A fruit company delivers its fruit in 2 types of boxes: large and small. A delivery of 3 large boxes and 5 small boxes has a total weight of 79 kilograms. A delivery of 12 large boxes and 2 small boxes has a total weight of 199 kilograms. How much does each type of box weight?
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Answer:
large: 15.5 kgsmall 6.5 kgStep-by-step explanation:
Let x and y represent the weights of the large and small boxes, respectively. Then the two delivery weights give rise to the equations ...
3x +5y -79 = 0
12x +2y -199 = 0
Using the "cross multiplication method" of solving these equations, we find ...
d1 = (3)(2) -(12)(5) = 6 -60 = -54
d2 = 5(-199) -(2)(-79) = -995 +158 = -837
d3 = -79(12) -(-199)(3) = -948 +597 = -351
1/d1 = x/d2 = y/d3
x = d2/d1 = -837/-54 = 15.5
y = d3/d1 = -351/-54 = 6.5
The large boxes weigh 15.5 kg; the small boxes weigh 6.5 kg.
_____
Additional comment
My preferred quick and easy way to solve equations like this is using a graphing calculator. In addition to that, an algebraic method is shown.
The "cross-multiplication method" shown here is what I consider to be a simplified version of what you would find in videos. It is a variation of Cramer's rule and the Vedic maths methods of solving pairs of linear equations. I find it useful when "elimination" or "substitution" methods would result in annoying numbers. In such cases, it uses fewer arithmetic operations than would be required by other methods.
Short description: writing the coefficients of the general form equations in 4 columns, where the last column is the same as the first, a "cross multiplication" is computed for each of the three pairs of columns. Those computations are of the form ...
[tex]\text{column pair: }\begin{array}{cc}a&b\\c&d\end{array}\ \Rightarrow\ d_n=ad-cb[/tex]
The relationship between the differences d₁, d₂, and d₃ and the variable values is shown above.
what is the measure of m?
The required value of m for the given triangle is given as m = 12.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.
Here,
Applying Pythagoras' theorem,
n² = m² - 6² - - - - (1)
m ² + base² = 24²
base² = 24² - m² - - - - (2)
n² + 18² = base²
From equation 1 and 2
m² - 6² + 18² = 24² - m²
2m² = 24² + 6² - 18²
m = 12
Thus, the required value of m for the given triangle is given as m = 12.
Learn more about Pythagorean triplets here:
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What value of x makes the equation 3x+7=22 true?
Answer:
[tex]x=5[/tex]
Step-by-step explanation:
Given [tex]3x+7=22[/tex], our goal is to isolate [tex]x[/tex] such that will have an equation that tell us [tex]x[/tex] is equal to something.
Start by subtracting 7 from both sides:
[tex]3x+7-7=22-7,\\3x=15[/tex]
Divide both sides by 3:
[tex]\frac{3x}{3}=\frac{15}{3},\\x=\frac{15}{3}=\boxed{5}[/tex]
Therefore, the value of [tex]x=5[/tex] makes the equation [tex]3x+7=22[/tex] true.
Answer:
x = 5
Step-by-step explanation:
Subtract 7 from both sides: 3x + 7- 7 = 22 - 7
Simplify: 3x = 15
Divide both sides by 3
Simplify: x = 5
Hope this helps:)
plssss
How much fat is in a mixture created
with x pints of 8% butterfat and y pints
of 15% butterfat?
Answer:
0.08x + 0.15y
Step-by-step explanation:
multiply the amount of pints with the given percent of fat
Answer:
Hence total fat in mixture is 8x+15y100 pints
The number of animals at a shelter from day to day has a mean of 37.6, with a standard deviation of 6.1 animals. The distribution of number of animals is not assumed to be symmetric. Between what two numbers of animals does Chebyshev's Theorem guarantees that we will find at least 89% of the days
Answer:
Between 19.3 and 55.9 animals.
Step-by-step explanation:
Chebyshev Theorem
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
In this question:
Mean of 37.6, standard deviation of 6.1.
Between what two numbers of animals does Chebyshev's Theorem guarantees that we will find at least 89% of the days?
Within 3 standard deviations of the mean, so:
37.6 - 3*6.1 = 19.3
37.6 + 3*6.1 = 55.9
Between 19.3 and 55.9 animals.
the legs of a right triangle have the following measurements: 5 and 10 inches. What is the length of the hypotenuse??
Write your answer in SIMPLIFIED SQUARE ROOT FORM
Answer:
[tex]5\sqrt{5}[/tex]
Step-by-step explanation:
1. [tex]5^2 + 10^2 = c^2[/tex]
2.[tex]125 = c^2[/tex]
3. [tex]c=5\sqrt{5}[/tex]
A Gallup survey of 2322 adults (at least 18 years old) in the U.S. found that 408 of them have donated blood in the past two years. Construct a 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years.
Answer:
The 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years is (0.1627, 0.1887).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
A Gallup survey of 2322 adults (at least 18 years old) in the U.S. found that 408 of them have donated blood in the past two years.
This means that [tex]n = 2322, \pi = \frac{408}{2322} = 0.1757[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1757 - 1.645\sqrt{\frac{0.1757*0.8243}{2322}} = 0.1627[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1757 + 1.645\sqrt{\frac{0.1757*0.8243}{2322}} = 0.1887[/tex]
The 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years is (0.1627, 0.1887).
You are installing new carpeting in a family room. The room is rectangular with dimensions 20 1/2 feet × 13 1/8 feet. You intend to install baseboards around the entire perimeter of the room except for a 3 1/2-foot opening into the kitchen. How many linear feet of board must you purchase?
Answer: 1. When you estimate, it is not an exact measurement. 3ft 8 in gets rounded to 4ft and 12 ft 3 in rounds to 12ft. now find the perimeter. P=2l+2w P= 2*12 +2*4 P=32feet
2. 3ft 8in = 3 8/12 or reduced to 3 2/3 12ft 3in = 12 3/12 or reduced to 12 1/4 The fractional part is referring to a fraction of a foot.
3. The perimeter of the room is P=2l+2w or P=2(12 1/4) + 2(3 2/3) p=24 1/2 + 7 1/3 P= 31 5/6 feet
4. The estimate and the actual are very close. They are 1/6 of a foot apart.
5a. Total baseboard 31 5/6ft - 2 1/4 ft = 29 7/12 feet needed.
5b. Take the total and divide it by 8ft = 29 7/12 divided by 8= 3.7 You are not buying a fraction of a board so you would need 4 boards.
Jul
attachments.office.net
6
7
A car journey is in two stages.
Stage 1 The car travels 110 miles in 2 hours.
Stage 2 The car travels 44 miles at the same average speed as Stage 1
Work out the time for Stage 2
Give your answer in minutes.
[3 m
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Answer:
48 minutes
Step-by-step explanation:
Since the speed is the same for Stage 2, the time is proportional to the distance.
t2/(44 mi) = (120 min)/(110 mi)
t2 = (44/110)(120 min) = 48 min . . . . . . multiply by 44 mi
The time for Stage 2 was 48 minutes.
What are the equations of the asymptotes for the functiony=tan2pix where 0
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Answer:
(b) x = 0.25, 0.75, 1.25, 1.75
Step-by-step explanation:
The asymptotes of tan(α) are found at ...
α = π/2 +nπ
We want to find x such that ...
2πx = α = π/2 +nπ
Dividing by 2π gives ...
x = 1/4 +n/2 . . . . . . . for integers n
In the desired range, the values of x are ...
x = 0.25, 0.75, 1.25, 1.75
HELP PLS DUE IN 6 MINUTES
6TH GRADE MATH
Answer:
C
Step-by-step explanation:
trust me its easy
Answer:
C: None of the above
Step-by-step explanation:
Can someone help me out please
when 3a^2-2a+5 is subtracted from a^2+a-1 the result is
Jessy pastes stamps for 160 envelopes in 2 hours. If she pastes the stamps at the same rate, for how many envelopes can she paste stamps in 30 minutes ?
2 hours=160
1 hours=160÷2=80
30 minutes=80÷2=40
Answer:She can paste 40 stamps in 30 minutes
Which statement IS true
about the equations -3x + 4y = 12 and +X- ~Y - 1?
The system of the equations has exactly one solution
at -8, 3).
• The system of the equations has exactly one solution at (-4, 3).
• The system of the equations has no solution; the two lines are parallel.
• The system of the equations has an infinite number of solutions represented by either equation.
Answer:
Second one(Not sure)
Step-by-step explanation:
I believe the system doesn't have an exact answer. But the line are parallel because of (3).
Ravi bought 50kg rice at the rate it tk40 per kg and sold it at the rate of tk44 per kg. What is the amount of profit or loss?
Here is your Answer
Step-by-step explanation:
Ravi bought rice = 50kg
Rate it =40kg
Sold it at the rate = = 44kg
Answer: -34Mark me as brainlist and give me 20 thx plshelp needed right away this is timed
The following data on price () and the overall score for stereo headphones that were tested by Consumer Reports were as follows. The estimated regression equation for these data is
(y-hat) = 27.922+0.302x
Brand Price Score
Bose 180 76
Scullcandy 160 76
Koss 95 69
Phillips/O'Neill 70 58
Denon 80 50
JVC 35 26
Required:
Does the t test indicate a significant relationship between price and the overall score?
Answer:
Relationship exists between price and overall score
Step-by-step explanation:
Given the data:
Brand Price Score
Bose 180 76
Scullcandy 160 76
Koss 95 69
Phillips/O'Neill 70 58
Denon 80 50
JVC 35 26
Using the correlation Coefficient calculator ; the correlation Coefficient, R = 0.875
H0 : no relationship exists
H1 : relationship exists
Using the R Coefficient ;
The test statistic :
T = r / √(1 - r²) / (n - 2)
n = 6
The test statistic :
T = 0.875 / √(1 - 0.875²) / (4)
T =0.875 / 0.05859375
T = 0.9333
The Pvalue from test statistic :
df = n - 2 ; 6 - 2 = 4
Pvalue(0.933, 4) = 0.02246
At α = 0.05
Pvalue < α ; We reject H0 ; and conclude that relationship exists between price and overall score
66. If the length of one side of a triangle 6 and the length of another side is 2, which of the following cannot be the length of the third side of the triangle?
A) 8
B) 7
C)
D) 5
Answer:
A)
Step-by-step explanation:
what is C ? 6 ?
if that is the case, then my answer is A) 8
why ? because then the other 2 sides together are just as long as this third side, and we would have just a flat line with the length of 8.
every side in a triangle must be shorter than the other two sides together.
but - fully formally such a flat line could be considered a special triangle with 2 angles of 0 degrees and one angle of 180 degrees.
that is why I am asking about the missing C answer. it could be a trick question. but if C is truly 6, then yes, A is the right answer. if C is larger than 8, then C is the right answer.
Britany wants to read a book. In her room, she has 5 mysteries, 15 historical fictions, 12 modern fantasies, and 7 blographies. how many different choices are available ?
a. 78
b. 34
c. 32
d.39
Answer
I guess
39 different choice are available
write your answer in simplest radical form
Answer:
n = 8√2
Step-by-step explanation:
It's a 30-60-90 triangle, so n = 2×4√6/√3 = 8√2
Name different types of triangles and illustrate how you can introduce each triangle to the foundation phase learner during a lesson presentation. Mention the resources that you will use
The types of triangles are: equilateral, isosceles, scalene, right angled, acute angled and obtuse angled triangle.
Triangles are plane shapes with three straight sides. Triangles are classified with respect to either their length of sides, or the measure of each internal angles.
1. Classification of triangles with their length of sides:
i. Equilateral triangle: This implies a triangle with equal length of sides.
ii. Isosceles triangle: This triangle has two of its side with equal length.
iii. Scalene triangle: In this triangle, non of its sides has equal length.
2. Classification of triangles with their internal angles:
i. Acute angled triangle: This triangle has all its angles less than [tex]90^{o}[/tex].
ii. Right angled triangle: This has one of its angles to be a right angle.
iii. Obtuse angled triangle: This triangle has one of its internal angles to be greater than [tex]180^{o}[/tex].
Therefore, there are generally six types of triangles of two classes.
Resources: Set squares, triangular prism, marking board and a marker etc.
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Brad is 12 years older than Sam. If Brad were 8 years older than he is now, he would
be twice as old as Sam. How old is Sam now?.
Answer:
Sam is 20 years old.
Find the measure of missing angle
Answer:
58 degrees
Step-by-step explanation:
90 - 32 = 58
What is cube root 16y^4/x^6
in simplest form?
Cube root of the given expression [tex]\frac{16y^{4} }{x^{6} }[/tex] in simplest form is equals to [tex]\frac{2y }{x^{2} }\sqrt[3]{2y}[/tex].
What is cube root?" Cube root is defined as the number when multiply three times and produce result as one original number one time."
According to the question,
Given expression,
[tex]\frac{16y^{4} }{x^{6} }[/tex]
Cube root of the given expression is,
[tex]\sqrt[3]{\frac{16y^{4} }{x^{6} }} \\\\\implies \sqrt[3]{\frac{(2)^{3}(2) y^{3} (y)}{(x^{2}) ^{3} }}\\\\\implies \frac{2y}{x^{2} } \sqrt[3]{2y}[/tex]
Hence, cube root of the given expression [tex]\frac{16y^{4} }{x^{6} }[/tex] in simplest form is equals to [tex]\frac{2y }{x^{2} }\sqrt[3]{2y}[/tex].
Learn more about cube root here
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Answer:
B on edge
trust me bro
Needs 20 characters even though the picture says it all.
Daphne has a rope that is 60 meters long. She wants to use it to mark the boundary of a circle whose radius is an integer. What's the largest possible radius for her circle, in meters?
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Answer:
9 m
Step-by-step explanation:
The relationship between radius and circumference is ...
C = 2πr
Daphne wants r an integer such that ...
60 m ≥ 2πr
r ≤ (60 m)/(2π)
r ≤ (30/π) m ≈ 9.549 m
The largest integer radius Daphne can use is 9 meters.
What is the x- intercept y =2x^2-8x+6?
Answer:
see your answer in the image
with full detail
mark me brainlist
Step-by-step explanation:
Answer:
(3,0) , (1.0)
Step-by-step explanation:
find the equation of a line perpendicular to 4x-y=4 that contains the points (0,3)
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Answer:
x + 4y = 12
Step-by-step explanation:
The perpendicular line can be found by swapping the x- and y-coefficients and negating one of them. Then those new coefficients can be used with the coordinates of the given point to find the required constant.
line: 4x -y = 4
perpendicular line: x +4y = constant
Through (0, 3):
0 +4(3) = constant = 12
The perpendicular line has standard form equation x +4y = 12.
Answer:
Step-by-step explanation:
y=-1/4x+3
GEOMETRY HELPPP PLEASEEE
Answer:
Step-by-step explanation:
