Rousseau believed that _____ corrupted the individual.

The mean of the sampling distribution of sample means is 5.3, and its standard deviation is 0.186.

By dividing the sum of the provided numbers by the total number of numbers, the mean—the average of the given numbers—is determined.

The mean of the sampling distribution of sample means is equal to the population mean, which is 5.3, regardless of the sample size. This is a fundamental property of the sampling distribution of the mean.

However, if we want to be more precise, we can use the formula for the standard error of the mean (SEM) to calculate the standard deviation of the sampling distribution of sample means:

SEM = σ / √(n)

where σ is the population standard deviation, n is the sample size, and sqrt represents the square root.

In this case, σ = 1.1 and n = 35, so:

SEM = 1.1 / √(35) = 0.186

Therefore, the mean of the sampling distribution of sample means is 5.3, and its standard deviation is 0.186.

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Answer:

141

Step-by-step explanation:

152 + 125 + 146 = 423

423/3 = 141

(423 divided by 3)

Answer:

the root index is 4 the radical is the expression under the radical. (2^7)

Step-by-step explanation:

An approximate volume of oil which the tank below can hold is most closest to [tex]119,000ft^{3}[/tex]. The Option A is correct.

We will use V = πr²h to find the volume of a cylinder. Our height and the diameter of the tank are 78ft and 25ft.

We can find the radius by dividing the diameter by 2. The radius is:

= 78ft / 2

= 39ft

The volume of the tank will be:

= π(39ft)²(25ft)

= 3.14*39ft*39ft*25ft

= 119398.5

= 119,399 ft.

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The expansion of (2t_3x)⁴ using Pascal's Triangle method is (2t_3x)⁴ = 16t_[tex]3^{4x^{4} }[/tex] + 96t_[tex]3^{3x^{3} }[/tex] + 216t_[tex]3^{2x^{2} }[/tex] + 192t_3x + 16.

A binomial expression is a mathematical expression that consists of two terms, which are typically separated by a plus or minus sign. The two terms can be constants, variables, or combinations of both, and they are raised to a certain power, called the degree of the binomial.

For example, (x + y) and (2a - b) are both binomial expressions. The first expression consists of the two terms x and y, which are both raised to the first power, so the degree of the binomial is 1. The second expression consists of the two terms 2a and b, which are both raised to the first power, so the degree of the binomial is also 1.

To expand the binomial (2t_3x)⁴ using Pascal's Triangle method, we need to write the fourth row of Pascal's Triangle, which is:

1 4 6 4 1

These numbers represent the coefficients of the terms in the expansion of (a+b)⁴, where a=2t_3x and b=1. Using this row, we can write the expansion of (2t_3x)⁴ as:

(2t_3x)⁴ = 1*(2t_3x)⁴ + 4*(2t_3x)³*(1)¹ + 6*(2t_3x)²*(1)² + 4*(2t_3x)¹*(1)³ + 1*(2t_3x)⁰*(1)⁴

Simplifying this expression gives:

(2t_3x)⁴ = 16t_[tex]3^{4x^{4} }[/tex] + 96t_[tex]3^{3x^{3} }[/tex] + 216t_[tex]3^{2x^{2} }[/tex] + 192t_3x + 16

Therefore, the expansion of (2t_3x)⁴ using Pascal's Triangle method is:

(2t_3x)⁴ = 16t_[tex]3^{4x^{4} }[/tex] + 96t_[tex]3^{3x^{3} }[/tex] + 216t_[tex]3^{2x^{2} }[/tex] + 192t_3x + 16

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To create a scatter plot using the data in the table, we can plot the year on the x-axis and the winning height on the y-axis.

What is scatter plot?

A scatter plot, also known as a scatter chart or scatter diagram, is a graph used in statistics to visually display the relationship between two variables. It is a collection of points on a two-dimensional plane, where each point represents the value of two different variables. One variable is plotted on the x-axis (horizontal) and the other variable is plotted on the y-axis (vertical).

To create a scatter plot using the data in the table, we can plot the year on the x-axis and the winning height on the y-axis. Here is a properly labeled scatter plot using the given data:

In this scatter plot, each data point is represented by a circle (o) located at the corresponding year and winning height.

The x-axis is labeled with the years 1912, 1932, 1952, 1972, 1982, and 2002, and the y-axis is labeled with the winning height in meters. The plot shows that the winning height increased steadily over time, with the largest jump being achieved by Australia in 2002.

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a. Andre needs to save $601.44 each month to reach his goal of $35,379 in 5 years.

b. Andre contributed a total of $36,086.40 of his own money into the savings account over the 5-year period.

5 a.

The minimum payment amount Walter will need to make for his car loan is $1,059.29 per month.

b. Walter will pay a total of $12,711.48 over the life of his car loan.

6. c.  Both men purchased the same car for the same amount, so they both spent $36,086.40

a. In order to calculate how much Andre needs to save each month, we can use the formula for the future value of an annuity:

[tex]FV = PMT * ((1 + r/n)^(n*t) - 1) / (r/n)[/tex]

where:

FV = future value (which is the goal of $35,379)

PMT = monthly deposit

r = annual interest rate (2.5%)

n = number of times interest is compounded per year (12 for monthly)

t = time in years (5)

Plugging in the values, we get:

35,379 = PMT * ((1 + 0.025/12)^(12*5) - 1) / (0.025/12)

Solving for PMT, we get:

PMT = 35,379 * (0.025/12) / ((1 + 0.025/12)^(12*5) - 1)

PMT = $601.44

Therefore, Andre needs to save $601.44 each month to reach his goal of $35,379 in 5 years.

b. To find out how much of his own money Andre contributed to the savings account, we can multiply the monthly deposit by the number of months he saved:

Monthly deposits = $601.44

Number of months = 5 years * 12 months/year = 60 months

Total amount contributed by Andre = Monthly deposits * Number of months

Total amount contributed by Andre = $601.44 * 60

Total amount contributed by Andre = $36,086.40

Therefore, Andre contributed a total of $36,086.40 of his own money into the savings account over the 5-year period.

5  a. To determine the minimum payment amount, we can use the formula for monthly payments on a loan:

P = (Pv*R) / (1 - (1+R)^(-n))

where P is the monthly payment, Pv is the present value of the loan, R is the monthly interest rate, and n is the total number of payments.

Plugging in the values given, we get:

P = (36086.400.0325/12) / (1 - (1 + 0.0325/12)^(-121))

P = $1,059.29

Therefore, the minimum payment amount Walter will need to make for his car loan is $1,059.29 per month.

b. To find out how much Walter will pay altogether over the life of his car loan, we can multiply the monthly payment by the total number of payments:

Total payments = P * n

Total payments = $1,059.29 * 12 * 1

Total payments = $12,711.48

Therefore, Walter will pay a total of $12,711.48 over the life of his car loan.

c. Both men purchased the same car for the same amount, so they both spent $36,086.40. Therefore, neither man spent more of their own money for the car.

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Note that the statement "the dihedral group Dn of a polygon is generated by {r1, s0}" means that every symmetry of the n-sided polygon can be obtained by composing rotations and reflections using r1 and s0. That is, r1 and s0 generate all possible symmetries of the polygon.

In group theory, the dihedral group Dn is a group of symmetries of an n-sided polygon. It consists of rotations and reflections that preserve the shape of the polygon.

The generators of the dihedral group Dn are the elements that can be used to construct all other elements of the group. In the case of a polygon, the two generators are a rotation r1, which rotates the polygon counterclockwise by an angle of 360/n degrees, and a reflection s0, which reflects the polygon over a line passing through two opposite vertices.

Therefore, the statement "the dihedral group Dn of a polygon is generated by {r1, s0}" means that every symmetry of the n-sided polygon can be obtained by composing rotations and reflections using r1 and s0. That is, r1 and s0 generate all possible symmetries of the polygon.

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Answer:

4 hours

Step-by-step explanation:

Let's call the distance between point A and point B "d", and let's call the speed of the bicycle "v" and the speed of the motorcycle "m".

When the bicycle left point A towards point B, it traveled for some time t at a speed v, so it covered a distance of d/2. We know that the motorcycle left two hours later and arrived at point B at the same time as the bicycle. This means that the motorcycle traveled for a time of t - 2 hours at a speed of m, so it also covered a distance of d/2.

If the bicycle and motorcycle left point A simultaneously and traveled towards each other, they would meet after 1 and 1/3 hours. During this time, the bicycle traveled for t + 1 and 1/3 hours at a combined speed of v + m, so it covered a distance of (v + m)*(4/3). The motorcycle also traveled for 1 and 1/3 hours at a combined speed of v + m, so it covered the same distance.

We can set up two equations based on these distances:

d/2 = vt

d/2 = m(t - 2)

(v + m)*(4/3) = d

We can use the first two equations to solve for v and m:

d = 2vt

d = 2mt - 4m

2(v + m)*(4/3) = d

Substituting the first equation into the third equation, we get:

2(v + m)*(4/3) = 2vt + 2mt - 4m

8/3(v + m) = 2v + 2m - 4m/3

8v/3 + 8m/3 = 2v + 2m - 4m/3

2v/3 = 4m/3

v = 2m

Substituting this into the first two equations, we get:

d = 4mt

d = 2mt - 4m

Solving for t, we get:

t = 4 hours

Therefore, the bicycle traveled for 4 hours to cover the distance between point A and point B.

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Answer: weeeell since the total is 6.07 you divide that by 2 that is  3.035 then u minus 1.11 from the brad and add 1.11 to the milk so the milk is  4. 145 you can round that if u need and the bread would be 1.925(you can round that as well ) hope this helped.

Answer: 5.3

Step-by-step explanation: (4/15)x20=5.3

Answer: 6/13

Step-by-step explanation:

Let the equation be represented as ANow , the value of A is Let the first number be p = 4 / 15Let the second number be q = 20And , A = p x qSubstituting the values in the equation , we getA = ( 4/15 ) x 20On simplifying the equation , we getA = ( 4/3 ) x 4A = 16/3

The dimensions that minimize the cost are a square base and top with a side length of 3.11 ft, and a height of 41.2 ft.

We have,

Let the side length of the square base and top be x, and the height of the rectangular box be y.

Then we know that the volume of the box is 400 ft³, so we can write:

x² y = 400

We want to minimize the cost of constructing the box, which is given by the cost of the bottom plus the cost of the top plus the cost of the sides.

The cost of the bottom and top is given by the area of a square with side length x, multiplied by the cost per square foot:

Cost of bottom and top = 2x² (0.20) = 0.4x²

The cost of the sides is given by the area of the four rectangles that make up the sides of the box, which have dimensions x by y:

Cost of sides

= 4xy (0.015)

= 0.06xy

Total cost = Cost of bottom and top + Cost of sides

Total cost = 0.4x² + 0.06xy

We want to find the dimensions that minimize this cost, subject to the constraint that the volume of the box is 400 ft³.

We can use the volume equation to eliminate y, and obtain a function of x alone:

x² y = 400

y = 400 / x²

Substituting this expression for y into the cost equation, we get:

Total cost = 0.4x² + 0.06x(400 / x²)

Total cost = 0.4x² + 24 / x

To minimize this function, we take its derivative with respect to x, set it equal to zero, and solve for x:

d(Total cost)/dx = 0.8x - 24/x² = 0

0.8x³ - 24 = 0

x³ = 30

x = (30)^(1/3) = 3.11 ft (rounded to two decimal places)

Using the equation for y in terms of x, we can find the corresponding value of y:

y = 400 / x²

y = 400 / (3.11)² = 41.2 ft² (rounded to one decimal place)

Therefore,

The dimensions that minimize the cost are a square base and top with a side length of 3.11 ft, and a height of 41.2 ft.

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PART A:  The correct measure of angle L_b is 27.5°.

PART B: The mistake Martin likely made is B: he subtracted 55° from 180° instead of 90°

In geometry, an angle is the figure formed by two rays, or line segments, that share a common endpoint called the vertex. The rays or line segments are called the sides of the angle. We measure the size of an angle in degrees or radians, which tells us how wide the angle is open.

PART A: Since angles 1 and 2 are vertical angles, they are congruent. Thus, m₁ = m₂. We also know that m₁ + m₂ + m_2b = 180° (because they form a straight line).

Substituting in the given values, we get:

m₁ = m₂

m₁ + m₂ + 125° = 180°

Simplifying the second equation, we get:

2m₁ + 125° = 180°

Subtracting 125° from both sides, we get:

2m₁ = 55°

Dividing both sides by 2, we get:

m₁ = 27.5°

Since angles 1 and L_b are alternate interior angles, they are congruent. Thus, m_Lb = m₁ = 27.5°.

Therefore, the correct measure of angle L_b is 27.5°.

PART B: We can see from the diagram that angle 1 is adjacent to angle 2b and angle 2 is adjacent to angle 2b. Thus, angles 1, 2, and 2b form a straight line and their measures must add up to 180°. Martin likely subtracted 55° from the wrong angle measure. Specifically, he likely subtracted 55° from m₂ (which is 90°) instead of m₁ (which is also 55°). Therefore, the mistake Martin likely made is B: he subtracted 55° from 180° instead of 90°.

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Complete question:

In the diagram below, lines a and b intersect at point V. Martin incorrectly writes m_2b = 125°.

 a

 |

 | 55°

 |

 V

 |

 |

 b

PART A: Find the correct measure of angle L_b.

PART B: What mistake did Martin likely make?

A. He subtracted 55° from 90° instead of 180°.

B. He subtracted 55° from 180° instead of 90°.

C. He added 55° to 180° instead of 90°.

D. He added 55° to 90° instead of 180°.

Clara can reach a height of 2.57 meters when she jumps.

Given information:

The ceiling in Clara’s basement is 2.75 meters high.

When Clara jumps she is 18 centimeters short of being able to touch the ceiling.

We can start by converting the height of the ceiling and Clara's jump to the same units, either meters or centimeters. Let's convert Clara's jump to meters:

18 centimeters = 0.18 meters

Now we can subtract Clara's jump from the height of the ceiling to find how high she can reach:

2.75 meters - 0.18 meters = 2.57 meters

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The fraction expression 9 ÷ 2 is 4.5

To evaluate an expression like (9/2), we need to perform the arithmetic operation indicated by the mathematical operator, which in this case is the division symbol "/".

So, we divide the number 9 by the number 2:

9 ÷ 2 = 4.5

The quotient we obtain from this division is 4.5, which means that (9/2) is equal to 4.5.

Therefore, the correct answer to the given question is D. 4.5.

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The area of the triangle is 14√2m²

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object

The area of a triangle is expressed as;

A = 1/2 absinC

where a = 7m, b = 8m and C = 45°

sin45° = 1/√2

therefore,

A = 1/2 ×7× 8× 1/√2

A = 28/√2

rationalizing 28/√2

= 28√2/(√2×√2)

= 28√2/2

= 14√2m²

therefore the area of the triangle is 14√2m²

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Answer: -7, -3

Step-by-step explanation:

Zeroes mean x's or roots

f(x) = [tex]3x^{2} +30x+63[/tex]         take out the greatest common factor, all the terms can be divided by 3

f(x) = [tex]3(x^{2} +10x+21)[/tex]      

You can factor to find the zeros. Factoring means to find 2 things that multiply to make original.

To factor, Find 2 numbers that multiply to the last number (21) but add to middle(10)

7 and 3 multiply to +21 and add to +10

put the 2 numbers you found in factor form

f(x)=3(x+7)(x+3)       Zeroes happen when y=0 you will solve for x

                              you can set each of the parentheses equal to 0 to solve for x

(x+7)=0     and     (x+3)=7

x= -7                      x= -3             these are your zeroes

Jack is 15 miles from the airport.

The Pythagorean theorem is a fundamental principle in geometry that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, it can be expressed as:

c² = a² + b²

Let's denote the distance between Jack and the airport as x, and the distance between Jack and Tom as y. Then, we can see that we have a right triangle JAX with sides x, y, and hypotenuse JA = 17 miles. We also know that AT = 12 miles.

Using the Pythagorean theorem, we can write:

x² + y² = JA²

Squaring both sides, we get:

x² + y² = 17²

We also know that the distance between Tom and the airport is 12 miles, so the length of TX is also 12 miles. Therefore, we can write:

y = TX = 12 miles

Substituting this value into the equation above, we get:

x² + 12² = 17²

Simplifying this equation, we get:

x² = 17² - 12² = 225

Taking the square root of both sides, we get:

x = 15

Therefore, Jack is 15 miles from the airport.

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The growth factor of the credit card balance is 1.0142. The Option B is correct.

The growth factor is equal to the slope of the line representing a linear relationship. To calculate the growth factor of the credit card balance, we need to add the monthly interest rate to 1.

Monthly interest rate = 1.42% = 0.0142

The Growth factor will be:

= 1 + monthly interest rate

= 1 + 0.0142

= 1.0142.

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Answer:

the statement 'the dilation changed the orientation of the figure' is NOT true

Step-by-step explanation:

the only transformations that can change a figure's orientation is a reflection, not a dilation like is shown.

the first statement is true because it is an enlargement of the shape

the third is true (look at point I and I', point I is (2,2) and becomes (4,4) which follows 2x 2y)

and the fourth is true because the ratios are 1:1:1:1 for both shapes

The value of x in the solution to this system of equations is,

⇒ x = - 8

We have to given that;

A system of linear equations is shown are,

x - 3y = 7   ... (i)

x - 2y = 2  ... (ii)

Now, We can simplify as;

From (i);

x = 7 + 3y

Put in (ii);

7 + 3y - 2y = 2

7 + y = 2

y = - 7 + 2

y = - 5

Hence, From (i);

x - 3 x - 5 = 7

x + 15 = 7

x = - 15 + 7

x = - 8

Thus, The value of x in the solution to this system of equations is,

⇒ x = - 8

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The options that are correct representations of the inequality are:

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:

-6x - 15 < 10 - 5x

and

x < 5

Therefore, the options that are correct representations of the inequality are:

Note that both of these options represent the solution to the inequality, but in different ways. The first option represents the solution as all values of x greater than 5, while the second option represents the solution as all values of x less than -5.

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Given

Let P = Percentage of people using signal

[tex]\text{P} = 78\%[/tex]

Let Q = Percentage of people not using signal

[tex]\text{P + Q} = 1[/tex] ---- Make Q the subject of formula

[tex]\text{Q} = 1 - 78\%[/tex]

[tex]\text{Q} = 1 - 0.78[/tex]

[tex]\text{Q} = 0.22[/tex]

The expected number of people is calculated as 1/Q

[tex]= \dfrac{1}{0.22}[/tex]

[tex]= 4.54[/tex]

[tex]= 5[/tex] ---- Approximated

Hence, the expected number of people a police officer expects to pull over until she finds a driver not using the turn signal is 5

Answer:

They should expect to pull over 5 people.

Answer:

The mean of the sampling distribution of sample means is equal to the population mean, which is 5.3 years.

give thanks for more! your welcome!

Step-by-step explanation:

Answer: Asmita is currently located about 6.4 km northeast of her home.

Step-by-step explanation: Asmita started from her home and went to her friend's house located 5 km northeast from her home. Then she traveled to her maternal uncle's house, which is located 4 km away from her friend's house.

To determine the direction and distance of Asmita's current location from her home, we need to combine these two displacements. One way to do this is to use vector addition.

If we draw a diagram with her home as the origin, we can represent the first displacement (from her home to her friend's house) as a vector pointing 5 km northeast. We can represent the second displacement (from her friend's house to her maternal uncle's house) as a vector pointing 4 km east.

To find the total displacement, we add these two vectors using vector addition. The resulting vector points northeast but is longer than the first vector (5 km) because it includes the second displacement (4 km). Using trigonometry, we can calculate that the length of the resulting vector is approximately 6.4 km.

Therefore, Asmita is currently located about 6.4 km northeast of her home.

The solution for the given one-variable linear equation as required to be determined in the task content is; -4 / 5.

It follows from the task content that the solution of the one-variable linear equation is to be determined.

By observation, the given equation is; 5h + 4 = 0.

By subtracting 4 from both sides of the equation; we have that;

5h + 4 - 4 = 0 - 4

5h = -4

Divide both sides by 5 so that we have;

h = -4 / 5.

Ultimately, the solution to the equation is; h = -4 / 5.

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We can expect 18 of the next 90 bagels sold at Ron's Bagel Shop to be sesame seed bagels based on the proportion of sesame seed bagels sold in the first 30 bagels. However, this is just an estimate and there may be variation in the actual proportion.

To determine how many sesame seed bagels to expect in the next 90 bagels sold at Ron's Bagel Shop, we can use the proportion of sesame seed bagels sold in the first 30 bagels.

Out of the 30 bagels sold, 6 were sesame seed bagels, and 24 were other bagels. Therefore, the proportion of sesame seed bagels to total bagels sold was:

6/30 = 0.2 or 20%

We can use this proportion to estimate the number of sesame seed bagels in the next 90 bagels sold by multiplying the total number of bagels by the proportion of sesame seed bagels sold:

90 x 0.2 = 18

Therefore, we can expect 18 of the next 90 bagels sold at Ron's Bagel Shop to be sesame seed bagels. It's important to note that this is just an estimate based on the data available, and there may be variation in the actual proportion of sesame seed bagels sold in the next 90 bagels.

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The correct answer is:  A.Y intercept will be less and X will be less.

The slope is computed as the ratio of the change in the y-axis to the change in the x-axis. The slope of a straight line will describe the line's angle of steepness from the horizontal whether it rises or falls. When the line neither rises nor falls, then its slope will be zero.

Increasing driver costs by 0.25 cents per kilometer increases the truck's operating costs for each kilometer driven. This means that the  profit of the transport company is reduced by 0.25 cents for each kilometer driven.

Assuming that the relationship between profit and miles driven remains linear, this change causes a downward shift in the graph between total profit and miles driven, as the y-intercept of the line decreases as the cost per mile increases.

Therefore, the correct answer is:

A. The Y-intercept is smaller and the X-intercept is smaller.

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