Cameron's scout leader organized a contest to see who could build the strongest boat out of aluminum foil. After building their boats, the scouts measured how many pennies the boats could support before sinking. This box plot shows the results.

The maximum possible value for the greatest common divisor (GCD) of 11n + 3 and 2n + 1 as n ranges over the positive integers is 1.

The GCD of two integers is the largest integer that divides both integers without leaving a remainder. We can use the Euclidean algorithm to find the GCD of two numbers.

The Euclidean algorithm states that for two integers a and b, we can find the GCD of a and b by repeatedly applying the following steps:

Divide a by b to get a quotient q and a remainder r

Replace a with b and b with r

Repeat the process until r is 0

If we apply this algorithm to 11n + 3 and 2n + 1, we get the following:

GCD(11n+3, 2n+1)

As 11n + 3 = 3(2n + 1) + 5n

= GCD(2n+1, 5n )

As 2n + 1 = (2/5)(5n) + 1

= GCD(5n, 1)

= GCD(1, 0)

= 1

So as n ranges over the positive integers, the maximum possible value for the GCD of 11n + 3 and 2n + 1 is 1.

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Answer:

Q1 : [tex]\frac{5}{8}[/tex]

Q2: [tex]\frac{2}{3}[/tex]

Q3: [tex]\frac{11}{12}[/tex]

Q4: [tex]\frac{4}{5}[/tex]

Q5:  [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Answer:

Q1. [tex]\frac{5}{8}[/tex]

Q2. [tex]\frac{2}{3}[/tex]

Q3. [tex]\frac{11}{12}[/tex]

Q4. [tex]\frac{4}{5}[/tex]

Q5. [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Q1.

[tex]\sqrt{\frac{25}{64}}[/tex] ⇒ [tex]\frac{\sqrt{25}}{\sqrt{64}}[/tex] = [tex]\frac{5}{8}[/tex]

Q2.

[tex]\sqrt{\frac{36}{81}}[/tex] ⇒ [tex]\frac{\sqrt{36}}{\sqrt{81}}[/tex] = [tex]\frac{6}{9} = \frac{2}{3}[/tex]

Q3.

[tex]\sqrt{\frac{121}{144}}[/tex] ⇒ [tex]\frac{\sqrt{121}}{\sqrt{144}} = \frac{11}{12}[/tex]

Q4.

[tex]\sqrt{\frac{64}{100}}[/tex] ⇒ [tex]\frac{\sqrt{64}}{\sqrt{100}} = \frac{8}{10} = \frac{4}{5}[/tex]

Q5.

[tex]\sqrt{\frac{4}{9}}[/tex] ⇒ [tex]\frac{\sqrt{4}}{\sqrt{9}} = \frac{2}{3}[/tex]

Answer:

Parallelogram, rectangle, rhombus, square, and isosceles trapezoid.

Answer:

58 degrees

Step-by-step explanation:

The answer is 58 degrees.

180 degrees in a triangle, subtract the angles of 65 and 57, you get 58 degrees.

180 - 57 -65 = 58

When solving the following system of equations,  the x in the first equation would be the easiest to solve for.

Systems of equations can be solved using one of three techniques: graphing, substitution, or elimination. Simply plot the provided equations on a graph and locate the point(s) where they all cross to solve a problem by graphing. You may find the values of the variables you are working for by finding the location of this point.

The result of the first equation is

x + 6y = 25

we can easily solve for x by subtracting 6y from both sides we have  

x + 6y - 6y = 25 - 6y

x - 25 - 6y

So, the first equation's x term can be simply solved.

When solving the following system of equations,  the x in the first equation would be the easiest to solve for.

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Answer:

-1.256165295×10×10×10×10×10×10×10×10×10×10×10

Step-by-step explanation:

negative changes everything

The statement whether each data set is likely to be distributed nor not:

Number of minutes required to complete a marathon - Yes.

Number of miles in a marathon: - No.

Average age of a person who runs a marathon: No.

The distribution of values in a field is described by a statistical distribution, often known as a probability distribution. In other words, the statistical distribution identifies the typical and unusual values. The bell-shaped normal distribution is one of many varieties of statistical distributions.

Let n miles in marathon.

To normally distribute, number of minutes required to complete a marathon:

The number of minutes required to complete a marathon is likely to be normally distributed with small amounts in tails (very slow, very fast) and large amount in middle.

So, yes.

To normally distribute,  number of miles in a marathon:

The number of miles is a fixed number, not normally distributed.

So, no.

To normally distribute, average age of a person who runs a marathon:

The average age is a fixed number

Average age is not likely to be normally distributed.

So, no.

Therefore, the first one is yes, and the other two are no.

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Based on the information provided, it seems that the product that should be displayed in the window in July is Product 5.

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations. Average refers to a number's average. It is straightforward to calculate:

Divide by how many digits there are after adding up all the digits. the total divided by the count.

Based on the information provided, it seems that the product that should be displayed in the window in July is Product 5. This can be determined by looking at the sales data for each product over the months of January through June.

In every month, Product 5 has the highest sales figures among all the products. This suggests that Product 5 is the most popular among customers and would likely attract the most attention if it were to be placed in the window.

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a and d are non-zero and ad = bc for the system to be consistent for all possible values of f and g.

By definition, a system is consistent if there exists a set of solutions that satisfy the equations. In this system, the constants a, b, c, and d are the coefficients of the two equations. Since the system is consistent for all possible values of f and g, then the coefficients must satisfy certain conditions. For example, a and d must both be non-zero in order for the equations to be solvable. Additionally, the coefficients of both equations must be in proportion to each other, meaning that ad must equal bc. This is necessary for the equations to have the same slope, which is necessary for them to be solvable. Thus, we can conclude that a and d are non-zero and ad = bc for the system to be consistent for all possible values of f and g.

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The probability of getting 2 blue is 1/9.

You are choosing replacement marbles. The trials (marble selections) are independent from one another and follow the binomial distribution.

1/3 of the time, a blue marble will be the first one chosen.

(This is due to the fact that 4 out of 12 marbles are blue, therefore 4/12 equals 1/3.

A blue marble is 1/3 more likely to be chosen the second time.

The two probabilities can be multiplied to obtain the following results because the marble selections are independent:

The likelihood of receiving two blues is (1/3)2 =1/9.

Therefore, there is a 1/9 chance of obtaining two blues.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

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The point satisfies the equation ! 8 = 4 × (2)

Answer:

Yes

Step-by-step explanation:

If you plug in the numbers to the equation, you should get:

8 = 4(2)

Then,

8 = 8

therefore, (2,8) does satisfy the equation y = 4x.

To verify the inverse we can use Horizontal Line Test.

Suppose F is a function.

F does not have an inverse if any horizontal line crosses the graph of f more than once. If no horizontal line crosses the graph of F more than once, then F does have an inverse. In mathematics, having an inverse is a very significant quality, and it has a name.

If and only if a function f has an inverse, then it is one-to-one. The following definition, which is also the one that is most frequently used, is equivalent. If f(a) = f(b) implies a = b for all a and b in its domain, then a function f is one-to-one.

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For a house that have a height of 6 meters and length of 4.5 meters. On a scale drawing if the height of the house is 30 mm the length of the house will be 22.5 mm

In general, the term proportion refers to a part, share, or amount that is compared to a whole.

According to the definition of proportion, two ratios are in proportion when they are equal.

The length of the house on the map is calculated using equality in proportions as follows

The required proportion is

= height of the house / length of the house

= 6 / 4.5

= 4/3

Using this proportion, the length of the house in the drawing is

= 30 mm / 4/3

= 22.5

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Answer:

B

Step-by-step explanation:

since the value is above 1 and your subtracting 1 to drop the value below the 0 point below making it negative.

The example of a proportion, is An alarm on a clock beeped 7 times in 6 seconds and beeped 14 times in 12 seconds.​

The term proportionality describes any relationship that is always in the same ratio.

Given are some statements,

a) A car used 3 gallons of gas to drive 72 miles on a highway and used 4 gallons of gas to drive 72 miles in a town.

Solution:- In this case, we see, a car is using 3 and 4 gallons of gas for driving in a highway and in a town for 72 miles respectively.

Since, the distance is same and quantity of gases is different therefore, this can not be represented as a proportion.

b) A store charged $20 for 2 shirts and charged $25 for 3 shirts.

Solution:- In this, let's first find the unit prices for each,

for $20 there are 2 shirts, therefore, for 1 shirt it will be $10, and for 3 shirts it costs $25, therefore, for 1 shirt it will cost $8.3

Since, unit price for both is not equal, therefore, this can not be represented as a proportion.

c) A signal light flashed yellow 7 times in 28 seconds and flashed red 5 times in 35 seconds.

Solution:- As in 2nd option, will here also find unit rate, since, yellow light is flashing 7 times in 28 seconds, therefore, in 4 seconds it will be flashed for 1 time, similarly, red  light is flashing 5 times in 35 seconds, therefore, in 7 seconds it will be flashed for 1 time,

Since, both unit rates are not equal, therefore, this can not be represented as a proportion.

d) An alarm on a clock beeped 7 times in 6 seconds and beeped 14 times in 12 seconds.​

Solution:- Again we will find unit rate, since, the alarm is beeping 7 times in 6 seconds, therefore, it will beep for 1 time in 6/7 seconds, similarly, it is beeping 14 times in 12 seconds, so for 1 time it will beep in 12/14 = 6/7 seconds.

Here, we see that, both the unit rates are equal, therefore, this is an example of a proportion.

Hence, the last option is the correct example.

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Answer: picture wont seem to load, maybe try again

Step-by-step explanation:

Answer:

x = 7.9

Step-by-step explanation:

Sin = Opposite over Hypotenuse

Thus,  [tex]sin(21)=\frac{x}{22}[/tex]

* multiply each side by 22 *

[tex]\frac{x}{22} *22=x\\22sin(21)=7.9[/tex]

we're left with x = 7.9 ( rounded )

David's deposit of $220 compounded continuously at a rate of 1.7% will become $260 after 10 years.

Here we have been given that David invested $220.

The interest rate was 1.7%

Since the amount was compounded continuously, there is no fixed date of when it was compounded, the whole process is taken as an exponential distribution.

There were no withdrawals or additional deposits to this, so our Principal is constant. Hence we can write the formula

Amount = Principal X eᵃˣ

where a = rate of interest/100

x = time

Therefore, we can say that

Ampunt after 10 years = 220 X e¹⁰ ˣ ⁰°⁰¹⁷

= $260.76707

rounding off to the nearest 10 dollars we get

= $260

Hence David's deposit of $220 compounded continuously at a rate of 1.7% will become $260 after 10 years.

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Answer:

30° and 12

Step-by-step explanation:

The sum of the exterior angle and the interior angle = 180°

sum the parts of the ratio, 1 + 5 = 6 parts

Divide 180° by 6 to find the value of one part of the ratio

180° ÷ 6 = 30° ← value of 1 part of the ratio

(i)

The exterior angle = 30°

(ii)

The sum of the exterior angles of a polygon is 360°

To find the number of sides n divide 360 by 30 , that is

n = 360 ÷ 30 = 12

The volume of the water walking ball is 43.71 m³

Surface Area of a Sphere. A = 4 π r2. The volume of a Sphere. V = (4 ⁄ 3) π r³. Where r is the radius of the circle

Given :

[tex]$V=\frac{1}{6\sqrt{\pi}}S^{3/2}$[/tex] and surface area of water walking ball is  60 m²

putting the values in the equation we get

V= 464.758/10.632

V=43.71

Hence, the volume of the water walking ball is 43.71 m³

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Answer:

35 dimes and 65 nickels

Step-by-step explanation:

We will need use a system of equations to find the total number of nickels and dimes.

Because there are 100 dimes and there are only nickels and dimes, one equation is N + D = 100, where N is the total number of nickels and D is the total number of dimes.

Because a dime is worth $0.10, a nickel is worth $0.05, and the total change in the jar is worth $6.75, the second equation is 0.05N + 0.1D = 6.75

Substitution will be the easiest method to solve:

[tex]0.05N+0.1D=6.75\\N+D=100\\\\N=-D+100\\\\0.05(-D+100)+0.1D=6.75\\-0.05D+5+0.1D=6.75\\0.05D+5=6.75\\0.05D=1.75\\D=35\\\\N+35=100\\N=65[/tex]

The final answer after solving the given equation could be 14.

What is Linear Equation ?

Linear Equation can be defined as the equation in which the highest degree of the variable is one. Linear equations are generally three types , they are standard form , slope intercept form , point slope form and linear equation is also called as the equation of straight line.

Given,

Given equation,

2x + 6 = 3x -8

separating the value into a similar term:

2x-3x = -8 - 6

subtracting the equation:

-x = -14

remove negative sign:

x = 14

Therefore , the final answer could be 14.

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Yes, the horizontal asymptote is at y = 4.

The term asymptote in math is known as a straight line that constantly approaches a given curve but does not meet at any infinite distance.

Here we have given the expression y = 4.

In order to find whether it is an horizontal asymptote or not, we have to plot it on the graph,

The first process is to label the graph with x and y axis.

And then we have to defines the scale for the for the graph.

Now, we have to input the expression y = 4 on the graph then we get the graph like the following.

While we looking into the given graph we have identified that the expression y = 4 makes the horizontal asymptote on the graph.

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Answer:

x² + 7x + 5

Step-by-step explanation:

(- 3x² + 2x - 4) + (4x² + 5x + 9)

since both parenthesis are being multiplies by 1 , remove parenthesis

= - 3x² + 2x - 4 + 4x² + 5x + 9 ← collect like terms

= (- 3x² + 4x²) + (2x + 5x) + (- 4 + 9)

= x² + 7x + 5

'The leangth of the shortcut is: '

guessing- '75'

Hope this helps!

Answer: Maisie walked 6.4 miles.

Step-by-step explanation:

Since Maisie is walking at a constant pace of 1.6 miles per hour we can set up the following equation:

y = 1.6(x)

In this equation, Y is the number of miles Maisie walked in total and X is the number of hours she walked. All we have to do is plug in 4 hours as x and solve.

y = 1.6(4)

y = 6.4 miles.