Answer:
e = 10
Step-by-step explanation:
In this problem we are told to solve for e. This means we need to isolate the variable e, leaving it completely by itself on one side of the equation.
9e + 4 = -5e + 14 + 13e
We can do this multiple ways, but I will show you how I would do it.
First I would subtract 4 from both sides.
9e + 4 = -5e + 14 + 13e
9e = -5e + 14 + 13e - 4
We can simplify the right side of the equation down by subtracting four from 14.
9e = -5e + 10 + 13e
Next, let's simplify our algebraic expressions. We can subtract 5e from 13e (or add -5e to 13e whatever tickles your fancy)
-5e + 13e = 8e
9e = 8e + 10
Now we subtract algebraic expression 8e from both sides
9e - 8e = 10
All of our expressions with the variable e are now on one side but we aren't done yet. Compute 9e - 8e.
9e - 8e = 10
1e = 10
or
e = 10
We have isolated e! Our final answer is e = 10
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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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
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
Which types of triangles can be formed by taking the cross-section of a rectangular prism like the one shown above?
Answer: Equilateral, isosceles and scalene.
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°.
How to find the area of the seating area
Parallelogram area is base times height. Base of 14, height of 10,
Answer: A = (14 ft)(10 ft) second choice
Answer:
choice B
Step-by-step explanation:
Find the values of the variable y, for which:
the difference between the fractions y+12/y-4 and y/y+4 is equal to their product
Answer:
y = 12
Step-by-step explanation:
Ordinarily, in math, when we say "the difference between ..." we mean the second listed item is subtracted from the first. (In English, we often mean "the positive difference between ..." so the order doesn't matter.)
We'll assume we are only interested in the case where the difference is in the order listed.
[tex]\dfrac{y+12}{y-4}-\dfrac{y}{y+4}=\dfrac{y+12}{y-4}\cdot\dfrac{y}{y+4}\\\\\dfrac{(y+12)(y+4)-(y-4)(y)}{y^2-16}=\dfrac{(y+12)(y)}{y^2-16}\\\\0=\dfrac{y^2-8y-48}{y^2-16}=\dfrac{(y-12)(y+4)}{(y-4)(y+4)}=\dfrac{y-12}{y-4}\qquad\text{$y\ne -4$}\\\\\boxed{y=12}[/tex]
There is one solution.
_____
Comment on the solution
If you were to "clear fractions" by multiplying the equation by (y^2-16), you would also obtain the extraneous solution y=-4. That is why we did not solve it that way.
How many different 12-letter arrangements can be made using the letters in the word indianapolis?
Answer:
764
Step-by-step explanation:
Round 0.378 to the place underlined digit 3
Answer:
0.38
Step-by-step explanation:
7 is the 3rd digit, so 8 is greater then 5, so you round up, if it is correct, can you give brainiest
Answer:
0.40
Step-by-step explanation:
this is because the number before it is up to five and even more than 5 so we round it up by adding one to the next number and the remaining digit to zero
Solve for a,b,and/or c
Help solve ASAP!
Answer:
a=90-67=23°
.................
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
What’s the correct answer for this?
ANSWER: D
Isosceles Right Triangle has 3 angles: 90 degrees, 45 degrees and 45 degrees
Answer:
D
Step-by-step explanation:
It is isosceles (having two sides and angles congruent) and it is right will provide enough information to find all the angles of the triangles.
12 divided by 9 tenths and hundredths
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
The states that dropped out of the Union, became the __________________ States of America 58 POINTS!!!
Answer:
Confederate
Step-by-step explanation:
During the time that led up to the conflict known as the Civil War of America, the major cause of tension was slavery. Southern plantation owners and farmers fiercely advocated slavery because they helped with the harvest of crops and the overall southern economy. The northerners, however, resisted slavery, saying it was immorally and inhumanely wrong.
At the culmination of this tension, many southern states, led by Jefferson Davis (who later became the "president" of the Confederate states), decided to secede from the Union (break away) and establish their own entity, which they called the "Confederate States of America".
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 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:
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 (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]
A 6-sided die is rolled three times. What is the probability of rolling a 4 each time?
A 0.00463
B. 0.99537
C 0.16667
D. 0.00231
Answer:
a
Step-by-step explanation:
math
Solve for x - y = -3
Answer:
0-3=-3
Step-by-step explanation:
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.
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! :)
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
Factorise 2y^2 + y + 6xy + 9x - 3
Answer: (2y+3)(3x+y-1)
Step-by-step explanation:
First regroup the terms.
6xy+9x+2y^2+y-3
Second factor 3x out of 6xy+9x
3x(2y)+9x+2y^2+y-3
3x(2y)+3x(3)+2y^2+y-3
And you get
3x(2y+3)+2y^2+y-3
Third factor by grouping
Look at recent question
Answer:
ok was it college math if so the I don't know
Solve |6k + 12| + 9=9 for k
Answer:
k= -2
Step-by-step explanation:
Ana has a rectangular garden with a width of 2.3 meters and a length of 2.8 meters. She makes the model below to help her determine the area of her garden. What is the area of Ana's garden?
Answer:
6.44 m2
Step-by-step explanation:
Harris Interactive® conducted a poll of American adults in August of 2011 to study the use of online medical information. Of the 1,019 randomly chosen adults, 60% had used the Internet within the past month to obtain medical information. Use the results of this survey to create an approximate 95% confidence interval estimate for the percentage of all American adults who have used the Internet to obtain medical information in the past month.
Answer:
[tex]0.60 - 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.570[/tex]
[tex]0.60 + 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.630[/tex]
The 95% confidence interval for the true proportion would be given by (0.570;0.630) .
And if we convert this into % we got (57.0%, 63.0%)
Step-by-step explanation:
The information given we have the following info given:
[tex] n = 1019[/tex] represent the sampel size
[tex] \hat p=0.6[/tex] represent the sample proportion of interest
The confidence level is 95%, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
The confidence interval for the mean is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
Replacing the info given we got:
[tex]0.60 - 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.570[/tex]
[tex]0.60 + 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.630[/tex]
The 95% confidence interval for the true proportion would be given by (0.570;0.630) .
And if we convert this into % we got (57.0%, 63.0%)
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
