Observational data collection might be best to study how voters might decide an upcoming ballot issue.
What kinds of information is observed?The majority of big data is observational data, such as bank transaction records, user viewing patterns on video streaming services, or social media posts. Observational data, however, can also be sparse data (based on just a few people).
The observational study method is what?In observational research, participants and phenomena are observed in their most natural environments. Instead of using structured environments like research labs or focus groups, this allows researchers to observe how their subjects make decisions and respond to situations in their everyday lives.
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Mrs. Smith calls customer care after she receives her phone bill. Her bill is normally $40. 00 per
month, however, this month it is $110. 0. Mrs. Smith negotiates a 50% credit of the difference
between the normal charge of $40. 00 and the current balance of $110. 0. How much will Mrs.
Smith be responsible for paying?
Mrs. Smith will be responsible for paying $75.00
The normal monthly charge is $40.00 and the current balance is $110.00,
so the difference is $110.00 - $40.00 = $70.00.
Mrs. Smith negotiated a 50% credit, so she will receive
$70.00 x 0.50 = $35.00 credit.
To find the amount she is responsible for paying, we subtract the credit from the current balance
$110.00 - $35.00 = $75.00
Thus, the amount Mrs. Smith will be responsible for paying is $75.00
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Problem 2
Use each of the numbers 4, 40, and 4000 once to make true statements.
The correct numbers to complete the statements given are 40, 400, and 4000.
What does this question require you to do?This question requires you to complete a statement with a given number (40, 400 or 4000) to make the statement true by dividing the number by 40.1. To find the correct order the numbers must be place using division, let's find out the results of each of these divisions:
40 / 40.1 = 0.997400 / 40.1 = 9.974000 / 40.1 = 99.7Based on the above, it can be concluded:
40 / 40.1 = is much less than 1400 / 40.1 = is close to 14000 / 40.1 = is much greater than 1Based on this, the complete statements are:
The value of 400 ÷40.01 is close to 1The value of 40 ÷40.01 is much less than 1.The value of 4000÷40.01 is much greater than 1.Note: This question is incomplete; here is the complete question:
Use each of the numbers 4, 40, and 4000 once to make true statements.The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is close to 1
The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is much less than 1.
The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is much greater than 1.
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How can you tell if a linear system has infinitely many solutions?
A linear system has infinite solutions if it consists of exactly the same equations.
The 3 possible solutions of a linear system are:
- Unique or one solution
- Infinite solutions
- No solution
- If the linear equations are exactly (or can be transformed to exactly) the same equations, the solution is infinite.
Example:
3x + 2y = -4 ..... (equation 1)
6x = -4y - 8 ..... (equation 2)
Add 4y to both sides of equation 2:
6x + 4y = -8
Divide both sides by 3:
3x + 2y = -4
Hence, equation 2 is exactly the same as equation 1. If we plot their graphs, they will share the same graph. Any solution of equation 1 is also solution of equation 2. Therefore, this linear system has infinite solutions.
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solve the following question
A 64 acre coconut farm is arranged in an 8 by 8 array. Mika wants to know the average number of coconut palms on each acre of land. The number in each cell tells how many coconut palms grow on that particular acre
Therefore , the solution of the given problem of median comes out to be
A. 44.3.
Specify median.The value that exactly falls in the center of an ordered dataset is the median value. A central tendency measure or average is the difference between both the lowest and highest 50% of the data. The methods for calculating the median and mode vary according to whether you have had an odd or perhaps even number of data points.
Here,
To do the average you add all the numbers then divide by how ever many numbers there are. I remember this through a rhyme:
=> 48 + 38 + 47 + 48+ 43+ 34+ 64+ 54 + 53+ 67 = 443/10 =44.3
Hey fiddle fiddle the medians the middle
You add and divide for the mean
The mode is the one you so the most
And the range is the difference between them
Therefore , the solution of the given problem of median comes out to be
A. 44.3.
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The solution of the given problem of median comes out to be
option (A) 44.3.
What is median?
The value that exactly falls in the center of an ordered dataset is the median value. A central tendency measure or average is the difference between both the lowest and highest 50% of the data. The methods for calculating the median and mode vary according to whether you have had an odd or perhaps even number of data points.
Here,
To do the average you add all the numbers then divide by how ever many numbers there are. I remember this through a rhyme:
=> 34 + 51 + 43 + 35 + 52 + 35 + 62 + 38 + 34 + 59 = 443/10 =44.3
Hey fiddle fiddle the medians the middle
You add and divide for the mean
The mode is the one you so the most
And the range is the difference between them
Therefore , the solution of the given problem of median comes out to be
A. 44.3.
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The complete question is:
A 64‐acre coconut farm is arranged in an 8‐by‐8 array. Mika wants to know the average number of coconut palms on each acre. Each cell in the table represents an acre of land. The number in each cell tells how many coconut palms grow on that particular acre.
45 54 40 34 44 66 32 65 66 33 42 36 33 51 50 35 51 45 66 33 47 43 66 61 46 35 48 67 60 59 52 67 46 32 64 35 55 47 61 59 45 48 53 62 55 58 51 41 48 38 47 48 43 34 64 54 53 67 44 59 58 48 62 45
The numbers in green represent Mika's random sample of 10 acres. What is the average number of coconut palms on the randomly selected acres? Round your answer to the nearest tenth. The average number of coconut palms is
A. 44.3
B. 49.3
Find the area of the circle shown. Use 3.14 as an approximation for T. Round your answer to the nearest tenth.
Here the exact values of circle is not given.so in general .Area of Circle = πr² or πd2/4 in square units, where (Pi) π = 22/7 or 3.14.
How to find the Area of Circle?The space a circle takes up in a two-dimensional plane is known as the area of the circle. Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. A = r2, where r is the circle's radius, is the formula for c
Area of Circle = πr2 or πd2/4 in square units, where (Pi) π = 22/7 or 3.14. Pi (π) is the ratio of circumference to diameter of any circle. It is a special mathematical constant.
Area of Circle:
[tex]\pi[/tex]×r²
Where [tex]\pi[/tex]=3.14
But Here we need correct values to find the area of the circle.
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A student constructs a regular square pyramid with a base that has sides of 13. 2 cm and a
slant height of 6 cm. Find the surface area of the pyramid. Find the surface are of the pyramid
The surface area of a regular square pyramid is 332.64 square cm
We know that the surface area of pyramid is nothing but the sum of the areas of its lateral faces and its base.
surface area of pyramid
= areas of lateral faces of pyramid + area of base of pyramid
We know that the formula for the lateral surface area of regular pyramid is:
A = ½ × P × l
where P is the perimeter of the base and l is slant height
Here, a base of regular square pyramid with has sides of 13. 2 cm
a = 13.2 cm and slant height of 6 cm i.e., l = 6 cm
Using the formula of area of square, the base area of pyramid would be,
B = (13.2)²
B = 174.24 sq.cm.
the perimeter of base is:
P = 4 × 13.2
P = 52.8 cm
So, using the above formula of lateral surface area of pyramid the lateral surface area would be
A1 = 1/2 × 52.8 × 6
A1 = 158.4 sq. cm.
So, the surface area of the pyramid is:
A = A1 + B
A = 158.4 + 174.24
A = 332.64 square cm
Therefore, the surface area of the pyramid = 332.64 square cm
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Draw a quadrilateral aBCD whose vertices are A (0,0) B(5,0), C(3,2) and D (0,2)
A graph of quadrilateral ABCD whose vertices are A (0, 0) B(5, 0), C(3, 2) and D (0, 2) is shown in the image attached below.
What are the types of quadrilateral?In Geometry, there are different types of quadrilateral and these include the following:
ParallelogramSquaresRectangleRhombusTrapeziumNext, we would use an online graphing calculator to construct (plot) quadrilateral ABCD on a cartesian coordinate based on the given vertices. Also, you should enter the value for each vertices of quadrilateral ABCD on the x-coordinate and y-coordinate respectively as shown in the table.
By critically observing the graph of quadrilateral ABCD, we can reasonably infer and logically deduce that it represents a trapezium.
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A hurricane blows onto the East Coast of the United States on September 16, 2017. The maximum sustained wind speed is 176 kilometers (109 miles) per hour and the sea level height is pushed 2.3 meters (7.5 feet) above normal. What category is this hurricane
This hurricane would be classified as a Category 2 hurricane on the Saffir-Simpson Hurricane Wind Scale.
What hurricane classification is this?This hurricane would be classified as a Category 3 hurricane. The Saffir-Simpson Hurricane Wind Scale is used to classify hurricanes based on their maximum sustained wind speeds.Category 3 hurricanes have wind speeds between 178 and 209 kilometers (111 and 130 miles) per hour.The maximum sustained wind speed of this hurricane is 176 kilometers (109 miles) per hour, which is below the threshold for Category 4 hurricanes, but still within the range of Category 3 hurricanes. The storm surge is also a major factor in the classification of hurricanes. Storm surges are caused by the winds of a hurricane pushing the water of the ocean up onto the coast.This hurricane has a storm surge of 2.3 meters (7.5 feet).The Saffir-Simpson Hurricane Wind Scale does not take into account the height of storm surges. Therefore, this hurricane would be classified as a Category 3 hurricane due to its maximum sustained wind speed of 176 kilometers (109 miles) per hour and the storm surge of 2.3 meters (7.5 feet).The Saffir-Simpson Hurricane Wind Scale is a useful tool for measuring the severity of a hurricane and can help to prepare people in its path.To learn more about the Saffir-Simpson Hurricane Wind Scale refer to:
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What is 72 1/4 in a decimal
Answer:
I think it's 0.18 in decimal
When a space shuttle returns from a mission, the last part of its descent to the ground
must be between 17 degrees and 19 degrees with the horizontal (ZZ). If the pilot of
space shuttle Pioneer plans to descend from 11,700 feet (UH) at an angle of 18
degrees (ZZ) from the runway, determine the horizontal distance from the landing site
(ZU) at which the pilot must begin the descent.
Use the diagram to determine the measure of the sought side.
Answer:
please see the followings,
11700 ÷ tan 18 = ZU
Please help will give Brain liest
Answer:
Lauren will finish the race faster 7 seconds faster, and 14 meters ahead.
Step-by-step explanation:
To answer this question, I will use the strategy of finding the slope of each of the proportional relationships (y = 8x for Lauren's run and y = ?x for Amani's run). The slope represents the rate at which the distance changes for each unit of time, so the person with the greater slope will finish the race faster.
To find the slope of Amani's run, I will use the tool of point-slope form, which is y - y1 = m(x - x1). I will plug in the coordinates for the second point listed in the table for Amani's run (5 seconds and 30 meters) to get y - 30 = m(5 - x1). Since I don't know the value of x1, I will solve for it in terms of m. I get x1 = 5 - (30/m).
Next, I will plug in the coordinates for the first point listed in the table for Amani's run (3 seconds and 18 meters) into the equation y - 30 = m(5 - (30/m)). I get 18 - 30 = m(5 - (30/m)). Solving for m, I find that Amani's run has a slope of m = -6.
Since Lauren's run has a slope of 8 and Amani's run has a slope of -6, Lauren will finish the race faster. To find out by how much, I will use the tool of proportional reasoning. Since the slope represents the rate at which the distance changes for each unit of time, the difference in the slopes (8 - (-6)) represents the difference in the rate at which the distance changes for each unit of time between the two runs. The difference is 14, so Lauren will finish the race 14 meters ahead of Amani for each second that they run. Since the race is 100 meters long, Lauren will finish the race approximately 7 seconds faster than Amani.
What's the fewest number of people in a room where it's probable (>50%) that a pair of them share a birthday
There is a probable (>50%) that two people in a room with 23 people will share the same birthday.
What is probability?Probable means likely to occur or prove true, or having more evidence for than against, or evidence that inclines the mind to belief but leaves some room for doubt, or affording ground for belief.
Even while it may appear odd that only 23 people are needed to achieve a 50% likelihood of a shared birthdate, this conclusion is made more logical by keeping in mind that birthday comparisons will be done between all potential pairs of people.
There is a 50% chance that two people in a room with 23 people will share the same birthday. Though it may seem strange, it is mathematically accurate.
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How do you solve composite functions examples?
The composite function is the result of first applying the function (x^2 - 1) to the input and then applying the function (5x + 2) to the result. The final result of the composite function is 5x^3 + 2x - 3.
Step 1: Apply (x^2 - 1) to the input:
(x^2 - 1) = x^2 - 1
Step 2: Apply (5x + 2) to the result:
(5x + 2)(x^2 - 1)
= 5x^3 - 5x + 2x - 2
Step 3: Simplify:
5x^3 - 5x + 2x - 2
= 5x^3 + 2x - 3
A composite function is the result of applying two or more functions in succession. The order of operations for a composite function is to first apply the first function, then apply the second function to the result of the first, and so on. In the example given, the composite function
f(x) = (5x + 2) ∘ (x^2 - 1)
is the result of first applying the function
(x^2 - 1)
to the input and then applying the function (5x + 2) to the result. The calculation can be broken down into three steps: Step 1 is to apply (x^2 - 1) to the input to get x^2 - 1, Step 2 is to apply (5x + 2) to the result to get 5x^3 - 5x + 2x - 2,
and Step 3 is to simplify the result to get the final answer of
5x^3 + 2x - 3.
To summarize, the composite function
f(x) = (5x + 2) ∘ (x^2 - 1)
is the result of first applying the function (x^2 - 1) to the input, and then applying the function (5x + 2) to the
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A scuba diver is at a depth of -14 ft. Her
elevation changes -2 ft per second. How many
seconds will it take her to reach a depth of
79ft? Write and solve an equation.
On solving the provided question, we can say that - by the help of unitary method seconds will it take her to reach a depth of 79ft is = 39.5
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
here,
scuba diver is at a depth of = -14 ft
elevation changes = -2 ft per second.
seconds will it take her to reach a depth of 79ft is = 39.5
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William spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -12.2°F. Between 9am and noon, the temperature rose 16.2°F. Between noon and 3pm, the temperature dropped 9.1°F. Between 3pm and 6pm, the temperature dropped 5°F. What was the temperature at 6pm?
If William spends a winter day recording the temperature once every three hours for science class. If the temperature dropped 9.1°F. Between 3pm and 6pm, the temperature dropped 5°F. The temperature at 6pm is: -11.1°F
How to find the temperature?Between 9am and noon, the temperature rose 16.2°F, so the temperature at noon will be:
Temperature at noon = -12.2 + 16.2
Temperature at noon = 3.0°F
Between noon and 3pm, the temperature dropped 9.1°F, so the temperature at 3pm will be:
Temperature at 3pm = 3.0 - 9.1
Temperature at 3pm = -6.1°F
Between 3pm and 6pm, the temperature dropped 5°F, so the temperature at 6pm was:
Temperature at 6pm =-6.1 - 5
Temperature at 6pm = -11.1°F
Therefore the temperature at 6pm is -11.1°F.
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more geometry stuff pls help
Answer:
[tex]y=\sqrt{10}[/tex]
Step-by-step explanation:
Using the geometric mean theorem, [tex]y=\sqrt{(2)(5)}=\sqrt{10}[/tex].
Shana, who lives in Canada, and Pearl, who lives in Pennsylvania, were discussing the weather. Shana complained about the cold temperature of Negative 20 degrees Celsius. Pearl, who lives in Pennsylvania, mentioned that her temperature was the opposite of Shana’s. Which is the correct way to represent “the opposite of Shana’s temperature is equal to Pearl’s”?
Answer:
You can represent "the opposite of Shana's temperature is equal to Pearl's" as follows:
(-20 C) + (-x) = x
Where x represents Pearl's temperature.
Alternatively, you can also write it as:
20 C - x = x
Both of these equations are equivalent and mean the same thing: the opposite of Shana's temperature is equal to Pearl's temperature.
Step-by-step explanation:
20 degrees Celsius
The temperature in Pennsylvania is the opposite of the temperature in Canada, therefore -20⁰ Celsius in Canada would then be 20⁰ Celsius in Pennsylvania.
sqrt{2x-1}-x=-8
solve for x
The values of x are 5 or 13.
What are equations?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given is an equation, [tex]\sqrt{2x-1}[/tex] - x = -8
[tex]\sqrt{2x-1}[/tex] - x = -8
[tex]\sqrt{2x-1}[/tex] = -8+x
Squaring both sides,
2x-1 = x²+64-16x
x²-16x-2x+1+64 = 0
x²-18x+65 = 0
Factorizing the equation,
x²-18x+65 = 0
x²-13x-5x+65 = 0
x(x-13)-5(x-13) = 0
(x-5)(x-13) = 0
x = 5 or 13
Hence, the values of x are 5 or 13.
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The triangle ACE, is a dilation image of triangle ABD. Point A is the center of dilation. Tell whether the dilation is an enlargement or a reduction. Then find the scale factor of the dilation. The length of side AC is 15.
Answer:
Enlargment and 5/4
Step-by-step explanation:
Big Ideas Math:
Q1. The graph of which of the following functions does not belong with the other three?
Answer: f(x) = 3x^2 + 24x - 6
Q2. This is the only function that does not have x-intercepts at x= Response and x= Response and a vertex at (Response, Response).
Function 3x²+24x-6 does not belong with the other three
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
From the option we have to simplify each function
a. f(x)=3x²+6x-24
b. f(x)=3x²+24x-6
c. f(x)=3(x-2)(x+4)
=3(x²+4x-2x-8)
=3x²+6x-24
d. f(x)=3(x+1)²-27
3(x²+1+2x)-27
3x²+3+6x-27
3x²+6x-24
So function 3x²+24x-6 does not belong with the other three
Hence, function 3x²+24x-6 does not belong with the other three
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Alex has five cups of strawberries. He wants to use 1 3/4 cups of strawberries for a fruit salad and 3 1/2 cups for jam. Does Alex have enough strawberries to make both recipes? Solve this problem any way you choose. Grade 5
Alex has five cups of strawberries and wants to use 1 3/4 cups of strawberries for a fruit salad and 3 1/2 cups for jam. Alex has enough strawberries to make both recipes.
To check if Alex has enough strawberries, we add the amount of strawberries needed for the fruit salad (1 3/4 cups) and the amount needed for the jam (3 1/2 cups)
1 3/4 cups + 3 1/5 cups
= 1 + 3/4 + 3 + 1/5
Multiplying 3/4 with 5/5 and 1/5 with 4/4 to make denominator equal
= 1 + 15/20 + 3 + 4/20
= 4 + 19/20
= 4 19/20 cups
4 19/20 is less than 5 cups. So Alex has enough strawberries for both recipes.
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NEED HELP QUICKLY!
x=?
y=?
Using expanded forms, explain why the following problems with unlike bases do not follow the multiplication and division rules of exponents
Pls hurry and thank you!!!!
113.778=one hundred thirteen million seven hundred seventy-eight thousand, and 11,664=eleven thousand six hundred sixty-four is the enlarged form.
What do you meant by expanded form ?1.Comprehensive Notation Form:
[tex]$$\begin{aligned}& 11,664= \\& 10,000 \\& +1,000 \\& +600 \\& +\quad 60 \\& +4 \\&\end{aligned}$$[/tex]
Increased Factors Form:
[tex]$$\begin{aligned}& 11,664= \\& 1 \times 10,000 \\& +1 \times 1,000 \\& +6 \times 100 \\& +6 x \quad 10 \\& +4 \times \quad 1 \\&\end{aligned}$$[/tex]
Increased Exponential Form:
[tex]$$\begin{aligned}& 11,664= \\& 1 \times 10^4 \\& +1 \times 10^3 \\& +6 \times 10^2 \\& +6 \times 10^1 \\& +4 \times 10^0 \\&\end{aligned}$$[/tex]
Text Format:
11,664=eleven thousand six hundred sixty-four
2. Comprehensive Notation Form:
[tex]$$\begin{aligned}& 113.778= \\& 100 \\& +10 \\& +3 \\& +\quad 0.7 \\& +\quad 0.07 \\& +\quad 0.008 \\&\end{aligned}$$[/tex]
Comprehensive Notation Form:
[tex]$$\begin{aligned}& 113.778= \\& 1 \times 100 \\& +1 \times \quad 10 \\& +3 \times \quad 1 \\& +7 \times \quad 0.1 \\& +7 \times \quad 0.01 \\& +8 \times \quad 0.001 \\&\end{aligned}$$[/tex]
Increased Exponential Form:
[tex]$$\begin{aligned}& 113.778= \\& 1 \times 10^2 \\+ & 1 \times 10^1 \\+ & 3 \times 10^0 \\+ & 7 \times 10^{-1} \\+ & 7 \times 10^{-2} \\+ & 8 \times 10^{-3}\end{aligned}$$[/tex]
Text Form:
113.778=one hundred thirteen million seven hundred seventy-eight thousand,
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Choose the equation that represents the line passing through the point (-3,-1) with a slope of 4.
y=4x-11
y = 4x + 11
y = 4x + 7
y=4x-7
On solving the provided question, we can say that - in the linear equation here the value will be
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
here,
y = 4x + 11
x = 8
y = 32 + 11
y = 43
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Graph the following linear function. f(x)= 5/2x+5
The graph of the linear function f(x) = 2/(x + 5) is attached.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is the linear function as -
f(x) = 5/(2x + 5)
Refer to the graph of the linear function attached. This graph represents the function f(x).
Therefore, the graph of the linear function f(x) = 2/(x + 5) is attached.
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PLEASE HELP ME I REALLY NEED IT!!!!!!!!
Answer: for A it is: 3 and 4 represent the number values for X and Y.
Step-by-step explanation:
Sorry, but you B and C you did not give enough information
What is the easiest way to learn linear equations class 8?
The easiest way to solve linear equations is to use the elimination method.
A linear equation is an equation that has two variables and when it is graphed it gives a straight line. Linear equations can be graphed according to their slope and y-intercept. The standard equation for a line is y = mx + b, where b is the y-intercept and m is the slope.
To solve linear equations in the easiest and simplest way use the elimination method. In this method, you either add or subtract the equations to obtain an equation in one variable. When the coefficients of one variable are opposites, you add the equations to eliminate a variable and when the coefficients of one variable are equal, you subtract the equations to eliminate a variable.
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What is the slope of an absolute value function?
Its slope is m = 1 on the right side of the vertex, and m = - 1 on the left side of the vertex.
Absolute Value Function:
An absolute value function is a function that contains an algebraic expression within the absolute value sign. Remember that the absolute value of a number is its distance from 0 on the number line. To graph the absolute value function, select some values of x and find some ordered pairs.
In mathematics, the absolute value or modulus of the real number x, represented as.
|x| is the non-negative value of x, regardless of sign.
x is positive and |xI =-x}. For example, the absolute value of 3 is 3, and the absolute value of -3 is also 3. The absolute value of a number can be thought of as the distance from zero.
Generalizations of the absolute value of real numbers are made in a variety of mathematical contexts. For example, absolute value is also defined for complex numbers, quaternions, ordinal rings, fields, and vector spaces. Absolute value is closely related to the concepts of magnitude, distance, and norm in various mathematical and physical contexts.
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giving 100 pts/ brainliest!! please help this is due in 20 minutes
Delaney would like to make a 5 lb nut mixture that is 60% peanuts and 40% almonds. She has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds. Let p represent the number of pounds of peanuts needed to make the new mixture, and let m represent the number of pounds of the 80% almond-20% peanut mixture.
What is the system that models this situation?
Which of the following is a solution to the system: 2 lb peanuts and 3 lb mixture; 2.5 lb peanuts and 2.5 lb mixture; 4 lb peanuts and 1 lb mixture? Show your work.
Answer:
p + m = 5, p + 0.2m = 0.6(5)2.5 lb peanuts; 2.5 lb almond mixStep-by-step explanation:
You have peanuts and an 80-20 almond-peanut mix, and you want to know how many pound of each are needed for 5 lb of a 60% peanut mix.
System of equationsThe system of equations relating the pounds of peanuts (p) and the pounds of almond mix (m) will describe the total mixture weight, and the weight of the peanuts.
p + m = 5 . . . . . . total mixture weight is 5 lb
p + 0.20m = 0.60(5) . . . . . weight of peanuts in the 60% peanut mix
SolutionWe can subtract the second equation from the first to eliminate the variable p:
(p +m) -(p +.2m) = (5) -(.6)(5)
0.8m = 0.4(5) . . . simplify
m = 2.5 . . . . . . . . divide by 0.8
p = 5 -m = 2.5
The solution to the system is 2.5 lb peanuts and 2.5 lb mixture.