Barbara, Mark, and Carlos participated in the third heat of “The Big Race”. Barbara thought she could win with a 3 meter head start even though she only pedaled 3 meters every 2 seconds. Mark began at the starting line and finished the 20-meter race in 5 seconds. Meanwhile, Carlos rode his tricycle so that his distance (y) from the starting line in meters could be represented by the equation y = x + 1, where x represents time in seconds. Who would win in a 20 meter race?

Answer: [tex]1.83\text{ feet}[/tex]

Step-by-step explanation:

Given : If a line of one billion people standing shoulder to shoulder stretches 346,439 miles long.

We know that 1 mile =5280 feet

Then, the length of line=[tex]346439\times5280=1829197920[/tex] feet

We know that 1 billion can be written as :

[tex]1,000,000,000=10^9[/tex]

Now, the average shoulder width of the people in the line :-

[tex]\dfrac{1829197920}{1000000000}=1.8291979\approx1.83\text{ feet}[/tex]

Hence, the average shoulder width of the people in the line is about [tex]1.83\text{ feet}[/tex]

To obtain a 35% antifreeze solution, you need to add approximately 1.857 gallons of water to 1 gallon of pure antifreeze.

To obtain a 35% antifreeze solution, you need to add a certain amount of water to 1 gallon of pure antifreeze. Let's assume that x gallons of water should be added. In a 35% antifreeze solution, the amount of antifreeze is 35% of the total solution. So, we can set up the following equation:

1 gallon of antifreeze = (35/100) * (1 + x) gallons of solution

Simplifying this equation, we get:

1 = 0.35 * (1 + x)

Now, let's solve for x:

Divide both sides of the equation by 0.35:

1/0.35 = 1 + x

2.857 = 1 + x

Subtract 1 from both sides of the equation:

2.857 - 1 = x

x = 1.857 gallons of water

Therefore, you need to add approximately 1.857 gallons of water to 1 gallon of pure antifreeze to obtain a 35% antifreeze solution.

Final answer:

To obtain a 35% antifreeze solution from 1 gallon of pure antifreeze, approximately 1.857 gallons of water needs to be added. This calculation is based on a simple concentration equation, resulting in the given ratio.

Explanation:

To calculate the amount of water to be added to 1 gallon of pure antifreeze to obtain a solution that is 35% antifreeze, we need to perform a simple concentration calculation.

We are starting with pure antifreeze, so it's 100% antifreeze. We want to end with a solution that is 35% antifreeze. Let's denote the amount of water added as x gallons. Because we are diluting the antifreeze, the total volume of the solution after adding water will be 1 gallon (the initial volume of the antifreeze) plus x gallons (the volume of water added).

The concentration of antifreeze after adding water is the volume of antifreeze divided by the total volume of the solution:

Concentration of antifreeze = Volume of antifreeze / Total volume of solution

Thus, 0.35 = 1 / (1 + x)

Multiplying both sides by (1 + x) and then by 0.35 we get:

1 = 0.35 * (1 + x)

Dividing by 0.35 and then subtracting 1:

x = 1 / 0.35 - 1

After calculating:

x ≈ 1.857 gallons

To obtain a 35% antifreeze solution, approximately 1.857 gallons of water should be added.

Answer:

The correct option is:  1

Step-by-step explanation:

Scale factor is the ratio of corresponding side lengths of two triangles.

Here....

[tex]\frac{DE}{AB}=\frac{5}{5}=1\\ \\ \frac{DF}{AC}=\frac{5}{5}=1\\ \\ \frac{EF}{BC}=\frac{5}{5}=1[/tex]

So, the scale factor of [tex]\triangle ABC[/tex] to [tex]\triangle DEF[/tex] is 1.

The distance from the tip of the shadow to the top of the tree is 42.426 meters.

Pythagoras theorem is a relation between sides of a right-angle triangle.

It states that for a right-angle triangle the square root of Hypotenuse is equal to the sum of the individual base and perpendicular square.

So,

Hyp² = Base² + Perp²

Given the situation is making a right angle triangle with base and perpendicular as 30 meters.

By Pythagoras theorem,

Hyp² = Base² + Perp²

Hyp² = 30² + 30²

Hyp² = 1800

Hyp = 42.426 meter.

Hence "The distance from the tip of the shadow to the top of the tree is 42.426 meters".

To learn more about Pythagoras' theorem,

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Answer is provided in the image attached.

Area of the trapezoid ABCD is

[tex]62\frac{1}{2}[/tex]

Given :

The diagram of a trapezoid ABCD

Area of trapezoid is [tex]\frac{base1+base2}{2} \cdot height[/tex]

Lets find the length of base 1  and base 2 using distance formula

Base 1 is AD. find the distance AD

[tex]AD=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\AD=\sqrt{\left(-13-\left(-1\right)\right)^2+\left(-11-5\right)^2}\\AD=20[/tex]

Now we find out BD that is base 2

[tex]BD=\sqrt{\left(0-3\right)^2+\left(-2-2\right)^2}\\BD=5[/tex]

Now find out height  AB

A is (-1,5) and B(3,2)

[tex]AB=\sqrt{\left(-1-3\right)^2+\left(5-2\right)^2}\\AB=5\\[/tex]

[tex]Area =\frac{AD+BC}{2} \cdot AB\\Area=\frac{20+5}{2} \cdot 5\\Area=\frac{125}{2}\\Area=62\frac{1}{2}[/tex]

Area of the trapezoid ABCD is

[tex]62\frac{1}{2}[/tex]

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To find the original cost price of a shirt on which an 8% discount was given, resulting in a sale price of Rs.161, the formula CP = Sale Price / (1 - (Discount Percent / 100)) is used, calculating the cost price as Rs.175.

If the sale price of a shirt after giving an 8% discount is Rs.161, to find the written price, or the cost price before the discount, we can use the formula for discount calculation. Let CP represent the cost price. The formula for calculating the sale price after discount is:

Sale Price = CP - (Discount Percent * CP) / 100

Here, the sale price is given as Rs.161, and the discount percent is 8%. Therefore, we can rearrange the formula to solve for CP:

CP = Sale Price / (1 - (Discount Percent / 100))

Plugging in the values gives us:

CP = 161 / (1 - (8 / 100)) = 161 / 0.92 = Rs.175

Therefore, the written price or the cost price of the shirt before the discount was applied is Rs.175.

Answer:

[tex]900000 + 60000+60[/tex]

Step-by-step explanation:

write 960,060 in expanded form

In 960,060, from left to right

0 is in ones place is 0

6 is in tens place is 6 times 10 = 60

6 is in ten thousands place is 6 times 10000= 60000

9 is in hundred thousands place 9 times 100000= 900000

So the expanded form of the given number is

[tex]900000 + 60000+60[/tex]

Answer:

Step-by-step explanation:

When dealing with consecutive integers, it often simplifies the problem to work with their average value. We know the average value of the integers in this problem is the even integer between the middle two. We can call it x, and write the equation ...

  (x-3) +(x-1) +(x+1) +(x+3) = -72

This simplifies to ...

  4x = -72 . . . . . . . we knew this before we wrote the above equation, since the sum of 4 numbers is 4 times their average.

  x = -18 . . . . . . . . the middle number of the sequence

So, the numbers are:

_____

A more conventional approach is to define the variable as the integer at one end or the other of the sequence. If we make it be the lowest number, then the equation is ...

  (x) +(x +2) +(x +4) +(x +6) = -72

and that simplifies to ...

  4x +12 = -72 . . . . . collect terms

  4x = -84 . . . . . . . . subtract 12

  x = -21 . . . . . . . . . . divide by 4

Now, the other three numbers are found by adding 2, 4, and 6 to this one.

The slope of a line is -1/3, and the y-intercept is 10/3. What is the equation of the line written in general form?

Answer:

x + 3y - 10 = 0

Hence, the number of students who listed Instagram as their favorite app is 409

Let x denote the number of students who listed Instagram their favorite app.

Now the number of people who listed Fb as their favorite app is 32 less than two times number of students who have Instagram as their favorite app.

Hence, the equation so obtained is given by:

786 = 2x - 32

i.e. 2x = 818

i.e. x = 409  

                  Hence, the answer is: 409