4000 g
Step-by-step explanation:
32 kg means 32000 g of watermelon
divided into 8 bowls
grams of watermelon in each bowl are 32000÷8 = 4000 g
Ally put 4,000 grams of watermelon in each bowl.
Explanation:
To find out how many grams of watermelon Ally put in each bowl, we need to divide the total weight of the watermelon slices by the number of bowls. Ally sliced 32 kg of watermelon and divided it equally between 8 large bowls. To convert kg to grams, we multiply by 1000. So, the total weight of watermelon in grams is 32,000 grams. To find out how many grams of watermelon went into each bowl, we divide the total weight by the number of bowls: 32,000 grams / 8 bowls = 4,000 grams.
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the quoient of 36 and 3 is j
Answer:
j = 12
Step-by-step explanation:
Quotient means the answer when you divide the dividend by the divisor.
In this example, we are dividing 36 by 3, so 36 = dividend, 3 = divisor.
36 / 3 = 12. See the attachment if you need extra help on long division!
Answer:
It is 12
Step-by-step explanation:
So first you divide 36 by 3. So 3 goes into 3 once. Now 3 goes into 6 twice so there you have it
write each ratio in simplest form:
3:6
10:5
16:24
Answer:
1:2
2:1
2:3
Step-by-step explanation:
3:6
Divide each side by 3
3/3: 6/3 1:2
10:5
Divide each side by 5
10/5 : 5/5 2:1
16:24
Divide each side by 8
16/8: 24/8 2:3
which function represents a parabola?
Answer:
b. g(x) only
Step-by-step explanation:
A investor has an account with stock from two different companies. Last year her stocking company A was worth $4600 in her stocking company B was worth $1000. Stocking company a has decreased 25% since last year in stock and Company B has decreased 22%. What was the total percentage decrease in the investor stock account round your answer to the nearest 10
Answer: 24.5%
Step-by-step explanation:
Last year her stock in company A was worth $4600. If her Stock in company A has decreased by 25% since last year in stock, then the amount by which it decreased is
25/100 × 4600 = $1150
The present worth is
4600 - 1150 = $3450
Also, her stock in company B was worth $1000. If her Stock in company B has decreased by 22% since last year in stock, then the amount by which it decreased is
22/100 × 1000 = $220
The present worth is
1000 - 220 = $780
The total worth of both stocks last year was
4600 + 1000 = $5600
The total worth of both stocks this year was
3450 + 780 = $4230
The amount by which it decreased is
5600 - 4230 = 1370
the total percentage decrease in the investor stock account is
1370/5600 × 100 = 24.5%
What is the slope of the line that contains these points?
x
12
13
14
15
y
-4
2
8
14
Answer:
6x-76
Step-by-step explanation:
If you graph it out, you'll realize it makes a line that cuts the y-intercept at -76, thus the last value. The slope also has a gradient of 6, thus the coeffecient of x.
Final answer:
The slope of the line through the points given is 6, calculated using the slope formula with the rise over run between the two points.
Explanation:
The slope of a line is calculated by finding the ratio of the vertical change (the rise) to the horizontal change (the run) between two points on the line. Using the coordinates provided (12, -4) and (15, 14), we can apply the slope formula slope (m) = (y_2 - y_1) / (x_2 - x_1). Plugging in the values gives us (14 - (-4)) / (15 - 12) = 18 / 3 = 6. Therefore, the slope of the line that contains these points is 6.
A manufacturer of cell phone screens is concerned because 12 percent of the screens manufactured using a previous process were rejected at the final inspection and could not be sold. A new process is introduced that is intended to reduce the proportion of rejected screens. After the process has been in place for several months a random sample of 100 screens is selected and inspection. Of the 100 screens 6 are rejected. What are the appropriate hypotheses to investigate whether the new process reduces the population proportion of screens that will be rejected
In hypothesis testing for this scenario, the null hypothesis (H-0) is that the proportion of rejected screens remains 12 percent (H-0: p = 0.12). The alternative hypothesis (Ha) is that the proportion of rejected screens is less than 12 percent (Ha: p < 0.12). A sample is taken and a significance test (such as a z-test for proportion) is conducted to decide if the null hypothesis can be rejected.
Explanation:The question is looking for you to conduct a hypothesis test to investigate whether a new process in manufacturing cell phone screens has led to a reduced proportion of rejected screens. When conducting such a hypothesis test, you'll need to consider a null hypothesis and an alternative hypothesis.
The null hypothesis (H-0) is often the initial claim about a population proportion. In this case, the null hypothesis would be that 12 percent of the screens (0.12) are still being rejected: H-0: p = 0.12.
The alternative hypothesis (Ha) is what you might believe to be true if the null hypothesis is proven to be incorrect. Here, the alternative hypothesis would be that less than 12 percent of screens are being rejected with the new process: Ha: p < 0.12.
To clarify, if the new process is effective, a lower proportion of screens should be rejected. Thus, the hypotheses to be tested are:
H-0: p = 0.12Ha: p < 0.12Lastly, after selecting the sample, compute the sample proportion. Here a total sample size of 100 screens with only 6 being rejected means the sample proportion (p) = 6/100 = 0.06.
From here, you would proceed to conduct a significance test (possibly a z test for proportion) and determine a p-value to make a decision regarding the null hypothesis.
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What are the differences between pyramids and cones?
Answer:
Pyramids are triangular in shape with a sided shape, whereas cones have circular bases that merely adjoin at a point.
Step-by-step explanation:
Answer:
A pyramid is a cone with a polygonal base ;)
Are the expressions equivalent? Use j = 3 and j = 8 to determine if they are. 7(j – 2) 4j – 5 No, because when j = 8, the values of the expressions are different. Yes, because when j = 3, the value of both expressions is 7 and when j = 8, the value of both expressions is 42. Yes, because when j = 3, the value of both expressions is 7. Yes, because when j = 8, the values of the expressions are different.
Answer:
No, because when j = 8, the values of the expressions are different.
for a shorter answer, A
Step-by-step explanation:
No, because when j = 8, the values of the expressions are different. Therefore, option A is the correct answer.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 7(j-2)4j-5.
Here, j=3 ad j=8
When j=3, we have
7(3-2)4×3-5
= 7×1×4×3-5
= 84-5
= 79
When j=8, we have
7(8-2)4×8-5
= 7×5×4×8-5
= 1115
Therefore, option A is the correct answer.
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A scientist estimated that a mixture would need 5 millimeters of a chemical to balance. The actual amount d was 7 millimeters. What was the percent error of the scientists estimation?
Answer:
29%
Step-by-step explanation:
If 7 is 100% correct then 5 would only be a portion of it
So you need to divide 5 by 7
So 5 divided by 7 is .714 or .71
this means the error was 29%
In a city school, 70% of students have blue eyes, 45% have dark hair, and 30% have blue eyes and dark hair. What is the probability (rounded to the nearest whole percent) that a randomly selected student has dark hair, given that the student has blue eyes
Answer:
The probability that a randomly selected student has dark hair, given that the student has blue eyes is 43%.
Step-by-step explanation:
Conditional probability:
Let A and B any two events connected to a given random experiment E. The conditional probability of the event A on the hypothesis that the event B has occurred, denoted by P(A|B), is defined as
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
Given that,
In a city school, 70% of students have blue eyes, 45% have dark eyes and 30% have blue eyes and dark hair.
A= students have blue eyes
B= Students have dark hair.
P(A)= 70% [tex]=\frac{70}{100}[/tex] [tex]=\frac7{10}[/tex]
P(B)=45% [tex]=\frac{45}{100}[/tex] [tex]=\frac9{20}[/tex]
P(A∩B)=30%[tex]=\frac{30}{100}[/tex] [tex]=\frac3{10}[/tex]
∴P(B|A)
[tex]=\frac{P(A\cap B)}{P(A)}[/tex]
[tex]=\frac{0.3}{0.7}[/tex]
[tex]=\frac37[/tex]
=0.429
=0.429×100 %
≈43%
The probability that a randomly selected student has dark hair, given that the student has blue eyes is 43%.
NEW YORK
The standard configuration for a New York license
plate is 3 digits followed by 3 letters.
Source: New York State Department of Motor Vehicles
How many different license plates are possible
if digits and letters can be repeated?
234 ABC
O 1757600
1577600
12812904
11232000
The total number of possible New York license plates is 17,576,000.
The number of different license plates possible for a standard configuration in New York, where a license plate is composed of 3 digits followed by 3 letters, can be determined through combinatorial math.
Step-by-Step Solution:
There are 10 possible digits (0-9) and 26 possible letters (A-Z).Since repetitions are allowed, we calculate the total number of combinations for digits and letters separately.The number of ways to choose 3 digits is 10 3 = 10 × 10 × 10 = 1000.The number of ways to choose 3 letters is 26 3 = 26 × 26 × 26 = 17576.Multiplying these two results together gives the total number of possible license plates: 1000 × 17576 = 17576000.The cereal box shown below is a rectangular prism. Find the surface area of the cereal box.
Answer:
= 1700 :)
Step-by-step explanation:
-multiply all the sides,
-add them,
- then double the answer (or times it by 2):
1) 30 times 20 = 600
30 times 5= 150
20 times 5 =100
2) Add them:
600+150+100 = 850
then times 850 by 2
850 times 2 = 1700
Hope that helped :)
Answer:
Guys for this one the 30, 20, 5 is 1700
Step-by-step explanation:
Drag and drop a statement or reason to each box to complete the proof. Given: parallelogram EFGH Prove: EG¯¯¯¯¯ bisects HF¯¯¯¯¯¯ and HF¯¯¯¯¯¯ bisects EG¯¯¯¯¯ . Parallelogram E F G H with diagonals E G and H F intersecting at point K. Statement Reason parallelogram EFGH Given EF¯¯¯¯¯∥HG¯¯¯¯¯¯ When two parallel lines are cut by a transversal, alternate interior angles are congruent. The opposite sides of a parallelogram are congruent. △EKF≅△GKH ASA Congruence Postulate CPCTC EG¯¯¯¯¯ bisects HF¯¯¯¯¯¯ and HF¯¯¯¯¯¯ bisects EG¯¯¯¯¯ .
By proving triangle HKE and triangle GKF congruent, it is proved EG bisects HF and HF bisects EG.
Given that, parallelogram EFGH.
Prove that, EG bisects HF and HF bisects EG.
Parallelogram EFGH with diagonals EG and HF intersecting at point K.
Proof:
Consider, ΔHKE and ΔGKF
∠HKE=∠GKF (Vertically opposite angles are equal)
∠FHE=∠GFH ( Alternate angles between the parallel line EF and HG)
∠GEH=∠FGE ( Alternate angles between the parallel line EF and HG)
By AAA congruency, ΔHKE and ΔGKF are congruent
By CPCT,
KE=GK
JF=HK
So, EG bisects HF and HF bisects EG.
Hence, proved.
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Final answer:
To prove that EG¯¯¯¯¯ bisects HF¯¯¯¯¯¯ and HF¯¯¯¯¯¯ bisects EG¯¯¯¯¯ in parallelogram EFGH, we can use the statements and reasons provided.
Explanation:
To prove that EG¯¯¯¯¯ bisects HF¯¯¯¯¯¯ and HF¯¯¯¯¯¯ bisects EG¯¯¯¯¯ in parallelogram EFGH with diagonals EG and HF intersecting at point K, we can use the following statements and reasons:
Statement: parallelogram EFGH4x + 3y = 6
-4x + 2y = 14
solve the system of equations
Answer:
I believe it is
x = -3/2 (-1.5)
y = 4
Answer:
A) 4x + 3y = 6
B) -4x + 2y = 14
Add the equations
5 y = 20
y = 4
Putting y into A)
A) 4x + 3*4 = 6
A) 4x = -6
x = -1.5
Step-by-step explanation:
What is the midpoint of ?
A: (2p – 2t, r)
B: (t + p, r)
C: (p, r)
D: (p – t, r)
The midpoint of a line segment is given by the formula ((x₁ + x₂) / 2, (y₁ + y₂) / 2). After applying this formula to the given options, the correct midpoint is (p, r).
Explanation:The midpoint of a line segment with coordinates (x₁, y₁) and (x₂, y₂) is given by the formula:
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
Applying this formula to the given options:
A: Midpoint = (2p - 2t, r)B: Midpoint = (t + p, r)C: Midpoint = (p, r)D: Midpoint = (p - t, r)After substituting the values, we find that the correct answer is Option C: (p, r).
Determine any data values that are missing from the table, assuming that the data represent a linear function.
Answer:
D
Step-by-step explanation:
If the circumference of a circle is 50. How many inches long is it’s radius?
Answer:
7.9617
Step-by-step explanation:
r=c/2pi so 50/2(3.14)
Answer: about 7.9617 !
Step-by-step explanation: you to divide 50 by 3.14 to get the diameter, then divide the diameter by 2 to get the radius, then round it!
Please can you help me with this question
1. Find g(x), where g(x) is the translation 7 units up of f(x) = x.
2. Find g(x), where g(x) is the translation 5 units left of f(x) = x2.
3. Find g(x), where g(x) is the translation 3 units right and 4 units up of f(x) = x2.
4. Find g(x), where g(x) is the translation 1 unit left and 5 units down of f(x) = |x|.
Translations of functions involve adjusting the graph horizontally by adding or subtracting values within the function's argument, and vertically by adding or subtracting values directly to the function. For the given functions, respective translations have resulted in g(x) expressions that have been adjusted according to these rules.
Explanation:To answer the student's mathematics questions about translations of functions, we will apply the concepts learned from algebra to transform each given function accordingly.
Translation 7 units up of f(x) = x results in g(x) = x + 7.For the translation 5 units left of f(x) = x2, we use g(x) = (x + 5)2.The translation 3 units right and 4 units up of f(x) = x2 gives us g(x) = (x - 3)2 + 4.Translation 1 unit left and 5 units down of f(x) = |x| leads to g(x) = |x + 1| - 5.In these function transformations, we've made use of horizontal and vertical translations, where adding or subtracting values within the function argument adjusts the graph horizontally, and adding or subtracting values outside the function adjusts it vertically.
Use the drop-down menus to identify the key values of the box plot. The median is . The minimum is . The maximum is . The lower quartile (Q1) is . The upper quartile (Q3) is .
Answer:
The median is - C
The minimum is - A
The maximum is - E
The lower quartile (Q1) is - B
The upper quartile (Q3) is - D
The median is C, the minimum is A, the maximum is E, the lower quartile (Q1) is B and the upper quartile (Q3) is D.
What is median?The value that divides the mathematical numbers or expressions in half is known as the median. The middle data point is known as the median value. Then, organize the data points in ascending order before calculating the median.
As per the given data, whiskers range from A to E.
The middle point of whisker is C.
Hence, the median is given by C.
And the whisker ranges to maximum E.
And range starts from A.
So the minimum is A.
Quartiles are three values that split sorted data into four parts, each with an equal number of observations.
The lower quartile is B and upper quartile is D.
Therefore, the answers of the median is C, the minimum is A, the maximum is E, the lower quartile (Q1) is B and the upper quartile (Q3) is D.
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What is 3x5 , answer is
Answer:15
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
5=1
10=2
15=3
Kevin is going to purchase sod for his backyard (see diagram below). How many square feet of sod will Kevin need?
Answer:
450 square feet
Step-by-step explanation:
Think of the shape as a complete rectangular
The area of the rectangular shape would be 25×30 = 750 square feet
Now find the area of the missing space and subtract it from 750
it would be 15×20 = 300 square feet
750 - 300 = 450 square feet
Mr Tan invested $5000 in an endowment fund for
5 years. The fund pays an interest compounded
yearly. At the end of 5 years, he received a total of
$5800. Find the interest rate.
Answer:
Compound Interest Formula Solved For Rate:
log (1 + rate) = {log(total) -log(Principal)} ÷ Years
log (1 + rate) = {log(5,800) -log(5,000)} ÷ 5
log (1 + rate) = [3.7634279936 -3.6989700043] / 5
log (1 + rate) = 0.0644579893 / 5
log (1 + rate) = 0.0128915979
Then we raise 10 to the power of 0.0128915979 which equals
1.0301289629 = 1 + rate
Therefore, rate = .0301289629 and we multiply by 100 to make a percentage:
3.01289629 %
Source: https://1728.org/compint2.htm
https://1728.org/compint.htm
Step-by-step explanation:
Using the compound interest formula and the provided values, the interest rate for Mr Tan's investment is calculated to be approximately 3.02%.
Explanation:The subject problem belongs to the topic of Compound Interest in mathematics. The formula used for compound interest is A = P (1 + r/n)^(nt), where A represents the total amount received, P represents the principal (initial investment amount), r represents the rate of interest, n represents the number of times interest is compounded per time period, and t represents the time period.
In this problem, Mr Tan's initial investment, P, is $5000. The total amount, A, he received after 5 years is $5800. The interest is compounded annually meaning that n is 1. We rearrange the compound interest formula to solve for the interest rate: r = [(A/P)^(1/nt) - 1]n .
Using Mr Tan's values, the calculation becomes: r = [(5800/5000)^(1/5) - 1]*1. Thus, the interest rate is approximately 0.0302 or 3.02%.
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The score of golfers for a particular course follows a normal distribution that has a mean of 73 and a standard deviation of 3. Suppose a golfer played the course today. Find the probability that her score is at least 74.
Answer:
0.3694
Step-by-step explanation:
In this question, we are asked to calculate the probability that a golfer scored at least 74 if she played on a particular day.
Given that ,
mean = µ = 73
standard deviation = σ = 3
P(x > 74) = 1 - P(x<74 )
= 1 - P[(x -µ) / σ < (74 -73) /3 ]
= 1 - P(z <0.3333 )
Using z table
= 1 - 0.6305
= 0.3694
probability= 0.3694
To find the probability of a golfer scoring at least 74 on a course with a mean score of 73 and a standard deviation of 3, we calculate the z-score for 74, find the corresponding probability in the z-table, and subtract this from 1 to get the upper tail probability. The probability is approximately 37%.
Explanation:The score of golfers for a particular course follows a normal distribution that has a mean of 73 and a standard deviation of 3. We want to find the probability that a golfer scores at least 74. This is a question of statistics and specifically involves the concept of the normal distribution and calculating z-scores.
Firstly, we need to calculate the z-score for the score of 74. The z-score is calculated as (X-μ)/σ, where X is the score we are interested, μ is the mean, and σ is the standard deviation. Substituting the given values, (74 - 73) / 3 gives a z-score of approximately 0.33.
Then, to find the probability that a score is at least 74, we need to find the proportion of data to the right of this z-score in a standard normal distribution. This is known as the 'upper tail'. We subtract the z-score from 1 because the total probability under the normal curve is 1. If we look up 0.33 in the z-table, we get a value of 0.6293. Subtracting this value from 1 gives us 0.3707.
Therefore, the probability that a golfer scores at least 74 on this course is approximately 0.37 or 37%.
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James has an ice cube tray that makes ice in the shape of spheres rather than cubes. Each sphere of ice has a radius of 22 2 2 cm. One tray makes 66 6 6 spheres.
Answer:
James has an ice cube tray that makes ice in the shape of spheres rather than cubes. Each sphere of ice has a radius of 2 cm. One tray makes 6 spheres.What is the total volume of ice the tray can make at one time?
Total volume of the tray James have = 201.06 cm^3
Step-by-step explanation:
Given:
Radius of the spherical ice cube = 2 cm
No. of spheres in the ice cube = 6
We have to find the total volume of the ice tray that can make at one time.
Let the total volume be "V".
Formula to be used:
Volume of sphere = [tex]\frac{4\pi r^3 }{3}[/tex] cubic unit.
Total volume = [tex]n\times \frac{4\pi r^3 }{3}[/tex] cubic unit.
So,
Total volume of the ice tray (V) :
⇒ [tex]V=n\times \frac{4\pi r^3 }{3}[/tex]
⇒ Plugging n = 6 and r = 2
⇒ [tex]V=6\times \frac{4\pi (2)^3 }{3}[/tex]
⇒ [tex]V=6\times \frac{4\pi (8) }{3}[/tex]
⇒ [tex]V=6\times \frac{32\pi }{3}[/tex]
⇒ [tex]V=\frac{32\times 6\pi }{3}[/tex]
⇒ [tex]V=32\times 2\pi[/tex]
⇒ [tex]V=201.06\ cm^3[/tex]
So,
The total volume of ice the tray can make at one time = 201.06 cm^3
Is (1,1) a function?
Answer:
I don't think it is a function
A function is a set of ordered pairs where a x-value is paired with only one y-value.
As long if the x-value (1) is sharing only one y-value then it makes it a function.
a scientist has 400ml of a 8% solution. how much water needs to be added to lower it to a 2% solution?
1200 ml of water needs to be added to lower it to a 2% solution.
Step-by-step explanation:
Given that,
A scientist has 400ml of a 8% solution.
you need to find how water is required to lower the 400 ml to 2% solution.
Let 'x' be the amount of water added to lower it 2% solution.
The formula is given by,
volume of the liquid × % of solution = volume of the new liquid × new %
This can be denoted in chemical relationship ⇒ c₁v₁=c₂v₂ where c is concentration and v is volume .
Now, to find the total volume of new liquid in ml :
400 ml = v₁
0.08= c₁
0.02=c₂
v₂=?
400 × 0.08 =v₂ × 0.02
v₂=1600 ml
To find the x value :
Amount to be added = volume of new liquid - volume of liquid before.
⇒ x =1600-400
⇒ x =1200 ml
∴ 1200 ml of water needs to be added to lower it to a 2% solution.
Solve the system of equations using the substitution method.
-5x − 3y = 16
y = x
Answer:
-5x - 3x = 16
-8x = 16
x = -2
y = x
Step-by-step explanation:
Answer:
(-2, -2)
Step-by-step explanation:
Make use of the 2nd equation to eliminate x or y in the 1st equation:
-5x - 3(x) = 16
Then -8x = 16, and x = -2. Since we are told that y = x, y = -2.
The solution is (-2, -2).
Metal Fabrication If an open box is made from a tin sheet 10 in. square by cutting out identical squares from each corner and bending up the resulting flaps, determine the dimensions of the largest box that can be made. (Round your answers to two decimal places.)
Answer:
ength (l) : (10-2*5/3) = 20/3 width(w): (10 - 2*5/3) = 20/3 height(h): 5/3Step-by-step explanation:
Let x is the side of identical squares
By cutting out identical squares from each corner and bending up the resulting flaps, the dimension are:
length (l) : (10-2x)width(w): (10-2x)height(h): xThe volume will be:
V = (10-2x) (10-2x) x
<=> V = (10x-2[tex]x^{2}[/tex]) (10-2x)
<=> V = 100x -20[tex]x^{2}[/tex] - 20[tex]x^{2}[/tex] + 4[tex]x^{3}[/tex]
<=> V = 4[tex]x^{3}[/tex] - 40[tex]x^{2}[/tex] + 100x
To determine the dimensions of the largest box that can be made, we need to use the derivative and and set it to zero for the maximum volume
dV/dx = 12[tex]x^{2}[/tex] -80x + 100
<=> 12[tex]x^{2}[/tex] -80x + 100 =0
<=> x = 5 or x= 5/3
You know 'x' cannot be 5 , because if we cut 5 inch squares out of the original square, the length and the width will be 0. So we take x = 5/3
=>
length (l) : (10-2*5/3) = 20/3 width(w): (10 - 2*5/3) = 20/3 height(h): 5/3To determine the dimensions of the largest box that can be made from a tin sheet, we need to find the side length of the square that will be cut out from each corner of the tin sheet. The dimensions of the largest box that can be made are approximately 6.67 inches by 6.67 inches by 1.67 inches.
Explanation:To determine the dimensions of the largest box that can be made from a tin sheet, we need to find the side length of the square that will be cut out from each corner of the tin sheet. Let's assume the side length of the square to be x inches. The length and width of the resulting box will be 10 - 2x inches and 10 - 2x inches, respectively. The height of the box will be x inches. To find the dimensions of the largest box, we need to find the value of x that maximizes the volume of the box.
The volume of the box is given by V = (10 - 2x)(10 - 2x)(x). We can write this as V = 4x^3 - 40x^2 + 100x. To find the value of x that maximizes the volume, we can take the derivative of V with respect to x and set it equal to 0. Differentiating V, we get dV/dx = 12x^2 - 80x + 100. Setting this equal to 0 and solving for x, we find x = 1.67 inches (rounded to two decimal places). Therefore, the dimensions of the largest box that can be made are approximately 6.67 inches by 6.67 inches by 1.67 inches.
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A house has increased in value by 38% since it was purchased. If the current value is $621,000 what was the value when it was purchased.
The original value of the house when it was purchased was $450,000.
Let us assume the original value of the house was x. This means that the house has increased by 38% from x to become $621,000.
In order to find the original value therefore, you can use the formula:
Original value + (Original value x Increase) = Current price
x + (38% × x) = 621,000
1.38x = 621,000
x = 621,000 / 1.38
= $450,000
In conclusion, the original value was $450,000.
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Final answer:
The original purchase price of the house was $450,000.
Explanation:
To find the original value of the house before it increased in value, we must first understand that the current value represents 138% of the original value, since the house has increased in value by 38%. This is because the original value is 100%, and the increase is 38%, making the total 138%. Therefore, the equation to find the original purchase price (which we can call 'P') is:
P * 138% = $621,000
We can rewrite this as:
P * 1.38 = $621,000
To solve for P, we divide both sides of the equation by 1.38:
P = $621,000 / 1.38
Now, doing the division:
P = $450,000
So, the house was originally purchased for $450,000 before it increased by 38% to its current value of $621,000.