A chessboard has 64 squares. George places 1 grain of rice on the first square, 2 grains on the second square, 4 grains on the third square, 8 grains on the fourth square, and so on, until he has placed grains of rice on 10 squares.
Once George has put rice on the 10th square, he has placed a total of _____ grains of rice on the chess board.
Hey there! I'm happy to help out!
As you can see, our number keeps on doubling. It's like 2×2×2×2.... so on and so forth. Whenever we multiply a number by itself, we can model it as an exponent, so if we had 2², it is two twos being multiplied, and 2×2=4. If it was 2³, it would be 2×2×2=8.
However, we have a one. This signifies a starting point and exponents have our back. Anything to the 0th power is always equal to one! So, this situation would look something like this:
[tex]2^0, 2^1, 2^2, 2^3,2^4,... etc.[/tex]
So, for the second square, we are going to the first power. For the fourth square it's going to the third power. Therefore, the 10th square will be the 9th power!
[tex]2^9=[/tex] 2×2×2×2×2×2×2×2×2= 512
However, we want to find how much he has done in total! So, let's find how much he did on the other squares!
[tex]2^8[/tex]= 256
[tex]2^7[/tex]=128
[tex]2^6[/tex]=64
[tex]2^5[/tex]=32
[tex]2^4[/tex]=16
2³=8
2²=4
[tex]2^1[/tex]=2
[tex]2^0[/tex]=1
Now, we add these all up to find the total grains of rice!
512+256+64+32+16+8+4+2+1=895
Therefore, George has placed a total of 895 grains of rice on the chess board.
I hope that this helps! Have a wonderful day!
Once George has put rice on the 10th square, he has placed a total of 1023 grains of rice on the chessboard.
What is a geometric sequence?A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
We have,
On the first square, George placed 1 grain of rice.
On the second square, he placed 2 grains.
On the third square, he placed 4 grains.
On the fourth square, he placed 8 grains.
In general, on the nth square, he places [tex]2^{n-1}[/tex] grains.
So,
On the first 10 squares,
1 + 2 + 4 + 8 + ... + [tex]2^9[/tex]
This is a geometric series with a first term of 1 and a common ratio of 2.
The sum of the first n terms of a geometric series.
[tex]S_n[/tex] =[tex]a(1 - r^n) / (1 - r)[/tex]
where a is the first term, r is the common ratio, and n is the number of terms.
Substituting the values,
[tex]S_{10}[/tex] = 1(1 - 2^10) / (1 - 2)
= 1(1 - 1024) / (-1)
= 1023
Therefore,
Once George has put rice on the 10th square, he has placed a total of 1023 grains of rice on the chessboard.
Learn more about geometric sequence here:
https://brainly.com/question/2321576
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what's the solution to the inequality 1 2/3 > r - 7/12
Answer:
r ≤ 2 1/4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesRewriting FractionsStep-by-step explanation:
Step 1: Define
1 2/3 ≥ r - 7/12
Step 2: Solve for r
Rewrite: 5/3 ≥ r - 7/12Isolate r: 9/4 ≥ rRewrite: r ≤ 9/4Reduce: r ≤ 2 1/4Here we see that any number r less than or equal to 2 1/4 will work as a solution to the inequality.
Which of the following are perfect squares? Check all that apply.
Answer: 16, 64, and 49
Step-by-step explanation: Perfect squares are products made by squaring or multiplying a whole number by itself twice.
11 is not a perfect square since nothing can
be multiplied by itself to give us 11.
The same is true for 62 and 15.
16 is a perfect square since it's possible to find a whole number that can be multiplied by itself to give us 16.
That number is 4 since 4 × 4 = 16.
64 is also one since 8 can be multiplied by itself twice to give us 64.
49 is also one since 7² or 7 × 7 is 49.
Answer:D,E and F
Step-by-step explanation:
Perfect squares are numbers in which their square roots are whole numbers.
From the options
√16 =4
√64 =8
√49 =7
How to add or subtract this polynomial
Answer:
18x^2 + 9x - 5
Step-by-step explanation:
Combine like terms:
(9x^2-8) + (9x^2+9x+3)
= 9x^2 + 9x^2 + 9x - 8 + 3
= 18x^2 + 9x - 5
Write an equation that is parallel to the line y=3x-5 and passes through the point (-1,2)
The vertices of ΔDEF have coordinates D(–1, 2), E(3, 3), and F (2, –4).What are the coordinates of the vertices of r(90°, O)(ΔDEF)?
Answer:
D,E
Step-by-step explanation:
hope I helped
A bookstore had 60 copies of a magazine. Yesterday, it sold 1/3 of them. Today, it sold 1/4 of what remained. How many copies does the bookstore have left?
Answer:
30
Step-by-step explanation:
1/3 of 60 is 20
40 would be left
1/4 of 40 is 10 so 30 would be left
50 POINTS!!!!!!! WILL MARK BRAINLIEST! NO COPY/PASTE! TWO TO THREE SENTENCES AND EXPLAIN! WILL REPORT STUPID ANSWERS! According to Nikita Khrushchev, Premier of the Soviet Union, which of the three events had the potential to advance Soviet interests the most? The three events are the Cuban Missile Crisis, The Space Race, and The Berlin Wall.
Answer: Soviet leader Nikita Khrushchev had gambled on sending the missiles to Cuba with the specific goal of increasing his nation's nuclear strike capability.
Step-by-step explanation:
The Soviet Union signed a treaty with Hitler, the U.S. kept the atomic bomb a secret, and the U.S. took a long time to attack Hitler. France, Britain, and the United States wanted to reunify Germany, so they combined their areas into West Germany. Soviets cut off transportation to West Berlin. This lead to the United States and Britain using the Berlin airlift to bring food/supplies into the isolated part of Soviet occupied West Berlin.-3b+7=13 solve for b
Answer:
b = -2
Step-by-step explanation:
Start with your given:
-3b + 7 = 13
Subtract 7 on both sides:
-3b = 6
Then, divide -3 on both sides and solve:
b = -2
Answer:
b = -2
Step-by-step explanation:
You start by subtracting the 7 on the left and move it to the other side. Then you have 6 on the right and -3b on the left. Then you divide the -3 on each side and that gives you b= -2.
Hope this helps.
find the value of p in the following equation: 6 * 2/4 = p * 1/4
Answer: [tex]p=12[/tex]
Step-by-step explanation:
[tex]6*\frac{2}{4}=p*\frac{1}{4}[/tex]
Solve the multiplication on the left side.
6 and 4 can be simplified.
6/2=3
4/2=2
Leaving it like;
[tex]3*\frac{2}{2}=p*\frac{1}{4}[/tex]
2 and 2 is 1 and 3 times 1 is 3.
[tex]3=p*\frac{1}{4}[/tex]
Multiply by 4 to eliminate the fraction and isolate p.
[tex]4*3=p*\frac{1}{4}*4\\12=p[/tex]
Tell the measure of the angles In degrees 1/4
Answer:
so 1/4 of a circle is 90 degrees 1/4 is equal to 90 over 360 C it's 90 parts of 360. so here we go with this one. this angle is 20 degrees remember that's 90 alright the square one and this little part would be 20 degrees each angle appears wider as the Rays get longer.
Step-by-step explanation:
Let me know if this help's you lol :)
arc length of a half of a circle with radius of 9
Answer:28.26
Step-by-step explanation:
Φ=180 since it's in a straight line
Radius=r=9
π=3.14
Length of arc=Φ/360 x 2 x π x r
Length of arc=180/360 x 2 x 3.14 x 9
Length of arc=0.5 x 2 x 3.14 x 9
Length of arc=28.26
3.5.49 X 0.67 *
Your answer
What is the answer
Answer:
2.37783 or 23.7783
Step-by-step explanation:
A child is laying on the ground relaxing and looking up at a plane that is passing by. If the plane’s altitude is 33,500 feet and the child’s eyes are located 8,200 feet away from a point on the ground directly beneath the plane, what is the angle of elevation for the child’s line of sight to the plane?
Answer:
about 76.2°
Step-by-step explanation:
The geometry can be modeled by a right triangle with the given dimensions being the side opposite the angle (height = 33,500 ft) and the side adjacent to the angle (8,200 ft). The fact that you know these two sides suggests the inverse of the tangent function may be useful.
Tan = Opposite/Adjacent
tan(angle) = (33,500/8,200)
angle = arctan (335/82) ≈ 76.246°
The angle of elevation is about 76.2°.
Kelly needs 1/8 cups of sugar to make 1/4 of her cookie recipe. How much sugar does she need to make the entire recipe?
Answer:
1/2 cup of sugar
Step-by-step explanation:
She needs to multiply 1/8 cup of sugar by 4 to make the entire recipe since 18 cup of sugar is only good for a fourth of the recipe.
The table shows the number of cups of water required when cooking different amounts of rice.
Amount of
Rice
(cups) Amount of
Water
(cups)
2 5
3 7.5
5 12.5
8 20
Which statements apply to the ratio of rice and water? Choose two options.
The amount of rice is the dependent value.
The amount of water is the dependent value.
The amount of rice is the independent value.
The amount of water is the independent value.
The values cannot be labeled as dependent or independent without a given equation
Answer:
The amount of water is the dependent value.The amount of rice is the independent value.Step-by-step explanation:
The wording "the amount of water required for different amounts of rice" suggests that the "output" value of the table is the amount of water, and the "input" value is the amount of rice.
That makes "water" the dependent variable, and "rice" the independent variable.
The amount of water is the dependent value.
The amount of rice is the independent value.
Answer:
The amount of water is the dependent value.
The amount of rice is the independent value.
Step-by-step explanation:
Solve for a,b,and/or c
Help solve ASAP!
Answer:
a=90-67=23°
.................
Find the volume of a right circular cone that has a height of 12 cm and a base with a diameter of 18 cm.
Answer:1017.36 cm^3
Step-by-step explanation:
Diameter=18cm
Radius=r=18/2=9cm
Height=h=12cm
Volume of cone=1/3 x π x r^2 x h
Volume of cone=1/3 x 3.14 x 9^2 x 12
Volume of cone=1/3 3.14 x 9 x 9 x 12
Volume =(1x3.14x9x9x12) ➗ 3
Volume =3052.08 ➗ 3
Volume =1017.36
Volume of cone=1017.36 cm^3
What's your real rate of return if your savings account pays 2.5% interest and inflation is at 1%?
A. 1.5%
B. 2.5%.
C. 3.5%
D. Can't calculate.
Answer:
Real rate of return = 1.5%
Step-by-step explanation:
Given:
Savings account return = 2.5%
Inflation rate = 1%
Find:
Real rate of return = ?
Computation:
⇒ Nominal rate of return = Real rate of return + Inflation rate
⇒ Real rate of return = Savings account return - Inflation rate
⇒ Real rate of return = 2.5% - 1%
⇒ Real rate of return = 1.5%
Fifteen mothers were asked how many months old their babies were when they cut their first tooth. The results are shown below.
8, 8, 6, 8, 9, 10, 5, 7, 9, 5, 9, 7, 6, 8, 7
Find the range and the outlier(s), if any, of the data set.
What percentage of students who take honors English are taking a non-honors math class?
Answer:
B
Step-by-step explanation:
Took quiz GL
Answer:
the answer is not B
Step-by-step explanation:
the answer is A I actually took the quiz
Yuri computes the mean and standard deviation for the sample data set 12, 14, 9, and 21. He finds the mean is 14. His steps for finding the standard deviation are below.
s = StartRoot StartFraction (12 minus 14) squared + (14 minus 14) squared + (9 minus 14) squared + (21 minus 14) squared Over 4 EndFraction EndRoot. = StartRoot StartFraction negative 2 squared + 0 squared + negative 5 squared + 7 squared Over 4 EndFraction EndRoot. = StartRoot StartFraction 4 + 0 + 25 + 49 Over 4 EndFraction EndRoot. = StartRoot StartFraction 78 Over 4 EndFraction EndRoot. = StartRoot 19.5 EndRoot.
What is the first error he made in computing the standard deviation?
A. Yuri failed to find the difference between each data point and the mean.
B. Yuri divided by n instead of n -1.
C. Yuri did not subtract 9 - 14 correctly.
D. Yuri failed to square -2 correctly.
Answer:
B. Yuri divided by n instead of n-1
Step-by-step explanation:
It was stated in the question that the dataset was sample dataset. For a sample dataset, the standard deviation is given by the formula,
σ = √ Σ (Xi - mean)²/(n - 1) where i = 1,2,3.....n
Since this is just a sample dataset and not the whole population, Yuri should have divided by n-1 instead of n.
Answer:
B.
Step-by-step explanation:
(Here's Answers for the Quiz I did so far!)
1. Abby is collecting rainfall data.
Answer: B.
2. The Monthly Mean Salaries
Answer: A.
3. The Number of Cars at a Dealer Ship
Answer: A. (6.9)
4. The Mean Set of Credit Card Scores.
Answer: C. (720)
Jason earned $54 at his job when he worked for 4 hours. What was his hourly pay rate in hours per dollar?
Answer:
$13.50
Step-by-step explanation:
$54 divided by 4 is $13.50.
Which of the following is a ray as shown in the drawing?
Answer:
DH
Step-by-step explanation:
this is just to comment to tell everyone this is multiple choice meaning it could be ad or ij togethe.
The (average) sales price for single family property in Seattle and Port Townsend is tabulated below.
Year Seattle Port Townsend
1970 $38,000 $8,400
1990 $175,000 $168,400
Find a linear model relating the year x and the sales price y for a single family property in Seattle.
Answer:
[tex]y=6,850x - 13,456,500[/tex]
Step-by-step explanation:
To find the linear model, we need to find a linear equation, where its slope is defined as
[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
So, we use the given points (1970, 38000) and (1990, 175000), to find the slope
[tex]m=\frac{175,000-38,000}{1990-1970}=\frac{137,000}{20} =6,850[/tex]
Now, we use the point-slope formula to find the equation
[tex]y-y_{1} =m(x-x_{1} )\\y-38000=6850(x-1970)\\y=6850x-13,494,500+38,000\\y=6,850x - 13,456,500[/tex]
Therefore, the linear model is
[tex]y=6,850x - 13,456,500[/tex]
PLS HELP ME!
Um doing venn digrams so u have to set one up for it to work... TWENTY POINTS
Answer:
Creating a diagram..
Step-by-step explanation:
Alrighty, I've made a diagram. I've even uploaded it so everyone can see how good at drawing I am (not)
a. 7 do not own anything.
b. the probability that someone owns a bone or a stick is 50%.
c. the probability that someone owns a rock and a bone is 14%.
d. the probability that someone owns at least 2 items is 42%.
e. the probability that someone owns only 1 of these items is 51%.
Please tell me if im wrong! im only a student .m.
Two forces are acting on an object at the same point. Determine the angle between the two forces. (-2,7) and (3,-1)
Answer:
It is 124 degrees.
Step-by-step explanation:
You square each coordinate like this:
sqrt(x^2+y^2 )
You will end up getting sqrt(53 and sqrt(10.
Then find the dot product which is -6+-7=-13.
Then cos^-1(-13/sqrt53*sqrt10)
=124 degrees
12 divided by 9 tenths and hundredths
Assume the average weight of an American adult male is 180 pounds with a standard deviation of 34 pounds. The distribution of weights follows a normal distribution. What is the probability that a man weighs somewhere between 120 and 155 pounds?
Answer:
Step-by-step explanation:
Find a-score of both
z-score = (x-mean)/SD
for 120
z =( 120- 180)/34 = -1.765
For 155
z = (155-180)/34 = -0.735
The probability to look for using z-score table is;
P(-1.765<z<-0.735) = 0.19239
Given: 5(x + 2) - 3 = 4(x - 1)
Prove: x = -11
Statement Reason
5(x + 2) - 3 = 4(x - 1) given
5x + 10 - 3 = 4x - 4 [?]
5x + 7 = 4x - 4 addition
5x = 4x - 11 subtraction
x = -11 subtraction
Answer:-11 proved
Step-by-step explanation:
5(x+2)-3=4(x-1)
Open brackets
5x+10-3=4x-4
Collect like terms
5x-4x=-4+3-10
x=-11
