Sarah should blend 80.5 pounds of the high-quality beans and 39.5 pounds of the cheaper beans to make 120 pounds of blended coffee.
In this problem, we are given that Sarah Meeham needs to prepare 120 pounds of blended coffee beans to sell at a rate of $4.17 per pound. She plans to blend two types of coffee beans: a high-quality bean costing $5.25 per pound and a cheaper bean costing $2.00 per pound.
Let x be the number of pounds of the high-quality coffee beans needed and y be the number of pounds of the cheaper coffee beans needed. Since we need 120 pounds of the blended coffee, we have:
x + y = 120
The cost of the blended coffee is $4.17 per pound. This means that the total cost of the blended coffee is:
4.17(120) = 501.6
We can also find the cost of the high-quality and cheaper beans in terms of x and y:
5.25x is the cost of the high-quality beans
2.00y is the cost of the cheaper beans
The total cost of the two types of beans is the sum of their individual costs:
5.25x + 2.00y
Since we need 120 pounds of the blended coffee, we can set up the following equation using the above expressions for total cost:
5.25x + 2.00y = 501.6
Now, we can use the system of equations consisting of x + y = 120 and 5.25x + 2.00y = 501.6 to solve for x and y. One way to do this is by substitution:
x = 120 - y (from the first equation)
5.25(120 - y) + 2.00y = 501.6 (substituting x in the second equation)
Simplifying and solving for y, we get:
630 - 5.25y + 2.00y = 501.6
3.25y = 128.4
y ≈ 39.5
Now we can use this value of y to find x:
x = 120 - y
x = 120 - 39.5
x ≈ 80.5
Therefore, Sarah needs to blend approximately 80.5 pounds of the high-quality coffee beans and 39.5 pounds of the cheaper coffee beans to make 120 pounds of blended coffee that she can sell for $4.17 per pound.
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12 pack can of soda is 8. 25 what is the price per can
The price per can of a 12 pack of soda is 8.25. the price per can of a 12 pack of soda is 0.6875.
To calculate this, we can use the following formula: Price per Can = Total Price of 12 Pack / 12 Price per Can = 8.25 / 12 Price per Can = 0.6875 Therefore, the price per can of a 12 pack of soda is 0.6875. To better understand the price per can of a 12 pack of soda, it is important to understand the concept of unit pricing. Unit pricing is the cost of a single item compared to a larger quantity. When shopping, it is beneficial to look at the unit pricing of items to ensure that you are getting the best deal. For example, if a 12 pack of soda is 8.25 and a 6 pack of soda is 4.00, then the unit price of the 12 pack is lower, which means it is a better deal. By understanding unit pricing, you can make the most cost-efficient decisions when shopping.
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The bank would exchange 1.6 Canadian dollars for one US dollar. How many Canadian dollars would the bank exchange for $160 US dollars?
The number of Canadian dollars the bank exchange for $160 US dollars is 100.
What is money?Money is any item or medium of exchange that is accepted by people for the payment of goods and services, as well as the repayment of loans.
A current medium of exchange in the form of coins and banknotes.
Given that, the bank would exchange 1.6 Canadian dollars for one US dollar.
Here, there are $160 US dollars.
So, number of Canadian dollars
= 160/1.6
= 100
Therefore, the number of Canadian dollars the bank exchange for $160 US dollars is 100.
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Divide ₹1750 into 2 parts such that if one part be lent out at 15% per annum for 2 years and the other part at 16% per annum for 3 years, the total interest is 624.
The amount of lent out at 15% and 16% will be ₹1,200 and ₹550, respectively.
What is simple interest?Let P be the principal, R be the rate of interest, and T be the time. Then the interest rate is given as,
The formula for interest is written as,
I = (PRT)/100
Divide ₹1750 into 2 parts such that if one part is lent out at 15% per annum for 2 years and the other part at 16% per annum for 3 years, the total interest is 624.
Let 'x' be the amount of lent out at 15%. Then the amount of lent out at 16% is (₹1750 - x). Then the equation is given as,
(x · 0.15 · 2) + [(1750 - x) · 0.16 · 3] = 624
Simplify the equation, then we have
(x · 0.15 · 2) + [(1750 - x) · 0.16 · 3] = 624
0.30x + 840 - 0.48x = 624
0.18x = 216
x = ₹1,200
Then the value of (₹1750 - x) is given as,
₹1750 - x = (₹1750 - ₹1,200)
₹1750 - x = ₹550
The amount of lent out at 15% and 16% will be ₹1,200 and ₹550, respectively.
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5x+2y=-7 and 10x+4y= -14 no solution, solution, or infinite solution?
The system of equations 5x+2y=-7 and 10x+4y= -14 has unique solution which is (-7/5,0).
In general, a system of linear equations can have one of three possible outcomes:
One unique solution (as in this case)
No solution (if the equations are inconsistent)
Infinitely many solutions (if the equations are dependent)
To solve this system of equations, we can use the method of elimination or substitution. Let's use the method of elimination, which involves adding or subtracting the equations to eliminate one variable.
First, we need to choose a variable to eliminate. Looking at the coefficients of x and y, we see that we can eliminate y by multiplying the first equation by -2 and adding it to the second equation:
-10x - 4y = 14
5x + 2y = -7
-5x = 7
Now we can solve for x:
-5x = 7
x = -7/5
We can substitute this value of x into one of the equations to solve for y. Let's use the first equation:
5x + 2y = -7
5(-7/5) + 2y = -7
-7 + 2y = -7
2y = 0
y = 0
Therefore, the solution to the system of equations is (x,y) = (-7/5,0).
This is called a unique solution, meaning there is only one possible solution for the system of equations.
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Complete Question:
Solve
5x + 2y = -7
10x + 4y = -14
And find the number of solutions for the equation
850 Miles on 25 Gallons. How many miles per gallon?
Answer:
34 miles per gallon
Step-by-step explanation:
850/25 = 34
if \cos \theta =(4)/(9), tan\theta <0, sin\theta =?
Answer: sinθ = [tex]-\frac{\sqrt{65}}{9}[/tex]
Step-by-step explanation:
cosθ = 4/9
tan < 0
This means our reference angle is either in Quadrants II or IV, (where tangent is negative). Since cosine is positive, it must be Quadrant IV.
Therefore we know that sinθ will be negative.
we also know that [tex]cos^2(\theta) + sin^2(\theta) = 1[/tex], from the Pythagorean identities
.: 16/81 + sin^2(θ) = 1,
.: sinθ = [tex]\sqrt{\frac{65}{81} }[/tex]= [tex]\frac{\sqrt{65}}{9}[/tex]
But since this angle is in Quadrant IV, sinθ will be negative.
.: sinθ = [tex]-\frac{\sqrt{65}}{9}[/tex]
y=x^2 6 units to the left 2 units up
The translation of the graph is represented by y = -6(x+2)² - 7.
What is translation ?A translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction.
Given that the graph of y= x² translated left 2 units and up 8 units. The translated equation is:-
Start with y = x².
Shift 2 units left to get y = (x+2)².
Vertically stretch to get y = 6(x+2)².
Reflect across x-axis to get y = -6(x+2)².
Shift 7 units down to get y = -6(x+2)² - 7.
Hence, the translation of the graph is represented by y = -6(x+2)² - 7.
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The question is incomplete so solved for,
Suppose the graph of y= x^2 translated left 2 units, and up 8 units
I need help is due today!!!
The length of a living room is 12 feet and it’s width is 10 1/2 feet. The length of the room is being expanded by x feet. Select all the expressions that represent the area of the living room in square feet.
A. 10.5 (12x) square feet
B. (10.5 + 12 + x) square feet
C.10.5( 12 + x) square feet
D.126x square feet
E.(126 + 10.5) square feet
F.( 22.5 + x) square feet
Answer:
answer is A
Step-by-step explanation:
because area of a rectangle is L × B
or length × width
since the length is expanded by x
10.5 (12x)
Answer:
Option C
Step-by-step explanation:
The original length of the room = 12 feet
After expansion, the new length = [tex](12 + x)[/tex] feet
Width of the room = 10[tex]\frac{1}{2}[/tex] feet = 10.5 feet
Area of a rectangle = Length × Width
The shape of the living room is a rectangle.
∴Area of living room = [tex](12 + x)[/tex] feet × [tex](10.5)[/tex] feet
[tex]= 10.5(12 + x)[/tex] square feet
Expand the brackets or parenthesis by applying the Distributive Law:
[tex]= (12)(10.5) + (10.5)(x)[/tex] square feet
= [tex](125 + 10x)[/tex] square feet
∴Option C
The scale of the model of a recreational facility is 3 inches = 5 feet. If the basketball court is 22.5 inches from the pool in the model, what is the actual distance between the basketball court and the pool
Answer:
Step-by-step explanation:
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The actual distance between the basketball court and the pool is 37.5 feet
Distance refers to the amount of space between two objects or points. It is a measure of how far apart two things are from each other.
The scale of the model is 3 inches = 5 feet. This means that every 3 inches on the model represents 5 feet in actual size. We are given that the distance between the basketball court and the pool on the model is 22.5 inches. To find the actual distance between these areas, we need to use the scale.
We can start by setting up a proportion using the scale. We know that 3 inches on the model represents 5 feet in actual size. Therefore, we can say that:
3 inches / 5 feet = 22.5 inches / x
We are trying to solve for x, which represents the actual distance between the basketball court and the pool. To solve for x, we can cross-multiply and simplify the equation:
3 inches x x = 5 feet x 22.5 inches
3x = 112.5
x = 37.5 feet
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Complete Question:
The scale of the model of a recreational facility is 3 inches = 5 feet. If the basketball court is 22.5 inches from the pool in the model, what is the actual distance between the basketball court and the pool?
in forecasting, there is more than one use for linear regression. what are they? check all that apply.
Casual relationship forecasting and Time series forecasting uses linear regression in forecasting.
Linear regression is a statistical tool used in forecasting to model the relationship between a dependent variable and one or more independent variables. Some of the common uses of linear regression in forecasting are:
Predictive modeling: Linear regression can be used to build a predictive model that estimates the value of the dependent variable based on the values of the independent variables..Trend analysis: Linear regression can be used to analyze the trend of the dependent variable over time.Forecast accuracy evaluation: Linear regression can be used to evaluate the accuracy of a forecasting model by comparing the predicted values to the actual values of the dependent variable. Causal analysis: Linear regression can be used to identify the causal relationship between the independent variables and the dependent variable. .Therefore, linear regression is a versatile tool in forecasting, with many useful applications for predicting future values, analyzing trends, evaluating accuracy, and identifying causal relationships.
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The complete question is :
In forecasting, there is more than one use for linear regression. What are the? Check all that apply.
1. Causal relationship forecasting
2. Time series forecasting
Which scatter plot most likely has a line of best fit represented by y = 3x + 1?
The graph showing the line of best fit for the function y = 3x + 1 is attached below
What is line of best fitThe line of best fit is a line that is used to represent the relationship between two variables in a scatterplot. It is a line that passes through the center of the data points in the scatterplot in such a way that the total distance between the line and the data points is minimized. The line of best fit can be used to make predictions about the value of one variable based on the value of another variable. There are several methods to obtain the line of best fit, including the method of least squares, which finds the line that minimizes the sum of the squares of the differences between the observed values and the values predicted by the line.
In the problem given, the line of best fit the line of best fit can be plotted on a graph using a graphing calculator.
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how to solve the first order linear differential equation
The solution to the given differential equation is y = e⁽ˣ³⁾⁽²⁸ˣ ⁺ ᶜ⁾, where C is a constant.
To solve the first-order linear differential equation of the form y' + p(x)y = q(x), where p(x) and q(x) are functions of x:
Find the integrating factor (IF) = e⁽∫ᵖ⁽ˣ⁾ᵈˣ⁾
Multiply both sides of the equation by the IF.
Apply the product rule to the left side and simplify the right side.
Integrate both sides with respect to x.
Solve for y.
Using this method, for the given equation:
y' - 3x²y = 28e⁽ˣ³⁾
Find the integrating factor (IF):
IF = e⁽∫ᵖ⁽ˣ⁾ᵈˣ⁾ = e⁽⁻³/¹ * ∫ˣ²ᵈˣ⁾ = e⁽⁻ˣ³⁾
Multiply both sides by the IF:
e⁽⁻ˣ³⁾y' - 3x²e⁽⁻ˣ³⁾y = 28
Apply the product rule to the left side and simplify the right side:
d/dx (e⁽⁻ˣ³⁾y) = 28
Integrate both sides with respect to x:
e⁽⁻ˣ³⁾)y = 28x + C, where C is the constant of integration.
Solve for y:
y = e⁽ˣ³⁾(28x + C)
Therefore, the solution to the given differential equation is y = e⁽ˣ³⁾(28x + C), where C is a constant.
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Complete question:
How to solve the first order linear differential equation
Y'- 3x²y=28eˣ³
y=-1/2x-1
y=1/4x-4
graphing method
each of two persons tosses three gair coincs. what is the probability that they obtain the same numbre of heads
The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.
1/8
The probability of getting a head or a tail when flipping a coin is 1/2.
Therefore, the probability of getting two heads when tossing two coins is 1/2 x 1/2 = 1/4.
The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.
Since each person is tossing three coins, the probability that they both obtain the same number of heads is 1/8.
The probability of getting n heads when tossing n coins is 1/2^n. Therefore, the probability of getting the same number of heads when two people toss n coins is 1/2^n. This means that if two people each toss a coin, the probability that they both get heads is 1/4; if they each toss two coins, the probability that they both get two heads is 1/16; if they each toss three coins, the probability that they both get three heads is 1/64; and so on.
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A triangular shaped region has side lengths of 829 miles, 911 miles, and 1,007 miles.
Does the region form a right triangle? Justify your answer.
Answer: no it does not
Step-by-step explanation: Because 1,007 squared is 1,014,049 and the sum of 911 squared is 829,921 and then 829 squared is 687,241 then add 829,921+687,241=1,517,162 when it should equal 1,014,049 which is the amount of 1,007 squared to make it a right triangle.
The solution is : no, it does not form a right triangle.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
given that,
A triangular shaped region has side lengths of 829 miles, 911 miles, and 1,007 miles.
now, we get,
Because 1,007 squared is 1,014,049
and the sum of 911 squared is 829,921
and then 829 squared is 687,241
then add 829,921+687,241=1,517,162
when it should equal 1,014,049
which is the amount of 1,007 squared to make it a right triangle.
as we know that,
in right triangle,
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a^2 + b^2 = c^2.
so, we get,
The solution is : no, it does not form a right triangle.
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HELLLPPPP PLEASEEEEEEEEEEEEE
Answer: look at the image for the answer and the solution
Step-by-step explanation:
Answer: the home of it is 78 degrees
Step-by-step explanation:
as the angular bisector is shown then we can say that its right
A tank in the shape of a hemisphere has a radius of 5 feet. If the liquid that fills the tank has a density of 62. 7 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
The total weight of the liquid in the tank which is hemisphere in shape is 16,415 pounds.
The density and mass are related to each other with the formula -
Density = mass/volume
So, we have the density. We need to calculate the volume of hemisphere which will be accomodating the liquid. Then we will find the mass.
Volume of hemisphere = 2/3πr³, where r represents radius.
Volume = 2/3×π×5³
Performing multiplication, division and taking cube
Volume = 261.8 feet³
Now, mass = density × volume
Mass = 62.7 × 261.8
Performing multiplication
Mass = 16,414.86 pounds
Rounding off
Mass = 16,415 pounds
Thus, the mass of liquid will be 16,415 pounds.
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Suppose the following sequence of matrix operations was used to translate AABC.
The horizontal and vertical translations applied to ΔABC:
A horizontal translation of 4 units right and a vertical translation of 7 units down has been applied to ΔABC.
What is matrix ?It is possible to represent linear transformations and solve systems of linear equations using matrices, which are collections of numbers arranged into a predetermined number of rows and columns. A matrix is a rectangular array of letters, numbers, or expressions in mathematics that are arranged in rows and columns. As well as in the sciences like physics, engineering, and economics, matrices are frequently used in computer graphics, image processing, and data analysis. Data manipulation and analysis can be done using well-defined matrix operations like addition, subtraction, multiplication, and inversion.
Given that,
[tex]\left[\begin{array}{ccc}1&1&4\\4&1&1\\\end{array}\right] + \left[\begin{array}{ccc}-7\\4\end{array}\right] * \left[\begin{array}{ccc}1&1&1\\\\\end{array}\right][/tex] = ?
After using matrix operation it can be further solved as,
[tex]\left[\begin{array}{ccc}5&5&8\\-3&-6&-6\\\end{array}\right][/tex]
Hence, A horizontal translation of 4 units right and a vertical translation of 7 units down has been applied to ΔABC.
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Latanya plans to repaint some classroom bookcases. She has 5 3/5 gallons of paint. All of the bookcases are the same size and each requires 1/2 gallon of paint. What is the maximum number of complete bookcases she can paint?
With her 5 3/5 gallons of paint, Latanya can paint up to 11 full bookcases.
What does the equation's solution consist of?Any value of the variable that makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation equal is a solution to the problem. Solving an equation is locating its solution or solutions.
Let's first translate 5 3/5 gallons of paint into an incorrect fraction:
5 3/5 = (5 x 5 + 3)/5 = 28/5
Next, we can find the number of bookcases she can paint by dividing the total amount of paint by the amount needed for each bookcase:
28/5 ÷ 1/2
= 28/5 x 2/1
= 56/5
=11 1/5.
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With the given budget, what’s the farthest distance a truck can travel from the warehouse to the retail outlet?
1. Which equation has a quotient of 1 1/5?
A 5÷6=
B 6÷5=
C 4÷5=
D 5÷4=
Answer:
none of them do
Step-by-step explanation:
5/6=0.83
6/5=1.2
4/5=0.8
5/4=1.25
11/5=2.2
???????????????????????????????????
Answer:
**DUE TOMORROW, NEED ANSWER ASAP**
NASA has asked you to evaluate a number of proposals for telescopes. These proposals include information about where the telescope would be built and what wavelengths it intends to observe at. Based only on these factors, evaluate whether NASA should consider funding each proposal. Justify your recommendations. (Some telescopes may have more than one "correct" answer depending on how you justify it).
a.) An ultraviolet telescope in space
b.) An optical telescope in a remote location in Michigan's upper peninsula
c.) A radio telescope in the Mojave desert in Arizona
d.) An x-ray telescope in the Andes mountains in Chile
e.) An optical telescope in space
Step-by-step explanation:
Jamal mows lawns and wants to save money. Jamal currently
has $25 and plans to save an additional $25 per month. Which
graph represents the number of months it will take Jamal to
save at least $250?
Answer: eat grass whor
Step-by-step explanation:
Given: ABCD is a parallelogram and AD is perpendicular to BD
Prove: AB congurent to BC
Answer:
...here is the answer...
the satellite is in the shape of a rectangular prism. which polynomial represents the volume of the satellite? a rectangular prism with length 4 x minus 3 feet, a width of x plus 1 feet, and a height of x plus 2 feet.
The volume of the rectangular prism will be (4x - 3)(x + 1)( x+2) cubic feet.
What is the volume?The volume of the rectangular prism is defined as the space in three-dimension covered by the rectangular prism having the sides Length, Width, and Height.
Given that the length, width, and height of the rectangular prism are,
The volume of the rectangular prism will be calculated as,
Volume = Length x width x Height
Volume = (4x - 3)(x + 1)( x+2) cubic feet
Therefore, the polynomial for the volume will be (4x - 3)(x + 1)( x+2) cubic feet.
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Help me with thiss Pllllllllll
Step-by-step explanation:
the answer for -1/4(-8x+12y)
2x-3y
Answer:
2x-3y
Step-by-step explanation:
For this equation we are using distributive property
-1/4(-8x) -1/4(12y)
↓ ↓
2x -3y
So, 2x-3y is the answer.
Solve the compound inequality and graph its solution:8r-3 ≥7r - 7 or 2r + 4≤ r-3
Answer:
Step-by-step explanation:
o solve the compound inequality, we'll start by solving each inequality separately, and then find the intersection of their solutions.
For the first inequality: 8r - 3 ≥ 7r - 7
Adding 7r to both sides: 8r - 3 + 7r ≥ 7r - 7 + 7r
Combining like terms: 15r - 3 ≥ 14r
Subtracting 14r from both sides: 15r - 14r - 3 ≥ 0
Combining like terms: r - 3 ≥ 0
Adding 3 to both sides: r ≥ 3
For the second inequality: 2r + 4 ≤ r - 3
Subtracting 2r from both sides: 2r + 4 - 2r ≤ r - 3 - 2r
Combining like terms: 4 ≤ -r - 3
Adding r and 3 to both sides: 4 + r + 3 ≤ -r
Combining like terms: 7 ≤ -r
Multiplying both sides by -1: r ≤ -7
The solution to the compound inequality is the intersection of the solutions to each inequality, which is the range of r that satisfies both conditions. So, the solution is 3 ≤ r ≤ -7.
To graph the solution, we can plot the two inequalities on the number line, and shade the region between 3 and -7:
Aldo debe escoger una camisa y un par de pantalones para su atuendo de hoy. Puede escoger entre 2 camisas y 3 pares
de pantalones. ¿Cuántos diferentes atuendos puede crear?
The number of different outfits that Aldo can create from the shirts and the pairs of pants are 6 outfits.
How to find the number of outfits ?In this case, Aldo has 2 options for his shirt and 3 options for his pants. To find the total number of outfits, we can multiply these numbers together:
= Number of shirts x Number of pairs of pants
= 2 x 3
= 6 outfits
Therefore, Aldo can create 6 different outfits by choosing a shirt and a pair of pants from the available options.
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Which graph shows the solution to the system of linear equations?
y = 2x − 2
4x − 2y = 4
- Coordinate plane with one line that passes through the points 0 comma negative 2 and 1 comma 0.
- Coordinate plane with one line that passes through the points 0 comma negative 1 and 1 comma 1 and another line that passes through the points 0 comma negative 2 and 1 comma 0.
- Coordinate plane with one line that passes through the points 0 comma 1 and 1 comma 2.
- Coordinate plane with one line that passes through the points 0 comma negative 2 and 1 comma 0 and another line that passes through the points 0 comma 1 and 1 comma 2.
Answer:
A
Step-by-step explanation:
Answer: the answer is A
Step-by-step explanation:
The temperature at noon was $-4\degree$ C. By midnight, the temperature dropped $8\degree$ C. Which expression represents the temperature at midnight?
The temperature at midnight would be -4°C - 8°C since the temperature at noon was -4°C and at midnight it dropped 8°C.
The temperature at midnight would be -4°C minus 8°C, which can be expressed as:
-4°C - 8°C = -12°C
Therefore, the temperature at midnight would be -12°C.
Temperature is a measure of the degree of hotness or coldness of a body or an environment. It is a physical quantity that expresses the amount of thermal energy in a substance or a system, typically measured using a thermometer in units such as Celsius (°C) or Fahrenheit (°F). In general, the higher the temperature, the more thermal energy is present in the system, and the lower the temperature, the less thermal energy is present.
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