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Soloha48 [4]
3 years ago
11

Gavin goes for a run at a constant pace of 9 minutes per mile. Ten minutes later, Lars goes for a run, along the same route, at

a constant pace of 7 minutes per mile. How many minutes does it take for Lars to reach Gavin?
Mathematics
1 answer:
sweet [91]3 years ago
6 0

Answer:  The answer is 35 minutes.


Step-by-step explanation:  Given that Gavin goes for a run at a constant pace of 9 minutes per mile and after 10 minutes, Lars started running along the same route, at a constant pace of 7 minutes per mile. We need to find the number of minutes Lars will take to reach Gavin.

In 9 minutes, distance run by Gavin = 1 mile.

So, in 1 minute, distance travelled by Gavin will be

d_G=\dfrac{1}{9}=\dfrac{7}{63}~\textup{miles}.

Similarly,

In 7 minutes, distance run by Lars = 1 mile.

So, in 1 minute, distance travelled by Lars will be

d_L=\dfrac{1}{7}=\dfrac{9}{63}~\textup{miles}.

Now, since Lars started after 10 minutes, so distance run by Gavin in those 10 minutes will be

d_{G10}=\dfrac{10}{9}=\dfrac{70}{63}~\textup{miles}.

Now, difference between Lars and Gavin's rate of runnings is

\dfrac{9}{63}-\dfrac{7}{63}=\dfrac{2}{63}.

Therefore, the time taken by Lars to reach Gavin is given by

t=\dfrac{\frac{70}{63}}{\frac{2}{63}}=35.

Thus, the required time is 365 minutes.  


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For a segment of a radio show , a disc jockey can play 7 records . If there are 9 records to select from , in how many ways can
ale4655 [162]

Answer: 72

Step-by-step explanation:

From the question, we are informed that a disc jockey can play 7 records and that there are 9 records to select from for a particular segment of a radio show.

The number of ways that the program for the segment be arranged will be:

= 9! / 7!

= (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (7 × 6 × 5 × 4 × 3 × 2 × 1)

= 9 × 8

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6 0
3 years ago
A couple plans to have 3 children. Assuming the probability of having either a boy or a girl is 50%, what is the probability the
Stels [109]

Answer:

0.375

Step-by-step explanation:

The probability of having at least one girl out of 3 children can be calculated as;

P(1 girl, 2 boys) or P(2 girls, 1 boy) or P(3 girls)

Since the P(b) = P(g) = 1/2

Then the probability at any point in time is 1/2 * 1/2 * 1/2 = 1/8

So we have ;

1/8 + 1/8 + 1/8 = 3/8 = 0.375

4 0
3 years ago
Find area of the shaded region.
Monica [59]

Answer:

The area of the shaded region is about 38.1 square centimeters.

Step-by-step explanation:

We want to find the area of the shaded region.

To do so, we can first find the area of the sector and then subtract the area of the triangle from the sector.

The given circle has a radius of 6 cm.

And the given sector has a central angle of 150°.

The area for a sector is given by the formula:

\displaystyle A=\pi r^2\cdot \frac{\theta}{360^\circ}

In this case, r = 6 and θ = 150°. Hence, the area of the sector is:

\displaystyle \begin{aligned}A&=\pi(6)^2\cdot \frac{150}{360}\\ &=36\pi\cdot \frac{5}{12}\\&=3\pi \cdot 5\\&=15\pi \text{ cm}^2\end{aligned}

Now, we can find the area of the triangle. We can use an alternative formula:

\displaystyle A=\frac{1}{2}ab\sin(C)

Where a and b are the side lengths, and C is the angle between them.

Both side lengths of the triangle are the radii of the circle. So, both side lengths are 6.

And the angle C is 150°. Hence, the area of the triangle is:

\displaystyle A=\frac{1}{2}(6)(6)\sin(150)=18\sin(150)

The area of the shaded region is equivalent to the sector minus the triangle:

A_{\text{shaded}}=A_{\text{sector}}-A_{\text{triangle}}

Therefore:

A_{\text{shaded}}=15\pi -18\sin(150)

Use a calculator:

A_{\text{shaded}}=38.1238...\approx 38.1\text{ cm}^2

The area of the shaded region is about 38.1 square centimeters.

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3 years ago
Suppose the solutions of a homogeneous system of four linear equations in five unknowns are all multiples of one nonzero solutio
Akimi4 [234]

Consider a homogeneous machine of four linear equations in five unknowns are all multiples of 1 non-0 solution. Objective is to give an explanation for the gadget have an answer for each viable preference of constants on the proper facets of the equations.

Yes, it's miles true.

Consider the machine as Ax = 0. in which A is 4x5 matrix.

From given dim Nul A=1. Since, the rank theorem states that

The dimensions of the column space and the row space of a mxn matrix A are equal. This not unusual size, the rank of matrix A, additionally equals the number of pivot positions in A and satisfies the equation

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dim NulA =n- rank A

Rank A = 5 - dim Nul A

Rank A = 4

Thus, the measurement of dim Col A = rank A = five

And since Col A is a subspace of R^4, Col A = R^4.

So, every vector b in R^4 also in Col A, and Ax = b, has an answer for all b. Hence, the structures have an answer for every viable preference of constants on the right aspects of the equations.

8 0
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