10 Two cyclists are traveling along a track in the same direction. Their motions are described
by the linear equations d = 10t and d-8t= 2, where t hours is the time and d miles is the
distance from a point on the track.

b When will the cyclists meet?

The graph of tan(x/4) < 1/5 over the interval 0<= x<=2pi radians is attached. An approximate solution to the trigonometric inequality tan(x/4)<1/5 over the interval 0<= x<=2pi radians is 0 <= x < 0.7896.

y = 1/5 is a horizontal straight line parallel to x-axis.

Plot of tan(x/4)<1/5 over the interval 0<= x<=2pi radians is attached. The shaded region is the solution.

tan(x/4) < 1/5

Taking tan inverse on both sides

tan⁻¹(tan(x/4)) < tan⁻¹(1/5)

x/ 4 <  tan⁻¹(1/5)

Multiplying by 4 on both sides

x < 4tan⁻¹(1/5)

x < 0.7896

Applying the limits of intervals

0 <= x <= 2pi ≈ 6.28

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Katie is correct. Any number with 4 as a factor will also have 8 as a factor; therefore, any number with 8 as a factor will have 4 as a factor.

Katie is correct. Any number that is a multiple of 8 will also be a multiple of 4 because 8 is divisible by 4. For example, 8 is a multiple of 4 (8 = 2 x 4) and 16 is a multiple of 8 (16 = 2 x 8) and also a multiple of 4 (16 = 4 x 4). So, any number that is a multiple of 8 will also be a multiple of 4.  So any number that is a multiple of 8 will also be a multiple of 4. Note that 80 is a multiple of 8, but not 4.

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1/7 is the probability that the product is an odd number.

What is the simple definition of probability?

A probability is a number that expresses the possibility or likelihood that a specific event will take place.

                   Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Total Cards are 7

2 cards out of 7 cards can be selected in ⁷C₂   = 21  ways

Product would be odd if both cards are odd

3 , 5 , 7  are odd cards

2 cards out of 3 Can be selected   in ³C₂  = 3  ways

( 3 , 5) , ( 3 , 7) , ( 5 , 7)

Hence probability  the product of the numbers on the 2 cards  is odd number

= 3/21

= 1/7

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y = -3x + 12   is the equation  for the line containing the side opposite the side containing the first two vertices.

Given coordinates:

(-3,4) ; (-2,1) ; and (2,6)

let us solve for the slope.

Since , parallel sides have the same slope.

m = y2-y1 / x2-x1

m = 1 - 4 / -2-(-3)

m = -3 / 1

m = -3

y = mx + b

Since , (2,6) is a point which passes through the line . Hence , it must satisfy the equation.

Therefore,

6 = -3(2) + b

6 = -6 + b

6 + 6 = b

12 = b

On Substituting , values of m and b in y = mx +b , we get y = -3x +12 which is the required equation of the line.

Hence, y = -3x + 12   is the equation  for the line containing the side opposite the side containing the first two vertices.

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Answer:

For the first line its distributive property
The 2nd is combining like terms

4th is simplifying it

Im not sure about the last one since its just the answer of the problem

Step-by-step explanation:

The equation equivalent to the equation x + y = 3 is 6x + 6y = 18.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

x + y = 3

Multiply 6 on both sides.

6x + 6y = 18

Thus,

The equation that is equivalent is 6x + 6y = 18.

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Answer: No

Step-by-step explanation:

Look at the 3 numbers in the sequence,

Geometric sequence means the ratio between two consecutive numbers in the sequence is a constant (eg. 10, 5, 2.5 is a geometric sequence as the ratio is a constant at 1/2)

However, for the sequence listed above

Looking at 1st and 2nd term,

Ratio = 110/120 = 11/12

Looking at 2nd and 3rd term,

Ratio = 105/110 = 21/22 which is not the same as 11/12.

Hence, since the ratio is not the same, this sequence is not a geometric sequence.

With a mass of 50 kg, Becky used 588 watts power to sprint up a 3.0 m high set of stairs in 2. 5 seconds. She is able to run up a 4.5 m high flight of stairs in 3.75 s.

Work (in joules) equals your weight (in newtons) x the height of the stairs (in meters.) The power you now possess is equal to the sum of your labor times the duration of that labor, or: Work (measured in joules) divided by time equals power, measured in watts (in seconds.)

Given that mass of Becky is 50 Kg

gravity of earth is 9.8 m/s²

height of stairs is 3.0 m

time taken to run up in stairs is 2.5 s

Power = work done/ time taken

P = (50*9.8*3.0)/2.5

P = 1470/2.5

P = 588 watt

Becky is able to run up a 3.0 m high flight of stairs in 2.5 s

She is able to run up a 4.5 m high flight of stairs in t =  (2.5 * 4.5)/3

t = 11.25/3

t = 3.75 s

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Annabelle collected data from a sample of people that were convenient for her to access, such as her immediate neighbors, and used this to draw her conclusion.

Annabelle performed a convenience sample investigation, which is a type of statistical investigation. This involves collecting data from a sample of people that are convenient for the researcher to access. In this case, Annabelle asked a couple of her immediate neighbors to find out how many people in her neighborhood were going to the rock concert..

Convenience sampling is useful when time or resources are limited, however the results may not be representative of the larger population. Therefore, it is important to consider the limitations of the sample when drawing conclusions. For example, Annabelle may not have considered that the neighbors she asked may not be representative of the whole neighborhood.

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The modulus of 2 - 3i is √13. So, the correct option is d.

Modulus is a mathematical operation used to find the remainder when dividing two numbers. This is called a percent sign (%) and is represented by a single number such as 12. Used to determine if two numbers are divisible (no remainder). You can also use the modulus to compare two numbers to see which is greater or lesser. Additionally, this module can be used to calculate the distance between two points on the coordinate plane.

It is computed by taking the square root of the sum of the squares of the real and imaginary components, so √(2^2 + (-3)^2) = √13. The modulus of a complex number, also called absolute value, is a measure of distance from the origin.

Let z = -2 - 3i

z = (-2) + (-3)i

Modulus of z = √((-2)² + (-3)²)

√(4 + 9) = √13

Modulus of z = √13

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Answer:

-30+18q

Step-by-step explanation:

First, distribute the five to the terms in the parenthesis.

5x-6 and 5x4q

so -30+20q-2q

20q-2q equals 18q

so we are left with -30+18q.

Answer:

Step-by-step explanation:

Given: Polynomial y = 5x²+3x⁶-10x-8

here, 5 is the coefficient of x², 3 is the coefficient of x⁶, -10 is the coefficient of x and -8 is the constant term.

option (D)

Answer:

down there.

Step-by-step explanation:

Look for a term that has no variables with it. Once you've found it you've found ur constant. The only such term is -8 so the constant is -8 or choice d.

hence choice d

To find the coordinates of a point in a coordinate system, do the inverse. Start at the point and trace a vertical line up or down to the x-axis. There you have your x-coordinate. Then repeat the process, but this time follow a horizontal line to determine the y-coordinate.

A point is identified by its ordered pair of (x, y). The first number represents the x-coordinate, while the second represents the y-coordinate.

To graph a point, you draw a dot at the coordinates of the ordered pair. It's usually a good idea to begin at the beginning.

An ordered pair of integers, such as an x-coordinate, which is a number on the x-axis, and a y-coordinate, which is a number on the y-axis, can be used to identify each point. Parentheses are used to indicate ordered pairings (x-coordinate, y-coordinate). The starting point is at (0,0).

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In Python an operator -= is subtracts the value on its right to the variable and assigns the result to the variable on its left.

As we know an operator is nothing but a symbol that represents a mathematical or logical process.

We know that in Python the operator -= provides a way to subtract a value to an existing variable and assign the new value back to the same variable.

If m -= n

This means,  the variable m the left side is getting added to the value on the right side (n), and the result is then reassigned to the variable on the left.

i.e., m = m - n

-= is an assignment operator.

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Answer:

  y = -x +3

Step-by-step explanation:

You want the equation of the line through the points (-3, 6) and (5, -2) in slope-intercept form.

The slope can be found using the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (-2 -6)/(5 -(-3)) = -8/8 = -1

The y-intercept can be be found using the formula ...

  b = y -mx

  b = 6 -(-1)(-3) = 3

The equation in slope-intercept form is ...

  y = mx +b

Using the found values, the equation is...

  y = -x +3

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Answer:

80

Step-by-step explanation:

80+10=90

90/18 = 5

Answer:

W=80

For both equations, you can substitute W for 80 and it would work/be true.

Answer:

Step-by-step explanation:

Derivation of composite functions concept.

h'(x)=g'(f(x))·f'(x)=(sin(5x))'×(5x)'=cos(5x)×5=5cos(5x)

So the number of parcels that Helen delivered on Monday ​is 120 parcels.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

An equality of two ratios is a percentage. We use proportions to construct comparable ratios and find solutions to problems involving unknown numbers.

If on Wednesday Helen delivered 50% fewer parcels than on Tuesday, then on Tuesday Helen delivered 72 / (1 - 0.5) = 72 * 2 = 144 parcels.

On Tuesday Helen delivered 20% more parcels than on Monday, so the number of parcels Helen delivered on Monday is (144 / 1.2) = 120

So Helen delivered 120 parcels on Monday.

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Answer: The table shows the number of pictures that a printer can print at different intervals of time (measured in minutes). To find the rate in pictures per minute, we need to divide the number of pictures printed by the number of minutes it took to print them.

For example, at 2 minutes the printer printed 16 pictures. The rate of pictures printed per minute is 16 pictures / 2 minutes = 8 pictures/minute.

Similarly, at 4 minutes the printer printed 32 pictures. The rate of pictures printed per minute is 32 pictures / 4 minutes = 8 pictures/minute

And, at 6 minutes the printer printed 48 pictures. The rate of pictures printed per minute is 48 pictures / 6 minutes = 8 pictures/minute.

And, at 8 minutes the printer printed 64 pictures. The rate of pictures printed per minute is 64 pictures / 8 minutes = 8 pictures/minute.

From this it can be seen that the printer has a constant rate of 8 pictures per minute, independent of the number of minutes, it is producing 8 pictures/min.

The value 15 is not related to the table, so it's not the rate, and 16 is not the rate either, it is the number of pictures printed at 8 minutes.

Step-by-step explanation:

When  C.I. is given as 80% then the margin of error will be 1.9591% as calculated from the given data.

We are given that the first margin of error (MOE) is 3%.

Also,  confidence interval

first C.I.=95%

second C.I.=80%

Therefore , MOE at 80% will be ,

The formula for proportion is given as (P),

P=x/n , here 64%.

The values are same or constant as in general, this means standard deviation is also constant

Now formula for MOE is given by

MOE = Z x ( SD ) / √n

where ,  Z is value for confidence interval

MOE ∞ Z-value

So we can say that ,

MOE = k x Z ( where k = proportionality constant).

So , for 95 % Z=1.96 and for 80% Z=1.28

MOE then calculated will be , 1.95% .

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The members voted 2 more for mars than earth.

The Solar System has at least eight planets: the terrestrial planets Mercury, Venus, Earth and Mars, and the giant planets Jupiter, Saturn, Uranus and Neptune.

Given here, Mars has 8 votes while earth has 6 votes

Thus difference in votes is =8-6

                                              = 2

Hence, Mars got two more members than earth

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From set theory, A and B: {4, 6} A or B: {2, 3, 4, 5, 6, 8} B's complement is 1, 2, 7, and 8.

Basic set theory describes these various kinds of sets as follows: Finite set: There are only a finite number of elements. A set with an infinite number of elements. A set that is empty has no elements. A singleton set consists of just one element.

The elements that appear in both A and B at the same time are referred to as A and B.

From 1 to 8, the even numbers are 2, 4, 6, and 8.

The numbers 3, 4, 5, and 6 are in that order.

Look for the components that are the same in both sets.

A and B: {4, 6}

The union of the two sets is either A or B.

Combine the components from both sets.

A or B: {2, 3, 4, 5, 6, 8}

All the components that are absent from B make up its complement.

Except for the event elements, write all of the sample space's components.

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Answer:

  25%

Step-by-step explanation:

Of the 12 girls and 16 boys in Mr. Johnson's class, 3 girls and 4 boys wear glasses. You want to know the percentage of students in the class who wear glasses.

The percentage is the fraction multiplied by 100%. The fraction is the ratio of glasses-wearers to total students.

  percentage = (girls w/ glasses + boys w/ glasses)/(girls + boys)×100%

  percentage = (3 +4)/(12+16) × 100% = 7/28 × 100% = 25%

25% of the students in Mr. Johnson's class wear glasses.

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The ordered array will be 9.1 9.4 9.7 10.0 10.2 10.2 10.3 10.8 11.1 11.2 11.5 11.5 11.6 11.6 11.7 11.7 12.2 12.2 12.3 12.4 12.8 12.9 13.0 13.2

What is leaf plot?

A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.

In this instance, the number on the left of the division stands in for the number in the tens place. The value or values on the right side are the ones that fall between the tens and ones places. The number "9.1" is the equivalent of the word "911," for instance. When a number appears more than once on the right side of a division, that number appears more than once in the tens place. In this case, the three numbers 9.1, 9.4, and 9.7 are represented by the string "9 | 147".

Hence, There is an ordered array when reading the stem and leaf plot from top to bottom:

9.1 9.4 9.7 10.0 10.2 10.2 10.3 10.8 11.1 11.2 11.5 11.5 11.6 11.6 11.7 11.7 12.2 12.2 12.3 12.4 12.8 12.9 13.0 13.2

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Answer:

Step-by-step explanation:

4/56\8

In Python, __main__ is the name of the environment where top-level code is run.

We know that in Python, the main function acts as the starting point of execution for any software program.

As we know the program executes only when it runs directly, and if it is imported as a module, then it will not run, the execution of the program starts only when the main function is defined in Python.

__main__ is the name of the top-level scope in which top-level code executes.

Also, all the functions and modules will be executed in the top-level scope __main___ in the interpreter shell.

Using the top-level scope __main__ increases the reusability.

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The values of x are 5 or 13.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given is an equation, [tex]\sqrt{2x-1}[/tex] - x = -8

[tex]\sqrt{2x-1}[/tex] - x = -8

[tex]\sqrt{2x-1}[/tex] = -8+x

Squaring both sides,

2x-1 = x²+64-16x

x²-16x-2x+1+64 = 0

x²-18x+65 = 0

Factorizing the equation,

x²-18x+65 = 0

x²-13x-5x+65 = 0

x(x-13)-5(x-13) = 0

(x-5)(x-13) = 0

x = 5 or 13

Hence, the values of x are 5 or 13.

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Therefore , the solution of the given problem of triangle comes out to be

OAC angle arc is = 55 degrees.

Triangular polygons in geometry are those with right side and three vertices. There are three straight sides to this two-dimensional shape. Three-sided polygons include triangles. A triangle's three angles add up to a whole 180 degrees. A single plane contains the triangle.

Here,

Half of the arc AB is the measure of angle OAC, hence the measure of angle OAC is:

OAC = 0.5 times 220 degrees.

110 degrees is OAC.

If the angle OAC is measured as a quarter of an arc AB, then the angle OAC is measured as follows:

OAC equals 0.25 x 220 degrees

OAC = 55 degrees

Therefore , the solution of the given problem of triangle comes out to be

OAC angle arc is = 55 degrees.

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Answer : in California there are 24 volcanoes while in Alaska there are 36 volcanoes.

Step-by-step explanation:

Total number of volcanoes = 60.

40% of the volcanoes where in California.

i.e 100% - 40% = 60%.

60% of the volcanoes were in Alaska.

In California = 40/100 × 60 = 24 volcanoes.

In Alaska = 60/100 × 60 = 36 volcanoes.