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Two cyclists, 68 miles apart, start riding toward each other at the same time. One cycles 3 miles per hour faster than the other, and they meet after 4 hours of riding.

a. Write an equation using the information as it is given above that can be solved to answer this problem. Use the variable r to represent the speed of the slower cyclist.

b. What are the speeds of the two cyclists? _______________

1/5=2/10

4/6=2/3

2/8=1/4

Answer:

147 cubic inches

Step-by-step explanation:

volume of the prism is length x breadth x height

3.5 x 7 x 6=147

Answer:

[tex](f + g)(2) = 21[/tex]

Step-by-step explanation:

[tex]f(x) = -x^2 - 4x +2[/tex]

[tex]g(x) = 4x^2 + 5x + 5[/tex]

Required

[tex](f + g)(2)[/tex]

This is calculated as:

[tex](f + g)(2) = f(2) + g(2)[/tex]

Where:

[tex]f(2) = -2^2 - 4*2 +2 = -10[/tex]

[tex]g(2) = 4*2^2 + 5*2 + 5 = 31[/tex]

So:

[tex](f + g)(2) = f(2) + g(2)[/tex]

[tex](f + g)(2) = -10 + 31[/tex]

[tex](f + g)(2) = 21[/tex]

Answer:  y = |x+4|

Explanation:

Imagine that the graph of y = |x| is carved in stone so it cannot move. What we can move though is the xy axis. If we move the xy axis 4 units to the right, then this gives the illusion the V shaped curve is moving 4 units to the left. It goes opposite whatever movement you do to the xy axis.

If we replaced x with x+4, then this moves the xy axis 4 units to the right.

Therefore, going from y = |x| to y = |x+4| will have the V shaped curve moving 4 units to the left.

Answer:

Yeah, the person above me is right. It's 2:1

Step-by-step explanation:

There are 2 arcade areas and 1 swimming pool. the arcade area to swimming pool ratio is 2: 1.

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b

or

[tex]\dfrac{a}{b}[/tex]

Remember that the ratio should always be taken of quantities with same unit of measurement.

Also the ratio is a unitless(no units) quantity.

There are 2 arcade areas and 1 swimming pool.

The arcade area to swimming pool ratio is 2: 1.

Learn more about ratios here:

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Answer:

[tex]Time = 560\ mins[/tex]

Step-by-step explanation:

Given

[tex]Candles = 2[/tex] --- candles melted

[tex]Divisions = 12[/tex]

[tex]Time = 4\ hrs[/tex] --- time to melt

Required

The time since the first was lit

If 1 candle melts in 4 hours, 2 candles will melt in 8 hours.

i.e.

[tex]x = Candles * Time[/tex]

[tex]x = 2 * 4hrs[/tex]

[tex]x = 8hrs[/tex]

For the 3rd candle that has melted, 4 inches

First, calculate the fraction that melt

[tex]Fraction = \frac{Melt}{Division}[/tex]

[tex]Fraction = \frac{4}{12}[/tex]

[tex]Fraction = \frac{1}{3}[/tex]

The time to melt is:

[tex]y = Fraction * Time[/tex]

[tex]y= 4 * \frac{1}{3}[/tex]

[tex]y= \frac{4}{3}hrs[/tex]

So, the required time is:

[tex]Time = x + y[/tex]

[tex]Time = 8hrs + \frac{4}{3}hrs[/tex]

Convert to minutes

[tex]Time = 8*60mins + \frac{4}{3}*60mins[/tex]

[tex]Time = 480mins + 80mins[/tex]

[tex]Time = 560\ mins[/tex]

Answer:

18,646

Step-by-step explanation:

>you can graph the equation on a calculator and see that the minimum is at the point (250, 18646) , so the minimum unit cost is 18,646

>you can use the first derivative to find the minimum

c'(x) = (0.2x²-100x+31,146)' = .4x -100

.4x-100= 0 , so x= 250

c(x=250) = 0.2(250)² -100*250 +31,146 =18,646

Answer:7.5=−k(2.5)−7.52.5=kma=−7.5x2.5my′′+9y′+−3y=0,y(0)=2.5,y(5)=0−9±81+4(m)(3)−−−−−−−−−−−√2m−92m±81+12m−−−−−−−−√2my=Ae−(9/2)xcos(81+12m−−−−−−−−√2mx)+Be−(9/2)xsin(81+12m−−−−−−−−√2mx)2.5=A+B⋅00=(2.5)e−45/2cos(81+12m−−−−−−−−√52m)+Be−45/2sin(81+12m−−−−−−−−√52m)

Step-by-step explanation:

Answer: 17 1/2 or decimal form = 17.5

Step-by-step explanation: Hope this helped!

Answer:

17.5 Statues im pretty sure.

Step-by-step explanation:

7/8 divided by 1/20

Answer: 1.4

Step-by-step explanation:

Answer: 1.4

Step-by-step explanation:

14 x 0.1 = 1.4

(10% = 10/10 0= 0.1)

Answer:

The decrease in the value of the truck, which is 12%

Step-by-step explanation:

f(x) = 29,000(0.88)^x

This is an exponential function of the form

y = ab^x

a is the initial value

b is the growth(decay) rate

x is the time

Since b is less than 1, we know it is decay

To find the rate

1-b = rate

1-.88 = .12

The decay rate is .12*100% = 12 %

Answer:

its A:The decrease in the value of the truck, which is 12%

Step-by-step explanation:

i got this correct

Answer:

(x+4)(x+11)

Step-by-step explanation:

x^2+11x+28

What two numbers multiply to 28 and add to 11

4*7 =28

4+11

(x+4)(x+11)

Answer:

(x + 4)(x + 11)

I agree with wegner

bye

Answer:

75.4cm

Step-by-step explanation:

To calculate the circumference, you need the radius of the circle:

Multiply the radius by 2 to get the diameter.

Multiply the result by π, or 3.14 for an estimation.

That's it; you found the circumference of the circle.

Answer:

C ≈ 75.4 cm

Step-by-step explanation:

[tex]2\pi r[/tex]

2 × 3.14 × 12

C ≈ 75.4 cm

Answer:

[tex]3x^2-1[/tex]

Step-by-step explanation:

Answer:

y = 2x/7 + 5

Step-by-step explanation:

the first line is defined by

7x - 2y + 3 = 0

in the most common way to write this we need an equation like y = ...

so, we isolate the y-expression in the equation :

2y = 7x + 3

y = (7x + 3) / 2 = 7x/2 + 3/2

the factor of x is the slope of the line, which is expressed by the y/x ratio indicating how many units y will change, when x changes e.g. 1 unit.

7/2 means that y will change by 7 units for every change in x by 2 units.

the slope of a perpendicular line is inverse to the slope of the original line, which means x and y are simply trading places (original x / original y).

so, the perpendicular slope of 7/2 is 2/7 (when x changes by 7 units, then y changes by 2 units).

that means the equation for the perpendicular line is something like

y = 2x/7 + c

the c we determine by using the coordinates of the given point (x and y values).

3 = 2×(-7)/7 + c = 2×(-1) + c = -2 + c

c = 5

so, the complete equation of the perpendicular line is

y = 2x/7 + 5

Answer:

A? maybe i dont know dont quote me on that

Step-by-step explanation:

The Probability distribution is

Apples =1/5

Bananas = 3/10

Lemons = 1/15

Oranges = 4/15

Pears = 1/6

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Total Fruits = 30

Now, the probability distribution for the 30 pieces of fruit is

Apples = 6/30

            = 1/5

Bananas = 9/30

               = 3/10

Lemons = 2/30

              = 1/15

Oranges = 8/30

               = 4/15

Pears = 5/30

          = 1/6

Learn more about Probability here:

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Answer:

[tex]7x - 21y = 14 - - - (a) \\ 2x + 3y = 11 - - - (b) \\ (a) + 7 \times (b) : \\ 21x + 0y = 91 \\ x = 4.33 \\ (2 \times 4.33) + 3y = 11 \\ 3y = 2.34 \\ y = 0.78 \\ { \boxed{x = 4.33}} \\ { \boxed{y = 0.78}}[/tex]

Answer:

you drew to much on it

Step-by-step explanation:

Answer:

9 is the answer

Step-by-step explanation:

Answer:

the answer should be 3 and 5 :)

Step-by-step explanation:

the answer speaks for itself

Answer:

not entirely sure but my answer is 87.6ft.

for the perimeter of the shape.

Step-by-step explanation:

I cut out the extra square-ish pieces of the sides and found

that both are 17.2 for their perimeter. so 17.2×2= 34.4

then I found the perimeter of the sides of the rectangular shape and the sides were both 18.4ft. so 2(18.4+8.2)= 53.2.

so 53.2+34.4 = 87.6ft.

Answer:

C 14n - 8

Step-by-step explanation:

rectangle area = length×width = 12n²-19n-21

width = 3n-7

what do we need to multiply with width to get the full area expression ?

think : what do we need to multiply with 3n to get 12n² (4n)?

and what to multiply with -7 to get -21 (3)?

=> length = 4n+3

perimeter is 2×length + 2×width

p = 2(3n-7) + 2(4n+3) = 6n-14+8n+6 = 14n-8

Answer:

60 cubic inches

Step-by-step explanation:

if its a triangle you have to divide it by 2 because its half of a square so its half of an answer so in this case you multiply 10 and 12 which gets you 120 divide that by 2 you get 60 and that's your answer.

Answer:

The final price of the television set is $ 20,520.

Step-by-step explanation:

Given that King Monatla surprised his wife on birthday by buying her a 55 inch television set, and the repayment period is 36 months and the monthly installment is $ 570.00, to determine the final price of the television set the following calculation must be performed:

570 x 36 = X

20.520 = X

Therefore, the final price of the television set is $ 20,520.

Answer:

Let m= x^4

m^2 -3m +2 = 0

Step-by-step explanation:

x ^ 8 - 3x ^ 4 + 2 = 0

Let m= x^4

m^2 -3m +2 = 0

Answer:

2

Step-by-step explanation:

10 column=10 space in number, aka 70(2)5

Answer:

The 90th percentile of the distribution is 6.512 ml.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 6 milliliters (ml) and a standard deviation of 0.4 ml.

This means that [tex]\mu = 6, \sigma = 0.4[/tex]

Find the dye amount that represents the 90th percentile (i.e. 90%) of the distribution.

This is X when Z has a p-value of 0.9, so X when Z = 1.28. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.28 = \frac{X - 6}{0.4}[/tex]

[tex]X - 6 = 1.28*0.4[/tex]

[tex]X = 6.512[/tex]

The 90th percentile of the distribution is 6.512 ml.

Answer:

Step-by-step explanation:

take angle C as reference angle

using tan rule

tan C=oppposite/adjacent

tan C=6/12

tan C=0.5

C=[tex]tan^{-1}[/tex]0.5

C=26.6 degree