One kilogram is approximately 2.2 pounds. Write a direct variation equation that relates x kilograms to y pounds.

A wire was bent into the shape of a rectangle with width 5 and length 7 . If this wire

Flauer [41]

Answer:

6

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Help please. Give the slope of y - 3 = 4(x + 8) and a point on the line

Sauron [17]

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Make y the subject :
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y - 3 = 4(x + 8)
y - 3 = 4x + 32 // Apply distributive property
y = 4x + 35 // Add 3 to both sides

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Identify Slope :
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Slope = 4

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Find a point on the line :
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When x = 0,
y = 4(0) + 35 // Sub x = 0 into the equation
y = 35 // Combine like terms
Point = (0, 35)

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Answers :
(a) Slope = 4
(b) One point on the line is (0, 35)
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4 0

4 years ago

Find a function that describes the sequence. Use y for the term in the sequence and n for its place in the list. Then use the fu

sammy [17]

B. y=n+20; 25,26,27 because if you plug in 1 into the equation it equals 21. 2+20=22, etc. so to find the next three terms of the equation plug in 5: y=5+20=25; plug in 6: y=6+20=26; and plug in 7: y=7+20=27

6 0

3 years ago

The population of the world grows exponentially at a rate of 1.1% per year.

natima [27]

Answer:

4

Step-by-step explanation:

Every year, the world grows by 1.1%. Converting to a decimal, we can divide by 100 to get 1.1% = 0.011. This means that the world grows by 0.011 exponentially each year. To put this into an expression, we can add 1 to our percentage to get 1.011. This represents 1 = 100% (the original population) and the growth of 1.1% = 0.011. We multiply the rate including the growth by the population to get the population after one year. After the first year, we have

population * 1.011 as the new population after one year. We do that for every year, so the second year's population is population*(1.011)*(1.011) and so on. If x represents the amount of years, then the population can be represented as

(original population)*1.011ˣ

Therefore, to get from 7 billion to 7.31 billion, we have

7 billion * 1.011ˣ = 7.31 billion

divide both sides by 7 billion to relatively isolate the x

1.011ˣ = 7.31/7

Another way of writing this is

log (base 1.011) (7.31/7) = x

≈ 3.96

Rounding to the nearest whole number, we get 4 as our answer

7 0

3 years ago

Suppose that 44% of all Americans approve of the job the President is doing. The most recent Gallup poll consisted of a random s

Novay_Z [31]

Since the possible outcomes of the poll are only two, approve or not, we are dealing with a binomial distribution, where:
n = 1400
p = 44% = 0.44

A) The mean of the sampling distribution is μ = 616
The mean of a binomial distribution can be calculated by the formula:
μ = n · p
 = 1400 · 0.44
 = 616

B) The standard deviation of the sampling distribution is σ = 18.6
The standard deviation of a binomial distribution can be calculated by the formula:
σ = √[n · p · (1 - p)]
 = √[1400 · 0.44 · (1 - 0.44)]
 = √344.96
 = 18.6

C) The normal approximation is N(616, 18.6)

In order to normally approximate a binomial distribution, two conditions must be satisfied:
n · p ≥ 10
n · p · (1 - p) ≥ 10

In our case,
n · p = 616 > 10
n · p · (1 - p) = 344.96 > 10

Since the two conditions are satisfied, the binomial distribution B(n, p) can be approximated with a normal distribution N(μ, σ).
In our case:
B(1400, 0.44) ≈ N(616, 18.6)

D) The probability that the Gallup poll will come up with a proportion within three percentage points of the true 44% is P = 0.98 or 98%

We need to apply the continuity correction to our normal approximation:
P(Y = 0.44) = P(0.44 - 0.03 ≤ Y ≤ 0.44 + 0.03)
= P(0.41 ≤ Y ≤ 0.47)

In order to calculate this probability, we need to calculate mean and standard deviation of the sample proportion:
$\hat{p} = p = 0.44$

$\sigma = \sqrt{ \frac{p(1-p)}{n} } \\ = \sqrt{ \frac{0.44(1-0.44)}{1400} } \\ = 0.013$

Now, we need to calculate the z-score for each Y-value:
z = (Y - p) / σ

z(Y = 0.41) = (0.41 - 0.44) / 0.013 = -2.31
z(Y = 0.47) = (0.47 - 0.44) / 0.013 = 2.31

Therefore, we can say that
P(0.41 ≤ Y ≤ 0.47) = P(-2.31 ≤ z ≤ 2.31)
= P(z ≤ 2.31) - P(z ≤ -2.31)

Looking at a normal standard distribution table, we find
P(z ≤ -2.31) = 0.0104
P(z ≤ 2.31) = 0.9896

Therefore:
P(0.41 ≤ Y ≤ 0.47) = 0.9896 - 0.0104
= 0.9792

Hence, the probability of the poll coming up with a proportion within three percent of the true mean is 0.98 which means 98%

6 0

3 years ago