Using matrix inversion, the value of x and y are 1.104 and 39.704 respectively
What is the solution to the equationsThe system of equations can be written in matrix form as:
| -650 1 | | x | | 175 |
| 120 1 | | y | | 25,080 |
To solve for x and y, we can use matrix inversion to get:
| x | | -650 1 |^-1 | 175 |
| y | = | 120 1 | | 25,080 |
Using matrix inversion, we get:
| x | | -0.00016 0.00875 | | 175 | | 1.104 |
| y | = | 0.00476 0.00004 | | 25,080 | = | 39.704 |
Therefore, the solution to the system of equations is x = 1.104 and y = 39.704.
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Sets A and B are subsets of the universal set U.
These sets are defined as follows.
U= {f, k, m, q, x,y}
A={f, k, m, y}
B = {f, m,q}
Find the following sets.
Write your answer in roster form or as Ø.
(a) AUB' =
(b) A' B' =
(a) The union set is AUB'={f, k, m, x, y}.
(b) The union set is A'UB'={q,k, x, y}.
What is the union of two sets?The union of two sets is also a set. This set contains all the elements of both two sets.
The universal set is U= {f, k, m, q, x,y} and two subsets are A={f, k, m, y} and B = {f, m,q}.
(a)
B' is the complementary set of B. So, find the elements of B'=U-B.
B'= {f, k, m, q, x,y}-{f, m,q}
={k, x,y}
Now, find the union set AUB'.
AUB' ={f, k, m, y}U{k, x,y}
={f, k, m, x, y}
Therefore, the required answer is AUB'={f, k, m, x, y}.
(b)
Also, A' is the complementary set of A. So, find the elements of A'=A-B.
A'= {f, k, m, q, x,y}-{f, k,m, y}
={q,x}
Now, find the union set A'UB'.
A'UB' ={q,x}U{k, x,y}
={q,k, x, y}
Therefore, the required answer is A'UB'={q,k, x, y}.
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CJ has three more pet pigs than Jacqui has. Let’s write an expression to represent how many pigs CJ has. To do that, we follow these steps:
Identify the constants and the variables.
There is one known number or constant here: it is 3. CJ has 3 more pigs than Jacqui. That number, 3, won’t change. The variable is the number of pets Jacqui has. Let’s call that j.
Identify the operations.
The phrase “more than” tells us we need to add. There are no other operations in this expression.
Rewrite the phrase as an expression.
“Three more pet pigs than Jacqui has” is 3 + j.
Last year, Shailyn read four fewer books than Oswaldo. Which expression shows how many books Shailyn read last year?
Answer: Let's follow the same steps as in the previous example:
Identify the constants and the variables.
The known constant here is 4. Shailyn read 4 fewer books than Oswaldo. Let's call the number of books Oswaldo read "o".
Identify the operations.
The phrase "four fewer" tells us we need to subtract.
Rewrite the phrase as an expression.
"Four fewer books than Oswaldo" is o - 4.
So, the expression that shows how many books Shailyn read last year is o - 4.
Step-by-step explanation:
Can someone please help me do this
The vertices of the image of triangle ABC are A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4) and C''(x, y) = (- 4, 4).
How to determine the image of a triangle set on Cartesian plane
Any triangle can be generated by three points that are not collinear, in this problem we need to determine the image of a triangle, which is the result of two rigid transformations: (i) Reflection over the y-axis, (ii) Dilation centered at the origin with a scale factor of 2, whose definitions are shown below:
Reflection over the y-axis:
(x, y) → (- x, y)
Dilation centered at the origin with a scale factor of 2:
(x, y) → (2 · x, 2 · y)
If we know that A(x, y) = (3, 4), B(x, y) = (4, 2), C(x, y) = (2, 2), then the image of the vertices are determined below:
Reflection over the y-axis
A'(x, y) = (- 3, 4), B'(x, y) = (- 4, 2), C'(x, y) = (- 2, 2)
Dilation centered at the origin with a scale factor of 2
A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4), C''(x, y) = (- 4, 4)
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Which equation represents the graph?
a graph of a line that passes through the points 0 comma negative 1 and 1 comma negative 4
y equals negative one third times x minus 1
y = −3x − 1
y equals negative one third times x plus one third
y equals negative 3 times x plus one third
The equation that represents the graph of a line passing through the points (0, -1) and (1, -4) is y = -3x - 1.
What is graph?
A graph is a visual representation of data or information that shows the relationship between different variables or quantities. Graphs can take many forms, including bar graphs, line graphs, scatterplots, and pie charts, among others. They are widely used in many fields, including mathematics, science, economics, and social sciences, to help visualize and analyze data, identify patterns, and communicate findings to others in a clear and concise manner. By representing complex information in a simple, easy-to-understand format, graphs can provide valuable insights and help us make informed decisions.
The equation that represents the graph of a line passing through the points (0,-1) and (1,-4) is:
y = -3x - 1
To find the equation of a line given two points, you can use the slope-intercept form:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is one of the given points.
First, we can find the slope of the line:
m = (y2 - y1) / (x2 - x1)
= (-4 - (-1)) / (1 - 0)
= -3
Next, we can choose one of the given points and substitute its coordinates and the slope into the slope-intercept form:
y - (-1) = -3(x - 0)
y + 1 = -3x
y = -3x - 1
Therefore, the equation that represents the graph is y = -3x - 1.
Option A, y = -1/3x - 1, has a slope of -1/3, which is not the slope of the line passing through the given points.
Option C, y = -1/3x + 1/3, also has an incorrect slope of -1/3, and it also does not pass through the point (0,-1).
Option D, y = -3x + 1/3, has the correct slope of -3, but it does not pass through the point (0,-1).
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Xin is going to invest in an account paying an interest rate of 5.8% compounded annually. How much would Xin need to invest, to the nearest hundred dollars, for the value of the account to reach $2,290 in 16 years?
The amount that should be invested in order to have $2,290 in 16 years is $929.11.
What is compound interest?
The interest on a deposit calculated using both the initial principle and the accrued interest from prior periods is known as compound interest. In other words, compound interest is interest that is earned on interest.
Here, we have
Given: Xin will invest in an account paying an interest rate of 5.8% compounded annually.
Amount to invest = Future value / (1 + r)ᵗ
Where:
r = interest rate
t = time
X = $2,290 / (1 + 0.058)¹⁶
X = 2,290 / 2.46474
X = $929.11
Hence, the amount that should be invested in order to have $2,290 in 16 years is $929.11.
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The total cost (in dollars) of producing x food processors is C(x) = 2400 + 40x - 0.4^2
find the exact cost of producing the 31st food processor
From given quadratic equation:
Exact Cost of 31st food processor = $15.6
Approx. cost of 31st food processor = $15.2
What is a quadratic equation?
The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).
It is given that the quadratic equation has two roots. Roots might have either a real or imaginary nature.
The given quadratic equation for the cost of producing x food processors is:
C(x) = 2400 + 40x - 0.4x²
a) The exact cost of producing the 31st food PROCESSOR is:
cost of 31 food processors - cost of 30 food processors = C(31) - C(30)
= (2400 + 40*31 - 0.4*31²) - (2400 + 40*30 - 0.4*30²)
= 3255.6 - 3240 = $15.6
b) The marginal cost at x = 31
Differentiate the quadratic equation
C'(x) = 40 - 0.8x
Marginal cost = C'(31) = 40 - 0.8*31 = $15.2
So the cost of producing the 31st food processor is approx $15.2.
Therefore from the given quadratic equation:
Exact Cost of 31st food processor = $15.6
Approx. cost of 31st food processor = $15.2
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When you use the distance formula you are building a right triangle whose ___ connects two given points
Answer:
Step-by-step explanation:
When we use the distance formula for two points ( x, y ) and ( x', y¹ ) Then formula is (distance)² = (x - x¹)² + (y - y¹)² This is quite similar to the formula used in a right angle triangle
A car travels 55 mph and passes a truck travelling 50 mph. How long will it take the car to be
more than 23 mi ahead?
Answer:you never asked for like in what minutes or hours?
Step-by-step explanation:
The car, traveling at a speed 5 mph faster than the truck, will take more than 4.6 hours to be more than 23 miles ahead.
Explanation:This question pertains to relative speed. When the car is traveling at 55 mph and the truck at 50 mph, the car is effectively moving away from the truck at (55 mph - 50 mph) = 5 mph. To calculate the time it will take for the car to be more than 23 miles ahead, we can use the formula: Time = Distance/Speed. So the time it would take is Time = 23 miles / 5 mph = 4.6 hours. Therefore, it will take the car more than 4.6 hours to be more than 23 miles ahead.
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A positive integer is twice another. The difference of the reciprocals of the two positive integers is frac(1,10). Find the two integers.
The two integers are 5 and 10.
What do you mean by Integers?
An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.
Integer is a Latin word which means 'whole' or 'intact'. This means integers do not include fractions or decimals.
A number is positive if it is greater than zero, so it said to be positive integers
A number is negative if it is less than zero, so it said to be negative integers.
A number line is a visual representation of numbers on a straight line. This line is used for the comparison of numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally.
Given:
Let x be the positive number
2x be the other positive number
Find the first integer
[tex]\frac{1}{x} - \frac{1}{2x} = \frac{1}{10}[/tex]
[tex]\frac{2x - x}{2x^2} = \frac{1}{10}[/tex]
[tex]\frac{x}{2x^2} = \frac{1}{10}[/tex]
[tex]\frac{1}{2x} = \frac{1}{10}[/tex]
2x = 10
x = 5
Therefore, the first positive integer is 5.
Find the other integer
2x = 2(5) = 10
Therefore, the other integer is 10.
To check:
[tex]\frac{1}{x} - \frac{1}{2x} = \frac{1}{10}[/tex]
[tex]\frac{1}{5} - \frac{1}{10} = \frac{1}{10}[/tex]
[tex]\frac{2}{10} - \frac{1}{10} = \frac{1}{10}[/tex]
[tex]\frac{1}{10} = \frac{1}{10}[/tex]
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One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 4.4 cubic feet of water weigh in pounds? In tons?
Answer:
4.4 cubic feet of water weighs approximately 273.5016 pounds or 0.13676 tons.
Step-by-step explanation:
To find the weight of 4.4 cubic feet of water in pounds, we need to find the number of gallons it contains and then multiply it by the weight of one gallon of water.
1 cubic foot = 7.48 gallons
So, 4.4 cubic feet = 4.4 * 7.48 = 32.912 gallons
And the weight of 32.912 gallons of water in pounds is:
32.912 gallons * 8.33 pounds/gallon = 273.5016 pounds
To convert this weight to tons, we divide the weight in pounds by 2000:
273.5016 pounds / 2000 = 0.13676 tons
So, 4.4 cubic feet of water weighs approximately 273.5016 pounds or 0.13676 tons.
Sheldon wants to buy two shirts at the store.
They were each originally $14.99, but one of the shirts is on sale this week for 10% off.
A 6% sales tax is applied to the total cost of the shirts.
Sheldon writes an equation to calculate the total cost, n, of his purchase.
0.90 • 14.99 + 14.99 • 1.06 = n
Which statement describes Sheldon’s equation?
Responses
His equation correctly represents the total cost of his order.
According to his equation, the discount will be applied to both shirts.
According to his equation, sales tax will only be added to one shirt.
He should have multiplied the cost of the shirts by 0.0 to calculate tax.
His equation correctly represents the total cost of his order is the statement describes Sheldon’s equation
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Sheldon wants to buy two shirts at the store.
They were each originally $14.99, but one of the shirts is on sale this week for 10% off.
A 6% sales tax is applied to the total cost of the shirts.
0.90 • 14.99 + 14.99 • 1.06 = n
The first term in the equation, 0.90 • 14.99, represents the cost of the shirt that is on sale.
The 10% discount is applied to the original price of $14.99, which is why we multiply by 0.90.
This term calculates the discounted price of the first shirt.
The second term in the equation, 14.99 • 1.06, represents the cost of the second shirt, plus the 6% sales tax that is applied to both shirts.
This term calculates the total cost of the second shirt with sales tax.
Hence, His equation correctly represents the total cost of his order is the statement describes Sheldon’s equation
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Write an equation to describe the sequence below. Use n to represent the position of a term
In the sequence, where n = 1 for the first term.
-25, -50, -100,...
Write your answer using decimals and integers.
a,
Blank 1:
Blank 2:
Submit
C
C
An equation to show the sequence is -25n.
What is a geometric series?When all the terms of the geometric sequence are added, than that expression is known as geometric series.
The sum of terms of a geometric sequence;
Now, lets suppose its initial term is , multiplication factor will be r
and let it has total n terms, then, its sum is given as:
[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
We are given that;
The first term of sequence=-25
D= -50-(-25)
=-25
Now,
an = a + (n-1)d
=-25+(n-1)-25
=-25-25n+25
=-25n
Therefore, the answer of the sequence will be -25n.
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Find the value of X
Please help! Asap
Answer:
Step-by-step explanation:
Need help on algebra please
Answer:
Step-by-step explanation:
please help meee
here is the picture
Answer:
f(-2) = 46
f(-1) = 17
f(0) = 2
f(1) = 1
f(2) = 14
Step-by-step explanation:
F(-2) = 46
F(-1)= 17
F(0)= 2
F(1)= 1
F(2)= 14
PLEASE HELP!!! PLEASE IM BEGGING SOMEONE TO HELP ME GHIS IS DUE TOMORROW
Answer:
D
Step-by-step explanation:
It's the most random and produces no bias.
Answer:
D
Step-by-step explanation:
a restaurant uses square tables with sides of length 1.3m, and round tablecloths with diameter 2m. Determine the percentage of each tablecloth which overhangs its table.
Answer:
46.21%
Step-by-step explanation:
The area of the table top is 1.3 x 1.3 = 1.69 m²
The area of the circular tablecloth is given by πr² where r is the radius of the table cloth
Give diameter of tablecloth is 2m, radius r = 2/2 = 1 m
Area of tablecloth = π · 1² = π
So the excess area of the tablecloth which overhangs
= π - 1.69 = 1.45 m² (taking π = 3.14)
So the fraction of the tablecloth that overhangs
= Excess area of tablecloth ÷ total area of tablecloth
= 1.45 /π
= 0.4621
As a percentage this would be
0.4621 x 100
= 46.21%
Timothy, Laurence and Mike went to a bookstore to buy some books. The ratio of the number of books bought by Laurence and Mike were 2: 7. Timothy and Laurence bought a total of 20 books while Timothy and Mike bought a total of 35 books. How many books did Timothy buy?
Answer:
[tex]\mbox{\large \textsf{Timothy bought 14 books}}[/tex]
Step-by-step explanation:
Let's use first letters of names to represent the number of books bought by that person. This makes it easier to explain.
Therefore, the books bought by each of the three persons are T(imothy), L(aurence) and M(ike)
We will now convert each of the word description into math equations and solve
We are given that the ratio of the number of books bought by Laurence and Mike were 2: 7
We can write this as:
[tex]\dfrac{L}{M} = \dfrac{2}{7}\\\\[/tex]
Multiplying both sides by M:
[tex]L = \dfrac{2}{7}M\cdots\cdots(1)[/tex]
Timothy and Laurence bought a total of 20 books can be represented as
[tex]T + L = 20\cdots\cdots(2)[/tex]
Timothy and Mike bought a total of 35 books can be represented as
[tex]T + M = 35\cdots\cdots(3)[/tex]
Eq (3) - Eq (2):
[tex]T + M - (T + L) = 35 - 20\\\\T + M - T - L = 15\\\\M - L = 15 \cdots\cdots (4)[/tex]
Substituting for [tex]\displaystyle L = \frac{2}{7}M[/tex] from equation (1) into equation (4) we get
[tex]M - \dfrac{2}{7}M = 15\\\\\dfrac{5}{7}M = 15\\\\M = \dfrac{7}{5} \times 15\\\\M = 21\\\\[/tex]
Given [tex]\displaystyle M = 21[/tex] using equation (3), [tex]\displaystyle T + M = 35[/tex] we get
[tex]T + 21 = 35\\\\T = 35 - 21\\\\\textrm{or}\\\\T = 14[/tex](Answer)
If we wanted to find out how many books Laurence bought use Eq(1)
[tex]L = \dfrac{2}{7}M\\\\L = \dfrac{2}{7} \times 21\\\\L = 6\\\\[/tex]
The value of a motorcycle changes according to the equation V=5,000(1.03)t^, where V= value in dollars and t= time in years.
Use the dropdowns to complete the statements.
In the equation, the number 5,000 represents the ________ of the motorcycle. The value of the motorcycle is __________ at a rate of ________ per year.
In the equation, the number 5,000 represents the initial value of the motorcycle. The value of the motorcycle is increasing at a rate of 3% per year.
What are Exponential Functions?Exponential functions are functions where the independent variable, x is in the exponent.
The given exponential equation is,
V = 5,000 (1.03)^t
Here V represents the value of the motorcycle in t years.
When t = 0,
V = 5000 (1.03)⁰ = 5000
So 5000 represents the initial value of the motorcycle.
V = 5,000 (1 + 0.03)^t
At t = 0, V = 5000
At t = 1, V = 5000 (1.03)¹ = 5150
At t = 2, V = 5000 (1.03)² = 5304.5
So the value of the motorcycle is increasing.
The rate is 0.03 or 3%.
Hence, 5,000 represents the initial value of the motorcycle and the value of the motorcycle is increasing at a rate of 3% per year.
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2. What is the equation of the parabola that passes
through the points (-1,0), (7, 0) and (3,-16)?
3. What is the equation of the parabola that passes
through the points (-4,9), (-3, 2) and (0,-7) and (4,9)?
The equations of the parabolas are y = x² - 6x - 7 and y = x² - 7
How to determine the equation of the parabolasParabola 1
Given that
The points (-1,0), (7, 0) and (3,-16)
The equation is represented as
y = ax² + bx + c
So, we have
a - b + c = 0
49a + 7b + c = 0
9a + 3b + c = -16
Make c the subject in a - b + c = 0
c = b - a
So, we have
49a + 7b + b - a = 0
9a + 3b + b - a = -16
48a + 8b = 0
8a + 4b = -16
Multiply 8a + 4b = -16 by 2
48a + 8b = 0
16a + 8b = -32
Subtract
32a = 32
So, we have
a = 1
Recall that 48a + 8b = 0
So, we have
48 + 8b = 0
This gives
8b = -48
Divide
b = -6
Also, we have
c = b - a
This gives
c = -6 - 1
c = -7
So, the equation is
y = x² - 6x - 7
Parabola 2
Given that
The points (-4,9), (-3, 2) and (0,-7) and (4,9)
The equation is represented as
y = ax² + bx + c
So, we have
16a - 4b + c = 9
9a - 3b + c = 2
c = -7
16a + 4b + c = 9
The equations become
16a - 4b = 16
9a - 3b = 9
16a + 4b = 16
Add (1) and (3)
32a = 32
So, we have
a = 1
Subtract (1) and (3)
-8b = 0
So, we have
b = 0
So, the equation is
y = x² - 7
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Endpoints of a diameter are (−5,−11) and (−1,1) Find the standard form of the equation for the circle with the following properties.
Answer:
Standard form of the equation for the circle
(x + 3)² + (y + 5)² = 40
Step-by-step explanation:
The equation of a circle in standard form is
[tex]\boxed{(x - a)^2 + (y-b)^2= r^2}[/tex]
where (a, b) is the center of the circle and r is the radius
To find center of circle
The end points of the diameter are (-5, -11) and (-1, 1)
The center of the circle is midway between these two points
The x-coordinate of the midpoint = (-5 + -1)/2 = -6/2 = -3
The y-coordinate of the midpoint is (-11 + 1) /2 = -10/2 = -5
So the center of the circle is at (-3, -5)
To find the radius,
Calculate the distance from (-3, -5) to any of of the endpoints.
Let's take the endpoint (-1, 1) and find its distance from (-3, -5)
The distance between any two points (x₁, y₁) and (x₂, y₂) is calculated from the formula
[tex]d^2 = {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2[/tex]
Substituting
(x₁, y₁) = (-1, 1)
(x₂, y₂) = (-3, -5)
and r for distance
we get
[tex]r^2 = {(-3 - (-1))^2 + (-5 - 1)^2[/tex]
[tex]r^2 = {(-2)^2 + (-6)^2}[/tex]
[tex]r^2 = {{4} + {36}}[/tex]
[tex]r^2 = {40}[/tex]
So the center (a, b) is (-3, -5) and r² =40
Plugging this into the circle equation:
(x - (-3))² + (y - (-5))² = 40
(x + 3)² + (y + 5)² = 40
If the scale factor of figure A to figure B is 3:8 find x
x^{2}-2x+ and completing the square ( Algebra 2 )
x^2 - 2x + 1 is the required quadratic equation using the completing the square
Perfect square trinomials using the completing the square
Given the quadratic expression below
x^2 - 2x
We need to determine the constant that will make the expression a perfect square.
The constant will be the half of the square of coefficient of 'x'
Coefficient of 'x' = -2
Half of the coefficient of 'x' = -2/2 = -1
Square of the coefficient = (-2/2)^2
Square of the coefficient = 1
Hence the complete quadratic expression using the completing the square is x^2 - 2x + 1
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Counting back from 18, what number follows 17?
Answer:
16
Step-by-step explanation:
As the question states, we are counting downwards which means with every interval we are going back -1. Therefore, 17 - 1 = 16
estimate the population in the year 2040
well, in 2007 it was 12000, so initially that's what it was, and in 2019 it went to 23000, so that's 12 years later, and in 2040, that'll be 33 years later.
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 23000\\ P=\textit{initial amount}\dotfill &12000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &12\\ \end{cases} \\\\\\ 23000 = 12000(1 + \frac{r}{100})^{12}\implies \cfrac{23000}{12000} =\left(1+ \cfrac{r}{100} \right)^{12} \\\\\\ \cfrac{23}{12}=\left(\cfrac{100+r}{100} \right)^{12}\implies \sqrt[12]{\cfrac{23}{12}}=\cfrac{100+r}{100}[/tex]
[tex]100\sqrt[12]{\cfrac{23}{12}}=100+r\implies 100\sqrt[12]{\cfrac{23}{12}}-100=r\implies \boxed{5.57\approx r} \\\\[-0.35em] ~\dotfill\\\\ \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &12000\\ r=rate\to 5.57\%\to \frac{5.57}{100}\dotfill &0.0557\\ t=years\dotfill &\stackrel{year~2040 }{33}\\ \end{cases} \\\\\\ A \approx 12000(1 + 0.0557)^{33} \implies \boxed{A \approx 71782}[/tex]
An electric clock is stopped by a power failure. What is the probability that the second hand is stopped between the 4 and the 9?
Answer: the answer is 5/12
product p of three numbers x ,y,and z
Answer:
p = x(y)(z)
Step-by-step explanation:
product is multiplication.
multiplication has no specific order.
The vertex of this parabola is at (5,-4). Which of the following could be its
equation?
The possible equation of the parabola is y = (x - 5)^2 - 4
How to determine the possible equationfrom the question, we have the following parameters that can be used in our computation:
Vertex = (5, -4)
The vertex form of a parabola is given by:
y = a(x - h)^2 + k
where (h, k) is the vertex of the parabola and "a" is a constant that determines the shape of the parabola.
We are given that the vertex of the parabola is (5,-4). Substituting these values into the vertex form, we get:
y = a(x - 5)^2 - 4
Let a = 1
So, we have
y = (x - 5)^2 - 4
Hnce, the possible equation is y = (x - 5)^2 - 4
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Rob loaded 9 trucks in 1 hour find his loading speed per hour
Answer:
9 trucks/hour
Step-by-step explanation:
If he loaded 9 trucks in one hour, his loading speed is 9 trucks per hour.
A certain antihistamine is often prescribed for allergies. A typical dose for a 100-pound person is 22 mg every six hours. Complete parts (a) and (b) below.
b. This antihistamine also comes in a liquid form with a concentration of 12.3 mg/ 6 mL. Following the prescribed dosage, how much liquid antihistamine should a 100-pound person take in a week?
300.5 ml of antihistamine is needed for a 100-pound person to take in a week
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
1 day = 24 hours
1 week = 7 days = 24 hours per day * 7 days = 168 hours
A typical dose for a 100-pound person is 22 mg every six hours. Hence for one week:
Dosage in one week = (22 mg per 6 hours) * 168 hours = 616 mg
Antihistamine also comes in a liquid form with a concentration of 12.3 mg/ 6 mL. For 616 mg:
Amount of antihistamine = 616 mg / (12.3 mg/ 6 mL) = 300.5 ml
300.5 ml of antihistamine is needed
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