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baherus [9]
3 years ago
12

Josie is training for a race. The ratio of the number of minutes she runs to the number of miles she runs is 24 to 3. She plans

to run 10 miles. How many minutes will it take her.
Mathematics
2 answers:
Elanso [62]3 years ago
4 0

Answer:

Step-by-step explanation:

if 3 miles = 24 minutes, then 1 mile = 24/3 = 8 minutes

therefore 10 miles = 8 x 10 = 80 minutes

ELEN [110]3 years ago
4 0

Answer:

80

Step-by-step explanation:

The ratio can be simplified and rewritten:

minutes : miles = 24 : 3 = 8 : 1 = 80 : 10

It will take Josie 80 minutes to run 10 miles at her 8 minutes/mile pace.

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Let X = the number of nonzero digits in a randomly selected 4-digit PIN that has no restriction on the digits. What are the poss
NISA [10]

Answer:

X = {0, 1, 2, 3, 4}

Step-by-step explanation:

If X is the number of nonzero digits in a 4-digit PIN with no restriction on the digits, the pin can have up to 4 nonzero digits.

Let's see some examples:

If the PIN is 0000 then X = 4

If the PIN is 2045 then X = 3

If the PIN is 7546 then X = 0

From the previous examples, we can see that the possible values for X are 0, 1, 2, 3, 4.

Thus X = {0, 1, 2, 3, 4}

4 0
3 years ago
.<br> Evaluate the series 1 + 0.1 + 0.01 + . . .
EastWind [94]

We can employ a simple repeated decimal trick:

x=1.111\ldots

0.1x=0.111\ldots

\implies x-0.1x=1\implies0.9x=1\implies x=\dfrac1{0.9}=\dfrac{10}9

###

Alternatively, we can compute the partial sum of the series.

\displaystyle S_n=\sum_{k=0}^n\dfrac1{10^k}

S_n=1+0.1+0.01+\cdots+\dfrac1{10^n}

0.1S_n=0.1+0.01+0.001+\cdots+\dfrac1{10^{n+1}}

\implies S_n-0.1S_n=0.9S_n=1-\dfrac1{10^{n+1}}

\implies S_n=\dfrac{10}9-\dfrac9{10^n}

As n\to\infty, the second term vanishes and we're left with \dfrac{10}9. Notice that this is really just a more formal version of the earlier trick.

6 0
3 years ago
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3 years ago
Who was responsible for inventing the first working four-stroke engine?<br>​
Verizon [17]

Answer:

Nikolaus Otto was  responsible for inventing the first working four-stroke engine.

​

Step-by-step explanation:

7 0
4 years ago
What is the component form of the vector whose tail is the point (-3,2) and whose head is the point (1, -6)?
Bess [88]

Answer:

  (4, -8)

Step-by-step explanation:

The components of a vector are found by subtracting the tail from the head.

__

  Head - Tail = (1, -6) -(-3, 2) = (1 -(-3), -6 -2) = (4, -8)

⇒ The component form is (4, -8), or maybe 4<em>i</em> -8<em>j</em>.

_____

<em>Additional comment</em>

There are many ways that the components of vectors can be described. The particular format you are expected to use will likely be found in your curriculum materials.

4 0
2 years ago
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