Terry takes a 800 mg Tylenol for his headache. Every hour that the Tylenol is in his system, a quarter of the medication dissolves in his body.

1. WRITE a function that models the amount of Tylenol in Terry’s body over time. Use x for hours, and y for the amount of Tylenol, in mg, remaining in the body.


2. When there is less than 100mg of medicine left in the body, it safe to take it again. HOW LONG will it take before Terry can take more medicine?

To solve the equation 3/4x + 3 - 2x = -1/4 + 1/2x + 5, we first need to simplify both sides by combining like terms:

3/4x - 2x + 3 = -1/4 + 1/2x + 5

Next, we can simplify the fractions on the right side by finding a common denominator of 4:

3/4x - 2x + 3 = -1/4 + 2/4x + 20/4

Simplifying the right side further, we get:

3/4x - 2x + 3 = 19/4 + 1/2x

Now we can isolate the variable x by moving all the terms containing x to one side of the equation and all the constants to the other side:

3/4x - 2x - 1/2x = 19/4 - 3

Combining like terms:

-5/4x = 5/4

Finally, we can solve for x by multiplying both sides by the reciprocal of -5/4:

x = -1

Therefore, the solution to the equation is x = -1.

The inequality used to determine the maximum number of days Miguel can afford to rent while staying within his budget is 202.5 + 36.39x ≤ 480.

What is an inequality?

An inequality is a comparison between two or more mathematical expressions. It can be of the form ≤, ≥, < or >.

We are given per day charges as $36.39 and the charges per mile as $0.90.

Also, it is given that in total 225 miles have been driven.

So, the charges of 225 miles are:

⇒225 x 0.90

⇒$202.5

It is given that he can spend maximum $480.

So, for the maximum number of x days, we get the inequality as

202.5 + 36.39x ≤ 480

Hence, the inequality used to determine the maximum number of days Miguel can afford to rent while staying within his budget is

202.5 + 36.39x ≤ 480.

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The height of the skyscraper is 201.49 meters.

Height is the measurement of an item in the vertical direction, whereas distance is the measurement of an object in the horizontal direction from a certain location.

Given that, Sadie is seeing a skyscraper making an angle of the elevation of 36°, she is 275 meters away from the skyscraper, we need to find the height of the skyscraper,

Using the concept of height and distance and trigonometric ratios,

Tan 36° = x / 275 [please refer to the figure attached]

x = 275 × Tan 36°

x = 199.80 meters

Therefore, the height of the skyscraper is x+1.69 = 199.80+1.69 = 201.45 m

Hence, the height of the skyscraper is 201.49 meters.

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The complete question is :-

From her eye, which stands 1.69 meters above the ground, Sadie measures the angle of elevation to the top of a prominent skyscraper to be 36. If she is standing at a horizontal distance of 275 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest hundredth of a meter if necessary.

The time it will take ;

a. 6 men is 1 hour

b. 5 men is 1 1/5 hours

c. 2 men is 3 hours

A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls. 0.25 are boys (by dividing 1 by 4)

If 3 men load for 2hours

1 will load for 2× 3 = 6hours

then;

a. for 6 men, they will load it for 6/6 = 1hour

b. for 5 men, they will load it for 6/5 = 1 1/5 hours

c for 2 men , they will load it for 6/2 = 3 hours

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The correct numerical expression for "12 times the sum of 5 and 25 minus 2" by simplification is option (b) , i.e 12 x (5 + 25) − 2.

Simplification means simplifying an expression by reducing it to a simpler form. Approximating means simplifying the formula to the nearest value, which is not exactly correct. 

BODMAS stands for Bracket, Off, Division, Multiplication, Addition, and Subtraction. BODMAS is used to describe the order of operations in formulas. In some areas, BODMAS is also known as PEDMAS. This represents parentheses, exponents, division, multiplication, addition, and subtraction. 

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Answer:

12 x (5 + 25) − 2

Step-by-step explanation:

hope this helps!

The base of the exponential function (1.75) is greater than 1, this represents exponential growth. As x increases, the value of the function will grow at an increasing rate.

Exponential growth is a mathematical concept that describes a process where a quantity grows at an increasing rate proportional to its current value. In other words, the larger the quantity, the faster it grows. This leads to a graph that is characterized by a rapid upward curve that becomes steeper and steeper over time.

Exponential growth is often represented by the equation y = abˣ, where y is the final amount, a is the initial amount, b is the growth factor or base, and x is the time or number of periods.

The function f(x) = a(1+r)ˣ represents exponential growth, where "a" is the initial value, "r" is the growth rate as a decimal, and "x" is the time variable.

In this case, the initial value is 50, and the growth rate is 75%, or 0.75 as a decimal. Therefore, the equation for the function becomes:

f(x) = 50(1+0.75)ˣ

Simplifying this expression, we have:

f(x) = 50(1.75)ˣ

Since the base of the exponential function (1.75) is greater than 1, this represents exponential growth. As x increases, the value of the function will grow at an increasing rate.

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Answer: If we let "the number of snakes" be represented by the variable "s", we can write the equation as:

s - 24 = 35

This can be simplified by adding 24 to both sides:

s = 59

Therefore, the number of snakes is 59.

Step-by-step explanation:

1) The volume of the first rectangular prism is 175 ft³

2) The volume of the second rectangular prism is 60ft³

3) The volume of the third rectangular prism 140ft³

4) The volume of the Fourth rectangular prism 216ft³

Note that in order to find the volume of area of a complex figure, you must deconstruct it into manageable proportions.

Shape 1 above, we deconstructed the rectangular prism into two 3 dimensional shapes with the following metrics:

a)

Length = 7ft

Height = 2ft

width = 2ft

Volume = Volume = 7ft x 2ft x 2ft

Volume = 28  ft³

b)

Length = 7ft

Height = 3ft

width = 7ft

Volume = 147 ft³

Total Volume = 28  ft³ + 147 ft³

Volume for Shape 1 = 175 ft³

In shape 2 above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:

a) Length = 3ft

Height = 2ft

width = 1ft

Volume = 6 ft³

b) Length = 6ft

Height = 3ft

width = 3ft

Volume = 54 ft³

Thus, total volume for shape 2 is:

Volume = 6 + 54

Volume = 40 ft³

Shape 3, above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:

a) Length = 7ft

Height = 1ft

width = 2ft

Volume = 14ft³

b)

Length = 7ft

Height = 3ft

width = 6ft

Volume = 126ft³

Thus, the total volume for shape 3, =

Volume = 14ft³ + 126ft³

Volume = 140ft³

Shape 4, above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:

a) Length = 4ft

Height = 3ft

width = 2ft

Volume = 24 ft³

b) Length = 4ft

Height = 12ft

width = 4ft

Volume = 192 ft³

Thus, the total volume for Shape 4:

Volume =  24 ft³+ 192 ft³

Volume = 216ft³

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Lim initially had $5145, and he withdrew an additional $1040 from his bank account, so he had a total of:

$5145 + $1040 = $6185

Lim divided this total amount equally among his 5 sons, so each son would receive:

$6185 ÷ 5 = $1237

Therefore, each son would receive $1237.

The requried, Chloe originally had 68 marbles.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,

Let's assume that Chloe originally had "x" marbles.

According to the problem, Chloe added 36 marbles to her collection. This means that she now has x + 36 marbles.

And we also know that she now has a total of 104 marbles.

So, we can set up an equation:

x + 36 = 104

To solve for x, we can isolate x on one side of the equation by subtracting 36 from both sides:

x + 36 - 36 = 104 - 36

x = 68

Therefore, Chloe originally had 68 marbles.

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The equations that gives true value for x = -2 and x = 2 are option A: x² - 4 = 0 and option D: 4x² = 16.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The equations that are true for x = -2 and x = 2 are -

x² - 4 = 0 (when x = -2, this becomes 4 - 4 = 0; when x = 2, this becomes 4 - 4 = 0)

4x² = 16 (when x = -2, this becomes 4(4) = 16; when x = 2, this becomes 4(4) = 16)

The other options are not true for x = -2 and x = 2.

Specifically -

x² = -4 is not true for any real value of x, since the square of any real number is always non-negative.

3x² + 12 = 0 is not true for x = -2 or x = 2, since plugging in these values gives 12 ≠ 0.

2(x - 2)² = 0 is only true for x = 2, but not for x = -2, since plugging in x = -2 gives 2(16) ≠ 0.

Therefore, the options x² - 4 = 0 and 4x² = 16 are the correct ones.

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The cardinality of (B ⋃ C) will be n(B ⋃ C)=3.

In mathematics, cardinality refers to the size or number of elements in a set. It is a concept used to compare the sizes of sets, regardless of their specific elements. For instance, the cardinality of the set {1, 2, 3} is 3, while the cardinality of the set {2, 4, 6, 8, 10} is 5. Cardinality is typically denoted using vertical bars, such that |S| represents the cardinality of set S.

Now,

The symbol "n(S)" represents the cardinality

To find the cardinality of the sets:

We have to see how many elements are there in (B ⋃ C) and

As we can see from Venn diagram there are 23 elements in (B ⋃ C) i.e.

5+3+1+2+4+8

Hence,

           The cardinality of n(B ⋃ C) will be 23.

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The number of different ways will be 108000.

Permutations are various ways to arrange things in a specific order. It can also be stated as the linear reordering of items in an already ordered set.

A first guess for the number of ways to select a committee consisting of 3 engineers, 2 physicists, and 2 computer scientists from 10 engineers, 5 physicists, and 6 computer scientists could be to simply multiply the number of ways to select each group separately:

10 choose 3 x 5 choose 2 x 6 choose 2

This would give us the number of ways to select 3 engineers out of 10, 2 physicists out of 5, and 2 computer scientists out of 6.

The number of ways can be,

N = ¹⁰C₃ x ⁵C₂ x ⁶C₂

N = 10 x 9 x 8 x 5 x 6 x 5

N = 108000

Therefore, the number of different ways will be 108000.

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The correct equation is P = (a x b) ÷ 43, 560

An equation is a mathematical statement that shows that two mathematical expressions are equal.

For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Given that, an agricultural research assistant, you often need to calculate the amount of pesticide needed for test fields.

For each acre, b pounds of pesticide are required.

1 acre = 43,560 ft²

Pesticide needed for each acre = b / 43,560

Pesticide needed for the given area = 43,560 (a x b)

Therefore,

P = 43,560 (a x b)

Hence, the correct equation is P = (a x b) ÷ 43, 560

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Therefore, the types of transformation and the value of k for each equation are: Horizontal compression by a factor of 1/2, k = 0. Vertical stretch by a factor of 2, k = 0. Horizontal stretch by a factor of 2, k remains the same as in f(x). Vertical compression by a factor of 1/2, k = 0.

Given by the question.

We can use the given table of values for f(x) and the transformed function g(x) to determine the type of transformation and the value of k for each equation.

g(x) = f(2x):

This is a horizontal compression by a factor of 1/2. The value of k is not affected by this transformation, so k remains the same as in f(x).

g(x) = 2f(x):

This is a vertical stretch by a factor of 2. The value of k is also multiplied by 2, so k = 2(0) = 0.

g(x) = f(1/2x):

This is a horizontal stretch by a factor of 2. The value of k is not affected by this transformation, so k remains the same as in f(x).

g(x) = 1/2 f(x):

This is a vertical compression by a factor of 1/2. The value of k is also divided by 1/2, so k = (0)/(1/2) = 0.

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After simplificatiοn οf the given expressiοn the factοr is 11. Thus, οptiοn b is cοrrect.

There is a need fοr mathematical οperatiοns like multiplying, splitting, adding, and even deleting. They wοuld result in the fοllοwing assertiοn if cοmbined: A mathematical fοrmula, sοme data, and an equatiοn A declaratiοn οf truth is made up οf values, elements, and mathematical οperatiοns like additiοns, erasures, algebraic expressiοns, and divisiοns. It is pοssible tο rate and analyze wοrds and sentences.

Here,

When we replace these in the statement, we get:

=[tex]\dfrac{(2^{10} \times 3^{10})(5^3 \times 11^3)(3^2 \times 5^2) }{(2^{10} \times 5^5)(3^{12})(11^{20})}[/tex]

= [tex]\dfrac{(11 \times 15^2) } {15^2}[/tex]

= 11

After simplificatiοn of the given expressiοn the factor is 11. Thus, οption b is correct.

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Answer:

C:  constant of proportionality is 5

Step-by-step explanation:

x       k       y

3       5        15

5       5        25

8       5        40

10      5        50

12      5        60

constant of proportionality (k) is 5.  All the rows check out.

y = kx = 5x

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{22\% of 72}}{\left( \cfrac{22}{100} \right)72}\implies 15.84~\hfill \underset{ new~price }{\stackrel{ 72~~ + ~~15.84 }{\text{\LARGE 97.84}}}[/tex]

Proportionately, if Lexi uses 360 g of flour, the quantity of blueberries she must use is 150 g of blueberries.

Proportion describes the two ratios equated to each other.

Proportions are fractional values between zero and one.

Recipe for making Blueberry Muffins

Ingredient  Quantity

Egg              1

Flour           120 g

Sugar         120 g

Butter          60 g

Blueberries 50 g

120 g of flour = 50 g of blueberries

The Ratio of flour to blueberries = 2.4:1

360 g of flour = 360/120 x 50

= 150 g of blueberries (360/2.4)

Thus, if Lexi uses 360 g of flour, based on the given recipe, she must use 150 g of blueberries.

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The values of f(-10) = 20101 , f(2) = 17 , f(3) = 142.

An expression consisting of variables, coefficients, and non-negative integer exponents is known as polynomial. For example, 2x² + 3x - 5 is a polynomial with three terms. The highest exponent of the variable is the degree of a polynomial. Polynomials can be used to represent many mathematical and scientific concepts, such as curves and functions.

To find f(-10), we need to substitute -10 for x in the given polynomial:

F(-10) = 2(-10)⁴ + (-10)²-10(-10) + 1

= 20000+100+100+1

= 20101

To find f(2), we again substitute 2 for x in the polynomial:

F(2) = 2(2)⁴ + (2)² -10(2) + 1

= 32+4-20+1

= 17

To find f(3), we can use synthetic division with 3 as the divisor. The coefficients of the polynomial are 2, 0, 1, -10, and 1.

F(3) = 142

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There are only one solution  x= 1/2 in the expression.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.\

Given that;

The expression is,

⇒ 8x - 4 = 3 - 6x

Now, We can simplify the expression as;

⇒ 8x - 4 = 3 - 6x

Add 6x both side,

⇒ 8x + 6x - 4 = 3 - 6x + 6x

⇒ 14x - 4 = 3

Add 4 both side,

⇒ 14x - 4 + 4 = 3 + 4

⇒ 14x = 7

Divide by 14;

⇒ x = 7/14

⇒ x = 1/2

Thus, There are only one solution  x= 1/2 in the expression.

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Answer: I think its true

explanation: Correct me if im wrong ty!

Answer: 5/7 of the kids chose New York or L.A.

Step-by-step explanation:

All you need to do in this problem is add the fraction of people that chose New York and the fraction of people that chose L.A:

4/7 + 1/7 = 5/7

The total cost of Joeli's purchases is $45.35.

What is the addition?

Addition is a mathematical operation that combines two or more numbers or quantities to produce a sum. It is one of the four basic arithmetic operations, along with subtraction, multiplication, and division. In addition, the numbers being combined are called addends, and the result is called the sum. The addition operator is represented by the symbol "+".

To find the total cost of Joeli's purchases, we need to add the cost of the helmet to the cost of the elbow pads:

Total cost = helmet cost + elbow pads cost

Total cost = $27.57 + $17.78

Total cost = $45.35

Therefore, the total cost of Joeli's purchases is $45.35.

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The value of the function g(x + a) - g(x) is a(-2x - a + 5).

To find the value of function g(x + a) - g(x), we first need to substitute g(x + a) and g(x) into the expression and simplify:

g(x + a) - g(x) = [- (x + a)^2 + 5(x + a)] - [-x^2 + 5x]

= [-x^2 - 2ax - a^2 + 5x + 5a] - [-x^2 + 5x]

= -x^2 - 2ax - a^2 + 5x + 5a + x^2 - 5x

= -2ax - a^2 + 5a

= a(-2x - a + 5)

Therefore, the value of g(x + a) - g(x) is a(-2x - a + 5).

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Answer:

A. (1,2), (2,4), (3,6), (4,8)

Step-by-step explanation:

The 1st number in parenthesis is the number of boxes of popcorn. The 2nd number is the cost.

In response to the aforementioned query, we may say that here, the exponent is [tex](x^2)^5 / (x^3)^2[/tex] = [tex]x^n[/tex] =>  [tex]x^4 = x^n[/tex] =>  so, n=4

Exponentiation, sometimes referred to as "b raised to the nth power," is a mathematical operation that includes two numbers: a base number, b, and an exponent, or power, n. It is represented by the sign bn. A number's exponent reveals how many times it has been multiplied by itself. For instance, the number 2-3 (written as 23) means 2 × 2 x 2 = 8. 2 + 3 = 6 does not equal 23. Remember that an integer multiplied by one equals itself. Exponents are a method for expressing large numbers as powers. The amount that shows how many times a number has been multiplied by itself is called an exponent. As an example, multiplying 6 by 4 results in 6 x 6 x 6.

here, the exponent is

[tex](x^2)^5 / (x^3)^2[/tex] = [tex]x^n[/tex]

[tex]x^{10} / x^{6}[/tex]

[tex]x^{10 - 6}[/tex]

[tex]x^4 = x^n[/tex]

so, n=4

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Answer:

look in the comments have a good day