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2 years ago

Factorise 4b^2 + 16b

1 answer:

5 0

Factorise 4b² + 16b ⇒ 4b(b+4)

expand (a-1)(a-2) ⇒ a(a-2) - 1(a-2) ⇒ a² - 2a - 1a + 2 ⇒a² - 3a + 2

factorise x² + 8x + 7 ⇒(x + 1) (x + 7)

evaluate y⁶ / y² ⇒ y * y * y * y * y * y / y * y = y⁴

if x = -1 and y = 5, find z when z = x² + 2y² ;
z = -1² + 2(5²) ⇒ 1 + 2(25) ⇒1 + 50 = 51

Make x the subject: y = 4x - 3
y = 4x - 3
+3 +3
3 + y = 4x
÷4 ÷4 
(3+y)/4 = x

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Devy likes to learn! Could someone please tell me how to answer this question?

Ronch [10]

Answer:

Step-by-step explanation:

Recall that if two functions, f and g, are inverses, then by definition:

$\displaystyle f(g(x)) = g(f(x)) = x$

Hence, the graph of f(g(x)) should be simply y = x.

Therefore, our answer is B, as both coordinates are equivalent for all three points.

4 0

3 years ago

A ski lift is designed with a total load limit of 20,000 pounds. It claims a capacity of 100 persons. An expert in ski lifts thi

Yanka [14]

Answer:

0.5 = 50% probability that a random sample of 100 independent persons will cause an overload

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the sum of n values of a distribution, the mean is $\mu \times n$ and the standard deviation is $\sigma\sqrt{n}$

An expert in ski lifts thinks that the weights of individuals using the lift have expected weight of 200 pounds and standard deviation of 30 pounds. 100 individuals.

This means that $\mu = 200*100 = 20000, \sigma = 30\sqrt{100} = 300$

If the expert is right, what is the probability that a random sample of 100 independent persons will cause an overload

Total load of more than 20,000 pounds, which is 1 subtracted by the pvalue of Z when X = 20000. So

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

$Z = \frac{20000 - 20000}{300}$

$Z = 0$

$Z = 0$ has a pvalue of 0.5

1 - 0.5 = 0.5

0.5 = 50% probability that a random sample of 100 independent persons will cause an overload

5 0

3 years ago

Graph the following equations - y = 2 x - 1

zalisa [80]

Answer:

f(x)= 1 - 2x

Step-by-step explanation:

7 0

3 years ago

What is the answer to 8(6+4×)=-176

taurus [48]

Answer:

Step-by-step explanation:

48+32x=-176

32x=224

x=7

3 0

3 years ago

What is a formula for the nth term of the given sequence? 15,75,375

spin [16.1K]

Answer:

3 × 5 ^ n

Step-by-step explanation:

since the series is exponential, the ratio between adjacent terms is 5.

nth term of geometric/exponential series is given by:

nth term = first term × (ratio)^(n-1)

= 15 × 5^ (n-1)

= 15 × 5^n × 5^-1

= 3× 5^n

7 0

2 years ago