A certain statistics instructor participates in triathlons. The accompanying table lists times (in minutes and seconds) he recorded while riding a bicycle for five laps through each mile of a 3mile loop. Use a 0.05 significance level to test the claim that it takes the same time to ride each of the miles. Does one of the miles appear to have a hill?

Answer: 83

Step-by-step explanation:

Since the student want to have a mean of 83 in the 7 tests, the total score of the tests will be:

= 83 × 7

= 581

Then, we add the value of the 6 tests and this will be:

= 88 + 73 + 81 + 83 + 79 + 94

= 498

We will now subtract 498 from 581 and this will be:

= 581 - 498

= 83

He needs to score 83 in the 7th test

Answer:

9

Step-by-step explanation:

Both sides are going to be exactly the same angle. So if its 35° on the right it will be 35° on the left also.

\((3x + 8)\)

\((3 \times 9 + 8)\)

9 goes into where X was

\(3 \times 9 = 27\)

\(27 + 8 = 35\)

\((3 \times 9 + 8 ) = 35\)

Answer:

angle y = 60

Step-by-step explanation:

They are equal due to the rule that vertical angles are always equal

"A pair of vertically opposite angles are always equal to each other."

hope this helps

Answer:

Hello im doing the same right now and i need help

Step-by-step explanation:

sorry though but its hard

Answer:

59

Step-by-step explanation:

Answer:

The mean of this data set is 10.6

Step-by-step explanation:

To find the Mean of a data set, you add up all the values and then divide by the number of values.

3 + 4 + 6 + 7 + 10 + 15 + 19 + 21 = 85

This data set has 8 values.

85 ÷ 8 = 10.6

The outer surface area of the ice coating on a spherical iron ball is decreasing at a rate of approximately 57.636 square centimeters per minute when the outer diameter (ball plus ice) is 146 cm.

To find the rate at which the outer surface area of the ice coating is decreasing, we need to use the concept of related rates. Let's denote the radius of the iron ball as "r" and the thickness of the ice coating as "h." The outer diameter of the ball plus ice is then given as 2r + 2h, which is equal to 146 cm in this case.

We know that the volume of the ice coating is equal to the volume of the spherical shell formed between the outer and inner surfaces of the ice coating. The volume of this shell can be expressed as V = 4/3π((r + h)^3 - r^3).

Since the ice melts at a rate of 39 ml/min, which is equivalent to 39 cm^3/min, we can differentiate the volume equation with respect to time to obtain dV/dt. This represents the rate at which the volume of the ice coating is changing.

To find the rate at which the outer surface area of the ice coating is decreasing, we need to find dA/dt, where A represents the outer surface area. We can relate dA/dt and dV/dt by using the formula for the surface area of a spherical shell: A = 4π(r + h)^2.

By substituting the given values into the equations and differentiating, we can solve for dA/dt. The resulting value will be approximately 57.636 square centimeters per minute, rounded to the nearest thousandth. This indicates the rate at which the outer surface area of the ice coating is decreasing when the outer diameter (ball plus ice) is 146 cm.

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Answer:

$46.75

Step-by-step explanation:

1 tile covers: 4*4= 16 m²

Tiles required: 120/16= 11

Cost: 11*$4.25= $46.75

Answer:

15\(x^{3}\) ( \(x\) + 1 )

Step-by-step explanation:

5\(x^{4}\) + 10\(x^{4}\) + 15\(x^{3}\)

Simply the expression where there are like terms.

15\(x^{4}\) + 15\(x^{3}\)

15 and \(x^{3}\) are common terms. Take them out and place the remaining inside the bracket.

15\(x^{3}\) ( \(x\) + 1 )

Answer:

Step-by-step explanation:

Answer:

this isnt a question? is it 853 times 4 and 853 times 3?

By algebra properties, the simplified form of the two expressions are listed below:

Case 1: \((4^{-2})^{-\frac{3}{4}}+(81 \cdot 10^{4})^{\frac {1}{4}} - (7 + \frac{19}{32})^{\frac{1}{5}}+(\frac {9}{2})^{0} = \frac{237}{8}\)

Case 2: \(\left(\frac{1}{1000}\right)^{-\frac{1}{3}}+\left(\frac{1}{4}\right)^{-1}\cdot (2^{6})^{\frac{2}{3}} - (2^{3})^{\frac {4}{3}} + (3^{3})^{0} = \frac{51}{10}\)

In this problem we find two case of arithmetic expressions involving powers, roots and algebraic operators. Each expression can be simplified by means of algebra properties, especially from powers and roots. Now we proceed to simplify:

Case 1

First, write the complete expression:

\((4^{-2})^{-\frac{3}{4}}+(81 \cdot 10^{4})^{\frac {1}{4}} - (7 + \frac{19}{32})^{\frac{1}{5}}+(\frac {9}{2})^{0}\)

Second, simplify the expression by power and root properties:

\(4^{-\frac {3}{2}}+30 - \frac {3}{2} + 1\)

√(1 / 4³) + 30 - 3 / 2 + 1

√(1 / 64) + 30 - 3 / 2 + 1

1 / 8 + 31 - 3 / 2

237 / 8

Case 2

First, write the complete expression:

\(\left(\frac{1}{1000}\right)^{-\frac{1}{3}}+\left(\frac{1}{4}\right)^{-1}\cdot (2^{6})^{\frac{2}{3}} - (2^{3})^{\frac {4}{3}} + (3^{3})^{0}\)

Second, simplify the expression by power and root properties:

1 / 10 + 4 + 16 - 16 + 1

51 / 10

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Answer:

\(\dfrac13y-\dfrac75x+\dfrac23-\dfrac23y-\dfrac49\)

Step-by-step explanation:

\(-\dfrac23y-\dfrac35x+\dfrac29-\dfrac45x+\dfrac13y\)

Collect like terms:

\(\implies -\dfrac23y+\dfrac13y-\dfrac35x-\dfrac45x+\dfrac29\)

Combine like terms:

\(\implies -\dfrac13y-\dfrac75x+\dfrac29\)

\(\dfrac13y-\dfrac75x+\dfrac23-\dfrac23y-\dfrac49\)

Collect like terms:

\(\implies \dfrac13y-\dfrac23y-\dfrac75x+\dfrac23-\dfrac49\)

Combine like terms:

\(\implies -\dfrac13y-\dfrac75x+\dfrac29\)

Therefore, \(\dfrac13y-\dfrac75x+\dfrac23-\dfrac23y-\dfrac49\) is equivalent to \(-\dfrac23y-\dfrac35x+\dfrac29-\dfrac45x+\dfrac13y\)

The game to be fair, the player should win 60.

In order to determine the fair winnings for this game, we need to calculate the probability of winning and then set it equal to the cost of playing the game.
Step 1: Calculate the probability of winning.
There are two scenarios for winning:
1. First roll is even, and the second roll matches the first.
2. The probability of rolling an even number on a six-sided die is 3/6 or 1/2, since there are three even numbers (2, 4, and 6).
Step 2: Calculate the probability of the second roll matching the first roll.
Since there are 6 sides to the die, the probability of the second roll matching the first is 1/6.
Step 3: Calculate the combined probability of both events.
To find the combined probability of both events, multiply the probabilities: (1/2) × (1/6) = 1/12. So the probability of winning is 1/12.
Step 4: Set up an equation to determine fair winnings.
Let x be the fair winnings for the game. The cost of playing the game is $5. In order for the game to be fair, the expected value (probability of winning multiplied by the winnings) should equal the cost of playing the game:
(1/12) × x = 5
Step 5: Solve the equation for x.
To solve for x, multiply both sides of the equation by 12:
x = 5 × 12
x = 60
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The ratio of the weight of a semi-truck trailer tire compared to the weight of a mobile home will be 51: 52.

The utilization of two or more additional numbers that compares is known as the ratio.

The weight of the semi-truck trailer tire is 102 pounds.

The weight of the mobile home is 104 pounds.

The ratio of the weight of a semi-truck trailer tire to a mobile home is given as.

Ratio = 102 / 104

Ratio = 51 / 52

Ratio = 51: 52

The ratio of the weight of a semi-truck trailer tire to a mobile home will be 51: 52.

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Answer: 5/96

Step-by-step explanation:

\((\stackrel{x_1}{-2}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-9}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{-9}-\underset{x_1}{(-2)}}} \implies \cfrac{-15}{-9 +2} \implies \cfrac{ -15 }{ -7 } \implies \cfrac{ 15 }{ 7 }\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{ \cfrac{ 15 }{ 7 }}(x-\stackrel{x_1}{(-2)}) \implies y -10 = \cfrac{ 15 }{ 7 } ( x +2) \\\\\\ y-10=\cfrac{ 15 }{ 7 }x+\cfrac{ 30 }{ 7 }\implies y=\cfrac{ 15 }{ 7 }x+\cfrac{ 30 }{ 7 }+10\implies {\Large \begin{array}{llll} y=\cfrac{ 15 }{ 7 }x+\cfrac{100}{7} \end{array}}\)

Answer:

\( \sqrt{ {12}^{2} - {3.5}^{2} } = \sqrt{131.75} = 11.5\)

The ladder will reach about 11.5 feet up the wall.

\(x = 80\) ✅

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\((x - 8)2 = 144 \\ ⇢ 2x - 16 = 144 \\ ⇢ 2x = 144 + 16 \\ ⇢ 2x = 160 \\ ⇢ x = \frac{160}{2} \\ ⇢ x = 80\)

\(\large\mathfrak{{\pmb{\underline{\orange{To\:verify }}{\orange{:}}}}}\)

\(2x - 16 = 144 \\ ➵ \: 2 \times 80 - 16 = 144 \\ ➵ \: 160 - 16 = 144 \\ ➵ \: 144 = 144 \\ ➵ \: L.H.S.=R. H. S\)

Hence verified.

\(\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘\)

Answer:

answer given in step by step...

Step-by-step explanation:

13x+13(x+1)+13(x+2)=312

13x+13x+13+13x+26=312

39x+39=312

39x=312-39

39x=273

x=7

first number=13x=13*7=91

second number=13(8)=104

third number=13(9)=117

Answer:

758

Step-by-step explanation:

The largest number that can be made is 875 but it ends in 5 which makes it an odd number.

The only even number is 8 so we have to use it last.

7 is bigger than 5 so 7 goes first which means it's 758

the work done is equal to the force applied (500 lb) multiplied by the distance (100 ft), resulting in 500 ft-lb of work done.

A force applied across a distance is what is referred to as work.

In this problem,

the force applied is the weight of the cable (5 lb/ft) multiplied by the length of the cable (100 ft).

Therefore, the work done is equal to the force applied (500 lb) multiplied by the distance (100 ft), resulting in 500 ft-lb of work done.Work is a force applied across a distance, and it is measured in a unit of energy called foot-pounds. In this problem, the force applied is the weight of the cable (5 lb/ft) multiplied by the length of the cable (100 ft). Therefore, the work done is equal to the force applied (500 lb) multiplied by the distance (100 ft), resulting in 500 ft-lb of work done. This means that 500 ft-lb of energy must be expended in order to move the cable 100 ft. This energy can be provided by a variety of sources, such as human labor, a motor, or some other mechanism.

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Perpendicularity law

The angle 1 can be named as follows:

∠RST

∠TSR

∠S

There are various ways to name an angles. You can name an angle by its vertex, by the three points of the angle (the middle point must be the vertex), or by a letter or number written within the opening of the angle.

Therefore, let's name the angle 1 indicated on the diagram as follows:

Hence, the different ways to name the angle 1 is as follows:

∠RST or ∠TSR

Or

∠S

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The value of E[X Y] is 44.25.

According to the question,

E[X] = ∑ x × P(X=x)

=0×P(x=0) + 5×P(x=1) + 10×P(x=2)

= 0+5×(0.49)+10×(0.31)

= 5.55

E[Y] = ∑ y × P(Y=y)

=0×P(x=0) + 5×P(x=5) + 10×P(x=10) + 15×P(x=15)

= 0+5×(0.49)+10×(0.31)+15×(0.21)

= 8.55

Now,

E [X²] =  ∑ x² × P(X=x)

= 0²×P(x=0) + 5²×P(x=1) + 10²×P(x=2)

= 0 + 25×0.49 + 100×0.31

= 43.25

E[Y²] = ∑ y² × P(Y=y)

= 0²×P(x=0) + 5²×P(x=5) + 10²×P(x=10) + 15²×P(x=15)

= 0 + 25×0.49 + 100×0.31 + 225×0.21

= 92.25

Therefore , V[X] = E[X²] - {E[X]} = 43.25 - 30.8025 =12.4475

V[Y] = E[Y²] - {E[Y]}² = 92.25 - 73.1025 = 19.1475

E[X Y] = ∑xy P(X=x, Y=y)

= {0×0×P(X=0,Y=0)} + {0×5×P(X=0,Y=5)} + {0×10×P(X=0,Y=0)} + {0×15×P(X=0, Y =15)} + {5×0×P(X=5,Y=0)} + {5×10×P(x=5,Y=10)} +  {5×5×P(x=5,Y=5)} +  {5×15×P(x=5,Y=15)} + {10×0×P(x=10,Y=0)} + {10×5×P(x=10,Y=5)} + {10×10×P(x=10,Y=10)} + {10×15×P(x=10,Y=15)}

= 0+0+0+0+0 + {50×0.20} +{25×0.15} + {75×0.10} + 0 + {50×0.15} + {100×0.14} + {150×0.01}

= 10 + 3.75 + 7.5 + 7.5 + 14 + 1.5

Hence the final answer is = 41.25

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The length and width of the plot that will maximize the area is 60 meters by 120 meters. The largest area that can be enclosed is 7200 square meters.

To maximize the area of the rectangular plot, Farmer Ed must use 9000 meters of fencing to enclose three sides of the plot. The fourth side, which borders the river, does not need to be fenced. To find the length and width of the plot that will maximize the area, the 9000 meters of fencing must be divided into two sides of equal length, with the remaining fencing used for the third side. This results in a length of 120 meters and a width of 60 meters, which maximizes the area of the plot. The largest area that can be enclosed is 7200 square meters.

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Answer:

1 inch is 6 feet

Step-by-step explanation:

Answer:

1 inch represents 6 feet

∪ω∪

Step-by-step explanation:

1 inch represents 6 feet

The revenue function, R for x tickets sold which is the product of the cost per ticket and the number of tickets sold is R(x) = 7x

The cost per ticket = $7

The Revenue made from ticket sales can be calculated as :

If the Number of tickets sold is represented as x

The revenue function becomes ;

Therefore, for any given Number of tickets sold, x ; the Revenue function, R(x) = 7x

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A) First derivative for y = 3x² + 5x + 10 is dy/dx = 6x + 5; B) First derivative of for, y = 100200x + 7x is dy/dx = 100207 ; C) First derivative for y = In (9x4) is dy/dx = 4 / (3x).

A. y = 3x² + 5x + 10:

First derivative of the given equation, y = 3x² + 5x + 10 is as follows:

dy/dx = d/dx (3x²) + d/dx (5x) + d/dx (10)dy/dx

= 6x + 5

Since there are no exponents in 5x, the derivative of 5x is simply 5.

Similarly, since 10 is a constant, the derivative of 10 is zero.

B. y = 100200x + 7x:

First derivative of the given equation, y = 100200x + 7x is as follows:

dy/dx = d/dx (100200x) + d/dx (7x)dy/dx

= 100200 + 7

= 100207

C. y = In (9x4):

The given equation is, y = In (9x4).

The first derivative of this function can be obtained as follows:

dy/dx = 1 / (9x4) * d/dx (9x4)dy/dx

= 1 / (9x4) * 36x3dy/dx

= 4x3 / (3x4)dy/dx

= 4 / (3x)

Therefore, the first derivative of the given function y = In (9x4) is 4 / (3x).

A) First derivative forgiven equation, y = 3x² + 5x + 10 is dy/dx = 6x + 5; B) First derivative for given equation, y = 100200x + 7x is dy/dx = 100207 ; C) First derivative for given equation, y = In (9x4) is dy/dx = 4 / (3x).

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Using Pythagorean theorem the value of x and y are 13 and 12 respectively in a right angle triangle.

what is Pythagorean theorem?

The Pythagorean theorem is a fundamental principle in geometry that relates to the three sides of a right triangle. It states that in a right 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 notation, the Pythagorean theorem can be written as:

\(c^2 = a^2 + b^2\)

According to the question:
We can use the Pythagorean theorem to solve for the unknown side length y in the right triangle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, we have:

\(x^2 = y^2 + 5^2\)

Simplifying the right-hand side, we get:

\(x^2 = y^2 + 25\)

Subtracting \(y^2\) from both sides, we get:

\(x^2 - y^2 = 25\)

Now we can use the difference of squares identity to factor the left-hand side:

\((x + y)(x - y) = 25\)

Since we know that x is the hypotenuse and is loger than y, we can conclude that x + y > x - y. Therefore, we can write:

\(x + y = 25\)

\(x - y = 1 (since 25 - 24 = 1)\)

Solving for y in the second equation, we get:

\(y = x - 1\)

Substituting this expression into the first equation, we get:

\(x + (x - 1) = 25\)

Simplifying, we get:

\(2x - 1 = 25\)

Adding 1 to both sides, we get:

\(2x = 26\)

Dividing both sides by 2, we get:

x = 13

Finally, we can substitute x = 13 into y = x - 1 to get:

\(y = 13 - 1 = 12\)

Therefore, the value of y is 12.

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The probability that at least one student fails STA 2023 in their first try when selecting three students at random is 0.271.

To solve this problem, we can use the complement rule. The complement rule states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

First, let's find the probability that none of the three students fail the course in their first try. This is (0.9)^3 since the probability of a student passing is 1 minus the probability of failing, which is 0.1. Therefore:

Probability of none failing = (0.9)^3 = 0.729

Now, we can use the complement rule to find the probability that at least one student fails:

Probability of at least one failing = 1 - Probability of none failing
Probability of at least one failing = 1 - 0.729
Probability of at least one failing = 0.271

Therefore, the probability that at least one of the three students fails the course in their first try is 0.271.

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The equation that makes a true statement when x = -1 is -4x - 5 = -15.

Substituting -1 for x in each equation, we get:

4(-1) + 9 = 5

-4(-1) - 5 = 1

-3(-1) + 15 = 18

-5(-1) - 15 = 10

Only the equation -4x - 5 = -15 results in a true statement when x = -1, since:

-4(-1) - 5 = -4 + 5 = 1, which is equal to the right-hand side of the equation (-15) when x = -1.

Therefore, the answer is -4x - 5 = -15.

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