One possible interpretation of the results is that the customer buys 6 pounds of almonds, 4 pounds of cashews, and 2 pounds of walnuts to achieve a total cost of $118.
To determine the amount of each type of nut the customer buys, we can set up a system of equations based on the given information.
Let's use the variables:
A = pounds of almonds
C = pounds of cashews
W = pounds of walnuts
From the given information, we can create the following equations:
A + C + W = 12 (since the customer buys a total of 12 pounds of mixed nuts)
7A + 10C + 12W = 118 (since the total cost of the nuts is $118)
W = C + 2 (since the customer buys 2 more pounds of walnuts than cashews)
We can now represent this system of equations as a matrix:
[1 1 1 12]
[7 10 12 118]
[0 -1 1 2]
To find the reduced row echelon form of this matrix, we can use Gaussian elimination or a similar method. Solving the system of equations represented by the matrix, we obtain the following reduced row echelon form:
[1 0 2 6]
[0 1 -3 4]
[0 0 0 0]
Now, let's interpret the results:
From the reduced row echelon form, we can deduce that there are infinitely many solutions to this system of equations. This means that there are multiple possible combinations of almond, cashew, and walnut quantities that satisfy the given conditions.
One possible interpretation of the results could be that the customer buys 6 pounds of almonds, 4 pounds of cashews, and 0 pounds of walnuts. This satisfies the equation A + C + W = 12, and the total cost of nuts is $7 * 6 + $10 * 4 + $12 * 0 = $42 + $40 + $0 = $82. However, since the given total cost is $118, this interpretation is not valid.
Another possible interpretation could be that the customer buys 6 pounds of almonds, 4 pounds of cashews, and 2 pounds of walnuts. This satisfies all the given conditions. The equation A + C + W = 12 holds true, and the total cost is $7 * 6 + $10 * 4 + $12 * 2 = $42 + $40 + $24 = $106, which matches the given total cost of $118.
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The average American consumes 3.4 x 10^3 mg of sodium daily. If there are
3.27 x 10^8 people in the United States, then how many milligrams of sodium is consumed each day? Express your answer in scientific notation.
Answer:
1.1 x 10¹² mg of sodium
Step-by-step explanation:
(3.4 x 10³ mg)(3.27 x 10⁸) = 1.1 x 10¹² mg
What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?
A:–12 – 20x ≤ –6x + 9
B:–12 – 20x ≥ –6x + 9
C:–12 + 20x ≤ –6x + 9
D:–12 + 20x ≥ –6x + 9
The correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9 is,
⇒ - 12 + 20x ≥ - 6x + 9
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
The inequality is,
⇒ - 4(3 - 5x) ≥ - 6x + 9
Now, We can simplify as;
⇒ - 4(3 - 5x) ≥ - 6x + 9
⇒ - 12 + 20x ≥ - 6x + 9
⇒ 20x + 6x ≥ 12 + 9
⇒ 26x ≥ 21
⇒ x ≥ 21/26
Thus, The correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9 is,
⇒ - 12 + 20x ≥ - 6x + 9
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You decide to buy a car that costs $10,000. The normal depreciation for such a car is 5% per year. How much will the car be worth in 2 years?
Answer:
11,000
Step-by-step explanation:
10% of 10,000 is 1,000 so 5% is 500 and add 2 of 5% you get 1,000 and add it to the old price thus you get 11,000.
Find the value of z if the volume of the cylinder is 1696.5m^3. Use 3.14 for pi and round your answer to the nearest whole number.
Answer:
πr²h= 1696
⇒r²=1696/3.14×15
⇒r²=36.009
⇒r=√36.009
∴r=6.0008=z
Write the equation of a line perpendicular to 2x + 3y = 4 and passing through (-3,-5).
Answer:
Step-by-step explanation:
A line perpendicular to the given line has a slope that is the negative inverse of the reference line.
Rewrite the given equation in the format of y=mx+b, where mi is the slope and b is the y-intercept (the value of y when x = 0.
2x + 3y = 4
3y=-2x+4
y = -(2/3)X + (4/3)
The reference slope is -(2/3). The negative inverse is (3/2), which will be the slope of a perpendicular line. We can write the new line as:
y = (3/2)x + b
Any value of b will still result in a line that is perpendicular. But we want a value of b that will shift the line so that it intersects the point (-3,-5). Simply enter this point in the above equation and solve for b.
y = (3/2)x + b
-5 = (3/2)(-3) + b
-5 = -(9/2) + b
-5 = -4.5 + b
b = - 0.5
The equation of the line that is perpendicular to 2x + 3y = 4 and includes point (-3,-5) is
y = (3/2)x - 0.5
Solve for x. Figures are not necessarily drawn to scale.
Answer:
13.2 units
Step-by-step explanation:
12 is to 7.2 as (12+10) is to x
12/7.2 = (12+10)/x
x = 22 * 7.2/12 = 13.2 units
I need help asap please? and this is for the math question? what is the missing angle?
Answer:
90
Step-by-step explanation:
its a right angle triangle so the angle between the adjacent and opposite is 90 degrees.Angles on a straight line add up to 180180-90=90Answer:
the missing angle or the missing exterior angle is 90
Step-by-step explanation:
180-90=90
Consider functions fand g.
f(x) = -x3
g(x) = |1/8x-1|
What is the value of (gof)(4)?
O A. -1/8
OB. 9
O C. -9
O D. 1/8
The value of (gof)(4) is 9 if the function f(x) is f(x) = -x³, and function g(x) is g(x) = |1/8x-1| option (B) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = -x³
[tex]\rm g(x) = |\dfrac{1}{8}x-1|[/tex]
Plug x = 4 in the f(x)
f(4) = -4³ = -64
Plug the above value in the g(x)
[tex]\rm g(x) = |\dfrac{1}{8}(-64)-1|[/tex]
g(f(4)) = |-8-1| = |-9| = 9
Thus, the value of (gof)(4) is 9 if the function f(x) is f(x) = -x³, and function g(x) is g(x) = |1/8x-1| option (B) is correct.
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What are two limiting factors that affect both deciduous forests and grasslands?
1. very low rainfall throughout the year
2. seasonal changes in the amount of sunlight
3. a wide range of temperatures throughout the year
4. soil that is low in nutrients and organic matter
The two limiting factors that affect both deciduous forests and grasslands very low rainfall throughout the year , a wide range of temperatures throughout the year , Option 1 and 3 are the correct answer.
What are Grasslands ?The places where there is not enough rainfall for the forest to sustain and grow , a layer of grass is spread out , these are called as grasslands.
The two limiting factors that affect both deciduous forests and grasslands is that they both receive very low rainfall throughout the year.
and a wide range of temperatures throughout the year , It can get very warm and simultaneously very cold .
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Find the surface area of the composite figure.
2 cm
7 cm
2 cm
12 cm
12 cm
7 cm
7 cm
SA = [?] cm2
Answer:
You are to write a five paragraph literary essay based on one of the 4 prompts and what you have read and learned in this module. These are your options:
1. How do the events of "The White Umbrella" teach the narrator a lesson about shame and acceptance?
2. What role does creativity play in "The Bat-Poet"?
3. How does the character of Squeaky change over the course of "Raymond's Run"?
4. Discuss the influences of older family members on the protagonists and speakers in the stories and poems of this unit.
You are to write a five paragraph literary essay based on what you have read and learned in this module. Your final submission should meet the following requirements.
• Submit completed pre-writing and outline documents.
• Write an essay that contains an introduction with hook and thesis statement, supporting paragraphs with evidence and at least one quotation, and a conclusion that restates the thesis and reviews main points.
• Use transitions appropriate to the pattern of organization.
• Use vocabulary to create tone and voice.
• Cite primary source (quotation).
• Submit completed revision checklist.
• Vary sentence structure.
• Create sentences with parallel structures.
• Use technology in the writing process.
Step-by-step explanation:
A polynomial function is represented by the data in the table. choose the function represented by the data.
choose the function represented by the data.
The polynomial function represented by the data is equal to D. f(x) = −x² + 10.
How to determine the polynomial function?In order to determine the polynomial function represented by the data, we would substitute the value of x (-3) into the given set of functions as follows:
For option A, we have:
f(x) = 6x + 15
f(-3) = 6(-3) + 15
f(-5) = -18 + 15
f(-5) = -3 (False).
For option B, we have:
f(x) = -6x - 45
f(x) = -6(-3) - 45
f(x) = 18 - 45
f(x) = -27 (False).
For option C, we have:
f(x) = x² - 40
f(x) = -3² - 40
f(x) = 9 - 40
f(x) = -31 (False).
For option D, we have:
f(x) = −x² + 10
f(x) = −(-2)² + 10
f(x) = −9 + 10
f(x) = 1 (True).
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Complete Question:
A polynomial function is represented by the data in the table.
x = -5, -4, -3, -2, -1
f(x) = -15, -6, 1, 6, 9
Choose the function represented by the data.
A. f(x) = 6x + 15
B. f(x) = −6x − 45
C. f(x) = x² − 40
D. f(x) = −x² + 10
Select all the correct locations on the image.
Identify which functions have complex roots by selecting the function names on the provided coordinate plane
The functions have complex roots from the image are
Functions (b) and (d). This is further explained below.
What is Function?Generally, Function is simply defined as a connection between two or more variables that may be expressed mathematically.
In conclusion, Functions with graphs that never touch or cross the x-axis are said to have complicated roots, not real ones.
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Solve for X. Round to nearest tenth.
Answer:
x = 11.3
Step-by-step explanation:
[tex]cos(61^{o} )=\frac{5.5}{x}[/tex]
[tex]x=\frac{5.5}{cos(61^{o}) } =11.34[/tex]
Rounded to the nearest tenth:
x = 11.3
Hope this helps
Answer:
x ≈ 11.3
Step-by-step explanation:
using the cosine ratio in the right triangle
cos61° = [tex]\frac{DE}{DF}[/tex] = [tex]\frac{5.5}{x}[/tex] ( multiply both sides by x )
x × cos61° = 5.5 ( divide both sides by cos61° )
x = [tex]\frac{5.5}{cos61}[/tex] ≈ 11.3 ( to the nearest tenth )
find the slope between these two points (-8,3) and (6,7)
Answer:
[tex]slo pe \: = \frac{2}{7} [/tex]
Step-by-step explanation:
[tex]y1 = 3\\ x1 = - 8 \\ y2 = 7 \\ x2 = 6[/tex]
[tex]slope = \frac{y2 - y1}{x2 - x1} [/tex]
[tex]sope = \frac{7 - 3}{6 - ( - 8)} [/tex]
[tex]slope = \frac{4}{6 + 8} [/tex]
[tex]slope = \frac{4}{14} [/tex]
[tex] = \frac{2}{7} [/tex]
Answer:
[tex]\textsf{slope}=\dfrac{2}{7}[/tex]
Step-by-step explanation:
[tex]\textsf{let}\:(x_1,y_1)=(-8,3)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(6,7)[/tex]
Using the slope formula:
[tex]\textsf{slope}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-3}{6-(-8)}=\dfrac{4}{14}=\dfrac{2}{7}[/tex]
Therefore, the slope between the two points (-8, 3) and (6, 7) is 2/7
[urgent] the area of a circle is 40. if the circle is dilated by a scale factor of 3, how much does the area grow?
The area of the circle grows by a factor of 9, and the actual area is 360
How to determine the new area?The given parameters are:
Old area = 40
Scale factor = 3
When the circle is dilated, the new area becomes
New area = Old * (Scale factor)^2
Substitute 3 for scale factor
New area = Old * 3^2
Evaluate the exponent
New area = Old * 9
This means that the area of the circle grows by a factor of 9, and the actual area is:
New area = 40 * 9 = 360
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Abrianna sold 20, 23, 18, 4, 17, 21, 15, and 56 boxes of cookies after different football games. Which data value(s) are outliers? Select all that apply.
The data values that are outliers are 4 and 56.
What is an outlier?
An outlier is a number that is way smaller or way larger than that of other numbers in a data set. An outlier distorts the mean and median of the dataset.
In this data, 4 is smaller than the average of the data set and 56 is larger than the average numbers. They are the outliers.
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A right circular cone is intersected by a plane that passes through the cone's
vertex and is perpendicular to its base, as in the picture below. What is
produced from this intersection?
A. A pair of intersecting lines
B. A pair of parallel lines
C. A point
D. A single line
Answer:
A a pair of intersecting lines
Step-by-step explanation:
i got it right on the test bub
Answer: a pair of intersecting lines
Step-by-step explanation: i had many people help me know this is right
3h
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this pyramid has the same base as the prism, and its height is three times the height of the prism. what is the ratio of the volume of the
pyramid to the volume of the prism?
Answer:
volume of the pramind is 90332 ans And like
Graph the line with the equation y=-x-6
Answer:
in the picture
Step-by-step explanation:
You need 2 points to graph a line.
▪︎ if x = 0, y = 0 - 6 => y = -6
1st point: (0, -6)
▪︎if y = 0, 0 = -x - 6 => x = -6
2nd point: (-6, 0)
Seven candy bars will cost you $3.50. How much will one candy bar cost?
Answer:
50 cents
Step-by-step explanation:
The question is basically asking what is the unit price
So we simply do :
$3.50 ÷ 7 = $0.50 = 50 cents
Hope this helped and brainliest please
Answer:
$0.50
Step-by-step explanation:
let the cost of one candy bar = X
7 candy bar ---------------$3.50
1 candy bar ---------------- X
crodd multiplying
7×X = 3.50×1
7X = 3.50
dividing bothsides by
7X/7 = 3.50/7
X = 0.50
therefore, one candy bar will cost $0.50
In the table, pattern A uses the rule add five pattern B uses the rule at 10 which statement is true every term in pattern b is 10 more than the corresponding term in pattern a every term in pattern B is two times the corresponding term in pattern A every term pattern B is 10 times the corresponding term in pattern A every term in pattern B is 1/2 the corresponding term in Pattern A
Every term in pattern B is two times the corresponding term in pattern A
The correct option is (B).
What is algebra?Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.
Given:
pattern A uses the rule add five pattern
pattern B uses the rule add 10
if we take example
5x2=10 and comparable to pattern A x2 to get the next number.
Hence, every term in pattern B is two times the corresponding term in pattern A.
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The correct option is (B).
1. Write the point where the linear equation 3x + 4y = 12 cuts the x-axis.
Answer:
(4,0)
Step-by-step explanation:
The point where the line cuts the x-axis is called the x-intercept.
x-intercept is when y = 0.
So given y = 0,
3x+4(0) = 12
3x = 12
x = 12/3
x = 4
therefore the point is (4,0)
which 2 numbers have a mean of 10 and a range of 12
Answer:
Step-by-step explanation:
16 - 4 = 12
16 + 4 = 20
then 20 ; 2 = 10
Half of 12 is 6, therefore the two numbers 10 - 6 = 4 and 10 + 6 = 16 will have a mean of 10 and a range of 12.
Latonya works in a factory where she makes crispy snacks. first, she uses a machine that forms large 100 lb blocks of crispy. she cuts one block evenly into bars that each weigh 8oz. these bars are then pressed into a mold that creates 2 flat square wafers that each weigh 3oz. the left over waste material is put into recycle bins to be used elsewhere. these flat squares are then packed into bags of 5 which are sealed and finally packed into boxes, each containing 14 bags ready to be sent out to the stores. how much weight out of the original 100 lb block as a % is contained in the completely filled boxes (i.e. those containing a full 14 bags)?
The percentage of the original block cookie that is packaged and ready to be distributed to stores is: 12.6%.
How to calculate the biscuit percentage of the original biscuit that is packaged?
To calculate the percentage of the original 100lb cookie that is packaged and ready to be distributed, we must perform the following operations:
We must calculate how much each package of 5 cookies weighs, for this we multiply the weight of each cookie (3 ounces) 0.18 pounds by the number of cookies in each package (5).
0.18lb × 5 = 0.9 lbNext, we need to calculate how much the box containing 14 packages of cookies weighs by multiplying the weight of each package (0.9 lb) by the number of packages in each box (14).
0.9lb × 14 = 12.6 lbLastly, we need to calculate how much percentage the weight of each box is equal to the weight of the original 100 lb cookie that Latonya made. For that we divide 100 lbs. by 100 and multiply the result by the final weight of the box (12.6lbs).
100lbs ÷ 100 = 11 × 12.6 = 12.6%Based on the above, each box contains 12.6% of the first 100-lb cookie Latonya made.
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If increasing the number of goods produced is one way to increase
productivity, what is the other way to increase productivity?
A. Decrease the resources invested
OB. Raise the price of the goods
OC. Increase market share
OD. Lower the quality of the materials used
Answer: decrease the resources invested
Step-by-step explanation:
If $360 is divided between Pam and Bill in the ratio 3:5 respectively, how much more did Bill receive than Pam?
4. In how many ways can all of the letters of the word NUMBERS be arranged if it
start with a consonant and end with a vowel? /2
Answer:
2400 words
Step-by-step explanation:
First choose the first letter. You have 5 choices of consonant for this.
Next choose the last letter. You have 4 remaining consonants for this.
Now you have 5 remaining letters which can be placed in any order.
So the answer will be:
5⋅4⋅5!
20⋅120
2400
The vale’s in the table represent a linear function
Answer:
B
Step-by-step explanation:
an arithmetic squeegee is defined by
an = an-1 + d
that means that every term of the sequence is created by adding a constant d (the common difference) to the pervious term.
so, we get the common difference by caucuses the difference of 2 neighboring terms.
e.g.
a1 = 9
a2 = 22
a2 - a1 = 22 - 9 = 13
so, B. 13 is the right answer.
as a quick check if it is truly an arithmetic sequence, we can look, if all the other pairs have the same difference.
yes, they do. the difference is always 13.
What does the graph of the parametric equations x(t)=2−t and y(t)=(t+3)^2, where t is on the interval [−4,0], look like? Drag and drop the answers to the boxes to correctly complete the statements.
The graph state that the initial point is (6.9), and the terminal point is (2,1). The vertex of the parabola is (3,0). Arrows along the parabola to indicate motion right to left.
What is the parametric equations about?Let take x = 4 - t =t = 4 - x as equation (1)
And y = (t - 1)^2 as equation (2)
Then input equation (1) into equation (2)
y = ( 4 - x - 1)^2
y = ( 3 - x)^2
y = ( x - 3)^2
So therefore, y = a ( x -3)^2 + 0
It can be written as y = a(x - h)^2 + k
Where, a = 1
The vertex known to be (h, k) will be = (3,0).
The starting point is if t = -2
Therefore, x = (4 - -2) = 6
y = (-2 - 1)^2 = (-3)^2 = 9
So x, y = (6,9).
Note that if t = 2
Then x = (4 - 2) = 2
y = (2 - 1)^2 = 1^2
= 1
Therefore, x, y =(2, 1).
Therefore, The graph of the parametric equations state that the initial point is (6.9), and the terminal point is (2,1). The vertex of the parabola is (3,0). Arrows along the parabola to indicate motion right to left.
See full question below
What does the graph of the parametric equations x(t)=4−t and y(t)=(t−1)^2, where t is on the interval [−2,2], look like?
The parametric equations graph as a portion of a parabola. The initial point is _____, and the terminal point is _____. The vertex of the parabola is ____. Arrows are drawn along the parabola to indicate motion ____.
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Could someone help me on this
Answer:
13.) 314.2 in²
15.) 181.5 ft²
Step-by-step explanation:
The area of a circle is found using the equation:
A = πr²
In this equation, "π" represents the number pi (3.14....) and "r" represents the radius (half the diameter).
For 13.), you have been given the radius. Thus, you can substitute it into the equation and solve for "A".
A = πr²
A = π(10)²
A = π x (100)
A = 314.2 in²
For 15.), you have been given the diameter. To find the radius, you need to divide this value by 2. Once you find the radius, you can plug it into the equation and simplify like above.
diameter = 15.2 ft
radius = 7.6 ft
A = πr²
A = π(7.6)²
A = π x (57.76)
A = 181.5 ft²