Please help.This is part C:c A penny is about 0.06 inch thick. About how tall is the tallest stack?
Answers
ANSWER
a. (1, 4), (2, 3), (3, 2) and (4, 1)
b. $655.36
c. 3932.16 inches
EXPLANATION
The row numbers are y and the column numbers are x.
Each position contains a stack of pennies and the number of pennies in each stack is given as:
\(n=2^x\cdot2^y\)a. We want to find the locations that have 32 as the number of pennies in the stack.
For a stack to contain 32 pennies, it means that:
\(32=2^x\cdot2^y\)Write 32 in form of powers of 2s, we have that:
\(\begin{gathered} 2^5=2^x\cdot2^y=2^{x\text{ + y}}\text{ (addition law of indices)} \\ A\text{ccording to the law of indices:} \\ \Rightarrow\text{ 5 = }x\text{ + y} \end{gathered}\)This implies that whichever location must contain 32 pennies must have row and column number which add up to 5.
The only combinations that allow for that are:
1 + 4 = 5
2 + 3 = 5
3 + 2 = 5
4 + 1 = 5
Therefore, the coordinates are (in form of (x, y)):
(1, 4), (2, 3), (3, 2) and (4, 1)
b. The tallest stack of pennies will be the one in the position:
\(2^8\cdot2^8\)This is because 8 is the highest number of rows and columns.
Therefore, the number of pennies in that position is:
\(\begin{gathered} n=2^{8\text{ + 8}}=2^{16} \\ n\text{ = 65536 pennies} \end{gathered}\)Each penny costs $0.01.
Therefore, the amount of money in the tallest stack is:
Amount = 65536 * 0.01
A = $655.36
c. A penny is about 0.06 inch thick.
Since there are 65536 pennies in the tallest stack, it means that, the height of the tallest stack is:
H = 65536 * 0.06
H = 3932.16 inches
Related Questions
Carmen has 54 golf balls. He wants to put the same number of balls into each of
9 buckets. Which multiplication equation shows a way to represent the number
of balls that should go into each bucket?
Answers
Answer:
54 divided by 9 = 6
Step-by-step explanation:
Find the value of each variable. (x and y)
Answers
Answer: x=3\(\sqrt{2\). y=3\(\sqrt{2\)
Step-by-step explanation: This is a 45-45-90 triangle. Both of the legs, x and y, are congruent. To find the length of the legs, divide 6, the hypotenuse, by \(\sqrt{2\). 6/\(\sqrt{2\)=3\(\sqrt{2\).
Heather's work to find the distance between two points, R(-3,-4) and S(5,7), is
shown:
RS = √(-4) (-3))² + (7 − 5)²
= √(-1)² + (2)²
= √1 + 4
= √5
-
What error, if any, did Heather make?
A. She substituted incorrectly into the distance formula.
B. She subtracted the coordinates instead of adding them.
C. She made a sign error when simplifying inside the radical.
OD. She made no errors.
Answers
The distance between points R and S is \(\sqrt{ (185)\). The correct answer is D. She made no errors.
Heather's work to find the distance between two points, R(-3,-4) and S(5,7), is shown:
RS = √(-4) (-3))² + (7 − 5)²
= √(-1)² + (2)²= √1 + 4
= √5
The error is with the order of subtraction in the formula for the distance between two points.
Heather did not make any errors in calculating the distance between two points. Therefore, the correct answer to the question above is (OD) She made no errors.
The formula for the distance between two points, A (x1, y1) and B (x2, y2), in the coordinate plane is given as;
dAB = \(\sqrt{ ((x^2 - x1)^2 + (y2 - y1)^2)\)
Comparing the given question with the formula above, we have;
A = R (-3, -4) and B = S (5, 7)The distance, AB = RS.
Therefore, we have;
RS = \(\sqrt{ ((5 - (-3))^2 + (7 - (-4))^2)\)
On solving the above equation;RS = \(\sqrt{ ((5 + 3)^2 + (7 + 4)^2)\)RS
= \(\sqrt{ (8^2 + 11^2)RS\)
= \(\sqrt{ (64 + 121)RS\)
= \(\sqrt{ (185)\)
Therefore, the distance between points R and S is \(\sqrt{ (185)\).
From the calculation, it is clear that Heather did not make any errors while calculating the distance between two points. The answer obtained by Heather is correct.
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Solve for x. Enter your answer in the box below as a fraction in lowest terms, using the slash (/) as the fraction bar.
6/9+x=7/10
Answers
Reduce 6/9 to 2/3, take 2/3 from both sides, then subtract the fractions
Can Someone Help REAL QUICK Me. ? Please
Answers
Answer: Option 3
Step-by-step explanation:
You can make equivalent fractions by multiplying or dividing both top and bottom by the same amount. You only multiply or divide, never add or subtract, to get an equivalent fraction.
I hope this helps.
please help me on thisuse pythagoras' theorem to find the third side
Answers
Adjacent = 12
Explanation:
The shape is a right angled triangle
Using pythagoras' theorem:
Hypotenuse² = opposite² + adjacent²
hypotenuse is the longest side = 13
opposite is the vertical side or the side opposite the angle = 5
Adjacent is the base. it is not given in the question.
So we need to find it.
using the formula:
13² = 5² + adjacent²
169 = 25 + adjacent²
collect like terms:
169 - 25 = adjacent²
144 = adjacent²
square root both sides:
√144 = √( adjacent²)
12 = adjacent
Adjacent = 12
Hence, the value missing side is 12
ME has the endpoints of M(-6,4) and E (5,-2) find the midpoint and distance of ME
Answers
Answer:
(-0.5, 1)- the midpoint, the distance is sqrt157
Step-by-step explanation:
The midpont is O
x0= (-6+5)/2= -0.5
yo= (4-2)/2=1
(-0.5, 1)
The distance is sqrt ((5-(-6))^2+(-2-4)^2)=sqrt 157
m/ABD is a straight angle.
m/CBD = 8x+16°
m/ABC = 6x - 60°
Find m/ABC:
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Answer:
Solution in attached photo.
Step-by-step explanation:
SolutionThe solution is attached as a photo. This Question tests on the concept of Angle Properties.
Properties required:
1) Angles in a straight line sums up to 180°.
Please help!!! Thank you!
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Answer:
C
Step-by-step explanation:
y=-2x+3
can someone help me with this?thank u
Answers
Answer:
Step-by-step explanation:
first one:
X= 10
Y = 14.14
use Tan45degrees X/10
Please help with this word problem, this is 6th grade mathematics.
Answers
Answer:
2 / 15 of the recommended amount
Explanation:
We know that 3/4 of a cup contains 1 /10 of the recommended amount. Therefore, the ratio of cups to recommended amount is
cups : recommended amount = 3 /4 : 1/10 < ---- (a)
Now, how much of the recommended amount does 1 cup of oatmeal contain?
Let us call this unknown value ( the recommended amount in 1 cup) x, then the ratio
cups: recommended amount is
cups : recommended amount = 1 : x <----- (b)
The ratio (a) and (b) must be equal; therefore,
\(\frac{3/4}{1/10}=\frac{1}{x}\)Now cross multiplication gives
\((3/4)x=(1)(1/10)\)\(\Rightarrow\frac{3x}{4}=\frac{1}{10}\)Cross multiplying one more time gives
\((3x)(10)=(4)(1)\)\(30x=4\)finally, dividing both sides by 30 gives
\(\frac{30x}{30}=\frac{4}{30}\)\(x=\frac{4}{30}\)\(x=\frac{4\div2}{30\div2}=\frac{2}{15}\)\(\boxed{x=\frac{2}{15}\text{.}}\)Therefore, there is 2/ 15 of the recommended amount in 1 cup of oatmeal.
write two equations that when graphed look like this *see image*. please help its due soon and i will give ya 75 points for answering CORRECTLY thanks, 5 stars, and brainlist. Thank ya
Answers
The graph is showing the equation of circle x²+y²=4
What is a circle?A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.
The given graph in the question represents the equation of the circle cutting the points on the x-axis and y-axis at 4 which is the radius of the circle.
The equation will be as follows:-
x²+y²=4
Hence the graph is showing the equation of circle x²+y²=4
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An aquarium holds 11.35 cubic feet of water, and is 2.6 feet long and 1.1 feet wide. What is its depth? Round your answer to the nearest whole number.
The depth is
feet.
Answers
The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).
To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,
which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).
Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.
Substituting these values into the formula for volume,
we get:11.35 = 2.6 × 1.1 × h
Simplifying this expression:
11.35 = 2.86h
Dividing both sides by 2.6 × 1.1,
we get:h ≈ 3.64 feet (rounded to two decimal places)
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Choose the true statement about virtue-based ethics.
i. According to the principles of virtue-based ethics, character is more important than actions.
ii. According to the principles of virtue-based ethics, right and wrong are assessed using culture as a guide.
iii. According to the principles of virtue-based ethics, the consequences of actions are very important.
iv. According to the principles of virtue-based ethics, rules are used to evaluate actions.
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Virtue based ethics holds that character is more important than actions.
Virtue based ethics is the aspect of ethics that holds that the moral character of a person if of more paramount importance than the person's actions and its consequences.
Hence, the true statement about virtue based ethics from the options is that; "according to the principles of virtue-based ethics, character is more important than actions."
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The serial number on a bill consists of a letter followed by nine digits and then a letter. How many different serial numbers
are possible, given the following conditions?
(a) Letters and digits cannot be repeated.
(b) Letters and digits can be repeated.
(c) The letters are nonrepeated consonants and the digits can be repeated. (Let y be a consonant.)
Answers
Answer:
(a) 2,358,720,000
(b) 676,000,000,000
(c) 420,000,000,000
Step-by-step explanation:
The serial number on a bill consists of a letter followed by nine digits and then a letter.
There are 26 different letters and 10 digits (0 through 9) available.
Part (a)If the letters and digits cannot be repeated, there are:
26 choices for the first letter and 25 choices for the second letter.10 choices for the first digit, 9 choices for the second digit, 8 choices for the third digit, and so on.Therefore, the number of serial numbers that are possible if the letter and digits cannot be repeated is:
26 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 25 = 2,358,720,000
Part (b)If the letters and digits can be repeated, there are:
26 choices for each letter.10 choices for each digit.Therefore, the number of serial numbers that are possible if the letter and digits can be repeated is:
26 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 26 = 676,000,000,000
Part (c)There are 21 consonants in the alphabet.
If the letters are non-repeated consonants and the digits can be repeated, there are:
21 choices for the first letter and 20 choices for the second letter.10 choices for each digit.Therefore, the number of serial numbers that are possible if the letters are non-repeated consonants and the digits can be repeated is:
21 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 20 = 420,000,000,000
question is in the image below
Answers
The perimeter of Sam's string is 178 inches.
Given information:
Sam has a rectangular shaped window.
Length = 65 inches.
Width = 24 inches.
To find the perimeter:
you can use the formula:
Perimeter = 2 x (Length + Width)
Substituting the values into the formula, we have:
Perimeter = 2 x (65 + 24)
Perimeter = 2 x 89
Perimeter = 178 inches
Therefore, the perimeter of the rectangular window is 178 inches.
So, the perimeter of the rectangular window is 178 inches. This means that if you were to walk along the outline of the window, you would cover a total distance of 178 inches. It's important to note that the perimeter represents the total length of all the sides combined, and it is measured in the same unit (in this case, inches) as the length and width of the window.
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A product 0.5% of which are defective is packet in
cartons of 100 what % of cartons
is free from defectives , contains 3 or more defectives
Answers
We must deduct the number of cartons that contain at least one defective product from the proportion of cartons that are defect-free. the percentage of cartons that contain 3 or more defectives is approximately \(3.6\) %.
What is the binomial distribution?Let's assume that there are N cartons of the product.
We know that 0.5% of the product is defective, which means that in one carton of 100 products, there are 0.5/100 * 100 = 0.5 defective products. Therefore, in N cartons, the total number of defective products would be
\(0.5/100 \times 100 \times N = N/2.\)
To find the percentage of cartons that are free from defectives, we need to subtract the number of cartons that contain at least one defective product.
the total number of cartons and then divide by the total number of cartons, which is N.
The probability of a carton containing no defective products is \((1-0.005)^100\approx 0.605.\)Therefore, the percentage of cartons that are free from defectives is approximately \(60.5%\) .
To find the percentage of cartons that contain 3 or more defectives, we need to use the binomial distribution.
The probability of a carton containing k defective products is given by the formula:
\(P(k) = (100 choose k) \times (0.005)^k \times (1-0.005)^(100-k)\)
We want to find the probability of a carton containing 3 or more defective products, so we need to sum up the probabilities for k=3,4,5,...,100:
P(3 or more defectives) = ∑ P(k) for k=3 to 100
Using a computer or a calculator, we can find that this probability is approximately \(0.036\) .
Therefore, the percentage of cartons that contain 3 or more defectives is approximately \(3.6\) %.
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Grams in this equation
Answers
30 .650 pounds of gramsin vegetables
Arianna runs up 4 flights of stairs and then runs down 4 flights of stairs.
Does this situation represent additive inverses? Explain.
A
Yes; The numbers combine to eight.
B
Yes; The numbers combine to zero.
No; The numbers are both represented by the same integer.
D
No; The numbers cannot be added together.
Answers
Answer:
Yes this represents additive inverse,
Step-by-step explanation:
Since you are subtracting the same number 4 to get to zero.
The depth of a local lake averages 38 ft, which is represented as |−38|. In February, it measured 6 ft deep, or |−6|, and in July, it was 25 ft deep, or |−25|. What is the difference between the depths in February and July?
A32 feet
B 31 feet
C 19 feet
D 13 feet
Answers
The difference between the depths in February and July is 31 feet.
How to measure depth?The method of measuring depth depends on what we are trying to measure the depth of. Here are some general methods for measuring different types of depth:
Depth of water: The depth of water can be measured using a sounding device such as a sonar or a simple depth gauge. A sonar uses sound waves to determine the distance from the water's surface to the bottom. A depth gauge is a simple device that measures the distance from the surface of the water to the bottom using a weight and a line.
Depth of a hole: The depth of a hole can be measured using a tape measure or a ruler. Simply insert the measuring device into the hole and measure the distance from the top of the hole to the bottom.
Depth of a trench: The depth of a trench can be measured using a measuring tape or a surveyor's level. Place the measuring device at the edge of the trench and measure the distance from the top of the trench to the bottom.
Depth of a pool: The depth of a pool can be measured using a pool depth marker or by using a measuring tape. A depth marker is usually located on the side of the pool and indicates the depth at various points. Alternatively, you can use a measuring tape to measure the distance from the surface of the water to the bottom of the pool.
Depth of a well: The depth of a well can be measured using a well sounder or a tape measure. A well sounder is a device that sends a signal down the well and measures the time it takes for the signal to bounce back. The time it takes is then used to calculate the depth of the well. Alternatively, a tape measure can be used to measure the distance from the surface of the water to the bottom.
Given, In February, it measured 6 ft deep, or |−6| and in July, it was 25 ft deep, or |−25|.
The difference between the depths in February and July is:
|−6| − |−25| = 6 − (−25) = 6 + 25 = 31
Therefore, the correct choice is B) 31 feet.
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In a survey 18 out of 50 people say their favorite type of movie is an action movie write the value as a percent
Answers
So,
18/50 x 100% = 36%
Therefore, 36% of the people surveyed said their favorite type of movie is an action movie.
————————
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Answer:
The percentage of 18 people out of 50 is 36 %
Step-by-step explanation:
The percentage refers to the per hundred or hundredths and is ended with the symbol %. By dividing two amounts, ratios and percentages are both used to compare the two amounts.
The formula for finding the percentage is to divide the value by the total value and then multiply the value by 100.percentage = ( given value / total value ) x 100so,
The given value is 18 people.The total value is 50 people.percentage = ( 18 / 50 ) x 100 = ( 0.36 ) X 100 = 36 %Therefore the percentage of 18 people out of 50 people is 36 %.
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Can you please help.
Answers
Answer:
1 pound = $3.75
Step-by-step explanation:
3.2 pounds = $12
→ Divide both sides by 3.2 to get 1 pounds worth
1 pound = $3.75
The cost of a cake varies directly with the number of cake bought suppose that the price of three cakes is $12, which direct variation equation represents this situation
Answers
The direct variation equation that represents the situation where the price of three cakes is $12 is C = 4N.
How to calculate the equation of the variationIf the cost of a cake varies directly with the number of cakes bought, we can write the direct variation equation as:
C = kN
where C is the cost of the cakes, N is the number of cakes bought, and k is the constant of variation.
To find the value of k, we can use the given information that the price of three cakes is $12.
Substituting N = 3 and C = 12 into the equation, we get:
12 = k * 3
Solving for k, we get:
k = 4
Now we can write the direct variation equation for the situation as:
C = 4N
Therefore, the direct variation equation of the situation is C = 4N.
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The table and the Circle Chart shown display the percentage of dogs in seven different groups of dog breeds in a dog competition.
How does the Circle Graph misrepresent the data in the table?
A. The percentages do not add up to 100.
B. The size of the section representing the Non-Sporting group is smaller than the section that represents Herding group.
C. The number of regions in the graph is not correct for the data.
D. One of the breeds in the table is not represented in the Circle Chart.
Answers
Answer:
a
Step-by-step explanation:
Answer:
Incorrect, it's actually B.
Step-by-step explanation:
Look at the Non-Sporting Group and Herding Group. The sizes of the slices are different (NSG being smaller than HG)
Which statement is correctly written as a conditional statement?
The number 10 is an even number, or it is a composite number.
If the number 10 is an even number, then it is a composite number.
The number 10 is an even number when it is a composite number.
A number, such as 10, is a composite number because it is even.
Answers
The statement that correctly written as a conditional statement is; A number, such as 10, is a composite number because it is even. so the correct option is D.
What are natural numbers, rational numbers, integers and irrational numbers?Natural numbers are: 1, 2, 3, ....
Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )
Rational numbers are numbers which can be written in the form of a/b
where a and b are integers.
Irrational numbers are those real numbers which are not rational numbers.
Here, Know that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.
A composite number is a number divisible by another number than 1 and the number itself.
To find example, a sum of two composite numbers, which is not a composite number, is needed.
The statement that correctly written as a conditional statement is; A number, such as 10, is a composite number because it is even.
Hence so the correct option is D.
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PLEASE HELP FAST & CORrect 50 POINTS
Answers
Answer:
105
Step-by-step explanation:
What is the missing side length??
Answers
The length of the missing leg for the triangles are: x = 7.01, f = 5.4, and d = 15.1 using the Pythagoras rule.
What is the Pythagoras rule?The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
By Pythagoras rule we can evaluate for b as follows:
x = √(7.5² - 2.5²)
x = √50
x = x = 7.0711
f = √[(√78)² - 7²]
f = √(78 - 49)
f = √29
f = 5.3852
d = 2 × √(11² × 8²)
d = 2 × √53
d = 15.0996
Therefore, the length of the missing leg for the triangles are: x = 7.01, f = 5.4, and d = 15.1 using the Pythagoras rule.
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A 100 N boxer punches a 10 kg punching bag with his fist using a 25 N force. Describe the
forces on the fist and the punching bag.
A) The force on the fist is greater than the force on the punching bag.
B) The force on the fist is equal to the force on the punching bag.
C) The force on the fist is smaller than the force on the punching bag.
D) Not enough information is given to determine which force is larger or smaller
Answers
Answer:
B
Step-by-step explanation:
B is the answer to your question
please help.
definitions: 1. definition of right triangle
2. definition of isosceles TrianglesReflexive
3. HL
4. definition of perpendicular
5. CPCTC
6. reflexive
Answers
From the two column proof below, we have seen ∠BAC ≅ ∠DAC by CPCTC
How to solve two column proof problems?The two column proof to show that ∠BAC ≅ ∠DAC is as follows:
Statement 1: ΔABD is Isosceles with base BD, AC ⊥ BD
Reason 1: Given
Statement 2: AB ≅ AD
Reason 2: Definition of isosceles Triangles
Statement 3: ∠1 and ∠2 are right angles
Reason 3: Definition of perpendicular
Statement 4: AC ≅ AC
Reason 4: Reflexive Property
Statement 5: ΔABC and ΔADC are right triangles
Reason 5: Definition of right triangle
Statement 6: ΔABC ≅ ΔADC
Reason 6: HL Congruency
Statement 7: ∠BAC ≅ ∠DAC
Reason 7: CPCTC
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A large hotel orders bars of soap to Stocketts rooms once per year if the hotel goes through an average of 750 bars of soap each week how many bars of soap should the hotel order per year
Answers
The hotel should order 39000 bars of soap if the hotel goes through on an average of 750 soaps each week.
In everyday terms, an average is one number chosen to represent a list of numbers; it is often the sum of the numbers divided by the number of numbers in the list (the arithmetic mean).
Average is calculated by dividing the sum of the data by the frequency of the data.
Average=sum ÷ frequency
For example if the average of the data set {1,2,3,5,10}=(1+2+3+5+10)÷5=21÷5=4.2
Now for the given question average is given as 750 bars of soap.
We know that there are 52 weeks in a year. ∴ frequency=52
Hence sum of all the averages will give the total number of soap ordered by the hotel in a year.
Sum=average × frequency
or, sum=750 × 52
or, sum=39000 bars of soap.
hence the hotel orders 39000 bars of soap in one year.
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