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Morgarella [4.7K]

3 years ago

12

While completing a race, Will spent 14 minutes walking. If his ratio of time walking to jogging was 7 : 6, how many minutes did

he spend completing the race?

1 answer:

worty [1.4K]3 years ago

8 0

Answer:

12 minutes

Step-by-step explanation:

$\frac{7}{6} =\frac{14}{x}$

$7x=84$

$x=12$

So, he spent 12 minutes jogging.

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A hair salon completed a survey of 367 customers about satisfaction with service(Dissatisfied, Neutral, Satisfied, or Very Satis

mamaluj [8]

The results of the survey are shown in the table.

It's required to calculate the following probabilities:

a) A customer is neutral

The row labeled as 'Neutral' has a total of 79 customers out of 367 in total.

The required probability is:

$p=\frac{79}{367}$

b) A customer is a walk-in

The first column labeled as 'Walk-in' has a total of 106 customers out of 367. The required probability is

$p=\frac{106}{367}$

c) A customer is dissatisfied and a walk-in.

We have to cross the row Dissatisfied with the column Walk-in. The number of customers that have both categories is 22 out of 367.

The required probability is:

$p=\frac{22}{367}$

d) A customer is very satisfied given he saw a TV ad.

This is a conditional probability, where the total is 111 because is the given condition. The customers that have both characteristics are 33, thus the required probability is:

$p=\frac{33}{111}=\frac{11}{37}$

e) A customer is satisfied or referred.

Total satisfied = 139

Total referred = 150

With both features = 62

Total customers with one or both features: 139 + 150 - 62 = 227

We have to subtract the common feature because it was counted twice.

The required probability is:

$p=\frac{227}{367}$

6 0

1 year ago

If the given values in a right triangle are cos A =

Vlad1618 [11]

See the picture attached to better understand the problem

we know that
in the right triangle ABC
cos A=AC/AB
cos A=1/3
so
1/3=AC/AB----->AB=3*AC-----> square----> AB²=9*AC²----> equation 1

applying the Pythagoras Theorem
BC²+AC²=AB²-----> 2²+AC²=AB²---> 4+AC²=AB²----> equation 2

substitute equation 1 in equation 2
4+AC²=9*AC²----> 8*AC²=4----> AC²=1/2----> AC=√2/2
so
AB²=9*AC²----> AB²=9*(√2/2)²----> AB=(3√2)/2

the answer is
the hypotenuse is (3√2)/2

5 0

3 years ago

If a translation takes triangle CAT to C'A'T', what is A'T'?

Marina86 [1]

Answer:

square root of 10

Step-by-step explanation:

since triangle CAT with vertex A at negative 2 comma 1, vertex T at negative 1 comma 4 and vertex C at 0 comma 0, side AT has a measure of square root of 10 units, side TC has a measure of square root of 17 units, and side AC has a measure of square root of 5 units, therefore the square root will be 10

7 0

3 years ago

Use Gauss's approach to find the following sums (do not use formulas). 1+3+5+7+...999

muminat

$S=1+3+5+\cdots+995+997+999$
$S=999+997+995+\cdots+5+3+1$
$\implies 2S=(1+999)+(3+997)+(5+995)+\cdots+(995+5)+(997+3)+(999+1)$

$2S=\underbrace{1000+1000+\cdots+1000+1000}_{500\text{ times}}$

(We are adding 500 instances of 1000 because that's how many odd numbers there are between 1 and 1000, inclusive.)

$2S=500\times1000=500000$
$\implies S=250000$

4 0

3 years ago

vladimir2022 [97]

(2x + 3y = 12) x (-2)
(4x - 3y = 6) x 1

-4x - 6y = -24
4x - 3y = 6

You can cancel out the x values by adding the two equations together.
(-4x + 4x) + (-6y - 3y) = (-24 + 6)
-9y = -18
y = 2

Solve for x now...
4x - 3(2) = 6
4x - 6 = 6
4x = 12
x = 3

Check... (x = 3, y = 2)
2(3) + 3(2) = 12
6 + 6 = 12
12 = 12 <- this works!

4(3) - 3(2) = 6
12 - 6 = 6
6 = 6 <- this works!

5 0

3 years ago

Read 2 more answers