If the two removed squares have the same color, then it is possible to cover the truncated checkerboard with non-overlapping dominoes. If they have different colors, then it will be impossible to cover the truncated checkerboard with non-overlapping dominoes.
To prove that the chess board can be completely covered by non-overlapping dominoes, where each domino covers exactly two squares, we can color the board alternatively in black and white. The two colors will make the board have 32 black squares and 32 white squares. Each domino will cover one white and one black square. Since there are the same number of black and white squares, there is an equal number of squares that each domino can cover so it is possible to cover the entire board with dominoes without overlap.
To determine whether the cut checkerboard can be covered by non-overlapping dominoes, note that we have 62 squares, 31 of which are black, and 31 white. This means that one color will have one extra square, in this case black. Therefore, if the two removed squares are of different colors, it will be impossible to cover the cut checkerboard with non-overlapping dominoes.However, if the two removed squares have the same color, then it will be possible to cover the checkerboard with non-overlapping dominoes. This is because we will still have an equal number of black and white squares even after the removal of the two squares.The same logic applies to the truncated checkerboard.
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56 tuna sandwiches were sold.
This was 40% of the total number of sandwiches sold.
(a) Work out the total number of sandwiches sold,
Answer:
140 sandwiches
Step-by-step explanation:
56/4=14 which is 10% of the sandwiches sold
14*10=140
Answer:
140 sandwiches.
Step-by-step explanation:
We know
56 tuna sandwiches were sold. This was 40% of the total number of sandwiches sold.
Work out the total number of sandwiches sold.
We Take
56 divided by 40, then time 100 = 140 Sandwiches
So, the total number of sandwiches sold is 140 sandwiches.
4. Adults were randomly selected for a poll and asked if they favored or opposed federal tax dollars being used for foreign aid. Of the 882 polled, 415 were opposed. A politician claims that more than 50% c
are opposed to federal tax dollars being used for foreign aid. Use a 0.01 significance level to test the claim. State the final conclusion.
There is sufficient evidence to support the claim that more than 50% of adults are opposed to federal tax dollars being used for foreign aid.
There is not sufficient evidence to support the claim that less than 50% of adults are opposed to federal tax dollars being used for foreign aid.
There is not sufficient evidence to support the claim.
There is not sufficient evidence to support the claim that more than 50% of adults are opposed to federal tax dollars being used for foreign aid.
The conclusion (a) is correct i.e., There is sufficient evidence to support the claim that more than 50% of adults are opposed to federal tax dollars being used for foreign aid.
What is Federal tax?In USA, an obligation to pay a tax to the federal government rather than a state government
Sample Size (n) = 882
Number of Success ( X) = 415
The Hypothesis is given by :
[tex]H_{0}[/tex] : p = 0.50
H₁ : p > 0.50
The point estimate of the proportion is calculated by :
p^ = X/n
= 415/882
= 0.47
Therefore, a point estimate is 0.47 .
The test statics is calculated by :
[tex]Z = \frac{\vec{}p - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]
= [tex]\frac{0.47 - 0.50 }{\sqrt{\frac{0.50(1-0.50)}{882} } }[/tex]
= - 1.781.
Therefore, the test statistics is -1.781.
The p-value is obtained from normal distribution at test statistic (-1.781).
The p-value is 0.037.
Since the p-value is less than level of significance (0.01) which means we reject the null hypothesis.
Therefore, The conclusion (a) is correct i.e., There is sufficient evidence to support the claim that more than 50% of adults are opposed to federal tax dollars being used for foreign aid.
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mixed in a drawer are blue socks, white socks, and gray socks. you pull out two socks, one at a time, without looking. find the probability of getting 2 socks of the same color.
The probability of getting 2 socks of the same color given by the following solution is 65/132.
Beginning with the first sock, we have three options: blue, white, or grey. If we wanted to know the likelihood of drawing only one blue sock, we might divide the number of blue socks in the drawer by the total number of socks (2 / 12).
We have three options for the second sock: blue, white, or grey. Keep in mind that we are drawing without replacement, so there is now one fewer sock in the drawer. Thus, with three alternatives for the first sock and three options for the second sock, the total number of combinations is three times three, or nine. The following are all of the potential combinations: (blue, blue), (blue, white), (blue, grey), (white, blue), (white, white), (white, grey), (white, blue), (white, white), (white, grey), (grey, blue), (grey, white) (gray, gray).
So the probability of 2 socks of the same color is, in equation form:
P(2 socks of same color) = P(blue sock first) * P(blue sock second) + P(white sock first) * P(white sock second) + P(gray sock first) * P(gray sock second).
= 2/12*1/11 + 4/12*3/11 + 6/12*5/11
= 65/132
Therefore, the probability of getting 2 socks of the same color 65/132.
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Complete question:
Mixed in a drawer are 2 blue socks, 4 white socks, and 6 gray socks. You pull out two socks, one at a time, without looking. Find the probability of getting 2 socks of the same color.
Show that, the sum of an infinite arithmetic progressive sequence with a positive common difference
is +∞
Answer:
Show that, the sum of an infinite arithmetic progressive sequence with a positive common difference
is +∞
Step-by-step explanation:
To show that the sum of an infinite arithmetic progressive sequence with a positive common difference is +∞, we can use the formula for the sum of the first n terms of an arithmetic sequence:
Sn = n/2 [2a + (n-1)d]
where a is the first term, d is the common difference, and n is the number of terms in the sequence.
Now, if we let n approach infinity, the sum of the first n terms of the sequence will also approach infinity. This can be seen by looking at the term (n-1)d in the formula, which grows without bound as n becomes larger and larger.
In other words, as we add more and more terms to the sequence, each term gets larger by a fixed amount (the common difference d), and so the sum of the sequence increases without bound. Therefore, the sum of an infinite arithmetic progressive sequence with a positive common difference is +∞.
Find the dimensions of the rectangular box with largest volume if the total surface area is given as 4 cm2. (Let x, y, and z be the dimensions of the rectangular box.)
(x, y, z) =
Answer:
x = y = z = (√6)/3 cm ≈ 0.8165 cm
Step-by-step explanation:
You want the dimensions of the cuboid with the largest volume and a total surface area of 4 cm².
Largest volumeFor a fixed surface area, the figure with the largest volume is a regular figure. In this case, it is a regular cuboid, or cube.
AreaThe total surface area of a cube with edge length s is ...
A = 6s²
Then the edge length of the desired cube is found from ...
4 = 6s²
s² = 2/3 = 6/9 . . . . . . divide by 6; write with square denominator
s = √(6/9) = (√6)/3
The dimensions of the box are ...
x = y = z = (√6)/3 cm ≈ 0.8165 cm
Evaluate the following integral in cylindrical coordinates.∫3−3∫√9−x20∫2011+x2+y2dzdydx
The value of the integral in cylindrical coordinates is -81π/2.
We have the following integral
∫ from 3 to -3 ∫ from 0 to √(9-x^2) ∫ from 20 to 11+x^2+y^2 dz dy dx
Converting to cylindrical coordinates, we have:
x = r cos(theta)
y = r sin(theta)
z = z
Also, from the equation of the cone, we know that r^2 = x^2 + y^2 = 9. Thus, we have
r = 3
Substituting these values, we get
∫ from 0 to 2π ∫ from 0 to 3 ∫ from 20 to 11+r^2 dz r dr dtheta
Evaluating the z integral, we get:
∫ from 0 to 2π ∫ from 0 to 3 (11+r^2-20) r dr dtheta
= ∫ from 0 to 2π ∫ from 0 to 3 (r^3-9r) dr dtheta
= ∫ from 0 to 2π [ (1/4) r^4 - (9/2) r^2 ] |_0^3 dtheta
= ∫ from 0 to 2π (81/4 - 81/2) dtheta
= -81π/2
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Solve the equation 3/4x - 5 = x give your answers correct to 2 decimal places
The solution to the equation 3/4x - 5 = x, is equals to -20.00 (correct to 2 decimal places).
To solve the equation 3/4x - 5 = x for x, we can start by isolating the variable term on one side of the equation and the constant term on the other side. We can do this by adding 5 to both sides of the equation:
3/4x - 5 + 5 = x + 5
3/4x = x + 5
Next, we can isolate x on one side of the equation by subtracting x from both sides:
3/4x - x = x + 5 - x
-1/4x = 5
Finally, we can solve for x by dividing both sides of the equation by -1/4:
x = -20
Therefore, by using isolating the variable term and solving for x. we find the solution of 3/4x - 5 = x, correct to 2 decimal places, is x = -20.00.
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Factor
[tex]25x^6 + 10x^3 + 12[/tex]
Answer:
Step-by-step explanation:
To factor 25x^6 + 10x^3 + 12, we can first factor out the greatest common factor of the three terms which is 1, then use a substitution:
Let's substitute y = x^3. Then, the expression becomes:
25y^2 + 10y + 12
We can now try to factor this quadratic expression. However, since the discriminant (b^2 - 4ac) of this quadratic equation is negative (10^2 - 4*25*12 = -440), this expression cannot be factored using real numbers.
Therefore, the final answer for the factoring is:
25x^6 + 10x^3 + 12 = (unfactorable)
define a function named signof that receives an integer argument and returns the value 1 if the argument is positive, 0 if the argument is 0, or -1 if the argument is negative.
The signof function is defined as follows:
def signof(num):
if num > 0:
return 1
elif num == 0:
return 0
else:
return -1
In the above code snippet, we have defined a function named signof which receives an integer argument named num. The if condition checks if the num is greater than 0, if yes, the function will return 1 as it is positive. Else if the num is equal to 0, then it will return 0, as per the requirement. Otherwise, it will return -1 as the number is negative. This code snippet will give the required output as per the requirement of the problem statement.
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Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 15 people took the trip. She was able to purchase coach tickets for $220 and first class tickets for $910. She used her total budget for airfare for the trip, which was $8130. How many first class tickets did she buy? How many coach tickets did she buy?
A train travelling at 40km/h takes 3 hours for a journey. How long will it take the train to complete the same journey, travelling at 90km/h?
Answer: 1 hour and 20 minutes
Step-by-step explanation:
We can use the formula:
time = distance / speed
Let's call the distance of the journey "d".
When the train is travelling at 40 km/h, it takes 3 hours to complete the journey. So we have:
3 = d / 40
Solving for "d", we get:
d = 3 x 40 = 120 km
Now we want to know how long it will take for the train to complete the same journey at 90 km/h. We can use the formula again:
time = distance / speed
Plugging in the values we know:
time = 120 / 90
Simplifying, we get:
time = 4/3 hours or 1 hour and 20 minutes
Therefore, the train will take 1 hour and 20 minutes to complete the journey at 90 km/h.
Required answer :-
1 hour 20 minutesStep-by-step explanation:
A train travelling at 40km/h takes 3 hours for a journey. So, Speed will be 40 km/hr
Time will be 3 hours.
Speed = Distance/time
Distance = Speed × time
Distance = 40 × 3
Distance = 120 km.
Now, we have to find that how long will it take the train to complete the same journey, travelling at 90km/h.
Now, Speed will be 90 km/hr
Distance = Speed × time
Time = Distance/speed
Time = 120/90
Time = 4/3 hours
1 hour = 60 minutes
4/3 × 60
4 × 20
80 minutes
1 hour 20 minutes.
Therefore, The train will take 1 hour 20 minutes to complete the journey, travelling at 90km/h.
Mr. McCoy's new ice cream shop is doing great! Last month, he sold out of his Boldly Buttered Popcorn ice cream and his Lovely Lavender Lemon ice cream. He sold x pints of Boldly Buttered Popcorn and y pints of Lovely Lavender Lemon. Each pint cost him $4 to make, and he charged $10 for each
After selling x pints of Boldly Buttered Popcorn icecream and y pints of Lovely Lavender Lemon on the charged of $10 for each, his profit equation is written as P = 6x + 6y = 6( x + y).
We have, Mr. McCoy's new ice cream shop. He sold two flavors of icecream. He sold his Boldly Buttered Popcorn ice cream and his Lovely Lavender Lemon ice cream. The quantity of sold Boldly Buttered Popcorn ice cream = x pints
The quantity of sold Lavender Lemon ice cream = y pints
Cost of each pint of ice cream = $4
Selling price of each pint of ice cream
= $10
First, total pints of icecream he sold
= pints of Boldly Buttered Popcorn ice cream+ pints of Lavender Lemon ice cream = ( x + y) pints
Now, Cost of (x + y) pints of ice cream
= $4 ( x + y)
Similarly, selling price of ( x + y ) pints of icecream = $ 10 ( x + y)
As we know, when selling price is greater than cost price then profit will occur. Equation for profit P = selling price - cost price = $ 10 ( x + y) - $4 ( x + y)
= 10 x + 10y - 4x - 4y
P = 6(x + y)
Hence, required equation is 6x + 6y.
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Complete question:
Mr. McCoy's new ice cream shop is doing great! Last month, he sold out of his Boldly Buttered Popcorn ice cream and his Lovely Lavender Lemon ice cream. He sold x pints of Boldly Buttered Popcorn and y pints of Lovely Lavender Lemon. Each pint cost him $4 to make, and he charged $10 for each. Write an equation for his profit or loss on ice cream selling.
For his craft project, James bought
10
1010 pieces of ribbon that were each
2. 1
feet
2. 1 feet2, point, 1, start text, space, f, e, e, t, end text long. How many total yards of ribbon did James buy?
James bought a total of 7 yards of ribbon for his craft project.
To begin with, let's first convert the length of the ribbon from feet to yards. There are 3 feet in a yard. So, to convert 2.1 feet to yards, we need to divide it by 3.
2.1 feet ÷ 3 = 0.7 yards
So, each piece of ribbon is 0.7 yards long.
Now, let's calculate the total length of ribbon James bought by multiplying the length of each piece of ribbon by the total number of ribbons he bought.
Total yards of ribbon = length of one ribbon × number of ribbons
Total yards of ribbon = 0.7 yards × 10
Total yards of ribbon = 7 yards
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Complete Question:
For his craft project, James bought 10 pieces of ribbon that were each 2.1 feet long. How many total yards of ribbon did James buy?
the car that Andrew used to UWC has a fuel consumption rate of 0,0052k /100km.The cost of petrol for the month of January is R11,90 /litre. calculate the cost of petrol for the trip to UWC.
The cost of petrol for the trip to UWC is R1.2384.
What is cost?In general, cost refers to the amount of resources (usually money) that must be expended to produce or acquire something. It can be thought of as the value of the resources that are given up in order to obtain something else.
According to the given information:To calculate the cost of petrol for the trip to UWC, we need to know the distance traveled and the amount of fuel consumed.
Let's assume that the distance from Andrew's home to UWC is 20 kilometers (km). Then, the amount of fuel consumed for the trip is:
[tex]Fuel consumed = (0.0052 k/100 km) * 20 km = 0.00104 k[/tex]
where k stands for liters of petrol.
To convert the amount of fuel consumed to liters, we need to multiply by 100, since the fuel consumption rate is given in liters per 100 km:
[tex]Fuel consumed = 0.00104 k * 100 = 0.104 liters\\Fuel consumed = 0.00104 k * 100 = 0.104 liters[/tex]
Now we can calculate the cost of petrol for the trip:
[tex]Cost of petrol = (0.104 liters) * (R11.90/liter) = R1.2384[/tex]
Therefore, the cost of petrol for the trip to UWC is R1.2384.
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Determine whether the graph is that of a function. If it is, use the graph to
find its domain and range, the intercepts, if any, and any symmetry with
respect to the x-axis, the y-axis, or the origin.
Answer:
D
Step-by-step explanation:
First, yes, it is a function. Functions are defined as having one output per input, and given a number on this graph, we can find only one output.
Domain is the range of x-values in a graph. The domain here is from [tex]-\pi[/tex] to [tex]\pi[/tex].
Range is the range of y-values in a graph. The range here is from -1 to 1.
This graph has three intercepts at [tex](-\pi ,0)(0,0)(\pi ,0)[/tex].
Symmetry: This graph has rotational symmetry, meaning it can be rotated about a point to map onto itself. Here, we can rotate it 180 degrees about the origin to map onto itself.
Although I can't see the final two points for answer D, answer A is similar but the symmetry portion is wrong, leading me to believe that it must be D.
Let me know if this helped by hitting thanks or brainliest! If not, comment below and I'll get back to you ASAP.
Shanika bought 1 Notebook and 5 pencils at a cost of $10.00. Jules paid $14.90 for 1 Notebook and 12 pencils. How much did Jules pay for 1 pencil if both pay the similar prices?
ANSWER
Jules paid $0.70 for one pencil
STEPS
Cost of One Pencil.
Let's assume the cost of one notebook be x and one pencil be y.
According to the given information,
Shanika bought 1 notebook and 5 pencils at a cost of $10.00. Therefore,
1x + 5y = 10 --- equation 1
Jules paid $14.90 for 1 Notebook and 12 pencils. Therefore,
1x + 12y = 14.9 --- equation 2
We need to find the cost of one pencil, i.e., y.
We can solve the above equations simultaneously to find the value of y.
Multiplying equation 1 by 12 and equation 2 by 5, we get:
12x + 60y = 120 --- equation 3
5x + 60y = 74.5 --- equation 4
Subtracting equation 4 from equation 3, we get:
7x = 45.5
x = 6.5
Substituting the value of x in equation 1, we get:
1(6.5) + 5y = 10
5y = 3.5
y = 0.7
Therefore, Jules paid $0.70 for one pencil.
ChatGPT
Answer:
Jules pay:
$0.7
Step-by-step explanation:
1n + 5p = 10 Eq. 1
1n + 12p = 14.9 Eq. 2
n = cost of one notebook
p = cost of one pencil
From Eq. 1
n = 10 - 5p Eq. 3
From Eq. 2
n = 14.9 - 12p Eq. 4
Equalizing Eq. 3 and Eq. 4:
10 - 5p = 14.9 - 12p
12p - 5p = 14.9 - 10
7p = 4.9
p = 4.9 / 7
p = 0.7
From Eq. 3:
n = 10 - 5p
n = 10 - 5*0.7
n = 10 - 3.5
n = 6.5
Check:
From Eq. 2:
n + 12p = 14.9
6.5 + 12*0.7 = 14.9
6.5 + 8.4 = 14.9
Then:
1 pencil = $0.7
A restaurant bill of $3200 is paid with $500 and $1000 bills. If 16 bills were used, determine how many $1000 and $500 bills were used.
Let's use variables to represent the number of $1000 and $500 bills used.
Let x be the number of $1000 bills used.
Then 16 - x is the number of $500 bills used.
The total amount paid is the sum of the values of the bills used:
$1000(x) + $500(16 - x) = $3200
Simplifying and solving for x:
$1000x + $8000 - $500x = $3200
$500x = $4800
x = 9.6
We can't have a fraction of a bill, so we'll round down to 9 $1000 bills.
Then the number of $500 bills used is:
16 - x = 16 - 9 = 7
Therefore, 9 $1000 bills and 7 $500 bills were used to pay the $3200 restaurant bill.
Arrange the steps to find an inverse of a modulo m for each of the following pairs of relatively prime integers using the Euclidean algorithm in the order. a = 2, m=17 Rank the options below. The ged in terms of 2 and 17 is written as 1 = 17-8.2. By using the Euclidean algorithm, 17 = 8.2 +1. The coefficient of 2 is same as 9 modulo 17. 9 is an inverse of 2 modulo 17. The Bézout coefficients of 17 and 2 are 1 and 8, respectively. a = 34, m= 89 Rank the options below. The steps to find ged(34,89) = 1 using the Euclidean algorithm is as follows. 89 = 2.34 + 21 34 = 21 + 13 21 = 13 + 8 13 = 8 + 5 8 = 5 + 3 5 = 3 + 2 3 = 2+1 Let 34s + 890= 1, where sis the inverse of 34 modulo 89. $=-34, so an inverse of 34 modulo 89 is -34, which can also be written as 55. The ged in terms of 34 and 89 is written as 1 = 3 - 2 = 3-(5-3) = 2.3-5 = 2. (8-5)- 5 = 2.8-3.5 = 2.8-3. (13-8)= 5.8-3.13 = 5. (21-13)-3.13 = 5.21-8. 13 = 5.21-8. (34-21) = 1321-8.34 = 13. (89-2.34) - 8.34 = 13.89-34. 34 a = 200, m= 1001 Rank the options below. By using the Euclidean algorithm, 1001 = 5.200 +1. Let 200s + 1001t= 1, where sis an inverse of 200 modulo 1001. The ged in terms of 1001 and 200 is written as 1 = 1001 - 5.200. s=-5, so an inverse of 200 modulo 1001 is -5.
We have that, using Euclid's algorithm, we find the inverse of 200 modules 1001 is -5 (or 1001+5).
How do we find the inverse of a modulus?To find the inverse of a module m using Euclid's algorithm, the steps are as follows:
1. Calculate the greatest common divisor (GCD) of a and m using the Euclidean algorithm.
2. Let a = GCD * s + m*t, where s is the inverse of a module m.
3. The GCD in terms of a and my is written as 1 = m-s*a.
4. Find s = -a, so the inverse of a module m is -a (or m+s).
For example, a = 2, m=17, so GCD = 1 = 17-8*2 and the inverse of 2 modulo 17 is -8 (or 17+8). Similarly, for a = 34, m= 89, the GCD = 1 = 89-34*2 and the inverse of 34 modulo 89 is -34 (or 89+34). Finally, for a = 200, m= 1001, the GCD = 1 = 1001-5*200 and the inverse of 200 modulo 1001 is -5 (or 1001+5).
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Write the expression in complete factored form.
5a(b + 1) + 3(b + 1) help
Answer:
(b+1)(5a+3)
Step-by-step explanation:
Notice how (b+1) appears on both sides. That means we can "factor it out" by moving it to the very left -
(b+1)
Now we know the form of the answer we can continue doing it.
For the next step, I take the terms 5a and 3 (what's left) and move them to the right as shown:
(b+1)(5a+3)
#Keep learning
Best regards
Binomial Problem:A jury has 12 jurors. A vote of at least 10 out of 12 for "guilty" is necessary for a defendant to be convicted of a crime. Assume that each juror acts independently of the others and that the probability that any one juror makes the correct decision on a defendant is .80. If the defendeant is guitly, what is the probability that the jury makes the correct decision?
The probability that the jury makes the correct decision is approximately 0.7063.
To solve this problem, we need to find the probability that the jury makes the correct decision if the defendant is guilty. Let's break down the problem into smaller steps.
We know that the probability of a single juror making the correct decision is 0.80. If the defendant is guilty, then the probability of a juror making the correct decision is still 0.80. Therefore, the probability that a single juror makes the correct decision if the defendant is guilty is 0.80.
We can use the binomial distribution formula to determine the probability of at least 10 out of 12 jurors making the correct decision. The formula is:
P(X ≥ k) = 1 - Σ(i=0 to k-1) [n!/(i!(n-i)!) x [tex]p^i \times (1-p)^{(n-i)}[/tex] ]
where:
P(X ≥ k) is the probability of at least k successes
n is the total number of trials (in this case, 12 jurors)
p is the probability of success in a single trial (in this case, 0.80)
k is the number of successes we want to find the probability of (in this case, 10)
Plugging in the values, we get:
P(X ≥ 10) = 1 - Σ(i=0 to 9) [12!/(i!(12-i)!) x [tex]0.80^i \times (1-0.80)^{(12-i)}[/tex]]
Using a calculator or software, we can calculate this to be approximately 0.7063.
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in an experiment, it takes you one hour to memorize all the terms on a list. two years later you relearn them in 45 minutes. the time difference of 15 minutes, or 25 percent (15 divided by 60 times 100), is called the
The time difference of 15 minutes, or 25 percent (15 divided by 60 times 100), is called the time saved.
What is an experiment?An experiment is a controlled study in which a scientist manipulates a variable in order to determine its effects. An experiment must have a testable hypothesis, be replicable, and produce empirical evidence.
Discussing the time difference in an experiment. In an experiment, it takes one hour to memorize all of the words on a list, and two years later, they are relearned in 45 minutes.
The time difference of 15 minutes, or 25 percent (15 divided by 60 times 100), is referred to as the time saved.
Time saved is the difference between the total time it takes to finish a process with a particular method and the total time it would take to complete the same process without that method.
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The scatter plot shows the relationship between the test scores of a group of students and the number of hours they study in a week:
On a grid, Label Hours Studying on x axis and Test Scores on y axis. The title of the graph is Test Scores and Hours Studying. The scale on the x axis shows the numbers from 0 to 10 at increments of 1, and the scale on the y axis shows numbers from 0 to 100 at increments of 10. Dots are made at the ordered pairs 1.1, 10 and 2, 25 and 3.1, 10.1 and 4, 30 and 4, 45 and 5, 45 and 6, 25 and 6.5, 60 and 7, 45 and 7.5, 50 and 7.5, 75 and 8, 60 and 8.5, 75 and 9, 60. The ordered pair 1, 100 is circled and labeled as M. All the other points are put in an oval and labeled as N.
Part A: What is the group of points labeled N called? What is the point labeled M called? Give a possible reason for the presence of point M. (5 points)
Part B: Describe the association between students' test scores and the number of hours they study. (5 points)
Part A: The group of points labeled N is called a scatter plot. The point labeled M is an outlier.
Part B: The association between students' test scores and the number of hours they study is that as the number of hours students study increases, their test scores tend to increase as well.
What is scatter plot?A scatter plot is a type of graph that displays the relationship between two variables. It is often used to show how one variable is affected by another.
Part A: The presence of point M could be due to an error in recording data, or it could be due to an unusual event or circumstance that is not representative of the population.
Part B: This suggests that the more time students put into studying, the better their test scores will be. However, it is important to note that the graph does not necessarily imply that studying for more hours will necessarily lead to higher test scores, as the scatter plot also shows that there are other factors that could affect test scores.
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Part A: The group of points labeled N is called a scatter plot.
The point labeled M is called an outlier.
The presence of point M is likely due to the fact that the student studied for only one hour, yet achieved a perfect score
Part B: The association between students' test scores and the number of hours they study is that as the number of hours students study increases, their test scores tend to increase as well.
What is scatter plot?A scatter plot displays the relationship between two variables. It is often used to show how one variable is affected by another.
Part A: The group of points labeled N is called a scatter plot.
The point labeled M is called an outlier.
The presence of point M is likely due to the fact that the student studied for only one hour, yet achieved a perfect score.
Part B: The scatterplot shows a weak positive association between students' test scores and the number of hours they study.
As the number of hours studying increases, the test scores tend to increase, although there is considerable variability in this relationship. The outlier at 1, 100 indicates that there may be other factors other than study time that influence test scores.
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This is the third part of a three-part problem. Consider the system of differential equations y_1' = 5y_1 + 3y_2, y_2' = 3y_1 + 5y_2, with solutions y_1(t) = c1 e^2t + c2 e^8t, y_2(t) = -c_1 e^2t + c_2 e^8t, for any constants c_1 and c_2. Rewrite the solution of the equations in vector form as y vector (t) = c_1 y_1 vector (t) + c_2 y_2 vector (t).
Solution is y(t) = ((c1e2t − c2e2t) (1 0) + (c1e8t + c2e8t) (0 1))
The differential equations of the given system are: y1′=5y1+3y2y2′=3y1+5y2 The solutions to these equations are:y1(t)=c1e2t+c2e8t y2(t)=−c1e2t+c2e8tNow,
let's rewrite the solution in the vector form y(t) = c1y1 vector(t) + c2y2 vector(t).The vector form of y1(t) and y2(t) is as follows: y1 vector(t) = (1 0) (c1e2t) + (0 1) (c2e8t)y2 vector(t) = (-1 0) (c1e2t) + (0 1) (c2e8t)
Therefore, the solution in the vector form y(t) = c1y1 vector(t) + c2y2 vector(t) is as follows: y(t) = c1((1 0) (c1e2t) + (0 1) (c2e8t)) + c2((-1 0) (c1e2t) + (0 1) (c2e8t))y(t) = (c1e2t − c2e2t) (1 0) + (c1e8t + c2e8t) (0 1)y(t) = ((c1e2t − c2e2t) (1 0) + (c1e8t + c2e8t) (0 1))
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I need to show my work please help
The table below shows how much Craig spent on ribbon at two different shops. What is the difference in the price of 300 cm of ribbon between shop A and shop B? Give your answer in pounds (£). Shop A Shop B Length of ribbon 140 cm 215 cm Cost £1.68 £1.72
Therefore, the difference in the price of 300 cm of ribbon between shop A and shop B is £1.20.
What is equation?In mathematics, an equation is a statement that two expressions are equal. It usually contains one or more variables, which are typically represented by letters, and may contain constants and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. An equation can be true or false depending on the values of the variables. Solving an equation means finding the values of the variables that make the equation true.
Here,
To find the difference in price between the two shops, we need to first calculate the cost per centimeter of ribbon for each shop:
Shop A: £1.68 / 140 cm = £0.012 per cm
Shop B: £1.72 / 215 cm = £0.008 per cm
Now, we can calculate the cost of 300 cm of ribbon at each shop:
Shop A: 300 cm x £0.012 per cm = £3.60
Shop B: 300 cm x £0.008 per cm = £2.40
The difference in price between the two shops for 300 cm of ribbon is:
£3.60 - £2.40 = £1.20
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choose one of the two boxes at random and select one of the balls in this box at random. if a blue ball is selected, what is the probability that this ball is from the second box?
Assume that the first box has 4 red balls and 3 blue balls and the second box has 5 red balls and 4 blue balls. the probability that this ball is from the second box is 12/55.
How to determine probabilityGiven that we need to choose one of the two boxes at random and select one of the balls in this box at random.
Let us assume that the first box has 4 red balls and 3 blue balls and the second box has 5 red balls and 4 blue balls.
Let the probability of selecting a blue ball from the first box be P(A) = (3/7)
Let the probability of selecting a blue ball from the second box be P(B) = (4/9)
So, the probability of selecting a blue ball is:
P(A) + P(B) = (3/7) + (4/9)= (27+28)/63= 55/63
If we have chosen a blue ball, then the probability that it is from the second box will be:
P(B|A) = P(B∩A) / P(A)P(B∩A) = P(A) × P(B|A) = (3/7) × (4/9) = 12/63
So, the probability that the blue ball is from the second box is:
P(B|A) = P(B∩A) / P(A)= (12/63) / (55/63)= 12/55
Therefore, the probability that this ball is from the second box is 12/55.
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in pascal's triangle, each entry is the sum of the two entries above it. in which row of pascal's triangle do three consecutive entries occur that are in the ratio 3:4:5?
The three consecutive entries in Pascal's Triangle that are in the ratio 3:4:5 occur in the 14th row.
The ratio 3:4:5 can be expressed as 3x, 4x, and 5x, where x is a constant. Using this ratio, we can find the values of the entries in the 14th row of Pascal's Triangle.
Starting from the left, the entries in the 14th row are 1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, and 1.
We can see that the ratio of the 5th, 6th, and 7th entries (715, 1287, and 1716) is 3:4:5. Therefore, the answer is the 14th row.
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someone please help!!
Adela paints a mural of Mount Rushmore. She uses the scale 6 ft to 1 ft from the actual monument to the mural. On Adela's mural, how much wider is George Washington's mouth than his eye? Show your work,
7/6 is wider George Washington's mouth than his eye.
What is unitary method?"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value. For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
According to our question-
eye length = 11/6
difference= 3 - 11/6
7/6
Hence, 7/6 is wider George Washington's mouth than his eye.
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The tires on Mavis’ car will have to be replaced when they each have 160 000 km of wear on them. If new tires cost $140.00 each, what is the total cost of the wear on Mavis’ tires for a year in which she drives 25 000 km?
Answer:
If the tires on Mavis’ car have to be replaced when they each have 160 000 km of wear, then the total distance Mavis can drive on a set of tires is:
4 tires * 160,000 km = 640,000 km
If Mavis drives 25,000 km in a year, she will need to replace her tires after:
640,000 km ÷ 25,000 km/year = 25.6 years
Since Mavis will need to replace her tires once every 25.6 years, the cost of the wear on her tires for a single year is:
$140.00/tire * 4 tires = $560.00
So the total cost of the wear on Mavis’ tires for a year in which she drives 25,000 km is $560.00.
Step-by-step explanation:
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What is the answer for y?
The linear function that models the data is y=3/5x - 2/5 which has the form y=mx+b, where m is the slope and b is the y-intercept.
What is linear function?This can be written in the form y = mx + b where m and b are constants and x is a variable. The graph of a linear function is a straight line that goes through the origin.
To calculate the linear function, we must first calculate the slope. The slope is the numerical change in y (rise) divided by the numerical change in x (run).
Subtracting the y-values for x=-9 and x=-8, we get
-29/5 - (-26/5) = -3/5.
Similarly, subtracting the x-values for x=-9 and x=-8, we get
-9 - (-8) = -1.
Now, -3/5 / -1, we get the slope, m, of 3/5.
Next, we must calculate the y-intercept, b.
To do this, we can use either of the points given.
Using the points (x=-9, y=-29/5), we can substitute the x and y values into the linear equation, y=mx+b.
-29/5 = 3/5(-9) + b, which can be simplified to
-29/5 = -27/5 + b.
Adding 27/5 to both sides, we get b = -2/5.
Therefore, the linear function that models the data is y=3/5x - 2/5.
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