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zhuklara [117]
3 years ago
15

Two cyclists, 55 miles apart, start riding toward each other at the same time. One cycles 5 miles per hour faster than the other

, and they meet after 5 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?
Mathematics
1 answer:
tangare [24]3 years ago
8 0

Answer:

r = 6 mph and f = 11 mph

Step-by-step explanation:

Representations:  

1) speed of faster cyclist:  f = r + 5

2) speed of slower cyclist:  r

Distances covered:

(r + 5)(5 hr) + r(5) = 55 mi (total distance covered)

Then 5r + 25 + 5r = 55, or, after reducing this equation:

r + 5 + r = 11, or

2r = 6

Then r = 6 mph and f = 11 mph

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A researcher is curious about the average IQ of registered voters in the state of Florida. The entire group of registered voters
mel-nik [20]

Answer:

Population

Step-by-step explanation:

A population can be defined as the total number of living organisms living together in a particular place and sharing certain characteristics in common.

A sample survey is a statistical method used for the collection of data from a target population in order to draw an inference and reach a logical conclusion.

In Statistics, sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.

In this scenario, the entire group of registered voters in Florida is an example of a population.

4 0
3 years ago
3 times a number is 54 less than the square of that number. Find the negative solution.
Pavel [41]

Answer:

x=-6

Step-by-step explanation:

Let x be the number

3x = x^2 -54

Subtract 3x

3x-3x = x^2 -3x-54

0 = x^2 -3x-54

Factor

What 2 numbers multiply to -54 and add to -3

-9*6 = -54

-9+6 = -3

0=(x-9) (x+6)

Using the zero product property

x-9=0    x+6=0

x=9  x=-6

The questions asks for the negative solution

x=-6

3 0
3 years ago
your dad is designing a new garden for your backyard. he has 21 ft of fencing to go around the garden. he wants the length of th
Gemiola [76]

Answer:

The garden is 4.5 ft by 6 ft.

Step-by-step explanation:

2x + 2(x+1.5) = 21

2x + 2x + 3 = 21

4x = 18

x = 4.5

4 0
3 years ago
Read 2 more answers
Write a proportion to find how many points x a student needs to score on a test worth 50 points to get a test score of 78%.
olganol [36]
The answer is:  "39 points" .
_______________________________________________________
Explanation:
_______________________________________________________
" x/ 50 = 78/100 " ;   in which "x" equals the number of points needed.

_______________________________________________________

To solve for "x" ; 
_______________________________________________________

Look at the denominators:  50 * (what value?) = 100.

→ "100 ÷ 50 = 2" .

→ So;  "50 * 2 = 100" ; 

So, let us look at the numerators:

x * 2 = 78 ; 

↔  2x = 72 ; 

Divide each side of the equation by "2" ; to isolate "x" on one side of the equation ; and to solve for "x" ;
_____________________________________________
 →  78 ÷ 2 = 39 ;

The answer is:  "39 points" .
_____________________________________________


4 0
3 years ago
a. Suppose a BMW dealer in Fullerton, CA is trying to calculate the probability of his car sale for next week. The dealer knows
egoroff_w [7]

Answer:

0.45576

Step-by-step explanation:

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

Standard Deviation = √variance

Mean = 50

= √9

= 3

z = 51 - 50/3

= 0.11111

Probability value from Z-Table:

P(x<51) = 0.54424

P(x>51) = 1 - P(x<51)

= 1 - 0.54424

= 0.45576

The probability that the dealer will sell 51 or more cars is 0.45576

8 0
4 years ago
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