D Each figure in the sequence shown
is composed entirely of 1 x 1 shaded
squares. If the pattern is continued,
how many 1 x 1 shaded squares will
there be altogether in the first 21
figures?
+000
Answers
The total number of 1 x 1 shaded squares that there will be in the first 21 figures is of:
924.
How to obtain the total number of squares?The number of squares for each figure is given as follows:
(4, 8, 12, 16).
As the difference between consecutive terms of the sequence is constant, this sequence is an arithmetic sequence, with first term of 4 and common difference of 4.
The sum of the first n terms of an arithmetic sequence is given as follows:
\(S_n = \frac{n(a_1 + a_n)}{2}\)
The parameters of the equation are given as follows:
n is the number of terms.\(a_1\) is the first term.\(a_n\) is the nth term.Applying the explicit form, the 21st term of the arithmetic sequence in this problem is given as follows:
\(a_{21} = 4 + 20 \times 4 = 84\)
Hence the total number of squares in the first 21 figures is obtained as follows:
\(S_{21} = 10.5 \times (4 + 84) = 924\)
Missing InformationThe figures are given by the image shown at the end of the answer.
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Related Questions
find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 3 x , x = 5, x = 10, y = 0; about the x-axis. V = ____?
Answers
The volume of the solid is V = 1450π/3 cubic units.
To find the volume of the solid obtained by rotating the region bounded by the curves y = 3x, x = 5, x = 10, and y = 0 about the x-axis, we can use the method of cylindrical shells.
For each value of x in the interval [5, 10], we can consider a thin cylindrical shell with radius x and height 3x. The volume of this shell is given by:
dV = 2πx (3x) dx
Integrating this expression from x = 5 to x = 10, we get:
V = ∫5^10 2πx (3x) dx
= 6π ∫5^10 x^2 dx
= 6π [(10^3)/3 - (5^3)/3]
= 1450π/3
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Estimate 0.95% of 700
Answers
Answer:
6.65
Step-by-step explanation:
0.95% of 700
= 0.0095*700
= 6.65
The value of 0.95% of the number 700 is 6.65.
What is the percentage?
The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the number 700 is 0.95%. The number will be calculated as below,
Number = 0.95% of 700
Number = 700 x 0.95/100
Number = 6.65
Therefore, the value of 0.95% of the number 700 is 6.65.
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Rewrite 2/5 book 1/2 hour as a unit rate
Answers
Answer:
4/5 book per hour
Step-by-step explanation:
In this question, we are to rewrite (2/5)/(1/2) as unit rate.
To write this as a unit rate, what we need to do
is to divide 2/5 by 1/2.
That means 2/5 divided by 1/2
Removing the division and replacing with multiplication will give 2/5 * 2/1 = 4/5 books/hour
Step-by-step explanation:
4/5 books/hour
Use Euclid algorithm to find greatest common factor of the following pairs of numbers
Answers
The greatest common factor of 12 and 78 is 6, and the GCF of 18 and 176 is 2, determined using Euclid's algorithm.
a. To find the greatest common factor (GCF) of 12 and 78 using Euclid's algorithm, we start by dividing the larger number, 78, by the smaller number, 12:
78 ÷ 12 = 6 remainder 6
We then divide the divisor of the previous step, which is 12, by the remainder of the previous step, which is 6:
12 ÷ 6 = 2 remainder 0
Since the remainder is 0, we have found that the GCF of 12 and 78 is the divisor of the last non-zero remainder, which is 6.
Therefore, GCF (12, 78) = 6.
b. To find the GCF of 18 and 176 using Euclid's algorithm, we start by dividing the larger number, 176, by the smaller number, 18:
176 ÷ 18 = 9 remainder 14
We then divide the divisor of the previous step, which is 18, by the remainder of the previous step, which is 14:
18 ÷ 14 = 1 remainder 4
We continue this process by dividing the divisor of the previous step, which is 14, by the remainder of the previous step, which is 4:
14 ÷ 4 = 3 remainder 2
Finally, we divide the divisor of the previous step, which is 4, by the remainder of the previous step, which is 2:
4 ÷ 2 = 2 remainder 0
Since the remainder is 0, we have found that the GCF of 18 and 176 is the divisor of the last non-zero remainder, which is 2.
Therefore, GCF (18, 176) = 2.
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The complete question is:
Find the largest common factor between the following pairs of numbers using Euclid's algorithm:
a. GCF (12, 78)
b. GCF (18, 176)
Using proportional reasonings make a prediction about how many students you would expect to have plans to attend college
Answers
The National Center for Education Statistics estimates that 69% of high school graduates in the US plan to attend college after graduation, but this is only an estimate based on general trends and assumptions. The actual proportion of college-bound students in a given population may differ depending on socioeconomic status, location, and individual interests and goals.
In a town with 20,000 residents, 30% are high school students. If 70% of high school students plan to attend college, how many students would you predict will attend college?Assuming that the percentage of high school students who plan to attend college in the town is representative of the national average, we can use proportional reasoning to make a prediction about the number of students who would attend college.
Out of 20,000 residents, 30% or 6,000 are high school students. If 70% of these students plan to attend college, we can calculate the number of students who will attend college as follows:
6,000 x 0.70 = 4,200
Therefore, based on the given data, we can predict that around 4,200 students in the town will attend college. However, this is just an estimation, and other factors such as economic conditions and the availability of colleges and universities may affect the actual number of students who attend college.
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Which problem can be solved by determining 5 ÷ 1/4?
Answers
Answer:
\(20\)
Explanation:
\(5\) ÷ \(\frac{1}{4}\)
To change the division sign into a multiplication sign, you need to change (1/4) into its reciprocal.
\(5\) × \(\frac{4}{1}\)
\(5\) × \(4\)
\(20\)
between which two consecutive numbers does the square root below lie ?
\( - \sqrt{128} \)
Answers
Answer:
where is the second one?
Step-by-step explanation:
Thank for doing it love you
Answers
Answer:
1 is 1/9 2 is 1/9 3 is 5/9 4 is 8/9
Step-by-step explanation:
A(Ab AC AA) B(ba bb bc) C(ac bc cc)
Lucy and Greg each want to buy a bicycle. Lucy has already saved $35 and plans to save $10 per week. Greg has $26 and plans to save $13 per week. How many weeks will it take for Lucy and
Gregory to have the same amount of money saved? How much money will they have saved?
Answers
Answer:
3 weeks
65 dollars
Step-by-step explanation:
Alright to answer this question we have to set up an equation. For greg the equation is y=13x+26 and for lucy the equation is y=10x+35. y is total amount of money saved and x is number of weeks. Since we want them to each of the same amount of money we set up the equations to be 10x+35=13x+26
then we want to get the constant and the variables alone on different sides of the equal sign so we first subtract 26 from each side to get 10x+9=13x. next we want to subtract 10x from each side and then we end up with 3x=9. Finally we divide 3 from each side to get x=3, We have answered the question to how many week it will take them to save the same amount of money but not the other part. To find out how much money they will both have in 3 weeks we plug in 3 to x. 10(3)+35 which is equal to 65. They will both have 65 dollars in three weeks
Joanne paid $28,000 for her new car. In addition, she paid $1,400 in taxes. What was the tax rate Joanne paid on her new car
Answers
Answer:
5%
Step-by-step explanation:
1400/28000=0.05
Test
5%*$28,000=$1400
someone please help I'll give brain list (I'm failing)
Answers
Answer:
1) 3rd one down 1 7/12 ( the one you've selected well doneee)
2)pretty sure its also the 3rd one down ( don't come for me if its wrong)
Step-by-step explanation:
4 1/6 = 25/6
5 3/4= 23/4
25/6 x4= 100/24
23/4 x 6 = 138/24
138/24 - 100/24 = 38/24
divide by 2:
19/12= 1 7/12
Let F=⟨x− (1/2)y^2,y-(1/2)z^2,z-(1/2)x^2 ⟩ and let C is the triangle with vertices (4,0,0). (0,4,0), and (0,0,4). Assume that C is oriented counterclockwise as viewed from above. 1. curl F= (enter a, b, c, d, or e) a ⟨z,x,−y⟩ b ⟨−z,x,−y⟩ C ⟨z,−x,y⟩ d ⟨−z,−x,−y⟩ e ⟨z,x,y⟩
Answers
The curl of vector field F is ⟨-x, -y, -z⟩. Therefore, the correct answer is (d) ⟨-z, -x, -y⟩, indicating that the curl consists of the components -z, -x, and -y
To find the curl of the vector field F, we use the formula for the curl in terms of partial derivatives. The curl of F is given by the cross product of the gradient operator and the vector field F.Using the formula, we expand the determinant:curl F = (∂/∂x, ∂/∂y, ∂/∂z) × (x - (1/2)y^2, y - (1/2)z^2, z - (1/2)x^2)
Expanding the determinant, we get:= (∂/∂x (z - (1/2)x^2) - ∂/∂z (y - (1/2)z^2), ∂/∂z (x - (1/2)y^2) - ∂/∂y (z - (1/2)x^2), ∂/∂y (y - (1/2)z^2) - ∂/∂x (x - (1/2)y^2))
Simplifying each term, we obtain:= (-x, -y, -z)
Therefore, the curl of F is given by:
curl F = ⟨-x, -y, -z⟩
Hence, the answer is (d) ⟨-z, -x, -y⟩.
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If the number of bacteria on the surface of your phone triples every hour and can be described by the exponential function: f(x)=1000x3^x
, complete the table of values to show how much bacteria is on your phone after 4 hours.
Answers
Answer: 81,000
Step-by-step explanation:
We can solve this by using the formula given.
If f(1)=1000x3^1, then 1,000x3=3,000
If f(2)=1000x3^2, then 3^2=9 and 1000x9=9000,
and so on,
Now, f(4) will equal 1000x3^4, and 3^4 is 3x3x3x3, which is 9x9 or 9^2, which would be equal to 81, and 81x1000=81,000
To complete the table of values for the exponential function f(x) = 1000*3^x, we can evaluate the function for x = 0, 1, 2, 3, and 4, since we are interested in the number of bacteria on the phone after 4 hours.
x f(x)
0 1000
1 3000
2 9000
3 27,000
4 81,000
Therefore, after 4 hours, there will be 81,000 bacteria on the surface of the phone, assuming the number of bacteria triples every hour and can be described by the exponential function f(x) = 1000*3^x.
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Allll workkkkkk!!!!
x/-4=-6
Answers
Answer:
x=24
Step-by-step explanation:
Answer:
x = 24Step-by-step explanation:
x / -4 = -6
x = -6 (-4)
x = 24
Choose the correct solution for this equation X/2-12 = 24
Answers
Answer:
Your answer would be x = -240
Step-by-step explanation:
1. First do 2-12 to get a denominator of -10.
2. Multiply -10 on both sides to get x = 24 * -10
3. Solve 24 * - 10 to get x = -240
brook states that the distance on the line is 4 units. caleb states that the whole line does not have a distance because it continues on forever. vivian states that the line is 6 units long. which distance did brook measure?
Answers
Brook measured the distance between two points on the line that are 4 units apart. This is a valid measurement of distance between those two points on the line.
Caleb's statement that the whole line does not have a distance because it continues on forever is a mathematical concept related to the idea of infinity. In mathematics, a line is considered to be an infinite set of points, and therefore, it does not have a finite length or distance.
However, when we talk about a specific segment or distance on the line between two points, we can measure that distance and express it as a finite number.
Vivian's statement that the line is 6 units long is incorrect, assuming that she is referring to the entire line.
As mentioned earlier, a line is considered to be infinite and therefore does not have a finite length or distance. If she is referring to a specific segment of the line between two points, then it is possible that the length of that segment is 6 units.
Therefore Brook measured the distance between two points on the line that are 4 units apart.
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Brook refers to a specific segment of the line, which is 4 units. Caleb correctly states that a geometric line is infinite. Vivian could be referring to a different segment, which she says is 6 units.
Explanation:In this scenario, we can infer that Brook is talking about a specific segment of the line rather than the entire line. He has measured a specific distance along the line, which he states is 4 units. Meanwhile, Caleb is correct in saying that the whole line does not have a specific length because it continues on forever. This is a property of a geometric line, which is infinite. Vivian's assertion that the line is 6 units could mean that she is referring to another specific segment of the line, different from the segment Brook measured.
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hello please help thanks
Answers
Answer:
D
Step-by-step explanation:
it states that the snikholes are from underneath when the soil it lose
The tanks at the Georgia Aquarium hold approximately 8.4 × 106 gallons of water. The tanks at the Audubon Aquarium of the Americas hold about 400,000 gallons of water. Use a single digit times a power of 10 to estimate how many times greater the amount of water is at the Georgia Aquarium
Answers
Answer:
the answer is 20
hope this helped
Step-by-step explanation:
The amount of water at the Georgia Aquarium is 20 times greater than the aquarium of the Americas hold.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the tanks at the Georgia Aquarium hold approximately 8.4 × 10⁶ gallons of water. The tanks at the Audubon Aquarium of the Americas hold about 400,000 gallons of water.
The number of the time will be calculated as below:-
= 8.4 × 10⁶ / 400,000
= 20.1
Therefore, the amount of water at the Georgia Aquarium is 20 times greater than the aquarium of the Americas hold.
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Ye uhm help please :))))
Answers
52-10.4=41.60
41.60*0.06=2.49
41.60+2.49=$44.09
x + 5 - 12
How can I do this
Answers
Hope you have a good day, Loves!
Also if I'm right can you let me know, please?
Also Also if I am right can I please have Brainliest??
You don't need to, I'm just glad I could help. ^^
answer is x-7
your welcome.
Write an equation of a line in SLOPE INTERCEPT FORM that goes through (3,4) and is perpendicular to the line y = -3/2x-2.
Answers
Answer:
y= 2/3x + 2
Step-by-step explanation:
I used desmos to find it, guesstimated a number and it worked <3
help me plsssssssssssssssssssssssssssss
Answers
So you can subtract all the given angles you have (90 degrees and 42.7 degrees) from 180.
180-42.7-90=47.3 degrees :)
A group of 26 friend are going to travel to a fetival together, 6 of them can drive. They have a 13 peron mini-bu (1 driver 12 paenger), two car (1 driver and 4 paenger in each car) and the remaining 3 friend will take the train. The number of way in which the friend can travel (ignoring paenger eat poition within each vehicle) i a×1012. Work out the value of a. Give your anwer correct to 3 ignificant figure
Answers
If passenger seat position within each vehicle is ignoring, then the number of ways that can the friends travel is 17847429600 ways
Total number of friends = 26 friends
They have 6 seat car and 13 seat car and remaining 3 will take a bus
In the first car 6 of the 26 friends are going to sit
The combination will be
26C₆ = 230230
The combination is defined as An arrangement of object where the order in which the objects are selected doesn't matter. The combination means Selection of things, where the order of things has no importance.
In the second car 13 of 20 friends are going to sit
The combination will be
20C₁₃ = 77520
Calculate combinations, use the formula n Cr = n! / r! * (n - r)!, where n represents the total number of items, and r represents the number of items being chosen at a time. Calculate a combination, will need to calculate a factorial.
The factorial of a number is the multiplication of all the numbers between 1 and the number itself. It is written like this: n! . So the factorial of 2 is 2! (= 1 × 2).
Remaining 3 will take the train
Therefore the number of ways = 26C₆ × 20C₁₃ × 3C₃
= 230230 × 77520 × 1
= 17847429600
Hence, the number of ways that can the friends travel is 17847429600 ways.
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please help
picture linked down ↓
Answers
Answer:
Let's take all factors into consideration first
The door is a rectangle and the area of a rectangle is length times width
Let the width be w
Let the length be l
Equation length × breadth = area
(w+48)w = 3024
w^2 + 48w = 3024
w^2 + 48w - 3024 = 0
w^2 + 84w - 36w - 3024 = 0
w(w + 84) -36 ( w + 84) = 0
(w + 84) (w - 36) = 0
w + 84 = 0 AND w - 36 =0
w = -84 and w = 36
Since width cannot be negative, the right answer is 36
How did I get 84 and 36? Well, I had to factorize 3024 and since 84 times 36 is 3024 and 84 minus 36 is 48, I chose them.
Solve the compound inequality. Graph the two inequalities on the first two number lines and the solution set on the third number line.
Answers
As a result, the compound inequality has the following solution: -1 ≤ x < 28/9
what is inequality ?An inequality in mathematics is a claim that two values or expressions are not equivalent to one another. A spectrum of potential values for a variable can be described by an inequality, which can also be used to compare the values of two quantities. There are various kinds of inequality, such as: Inequalities involving linear expressions or formulae are referred to as linear inequalities. An illustration of a linear inequality is 2x + 3 7. Inequalities involving quadratic expressions or formulae are known as quadratic inequalities. x2 - 4x + 3 > 0 is an illustration of a quadratic equation.
given
The compound inequality is as follows:
-4 ≤ 3x - 1 < 8
This can be resolved by splitting it into two distinct inequalities:
-4 <= 3x - 1 and 3x - 1 < 8
By adding 1 to both sides and dividing by 3, we can solve the first equation for x:
-4 + 1 ≤ 3x - 1 + 1/3
-3/3 ≤ x
-1 ≤ x
Solving the second inequality for x, we add 1 to both sides and split by 3:
3x - 1 + 1/3 < 8 + 1/3
3x < 9 + 1/3
3x < 28/3
x < 28/9
As a result, the compound inequality has the following solution: -1 ≤ x < 28/9
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Please help!!
What is the formula that is used for DISCOUNT SALES?
Answers
Answer:
discounted price = original price ( 1 - discount rate)
Step-by-step explanation:
please help it's due today
Answers
Answer:
9/7, 1/6, -3, 4/5
Step-by-step explanation:
Use the \(gradient =\frac{rise}{run}\) formula to solve this.
4: \(gradient = \frac{14-5}{8-1} = \frac{9}{7}\)
5: \(gradient = \frac{10-9}{2-(-4)} = \frac{1}{6}\)
6: \(gradient = \frac{-5-4}{6-3} = \frac{-9}{3} = -3\)
7: \(gradient = \frac{-1-(-5)}{7-2} = \frac{4}{5}\)
What is 1.3 divided by 4.7
Answers
Answer:
0.27659574
Step-by-step explanation:
If 1/2+4x=-x+2, what is the value of x?
Answers
x equals 3/10 or .33
How many cubic millimeters are in one cubic kilometer?
Answers
Answer:
I think 1000000000000000000
Step-by-step explanation:
Hope it's right
Answer:
it is 10000
Step-by-step explanation: