Answer:
A
Step-by-step explanation:
Answer:1/3 is bigger
Step-by-step explanation:
A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares, how many grains of wheat should be placed on square 24 ? Also find the total number of grains of wheat on the board at this time and their total weight in pounds. (Assume that each grain of wheat weighs 1/7000 pound.)
Answer:
1) 8,388,608 grains of wheat.
2) 16,777,215 grains of wheat.
3) 239,674.5 pounds.
Step-by-step explanation:
Question 1)
We know that on the first square, there is 1 grain of wheat.
On the second, 2 grains of wheat.
On the third, 4 grains of wheat.
And on the fourth, 8 grains of wheat.
Therefore, we have a geometrically increasing sequence. It looks like:
1, 2, 4, 8...
Therefore, to find the number of grains on the 24th square, we can write an explicit formula.
The standard form for the explicit formula for a geometric sequence is:
[tex]x_n=a(r)^{n-1}[/tex]
Where a is the initial amount, r is the common ratio, and n is the nth term (starting from 1).
We know that the initial term a is 1 because there’s one grain of wheat on the first square.
And the common ratio will be 2 because each square has double the amount of the previous square.
So, substitute 1 for a and 2 for r. This yields:
[tex]x_n=1(2)^{n-1}\\[/tex]
We can simplify this:
[tex]x_n=2^{n-1}[/tex]
So, to find the amount of wheat on the 24th square, we simply need to substitute 24 for n and evaluate. So:
[tex]x_{24}=2^{24-1}=2^{23}[/tex]
Evaluate. Use a calculator:
[tex]x_{24}=8,388,608[/tex]
Therefore, on the 24th square, there are 8,388,608 grains of wheat.
Question 2.1)
We want to find the total number of grains of wheat on the board at this time.
In other words, we want to find the sum of our geometric sequence when n is 24.
The formula for the sum of a geometric series is:
[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]
Where rⁿ is the value of the number of terms n, r is the common ratio, and a is the initial term.
We want to find the sum after 24 times. So, n is 24.
So, substitute 24 for n, 2 for r, and 1 for a. This yields:
[tex]S_{24}=\frac{(1)(2^{24}-1)}{2-1}[/tex]
Evaluate. Use a calculator:
[tex]S_{24}=16, 777, 215[/tex]
Therefore, the total sum of the number of grains of wheat at the board at the 24th square is 16,777,215.
Question 2.2)
And to find the weight, we will just have to multiply our total amount by 1/7000. So:
[tex]W=16777215(\frac{1}{70})[/tex]
Use a calculator:
[tex]W=239,674.5\text{ lbs}[/tex]
So, the total weight is 239,674.5 pounds.
HELP ME PLS T^T
Use point-slope form, y - y1 = m(x - x1), to find the linear equation of a line that passes through the points (3, -1) and (1, 1).
that's the answer. good luck
Step-by-step explanation:
Hope it helps man .................
Find the value of the expression:
70–a2 for a=–25; 1; 10
Simple answer.
You will have to replace a, with the given numbers.
For the 1st one)
70-25² since a=25. 70-625=-55
2nd)
70-1²=70-1=69
3d)
70-10²=70-100=-30
Hope this helped.
A lottery game called Quinto is played by choosing five numbers each, from 0 through 9 how many numbers are possible?
Answer:
0-9 gives you 10 possibilites.
10x10x10x10x10=100,000
Step-by-step explanation:
A lottery game called Quinto is played by choosing five numbers each, from 0 through 9, there are 10 possibilities
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given that lottery game called Quinto is played by choosing five numbers each, from 0 through 9
Therefore, we are asked to find the number of possibilities.
10 x 10 x 10 x 10 x 10
=100,000
Thus, there are 100,000 number
This means that from 0 through 9 there are 10 possibilities.
Hence, A lottery game called Quinto is played by choosing five numbers each, from 0 through 9, there are 10 possibilities
Learn more about multiplications;
https://brainly.com/question/14059007
#SPJ2
(2fg)7 simplify the expression
Answer:
14 f g
Step-by-step explanation:
Multiply 7 by 2 .
Looking around in your own country, discuss two practical applications in which “piecewise functions” are used either explicitly or implicitly
Answer:
Piecewise functions are functions that behave differently in different regions of the domain.
One example that you may see in your city is the case of the street illumination, such that can be modeled as:
x = time
Suppose that the lights are turned on at a given hour x0 and then turn off at the hour x1, we can define:
f(x) = 0 if x1 < x < x0
f(x) = 1 if x0 ≤ x ≤ x1
Where f(x) represents the intensity of the light at the time x.
Between x1 and x0, the lights are not working, so the illumination that they provide is zero.
Between x0 and x1 the lights are turned on, so the illumination is 1.
Another example can be the accurate description of the velocity of a car as a function of time.
For some pieces, the car will be stopped (maybe in a red light)
For some pieces, the car will be moving slow (maybe there is a lot of traffic)
For some pieces, the car will be moving fast or accelerating (in an empty street).
So we can define this motion as a piecewise function that obviously will depend on how the car moves.
suppose the retail price of an automobile is $28,000 in 1998 and that it increase at 3% per year. a) write a equation exponential function y=a(1 +r) b) use the model to predict the retail of the automobile in 2016
Answer:
......................................
Find the measure of the missing angle
Solve for x: x + 4 = 10 *
Your answer
Answer:
6
Step-by-step explanation:
A way to answer these questions like I usually do is to subtract the result by the number you already know, like this; 10-4=6, so 6 would be what X equals, or you can just take the long way and keep guessing what the answer would be and keep doing the problems, but that would be very time consuming so I would recommend just doing the subtraction method!
Hope this helps!
Answer:
x = 6
Step-by-step explanation:
x + 4 = 10
=> x = 10 - 4
=> x = 6
-2/3 - (-1 1/3)
A. -1 2/3
B. -2/3
C. -1/3
D. 2/3
Answer is 2/3
Hope this helps
After 5.5 hours, Allie had traveled 264 miles. If she travels at a constant speed, how far will she have traveled in 6 hours?
Answer:
288 Miles
Step-by-step explanation:
Solve for x (speed)
5.5x = 264
Divide by 5.5
x = 48
y = 48x
Subsitute 6 hours in for x
y = 48(6)
y = 288
Answer: Allie went 288 miles in 6 hours.
Step-by-step explanation:
First, you must find out how many miles Allie travled in one hour
= 264/5.5
= 48
Next, multiply the quotient by the number of hours to get the answer.
= 48 x 6
= 288
in the diagram below m abc equals 165°
find the measure of ABD
The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 1100 voters in the town and found that 54% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is more than 50%. Determine the P-value of the test statistic. Round your answer to four decimal places.
Answer:
The p-value is [tex]p-value = 0.0039854[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 1100
The population proportion is p = 0.50
The sample proportion is [tex]\^ p = 0.54[/tex]
The null hypothesis is [tex]H_o : p = 0.50[/tex]
The alternative hypothesis is [tex]H_a : p > 0.50[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\^ p - p }{ \sqrt{\frac{ p(1 - p)}{n} } }[/tex]
=> [tex]z = \frac{ 0.54 - 0.54 }{ \sqrt{\frac{ 0.50 (1 - 0.50)}{1100} } }[/tex]
=> [tex]z = 2.6533[/tex]
Generally from the z-table the probability of 2.6533 for a right tailed test is
[tex]p-value = 0.0039854[/tex]
Write as the sum and/or difference of logarithms. Express powers as factors \log _4\left(\sqrt{\frac{mn}{19}}\right). g
Answer:
[tex]f = \log_{4}\left(\sqrt{\frac{m\cdot n}{19}}\right)[/tex] is equivalent to [tex]f = 0.5\cdot \log_{4} m + 0.5\cdot \log_{4}n -0.5\cdot \log_{4}19[/tex].
Step-by-step explanation:
Let be [tex]f = \log_{4}\left(\sqrt{\frac{m\cdot n}{19}}\right)[/tex], we transform this into an equivalent expression with sums and differences of logarithms by applying logarithm properties:
1) [tex]\log_{4}\left(\sqrt{\frac{m\cdot n}{19}}\right)[/tex] Given.
2) [tex]\log_{4}\left[\left(\frac{m\cdot n}{19} \right)^{0.5}\right][/tex] Definition of square root.
3) [tex]0.5\cdot \log_{4}\left(\frac{m\cdot n}{19} \right)[/tex] [tex]\log_{a} b^{c} = c\cdot \log_{a} b[/tex]
4) [tex]0.5\cdot (\log_{4}m\cdot n -\log_{4} 19)[/tex] [tex]\log_{a} \frac{b}{c} = \log_{a} b - \log_{a} c[/tex]
5) [tex]0.5\cdot \log_{4} m\cdot n -0.5\cdot \log_{4} 19[/tex] Distributive property.
6) [tex]0.5\cdot (\log_{4}m + \log_{4}n)-0.5\cdot \log_{4}19[/tex] [tex]\log_{a} b\cdot c = \log_{a}b +\log_{a} c[/tex]
7) [tex]0.5\cdot \log_{4} m + 0.5\cdot \log_{4}n -0.5\cdot \log_{4}19[/tex] Distributive property/Result.
[tex]f = \log_{4}\left(\sqrt{\frac{m\cdot n}{19}}\right)[/tex] is equivalent to [tex]f = 0.5\cdot \log_{4} m + 0.5\cdot \log_{4}n -0.5\cdot \log_{4}19[/tex].
Rosanne makes 1 1/2 liters of strawberry lemonade. She pours 1/4 of a liter of lemonade into a thermos to take to the park. Her brother drinks 2/5 of the remaining lemonade. How much lemonade does rosanne’s brother drink?
Answer:
1/2 liters
Step-by-step explanation:
Rosanne makes 1 1/2 liters of strawberry lemonade
She pours 1/4 of the lemonade into a thermos
The quantity left is
= 1 1/2 - 1/4
= 3/2 - 1/4
= 5/4
Her brother drinks 2/5 of the remaining lemonade
Therefore the quantity of lemonade that Rosanne brother drinks can be calculated as follows
= 2/5 × 5/4
=1/2
Hence the quantity of lemonade that Rosanne brother drinks is 1/2 liters
Answer:
1/2 liters
Step-by-step explanation: Rosanne makes 1 1/2 liters of strawberry lemonade
She pours 1/4 of the lemonade into a thermos
The quantity left is
= 1 1/2 - 1/4
= 3/2 - 1/4
= 5/4
Her brother drinks 2/5 of the remaining lemonade
Therefore the quantity of lemonade that Rosanne brother drinks can be calculated as follows
= 2/5 × 5/4
=1/2
Round the decimal to a place of the underlined digit 5.657
Answer:
5.6
Step-by-step explanation:
Suppose that X is a random variable with mean 20 and standard deviation 5. Also suppose that Y is a random variable with mean 40 and standard deviation 10. Assume that the correlation between X and Y is 0.5. Find the mean and variance of the random variable Z = ????3X ???? 2Y . Be sure to show all your work.
Answer:
a
[tex]E(Z) = 202 [/tex]
b
[tex]E(Z) = 198[/tex]
c
[tex]E(Z) = -140 [/tex]
Step-by-step explanation:
From the question we are told that
The mean of X is [tex] E(X) = 20[/tex]
The standard deviation of X is [tex]s_1 = 5[/tex]
The mean of Y is [tex]\= y = 40[/tex]
The standard deviation of Y is [tex]s_2 = 10[/tex]
Considering question a
Generally the mean of Z = 2 + 10X. is mathematically represented
[tex]E(Z) = E[2 + 10X ][/tex]
=> [tex]E(Z) = 2 + 10 E(X)[/tex]
=> [tex]E(Z) = 2 + 10 * 20 [/tex]
=> [tex]E(Z) = 202 [/tex]
Considering question b
Generally the mean of Z = 10X - 2.. is mathematically represented
[tex]E(Z) = E[10X -2 ][/tex]
=> [tex]E(Z) = 10E(X) - 2[/tex]
=> [tex]E(Z) = 10* 20 - 2[/tex]
=> [tex]E(Z) = 200 - 2[/tex]
=> [tex]E(Z) = 198[/tex]
Considering question c
Generally the mean of -3X - 2Y is mathematically represented
[tex]E(Z) = E[-3X -2Y ][/tex]
[tex]E(Z) = -3 E(X) -2E(Y) [/tex]
=> [tex]E(Z) = -3 * 20 -2* 40 [/tex]
=> [tex]E(Z) = -140 [/tex]
PLZ HELP WILL GIVE BRAINLYIST
Answer:
400 40
Step-by-step explanation:
If f(x) = 3a|4x - 4| - ax, where a is some constant, find f '(1). (4 points)
Select one:
a. 0
b. not enough information
c. e
d. 1
Annswer girl
Step-by-step explanation:
just trying to get answers
Charlene and Gary want to make confetti. In order to get the right balance of ingredients for their tastes they bought 3 pounds of paper hearts at $2.46 per pound, 5 pounds of sparkling stars for $3.05 per pound, and 3 pounds of shiny coils for $2.33 per pound. Determine the cost per pound of the coffeti.
Answer:
0.712 cents per pound
Step-by-step explanation:
Since we are given the exact amount of each ingredient as well as the price for that amount then we simply need to calculate how much each pound of the confetti actually costs. We do this by adding together all of the pound of all of the ingredients and then adding together all of the costs. Lastly, we divide the cost by the total amount of pounds to find the cost per pound of the confetti like so...
3lbs. + 5lbs. + 3lbs. = 11 lbs.
$2.46 + $3.05 + $2.33 = $7.84
$7.84 / 11 lbs. = 0.712 cents per pound
Therefore, the cost per pound of the confetti is 0.712 cents per pound
compare the price per dozen eggs at the local grocery store and at the supermarket Edward bought 8 dozen eggs in the supermarket how much did he save by buying eggs at the supermarket instead of the local store
Answer:
8
Step-by-step explanation:
i'm a 12 year old girl and i get it so you have to think about the local store would be half witch would be 4 so the answer is 8Which expression is equivalent to Y.Y.Y.Z.Z.Z.Z?
O y 24
O 12xy
o (yz)
07xy
HURRYPLEASEEEE
A local little league has a total of 60 players, of whom 20% are left-handed. How many left-handed players are there?
Answer:
There are 12 left-handed players in the league
Step-by-step explanation:
To find the value of the percentage of a given number, change the percentage at first to decimal by divide it by 100, then multiply the decimal by the number.Ex: 5% of 50 ⇒ 5% = [tex]\frac{5}{100}[/tex] = 0.05 ⇒ 5% × 50 = 0.05 × 50 = 2.5Let us solve the problem
∵ A local little league has a total of 60 players
∵ 20% of them are left-handed
→ Find 20% of 60
∴ The number of left-handed players = 20% × 60
→ Change 20% to a decimal
∵ 20% = [tex]\frac{20}{100}[/tex] = 0.20
∴ The number of left-handed players = 0.20 × 60
∴ The number of left-handed players = 12
∴ There are 12 left-handed players in the league
Which of the following are like terms
Answer:
i would say a but i could be wrong
Step-by-step explanation:
////////////////////////////
Answer:
///////////////////
Step-by-step explanation:
Which is the better deal 8 ounces of shampoo for $0.99 or 12 ounces for $1.47?
Answer:
12 ounces for $1.47.
Step-by-step explanation:
:) ello
Walter is helping to make cookies for a basketball tournament. He's made 15 cookies so far. His coach asked him to make at least 20 cookies but no more than 55. Solve the inequality and interpret the solution.
Answer:
[tex]5\leq x\leq 40[/tex]
Here, [tex]x[/tex] denotes the additional cookies that need to be made by Walter besides 15 cookies made by him so far
Step-by-step explanation:
Number of cookies made by Walter so far = 15
He is asked by his coach to make at least 20 cookies but no more than 55.
Let [tex]x[/tex] denotes the additional cookies that need to be made by Walter besides 15 cookies made by him so far.
The inequality is [tex]20\leq x+15\leq 55[/tex]
Now solve this inequality.
[tex]20\leq x+15\leq 55\\20-15\leq x\leq 55-15\\5\leq x\leq 40[/tex]
Answer: a
Step-by-step explanation: because its right
Help me !!!
!!!
!!
!!
!!
Answer:
one hundred and sixty.Thank you ☺️
Answer:
One Hundred Sixty
Step-by-step explanation:
I’LL MARK BRAINLEST! :)
Answer:
9.1
Step-by-step explanation:
I think this because it is 9 boxes away from the other points, plus it sloped a bit...
Answer:
9.1
Step-by-step explanation:
Distance=[tex]\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2} }[/tex]
=[tex]\sqrt{(4-3)^{2} +(-5-4)^{2} }[/tex]
=[tex]\sqrt{(1)^{2}+(-9)^{2} }[/tex]
=[tex]\sqrt{1+81}[/tex]
=[tex]\sqrt{82}[/tex]
≈9.1
g÷2+ 19 > 15
what is g?
Answer: g > -8
Step-by-step explanation:
sadmep