Use the formula pH=log(1/[H^+]) to write an expression for the concentration of hydrogen ions in a liter of a sports drink that has a pH of 2. 4. What is the concentration of hydrogen ions?

Answer:

11

Step-by-step explanation:

\text{Compounded Daily:}

Compounded Daily:

A=P\left(1+\frac{r}{n}\right)^{nt}

A=P(1+  

n

r

​  

)  

nt

Compound interest formula

A=70900\hspace{35px}P=37000\hspace{35px}r=0.057\hspace{35px}n=365

A=70900P=37000r=0.057n=365

Given values

70900=

70900=

\,\,37000\left(1+\frac{0.057}{365}\right)^{365t}

37000(1+  

365

0.057

​  

)  

365t

Plug in values

70900=

70900=

\,\,37000(1.0001562)^{365t}

37000(1.0001562)  

365t

Simplify

\frac{70900}{37000}=

37000

70900

​  

=

\,\,\frac{37000(1.0001562)^{365t}}{37000}

37000

37000(1.0001562)  

365t

​  

Divide by 37000

1.9162162=

1.9162162=

\,\,1.0001562^{365t}

1.0001562  

365t

\log\left(1.9162162\right)=

log(1.9162162)=

\,\,\log\left(1.0001562^{\color{blue}{365t}}\right)

log(1.0001562  

365t

)

Take the log of both sides

\log\left(1.9162162\right)=

log(1.9162162)=

\,\,\color{blue}{365t}\log\left(1.0001562\right)

365tlog(1.0001562)

Bring exponent to the front

\frac{\log\left(1.9162162\right)}{\log\left(1.0001562\right)}=

log(1.0001562)

log(1.9162162)

​  

=

\,\,\frac{365t\log\left(1.0001562\right)}{\log\left(1.0001562\right)}

log(1.0001562)

365tlog(1.0001562)

​  

Divide both sides by log(1.0001562)

4164.8632402=

4164.8632402=

\,\,365t

365t

Use calculator

\frac{4164.8632402}{365}=

365

4164.8632402

​  

=

\,\,\frac{365t}{365}

365

365t

​  

Divide by 365

11.4105842=

11.4105842=

\,\,t

t

t\approx

t≈

\,\,11

11

Using compound interest, it is found that it would take 11 years for the value of the account to reach $70,900.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

Hence, the parameters are given as follows:

\(A(t) = 70900, P = 37000, n = 365, r = 0.057\)

We have to solve for t, then:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(70900 = 37000\left(1 + \frac{0.057}{365}\right)^{365t}\)

\(\left(1 + \frac{0.057}{365}\right)^{365t} = \frac{70900}{37000}\)

\(\left(1 + \frac{0.057}{365}\right)^{365t} = 1.91621622\)

\((1.00015616)^{365t} = 1.91621622\)

\(\log{(1.00015616)^{365t}} = \log{1.91621622}\)

\(365t\log{1.00015616} = \log{1.91621622}\)

\(t = \frac{\log{1.91621622}}{365\log{1.00015616}}\)

t = 11.41

Rounding to the nearest year, it would take 11 years for the value of the account to reach $70,900.

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Answer: 8x - 32

Step-by-step explanation:    x + 3 + 7(x - 5)

                                                     x + 3 - 35

                          which gives you   8x - 32                              

Answer:

D

Step-by-step explanation:

Graph D has a positive slope. The line goes up 2 units and right 3 units.

Honesty can be measured by asking people to rate themselves on a scale of 1-10 for honesty, ranking their fellow participants in terms of honesty, conducting a polygraph test to assess physiological responses when presented with specific questions, and conducting interviews to assess how forthright people are in their answers.

An operational definition of honesty can be measured by asking people to rate themselves on a scale of 1-10 for honesty. This would allow participants to self-assess their own level of honesty and provide a baseline for comparison. By observing how often people tell the truth in a given situation, one can measure the level of honesty of a person.

Additionally, a polygraph can be used to measure physiological responses when asking a series of specific questions. This can provide a more accurate measurement of a person’s honesty in comparison to a self-reported scale.

Lastly, conducting interviews with participants can help to assess how forthright people are in their answers. This allows for a more in-depth assessment of honesty by allowing interviewers to observe and assess the sincerity of participants’ answers.

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Answer: 1) 8x + 2 = 90 1a. 11 2. 13x-10= 133 2a. 11

Both solve for 11.

Step-by-step explanation: 1) they’re both the same measure so they equal each other

Subtract 2 from each side 8x = 88 and x is 11

13x - 10 = 133 they’re both the same measures so they equal each other.

Add 10 to both sides because it’s already negative and 13x = 143 and you get 11

Answer:

11 for both

Step-by-step explanation:

To determine if a polynomial graph is positive or negative, you need to look at the sign of the leading coefficient of the polynomial. If the leading coefficient is positive, the graph will be positive.

If the leading coefficient is negative, the graph will be negative. This is because the highest degree of the polynomial will determine the sign of the graph as the graph will either be increasing (positive) or decreasing (negative). To determine the leading coefficient, look at the polynomial expression and identify the term with the highest degree. The sign of this term will be the sign of the graph. For example, if the highest degree is 3, then the term would be ax^3, and the graph will be positive if a is positive, and negative if a is negative.

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The interquartile range for the data set are

Andre

Interquartile Range: = 2

For Lin

Interquartile Range = 8

For Noah

Interquartile Range = 8

For Andre

Min: 25 the minimum number

Q1: 27 (the third position)

Median: 28 (the sixth position)

Q3: 29 (the 9th position)

Max: 30 (the maximum number)

Interquartile Range: Q3 - Q1 = 29 - 27 = 2

For Lin

Min: 20 the minimum number

Q1: 21 (the third position)

Median: 28 (the sixth position)

Q3: 29 (the 9th position)

Max: 32 (the maximum number)

Interquartile Range: Q3 - Q1 = 29 - 21 = 8

For Noah

Min: 13 the minimum number

Q1: 15 (the third position)

Median: 20 (the sixth position)

Q3: 23 (the 9th position)

Max: 25 (the maximum number)

Interquartile Range: Q3 - Q1 = 23 - 15 = 8

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the maximum height of a quadratic equation can be find Use the formula: x = -b / (2a) then Substitute the value of x back into the quadratic equation to find the corresponding maximum height.

To find the maximum height of a quadratic equation, you need to determine the vertex of the parabolic curve. The vertex represents the highest or lowest point of the quadratic function, depending on whether it opens upward or downward.

A quadratic equation is generally written in the form of y = ax² + bx + c, where "a," "b," and "c" are coefficients.

The x-coordinate of the vertex can be found using the formula: x = -b / (2a). This formula gives you the line of symmetry of the parabola.

Once you have the x-coordinate of the vertex, substitute it back into the original equation to find the corresponding y-coordinate.

The resulting y-coordinate represents the maximum height (if the parabola opens downward) or the minimum height (if the parabola opens upward) of the quadratic equation.

Here's an example:

Consider the quadratic equation y = 2x² - 4x + 3.

1. Identify the coefficients:

a = 2

b = -4

c = 3

2. Find the x-coordinate of the vertex:

x = -(-4) / (2 * 2) = 4 / 4 = 1

3. Substitute x = 1 back into the equation to find the y-coordinate:

y = 2(1)² - 4(1) + 3 = 2 - 4 + 3 = 1

Therefore, the maximum height of the quadratic equation y = 2x² - 4x + 3 is 1.

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The maximum height of a quadratic equation can be found by determining the vertex of the parabolic shape represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), and the corresponding y-coordinate represents the maximum height.

To find the maximum height of a quadratic equation, we need to determine the vertex of the parabolic shape represented by the equation. The vertex is the point where the parabola reaches its highest or lowest point.

The general form of a quadratic equation is ax^2 + bx + c, where a, b, and c are constants. To find the x-coordinate of the vertex, we can use the formula x = -b / (2a).

Once we have the x-coordinate, we can substitute it back into the equation to find the corresponding y-coordinate, which represents the maximum or minimum height of the quadratic equation.

Let's take an example to illustrate this process:

Suppose we have the quadratic equation y = 2x^2 + 3x + 1. To find the maximum height, we first need to find the x-coordinate of the vertex.

Using the formula x = -b / (2a), we can substitute the values from our equation: x = -(3) / (2 * 2) = -3/4.

Now, we substitute this x-coordinate back into the equation to find the y-coordinate: y = 2(-3/4)^2 + 3(-3/4) + 1 = 2(9/16) - 9/4 + 1 = 9/8 - 9/4 + 1 = 9/8 - 18/8 + 8/8 = -1/8.

Therefore, the maximum height of the quadratic equation y = 2x^2 + 3x + 1 is -1/8.

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Answer:

\(x=4\)

Step-by-step explanation:

Given \(\displaystyle\\\sqrt{x+12}-\sqrt{2x+1}=1\), start by squaring both sides to work towards isolating \(x\):

\(\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\)

Recall \((a-b)^2=a^2-2ab+b^2\) and \(\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}\):

\(\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\\\implies x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\)

Isolate the radical:

\(\displaystyle\\x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\\\implies -2\sqrt{(x+12)(2x+1)}=-3x-12\\\implies \sqrt{(x+12)(2x+1)}=\frac{-3x-12}{-2}\)

Square both sides:

\(\displaystyle\\(x+12)(2x+1)=\left(\frac{-3x-12}{-2}\right)^2\)

Expand using FOIL and \((a+b)^2=a^2+2ab+b^2\):

\(\displaystyle\\2x^2+25x+12=\frac{9}{4}x^2+18x+36\)

Move everything to one side to get a quadratic:

\(\displaystyle-\frac{1}{4}x^2+7x-24=0\)

Solving using the quadratic formula:

A quadratic in \(ax^2+bx+c\) has real solutions \(\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\). In \(\displaystyle-\frac{1}{4}x^2+7x-24\), assign values:

\(\displaystyle \\a=-\frac{1}{4}\\b=7\\c=-24\)

Solving yields:

\(\displaystyle\\x=\frac{-7\pm \sqrt{7^2-4\left(-\frac{1}{4}\right)\left(-24\right)}}{2\left(-\frac{1}{4}\right)}\\\\x=\frac{-7\pm \sqrt{25}}{-\frac{1}{2}}\\\\\begin{cases}x=\frac{-7+5}{-0.5}=\frac{-2}{-0.5}=\boxed{4}\\x=\frac{-7-5}{-0.5}=\frac{-12}{-0.5}=24 \:(\text{Extraneous})\end{cases}\)

Only \(x=4\) works when plugged in the original equation. Therefore, \(x=24\) is extraneous and the only solution is \(\boxed{x=4}\)

Answer:

y = x + 5

Step-by-step explanation:

m = slope

slope = y2 - y1 / x2 - x1

8 - 6 / 3 - 1 = 2/2 = 1

m = 1

b = y-intercept

b = 5

y = mx + b

y = 1x + 5

y = x + 5

Answer:

Below

Step-by-step explanation:

To find the equation of this graph you can use this formula :

m = y2 - y1 / x2 - x1

For this, you can pick any 2 points on the graph and just plug em in!

I'm just going to chose points ( 4, 9 ) and ( 2, 7 )

m = 9 - 7 / 4 - 2

m = 2 / 2

m = 1

Now to find b, we just need the coordinates of the y-intercept which are :

      ( 0, 5 )

Here is the final equation of this line :

     y = x + 5

If you plug this into desmos it will give the same line!

Hope this helps! Best of luck <3

Answer: cot B

Step-by-step explanation: if i am right mark me as brainliest

Answer:

(-3)/5 + (4/7 * 3/5) - 4/9 * ( 2/3 * 1/5 ) - 15/16 + ( 1/5 * 4/3 )

To find :

Simply the problem using suitable properties of rational number .

Solution :

This type of problems can be solved using the rule of BODMAS .

=> (-3)/5 + ( 4/7 * 3/5 ) - 4/9 * ( 2/3 * 1/5 ) - 15/16 + ( 1/5 * 4/3 )

=> (-3)/5 + ( 12/35 ) - 4/9 * ( 2/15 ) - 15/16 + ( 4/15 )

=> (-3)/5 + ( 12/35 ) - 8/135 - 15/16 + ( 4/15 )

=> 64/105 - 3/5 - 8/135 - 15/16

=> 1/105 - 8/135 - 15/16

=> (-47)/945 - 15/16

=> -14927 / 15120

(-3)/5 + ( 4/7 * 3/5 ) - 4/9 * ( 2/3 * 1/5 ) - 15/16 + ( 1/5 * 4/3 ) = (-14927)/15120

Step-by-step explanation:

Answer:

16 inches

Step-by-step explanation:

c = πd

50.26 = 3.14 * d

Divide both sides by 3.14

d = 16.0

16 inches

Answer:

The diameter is 16 inches

Answer:

gimme a sec

Step-by-step explanation:

Answer:

What do you mean "how do solve" ?????

Step-by-step explanation:

The formula for a line segment is:

segment = √((x2 - x1)^2 + (y2 - y1)^2)

1. Calculate the difference between the x-coordinates: x2 - x1

2. Square the result of step 1: (x2 - x1)^2

3. Calculate the difference between the y-coordinates: y2 - y1

4. Square the result of step 3: (y2 - y1)^2

5. Add the results of step 2 and step 4: (x2 - x1)^2 + (y2 - y1)^2

6. Calculate the square root of the result of step 5: √((x2 - x1)^2 + (y2 - y1)^2)

This final result is the length of the line segment.

The formula for a line segment is relatively straightforward. Begin by calculating the difference between the x-coordinates (x2 - x1) and square the result. Then find the difference between the y-coordinates (y2 - y1) and square the result. Add the two results together and take the square root of the sum. This final result is the length of the line segment. This formula can be used to calculate the length of any line segment, regardless of its size or shape.

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An example of a geometric formula that contains pi(π) is the formula for the circumference of a circle, which is

C = 2πr. This formula is used to calculate the distance around a circle.

A geometric formula is a mathematical equation that describes a relationship between geometric figures or their properties.

Geometric formulas are used to calculate the area, perimeter, volume, surface area, and other properties of shapes such as circles, triangles, rectangles, spheres, cubes, and cylinders. For example, the formula for the area of a triangle is

A = 1/2 b×h, where b is the base of the triangle and h is its height.

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The value of x in the right angle triangle is approximately 45 degrees.

The angle of the right angle triangle can be found as follows:

Therefore, let's find the hypotenuse side using Pythagoras theorem,

6² + 6² = c²

c² = 72

c = √72

c = 8.48528137424

c = 8.5 cm

Hence,

sin x = opposite / hypotenuse

sin x = 6 / 8.5

sin x = 0.70588235294

x = sin⁻¹ 0.70588235294

x = 44.9006818301

x = 45°

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Answer:

can u add more info plz

Step-by-step explanation:

Answer:

The absolute value of a number is how far that number is from 0.

|-9| = 9

This is true because the absolute value of 9 is 9 spaces away from 0.

Answer:

1989.674m³

Step-by-step explanation:

It’s difficult to see the picture, and I can’t read the question.  Are you looking for the volume of the composite shape?  If so:

Cylinder: V=\(\pi\)r²h =

Cone: V=\(\pi\)r²h/3 =

Hemisphere: V=2/3\(\pi\)r³ = 2/3

TOTAL: 1570.796+157.079+261.799=1989.674m³

Answer:

BALALALALALAL

Step-by-step explanation:

7+5373)393()3

Answer:

x=2

Step-by-step explanation:

4x=8

/4   /4

divide both sides by 4

x=2

Answer:

x = 2

Step-by-step explanation:

140,608 possible ways are there to draw a hand of 5 cards such that you draw 3 cards from one suit and 2 cards from another different suit.

In a standard deck of 52 playing cards, there are 13 cards in each of 4 suits: clubs, diamonds, hearts, and spades. To draw a hand of 5 cards such that you draw 3 cards from one suit and 2 cards from another distinct suit, you have several options for the suits you choose.

There are C(4,2) = 6 ways to choose 2 suits out of 4. Once you have chosen the suits, you have C(13,3) = 286 ways to choose 3 cards from one suit and C(13,2) = 78 ways to choose 2 cards from the other suit.

Therefore, the total number of ways to draw a hand of 5 cards such that you draw 3 cards from one suit and 2 cards from another distinct suit is 6 x 286 x 78 = 140,608.

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Answer: $5.19

Step-by-step explanation:

If there are 40 working hours in a week and 52 weeks in a year, 40 * 52 should be the amount of working hours in a year.

40 * 52 = 2080 working hours

Nate needs $900 to live each month and there are 12 months in a year, so $900 * 12 would equal how much he spends per year.

$900 * 12 = $10800

Divide $10800 by 2080 working hours to get how much he needs to make per working hour.

10800/2080 = approximately 5.19, rounded down from the nearest hundredth

He needs to make $5.19 per hour, so the answer is the last option.

\(\text{Hey there!}\)

\(\bf{(-243) \times \dfrac{1}{5}}\)

\(\bf{-243 \rightarrow \dfrac{-243}{1}}\)

\(\bf{\dfrac{-243}{1}\times \dfrac{1}{5}}\)

\(\bf{\dfrac{-243(1)}{1(5)}}}\)

\(\frak{-243 \times 1 = -243}\) \(\leftarrow\bf{Your\ numerator}\)

\(\frak{1\times 5 = 5}\) \(\leftarrow \bf{Your\ denominator}\)

\(\bf{ = \dfrac{-243}{5}}\)\(\leftarrow\bf{The\ answer}\)

\(\bf{Your\ answer: \boxed{\bf{\dfrac{-243}{5} or \ as\ a\ decimal\ its: -48.6}}}\checkmark\)

\(\text{Good luck on your assignment and enjoy your day!}\)

~\(\frak{LoveYourselfFirst:)}\)

The inequality shaded in the graph is given as follows:

y ≥ 5x/2 + 3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = -3, hence the intercept b is given as follows:

b = 3.

When x increases by 2, y increases by 5, hence the slope m is given as follows:

m = 5/2.

Then the equation of the line is given as follows:

y = 5x/2 + 3.

The line is a solid line, and values above it are plotted, hence the inequality is given as follows:

y ≥ 5x/2 + 3.

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Based on the given problem, when written in the simplest form, the result would be 19 ²/₃

To divide 59 by 3 and then write it in its simplest form, you first need to find the number of times 3 can go into 59 without leaving a remainder:

= 59 / 3

= 19 times

Then find the quotient of 19 multiplied by 3:

= 19 x 3

= 57

Then use this to find the remainder:

= 59 - 57

= 2

This remainder will then be used to find the answer in the simplest form:

= 19 + Remainder / Divisor

= 19 + 2/3

= 19 ²/₃

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Elizabeth can dress up in 720 different ways.

We must add up the alternatives for each piece of clothing to reach the total number of outfits Elizabeth can wear.

Six skirt choices are available.

5 variations for shirts are available.

Given that she must select one pair from a possible four pairs of shoes, there are four possibilities available.

There are two different necklace alternatives.

3 different bracelet choices are available.

We add these values to determine the total number of possible combinations:

Total number of ways = (Number of skirt choices) + (Number of top options) + (Number of pairs of shoes options) + (Number of necklace options) + (Number of bracelet options)

Total number of ways is equal to 720 (6, 5, 4, 2, and 3).

Elizabeth can therefore dress up in 720 different ways

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Answer:

(35),(−3r),m=34(35),(−3),=3/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

y - 9 = 3(x - 0)

y - 9 = 3x - 0

y = 3x + 9