Here is your solution for the problem.
Thanks
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.
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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 sum of a number and twice its square is 105. Find the number.
Please someone help me
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Answer:
121/14 or 8 9/14
Step-by-step explanation:
The quotient of 1/8 and 1/4 is ...
(1/8)/(1/4) = (1/8)(4/1) = 4/8 = 1/2
The product of 2 2/3 and 3 3/7 is ...
(2 2/3)(3 3/7) = (8/3)(24/7) = (8·24)/(3·7) = 64/7
Subtracting the first result from the second gives ...
64/7 -1/2 = (128 -7)/14 = 121/14 = 8 9/14
_____
Additional comment
When subtracting fractions with denominators that have no common factors, I find it useful to make use of the formula ...
[tex]\dfrac{a}{b}-\dfrac{c}{d}=\dfrac{ad-bc}{bd}[/tex]
In this case, that gives us (64·2 -7·1)/(7·2) = (128 -7)/14.
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 wire is to be cut into two pieces. One piece will be bent into an equilateral triangle, and the other piece will be bent into a circle. If the total area enclosed by the two pieces is to be 64 m2, what is the minimum length of wire that can be used? What is the maximum length of wire that can be used?
(Use decimal notation. Give your answer to one decimal place.)
⠀⠀⠀⠀⠀⠀⠀⠀⠀Stolen from GoogIe :p
The minimum length of wire needed is approximately 22.5 meters and the maximum length of wire needed is also approximately 22.5 meters.
How to get the Length?Let's assume the length of the wire is "L" meters. We need to find the minimum and maximum values of L that satisfy the given conditions.
To find the minimum length of wire needed, we should minimize the combined area of the equilateral triangle and the circle. The minimum occurs when the wire is distributed in a way that maximizes the area of the circle while minimizing the area of the equilateral triangle.
Minimum length (L_min):
Let "x" be the length of the wire used to form the equilateral triangle, and "y" be the length used to form the circle.
The area of an equilateral triangle is given by (√(3)/4) * side², where the side is the length of one of the triangle's equal sides.
The area of a circle is given by π * radius².
Since the perimeter of an equilateral triangle is three times the length of one of its sides, and the circumference of a circle is given by 2 * π * radius, we have:
x + y = L ...(1) (The total wire length remains constant)
x = 3 * side ...(2) (Equilateral triangle perimeter)
y = 2 * π * r ...(3) (Circle circumference)
The area enclosed by the two pieces is given by:
Area = (√(3)/4) * side² + π * r²
We want to minimize this area subject to the constraint x + y = L.
To find the minimum, we can use the method of Lagrange multipliers.
By solving this optimization problem, we find that the minimum value of the combined area is approximately 64 m² when x ≈ 7.5 m and y ≈ 15 m. Thus, the minimum length of wire needed (L_min) is approximately 7.5 + 15 = 22.5 meters.
Maximum length (L_max):
To find the maximum length of wire needed, we should maximize the combined area of the equilateral triangle and the circle. The maximum occurs when the wire is distributed in a way that minimizes the area of the circle while maximizing the area of the equilateral triangle.
By solving this optimization problem, we find that the maximum value of the combined area is approximately 64 m² when x ≈ 15 m and y ≈ 7.5 m. Thus, the maximum length of wire needed (L_max) is approximately 15 + 7.5 = 22.5 meters.
So, the minimum length of wire needed is approximately 22.5 meters, and the maximum length of wire needed is also approximately 22.5 meters.
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The formula for the area of a triangle is A - 1/2bh. Hiro is solving the equation for h; his work is shown below. What mistake did Hiro make?
2 A-2
2A-bh
24-bmh
Hiro should have divided both sides of the equation by 2.
Hiro should have divided both sides of the equation by b.
Hiro should have added b to both sides of the equation
Hiro should have subtracted 2 from both sides of the equation
Answer:
a , hiro should have divided both sides of the equation by 2
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).
Does the point (6, 0) satisfy the equation y = x2?
Replace x in the equation with the x value of the point (6) and solve. If it equals the y value (0) it is a solution if it noes not equal (0) it is not a solution.
Y = 6^2 = 36
36 is not 0 so (6,0) is not a solution
Answer:
No, point (6, 0) is not on the equation.
Step-by-step explanation:
To do this question the easiest way, you would use your scientific/graphing calculator and type in your equation. But you can do this with your mind.
Since the equation y = x^2 does not have any number in it (such as m = slope) it does not start anywhere. You will put it in the origin which is (0, 0) from there, you can tell that the equation will not reach (6, 0), but only (1, 1).
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.
Evaluate each expression.
HELP!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
19. Which of the following
statements is true about
angle K?
K
R
a. Angle K is obtuse
b. angle K is acute
C. angle K is greater than
90
d. angle K is a right angle
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Answer:
b. angle K is acute
Step-by-step explanation:
We're often told not to draw any conclusions from the appearance of a figure in a geometry problem. Here, angle K appears to be somewhat less than 90°, so angle K is acute.
__
Additional comment
This choice of answer is confirmed by the fact that the other two (visible) choices say the same thing. If one of them is correct, so is the other one. Hence they must both be incorrect. (An obtuse angle is more than 90°.)
3/5x 2/7x 5/12 whats the Answer I've tried everything I still don't understand
Answer:
30/420 or 1/14
Step-by-step explanation:
3*2*7/5*7*12= 30/420 simplify the you get 1/14
Consider the function ƒ(x) = (x + 1)2 – 1. Which of the following functions stretches ƒ(x) vertically by a factor of 4?
A) ƒ(x) = 1∕4(x + 1)2 – 4
B) ƒ(x) = (1∕4x + 1)2 + 3
C) ƒ(x) = 4(x + 1)2 – 1
D) ƒ(x) = 4(4x + 1)2 – 1
Answer:
C f(x) = 4(x+1)2-1
Step-by-step explanation:
factor of 4 = 2^2
(x+1)2-1 = 4(x+1) 2-1 = with x
= 4(+1) 2-1 = without x
= (4 - 4) 2 = individual products of -1
= (8 - 8 ) = individual products of 2
= 8 - 8 = 2^2 -2^2
= 2^2 - 2^2
(x+1)2-1 = 4(x+1)2-1 = with x
= 2x^2 -2^2
-x = 2^2 -2^2
x = -2^2-2^2
x = 4
which proves f(x) is a factor of 4
Describe how to determine the average rate of change between x=4 and x=6 for the function f(x)=2x^3+4. Include the average rate of change in your answer.
Answer:
Step-by-step explanation:
Average rate of change is the same thing as the slope of the line between 2 points. What we have are the x values of each of 2 coordinates. What we don't have are the y values that go with those. But we can find them! Aren't you so happy?
We can find the y value that corresponds to each of those x values by evaluating the function at each x value, one at a time. That means plug in 4 for x and solve for y, and plug in 6 for x and solve for y.
[tex]f(4)=2(4)^3+4[/tex] and doing the math on that gives us
f(4) = 132 and the coordinate is (4, 132).
Doing the same for 6:
[tex]f(6)=2(6)^3+4[/tex] and doing the math on that gives us
f(6) = 436 and the coordinate is (6, 436). Now we can use the slope formula to find the average rate of change (aka slope):
[tex]m=\frac{436-132}{6-4}=\frac{304}{2}=152[/tex] where m represents the slope
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:
A rectangular plot of land is 100 feet long and 50 feet wide. How long is the walkway along the diagonal? Round to the
nearest foot
A) 75 feet
B) 87 feet
C) 112 feet
D) 150 feet
Answer:
Step-by-step explanation:
Which expression is equivalent to One-fourth minus three-fourths x?
Answer:
C: 112 feet
Step-by-step explanation:
Can someone help me out please
Black Diamond Ski Resort charges $25 for ski rental and $10 an hour to ski. Bunny Hill Ski Resort charges $50 for ski rental and $5 an hour to ski. Create an equation to determine at what point the cost of both ski slopes is the same.
Answer:
25 + 10h = 50+5h
Step-by-step explanation:
Black Diamond Ski Resort
25 + 10h
Bunny Hill Ski Resort
50+5h
Set them equal to each other to find when the cost is the same
25 + 10h = 50+5h
when 3a^2-2a+5 is subtracted from a^2+a-1 the result is
Hank has a bottle of diluted syrup that is 60% maple syrup and a bottle of pure syrup that is 100% maple syrup in his restaurant. How many ounces of pure syrup should he mix with the diluted syrup in order to make 100 ounces of 85% maple syrup? Express your answer as a decimal rounded to the nearest hundredth if necessary.
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Answer:
62.5 oz of 100%
Step-by-step explanation:
Let p represent the number of ounces of pure syrup. Then (100-p) is the number of ounces of 60% syrup. The amount of maple syrup in the desired mix is ...
p +0.60(100 -p) = 0.85(100)
0.40p +60 = 85 . . . . . . . . . . . simplify
0.40p = 25 . . . . . . . . . . subtract 60
p = 62.5 . . . . . . . . . divide by 0.4
62.5 ounces of pure syrup should be mixed with the diluted syrup to make 100 ounces of 85% maple syrup.
_____
The other 37.5 ounces will be 60% syrup.
HELP ASAP PLEASE!!
stroller rental at the zoo costs $14.00 per day, but members get an 8% discount. What price do members pay for stroller rental?
Answer:
$10.08
Step-by-step explanation:
100%=$14
72%= x (cross multiple)
100% × x =72% × $14
100x =1008
divide both sides by 100
100x÷100=1008÷100
x=$10.08
Josh spread a total of 281.4 pounds of soil onto the gardens on campus. He used 40.2 pounds on each garden. How many gardens does the campus have
Answer:7
Step-by-step explanation: I would say just divide unless there is more context.
Given the figure, which method will you most
likely use to prove that triangle ADE and
triangle ABC are similar?
A.The SSS Postulate
B.The SAS Postulate
C.The ASA Postulate
D.The AA Postulate
Answer:
B. The SAS Postulate
Step-by-step explanation:
In the given figure, we are shown two triangles, [tex]\triangle ADE[/tex] and [tex]\triangle ABC[/tex].
Since triangle ADE is inscribed in triangle ABC, both triangles must share angle [tex]A[/tex]. Furthermore, let's take a look at the two legs of each triangle, if we say that their respective bases are DE and BC.
Compare the corresponding legs of each triangle with proportions:
[tex]\frac{AC}{AE}=\frac{10}{5}=2,\\\\\frac{AB}{AD}=\frac{8}{4}=2,\\\\\overline{AC}:\overline{AE}=\overline{AB}:\overline{AD}[/tex]
Since two corresponding legs/sides of triangle are in a constant proportion, the triangles must be similar from the SAS (Side-Angle-Side) Postulate.
Which describes the transformations applied in the figure above?
7 units up and 10 units to the left
5 units down and a reflection about the y-axis
5 units up and a counterclockwise rotation of 180 degrees
5 units down and a counterclockwise rotation of 90 degrees
Answer:
Step-by-step explanation:
(4). 5 units down and a counterclockwise rotation of 90 degrees
Option D is the correct answer.
We need to find which options describe the transformations applied in the given figure.
What are the transformations?There are four common types of transformations - translation, rotation, reflection, and dilation. From the definition of the transformation, we have a rotation about any point, reflection over any line, and translation along any vector. These are rigid transformations wherein the image is congruent to its pre-image. They are also known as isometric transformations. Dilation is performed at about any point and it is non-isometric.
From the given figure we can see 5 units down and a counterclockwise rotation of 90°.
Therefore, option D is the correct answer.
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