A pharmaceutical scientist studying two medications wonders how long different amounts of each medicine stay in someone's bloodstream. The amount of time (in hours) one medication stays in the bloodstream can be modeled by f(x)=-1.25\cdot \ln{\left(\dfrac{1}{x}\right)}f(x)=−1.25⋅ln( x 1 ​ )f, left parenthesis, x, right parenthesis, equals, minus, 1, point, 25, dot, natural log, left parenthesis, start fraction, 1, divided by, x, end fraction, right parenthesis, where xxx is the initial amount of the medicine (in milligrams). The corresponding function for the other medication is g(x)=-1.8\cdot\ln\left(\dfrac{2.1}{x}\right)g(x)=−1.8⋅ln( x 2.1 ​ )g, left parenthesis, x, right parenthesis, equals, minus, 1, point, 8, dot, natural log, left parenthesis, start fraction, 2, point, 1, divided by, x, end fraction, right parenthesis. Here are the graphs of

The value of exponential 4 is 4^4, or 256. it means that 4 should be multiplied by itself 4 times.

In mathematics, an exponential is a number that is multiplied by itself a certain number of times. For example, when 4 is used as an exponential, it means that 4 should be multiplied by itself 4 times. This is written as 4^4, or 4 to the fourth power. This means that 4 is multiplied by itself 4 times, resulting in the value of 256.

Exponentials can be used to calculate the power of a number. For example, in the case of 4^4, 4 is the base number and 4 is the exponent. An exponent is the number of times a base number is multiplied by itself. In this case, the base number (4) is being multiplied by itself 4 times, resulting in a value of 256.

In addition, exponentials can be used to solve equations. For example, if we need to solve for x in the equation 4^x = 256, we can use the exponential 4 to determine the value of x. In this case, x = 4 because 4^4 = 256.

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Therefore , the solution of the given inequality problem comes out to be

-8/5.

The equation-like form of the expression 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequality. This shows that the left part, 5x 4, is bigger than the right part, 2x + 3. Finding the x variable values for which the inequality holds true is what we are most interested in.

Here,

Give:

=> -3(2x+2) < 10

=>2x+2>10/3

=>x+1>-10/6

=>> -10/6-1 >1

=> -8/5

Therefore , the solution of the given inequality problem comes out to be

-8/5..

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This may be computed by dividing his hitting % by the number of times he bats (20). (0.8). 20 x .8 = 16

Percentage:

a: a part of a whole expressed in hundredths a high percentage of students attended.

b: the result obtained by multiplying a number by a percent the percentage equals the rate times the base.

c: a share of winnings or profits.

If Henrie hits 80% of the time he's at bat, and he is up to bat 20 times this weekend, he is expected to hit 16 times. This can be calculated by multiplying the number of times he is up to bat (20) by his hitting percentage (0.8). 20 x .8 = 16

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The 0 = 0 in the solution to the system implies that the system of equations involving the equations 6x - 5y = -8 and 6x - 5y = -8 have infinitely many solutions.

Linear equations are equations that have constant average rates of change, slope or gradient.

A system of linear equations is a collection of at least two linear equations.

here, we have,

In this case, the system of equations is given as

6x - 5y = -8

6x - 5y = -8

Subtract the equation 6x - 5y = -8 from the equation 6x - 5y = -8

6x - 5y = -8

(-) 6x - 5y = -8

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

0 = 0

This in other words means that the difference between both equations is 0.

When the solution to a system of equation is 0 = 0, it means that the system of equations have infinitely many solutions.

Hence, the 0 = 0 in the solution to the system implies that the system of equations involving the equations 6x - 5y = -8 and 6x - 5y = -8 have infinitely many solutions.

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On adding the integers we get:

The collection of whole numbers and negative numbers is known as an integer in mathematics. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions.

For, (-78) + (98)

Step 1: Locate the first number, which is -78.

Step 2: Locate the second number, which is 98.

Step 3: Add the two numbers together by starting with the first number and counting up or down according to the sign of the second number. In this case, 98 is positive, so we count up 98 from -78.

Step 4: The answer is 20

Similarly, solving for the rest of the sub-parts we get:

2. 45+23=68

3. 67+56=123

4. 98 + (-73)=25

5. -971+237= -734

Therefore, On adding the integers we get:

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The graph of the following coordinates can be graphed by plotting the points of given coordinates on the graph.

Coordinates are a pair of integers (also known as Cartesian coordinates), or occasionally a letter and a number, that identify a specific point on a grid, also known as a coordinate plane.

A point is a dot on a sheet of paper or in a plane. There are no lengths, widths, or heights in a point. It establishes a plane's position or location.

Plot the points according to the given coordinates. Connect all the points with with a smooth curve.

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Answer:

a. $2908.93

Step-by-step explanation:

We use the formula:

A = P( 1 + r)^t

P = $1986

r = 4% = 0.04

t = 23 years

Let's solve

A = 1986(1 + 0.04)^23

A = 1986( 1 + 0.04)

A = 1986( 1.04)^23

A = $4894.925

Now we take

$4894.925 - $1986 = $2908.925

$2908.925 round-up =  $2908.93

So, the answer is A

Answer:3520.000

Step-by-step explanation:

ft/min =mph * 88.00000

ft/min =40 * 88.00000

ft/min =3520.000

A) The standard equation of the circle, with center at (f, g) and a point on the circle at (x, y) is; (x - f)² + (y - g)² = h²

B) The domain and range of the circle are respectively;

[-5, 11] and [-9, 7]

C) Yes the point (10, –4) is inside the border of the circle

A) Using the Pythagorean theorem will generate the equation for a circle as follows;

Sum of squares of sides = square of hypotenuse

From the given image, we have;

(x - f)² + (y - g)² = h² . . . . . . circle centered on (f, g) with radius h

B) The circle is defined for values of x in the domain f ± h, and for values of y in the range g ± h.

Domain: 3 ± 8 = [-5, 11]

Range: -1 ± 8 = [-9, 7]

C) The distance from point (10, -4) to (f, g) calculated as;

h² = (10 - 3)² + (-4 - (-1))²

h² = 7² + (-3)²

h²  = 49 + 9 = 58

h = √58 < 8

Thus, the distance to the point is less than h=8 and it implies that the point is inside the circle.

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The base in the exponential function is greater than 1 because exponential growth is defined as a constant multiplication of the original value, rather than a constant addition as in linear growth. A base greater than 1 results in a growth rate that increases over time, while a base less than 1 results in a growth rate that decreases over time.

The exponential function is written as bˣ, where b is the base and x is the exponent. The base is the number that is being multiplied by itself a certain number of times, as determined by the exponent.

A base greater than 1 means that the value of the function is increasing at an increasing rate. This is because as the exponent (x) increases, the base (b) is being multiplied by itself more and more times, leading to a larger and larger result. This is known as exponential growth.

On the other hand, a base less than 1 means that the value of the function is decreasing at an decreasing rate. This is because as the exponent (x) increases, the base (b) is being multiplied by itself more and more times, leading to a smaller and smaller result. This is known as exponential decay.

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To find the equation of a graphed line, find the y-intercept and the slope in order to write the equation in y-intercept (y=mx+b) form. Slope is the change in y over the change in x.

Linear equations with two variables have straight line graphs. There are numerous ways to express linear equations:

Slope-Intercept Formula: y=mx+b

The slope is m and the y-intercept is the point in an equation of the type y = mx + b, such as y = 2x 3. (0, b). Create a table of values (Method 1) or use the slope and y-intercept (Method 3) to graph equations of this kind (see Examples 1 and 6).

Basic Formula: axe + by = c

Find the x- and y-intercepts (Method 2) to graph equations of this type, such as 3x 2y = 6, or solve the equation for y to form y = mx + b and create a table of numbers (see Example 2).

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Inequality is a situation in which people do not have the same rights, resources, or opportunities. It can be seen in many aspects of society, including income, education, health care, and access to resources.

Inequality affects people in many different ways. It can limit access to education and employment opportunities, as well as health care, good housing, and basic services.

It can also lead to disparities in income and wealth, which can further limit opportunities for those in disadvantaged social classes. Inequality can have a negative impact on individuals, as it can limit their ability to access resources needed for a better life.

It can also lead to social unrest, as people may feel that they are not being treated fairly. Inequality can also lead to a lack of trust in government and institutions, which can further hinder progress and development. In order to reduce inequality, governments, businesses, and individuals must work together to create a more equitable society.

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In a 45°−45°−90° triangle, the length of the hypotenuse is √2 times the length of a leg.

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The perimeter of the square is calculated to be (8 - x) cm

The perimeter of a square is calculated using the formula

= 4 * length

From the problem we have that the length of the square

= 1/4 length of rectangle

perimeter of rectangle

8 = 2(Length + width)

dividing through by 2

4 = L + w

substituting w = x

8 = L + x

L = 8 - x

length of square = 1/4 * 8- x = (8 - x)/4

perimeter of a square = 4 *  (8 - x)/4

perimeter of a square = 8 - x

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On solving the provided question, we can say that  using properties of triangle, the value of x is 7.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

By using the property of triangle,

The exterior angle of the triangle is the sum of opposite two angle of the triangle.

Hence,

64 + 8x  = 18x - 6

10x = 70

x = 7

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Negative of an image can be obtained by subtracting each pixel values from 1.

Pixel value is the numerical representation of a color in an image. It is the amount of brightness or darkness of a pixel in an image, usually ranging from 0 (black) to 255 (white). Pixel values are used to determine how an image should be displayed on a monitor or printed on a page.It is usually measure of brightness of pixel with the higher number indicating brighter pixel and lower number indicating darker pixel.

This can be done by subtracting the pixel values r and s from 1, so the new value of each pixel would be 1-r and 1-s. This process of subtracting each pixel value from 1 is known as “inverting”.

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a. We cannot calculate the probability, because we do not know the shape of the distribution.

b. The mean and standard deviation of the sampling distribution of x are 12 and 0.0566.

c. The shape of the distribution described in part b is symmetrical.

d. The probability that a random sample of 50 cans produces a sample mean amount of 11.9 ounces or less is 0.0386.

We do not know the shape of the distribution, so we cannot calculate the probability that a single randomly selected can contains 11.9 ounces or less. The question given have not told us that the distribution of individual cans was normal, and we cannot assume it is so; therefore, we cannot calculate its probability.

As given information the mean μx = 12.

And standard deviation σx = σ / √n = 0.4 / √50 = 0.566.

The shape of the distribution described in part b is symmetrical, because the two sides of the distribution are a mirror image of each other. Therefore, it is normal distribution.

Since the sample is large n = 50 and 50 > 30, so by CLT (Central Limit Theorem), the distribution of sample means is approximately normal N(12, 0.0566). So, P(x ≤ 11.9) = normalcdf (0, 11.9, 12, 0.0566) = 0.0386.

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Answer: 57

Step-by-step explanation:

1. Multiply 95 and 60

2. You get 5700, then you divide by 100

3. 5700/100 = 57

The solution set is (A) TV/RS = TQ/ RQ.

What is the similarity of the triangle?

If the measures of the corresponding sides of two triangles are proportional then the triangles are similar. Likewise if the measures of two sides in one triangle are proportional to the corresponding sides in another triangle and the including angles are congruent then the triangles are similar.

We have given,

Triangle QRS and triangle QTV are similar,

ΔQRS ≈ ΔQTV

If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar.

so, TV/RS = TQ/ RQ

Therefore, The solution set is (A) TV/RS = TQ/ RQ.

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No, the given statement 45 is a prime number is false statement as 45 represents the composite number.

As given in the question,

Given number is equal to :

45

Prime numbers represents such numbers which is having only two factors one and the given number itself.

Prime numbers does not get exactly divided by any other integer.

Factors of 45 are equals to :

1, 3, 5, 9, 15, 45

It represents 45 has more than two factors.

And number 45 exactly get divided by 3, 5, 9, 15 .

So it is not a prime number rather it represents the composite number.

Therefore, the given statement 45 is a prime number is false statement as 45 is a composite number.

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The arithmetic sequence function is c)f(n)=25 + 6(n-1).

What is arithmetic sequence?

An arithmetic sequence is one in which each phrase grows by adding or removing a certain constant, k. In a geometric sequence, each term rises by dividing by or multiplying by a certain constant k.

Here the given series 25,31,37,43,...

First term [tex]a_1[/tex]= 25

Now Common difference d = [tex]a_2-a_1[/tex]=31-25 = 6.

Now using arithmetic sequence formula,

[tex]f(n)=a_1+(n-1)d[/tex]

Here putting indicated value  [tex]a_1[/tex]= 25 and d=6

=> f(n) = 25 + (n-1)6

=> f(n) = 25 + 6 (n-1)

Hence the correct option is c)f(n)=25 + 6(n-1).

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Answer:

C. f(n)=25 + 6(n-1).

Step-by-step explanation:

got it right on test

Answer: 5 triangles

Step-by-step explanation:

we can take the circles out of the top scale and see that 2 triangles equal a square, so we see 2 squares on the bottom so that is 4 triangles plus one extra

The correct equation for this given situation is,

⇒ d = 9.5t + 11

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

Given that;

John is driving around town. When he reaches the gas station, he notes that he has traveled 11 miles.

And, He reaches home 2 hours later and notes that he has traveled 30 miles.

Now, Let d represents the distance and t represents the time, in hours

So we get;

Let the equation which model this situation,

⇒ d = a t + b

Where a and b are constant.

Let the gas station is the starting point.

So, at gas station t = 0 , d = 11

Hence,

⇒ 11 = 0 × a + b

⇒ b = 11

When he reaches home 2 hours later notes that he has traveled 30 miles.

And, with substituting with b = 20

⇒ 30 = 2 × a + 11

⇒2a = 30 - 11 = 19

⇒ a = 19/2 = 9.5

So, We get the equation,

⇒ d = 9.5t + 11

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This is equal to 0.04 plus 1.96 into root over 0.04 into 0.96 divided by 400 point. This is equal to 0.059, which is equal to 5.9 percent. Therefore, double 0 to 5.9 percent represent babies born with defect.

According to one research, 28 out of every 400 kids born in the globe suffer some form of serious birth problem. To execute a simulation based on this data, the easiest approach to assign random numbers is to use 00-06 (7%) to identify the newborns with birth abnormalities.

It is to be noted that:

The sum total of births is: 400

The sum of defective babies = 28

Hence, the fraction or ratio of this is:

28/400

= 7/100

= 7%.

The implication here is that that 07-99 (93%) will represent the babies without birth defects.

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Answer:

63kg x 2.2 = 138.6 pounds

138.6 pounds/14 = 9.9 stones

Step-by-step explanation:

Answer:

63kg×2.2=138.6 pounds

138.6 pounds/14=9.9

Marhall made 9 ales this week, earning a base of $186 plus $15 per ale. Vickie earned a base of $48 plus $18 per ale. Since both of them earned the same amount, we can set up the equations

Marhall made 9 ales this week.

Step by explanation

We can use an equation to solve this problem.

Let x = number of ales Marhall made

Marhall's Earnings = 186 + (15 x)

Vickie's Earnings = 48 + (18 x)

Since both of them earned the same amount, we can set up the equations and solve for x:

186 + (15 x) = 48 + (18 x)

15x = 138

x = 9

Therefore, Marhall made 9 ales this week.

Marhall made 9 ales this week, earning a base of $186 plus $15 per ale. Vickie earned a base of $48 plus $18 per ale.

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Time spend on science homework is 16 minutes and time spend on math homework is 48 minutes.

Two or more expressions with an Equal sign is called as Equation

Given that,

The time spend on math homework =  3 times time spend on science homework,

Also, total time spent on math and science both homework = 64 minutes.

Let time spend by Max on science homework is t minutes,

Then by given condition, time spend on math homework = 3t

Total time = 64 minutes

t + 3t = 64 minutes

4t = 64 minutes

Divide both sides by t

t = 16 minutes

Hence, Time spend on science homework is 16 minutes and time spend on math homework is 48 minutes.

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Answer:

Step-by-step explanation:

and 2.3333333333

Examples of inequalities are mathematical statements that compare two expressions and express the relationship between them using symbols such as "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to). Here are a few examples:  x + 2 > 5, |x - 2| < 4, sin(x) > 1/2, log2(x) > 3.

Linear Inequality: x + 2 > 5, this inequality states that x is greater than 3.

Quadratic Inequality: x^2 - 3x + 2 < 0, this inequality states that the value of the quadratic expression is less than zero.

Absolute value inequality: |x - 2| < 4, this inequality states that the absolute value of the difference between x and 2 is less than 4.

Rational Inequality: (x + 2)/(x - 3) < 0, this inequality states that the value of the rational function is less than zero.

Logarithmic Inequality: log2(x) > 3, this inequality states that the logarithm base 2 of x is greater than 3.

Trigonometric Inequality: sin(x) > 1/2, this inequality states that the sine of x is greater than 1/2.

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