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3 years ago

A cyclist travels 3 miles in 15 minutes and then a further 7 miles in 25 minutes without stopping.

Mathematics

1 answer:

Oduvanchick [21]3 years ago

5 0

Answer:

v = 15 mph

Step-by-step explanation:

Given that,

A cyclist travels 3 miles in 15 minutes and then a further 7 miles in 25 minutes without stopping.

Total distance, d = 3 + 7 = 10 miles

Total time, t = 15 + 25 = 40 minutes = 0.6667 hours

Average speed,

$v=\dfrac{d}{t}$

Put all the value,

$v=\dfrac{10}{0.6667}\\\\= $$14.99\ mph$

v = 15 mph

So, the required average speed is equal to 15 mph.

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general admission tickets to the fair cost $3.50 per person rides pass cost an additional $5 and fifty per person parking cost $

horrorfan [7]

Total people x,

then, 3.5x + 5.5x + 6 = 51

simplify, 9x +6 = 51

subtract 6 on both sides, 9x= 45

divide by 9 on both sides, x= 5

therefore, total 5 people in the family.

8 0

3 years ago

Find the 6th term of the arithmetic sequence X – 9, -X – 11, -3.3 – 13, ...

MrMuchimi

Answer:

$-13x-23$

Step-by-step explanation:

Given sequence: $x-9, -x-11, -3x-13$

Therefore,

$a_1=x-9$
$a_2=-x-11$
$a_3=-3x-13$

General form of an arithmetic sequence: $a_n=a+(n-1)d$

(where a is the first term and d is the common difference)

To find the common difference, subtract a term from the next term:

$\begin{aligned}d & =a_2-a_1\\ & =(-x-11)-(x-9)\\ & = -x-11-x+9\\ & = -2x-2\end{aligned}$

Therefore,

$a_n & =(x-9)+(n-1)(-2x-2)$

To find the 6th term, input n = 6 into the equation:

$\begin{aligned}\implies a_6 & =(x-9)+(6-1)(-2x-2)\\ & = (x-9)+7(-2x-2)\\ & = x-9-14x-14\\ & = -13x-23\end{aligned}$

3 0

3 years ago

Records indicate that for parts coming out a hydraulic repair shop at an airplane rework facility, 30\% will have a shaft defect

mrs_skeptik [129]

Answer:

P(A|B) = P(A∩B)/P(B) = 100%

Which means that there is 100% probability that the item has at least one type of defect given that the item has only a shaft defect.

Step-by-step explanation:

Conditional probability P(A|B) can be expressed as;

P(A|B) = P(A∩B)/P(B) .....1

Given;

30% will have a shaft defect,

15% will have a bushing defect,

and 65% will be defect-free

Total probability = 100% = P(shaft or/and bushing defect) + P(defect free)

P(shaft or/and bushing defect) = 100% - P(defect free)

= 100% - 65% = 35%

And

P(shaft or/and bushing defect) = P(shaft def only) + P(bushing def only) + P(shaft and bushing defect)

P(shaft or/and bushing defect) = P(shaft defect) + P(bushing defect) - P(shaft and bushing defect)

Substituting the values we have;

35% = 30% + 15% - P(shaft and bushing defect)

P(shaft and bushing defect) = 45% - 35% = 10%

Let A="The item has at least one type of defect"; and B="The item has only a shaft defect".

P(A) = P(shaft or/and bushing defect) = 35%

P(B) = P(shaft only defect) = 30% - 10% = 20%

P(A∩B) = 20%

Substituting into equation 1

P(A|B) = P(A∩B)/P(B) = 20%/20%

P(A|B) = 1/1 = 100%

Which means that there is 100% probability that the item has at least one type of defect given that the item has only a shaft defect.

5 0

3 years ago

Consider the rational expression (IMAGE ATTACHED)

Keith_Richards [23]

Answer:

3x² is a term in the numerator
x + 1 is a common factor
The denominator has 3 terms

Step-by-step explanation:

You can identify terms and count them before you start factoring. Doing so will identify 3x² as a term in the numerator, and will show you there are 3 terms in the denominator.

When you factor the expression, you get ...

$\dfrac{3x^2-3}{3x^2+2x-1}=\dfrac{3(x^2-1)}{(3x-1)(x+1)}=\dfrac{3(x-1)(x+1)}{(3x-1)(x+1)}$

This reveals a common factor of x+1.

So, the above three observations are true of this rational expression.

3 0

4 years ago

Please Help-

Sloan [31]

You take 94.5 and divide by 4.5 get 21

4 0

3 years ago

Read 2 more answers