Belinda is thinking about buying a house for $249,000. The table below shows the projected value of two different houses for three years:


Number of years 1 2 3
House 1 (value in dollars) 253,980 259,059.60 264,240.79
House 2 (value in dollars) 256,000 263,000 270,000


Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer. (2 points)

Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years. (4 points)

Part C: Belinda wants to purchase a house that would have the greatest value in 45 years. Will there be any significant difference in the value of either house after 45 years? Explain your answer, and show the value of each house after 45 years. (4 points)

Answers

Answer 1

A)

House 1 value is an exponential function.

House 2 value is a linear function.

B)

House 1:

f(x) = 253,980 x

House 2:

f(x) = 256,000 + 7000x

C)

House 1 will have the greatest value.

The significant difference in the value of either house after 45 years is $168844

The value of house 1 after 45 years:

f(45) = $739844

The value of the house 2 after 45 years:

f(45) = $571000

What is a function?

function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.


We have,

House 1:

The value of the hours is described by an exponential function.

There is an increase of 2% per year.

f(x) = 253,980 x [tex]1.02^x[/tex]

Where x is the number of years.

House 2:

The value of the hours is described by a linear function.

There is an increase of $7000 per year.

f(x) = 256,000 + 7000x

Where x is the number of years.

Now,

For x = 45,

f(45) = 253,980 x [tex]1.02^x[/tex]

f(45) = 253,980 x [tex]1.02^{45}[/tex]

f(45) = $739843.74

f(45) = $739844 ____(1)

f(x) = 256,000 + 7000x

f(45) = 256,000 + 7000 x 45

f(45) = 256,000 + 315000

f(45) = $571000 ______(2)

From (1) and (2),

House 1 will have the greatest value.

The significant difference in the value of either house after 45 years

= $739844 - $571000

= $168844

The value of house 1 after 45 years:

f(45) = $739844

The value of the house 2 after 45 years:

f(45) = $571000

Thus,

The Part  A, Part B, and Part C are given above.

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Related Questions

Lorenzo orders 3 pizzas for delivery. The total bill, including a $4.00 delivery fee, is $42.85. He uses the following equation to figure out the cost of each pizza. 3c+4.00=42.85

Answers

Lorenzo uses the following equation to figure out the cost of each pizza. 3c+4.00=42.85

The cost of each pizza is $12.95.

What is linear equation?

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

Lorenzo orders 3 pizzas for delivery.

The total bill, including a $4.00 delivery fee, is $42.85.

He uses the following equation to figure out the cost of each pizza. 3c+4.00=42.85

3c = 42.85 - 4

3c = 38.85

c = 12.95

Therefore, the cost of each pizza is $12.95.

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a pitcher won 75%of the games she pitched. she pitched 60 games. how many games did she win

Answers

= 75

75 ___ × 60

75 ___ × 60 100

75 ___ × 60 100= 3

75 ___ × 60 100= 3 ___ × 60

75 ___ × 60 100= 3 ___ × 60

75 ___ × 60 100= 3 ___ × 60 4

75 ___ × 60 100= 3 ___ × 60 4= 45

A 5. 5kg bowling ball initially at rest is dropped from the top of a 12 m building. It hits the ground 1. 75s later. Find the net external force on the falling ball?

Answers

The net external force acting on the freely falling ball is 43.12 N.

We are provided with the following information:

Mass of bowling ball (m) = 5.5kg

Distance travelled by the ball (h) = 12m

Time taken by the ball = 1.75 s

To calculate the net force acting on the ball, we first need to calculate the acceleration experienced by the ball under free fall.

We can determine the acceleration using the formula,

d= ut + (1/2)at^2

since, the ball was initially at rest, u=0.

Thus, formula becomes,

d= (1/2)at^2.

Therefore, a= 2d/t^2

=> a= 2*12/(1.75)^2

=> a=24/ 3.0625

=> a= 7.84 m/s^2

Now, according to Newton's 2nd law of Motion,

[tex]F_{net} = mass * acceleration[/tex]

[tex]F_{net}[/tex] = 5.5 * 7.84 N =  43.12 N

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a couple has three children. assuming each child has an equal chance of being a boy or a girl, what is the probability that they have at least one girl? a. .5 b. .125 c. .875 d. 1

Answers

The probability of the couple having at least one girl is 0.875 0r 87.5 % by probability method. So, the option C is correct.

Having at least 1 girl out of 3 children means that there can be 1, 2 or 3 girls out of the 3 children.

So having at lest 1 girl out of 3 children is the same as saying that all 3 children are not boys.

The probability that all 3 children are boys would be

chance that child 1 is a boy * chance that child 2 is a boy * chance that child 3 is a boy = 0.5 * 0.5 * 0.5 = 0.125

since given that there is equal chance of both.

And the probability that NOT all 3 children are boys would be

100% - probability that all 3 children are boys = 1 - 0.125 = 0.875.

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Tim went 8 mile eat and 15 mile north. Jan went 5 mile wet and 12 mile north. How far apart are​ they? Round your anwer to the nearet tenth. How do we get the anwer to thi

Answers

The distance between Tim and Jan rounded to the nearest tenth is 21.4 miles.

The formula used in this problem is the Pythagorean Theorem. The Pythagorean Theorem states that the square of the hypotenuse (the longest side of a right triangle) is equal to the sum of the squares of the other two sides. This can be shown as A2 + B2 = C2.

In this problem, we need to find the hypotenuse, which is the distance between Tim and Jan. To do this, we will use the Pythagorean Theorem. First, we need to find the sum of the squares of the distances traveled by Tim and Jan.

For Tim, the square of 8 miles plus the square of 15 miles equals 289. For Jan, the square of 5 miles plus the square of 12 miles equals 169. Adding these together gives a total of 458. We then take the square root of 458 and get 21.38. This is the answer we are looking for, the distance between Tim and Jan rounded to the nearest tenth is 21.4 miles.

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Suppose 60% of the graduating class in a certain high school goes to collage if 240 students from this graduating class are going to collage how many student's are in this class

Answers

Total number of students in the graduating class when 60% of the students are going to college is equal to 400 students.

Percent of students of the graduating class going for college  is equal to 60%

let 'y' represent the total number of students in the graduating class.

Number of students of the graduating class going  to the college are 240.

60% of y = 240

⇒ ( 60 / 100 ) × y = 240

⇒ y = 240 × ( 100 / 60 )

⇒ y = 400 students.

Therefore, when 240 students of the graduating class going for a college then total number of students in the graduating class is equal to 400 students.

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A group of randomly selected Gamin Middle School athletes were asked to pick their favourite sport. Number of athletes Sport Sport Based on the data, what is the most reasonable estimate for the number of Gamin Middle School athletes whose favourite sport is hockey?

Answers

92 is the most reasonable estimate for the number of Gamin Middle School athletes whose favorite sport is hockey.

A reasonable estimate does not exceed the original numbers in a problem.

Reasonableness can be defined as checking to verify that the result of the solution or the calculation of the problem is correct or not, either estimating or plugging in your result to check it

The most reasonable estimate for the number of Gamin Middle School athletes whose favorite sport is hockey.

Estimate= population size x sample proportion.

population size=114

sample proportion=10/45

Estimate=114*10/45

Estimate=92.

Therefore, 92 is the most reasonable estimate for the number of Gamin Middle School athletes whose favorite sport is hockey.

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substitute 6x-5y=-1 and 6x+4y=-10

Answers

Answer:

x=-1 y=-1

Step-by-step explanation:

i am lazy to type

Answer:{x = -1}{y = -1}

Step-by-step explanation:

subtract the two equations

{6x - 5y = -1                       ^

{6x + 4y = -10                      ^

determine the sign

6x - 5y - (6x +4y) = -1 - (-10) ^

simplify

6x - 5y - 6x - 4y = -1 + 10 ^

substitute

y = -1      ^

solve the equation

6x + 4 x (-1) = -10  ^

write the solution

x = -1                     ^

What is 223,692 divided by 42 using the standard algorithm and showing work?

Answers

The value of 223,692 divided by 42 using the standard algorithm and showing work is 5326.

What is division?

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

The value of 223,692 divided by 42 using the standard algorithm and showing work is given below:

Dividing the two values by 2, a common factor

223,692 / 42

= 111,846 / 21

Dividing the two values by 3, a common factor

111,846 / 21

= 37282 / 7

Dividing the two values by 7, a common factor

37282 / 7

= 5326 / 1

Hence, the value of the division is 5326.

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why use the sum function with a range of cells when adding the values together accomplishes the same thing?

Answers

It saves time, doesn't need to be changed if a row or column is added to the range, and adjusts the range when the function is copied to another cell.

Based on the values in another column, we'll discover how to add up a column of numerical data. We are attempting, for instance, to assess product sales based on the typical customer rating. Thus, each of our products has an average rating of 9.8, 7.2, 6.1, and so on because customers score our products on a scale of 1 to 10. The sales totals for goods with ratings of 9 to 10, 7 to 8, and so forth should be calculated.

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Your cousin is building a new house. The layout of the first floor is shown in the diagram above. Using the
diagram and knowledge of polynomials find the following:
1. Write a polynomial that represents the length of the north side of the house. Then simplify the
expression.
2. Write a polynomial expression that represents the area of the kitchen. Then multiply to put the
polynomial in standard form.
3. Write a polynomial expression that represents the area of the bedroom. Then multiply to put the
polynomial in standard form.
4. Find the dimensions of the bathroom in terms of x. (Hint the west and east side of the house
should be equal.)

Answers

The polynomial for the north side of the house will be 2x^2+9x-32.

What are polynomials?

Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable. An example of a polynomial with one variable is x^2+x-12. In this example, there are three terms: x^2, x and -12.

Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial.

Now,

As the north side will be the sum of 5x-4,x^2-23 and 4x-5

so the polynomial for north will also be the sum of  5x-4,x^2-23 and 4x-5.

Hence,

          Polynomial for north side= 5x-4 + x^2-23 + 4x-5

         Polynomial for north side   =2x^2+9x-32

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-(-8.2w+10) Im confused about this problem can you help me

Answers

Answer:   8.2w - 10

Reason:

The negative out front is distributed to each term inside the parenthesis.

This will flip the sign of each term.

The -8.2 flips to +8.2w which is the same as 8.2wThe +10 flips to -10

For more information, search out "distributive property".

Carver's Auto Custom has two potential retail spaces to choose from.



Warehouse Space A: Includes 8000 sq. Ft. Of showroom and workshop space. It rents for. 85 cents



ar safl per month and an additional 25. Cents per sq. Ft, per month for operations expenses. One



half of this warehouse space will be used to stock paint cans and rims.

Answers

According to the area value, the amount required to be paid for the showroom is $2000.85

The term area in math is known as the region bounded by the shape of an object or it is the space covered by the figure or any two-dimensional geometric shape.

Here we have know that Warehouse Space A Includes 8000 sq. Ft. Of showroom and workshop space and it rents for. 85 cents per month and an additional 25. Cents per sq. Ft, per month for operations expenses.

While we looking into the question, we know that the following are known,

Area = 8000 square feet.

Rent = 85 cents.

Additional expenses = 25 cent per square feet.

Then the total expense is calculated as,

=> 85 + (8000 x 25)

=> 200085 cents.

When we convert into dollars, then we get,

=> One dollar = 100 cents.

Then the resulting value is

=> $2000.85

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Consider the equations f(x)=1/x and g(x) = (x-1)^2-1. To the nearest tenth, what is the solution of f(x)=g(x)?

Answers

The solution of equation f(x)=g(x) is 2.

How do equations work?

a formula that illustrates the relationship between the two expressions on either side of a sign. Usually, it has one variable and an equal sign. similar to 2. 2x - 4 = 2. The equals sign (=) in equations indicates that two expressions are equal. Point-slope, standard, and slope-intercept equations are the three main types of linear equations.

The "left hand side" and "right hand side" of the equation refer to the expressions on each side of the equals sign. The right side of an equation is frequently thought of as zero.

Given : f(x)=g(x)

          1/x = (x-1)^2-1

          1 = x (x-1)² - 1

          x (x-1)² = 2

         x ( x² + 1 - 2x ) = 2

         x³ + x - 2x² = 2

         x³ + x - 2x² - 2 = 0

         x³ - 2x² + x - 2= 0

        x²(x-2) + 1(x-2) = 0

       (x² +1) + (x-2) = 0

So,   x = 2 .

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Which number is less than 5/8 but greater than 1/9?

Answers

A number that is less than 5 / 8 but is greater than 1 / 9 is A. 0. 5.

How to find the number ?

To find the number that is less than 5 / 8 but greater than 1 / 9, first convert both fractions to decimals.

5 / 8 in decimals is:

= 5 / 8

= 0. 625

1 / 9 in decimals is:

= 1 / 9

= 0. 111

The number from the given options that is less than 5/8 but greater than 1/9 is therefore 0. 5 as it is less than 5 / 8 but more than 1 / 9.

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The options for the question include:

0.50.80.90.05

Please help like ASAP find the value of X please ASAP

Answers

The value of x is 15 and the angles in the pentagon are 105,49,90,33,83

What is interior angles in a pentagon ?

The interior angles in a pentagon are the angles which are inside the pentagon and sum of the interior angles in a pentagon is 540 degrees.

Given ,

From the figure we can say that it is pentagon.

And the sum of exterior angles in a pentagon is always 360 degrees.

SO,

7x+49+6x+33+83 = 360

13x + 165 = 360

13x = 360 - 165

13x = 195

x = 195 / 13

x = 15

So, the angles could be 7x = 7*15 = 105  and 6x = 6*15 = 90

Therefore, The value of x is 15 and the angles in the pentagon are 105,49,90,33,83 .

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50 POINTS (and its easy im just kinda dmb)
find the number of possible outcomes
1. A softball player bats six times in a game. Each at-bat results in an out, getting on base or hitting a homerun.
2. A sandwich shop has three types of sandwiches: ham, turkey, and chicken. Each s andwich can be ordered with white bread or multi-grain bread. Customers can add any combination of the six available toppings h

Answers

The number of outcomes for each case is given as follows:

1. 729 outcomes.

2. 36 outcomes.

How to obtain the number of outcomes?

The number of outcomes for each case is obtained using the Fundamental Counting Theorem, with the multiplication of the number of outcomes for each trial.

For item 1, we have six trials, each with three possible outcomes, hence the total number of outcomes is given as follows:

3^6 = 729.

For item 2, the outcomes are given as follows:

3 types of sandwich.2 types of bread.Six toppings.

Hence the number of outcomes is given as follows:

3 x 2 x 6 = 36 outcomes.

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Brad is standing on a hill which places him at the same height as a nearby flagpole.

The flagpole is 15 ft. High and Brad is 20 ft. Horizontally from the top of the pole.

Brad can see the bottom of the flag pole.

What is the length in feet of Brad's "line of sight" to the base of the flagpole?

Answers

As per the Pythagoras theorem the length in feet of Brad's "line of sight" to the base of the flagpole 25 feet².

In math the term called Pythagoras theorem is states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

The standard form of the Pythagoras theorem is written with the help of the triangle ABC as,

=> AC² = AB² + BC²

where AC refers the hypotenuse and AB and BC refers the sides of the triangle.

Here we know that it follows from the task content that the length in feet of Brad's line of sight to the base of the flag pole is to be determined.

And here we also know that the flag pole in discuss is said to be 15 feet high.

And here we have also identified that Brad is at the same height as the pole and is at a horizontal distance of 20 feet from the top of the pole.

Then the length is calculated as,

=> l² = 15² + 20²

=> l² = 225 + 400

=> l² = 625

=> l = 25.

Hence the length of the line of sight is 25 feet.

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You spent $250 on your credit card. It has been 5 years and you have a 3.75% interest rate. How much interest do you owe?

Answers

Answer:

1050$

Step-by-step explanation:

preciso de ajuda por que eu não sei matemática

Answers

Answer:

¡Hola, soy Za'Riah! Con gusto te ayudaré con este problema. (ver explicación)

Step-by-step explanation:

Resolvamos tu problema usando la división larga.

(See image)

A number of major tructural repair completed at the beginning of the current fical year at a cot of $1,000,000 are expected to extend the life of a building 10 year beyond the original etimate. The original cot of the building wa $6,552,000, and it ha been depreciated by the traight-line method for 25 year. Etimated reidual value i negligible and ha been ignored. The related accumulated depreciation account after the depreciation adjutment at the end of the preceding fical year i $4,550,000.

Answers

The total cot of the building (original cot of $6,552,000 le the Accumulated Depreciation of $4,550,000 pre-adjutment) divided by the new life of 35 year equal the annual depreciation amount of $188,514.29. The econd journal entry would therefore debit Building for $5,552,000 ($188,514.29 x 10 year) and credit Accumulated Depreciation for the same amount.

The journal entry to record the tructural repair and the related  adjutment i:

Debit: Accumulated Depreciation $1,000,000

Credit: Building $1,000,000

Debit: Building $5,552,000

Credit: Accumulated Depreciation $5,552,000

The first journal entry record the cot of the tructural repair. The $1,000,000 tructural repair cot reduce the value of the building, and therefore the amount debited to Accumulated Depreciation will equal the amount credited to Building.

The econd journal entry adjust the Accumulated Depreciation for the change in the life of the building. Since the life of the building wa extended 10 year, the Accumulated Depreciation need to be reduced by 10 year of depreciation. The total cot of the building (original cot of $6,552,000 le the Accumulated Depreciation of $4,550,000 pre-adjutment) divided by the new life of 35 year equal the annual depreciation amount of $188,514.29. The econd journal entry would therefore debit Building for $5,552,000 ($188,514.29 x 10 year) and credit Accumulated Depreciation for the same amount.

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The temperature of one furnace is 1,200°C and cools at a rate of 3.5°C per minute. The temperature of another furnace is 900°C and is heated at a rate of 0.5°C per minute. After how many minutes will the furnaces be the same temperature?

Answers

Answer:

525 minutes

Step-by-step explanation:

Let us find the temperature of each furnace after 't' minutes.

Furnace1:

Temperature in furnace1 is reducing at rate of 3.5°C per minute.

Rate of cooling after t minute = 3.5*t = 3.5t

We have to subtract 3.5t from 1200°C as it is cooling.

Temperature of furnace1 after 't' minutes = 1200 - 3.5t

Furance2:

Temperature in furnace2 is increasing at rate of 0.5°C per minute.

Rate of heating after t minute = 0.5*t = 0.5t

We have to add 3.5t from 900°C as it is getting heated.

Temperature of furnace1 after 't' minutes = 900 +0.5t

After some minutes, both furnace reach the same temperature.

              900 + 0.5t = 1200 - 3.5t

    900 + 0.5t + 3.5t = 1200

                           4t   = 1200 + 900

                           4t   = 2100

                             t =  2100 ÷ 4

                             [tex]\boxed{t = 525 \ minutes}[/tex]

100 POINTS! How many roots does the polynomial equation have?

0=x^3(x+3)(x−1)^2

Answers

Answer: There are none

Step-by-step explanation:

how do you prove an angle is a right angle when the other 2 angles are complementary in a triangle theorem

Answers

The two non-right angles in a right angled triangle balance each other out because the right angle already takes up 90 degrees of the triangle's 180 total angles. We refer to two angles as complementing each other when their sums equal 90 degrees.

The right angle, or 90°, is always one angle. The hypotenuse is the side with the 90° angle opposite. The longest side is always the hypotenuse. The sum of the other two inner angles is 90 degrees. Base and perpendicular are the names of the other two sides that are close to the right angle. The Pythagorean Theorem is a triangle formula.

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Prove that circle A with center (1, 1) and radius 4 is similar to circle B with center (–4, –2) and radius 3

Answers

Since they are not the same, they are not the exact same circles.  In other words they are similar.

Since the center point does not affect the size of the circle.

Now, According to the question:

Figures can be proven similar if one, or more, similarity transformations

reflections, translations, rotations, dilations can be found that map one

figure onto another.

To prove all circles are similar, a translation and a scale factor from a

dilation will be found to map one circle onto another

Lets solve the problem

Circle A has center (1 , 1) and radius 4

The standard form of the equation of the circle is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex] , where (h , k) are the coordinates the center

and r is the radius

Equation circle A is [tex](x -1)^2 + (y - 1)^2 = (4)^2[/tex]

Equation circle A is : [tex](x -1)^2 + (y - 1)^2 = 16[/tex]

[tex]x^{2} +1-2x+y^2+1-2y=16\\\\x^2 +y^2-2x-2y+2=16\\\\x^2 +y^2-2x-2y-14=0\\\\x^2+y^2= 14+2x+2y[/tex]

Circle B has center (-4 , -2) and radius 3

Equation circle B is [tex](x - (-4))^2 + (y - (-2))^2 = (3)^2[/tex]

Equation circle B is [tex](x +4)^2 + (y +2)^2 = 9[/tex]

[tex]x^2+16+8x+y^2+4+4y=9\\\\x^{2} +y^2+20+8x+4y=9\\\\x^2+y^2+8x+4y+11=0[/tex]

By comparing between the equations of circle A and circle B

As you can see, if we try to equate the [tex](x^2 + y^2)'s[/tex], the values of them are not the same.  Since they are not the same, they are not the exact same circles.  In other words they are similar.

You can also compare the radii as well, since the center point does not affect the size of the circle.

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A persons blood has a pH of 7.371 and a carbonic acid concentration of 1.5, Approximate the concentration of bicarbonate in the persons blood.

Answers

Answer: The pH of blood is a measure of its acidity or basicity and is related to the concentration of hydrogen ions (H+) in the blood. The pH of 7.371 indicates that the blood is slightly basic. Carbonic acid (H2CO3) is a weak acid that dissociates into bicarbonate (HCO3-) and hydrogen ions (H+) in water. The carbonic acid concentration of 1.5 indicates the concentration of H2CO3 in the blood.

The concentration of bicarbonate (HCO3-) in the blood can be approximated by using the relationship between the pH, carbonic acid concentration and the bicarbonate concentration. The Henderson-Hasselbalch equation, which relates the pH and the pK of a buffer, to the ratio of the buffer's conjugate base to its acid form is:

pH = pK + log [HCO3-]/[H2CO3]

The pK of carbonic acid is 6.1 and the concentration of H2CO3 is given as 1.5.

Plugging these values into the Henderson-Hasselbalch equation,

7.371 = 6.1 + log [HCO3-]/1.5

Solving for [HCO3-],

[HCO3-] ≈ 25.8 mM

The approximate concentration of bicarbonate (HCO3-) in the person's blood is 25.8 mM.

Please note that this is an approximation, the actual value may vary depending on the person's health condition.

Step-by-step explanation:

1. The expression that represents the mass of an atom is:
a) p+ + n
b) e- + n
c) p+ + e-
d) p+ + e. + n​

Answers

Answer:

It is the a) p+ + n

Step by step explanation:

[tex] \large\boxed{ \bold{A=p^{+}+n}}[/tex]

Protons are used since they do not change, otherwise with electrons, of which some elements can give or receive them.

HELP!!!!!!
50 POINTS

Answers

Answer:

see explanation

Step-by-step explanation:

1

20% of 35

= [tex]\frac{20}{100}[/tex] × 35

= 0.2 × 35

= 7

(2)

60% of 70

= [tex]\frac{60}{100}[/tex] × 70

= 0.6 × 70

= 42

(3)

45% of 80

= [tex]\frac{45}{100}[/tex] × 80

= 0.45 × 80

= 36

Answer:

busy work lol. its = not smart

Step-by-step explanation:

Factored form of 6+27 using GCF

Answers

The factored form of 6 + 27 is 3(2 + 9) using GCF.

What is GCF?

The greatest common factor, which is the product of two or more numbers, is the biggest number (GCF). A natural number is created by dividing them by the biggest number (factor). There are a few factors that both share once all the number's components have been identified. The greatest common factor is the one with the largest number among the common factors. The highest common factor is another name for the GCF (HCF)

The given expression is:

6 + 27

Take the factors of the individual numbers:

6 = 1, 2, 3, 6

27 = 1, 3, 9, 17

Take the common factor from both the numbers, in this case it is 3.

Now, factor out the number from the given expression:

6 + 27

3(2 + 9)

Hence, the factored form of 6 + 27 is 3(2 + 9) using GCF.

Learn more about GCF here:

https://brainly.com/question/11444998

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[tex]\frac{1}{4}b[/tex]+ [tex]\frac{1}{4}[/tex]=[tex]-\frac{1}{2}[/tex]
Solve for bb. Express your answer as a proper or improper fraction in simplest terms.

Answers

The fraction 1/4b + 1/4 = -1/2 is simplified to b = -12/4

What is a fraction?

A fraction can be defined as the part of a whole variable, or number.

The types of fractions are;

Mixed fractionsProper fractionsImproper fractionsComplex fractionsSimple fractions

From the information given, we have that;

1/4b + 1/4 = -1/2

Now, collect iike terms

1/4b = -1/2 - 1/4

find the lowest common denominator

1/4b = -2 -1 /4

Add the numerators

1/4b = -3/4

Now, divide both sides by the coefficient of b

b = -3/4 × 4/1

Multiply the values

b =-12/4

Hence, the value is - 12/4

Learn about fractions here:

https://brainly.com/question/11562149

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