If the amount of medication in the body decrease by a factor of 1/3 each hour , then the exponential function is y = 1.8(2/3)ˣ .
Let M = the initial amount of medication administered = 1.8 milliliters , and
Let y = the amount of medication remaining in the patient's body after x hours.
We know that the medication amount will decrease by a factor of 1/3 each hour, which means that after 1 hour, only (1-1/3) = 2/3 of the medication will remain, after 2 hours, only (2/3)² will remain, and so on.
So we can write the equation in exponential form as :
⇒ y = M × (1-1/3)ˣ
⇒ y = M × (2/3)ˣ ;
substituting the initial value as 1.8 ,
we get ;
⇒ y = 1.8 × (2/3)ˣ ;
where x = number of hours that have passed since the medication was administered.
Therefore , the exponential function for the situation is y = 1.8 × (2/3)ˣ .
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The given question is incomplete , the complete question is
Elizabeth is a nurse, and she just administered 1.8 milliliters of medication to one of her patients. Elizabeth knows that the amount of medication remaining in the patient's body will decrease by a factor of 1/3 each hour .
Write an exponential equation in the form y = a(b)ˣ that can model the amount of medication (y) , remaining in the patient's body after x hours .
A rectangle is 3/4 of a feet long and 5/12 of a feet wide. What fraction represents the area of the rectangle
The area of the rectangle can be expressed as a fraction by multiplying 3/4 and 5/12. The answer is 5/16, which represents the area of the rectangle.
1. Multiply the length and width of the rectangle: 3/4 x 5/12 = 15/48
2. Reduce the fraction to its simplest form: 15/48 = 5/16
3. The answer is 5/16, which represents the area of the rectangle.
To find the area of a rectangle, you need to multiply the length and width of the rectangle together. In this case, the rectangle is 3/4 of a foot long and 5/12 of a foot wide. To express the area as a fraction, you need to multiply the two fractions together. 3/4 x 5/12 = 15/48. Since 15 and 48 have a common factor of 3, the fraction can be reduced to its simplest form, 5/16. Therefore, the area of the rectangle can be expressed as 5/16. This fraction represents the area of the rectangle.
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The complete question is
A rectangle is 3/4 of a feet long and 5/12 of a feet wide. What fraction represents the area of the rectangle of a feet wide.
Amy ray Kim and jammel are on a Trivia team. They gained for correct answers and lose points for incorrect answers. During the contest, Amy gains 3 point, ray loses 4 point, Kim loses 2 points, and jammel gains 5 points. How many points does a team have at the end of the contest?
Answer:
2
Step-by-step explanation:
Amy +3
Ray -4
Kim -2
Jammel +5
So,
3 - 4 - 2 +5 = ?
Answer is 2 points.
How many solutions does the following system of equations have?
a. 1
b. Infinitely many
c. 0
d. Not enough information
The correct option is B, the system of equations has infinitely many solutions.
How many solutions does the system of equations has?When we graph a system of equations, the points where the graphs of the equations intercept are the solutions.
In this case we can see a single line graphed, which only can happen when both equations of the system represent the exact same line.
Then the graphs intercept at infinite points, thus, the system of equatios has infininitely many solutions.
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What is the period of the function f(x) shown in the graph?
Enter your answer in the box.
Basic
Answer:
Period is [tex]\mbox{\huge {\boxed{\pi }}}[/tex]
Step-by-step explanation:
Each gridline marker on the horizontal axis is π/4
The period of this function is the horizontal displacement at which the function starts to repeat itself
Looking at the function we see that the minimum value of the function is 1 and occurs first at -π/4 and then at 3π/4
So the period is 3π/4 - (-π/4) = 3π/4 + π/4 = (3/4 + 1/4)π = π
We could also double check this using another point of reference
let's take the peaks of the function
The first peak visible is at -3π/4 and the next peak at π/4
So the period = π/4 - (-3π/4) = π/4 + 3π/4 = π
The point A(2, 1) is a vertex of a square ABCD. M(5, 1) is the point of intersection of the
diagonals of the square. Find the coordinates of B, C and D. (Remember: The diagonals
of a square are equal in length and bisect each other at right angles.)
pls give serious answers!!
Answer:
Step-by-step explanation:
Since M is the point of intersection of the diagonals of the square, it is also the midpoint of both diagonals. This means that AM is equal to half the length of a side of the square and also bisects the angle formed by the two sides that it connects.
Let's call the length of a side of the square s. Then, the distance AM can be found using the Pythagorean theorem:
AM = sqrt((5 - 2)^2 + (1 - 1)^2) = sqrt(3^2 + 0^2) = sqrt(9) = 3
So, the length of a side of the square is 2 * AM = 2 * 3 = 6.
Next, we can use the length of a side and the coordinates of A to find the coordinates of B. Since AB is a side of the square and is 6 units long, we can find B by moving 6 units to the right of A:
B = (2 + 6, 1) = (8, 1)
We can also find the coordinates of C by moving 6 units up and 6 units to the left of A:
C = (2 - 6, 1 + 6) = (-4, 7)
Finally, we can find the coordinates of D by moving 6 units down and 6 units to the right of A:
D = (2 + 6, 1 - 6) = (8, -5)
So, the coordinates of the other vertices of the square are B = (8, 1), C = (-4, 7), and D = (8, -5).
C. a third bond is worth $100 and grows in value by 4 percent each year, but the interest is applied continuously, at every moment. The value of this bond after years is given by 100-Order the bonds from slowest growing to fastest growing. Explain how you know
We can order the bonds from slowest-growing to fastest-growing as:
First bond: fixed growth rate of $50 per year
Third bond: growth rate of 4% per year, compounded continuously
Second bond: growth rate of 6% per year, compounded annually
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To order the bonds from slowest growing to fastest growing, we need to compare their growth rates.
The first bond grows at a fixed rate of $50 per year, regardless of how long it is held.
So its growth rate is constant and does not change with time.
The second bond is worth $500 and grows at a fixed annual rate of 6%, so its value after one year will be:
Value after one year
= $500 + 0.06 x $500
= $530
After two years, its value will be:
Value after two years.
= $530 + 0.06 x $530
= $561.80
We can see that the second bond's growth rate is increasing over time since the increase in value each year is calculated as a percentage of the new value.
The third bond is worth $100 and grows at an annual rate of 4% that is applied continuously.
The formula for the value of a continuously compounded bond after t years = $100 x e^(0.04t)
where e is the mathematical constant approximately equal to 2.718.
After one year,
The value of the third bond.
= $100 x e^(0.04 x 1) = $104.08
After two years,
Value after two years
= $100 x e^(0.04 x 2)
= $108.24
We can see that the growth rate of the third bond is also increasing over time because the interest is being compounded continuously.
Now,
We can order the bonds from slowest-growing to fastest-growing as:
First bond: fixed growth rate of $50 per year
Third bond: growth rate of 4% per year, compounded continuously
Second bond: growth rate of 6% per year, compounded annually
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The number of calories consumed during a snack varies directly with the number of chocolates eaten. If Jodi eats 2 chocolates, she will consume 72 calories. How many calories will she consume if she eats 5 chocolates.
The required Jodi will consume 180 calories if she eats 5 chocolates.
What is directly Proportional?When two quantities are directly proportional, it indicates that if one increases by a specific percentage, the other also increases by the same percentage. As gas costs increase, the cost of food may as well as well.
According to question:We can use proportionality to solve this problem. Since the number of calories consumed varies directly with the number of chocolates eaten, we can write:
calories consumed / chocolates eaten = constant
Let's call this constant k. We can solve for k using the information given:
72 calories / 2 chocolates = k
k = 36 calories/chocolate
Now we can use this constant to find the number of calories Jodi will consume if she eats 5 chocolates:
calories consumed / chocolates eaten = k
calories consumed / 5 chocolates = 36 calories/chocolate
calories consumed = 5 chocolates * 36 calories/chocolate
calories consumed = 180 calories
Therefore, Jodi will consume 180 calories if she eats 5 chocolates.
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If each base angle in an isosceles triangle is 10 degrees larger then the vertex angle, find the measure of the vertex angle.Write the equation how to use to solve for the vertex angle?
The measure of the vertex angle is 53.3degrees, the equation is 3x+20=180.
What is an isosceles right angled triangle?It has two equal sides, and those two equal sides make 90 degrees (right angle) internally. The triangles on either side of the diagonals are isosceles and congruent.
Given;
Each base angle in an isosceles triangle is 10 degrees larger then the vertex angle.
The addition of the internal angles of triangle is 180
So, let vertex angle be x
The other two sides will be x+10,
x+x+10+x+10=180
3x+20=180
x=160/3
x=53.3
Therefore, the vertex angle of the triangle will be 53.3degrees.
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What is the equation of the line that is parallel to the line x = -2 and passes through the point (-5, 4)?
x = -5
x=4
y = -5
y = 4
The equation of the line that is parallel to the line x = -2 and passes through the point (-5, 4) is x = -5.
How do equations work?A mathematical statement that equates two algebraic expressions is known as an equation. The equal to (=) sign appears between the expression and an equation.
How do parallel lines work?Parallel lines are straight lines in the same plane that never cross each other.
The parallel lines have the same slope.
Given that,
Equation of the given line is x = -2
Any line parallel to this line will be in the form x = K, where K is a constant.
The line will pass through ( -5 , 4).
The line x = K will satisfy the point ( -5 , 4)
-5 = K
x = -5
Hence, the equation of the line that is parallel to the line x = -2 and passes through the point (-5, 4) is x = -5.
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what is the percent of the sugar in a syrup made of 10 kg of water and 15kg of sugar? I need answers now pls help
Answer:
Your answer is 60%.
Step-by-step explanation:
[tex]10 + 15=25[/tex] and [tex]\frac{15}{25}[/tex] [tex]=0.6[/tex] [tex]= 60[/tex]%
help i’m doing a test and i really need to know the answer! this is urgent
Answer:
(4-g) X 1.5
Step-by-step explanation:
a coordinator will select 4 songs from a list of 10 songs to compose an event's musical entertainment lineup. how many different lineups are possible?
There are [tex]10^{4}[/tex] = 10,000 different possible musical entertainment lineups that can be created from a list of 10 songs.
This is computed by using the formula for combinations without repetition, which is [tex]n^{r}[/tex], where n is the number of items in the list and r is the number of items to be selected. In this case, n = 10 and r = 4, which results in [tex]10^{4}[/tex] = 10,000.
It is important to note that this calculation does not take into account any repetitions of songs, so if the same song appears more than once in the list, then the actual number of possibilities could be less. For instance, if there is a list of 10 songs, but 5 of them are the same, then the number of possible lineups would be[tex]10^{4/5}[/tex]! = 800, taking into account the repetitions.
To illustrate this further, if we were to list all the possible lineups, then we would end up with 10,000 unique combinations of 4 songs. For instance, a possible lineup could be Song 1, Song 5, Song 8, Song 10. Another possible lineup could be Song 4, Song 7, Song 9, Song 10. This process could be repeated with any combination
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Factor out the Greatest Common Factor (GCF): 64d^(5)-24d^(2)
Answer: [tex]8d^{2} (8d^3 - 3)[/tex]
Step-by-step explanation:
8d^2 is the GCF for this binomial
five times a number is at most 15 what are the possible values for the number
Answer:
x <= 3 represents all values such as: -∞, -100, -4, -3, -2, -1, 0, 1, 2, 3.
Step-by-step explanation:
5x <= 15
Next, we'll solve for x by dividing both sides by 5:
x <= 3
So, the possible values for the number are any value less than or equal to 3, including negative numbers.
x <= 3 represents all values such as: -∞, -100, -4, -3, -2, -1, 0, 1, 2, 3.
4/3 divided by 1/4+2/5 divided by 1/4+4/15 divided by 1/4
On solving the provided question we can say that by bodmas ((4 / 3) / (1/4)) + ((2 / 5) / (1/4)) + ((4 / 15) / (1/4)) =8
what is BODMAS ?The acronym BODMAS helps children learn the hierarchy of math operations (the correct order for solving math problems). The acronym BODMAS is made up of the following terms:
B Bracket, O Degrees (Power/Exponent or Square Root), D Division, M Multiplication, A Addition, and S Subtraction. BODMAS is also known as PDMAS in some areas. It symbolizes exponents, division, multiplication, addition and subtraction. It also represents brackets. The BODMAS rule states that parentheses must be handled first, then powers or roots (that is, of), division, multiplication, addition, and finally subtraction. Known as BODMAS in India and the UK, PEMDAS is primarily used in the US. However, they are identical to each other. The parentheses, order, and order of addition, subtraction, multiplication, and division are the same for the two rules.
by bodmas
((4 / 3) / (1/4)) + ((2 / 5) / (1/4)) + ((4 / 15) / (1/4)) =8
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What is the area of this compound figure?
the answer is 66
its easy... you posted this as high-school... this is 6th grade work
Area is 69 km2
………..,……….
e
s
3
A shop sells cupcakes packed in different-sized boxes: small, medium
and large.
The table shows the number of cupcakes in each box.
Small
Medium
6 cupcakes
15 cupcakes
Large
24 cupcakes
The bakers in the shop fill 60 boxes.
40% of the boxes are medium, 35% of the boxes are small and the
rest are large.
How many cupcakes have been packed?
The total number of cupcakes packed is 846 cupcakes.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Let's first find out the number of boxes of each size:
40% of 60 boxes = 24 boxes are medium
35% of 60 boxes = 21 boxes are small
The remaining 60 - 24 - 21 = 15 boxes are large
Now we can calculate the total number of cupcakes packed:
24 boxes x 15 cupcakes per medium box = 360 cupcakes in medium boxes
21 boxes x 6 cupcakes per small box = 126 cupcakes in small boxes
15 boxes x 24 cupcakes per large box = 360 cupcakes in large boxes
Therefore, the total number of cupcakes packed is 360 + 126 + 360 = 846 cupcakes.
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You have a 6oz container and a 10oz container and a spout with unlimited water how do you measure exactly 8oz
Answer:
firstly, I would fill up the 10-oz glass with juice and use it to fill the 6-oz glass. This would leave me with 4 oz left in the 10-oz glass
Step-by-step explanation:
a motorist buys a 5litre can of gear oil.she uses 800ml.what percentage of oil has she used and what remains
Step-by-step explanation:
1000ml=1 litre
800 divided by(1000 multiplied by 5)=16%
Y less than 9 in algebra expression
Answer:
9 - y
Step-by-step explanation:
less than means Subtraction
HELP POLSSSSSSSSSSSSSSSSSSS
Answer:
The angle is 180°
Step-by-step explanation:
[tex]{}[/tex]
Answer: look at the image for the answer and solution
Step-by-step explanation:
if the expression x^(-3/4)y^-(-4/3)∜16x^2y^4 is written in the form ax^by^c, then what is the product of a, b and c?
The value of a, b, and c will be 2, -1/4, and 7/3, respectively. Then the product of a, b, and c will be - 7/6.
What is an equivalent?The equivalent is the expression that is in different forms but is equal to the same value.
The meaning of straightforwardness is simplifying something to accomplish or get a handle on while likewise making it somewhat less troublesome.
The expression is given below.
[tex]\rm \rightarrow x^{-3/4 } \cdot y ^{-(-4/3)} \cdot \sqrt[4]{16x^2y^4}[/tex]
Simplify the expression, then we have
[tex]\rm \rightarrow x^{-3/4 } \cdot y ^{-(-4/3)} \cdot \sqrt[4]{16x^2y^4}\\\\\rightarrow x^{-3/4 } \cdot y ^{(4/3)} \cdot (16x^2y^4)^{1/4}\\\\\rightarrow x^{-3/4 } \cdot y ^{4/3} \cdot 2x^{1/2}y\\\\\rightarrow 2 x^{1/2 - 3/4} \cdot y^{4/3 + 1} \\\\\rightarrow 2x^{-1/4} \ \cdot y^{7/3}[/tex]
The given expression is [tex]\rm ax^by^c[/tex]. Compare the expression with given expressions, then we have
a = 2, b = - 1/4, and c = 7/3
Then the product of a, b, and c is given as,
⇒ 2 x (-1/4) x (7/3)
⇒ - 7/6
The value of a, b, and c will be 2, -1/4, and 7/3, respectively. Then the product of a, b, and c will be - 7/6.
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ayuda ES URGENTE 911
Answer: B D I J M
Step-by-step explanation: you just gotta see if any of the two answers work an if they don’t it’s nethier!
What is the length of CD
Answer:
Three months to five years
Step-by-step explanation:
look it up
8q≥– 8 I need the answer pls
Answer:
=q > - 1
Step-by-step explanation:
8q > - 8
= 8q/8 > -8/8
=q > - 1.
in a certain culture of bacteria, the number of bacteria is increased sixfold in 10 hours. how long did it take for the population to double? [use the natural growth equation.]
To double, the population must increase by a factor of 2, which would take ln(2) / ln(6) = ln(2) / ln(6) * 10 hours = 2.817 hours.
To solve for the time it took for the bacterial population to double, we need to use the exponential growth formula:
[tex]N(t) = N_0 * e^{(kt)[/tex]
where N0 is the initial population, N(t) is the population at time t, k is the growth rate, and e is the base of the natural logarithm (approximately 2.71828).
Since the population is increased sixfold in 10 hours, we can set up the equation as:
[tex]N_0 * e^{(kt)} = 6 * N_0[/tex]
Taking the natural logarithm of both sides gives:
kt = ln(6).
Dividing both sides by k and using the fact that the natural logarithm of 2 is approximately 0.693,
ln(2) / ln(6) = ln(2) / ln(6) * 10 hours = 2.817 hours.
So it took approximately 2.817 hours for the population to double.
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find an obtuse angle, θ, such that 0 ≤ θ ≤ 2π and has the same sine as -275° (please explain)
The obtuse angle such that has the same sine as -275° is θ = 95°
How to find the angle θ?We want to find an obtuse angle (with a measure larger than 90°) in the range 0 ≤ θ ≤ 2π (or 0 < θ < 360°, after that we can change the units from degrees to radians) such that sin(θ) = sin(-275°)
First, remember that the sine function has a periodicity of 360°, then:
sin(-275°) = sin(-275° + 360°) = sin(85°)
Now we know that the sine function is symmetric around x = 90°
Then:
sin(90° + x) = sin(90° - x)
if we take x = 5° we will get:
sin(90° + 5°) = sin(90° - 5°)
sin(95°) = sin(85°) = sin(-275°)
Thus we can conclude that θ = 95°
That is the obtuse angle.
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Let f(x)=-5x^(3)-8x^(2)-4x+3 and g(x)=3x^(3)-2x^(2)-8x-4.
Find (F-G)(X) Find(f-g)(-1)
The value of (f - g)(-1) is 5.
What is a function?A 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,
f(x) = -5x³ - 8x² - 4x + 3
g(x) = 3x³ - 2x² - 8x - 4
Now,
(f - g)(x)
= f(x) - g(x)
= -5x³ - 8x² - 4x + 3 - (3x³ - 2x² - 8x - 4)
= -5x³ - 8x² - 4x + 3 - 3x³ + 2x² + 8x + 4
= -8x³ - 6x² + 4x + 7
Now,
(f - g) (-1)
Substitute x = -1.
= -8(-1)³ - 6(-1)² + 4(-1) + 7
= -8 x -1 - 6 - 4 + 7
= 8 - 6 - 4 + 7
= 8 - 10 + 7
= 15 - 10
= 5
Thus,
(f - g)(-1) = 5
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What are the coordinates of the point on the directed line segment from (1, 2)to(6,7) that partitions the segment into a ratio of 2 to 3?
Coordinates of the point on the directed line segment from (1, 2) to (6,7) that partitions the segment into a ratio of 2 to 3 are (3, 4).
Using proportions, it is found that the coordinates of the desired point are (2,2).
The first point is A(1, 2)
The second point is B(6, 7)
The desired point is C(x, y)
The point C partitions the segment AB into a ratio of 3 to 2, hence:
[tex]C - A = \frac{2}{5}(B - A)[/tex]
This proportion is applied using both the x and y coordinates of the points, hence:
[tex]x - 1 = \frac{2}{5}(6 - 1)[/tex]
x - 1 = 2
x = 3
Now, [tex]y - 2 = \frac{2}{5} (7 - 2)[/tex]
y - 2 = 2
y = 4
Therefore the coordinates of the points are (3, 4).
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Use the table to work out the values of a , b , c , and d. X y = 2 x + 1 − 3 a − 2 − 3 − 1 b 0 1 1 c 2 d a = b = c = d =
By Using the table to work out the values of a , b , c , and d. X y = 2 x + 1 − 3 a − 2 − 3 − 1 b 0 1 1 c 2 d a = b = c = d =
Therefore, The solutions are : a = -3, b = 0, c = 6, d = 9
Equation:
In mathematics, an equation is an expression that indicates equality of two expressions by connecting them with the equal sign = . The word "equation" and related words in other languages can have slightly different meanings. For example, in French an equation is defined as containing one or more variables, whereas in English a well-formed formula consisting of two expressions connected by an equal sign is an equation.
Given:
This table;
x y = 3x+3
-3 -6
-2 a
-1 b
0 3
1 c
2 d
To Find:
Values of a, b, c and d
Consider the 2nd row,
x = -2, y = a
Putting the values in the equation,
we get,
a = 3(-2) + 3
⇒ a = -3
Consider the 3rd row,
x = -1, y = b
Putting the values in the equation,
we get,
b = 3(-1) + 3
⇒ b = 0
Consider the 5th row,
x = 1, y = c
Putting the values in the equation,
c = 3(1) + 3
⇒ c = 6
Consider the 6th row,
x = 2, y = d
d = 3(2) + 3
⇒ d = 9
The final answer is,
a = -3, b = 0, c = 6, d = 9.
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