In the Tour De France, Alex biked 198 km in 5 hours and Sam biked 298 km in 7 hours. Who biked at a faster rate? Show your work and explain your reasoning. (You may use a calculator).

The conditions for constructing a t-confidence interval are met.

In order to construct a t-confidence interval for the mean amount of time the students spend completing the homework assignment, the following conditions must be met:

The data must be a random sample from the population of interest
The sample size must be sufficiently large (typically, n > 30)
The data should be approximately normally distributed
The population standard deviation or variance must be unknown
From the information provided it can be inferred that the data is a random sample (30 students out of 75 students) and that the population standard deviation or variance is unknown. If the sample size is greater than 30, and the data is approximately normal or the sample size is large, then the conditions for constructing a t-confidence interval are met.

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Answer: he use 4 pepperoni more than sausage every times he put 10 meat on the pizza

Step-by-step explanation: both are on 10 so you don't need to change it so 7-3=4 and it's on ten which mean that every times he put 3 sausage, he have to put 7 pepperoni

Answer:A system of linear equations has no solution when the graphs are parallel. Infinite solutions. A system of linear equations has infinite solutions when the graphs are the exact same line.

Step-by-step explanation:

Scientific notation 295000 is 295×10³ and standard notation of  7.3×10⁻⁴ is 0.00073 and From least to greatest is 1, 3/2, π/2, √3, 9 and E is the best estimate of √3

A number system is defined as a system of writing to express numbers.

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

295000 is 295×10³

Now let us write 7.3×10⁻⁴ is standard notation

7.3/10000=0.00073

We have to arrange from least to greatest

1, 9, 3/2, √3, π/2

1, 9, 1.5, 1.732, 1.57

From least to greatest is 1, 3/2, π/2, √3, 9

E is the best estimate of √3

Hence, scientific notation 295000 is 295×10³ and standard notation of  7.3×10⁻⁴ is 0.00073 and From least to greatest is 1, 3/2, π/2, √3, 9

E is the best estimate of √3

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50 different greek armies, the upper class and the lower class soldiers battalions can be sent.

The Greek army can form different battalions by choosing 4 upper class soldiers and 8 lower class soldiers from a total of 5 upper class soldiers and 10 lower class soldiers. This problem can be solved using a combination formula known as a binomial coefficient.

The number of different battalions that can be sent is:

(5 choose 4) * (10 choose 8) = 5*10 = 50

Different battalions can be formed by choosing 4 upper class soldiers and 8 lower class soldiers from a total of 5 upper class soldiers and 10 lower class soldiers. Therefore, 50 different battalions can be sent.

So, 50 different battalions can be sent.

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Answer:

2.92 it is so easy. Just you have to subtract them

Answer:2.92 pounds

Step-by-step explanation:

The probability of flipping four coins is 0.0625

Total coins = 4

The study of chances, which are determined by the ratio of favourable occurrences to probable cases, is known as probability.

When flipping a coin, there are two possible outcomes (heads or tails), hence the likelihood of flipping a head-up coin is equal to the likelihood of flipping a tail-up coin.

Thus, the probability is = 1/2

Calculating the probability of getting all heads or all tails when flipping 4 coins -

= 1/2 x 1/2 x 1/2 x 1/2

= 1/16

In decimal form, this will be 0.0625

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The 205th term of the given geometric sequence is given by 6

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

Given here: The first term of a given geometric sequence as 6 and second term -6.

Thus clearly we can deduce that the common ratio of the sequence is given by -1

Therefore the geometric sequence has two elements that are alternating sequence of the form 6,-6,6,-6,6.........

Therefore the 205th term of the sequence will be given by

T₂₀₅=6×-1²⁰⁵⁻¹

       =6×1

        =6

Hence, The 205th term of the given geometric sequence is given by 6

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The value of a is 16 and b is 18 by similarity of triangles.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

If the respective sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are comparable (or proportion). Triangles that are similar will have the same form but may not be the exact same size.

Two triangles are said to be similar if their corresponding angles are equal. Equiangular triangles are what they are called. Two equiangular triangles were the subject of a significant finding made by the well-known Greek mathematician Thales. He applied the Basic Proportionality Theorem, sometimes known as the Thales Theorem, as a conclusion.

In triangle OXY and ONM

[tex]\frac{4}{16} = \frac{6}{6 + b}[/tex]

⇒ 24 + 4b = 96

⇒ 4b = 72

⇒ b = 18

again ,

[tex]\frac{4}{16} = \frac{4}{a}[/tex]

⇒ a = 16

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3/7 of the posters are hanged in the hallway.

A fraction represents a part of a whole.

Given that Dave spreads out a roll of paper and cuts it into 7 equal-sized posters.

He decorates the posters and takes them to school.

Dave hangs 4 posters on the side of the gym

4/7 of the posters are on the  side of the gym.

The remaining posters are in the hallway.

1-4/7

LCM is 7

7-4/7

3/7

Hence, 3/7 of the posters are hanged in the hallway.

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1) The function f(x) is defined as follows: B. F(x) = -(x + 2)²(x - 2).

2) The standard definition of function f(x) is given as follows: A. F(x) = ax³ + bx² + cx + d.

4. The solution to the system of equations is approximated by the following option:

A. (-3.43, 6.30).

The function for item 1 is defined considering it's roots, as follows:

Hence the function is defined as follows:

F(x) = a(x + 2)²(x - 2).

The y-intercept is positive, meaning that:

-8a > 0.

Thus the leading coefficient a is negative, and the correct option is given by option B.

The cube function, with all positive coefficients, is given by option A in item 2.

The graphic solution of a system of equations is given by the point of intersection of all the equations that compose the system.

The equations that compose the system in this problem are given as follows:

For this problem, the systems are composed by a third degree function v(x) and a linear function b(x), hence we graph them and obtain the point of intersection.

From the graph given by the image presented at the end of the answer, the coordinates of the point of intersection are presented as follows:

(-3.432, 6.296).

This means that, using rounding, the correct option is given by option A for the solution of the system of equations.

Item 1 asks to define the graphed function, while item 2 asks for the standard cube function.

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Answer:

3x^2−2

Step-by-step explanation:

Given f(x)=3x−5 and g(x)=x^2+1

∴f(g(x))=f(x^2+1)

=3(x^2+1)−5

=3x^2−2

The measure of the largest angle of the quadrilateral is 88 degrees.

The sum of the angles of a quadrilateral is 360 Degrees. This is derived from the property named Angle Sum property of quadrilateral. We can use this fact to set up an equation using the given information:

x + (5x + 15) + (3x - 25) + (4x - 20) = 360

Simplifying this equation:

13x = 350

x = 27^

Now we can substitute this value of x back into the equation for any of the four angles to find the largest angle:

4x - 20 = 4(27) - 20 = 108 - 20 = 88

Therefore, the measure of the largest angle of the quadrilateral is 88 degrees.

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The simple interest rate that you are charged, based on the loan amount and the period of the loan, is 3. 5 %

Borrowers must pay lenders simple interest as a fee in exchange for a loan. Compound interest is excluded from the calculation and just the original principal is used. Simple interest applies to all loans, not just specific ones. Additionally, it refers to the kind of interest that banks give their customers on their savings accounts.

Simple interest is the amount of interest charged on a specific principal amount at a specific interest rate. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.

To find the simple interest rate, find the simple interest charged per year to be:

= 175 / 2

= $ 87. 50

Then , the simple interest rate would be:

= Simple interest per year / Loan amount

= 87. 50 / 2, 500

= 3. 5 %

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Answer: 21 boxes are needed

Step-by-step explanation:

Total area:  length  =  1.5 + 6.25 + 1.5  =  9.25     height  =  1.5 + 6.25  =  7.75

Total Area  =  9.25 x 7.75  =  71.6875

Area of the patio  =  6.25 x 6.25  =  39.0625

Area of the extension  =  Total Area - Area of the patio  =  71.6875 - 39.0625  =  32.625

Area covered by one box of tiles:  25 x 0.25 x 0.25  =  1.5625

Number of boxes needed:  32.625 / 1.5625  =  20.88  =  21 boxes

I hope this helps even though you already figured it out!

Step-by-step explanation:

Let x be the number of bricks Ram laid.

Shyam laid x/2 bricks.

Therefore, x + x/2 + 250 = x(3/2) + 250 = x(3/2) = 300

x = (2*300)/3 = 200

Ram laid 200 bricks.

Shyam laid 200/2 = 100 bricks.

We can use a proportion to determine how many flyers Sam needs to deliver to earn $45. A proportion is an equation that states that two ratios are equal. In this case, we can use the ratio of the number of flyers delivered to the amount of money earned.

What in mathematics is a linear equation?

According to Wolfram MathWorld A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Let x be the number of flyers Sam needs to deliver to earn $45. The proportion can be written as:

x/45 = 10/1

We can solve for x by multiplying both sides of the proportion by 45:

x = (10/1)*45 = 450

So, Sam needs to deliver 450 flyers to earn $45.

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Answer:

Step-by-step explanation:

You need to give more information. There is nothing you can tell from the information you gave. Nothing is fixed.

Answer: b+164

Step-by-step explanation:

Answer: B + 164 = T

Step-by-step explanation:

T = TOTAL

B = LAST WEEK

To solve the differential equation y" + y = csc(x) using variation of parameters, we first need to find a particular solution.

Since the non-homogeneous term is csc(x), we can try a particular solution of the form yp = u(x) csc(x), where u(x) is a function to be determined.

Substituting yp into the differential equation:

u''(x)csc(x) + u(x)csc(x) = csc(x)

To find u(x), we can multiply both sides by csc(x) and integrate with respect to x:

∫u''(x)csc(x) dx + ∫u(x)csc^2(x) dx = ∫csc(x) dx

Integrating the first term by parts:

u'(x) = ∫csc(x) dx = ln|cot(x/2)| + C1

Integrating the second term by parts:

u(x) = -∫csc(x)cot(x) dx = -ln|sin(x)| + C2

So, the particular solution for yp is:

yp = u(x)csc(x) = -ln|sin(x)|csc(x) + C1csc(x) + C2

Now we need to find the general solution y = yc + yp

where yc is the general solution for the complementary homogeneous equation y" + y = 0

yc = C1cos(x) + C2sin(x)

Now we can use the method of variation of parameters to find the general solution for the non-homogeneous equation

By this method, we need to find two functions v1(x) and v2(x) such that W(yc, yp) = v1(x)cos(x) + v2(x)sin(x)

W(yc, yp) = (yc * yp') - (yp * yc')

W(yc, yp) = (C1cos(x) + C2sin(x)) * (-cot(x)csc(x) + C1) - (-ln|sin(x)|csc(x) + C1csc(x) + C2) * (-sin(x)cos(x) + cos(x)sin(x))

W(yc, yp) = -C1cot(x)csc(x) + C1^2 + C2csc(x)

As W(yc, yp) is not identically zero, we can proceed to find v1(x) and v2(x)

v1'(x) = -cot(x)csc(x) + C1

v2'(x) = csc(x)

Integrating both sides by parts:

v1(x) = ln|cot(x/2)| - cot(x) + C3

v2(x) = -cot(x) + C4

The general solution for the non-homogeneous equation y" + y = csc(x) is:

y = yc + yp = (C1cos(x) + C2sin(x)) + (sin(x)ln|sin(x)|

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Eli needs to buy at least 24 sets of knives, as each set contains 10 knives and the restaurant needs 546 knives in total. This can be determined by solving the inequality 10x ≥ 234, where x is the number of sets of knives.

1. 312 + 10x ≥ 546

2. 10x ≥ 234

3. x ≥ 23.4

4. Therefore, Eli needs to purchase at least 24 sets of knives for the restaurant to have enough knives.

Eli needs to order new supplies for the restaurant where he works, and he needs to order at least 546 knives. There are currently 312 knives, so he needs to order more. If each set of knives contains 10 knives, then he needs to determine how many sets of knives he needs to order in order to have enough knives. To do this, we need to set up and solve an inequality. The inequality we need to solve is 10x ≥ 234, where x is the number of sets of knives. This can be solved by dividing both sides by 10, which gives us x ≥ 23.4. This means that Eli needs to purchase at least 24 sets of knives for the restaurant to have enough knives.

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The probability of having a 2 on first roll, 3 on second roll and 4 on third roll is 1 / 216

A fair dice is a dice that is equally likely to land on any of its faces, meaning that each face has the same probability of facing up after a roll. The probability of getting a specific face on a fair dice is represented by the number of ways that face can appear divided by the total number of possible outcomes.

For a standard six-sided fair dice, the total number of possible outcomes is 6, since there are six faces on the dice. The probability of getting a specific face (for example, the number 4) is 1/6, because there is only one way to get that number out of the six possible outcomes.

The probability of landing 2 on first roll, 3 on second roll and 4 on third roll is given as;

P = (1/6 * 1/6 * 1/6)

P = 1 / 216

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The equation to find the amount the rental car company will charge for any number of days is y = 75+20(n-3).

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.

Given that,

The charge per day for a 3-day rental = 75/3 = 25

The additional charge for an extra 4 days is (155-75)= 80 which is $20 per day.  

The charge for a period of n days (n>3) is then 75+20(n-3).

Thus, The equation to find the amount the rental car company will charge for any number of days is y = 75+20(n-3).

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Answer:

There were 3 children in the room

Step-by-step explanation:

Let x be the number of children in the room

Since each child has 10 fingers including their thumbs, total number of fingers =10x

Each child has 2 ears so total number of ears = 2x

Since they had 24 more fingers than ears we get the equation:
10x - 2x = 24

8x = 24

x = 24/8 = 3

The height of the tree to the nearest hundredth of a meter is 29.1m.

We can use the concept of similar triangles to find the height of the tree. The ratio of the height of the tree to the length of its shadow is the same as the ratio of Hunter's height to the length of his shadow.

Let h be the height of the tree.

Hunter's height : h = 1.75m : x (where x is the height of the tree)

Hunter's shadow : Tree's shadow = 1.75m : 30.85m

We know that Hunter is 26.8 meters away from the tree, and the tip of his shadow meets the tip of the tree's shadow.

Hunter's shadow = Hunter's height + Tree's shadow

1.75 + x = 30.85

x = 29.1m

Therefore, the height of the tree to the nearest hundredth of a meter is 29.1m.

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Answer:

scalene

Step-by-step explanation:

It is a scalene triangle, meaning all sides are different lengths.  It is NOT a right triangle because the 6 cm side is "too short" to be a hypotenuse.  

Substitute 2x+3y=6 into the first equation:

4x^2+4y^2=(2x+3y)^2

4x^2+4y^2=4x^2+12xy+9y^2

0=12xy+5y^2

Divide both sides by 5:

0=2.4xy+y^2

Subtract 2.4xy from both sides:

-2.4xy=y^2

Take the square root of both sides:

y=±√-2.4xy

Substitute y=±√-2.4xy into the equation 2x+3y=6:

2x+3(±√-2.4xy)=6

2x±3√-2.4xy=6

Add 2x to both sides:

4x±3√-2.4xy=6+2x

Subtract 4x from both sides:

±3√-2.4xy=6-4x

Divide both sides by 3:

±√-2.4xy=2-4/3x

Square both sides:

-2.4xy=(2-4/3x)^2

-2.4xy=4-16/3x+8/9x^2

8/9x^2-16/3x+4+2.4xy=0

Use the quadratic equation to solve for x:

x= (16 ± √(256+192y^2))/18

Substitute this back into the equation 2x+3y=6 to solve for y:

2(16 ± √(256+192y^2))/18 + 3y = 6

3y = 6 - 32 ± √(256+192y^2))/9

3y = -26 ± √(256+192y^2))/9

y = (-26 ± √(256+192y^2))/27

Therefore, the solution is:

x = (16 ± √(256+192y^2))/18

y = (-26 ± √(256+192y^2))/27

The fraction of red apples in the bag is 3/ (4+x).

Let there be "x" number of green apples and "y" number of red apples in the bag.

According to the given information,

3/4 * x = y

Therefore, y = 3/4 * x

Since the fraction of red apples is y/ (x+y)

Therefore, fraction of red apples = 3/4 * x / (x+3/4 * x)

Simplifying,

Fraction of red apples = 3/ (4+x)

Therefore, the fraction of red apples in the bag is 3/ (4+x).

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At the end of 1.51 seconds, the velocity is 6.9 m/s, and at the end of 2.86 seconds, it is 24.64 m/s.

The dislocation that an article of particle experiences with regard to the time is expressed vectorially as velocity. The meter per moment (m/s) is the accepted unit of velocity profiles (also known as speed).

A. F = ma, where F is force, m is mass and a is acceleration.

a = 2.65/0.58

Performing division

a = 4.57 m/s²

With respect to final and starting velocities, acceleration, and time, the formula is v = u + at.

v = 4.57×1.51

The act of multiplying

v = 6.9 m/s.

B). New acceleration = 3.60/0.58

The act of multiplying

New acceleration = 6.2 m/s²

v = u + at

v = 6.9 + 6.2×2.86

Performing multiplication

v = 6.9 + 17.75

Performing addition

v = 24.64 m/s.

At two different locations, the velocities are 6.9 m/s or 24.64 m/s.

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The earned commission would be $437.50.

What is a commission?

A commission is a payment made to an employee, typically in sales or finance, for services rendered in the form of a percentage of the revenue generated by the employee's efforts. It is a way for companies to incentivize employees to sell more products or services, as the employee's income is directly tied to the success of their sales efforts.

The salesperson earns $437.50 on commission. This can be calculated by multiplying $1,750.00 by 25% (0.25).

$1,750.00 * 0.25 = $437.50

Hence, the earned commission would be $437.50.

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