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2 years ago

What number must be added to the sequence of 7,13 and 10 to get an average of 13

Mathematics

1 answer:

Anna71 [15]2 years ago

7 0

Answer:

Step-by-step explanation:

We can write an equation:

(7+13+10+x)/4=13

x represents the number that needs to be added to get an average of

(7+13+10+x)/4=13

(30+x)/4=13

30+x=52

x=22

The number is 22

Hope this helps! Have a wonderful day :)

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9. Gold miners in Alaska have found, on average, 12 ounces of gold per 1000 tons of dirt excavated with a standard deviation of

netineya [11]

Answer:

9.18% probability the miners find more than 16 ounces of gold in the next 1000 tons of dirt excavated

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 12, \sigma = 3$

What is the probability the miners find more than 16 ounces of gold in the next 1000 tons of dirt excavated?

This is 1 subtracted by the pvalue of Z when X = 16. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{16 - 12}{3}$

$Z = 1.33$

$Z = 1.33$ has a pvalue of 0.9082

1 - 0.9082 = 0.0918

9.18% probability the miners find more than 16 ounces of gold in the next 1000 tons of dirt excavated

5 0

2 years ago

PLEASE HELP!! ASAP!!! 20 POINTS. David proved the Law of Cosines with reference to triangle abc using a different method.Arrange

sleet_krkn [62]

Answer:

Top-to-bottom, the boxes have this order in the proof: 1, 7, 4, 3, 9, 8, 5, 2, 6.

Step-by-step explanation:

The basic idea is to use the Pythagorean theorem to write two expressions for the length of altitude BD, also called "k", then equate them and simplify the result. This leaves an expression for DC, also called "x", which is replaced by a cosine expression to complete the proof.

Finally, the variations involving other combinations of sides and angles are suggested as being provable in the same way.

3 0

2 years ago

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Rachel is bowling with her friends. her bowling ball has a radius of 4 inches. as she bowls she tracks the location of the finge

Goshia [24]

Question Continuation

The finger hole changes by 45 degrees.

Define a function, f, that gives the height of the finger hole above the ground (in inches) in terms of the angle of rotation (measured in radians) it has swept out from the 12 o'clock position.

Answer:

f(θ) = r(1 + cos(θ)) for 0 ≤ θ ≤ π/4

Step-by-step explanation:

Given

Let represent radius

r = 4 inches

Considering that she starts tracking the location when the finger hole is at the 12 o'clock; this means that the angle measurement at this point is 0°.

Let θ represent the angle

At 12 o'clock mark

θ = 0

When the finger hole changes by 45 degrees

θ = 45°

Convert 45° to radians

θ = 45° * π/180

θ = π/4

So, angle θ is such that θ∈[0, π/4]

This can be represented as

0 ≤ θ ≤ π/4

Calculating the measure of f(θ) in polar coordinates

When θ = 0, f(θ) = r (i.e. the current position of the bowl)

When θ = π/2, f(θ) = rcosθ

This is so because f(θ), being the function of the height is a measure of the radius* cos(θ)

Taking measurement of f(θ) from 0 to π/2

f(θ) = r + rcosθ

f(θ) = r(1 + cos(θ))

So, f(θ) = r(1 + cos(θ)) for 0 ≤ θ ≤ π/4

7 0

2 years ago

David drove a distance (d) of 187 km, correct to 3 significant figures.

Bogdan [553]

Answer: 6.68km/litre

Step-by-step explanation:

Distance(d) = 187km ( to 3 significant figures)

Petrol(p) = 28litres ( to 2 significant figures)

A number, x, rounded to 1 significant figure is 200

Write down the error interval for x

Calculating the lower and upper bound for both 'd' and 'p'

Upper bound 'd' = 187.5km

Lower bound 'd' = 186.5km

Upper bound 'p' = 28.5km

Lower bound 'p' = 27.5km

Therefore,

Petrol consumption (C) = d/p

Upper C = 187.5 / 28.5 = 6.57894

Lower C = 186.5 / 27.5 = 6.781818

Accuracy answer for C = (6.57894 + 6.781818) / 2 = 6.680379

= 6.68km/ litre ( to 3 significant figures)

To achieve a reasonable level of accuracy, the upper and lower bounds of P and D was used to calculate C, which was then averaged.

Using 3 significant figures ensure that we capture the C better, instead of early rounding.

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2 years ago

I am factor of 12. The other factor is 3. What number am I

Goryan [66]

12*3= 36

12 and 3 could be factors of 36.

I hope this helped you! <3

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2 years ago

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