Answer:
The inequality to determine the number of rotations is given by
r ≤ 5.25
Therefore the maximum number of rotations possible is 5.
Step-by-step explanation:
i.) The bottom of Ignacio's desktop is 74.5 cm from the floor.
ii.) The tops of his legs are 49.3 cm from the floor.
iii.) the difference between the bottom of Ignacio's desktop and the top of his legs = 74.5 - 49.3 = 25.2 cm.
iv.) Each clockwise rotation of the knob on the chair raises Ignacio's legs by 4.8 cm.
v.) let the number of clockwise rotations be r.
vi.) therefore the inequality to determine the number of rotations is given by
4.8r ≤ 25.2 therefore r ≤ 25.2/4.8 therefore r ≤ 5.25
Calculate the distance
Benjamin rides
his scooter if he rides 3/5mile
each day
for 10 days.
Answer:
Step-by-step explanation:
30/5=6
Final answer:
Benjamin rides his scooter for a total of 6 miles over a period of 10 days, by multiplying the daily distance of 3/5 mile by 10 days.
Explanation:
To calculate the distance Benjamin rides his scooter over 10 days, we multiply the daily distance by the number of days. Benjamin rides 3/5 of a mile each day.
Distance per day = 3/5 mile
Number of days = 10 days
The total distance is:
3/5 mile/day × 10 days = 6 miles
Therefore, the correct answer is Benjamin will have traveled a total of 6 miles over the course of 10 days.
Nancy and Matilda are 60 miles apart, cycling towards each other on the same road. Matilda rides 12 miles per hour and Nancy rides 8 miles per hour. In how many hours will they meet?
Nancy and Matilda will meet in 3 hours.
Step-by-step explanation:
Given,
Distance to cover = 60 miles
Speed of Matilda = 12 miles per hour
Speed of Nancy = 8 miles per hour
Combined speed of Nancy and Matilda = 8+12 = 20 miles per hour
Let,
x be the time taken by them
Distance = Speed * Time
[tex]60=20*x\\60=20x\\20x=60[/tex]
Dividing both sides by 20
[tex]\frac{20x}{20}=\frac{60}{20}\\x=3[/tex]
Nancy and Matilda will meet in 3 hours.
Keywords: distance, speed
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In 3 hours Nancy and Matilda meet.
Given
Nancy and Matilda are 60 miles apart, cycling towards each other on the same road.
Matilda rides 12 miles per hour and Nancy rides 8 miles per hour.
What is speed?Speed is defined as the ratio of distance and time.
The time will take to meet Nancy and Matilda is given by;
[tex]\rm \dfrac{12}{8}=\dfrac{x}{60}\\\\8 \times x=60\times 12\\\\8x=720\\\\x = \dfrac{720}{8}\\\\x=90[/tex]
Therefore.
The time taken to meet them is;
[tex]\dfrac{12}{8}+\dfrac{90}{60}\\\\1.5+1.5= 3[/tex]
Hence, in 3 hours will they meet.
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EASY POINTS Double the product of 6y and 3bc
Answer:
12y and 6bc
Step-by-step explanation:
multiply by 2
The product of [tex]6y[/tex] and [tex]3bc[/tex] after doubling would be as follows:
[tex]36bcy[/tex]
Variable
A variable is a symbol and placeholder for a changing amount or any mathematical object.An algebraic expression is one that is composed of integer constants, variables, and algebraic operations.Product of [tex]6y,3bc=18bcy[/tex]
Double the product of [tex]6y,3bc=2(18bcy)[/tex]
[tex]=\textbf{36bcy}[/tex]
Thus, it is the correct answer.
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Match the vocabulary word with the correct definition.
1. circle
a chord of a circle that contains the center of the circle
2. diameter
a segment joining the center of a circle to a point of the circle
3. congruent circles
the set of all points in a plane that are at a given distance from a given point in the plane
4. concentric circles
circles that have equal radii
5. radius
two or more circles that lie in the same plane an have the same center
Answer:
1) the set of all points in a plane that are at a given distance from a given point in the plane
2)a chord of a circle that contains the center of the circle
3)circles that have equal radii
4)two or more circles that lie in the same plane an have the same center
5)a segment joining the center of a circle to a point of the circle
what would be the amount of a check issued for an 08/11 invoice for 648.50 paid on 09/13 with the terms: 3/10, 2/15, N30-5%APR?
Answer:
The amount of a check issued for an 08/11 invoice, would depend on when the invoice is paid.
If it's paid within 13 days, there's a 3% discount . which will be calculated as
648.50 x 3% = $19.455 discount
If it's paid within 11 - 15 days, there's a 2% discount.
648.50 x 2% = $12.97 discount
If it's paid within 16 - 30 days, there is no discount
If it's paid after 30 days, 5% APR is added to the bill
The check would be for the invoice amount of $648.50 plus a late fee of $2.67, totaling $651.17. The late fee is applied since the payment was made 3 days after the 30-day period from the invoice date and calculated using a daily rate derived from the 5% APR.
Explanation:The invoice has specific payment terms: 3/10, 2/15, N30. These are discounts offered for early payment. The first part '3/10' means that the payer gets a 3% discount if they pay within 10 days. The second part '2/15' offers a 2% discount if the payer pays within 15 days. 'N30' means that the full amount due needs to be paid within 30 days from invoice date. Additionally, there is a 5% APR (annual percentage rate) charge for late payments.
The invoice was issued on 08/11, and the payment was made on 09/13, which is 33 days after the invoice date. Therefore, there aren't any discounts for the payment because it's not within the 10 or 15 days period. However, it's slightly over the 30 days, so there will be a late fee applied. The late fee is commonly calculated based on a daily rate. The daily rate is the APR divided by 365 (5%/365=0.0137%). Multiply the daily rate by the number of late days (33-30=3) and the invoice amount ($648.50).
So the late fee is 648.50*0.0137%*3=$2.67. The amount of the check would be the original invoice amount $648.50 plus late fee $2.67, so the total is $651.17.
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Which polynomial represents a sum of cubes?
x^3+9
4x^3+1
8x^3+1
64x^3-27
Which of the following polynomials represents a difference of squares?
4x^2-8
9x^2+16
16x^2-2
49x^2-25
Answer:
1) The polynomial [tex]8x^3+1[/tex] represents a sum of cubes
2) The polynomial [tex]49x^2-25[/tex] represents a difference of squares
Step-by-step explanation:
1) To find the polynomials represents a sum of cubes :
[tex]8x^3+1[/tex] represents a sum of cubes
For [tex]8x^3+1[/tex]
[tex]=2^3x^3+1^3[/tex]
[tex]=(2x)^3+1^3[/tex]
Therefore [tex]8x^3+1=(2x)^3+1^3[/tex]
Therefore [tex]8x^3+1[/tex] represents a sum of cubes
2)To find the polynomials represents a difference of squares :
[tex]49x^2-25[/tex] represents a difference of squares
For [tex]49x^2-25[/tex]
[tex]=7^2x^2-5^2[/tex]
[tex]=(7x)^2-5^2[/tex]
Therefore [tex]49x^2-25=(7x)^2-5^2[/tex]
Therefore [tex]49x^2-25[/tex] represents a difference of squares
Enter the number
15.666666666667
15.666666666667
rounded to the nearest hundredth (two decimal places):
Answer:
15.666666666667=15.67 to the nearest hundredth or to two decimal places.
Step-by-step explanation:
We want to round 15.66666666667 to the nearest hundredth or to two decimal places.
We count two numbers after the decimal place to get:
15.66|6666666667
The next digit is 6
Since 6>5, we round up.
This means we add 1 to the number the hundredth place to get
15.67
Suppose 4/5 of a different box of oranges weighs 8 pounds how many pounds of oranges are in the full box
Answer:
10
Step-by-step explanation:
if you take 8 and divide it by 4 you get 2 meaning that each fifth is 2 pounds. if there are 5/5 that means there are 10 pounds
A professor announced to her class that the average score for the 37 exams received was 86. She later discovered
three additional exams with scores of 76, 81 and 97. These exams were not included in the class average she
reported to the class. Is it possible to calculate the new class average? If so, what is it? If not, justify why.
Answer:
New average = 85.9.
Step-by-step explanation:
Yes, the new class average can be calculated.
The New total of the scores = 37*86 + 76 + 81 + 97
= 3436.
The new total of examinations sat = 37 + 3 = 40.
Therefore the new class average = 3436 / 40
= 85.9
Joe gave 1⁄4 of his total candies to his classmates. Then he gave 4/6 of what he had left to his brother when he went home. He then realized that he didn’t give any to his sister, so he gave 25% of the remaining candies to her. After all this, he realized he only had 21 candies left. How many candies did he have in the beginning
Answer:
112 candies
Step-by-step explanation:
Start from the end.
Joe gave 25% of the remaining candies to his sister and has 21 candies left. Then
[tex]21 \ candies - 75\%\\ \\x \ candies - 25\%[/tex]
Write a proportion:
[tex]\dfrac{21}{x}=\dfrac{75}{25}\\ \\75x=21\cdot 25\\ \\x=\dfrac{21}{3}=7[/tex]
Joe gave 7 candies to his sister, so before this he had 21 + 7 = 28 candies.
He gave 4/6 of what he had left to his brother when he went home, so 2/6 of all his candies left ot him. Hence,
[tex]28\ candies - \dfrac{2}{6}\\ \\x\ candies - \dfrac{4}{6}[/tex]
Write a proportion:
[tex]\dfrac{28}{x}=\dfrac{\frac{2}{6}}{\frac{4}{6}}\\ \\\dfrac{28}{x}=\dfrac{1}{2}\\ \\x=28\cdot 2=56[/tex]
Joe gave 56 candies to his brother, so Joe had 28 + 56 = 84 candies when he went home.
Joe gave 1/4 of his total candies to his classmates, so 3/4 of his candies left to him. So,
[tex]x\ candies - \dfrac{1}{4}\\ \\84\ candies - \dfrac{3}{4}[/tex]
Write a proportion:
[tex]\dfrac{x}{84}=\dfrac{\frac{1}{4}}{\frac{3}{4}}\\ \\\dfrac{x}{84}=\dfrac{1}{3}\\ \\3x=84\\ \\x=28[/tex]
Therefore, initially, Joe had 28 + 84 = 112 candies.
Hey can somebody help me with this, I’m having a hard time knowing what it is...???
Answer:
[tex]\left[\begin{array}{cc}0&2\\3&3\\6&4\\9&5\end{array}\right][/tex]
Step-by-step explanation:
+2 means that when c is at 0 w is at 2.
1/3c means that c moves up 3 at a time.
7(3+9) pls help me ASAP
Answer:
84
Step-by-step explanation:
Using PEMDAS: (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)
7*(3+9)
7*(12)
84
Answer:
83
Step-by-step explanation:
If AC = 4x – 60 and BD = 30 – x, find BD.
Answer:
Since AC is perfectly equal to BD, 4x-60=30-x. If you solve for x, x=18. Then plug 18 into BD=30-x. Therefore, BD=12.
Wat does it mean to estimate a math problem
Answer: Estimate means a close guess.
For example, when estimating with decimals, we would round them to the nearest whole number to estimate the answer.
Example: 3.6 + 1.2
1.2 is closest to 1
3.6 is closes to 4
4 + 1 = 5
A good estimate is 5
3.6 + 1.2 = 4.8
4.8 is very close to 5, so 5 is a very good estimate.
Final answer:
Estimating a math problem involves making an educated approximation of a quantity using prior knowledge and reasoning. It applies to various fields and helps to rule out unrealistic numbers, as well as develop important problem-solving skills.
Explanation:
To estimate a math problem means to find a rough approximation or a ballpark figure of the quantity in question, rather than calculating the exact number. Estimations are based on sound reasoning, prior experience, and a strong grasp of the relevant variables and physical principles. The process is not a wild guess but a calculated approximation that can be derived from formulas where the input quantities are known to a limited precision.
For example, to estimate the mean rent for a two-bedroom apartment in a town, you might calculate the average of several listed rents. Or, in physics, to estimate how large a current will be in a circuit when it is turned on, you would apply the relevant principles and any known quantities to arrive at an approximate value. The goal of estimation is to get within a reasonable range of accuracy without needing a precise computation.
The skills of estimation are vital in many fields, including physics, and they help in ruling out unrealistic results. Practicing these skills, getting familiar with units, and understanding relationships between variables all contribute to making better estimates. Moreover, after arriving at an estimate, it's important to do a sanity check to make sure the result seems reasonable within the context of what is known.
Rita works at a gym where she gets paid $450 each week plus $15.50 for any new gym membership she sells. If y represents the total pay per week and x represents the number of new memberships sold, which of the following equations represents a higher rate per membership sold?
Answer:
D
Step-by-step explanation:
HELP HELP HELP PLEASE
1. solve the eqation. First combine any like terms on each side of the equation
x-6 = -3+8 the solution is x =
2. Solve. First combine any like terms on each side of the equation.
3w - 8w = 35 w=
3. Solve the equation. First combine any like terms on each side of the equation.
- 4 x - 4 x = 44 - 4 the solution x =
4. Solve the equation. First combine any like terms on each side of the equation -5 -8 = 3x +2 - 2x the solution is x
5. Solve. First multiply to remove the parentheses.
3(3x - 3) = 10x x=
x - 6 = - 3 + 8
x = 5 + 6
x = 11
3w - 8w = 35
- 5w = 35
5w = - 35
w = - 35 : 5
w = - 7
3(3x - 3) = 10x
9x - 9 = 10x
- 9 = 10x - 9x
x = - 9
Answer:
1. x = 11,
2. w = -7,
3. x = -5
4. x = -5
5. x = -9
Step-by-step explanation:
1. x-6 = -3+8
x - 6 = 8 -3
x - 6 = 5
Adding 6 to both sides:
x - 6 + 6 = 5 + 6
x = 11
2. 3w - 8w = 35
3w - 8w = 35
-5w = 35
Divide both sides by -5
-5w/-5 = 35/-5
w = -7
3. - 4 x - 4 x = 44 - 4
- 4 x - 4 x = 44 - 4
-8x = 40
Divide both sides by -8
-8x/-8 = 40/-8
x = -5
4. 5 -8 = 3x +2 - 2x
Collecting like terms and rearranging equation
3x - 2x = 5 - 8 - 2
x = 5 - 10
x = -5
5. 3(3x - 3) = 10x
3(3x - 3) = 10x
Expanding and removing parenthesis
9x - 9 = 10x
Collecting like terms and rearranging equation
10x - 9x = -9
x = -9
To make a soup, 2 cups of chicken broth are needed for each 1/4 cup of dried lentils. How many cups of chicken broth are needed if 2 1/4 cups of dried lentils are used?
Answer:
You'll need 18 cups of chicken broth!
Step-by-step explanation:
You are using a ratio of 1/4 cup (lentils) to 2 cup (broth). Therefore, you need to find the relationship between lentil and broth.
In order to get from 1/4 to 2, you multiply by 8. (1/4 * 8 = 2)Therefore, the common relationship is multiplying the lentil amount by 8So, 2 1/4 * 8 = 18Therefore, 18 cups are needed :D
To make a soup with 2 1/4 cups of dried lentils, you would need 9 cups of chicken broth.
Explanation:To find the number of cups of chicken broth needed, we need to multiply the given number of cups of dried lentils (2 1/4 cups) by the ratio of chicken broth to dried lentils. The ratio is 2 cups of chicken broth per 1/4 cup of dried lentils. So, for 2 1/4 cups of dried lentils, we would need:
2 1/4 cups × (2 cups/1/4 cup) = 9 cups of chicken broth
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Add: (8x – 2y) +(4x + 4y – 6)
+ 2y - 6
12x – 6y - 6
12x – 2y - 6
14xy – 6
The difference between four times a number and one
The difference between four times a number and one can be expressed as 4x - 1, where "x" represents the number. This expression involves multiplying the number by 4 and then subtracting 1.
The difference between four times a number and one can be succinctly expressed as the result of multiplying that number by four and then subtracting one from the product. In mathematical notation, this difference can be represented as:
4x - 1
Here, "x" represents the unknown number, and we are performing two operations: multiplying it by 4 and subtracting 1 from the result. Let's break this down further:
Four times a number: When you multiply a number by 4, you are essentially scaling it up by a factor of 4. For example, if the number is 5, then four times that number would be 4 * 5 = 20.
Subtracting one: After obtaining the result of four times the number, we subtract 1 from it. In our example, if the number is 5, then after four times the number (20), subtracting 1 results in 19.
So, the difference between four times a number and one is the value obtained after performing these two steps. It's a simple arithmetic expression that can be calculated for any given value of "x."
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Determine whether a figure with the given vertices is a parallelogram. A(4,5), B(-7,-10), C(-4,-9), D(7,6) distance and slope formula
Answer:
C i think..
Step-by-step explanation:
10)
Simplify.
2(x + 3y - 3) - (2x + 6y - 7)
A) 0
B) 1
C) -3y + 4
D) -6x + 10
Answer:
B) 1
Step-by-step explanation:
Answer:1
Step-by-step explanation:
What’s the average of 14,17,22,27
Answer:
20
Step-by-step explanation:
Average =
sum of scores/number of score
= 14 + 17 + 22 + 27 / 4
= 80/4
= 20
Factor 9x2 + 6x + 12x + 8
Step-by-step explanation:
9x2= 3 • 3 • x2
6x= 3 • 2 • x
12x= 2 • 2 • 3 • x
8= 2 • 2 • 2
What is an equivalent expression to 4x - 16
Answer: x-4, 2x-8, 8x-32
Step-by-step explanation:
Combine the like to simplify the expression: -5y + 12 + 8y − 6 − 2 =
First, let's move combine like terms:
-5y + 8y = 6 + 2 -12.
3y = -4.
y = -4/3
Answer:
x = -3 + 2y
Step-by-step explanation:
I'm not sure if that's correct, sorry, dear~!
The population of North Carolina in 2010 was 9,535,483 people. The population of South Carolina in 2010 was 4,625,364 people.
a) Approximately how much larger is the population of North Carolina than South Carolina? Show or explain your thinking.
b) Approximately how many times larger is North Carolina’s population than South Carolina’s population? Show or explain your thinking.
a) North Carolina has 4,910,119 more people than South Carolina
b) the population of North Carolina is 2.06 times larger than that of South Carolina
Step-by-step explanation:
a)
Here the question is asking "how much larger is the population of North Carolina than South Carolina". This means that we have to compare the absolute value of the population of North Carolina with the population of South Caroline.
We have:
NC = 9,535,483 is the population of North Carolina
SC = 4,625,364 is the population of South Carolina
In order two compare the two, we have to calculated the difference between NC and SC. Plugging into a calculator, we get:
[tex]NC-SC=9,535,483-4,625,34=4,910,119[/tex]
So, North Carolina has 4,910,119 more people than South Carolina.
b)
In this question, we are asked "how many times larger is North Carolina’s population than South Carolina’s population". This is equivalent to ask what is the ratio between the population of North Carolina to that of South Carolina.
As we said before, we have:
NC = 9,535,483 is the population of North Carolina
SC = 4,625,364 is the population of South Carolina
And by calculating the ratio, we find:
[tex]\frac{NC}{SC}=\frac{9,535,483}{4,625,364}=2.06[/tex]
So, the population of North Carolina is 2.06 times larger than that of South Carolina.
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Answer: the population of North Carolina is 2.06 times larger than that of South Carolina.
Write 79/10 as a mixed number.
[tex]\frac{79}{10}[/tex], which is a complex fraction, can be written as a mixed number resulting in [tex]7\frac{9}{10}[/tex].
What is a mixed number?A mixed number is a combination of a whole number, a numerator and a denominator.
The numerator is always less than the denominator in a mixed number because it has been converted from a complex fraction to its current status as a mixed number.
Mixed numbers are complex fractions, like [tex]\frac{79}{10}[/tex]. Before the conversion, complex fractions are fractions where the numerator is greater than the denominator.
Thus [tex]\frac{79}{10}[/tex] written as a mixed number is [tex]7\frac{9}{10}[/tex].
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the difference of n and 23 is greater than or equal to 33
23-n > 33
- <--- that's a greater than or equal to sign
Answer:
23-n > 33
Step-by-step explanation:
Can someone please help me with this 7th grade math homework
Answer:
1) D
2) A, D, F
3) 3.5 mph
4) equation in explanation $15
Step-by-step explanation:
4) equation: 27.50-12.50
Edward is part of a bird watching club and keeps track of the robins in a local park. To do so, he puts tags on 20 robins and releases them. Later, he catches 120 robins; 12 robins were tagged.
What is the best estimate for the robin's population?
Answer:
Total population = 200
Step-by-step explanation:
recaptured tagged/recaptured total ≈ tagged/total population
The best estimate for the total population of Robin's is 200.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given that,
Number of robins which are tagged = 20
Let x be the total population of robins.
Her catches some other robins.
Number of robins that he catched = 120
Number of robins he catched also is tagged = 12
We can write the expression as,
20 / x = 12 / 120
Cross multiplying, we get,
12x = 120 × 20
12x = 2400
x = 2400 / 12
x = 200
Hence the number of robins is 200.
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