A car traveling at 48 mph overtakes a cyclist who is riding at 16mph had a 3 hour head start how far from the starting point does the car overtake the cyclist?

[tex]\boxed{\boxed{\Large \text{Ted will run 60 kilometres in 285 minutes.}}}[/tex]

Using the distance-time-speed relationship:

[tex]\boxed{\Large \text{speed = $\frac{\rm distance}{\rm time}$}}[/tex]

[tex]\boxed{\Large \text{distance = speed $\times$ time}}[/tex]

[tex]\boxed{\Large \text{time = $\frac{\rm distance}{\rm speed}$}}[/tex]

so if Ted can run 20 kilometres (distance) in 95 minutes (time), then his speed = 20 ÷ 95 = 4/19 km/min.

Using this result, to calculate how far Ted will run in 285 minutes, we can say that distance = 4/19 × 285 = 60 kilometres.

∴ Ted will run 60 kilometres in 285 minutes.

[tex]\hrulefill[/tex]

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Answer:

C. A rate with one (1) in the denominator

A unit rate is basically a ratio of something to one.

example:

if 10 bananas costs ten dollars then one banana would cost one dollar.

Step-by-step explanation:

Answer:

A.  A rate with one in the numerator

Step-by-step explanation:

We can find the unit rate when given a rate by dividing the unit in the numerator by the quantity in the denominator. For example, if we are given the rate $4.50/5 gallons of milk, we can divide 4.50 by 5 to find the unit price, which is dollars per one gallon of milk. A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

Answer:

11 11/12

Step-by-step explanation:

Answer:

≈ 12

Step-by-step explanation:

To estimate, we'll round these mixed numbers to the nearest whole number, then multiply. Let's start with 4 1/3. 4 1/3 is closest to 4, since 1/3 is smaller than 1/2. Then, we can look at 2 3/4. This mixed number is closest to 3, since 3/4 is greater than 1/2.

Now, the two numbers we have are 4 and 3. What is 4 × 3? Well, that's pretty simple - the answer is 12. So, 4 1/3 × 2 3/4 ≈ 12. Hopefully that's helpful! :)

Answer:

Step-by-step explanation:

Simplified this is 9 :)

Answer:

12.4

Step-by-step explanation:

Answer:

1. decrease by 8%

2. decrease by 11%

3. increase by 8%

4. increase by 11%

Step-by-step explanation:

Answer:

b) you need one set of | | for the inside of the logarithm only.

c) pi^2 /56

Step-by-step explanation:

For b, you just need | | instead of ( ) for the inside of the natural logarithm part... .

For c...

Integral( arcsin(7/6x)/sqrt(36-49x^2),x=0..6/7).

Lets go ahead and fix up the the denominator so the multipler on x is the same as it is in numerator.

Factor our sqrt(36) on bottom. Note sqrt(36)=6.

1/6Integral(arcsin(7/6x)/sqrt(1-(7x/6)^2),x=0..6/7)

Let 7/6x=sin(v). Then 7/6 dx=cos(v) dv.

If x=0 then we solve 7/6(0)=sin(v) giving us v=0. Note sin(0)=0.

If x=6/7 then we solve 7/6(6/7)=sin(v) giving us v=pi/2. Note sin(pi/2)=1...and I chose this particular value for v so the sine curve didn't have a chance to make a new or start a new cycle.

1/6×6/7Integral(v/sqrt(1-(sinv)^2) cos(v)),v=0..pi/2)

Next step invokes the Pythagorean Identity sin^2(v)+cos^2(v)=1:

1/7Integral(v/cos(v) cos(v), v=0..pi/2)

1/7Integral(v, v=0..pi/2)

1/7(v^2/2, v=0..pi/2)

1/7((pi/2)^2/2-(0)^2/2)

1/7(pi^2/4/2)

1/7(pi^2/8)

pi^2/56

Answer:

x = 84 y = 59°

Step-by-step explanation:

x = (40/30)×63

x = 84

∆ABC = ∆PQR

so y = 59°

Answer:

1.) 47

2.) 28

Step-by-step explanation:

you just had to use the sin equation for both

Answer:

v is independent

Step-by-step explanation:

v because v isn't depended on m

m depends on how many visitors there are so it's depended on v.

:)

The distance Jen is from the base of the lighthouse is 86.6 meters.

Trigonometric ratio is used to show the relationship between the sides of a and angles of a right angled triangle.

Let d represent the distance Jen is from the base of the lighthouse.

Using trigonometric ratios:

[tex]tan(30)=\frac{50}{d} \\\\d=\frac{50}{tan(30)} \\\\d=86.6\ m[/tex]

The distance Jen is from the base of the lighthouse is 86.6 meters.

Find out more on Trigonometric ratio at: https://brainly.com/question/10417664

Answer:

alr yeah i get it now

Step-by-step explanation:

its A 11/14

Answer:

[tex]\frac{11}{14}[/tex]

Step-by-step explanation:

[tex]\frac{2}{7}[/tex] + [tex]\frac{7}{14}[/tex]

Before adding er require the fractions to have the same denominators.

Multiply the numerator/ denominator of the first fraction by 2

= [tex]\frac{2(2)}{7(2)}[/tex] + [tex]\frac{7}{14}[/tex]

=[tex]\frac{4}{14}[/tex] + [tex]\frac{7}{14}[/tex]  ( now add numerators leaving the common denominator )

= [tex]\frac{4+7}{14}[/tex]

= [tex]\frac{11}{14}[/tex]

Answer:

14 to 5

Step-by-step explanation:

9 + 5 = 14(total books)

new books = 5

so ratio of total books to new books is 14 to 5

Answer:

x³ - 4x² + 2x + 4 = 0

Here's how I solved this:

You start off by rewriting the zeros into factors:

1 - √3    →    x = 1 - √3    →    (x - 1 - √3)

  2        →    x = 2           →    (x - 2)

1 + √3   →    x = 1 + √3   →    (x - 1 + √3)

Now you want to multiply the factors together:

     (x - 1 - √3) · (x - 2) · (x - 1 + √3)

- Multiply the first two factors together -

                (x - 1 - √3) · (x - 2)

                              ↓

    (x · x - x · 2 - √3 · x + √3 · 2 - x + 2)

   - Combine like terms and simplify -

    (x · x - x · 2 - √3 · x + √3 · 2 - x + 2)

                              ↓

          (x² - 3x - √3 · x + 2√3 + 2)

      - Now multiply the third factor -

   (x² - 3x - √3 · x + 2√3 + 2)(x - 1 + √3)

                              ↓

(x² · x + x² · √3 - x² - 3x · x - 3x · √3 + 3x - √3 · xx - √3 · x · √3 +√3 · x + 2 · √3 · x + 2 · √3 · √3 - 2 · √3 + 2x + 2 · √3 - 2)

                              ↓

(x³ + x² · √3 - x² - 3x² - 3x · √3 + 3x - √3 + 3x - √3 * x² - x · 3 + √3 · x + 2 · √3 · x + 2 · 3 - 2 × √3 + 2x + 2 √3 - 2)

   - Combine like terms and simplify -

(x³ + x² · √3 - x² - 3x² - 3x · √3 + 3x - √3 + 3x - √3 * x² - x · 3 + √3 · x + 2 · √3 · x + 2 · 3 - 2 × √3 + 2x + 2 √3 - 2)

                              ↓

                 x³ - 4x² + 2x + 4

--------------------------------------------------------------------------------------------------------------

And there we get our solution: x³ - 4x² + 2x + 4  

Answer:

4 fluid ounces

Step-by-step explanation:

A waitress is filling coffee mugs at a diner. She pours 12 fluid ounces into each of 5 mugs from a full pot of coffee. If her coffee pot holds 8 cups, how many fluid ounces does she have left?

Remember

8 fluid ounces = 1 cup.

First you need to do find out how many fluid ounces she poured in total.

So do,

5 mugs × 12 fluid ounces.

which is 60 fluid ounces.

Now that you now that you need to convert 8 cups into fluid ounces.

Like I said at the top 8 fluid ounces = 1 cup.

So you need to do,

8 cups × 8 fluid ounces.

Which is 64 fluid ounces she can hold in her coffee pot.

Now you subtract,

64 fluid ounces - 60 fluid ounces.

Which is 4 fluid ounces left in her coffee pot.

The number of fluid ounces she has left is 4 fluid ounces if the waitress is filling coffee mugs at a diner. She pours 12 fluid ounces into each of the 5 mugs from a full pot of coffee.

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.

It is given that:

A waitress is filling coffee mugs at a diner. She pours 12 fluid ounces into each of 5 mugs from a full pot of coffee.

Let x be the number of fluid ounces she has left.

4 fluid ounces

As we know,

8 fluid ounces = 1 cup

The total amount of coffee = 5×12

The total amount of coffee = 60

Total amount = 8 cups × 8 fluid ounces.

x = 64 fluid ounces - 60 fluid ounces.

x = 4 fluid ounces

Thus, the number of fluid ounces she has left is 4 fluid ounces if the waitress is filling coffee mugs at a diner. She pours 12 fluid ounces into each of the 5 mugs from a full pot of coffee.

Learn more about the unit conversion here:

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Answer: look at explanation

Step-by-step explanation:

1st question: 48 / 60 = 80 %

2nd : 1/4 of 60 = 15 people

3rd : If 60% is 48 miles, than 10% is 8 miles. Therefore, 100% (his goal) = 80 miles.

4th: 1/4 of 88 = £22

Answer:

D 280

Step-by-step explanation:

Pythagoras theorem

Answer:

a

Step-by-step explanation:

LN=√19＾2 - 9＾2

=√361 - 81

=√280

Answer:

Option B,option D and option F are the correct statements.

Answer:

1 1/2 pound

Step-by-step explanation:

If each coin weighs 3/4 ounces and she picked up 6 then you do 3/4 x 6/1 which equals 18/4 and since there is 16 ounces in a pound it simplifies to 1 2/4 or 1 1/2 pounds

Answer:

(-4,-5)

Step-by-step explanation:

The coordinates of the midpoint for x = sum of x/2=2

The coordinates of the midpoint for y = sum of y/2=-2

firstly to work out x coordinate:

[tex] \frac{x + 8}{2} = 2[/tex]

rearrange to find x which is -4

work out y coordinate:

[tex]\frac{y + 1}{2} = - 2[/tex]

rearrange to find y which is -5

so coordinates are (-4,-5)

Answer:

Here is your answer hope I helped! <3

Step-by-step explanation:

t=k/3-p/3

Answer:

155°

Step-by-step explanation:

We know that the sum of the sections must be 360°. So, by removing a section of 75° he leaves the paper circle with a section of 185°, then removes another 130° section, leaving the last section of 155°.

Answer:

Step-by-step explanation:

Answer:

Let +d+ = the one-way distance to the mountains in miles

Let +s+ = his speed going to the mountains in mi/hr

+s+%2B+27+ = his speed on the trip home in mi/hr

equation for going to the mountains:

(1) +d+=+s%2A7+

Step-by-step explanation:

I hope this helps mark as brainliest if correct

Answer:

Below in bold.

Step-by-step explanation:

1. 165/3.3 = 50 meters/second.

2. In 4 seconds the skydiver will fall 4*50 = 200 meters.

Answer:

I would say either pic 2 or four.

Step-by-step explanation:

Hopes This Helps

Answer:

E= 0 Good luck answering the other questions :)

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Circumference=72

pi=3.14

Radius=C /2π

72/6.28=11.4649681529

Rounded to the whole would be 11

=11