Answers
For rectangle type books, the difference in the heights of their stacks of books is 15 3/4 inches.
What exactly is a rectangle?
A rectangle is a type of quadrilateral (a four-sided polygon) that has four straight sides and four right angles. It is a two-dimensional shape, meaning it lies flat in a plane, and is defined by its two sets of parallel sides, each pair of which are equal in length.
In a rectangle, opposite sides are parallel and congruent (equal in length), and adjacent sides are perpendicular (meet at a right angle). The diagonals of a rectangle bisect each other (divide each other into two equal parts) and are congruent.
The area of a rectangle is calculated by multiplying its length and width, while its perimeter is found by adding the lengths of all its sides. The area of a rectangle is A = l x w, where A is the area, l is the length, and w is the width.
Now,
To solve this problem, we need to first find out the height of Rick's stack of books. We know that his stack is 3 times as tall as Trevor's stack, so:
Rick's stack = 3 x Trevor's stack
Rick's stack = 3 x 7 7/8 inches
Rick's stack = 23 5/8 inches
Now that we know the height of both stacks, we can find the difference between them:
Difference = Rick's stack - Trevor's stack
Difference = 23 5/8 inches - 7 7/8 inches
Difference = 15 6/8 inches
Difference = 15 3/4 inches
Therefore, the difference in the heights of their stacks of books is 15 3/4 inches.
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Related Questions
The local movie theater increased its admission price by 18%. If the original admission price was $5.50, how many dollars is the new admission price? sorry for asking another question
Answers
Answer:
$6.49
Step-by-step explanation:
The original admission price was $5.50, and it increased by 18%. Let's find 18% of 5.50 and then add it to $5.50, meaning $5.50 would increase by 18% (of itself.)
So 18% of 5.50 = 0.99 ( thats 0.18 x 5.50)
Add the 99 cents (0.99) to $5.50
and then you get $6.49
here is the equation I used:
(5.50 x 0.18) + 5.50
hope this helped :)
Rachel goes to a shopping mall to buy shirts and pants for her
children. She has a total budget of $200, and she's going to
buy shirts for $25 each and pants for $20 each. Write an
inequality to describe the possible number of shirts and Pants
that Rachel can buy. If Rachel buys 5 Pants, what is the
maximum number of shirts she can buy?
Answers
Answer:
4
Step-by-step explanation:
Let x be the number of shirts that Rachel can buy, and y be the number of pants she can buy. Then the cost equation would be:
Cost = 25x + 20y
Since Rachel has a total budget of $200, we can write:
25x + 20y ≤ 200
To find the maximum number of shirts that Rachel can buy if she buys 5 pants, we can substitute y = 5 into the inequality and solve for x:
25x + 20(5) ≤ 200
25x ≤ 100
x ≤ 4
Therefore, Rachel can buy a maximum of 4 shirts if she buys 5 pants.
zoe the goat is tied by a rope to one corner of a 15 meter-by-25 meter rectangular barn in the middle of a large, grassy field. over what area of the field can zoe grace of the rope is:
Answers
If Zoe the goat is tied to a corner of a rectangular barn measuring 15m by 25m in the middle of a field, Zoe can graze within an area of 2660.5 sqm.
The area of the field that Zoe can graze depends on the length of the rope, which is not given in the problem. However, we can use the Pythagorean theorem to find the length of the diagonal of the barn, which represents the maximum length of the rope.
The diagonal of a rectangle with sides of length 15 meters and 25 meters can be found using the Pythagorean theorem:
diagonal² = 15² + 25²
diagonal² = 225 + 625
diagonal² = 850
diagonal =[tex]\sqrt{850}[/tex] ≈ 29.15 meters
This means that the maximum length of the rope is about 29.15 meters. The area that Zoe can graze is a circle with radius equal to the length of the rope. We can use the formula for the area of a circle to find this area:
Area = π(radius)²
Area = π(29.15)²
Area ≈ 2660.5 square meters
Therefore, the correct answer is approximately 2660.5 square meters
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During the National Brushing Day, each student receives 10 pamphlets each on tooth brushing drills. If there were 756 students the school, how many pamphlets were given out?
Answers
If there were 756 students in the school and each student receives 10 pamphlets on the tooth brushing drills, the total number of pamphlets given out, using multiplication operation, is 7,560.
What is multiplication operation?Multiplication operation is one of the four basic mathematical operations.
Multiplication operation involves the number being multiplied (the multiplicand), the multiplier or the number multiplying the multiplicand, and the product, which is the result.
The number of pamphlets given to each student on tooth brushing drills = 10
The total number of students at the school.
The total number of pamphlets given out to the students = 7,560 (756 x 10)
Thus, based on multiplication operation, the total pamphlets were 7,560.
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Graph the solution to the following system of inequalities in the coordinate plane.
y < -2x - 4
x ≥ -3
Answers
Answer:
green is x ≥ -3
blue is y < -2x - 4
Step-by-step explanation:
What is the missing reason in step 8? statements reasons 1. circle m with inscribed ∠kjl and congruent radii jm and ml 1. given 2. △jml is isosceles 2. isos. △s have two congruent sides 3. m∠mjl = m∠mlj 3. base ∠s of isos. △are ≅ and have = measures 4. m∠mjl m∠mlj = 2(m∠mjl) 4. substitution property 5. m∠kml = m∠mjl m∠mlj 5. measure of ext. ∠ equals sum of measures of remote int. ∠s of a △ 6. m∠kml =2(m∠mjl) 6. substitution property 7. measure of arc k l = measure of angle k m l 7. central ∠ of △ and intercepted arc have same measure 8. measure of arc k l = 2 (measure of angle m j l) 8. ? 9. one-half (measure of arc k l) = measure of angle m j l 9. multiplication property of equality reflexive property substitution property base angles theorem second corollary to the inscribed angles theorem
Answers
The answer fοr this is Substitutiοn Prοperty
What is Substitutiοn Prοperty?
The substitutiοn prοperty is a cοncept in algebra that is used tο substitute the value οf a given variable οr a quantity intο an expressiοn tο find the value οf the unknοwn. In simple wοrds, we can say that the substitutiοn prοperty is used tο replace the value οf a quantity in an equatiοn οr an expressiοn tο sοlve a mathematical prοblem. We will discuss the meaning οf the substitutiοn prοperty οf equality, the substitutiοn prοperty in geοmetry, and the direct substitutiοn prοperty in limits in the fοllοwing sectiοns.
Substitutiοn Prοperty is cοnsidered as οne οf the mοst intuitive οf the mathematical prοperties that yοu'll prοbably encοunter. Yοu may have been using substitutiοn withοut even knοwing it. This prοperty says that if x=y, then in any true equatiοn invοlving y, yοu can replace y with x, and yet yοu'll still have a true equatiοn.
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Take a loοk at the attached example shοwn below.
please help i will give 100 points
Answers
Answer:
x= 3
Step-by-step explanation:
Since triangle is equilateral...
2y = 25x - 15
And....
Here,
2y + 2y + 2y = 180
6y = 180
y = 180/6
= 30
Again,
2y = 25x -15
2*30 + 15 = 25 x
x = 75/25
= 3
If Chandler uses 3 gigabytes of data this
month, how much will his cell phone bill be?
Answers
explanation :
3x5 (15 is the answer) why: amount per gigabyte, and the gigabyte
it says above: $20 + whatever amount of gigabytes
20+15
= $35
Father's age is five times than the son's age. If the sum of their ages is 60 years, find their present ages.
Answers
Father : 50 years old
Son : 10 years old
Cola makers test new recipes for loss of sweetness during storage. Trained tasters rate the sweetness before and after
storage. Here are the sweetness losses (sweetness before storage minus sweetness after storage) found by 10 tasters
for one new cola recipe:
2. 0,0. 4,0. 7, 2. 0-0. 4 2. 2-1. 3 1. 2 1. 12. 3
Are these data good evidence that the cola lost sweetness? Use the four-step process and use a significance level of
5%. Assume the data is taken from a normal distribution.
Answers
The null hypothesis was rejected as the mean of the sweetness losses was greater than the critical value. Thus, the cola did lose sweetness.
1. State the null hypothesis: The null hypothesis is that the cola did not lose sweetness.
2. Determine the level of significance: The level of significance is 5%.
3. Calculate the test statistic and The test statistic is calculated by subtracting the mean of the sweetness losses from zero.
4. Make a decision: If the test statistic is greater than the a critical value, then the null hypothesis should be rejected and the cola did lose sweetness. which is greater than the a critical value of 0.05. Therefore, the null hypothesis should be rejected and the cola did indeed lose sweetness.
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(06.01 MC) What is the value of the expression shown below? 7 + (2 + 6) 2 ÷ 4 ⋅ (1/2)4
Group of answer choices
23
9
8
18
Answers
Answer:
8
Step-by-step explanation:
Solving numeric expression:Use PEDMAS
P - Parenthesis
E - Exponents
D -Division
M - Multiplication
A & S - Addition and subtraction. [tex]\bf 7 + (2 +6)^2 \div 4 * (\dfrac{1}{2})^2 = 7 + 8^2 \div 4 * \dfrac{1}{16}\\\\\\\text{\bf First perform the operation inside the parenthesis and then the exponents}[/tex]
[tex]= 7 + 64 \div 4 * \dfrac{1}{16}[/tex]
Here, exponents 8² = 64 is done
[tex]\bf = 7 + 16 * \dfrac{1}{16} \ {(\bf Division \ is \ done)}[/tex]
= 7 + 1
= 8
Answer:
wait I big speak. it's important for learn how.
Assume X is normally distributed with a mean of 10 and a standard deviation of 2. Determine the value for x that solves each of the following:
(a) P(X > x) = 0.5
(b) P(X > x) = 0.95
(c) P(x < X < 10) = 0.2
(d) P(-x < X - 10 < x) = 0.95
(e) P(-x < X - 10 < x) = 0.99
Answers
The values of 'x' that solve for given conditions are (a) 11.349 (b) 13.29 (c) 7.44 and 12.56 (d) 6.08 and 13.92 (e) 5.84 and 14.16.
The formula for z-score:The z-score, also known as the standard score, is a measure of how many standard deviations a data point is away from the mean of its distribution.
The formula for calculating the z-score of a data point x, with mean μ and standard deviation σ, is:
z = (x - μ) / σwhere z is the z-score.
Here we have
X is normally distributed with a mean of 10 and a standard deviation of 2
As we know z score, z = (x - μ) / σ.
=> x = μ + zσ
Hence, to find the 'x' value we need to know the value of the z score in each situation
(a) P(X > x) = 0.5
The z-score corresponding to a right-tail probability of 0.5 is 0.6745.
=> x = 10 + 0.6745 * 2
=> x = 11.349
(b) P(X > x) = 0.95
The z-score corresponding to a right-tail probability of 0.05 is 1.645.
Substituting the given values into the formula, we get:
x = 10 + 1.645 * 2
x = 13.29
(c) P(x < X < 10) = 0.2
The z-score corresponding to a left-tail probability of 0.1 is -1.28 and the z-score corresponding to a right-tail probability of 0.1 is 1.28.
From formula, z = (x - μ) / σ
=> -1.28 = (x - 10) / 2
=> x = 7.44
and
=> 1.28 = (x - 10) / 2
=> x = 12.56
Therefore,
The values of x that solve P(x < X < 10) = 0.2 are 7.44 and 12.56.
(d) P(-x < X - 10 < x) = 0.95
The z-score corresponding to a right-tail probability of 0.025 is 1.96.
=> -1.96 = (-x - 10) / 2
=> x = 6.08
and
=> 1.96 = (x - 10) / 2
=> x = 13.92
Therefore,
The values of x that solve P(-x < X - 10 < x) = 0.95 are 6.08 and 13.92.
(e) P(-x < X - 10 < x) = 0.99
The z-score corresponding to a right-tail probability of 0.005 is 2.58.
=> -2.58 = (-x - 10) / 2
=> x = 5.84
and
=> 2.58 = (x - 10) / 2
=> x = 14.16
Therefore,
The values of x that solve P(-x < X - 10 < x) = 0.99 are 5.84 and 14.16.
Therefore,
The values of 'x' that solve for given conditions are (a) 11.349 (b) 13.29 (c) 7.44 and 12.56 (d) 6.08 and 13.92 (e) 5.84 and 14.16.
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The first four terms in a sequence are
2 5 8 11
If the 19th term in the sequence is 56.
Answers
Answer:
We can see that each term in the sequence is 3 more than the previous term. So we can find the 5th term by adding 3 to the fourth term, the 6th term by adding 3 to the 5th term, and so on.
5th term = 11 + 3 = 14
6th term = 14 + 3 = 17
7th term = 17 + 3 = 20
...
We can see that each term can be written as:
term = 2 + 3n
where n is the position of the term in the sequence starting from 0 (i.e. the first term is at position 0, the second term is at position 1, etc.)
To find the 19th term, we can substitute n = 17 into the formula:
19th term = 2 + 3(17) = 53
However, the problem states that the 19th term is actually 56. This means that we need to adjust our formula to account for any initial shift in the sequence. We can do this by subtracting a certain value from n, so that the first term in the sequence corresponds to n = 0.
Let's call this adjustment value "a". We know that when n = 0, the first term in the sequence is 2. So we can set up an equation:
2 + 3a = 2
Solving for a, we get a = 0.
Therefore, the adjusted formula for the nth term is:
term = 2 + 3(n-1)
where n is the position of the term in the sequence starting from 1.
Substituting n = 19, we get:
19th term = 2 + 3(18) = 56
So our adjusted formula is correct, and the answer is 56.
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Multiplying polynomials coloring activity answer key 2x^2+10x-36
3
2x^2-32
4
2x^2-17x+39
5
5x^2-15x-39
6
5x^2-23x+3
7
2x^2-68x-30
8
3x^2+15
9
6x^2+5x-39
10
8x^2-18x-35
11
7x^2-6x-34
12
x^3-18x^2+27x+17
Answers
The activity involved multiplying two polynomials using the distributive property to find the product, which has a degree equal to the sum of the degrees of the terms being multiplied together.
The activity involved multiplying two polynomials. This involves using the distributive property to multiply each term of one of the polynomials with each term of the other polynomial.
For example, when multiplying [tex]2x2+10x-36[/tex] with 3 we use the distributive property to get [tex]6x2+30x-108[/tex].
To find the product of two polynomials, each term of one polynomial must be multiplied with each term of the other polynomial. The terms of the product of two polynomials will have the same degree as the sum of the degrees of the terms being multiplied together.
For example, when multiplying [tex]2x2-32[/tex] with 4 we use the distributive property to get [tex]8x2-128[/tex]. Here the degree of the product is 2, which is the sum of the degrees of the terms being multiplied together [tex](2+0=2)[/tex].
To multiply two polynomials, we use the distributive property to multiply each term of one polynomial with each term of the other polynomial. The degree of the product will be the sum of the degrees of the terms being multiplied together.
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Complete question:
What is the product of [tex]2x^2+10x-36[/tex] and [tex]3x-4[/tex]?
A teacher just asked everyone to measure a segment on a worksheet. Based solely on the data, which measure of central tendency should be used based on the following measurements: 8. 3 cm, 8. 4 cm, 8. 8 cm, 8. 2 cm, 8. 3 cm, 8. 0 cm, 8. 1 cm, 8. 5 cm
Answers
The mean of the data is 8.1 cm, which is the most appropriate measure of central tendency to use in this situation.
The most appropriate measure of central tendency to use in this situation is the mean. The mean is the sum of all of the values divided by the number of values. In this case, this would be 8.1 cm (the sum of 8.3 cm, 8.4 cm, 8.8 cm, 8.2 cm, 8.3 cm, 8.0 cm, 8.1 cm, and 8.5 cm divided by 8).
The formula for mean is as follows:
Mean = Sum of values / Number of values
In this situation, the sum of values is 8.3 cm + 8.4 cm + 8.8 cm + 8.2 cm + 8.3 cm + 8.0 cm + 8.1 cm + 8.5 cm = 67.7 cm
Number of values = 8
Mean = 67.7 cm / 8 = 8.1 cm
The mean is the best measure of central tendency to use in this situation because it is the most accurate representation of the data, as it takes into account all of the values in the dataset.
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Four identical circles are lined up in a row with no gaps between them such that the diameters for a segment that is 68 centimeters long. What is the combined area of all the circles to the nearest hundredth? Use 3. 14 for π
Answers
The combined area of all the circles is 907.46 sq. cm.
What is the area of a circle?The area of a given circle is the amount of space that the circle would cover in a 2 dimensional plane. The area of a circle can be determined by;
area of a circle = π r^2
In the given question, the diameters of the circles form a segment that is 68 cm. Thus;
diameter of one circle = 68/ 4
= 17 cm
So that,
radius of each circle = diameter/ 2
= 17/ 2
= 8.5 cm
area of each circle = 3.14 *(8.5)^2
= 226.865
The area of the circles combined = 4*226.865
= 907.46
The combined area of all the circles is 907.46 sq. cm.
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6% of a length is 570m what is the origin length give your answer in meters
Answers
6% of a length is 570m and the original length can be calculated by dividing 570m by 0.06, resulting in 9500m.
To calculate the original length given that 6% of it is 570m, we can use the following formula: Original length = (570 ÷ 0.06) Original length = 9500mTo solve this problem, firstly the percentage of 6% needs to be converted into a decimal by dividing 6 by 100. This will give us 0.06. Then, the original length is found by dividing the given value of 6% (570m) by the decimal equivalent (0.06). Therefore, the original length is 9500m. To summarise, 6% of a length is 570m and the original length can be calculated by dividing 570m by 0.06, resulting in 9500m.
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An ant walked 475 millimeters at a steady
speed. It took the ant 10.0 seconds to walk
that distance. What was the ant's speed?
Write your answer to the tenths place.
millimeters per second
Answers
answer:Average velocity is displacement divided by the time over which the displacement occurs. v avg = displacement time = Δ d Δ t = d f − d 0 t f − t 0. Velocity, like speed, has SI units of meters per second (m/s), but because it is a vector, you must also include a direction.
Step-by-step explanation:
You pick a card at random. Without putting the first card back, you pick a second card at random.What is the probability of picking a 2 and then picking a number less than 4?
Answers
The probability of picking a 2 and then picking a number less than 4will be 0.56%
What is prοbability?By simply dividing the favοrable number οf pοssibilities by the entire number οf pοssible οutcοmes, the prοbability οf an οccurrence can be determined using the prοbability fοrmula. Because the favοrable number οf οutcοmes can never exceed the entire number οf οutcοmes, the chance οf an event οccurring might range frοm 0 tο 1.
The number οf favοurable οutcοmes tο all pοssible οutcοmes οf an event is the ratiο, which is knοwn as prοbability. The number οf gοοd οutcοmes can be represented by the symbοl x fοr an experiment with 'n' number οf οutcοmes. The fοllοwing equatiοn can be used tο determine an event's prοbability.
Yοu pick a card at randοm. Withοut putting the first card back, yοu pick a secοnd card at randοm.
1/13 chance οf picking a 5.
4/51 chance οf picking a 3 οn secοnd draw.
4/(13*51) οf dοing these sequentially = 0.56%
Hence the prοbability will be 0.56%
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P= {factors of 16), Q=-{multiples of 4 of less than 17} and R={whole numbers from 12 to 16
Answers
The factors of 16 are 1, 2, 4, 8, and 16, so we have:
P = {1, 2, 4, 8, 16}
What else does factor go by?Divisors are another name for factors. As a result, they can equally split into the number of which they are a factor. In other words, they do not even leave a remnant when you divide with them. For instance, 36 has a factor of 4 in it.
We can write the sets P, Q, and R using set-builder notation as follows:
P = {1, 2, 4, 8, 16} (the factors of 16)
Q = {0, 4, 8, 12, 16} (the multiples of 4 less than 17)
R = {12, 13, 14, 15, 16} (the whole numbers from 12 to 16)
The multiples of 4 less than 17 are 4, 8, 12, and 16. However, Q is defined as the complement of this set, so we have:
Q = {-3, -2, -1, 0, 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15}
The whole numbers from 12 to 16 are 12, 13, 14, 15, and 16, so we have:
R = {12, 13, 14, 15, 16}
Due to the fact that it is a combination of 4 and less than 17, we have included 0 in set Q.
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Triangle ABC is dilated by a scale factor of one half about the origin and then reflected over the x-axis. What is the location of A″ after the sequence of transformations?
(8, −2)
(4, 1)
(4, −1)
(−4, 1)
Answers
The location of A using graphs, is at (4, -1).
What are graphs?An organised representation of the data is all that the graph is. It facilitates our understanding of the facts. Data is the term used to describe the numerical information obtained through observation.
The development of a research question is followed by the ongoing observational collection of data. The data is then organised, distilled, categorises, and visually represented.
Here in the question,
Coordinates of A= (8,2)
Now it is dilated by a scale factor of 1/2. So,
New coordinates, A' = (8/2,2/2)
= (4,1)
Now the triangle is reflected over the x-axis.
A' now becomes A" which is (4, -1).
Therefore, the new coordinate of A is (4, -1).
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The complete question is:
Triangle ABC is shown on the coordinate plane. Triangle on coordinate plane with vertices A at 8 comma 2, B at 10 comma 6, and C at 4 comma 4. Triangle ABC is dilated by a scale factor of one half about the origin and then reflected over the x-axis. What is the location of A″ after the sequence of transformations? (8, −2) (4, 1) (4, −1) (−4, 1)
Which one of the following graphs represents the solution of the inequality −3x+16≥−2
?
Answers
Answer:
B
Step-by-step explanation:
the answer is B please see on the attached.
Pls answerrrrr
with simple working
Answers
the answer will be -137
(
6. 25
x
+
12
)
−
(
4. 25
x
−
7
)
(
6. 2
5
+
1
2
)
−
(
4. 2
5
−
7
)
Answers
The expression (6.25x + 12) - (4.25x - 7) / (6.25 + 12) - (4.25 - 7) to its simplest form, which is (2x + 19) / 21.
To simplify the given expression, we need to apply the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
First, we will simplify the expression inside the parentheses using the distributive property.
(6.25x + 12) - (4.25x - 7) = 6.25x + 12 - 4.25x + 7
Next, we will combine like terms, which are the terms with the same variable and exponent.
6.25x - 4.25x = 2x
12 + 7 = 19
Therefore, the simplified expression becomes:
2x + 19
Now, we will simplify the expression in the denominator.
(6.25 + 12) - (4.25 - 7) = 18.25 - (-2.75)
Remember that subtracting a negative number is the same as adding a positive number.
18.25 + 2.75 = 21
Finally, we can write the simplified expression as:
(2x + 19) / 21
This is the simplest form of the given expression, and it cannot be further simplified.
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Complete Question:
Simplify the expression: ( 6. 25 x + 12 ) − ( 4. 25 x − 7 ) ( 6. 2 5 + 1 2 ) − ( 4. 2 5 − 7 )
Tommy picked 2 baskets full of apples. One basket weighed 18. 63 kilograms. The
other basket weighed 9. 97 kilograms. How much more did the first basket weigh?
Answers
The weight of the first basket full of apples is 8.66 kilograms more as compare to weight of the second basket.
Number of full of apples basket with Tommy = 2
Weight of first basket full of apples = 18.63 kilograms
Weight of second basket full of apples = 9.97 kilograms
Weight of first basket is greater than the weight of the second basket.
More weight in first basket
= Subtract the weight of the second basket from the weight of the first basket
⇒ More weight in first basket = Weight of first basket - Weight of second basket
⇒ More weight in first basket = ( 18.63 - 9.97 ) kilograms
⇒ More weight in first basket = 8.66 kilograms
Therefore, the first basket weighed 8.66 kilograms more than the second basket.
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PLEASE HELP ME SOMEONE
Answers
Knowing that the drum is a cylinder, we will get that:
The area of leather needed 2,769.48 cm^2The area of wood needed 1,378.42 cm^2How to find the areas?Here we can see that the drum is a cylinder, remember that the circular areas of a cylinder of radius R and height H are:
A = 2*3.14*R^2
And the curved surface is:
S = 2*3.14*R*H
Here we can see that:
R = 21cm
H = 9.5cm
a) The area of leather needed is:
A = 2*3.14*(21cm)^2 = 2,769.48 cm^2
b) The area of wood needed is:
S = 2*3.14*21cm*9.5cm = 1,378.42 cm^2
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Mrs. Smith wants to add a 2 feet concrete walkway around the edge of the pool.
Write a polynomial expression, in simplified form, that represents the total area of the pool and the walkway. Show and explain how you got the area of the pool and the walkway. 
Answers
To find the total area of the pool and the walkway, we can add the areas of the pool and the walkway together.
Let's assume that the pool has dimensions of length L and width W, and that the walkway has a uniform width of 2 feet all around the pool. This means that the dimensions of the pool plus the walkway will be (L + 4) feet by (W + 4) feet, since we add 2 feet on each side.
The area of the pool alone is given by L x W. The area of the pool plus the walkway is then given by (L + 4) x (W + 4). To simplify, we can use FOIL (First, Outer, Inner, Last) method to expand the expression:
(L + 4) x (W + 4) = LW + 4L + 4W + 16
Therefore, the polynomial expression that represents the total area of the pool and the walkway is:
A(L,W) = LW + 4L + 4W + 16
where A(L,W) is the total area of the pool and walkway as a function of the pool's length and width.
1.Start by assuming that the pool has dimensions of length L and width W, in feet.
2.Since Mrs. Smith wants to add a 2-foot walkway around the edge of the pool, we need to add 2 feet to both the length and width of the pool to get the dimensions of the pool plus the walkway. This means that the dimensions of the pool plus the walkway are (L + 2) feet by (W + 2) feet.
3.To find the area of the pool alone, we can simply multiply the length by the width: A_pool = L x W.
4.To find the area of the pool plus the walkway, we need to multiply the length and width of the larger rectangle that includes both the pool and the walkway. This rectangle has dimensions of (L + 2) feet by (W + 2) feet. Therefore, the area of the pool plus the walkway is:
A_total = (L + 2) x (W + 2)
5.We can simplify this expression by using the distributive property of multiplication. We first multiply L by W to get LW. Then, we multiply L by 2 and W by 2 to get 2L and 2W, respectively. Finally, we add 2 x 2 = 4 to account for the extra area added by the walkway. Therefore, the total area of the pool plus the walkway can be written as:
A_total = LW + 2L + 2W + 4
6.Finally, we can rewrite this expression as a polynomial in standard form, by rearranging the terms in descending order of degree:
A_total = LW + 2L + 2W + 4
= LW + 2L + 2W + 0x² + 4
= 0x² + LW + 2L + 2W + 4
So the polynomial expression that represents the total area of the pool and the walkway is:
A(L,W) = LW + 2L + 2W + 4
where A(L,W) is the total area of the pool and walkway as a function of the pool's length and width.
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A rectangle has sides of 72 cm and 36 cm. Another rectangle has sides of 4 cm and 8 cm. What is the scale ratio?
Answers
Scale ratio is 9 cm which can be calculated by comparing lengths and using division.
The scale ratio between two rectangles is a way to compare the size of their corresponding sides. It is calculated by dividing the length of one side of the first rectangle by the length of the corresponding side of the second rectangle.
In this case, let's compare the length of the longer side of the first rectangle (72 cm) with the length of the longer side of the second rectangle (8 cm):
scale ratio = 72 cm ÷ 8 cm = 9
This means that the longer side of the first rectangle is 9 times as long as the longer side of the second rectangle. We could also calculate the scale ratio using the shorter sides:
scale ratio = 36 cm ÷ 4 cm = 9
In either case, the scale ratio is 9, which tells us that the first rectangle is 9 times as large as the second rectangle. This can be useful for creating accurate scale drawings or models of objects.
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Out of 100 problems on a test,15 problems,or 15% of the problems, have two parts. So far, you have completed 40 problems. If the two-part problems appear throughout the test, about how many of those 40 problems have two parts?
Answers
Thus, out of 40 problems, 6 problems will have two parts problems which is 15% of the 40.
Explains about the percentage:The phrase "percent" refers to a number out of 100 or per 100. The term is derived from the Roman expression per centum, which means "by the hundred." Hence, a single percent would be one of those hundred units, and one percent, for every one hundred of anything.
Given data:
Out of 100 problems - 15% have two parts.
Out of 100 problems - 85% will not have two parts.
Thus, out of 40 problems, also 15% will contain two parts.
Then,
Number of two-part problem = 15% of 40
Number of two-part problem = 15 * 40 / 100
Number of two-part problem = 600 / 100
Number of two-part problem = 6
Thus, out of 40 problems, 6 problems will have two parts which is 15% of the 40.
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Bert is at the bakery. He is looking at different types of cakes. He sees one that serves 2 and costs $4.50, another serves 8 and costs $10.00, and another cake that serves 10 and costs $20.00. Which cake is the most expensive per serving?
Answers
Answer:
To find out which cake is the most expensive per serving, we need to calculate the cost per serving for each cake.
The first cake serves 2 people and costs $4.50. So the cost per serving is:
$4.50 ÷ 2 = $2.25 per serving
The second cake serves 8 people and costs $10.00. So the cost per serving is:
$10.00 ÷ 8 = $1.25 per serving
The third cake serves 10 people and costs $20.00. So the cost per serving is:
$20.00 ÷ 10 = $2.00 per serving
Therefore, the first cake is the most expensive per serving, at $2.25 per serving.
$2.25 per serving.
Step by step Explanation
To determine which cake is the most expensive per serving, we need to calculate the cost per serving for each cake.
The first cake serves 2 and costs $4.50, so the cost per serving is:
$4.50 ÷ 2 = $2.25 per serving
The second cake serves 8 and costs $10.00, so the cost per serving is:
$10.00 ÷ 8 = $1.25 per serving
The third cake serves 10 and costs $20.00, so the cost per serving is:
$20.00 ÷ 10 = $2.00 per serving
Therefore, the first cake is the most expensive per serving at $2.25 per serving.