it 'P'.

As we know that area of triangle is

[tex] = \frac{1}{2}\times b \times h [\tex]

Here base 'b' will be LK and height 'h' will be JP

Here,

LK= 4 units JP=4 units

Area ={1}{2} *(4)*(4)

On solving the equation we get,

Area=8 Sq units

Alright, so i'm looking at the graphs and i'm seeing B as an answer, Probably not A. C and D are confusing,

In the end, i'd say B and D.

If i'm wrong, please tell me.

The correct answers are (B), (C), and (D).

(C) is pretty straight forward. The graph resembles the graph of a quadratic function that us concave upwards. A quadratic function, and functions with an even degree like [tex]x^4, x^6[/tex] will be concave upwards if the leading term is positive.

For function with an odd degree such as [tex]x^3, x^5[/tex] will be mostly negative on the side of the negative x axis and positive on the side of the positive x-axis if the leading coefficient is positive.  A cubic function with a positive leading term will be negative on the side of the negative x-axis  for large negative numbers and positive on the side of the positive x-axis for large positive numbers.  From this explaination we can gather that (B) and (D) are also correct .

The correct options are (B),(C) and (D).

Multiply these as you would any binomial expressions, then replace i² with -1.

(4 -5i)·(2 +3i) = 4·2 +4·3i -5i·2 -5i·3i

... = 8 +12i -10i -15i²

... = 8+15 +2i

... = 23 +2i

_____

Your calculator may be able to do this problem for you.

Answer:

f(2) = 0

Step-by-step explanation:

Plug x = 2 into the formula for f(x):-

f(2) = 2(2) - 4

= 4 - 4

= 0

f(2) = 0

substitute x = 2 into f(x)

f(2) = (2 × 2 ) - 4 = 4 - 4 = 0

Answer: 6280 cm

Step-by-step explanation:

Given: The diameter of hamster wheel = 20 cm

The circumference of hamster wheel is given by :-

[tex]C=\pi d[/tex], where d is the diameter of the hamster wheel.

[tex]\Rightarrow C=(3.14)(20)=62.8\text{ cm}[/tex]

During one race, the number of rotations of the wheel = 100

Therefore, the distance run by chubby is given by :-

[tex]D=100\times C\\\\\Rightarrow D=100\times62.8\\\\\Rightarrow D=6280\text{ cm}[/tex]

Answer:

6283 cm.

Step-by-step explanation:

We have been given that Avi's pet hamster Chubby completed 100 rotations of the wheel. The diameter of the hamster wheel is 20 cm.

Since wheel is a circle, so the distance covered by Chubby in one rotation will be equal to the circumference of wheel.

[tex]\text{Circumference of circle}=2\pi r=\pi D[/tex], where,

r = Radius of circle,

D = Diameter of circle.

Now we will find the circumference of wheel by substituting [tex]D=20[/tex] in above formula.

[tex]\text{Circumference of wheel}=\pi*20[/tex]

[tex]\text{Circumference of wheel}=62.83185307[/tex]

Since Chubby covers a distance of 62.83185307 cm in one rotation, so in 100 rotations distance covered by Chubby would be:

[tex]\text{Distance covered in 100 rotations}=100\times 62.83185307[/tex]

[tex]\text{Distance covered in 100 rotations}=6283.185307\approx 6283[/tex]

Therefore, Chubby ran a distance of 6283 centimeters.

Let x represent the number of half-gallons purchased by the store. Then x-13 is the number sold, and 2.80x is the store's cost. The revenue is 4.06(x-13) and the difference between that and cost is the profit.

... 4.06(x -13) -2.80x = 63.14

... 1.26x - 52.78 = 63.14 . .  . . eliminate parentheses, collect terms

... 1.26x = 115.92 . . . . . . . . . . add 52.78

... x = 115.92/1.26 = 92 . . . . . divide by the coefficient of x

The store purchased 92 half-gallons of milk.

Yes. You can solve in the usual way.

Take the square root:

... x-7 = ±√0 = 0

Add 7:

... x = 7

_____

There is one distinct real solution (with multiplicity 2).

C) p ≤ 78

I got 78 by subtracting 118 by 40. Since we know the maximum is 118 we can't get any higher than 78 so it has to be equal or less than.  

Answer:

C) p ≤ 78

Step-by-step explanation:

so we know the plane has a maximum capacity of 118

and 40 have already been loaded.

118-40= 78

we know it cannot have greater than 78 but it can equal 78

there fore passengers are less than or equal to 78

also shown like this p ≤ 78 or option C

D. John Felton kills the Duke of Beckingham

Here is some proof: https://en.wikipedia.org/wiki/John_Felton_(assassin)

Answer:

d

Step-by-step explanation:

In triangle ABC, when ∠A = 20°, then ∠B = 70°, ∠C = 90°. In triangle CAD, when ∠CAD = 20° and ∠CDA = 90°, ∠ACD = 70°. In triangle CBD, with ∠CBD = 90° and ∠BCD = 70°, ∠CDB = 20°.

In triangle ΔABC, ∠C is a right angle and CD is the height to AB. Considering ∠A = 20°, by the angles sum property of a triangle, ∠B = 180° - ∠A - ∠C = 180° - 20° - 90° = 70°.

Moving on to triangle ΔCAD, this is a right triangle with ∠CDA=90°. ∠CAD is given as 20° (the same as ∠A of triangle ΔABC). Therefore, ∠ACD = 180° - ∠CAD - ∠CDA= 180° - 20° - 90° = 70°.

For triangle ΔCBD, ∠CBD is 90°, and ∠BCD corresponds to ∠B of triangle ΔABC, which we've determined as 70°. Hence, ∠CDB = 180° - ∠CBD - ∠BCD = 180° - 90° - 70° = 20°.

https://brainly.com/question/28144214

#SPJ12

In triangle ΔCBD, the angles are: m∠CDB = m∠CBD = 90° and m∠BCD = 90°. In triangle ΔCAD, the angles are: m∠CDA = 70° and m∠CAD = 70°. Finally, m∠ACD = 40°.

In triangle ΔCBD, since ∠C is a right angle, ∠CBD = 90° and ∠BCD = 90°.

In triangle ΔCAD, using the fact that the sum of angles in a triangle is 180°, we can find that ∠CDA = 90° - ∠CBD = 90° - 20° = 70°.

Similarly, ∠CAD = 90° - ∠BCD = 90° - 20° = 70°.

Finally, since ∠CDA = ∠CAD, ∠ACD = 180° - ∠CDA - ∠CAD

= 180° - 70° - 70°

= 40°.

https://brainly.com/question/22262639

#SPJ12

Answer:By multiplying with (1+0.01x) where x is the percentage of increase, monthly pay rate of 21$ after marked up 78.7% and 10% profit will be $41.28.

Step-by-step explanation:

Given that pay rate is 21$ and it is marked up by 78.7% and made a 10% profit.

If any value marked up or made a profit of x% then we have to multiply with (1+0.01x) to find the new value.

New pay after 78.7% marked up using above formula is [tex]21X(1+0.01X78.7)=21X1.787=37.527[/tex]

Now we have to use above formula again for 10% profit.

Hence new value [tex]=37.527(1+0.01X10)=37.527X1.1=41.2797[/tex]≈$41.28

| u + v | = 2

u + v = - 4i + 1j + 4i + 1j = 2j

the magnitude of a vector ai + bj is

| ai + bj | = √(a² + b² )

for u + v = 0 + 2j

| u + v | = √(0² + 2² ) = √4 = 2

The total amount of the purchase was ...

... $2.50 + 3c = $5.05

This equation can be solved by subtracting 2.50 and dividing by 3. Both these operations are done to both sides of the equation in accordance with the rules of equality.

... 3c = $2.55

... c = $0.85

The cost of a bag of chips was $0.85.

The cost of a bag of chips can be found by subtracting the juice price from the total cost and then dividing by the number of chip bags. This gives us an answer of $0.85 per bag.

To solve this problem, we need to subtract the cost of the juice from the total cost, then divide that answer by the total number of chip bags bought to find the cost of one bag. First, we subtract the juice price ($2.50) from the total spent ($5.05), which gives us $2.55. This is the total cost of the chips. Then, we divide that $2.55 by the number of chip bags bought (which is three) to find the cost of one bag. This can be represented by the equation: c = (total cost - juice price) / number of chip bags, or c = ($5.05 - $2.50) / 3. Calculating this, we find that c equals $0.85, so a bag of chips costs $0.85.

https://brainly.com/question/18262581

#SPJ3

The volume drop is 432-297= 135

135 books is a fraction 135/432 of the original volume 432. That is (x100): 31.25%

So the sales went down by 31.25%

31.25 percent of sales go down in second week as compared to first week.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, the sales volume for an online bookstore was 432 books in the first week.

Then due to the new policy of tax for on-line shopping, the sales volume dropped to 297 books at the second week.

Percentage dropped= 297/432 ×100

= 0.6875×100

= 68.75%

Now, 100-68.75=31.25%

Therefore, 31.25 percent of sales go down in second week as compared to first week.

To learn more about the percentage visit:

brainly.com/question/24159063.

#SPJ3

Answer: [tex]\text{P(A or B)}=0.90[/tex]

[tex]\text{P(A and B)}=0.18[/tex]

Step-by-step explanation:

Given : P(A)=0.60 and P(B)=0.30

We will say A and B are independent events if :

[tex]\text{P(A or B)=P(A)+P(B)}\\\\=0.60+0.30=0.90[/tex]

[tex]\text{P(A and B)=P(A) x P(B)}\\\\=0.60\times0.30=0.18[/tex]

Thus , A and B are independent events if :

[tex]\text{P(A or B)}=0.90[/tex]

[tex]\text{P(A and B)}=0.18[/tex]

Answer: P( A and B)= 0.18

Answer:

The price over three days fell linearly

Step-by-step explanation:

s = stock

s = -4x

s = -4(3)

s = -12

The stock decreased by 12 dollars over 3 days.

Answer: -12

Step-by-step explanation:Hello!I hope you are having a good day or evening and I hope this helps :) !!

6

24% = [tex]\frac{24}{100}[/tex]

multiply 25 by this fraction

25 × [tex]\frac{24}{100}[/tex] = [tex]\frac{25(24)}{100}[/tex] = 6

The interest is computed from

... I = Prt

where P is the principal amount ($569), r is the rate (0.045) and t is the time in years (250/360).

... I = $569×0.045×250/360 ≈ $17.78

Please note that time is not rounded. Rather, the exact value (25/36) is used in the calculation. The only rounding of any number is done at the end, where the amount is rounded to the nearest cent. (Your text authors should know this.)

_____

If you follow the problem instructions (which Valerie's lender will not do), the interest is calculated as ...

... t = 250/360 = 0.6944444... ≈ 0.69 . . . . years

... I = $569×0.045×0.69 ≈ $17.67

_____

Note the rounding of intermediate numbers (time) introduces an error of about $0.11 in the answer.

Answer:$17.41 (A+)

Step-by-step explanation:

(b)

using the 'laws of exponents '

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]

2² × [tex]\frac{2}{2^{4} }[/tex] = [tex]\frac{2^{3} }{2^{4} }[/tex] = [tex]2^{(3-4)}[/tex] = [tex]2^{-1}[/tex]

y = -x² + 9

the x-intercepts are x = - 3 and x = 3 hence the factors are

(x + 3 ) and (x - 3 )

polynomial is the product of its factors

y = a(x - 3 )(x + 3) ← ( a is a multiplier )

from the end behaviour the parabola opens down and is a maximum and so the value of a is negative

y = -(x - 3)(x+3) = - (x² - 9 ) = - x² + 9

The polynomial function with the given features is f(x) = -(x + 3)(x - 3), which is a quadratic function with the required y-intercept, x-intercepts, and end behavior.

The question involves finding a polynomial function given certain characteristics: a y-intercept of (0, 9), x-intercepts at (-3, 0) and (3, 0), a degree of 2, and specific end behavior.

Since the degree is 2, we are dealing with a quadratic function.

The x-intercepts tell us that the factors of the polynomial are (x + 3) and (x - 3).

The y-intercept indicates that when x is 0, the function equals 9.

The end behavior suggests that the leading coefficient is -1 because as x goes to infinity or negative infinity, f(x) goes to negative infinity.

Considering all the information, the function can be expressed as:

f(x) = -(x + 3)(x - 3)

To verify, expanding the factors gives:

f(x) = -(x^2 - 9)

f(x) = -x^2 + 9

This function has the required y-intercept of 9, x-intercepts of -3 and 3, and the correct end behavior.

Differentiating both sides of PV = C with respect to t gives us ...

... P'V +PV' = 0

Filling in the given numbers gives us ...

... (40 kPa/min)(900 cm³) + V'(150 kPa) = 0

Solving for V' gives ...

... V' = -(40 kPa/min)(900 cm³)/(150 kPa)

.. V' = -240 cm³/min

The volume is decreasing at the rate of 240 cm³/min.

Final answer:

In Physics, Boyle's Law relates the pressure and volume of a gas at constant temperature. To find the rate at which volume is decreasing as pressure increases, we differentiate the equation PV = C with respect to time and solve for [tex]\frac{dV}{dt}[/tex] , given the pressure, volume, and rate of change of pressure which comes out to be 240 cm³/min.

Explanation:

The subject of this question is Physics, specifically relating to Boyle's Law, which is part of gas laws studied in chemistry and physics. The level of this question is appropriate for High School students. We know from Boyle's Law that for a given amount of gas at constant temperature, the pressure P is inversely proportional to the volume V, meaning that PV = C or k, where C is a constant.

To solve the problem stated, we differentiate both sides of PV = C with respect to time t. This will give us P[tex]\frac{dV}{dt}[/tex] + V[tex]\frac{dP}{dt}[/tex] = 0. With the known values of P, V, and[tex]\frac{dP}{dt}[/tex] , we can solve for [tex]\frac{dV}{dt}[/tex], which will give us the rate at which the volume is decreasing as the pressure increases.

By substituting the given values into the differentiated equation: 150 kPa x   [tex]\frac{dV}{dt}[/tex]+ 900 cm³ x 40 kPa/min = 0, we solve for [tex]\frac{dV}{dt}[/tex]  to find the rate at which the volume is changing.

[tex]\frac{dV}{dt}[/tex] = - [tex]\frac{900}{150}[/tex] x  40

[tex]\frac{dV}{dt}[/tex] = -6 x 40

[tex]\frac{dV}{dt}[/tex] = -240 cm³/min

Following this method, we find that the volume is decreasing at a rate of 240 cm³/min.

2c. We assume that the equations for ballistic motion in a vacuum apply, and the rate of downward acceleration is 32 ft/s². Then it will take ...

... (288 ft/s)/(32 ft/s²) = 9 s

for the rocket to reach its maximum height (its vertical velocity to decrease to zero).

2d. The trip down takes the same amount of time as the trip up, so the round trip time is ...

... (9 s)×2 = 18

_____

The acceleration due to gravity decreases the vertical velocity by the same amount (32 ft/s) each second. An equation for that might be ...

... v = 288 -32t

When the vertical velocity is zero, the rocket is no longer going up. It has reached its maximum height. Then the equation for that looks like ...

... 0 = 288 -32t

... 32t = 288

... t = 288/32 = 9 . . . . . compare to the solution above

After 9 seconds, the rocket reaches its maximum height.

___

Simplifying the description of free-fall is a little harder. In physics terms, the potential energy the rocket has at its maximum height all gets converted to kinetic energy on the way down. At impact with the ground, the kinetic energy is the same as it was when the rocket was launched. That is, its velocity is 288 ft/s earthward at impact. The above equation for velocity still applies, but now we're solving for v = -288.

... -288 = 288 -32t

... -576 = -32t

... 576/32 = t = 18 . . . . . twice the time it took to reach maximum height.

The round trip takes 18 seconds.

Try this solution; note, this way is not the shortest one.

The solutions for the modular equation are:

[tex]x = \frac{c - b}{a}[/tex] or [tex]x = -\frac{c + b}{a}[/tex]

-----------------------

A modular equation |f(x)| = a means that:

[tex]f(x) = a[/tex] or [tex]f(x) = -a[/tex]

-----------------------

The equation given is:

[tex]|ax + b| = c[/tex]

Which means that:

[tex]ax + b = c[/tex]

[tex]ax = c - b[/tex]

[tex]x = \frac{c - b}{a}[/tex]

Or

[tex]ax + b = -c[/tex]

[tex]ax = -c - b[/tex]

[tex]ax = -(c+b)[/tex]

[tex]x = -\frac{c + b}{a}[/tex]

The solutions are [tex]x = \frac{c - b}{a}[/tex] or [tex]x = -\frac{c + b}{a}[/tex]

A similar problem is given at https://brainly.com/question/5123313

Answer:

The answers would be

1. C

2. B

3. A

Step-by-step explanation:

The term product refers to multiplication. So in question 1, when we see the term quotient, we are looking to multiply.

The term quotient refers to division. So in questions 2 and 3, when we see this term, we look to divide.

Answer:

C. [tex]6n[/tex]

B. [tex]\frac{6}{(x+y)}[/tex]

A. [tex]\frac{Z}{3}[/tex]

Step-by-step explanation:

1. This expression refers to the product operation between real numbers, therefore the correct algebraic form is [tex]6n[/tex]

2. This expression refers to the operation division between real numbers, therefore the correct algebraic form is [tex]\frac{6}{(x+y)}[/tex]

3. This expression refers to the operation division between real numbers, therefore the correct algebraic form is [tex]\frac{Z}{3}[/tex]