Answer:
Step-by-step explanation:
In mathematics, the domain or set of departure of a function is the set into which all of the input of the function is constrained to fall. It is the set X in the notation f: X → Y. Since a function is defined on its entire domain, its domain coincides with its domain of definition, the subset of the domain for which the function associates an image. However this coincidence is no longer true for a partial function since the domain of definition of a partial function can be a proper subset of the domain.
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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Solve for a,b,and/or c
Help solve ASAP!
Answer:
a=90-67=23°
.................
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
6 to the power of 3 +7 times 4
Answer:
892
Step-by-step explanation:
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
1. Si pide prestado $ 600 por siete años a una tasa de interés del 7%, ¿cuánto interés pagará?
Answer:
Su pago mensual sería de $9.06 (Espero que esto ayude)
Step-by-step explanation:
solve for the coefficient -5=a(0-2)(0-3)(0-5)
Answer:
a = 1/6
Step-by-step explanation:
-5=a(0-2)(0-3)(0-5)
Simplify
-5=a(-2)(-3)(-5)
-5 = a(-30)
Divide each side by -30
-5/-30 = -30a/-30
1/6 =a
Answer:
1/6
Step-by-step explanation:
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 :)
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
Marco bought gifts for his family at the school gift shop for the holidays. Marco bought 10gifts and spent $11.50. How many of each item did he buy if friendship bracelets cost $1.50 and stickers cost $1?
Step-by-step explanation:
Marco bought 10 gifts = 11. 50
If 5 bracelets = 1.50 x 5 = 7.5
4 stickers = 4 x 1 = 4
So total cost = 7.5 + 4 = 11.5
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
Distance between (-1,0) and (8,6)
Answer:
3 √ 13
Step-by-step explanation:
Answer:
3√13
Step-by-step explanation:
We want to find the distance between these two points. To do so, we need to use the distance formula which states that the distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is:
d = [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
Here, [tex]x_1=-1,x_2=8,y_1=0[/tex], and [tex]y_2=6[/tex]. So:
d = [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
d = [tex]\sqrt{(-1-8)^2+(0-6)^2}=\sqrt{(-9)^2+(-6)^2} =\sqrt{81+36} =\sqrt{117} =3\sqrt{13}[/tex]
Thus, the answer is 3√13.
~ an aesthetics lover
The formula A=12(b+c)h. Write the equation in term of c?
Answer:
[tex]c = \frac{A}{12h} - b[/tex]
Step-by-step explanation:
Okay, so the goal is to isolate c on one side with all the other terms on the other side. So, let's start by dividing both sides with 12h. After we do that, we will be left with [tex]\frac{A}{12h} = b+c[/tex]. Now, we can subtract both sides by b, and we will be left with [tex]\frac{A}{12h} - b = c[/tex]. Yay! We've now isolated c and that is our final answer!
Hope this helped! :)
Which of the following statements is FALSE? The correlation coefficient equals the proportion of data points that lie on a straight line. The correlation coefficient will be +1.0 only if all the data lie on an upward-tilting straight line. The correlation coefficient is undefined if all the data lie on a perfectly horizontal straight line. The correlation coefficient is a unitless number and must always lie between –1.0 and +1.0, inclusive.
Answer:
The first one is False.
Step-by-step explanation:
If the correlation coefficient can also be -1 if the data lies on an upward tilting straight line.
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]
Classify each representation shown below as either linear or exponential.
x y
0 5
1 7.5
2 11.25
y = 2x + 4
One person sends an email to 2 people. Those 2 people send it to 4 people, and those 4 send it to 8 people.
1. Exponential
2. Linear
3. Exponential
The sum of five consecutive integers is 70. What are the numbers?
Answer: The numbers are 12, 13, 14, 15, and 16.
Step-by-step explanation:
Write an algebraic equation.
x + (x+1) + (x+2) + (x+3) + (x+4) = 70
5x + 10 = 70
subtract 10 from both sides
5x = 60
divide each side by 5
x = 12
The numbers are 12, 13, 14, 15, and 16.
Answer:
12 to 16 :) hope it helped
Find the area of the triangle
Answer:
84mm
Step-by-step explanation:
Formula of a triangle:
A =bh/2
A=14(12)/2
A=168/2
A=84mm
Look at recent question
Answer:
ok was it college math if so the I don't know
1.] What is the probability of choosing a king
from a standard deck of playing cards?
Answer:
1/13
Step-by-step explanation:
there are 4 kings in a deck of 52 cards.
4/52 = 1/13
How do you determine similarities in shapes?
Answer:
Step-by-step explanation:
. if every corresponding internal angles in both shapes are equal
. if all corresponding sides are equal or have same ratio.
more rules but depends on the shape also ( triangle, rectangle, hexagon,...)
If V = 15 cm, W = 20 cm, X = 25 cm, Y = 7 cm, and Z = 22 cm, what is the perimeter of the object?
A.
53 cm
B.
64 cm
C.
118 cm
D.
78 cm
Answer:
Sum of all the sides.
Step-by-step explanation:
Perimeter is the sum of the distance in length or width, or height or circumference of all the sides of an object.
Therefore the sum total of the given sides V, W, x ,Y, Z are;
15 +20 + 25 + 7 + 22 = 89cm
Since a picture isn't available to know which sides of the objects can be added.
One brand of coffee is packaged in cylinders where the height is equal to the radius, r. The volume of the package, in cubic centimeters, can be found using the function V(r) = πr3. The number of ounces of coffee in the cylinder depends on the volume of the cylinder, V, in cubic centimeters. This can be modeled by the function C(V) = 3.2V. Which function can be used to find the number of ounces of coffee in the can based on its radius? C(V(r)) = 32.768πr3 C(V(r)) = 3.2πr3
Answer:
C(V(r)) = 3.2πr3Step-by-step explanation:
This problem is a composition of function defined by C(V(r)), now we have the functions [tex]V(r)= \pi r^{3}[/tex] and [tex]C(V)=3.2V[/tex], where the first depends on the radius, and the second dependes on the volume, that means, to find the number of ounce of coffe, we need to determine the volume of the cylinder, that's why we have to replace the volume function inside the ounces function,
[tex]C(V(r))=3.2(\pi r^{3} )[/tex]
Therefore, the right answer is the last choice.
12 divided by 9 tenths and hundredths
an automobile traveled 21 miles north from the airport. it then turned directly west and traveled 28 miles. how far is the automobile from the airport??
The automobile is 35 miles away from the airport
The quadratic equation x^2 - 8x = -4 is rewritten in the form (x + p)^2 = q. when q is a constant. What is the value of p ?
Answer:
-4
Step-by-step explanation:
If you multiply out the square, you can see ...
(x +p)^2 = q
x^2 +2px +p^2 = q
The coefficient of the x-term is 2p, so ...
2p = -8
p = -8/2 = -4
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
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
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°.
Solve for x - y = -3
Answer:
0-3=-3
Step-by-step explanation:
