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frozen [14]
2 years ago
5

What is the value of x in the figure below? In this diagram, ABD ~ CAD.

Mathematics
1 answer:
swat322 years ago
5 0

Answer:

\sqrt{30}

Step-by-step explanation:

altitude rule

10 / x = x / 3

x^2 = 30

x = sqrt(30)

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A deli sells meat and cheese by the pound. The expression 7.99m + 5.99c represents the total cost of m pounds of mest and c poun
LenaWriter [7]
Statement A is correct.

7.99m is the unit rate for how much you will pay for each pound of meat.

5.99c is the unit rate for how much you will pay for each pound of cheese.
6 0
3 years ago
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The time intervals between successive barges passing a certain point on a busy waterway have an exponential distribution with me
lisov135 [29]

Answer:

a) <u>0.4647</u>

b) <u>24.6 secs</u>

Step-by-step explanation:

Let T be interval between two successive barges

t(t) = λe^λt where t > 0

The mean of the exponential

E(T) = 1/λ

E(T) = 8

1/λ = 8

λ = 1/8

∴ t(t) = 1/8×e^-t/8   [ t > 0]

Now the probability we need

p[T<5] = ₀∫⁵ t(t) dt

=₀∫⁵ 1/8×e^-t/8 dt

= 1/8 ₀∫⁵ e^-t/8 dt

= 1/8 [ (e^-t/8) / -1/8 ]₀⁵

= - [ e^-t/8]₀⁵

= - [ e^-5/8 - 1 ]

= 1 - e^-5/8 = <u>0.4647</u>

Therefore the probability that the time interval between two successive barges is less than 5 minutes is <u>0.4647</u>

<u></u>

b)

Now we find t such that;

p[T>t] = 0.95

so

t_∫¹⁰ t(x) dx = 0.95

t_∫¹⁰ 1/8×e^-x/8 = 0.95

1/8 t_∫¹⁰ e^-x/8 dx = 0.95

1/8 [( e^-x/8 ) / - 1/8 ]¹⁰_t  = 0.95

- [ e^-x/8]¹⁰_t = 0.96

- [ 0 - e^-t/8 ] = 0.95

e^-t/8 = 0.95

take log of both sides

log (e^-t/8) = log (0.95)

-t/8 = In(0.95)

-t/8 = -0.0513

t = 8 × 0.0513

t = 0.4104 (min)

so we convert to seconds

t = 0.4104 × 60

t = <u>24.6 secs</u>

Therefore the time interval t such that we can be 95% sure that the time interval between two successive barges will be greater than t is <u>24.6 secs</u>

6 0
3 years ago
Please solve very urgent
Snezhnost [94]

Step-by-step explanation:

Can't see the picture very So can you updated

3 0
2 years ago
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100 POINTS PLEASE BRAINIEST IF CORRECT!!!!!!<br> What is the slope of this graph?
Viefleur [7K]

Step-by-step explanation:

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4 0
3 years ago
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A group of naturalists catch, tag and release 121 trout into a lake. The next day they catch and release 48 trout, of which 22 h
RideAnS [48]

Answer:

264.

Step-by-step explanation:

Let x represent the number of trout in the lake.

We have been given that a group of naturalists catch, tag and release 121 trout into a lake. The next day they catch and release 48 trout, of which 22 had been tagged.

Using proportions, we will get:

\frac{\text{Total trouts}}{\text{Tagged trouts}}=\frac{48}{22}

\frac{x}{121}=\frac{48}{22}

\frac{x}{121}*121=\frac{48}{22}*121

x=\frac{24}{11}*121

x=24*11

x=264

Therefore, there would be approximately 264 trout in the lake.

8 0
3 years ago
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