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3 years ago

Write an inequality and solve each problem.For exercises 11 and 12, interpret the solution.

Mathematics

1 answer:

kifflom [539]3 years ago

5 0

9) inequality: 4+x>13 Solution: x>9
10) x+19 ≥ 8.2 ; x≥-10.8
11) (Sorry I don’t know what the question means by “interpret”) 17+x ≤ 26; Solution: x ≤9
12) 785+x≤1500; Solution: x≤715

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A bag contains 1p, 2p and 5p coins

garri49 [273]

Answer:

160 2p coins

Step-by-step explanation:

3/8 x 640 = 240 = 1p coins

240 = 5p coins

240 + 240 = 480

640 - 480 = 160

4 0

3 years ago

Suppose the horses in a large stable have a mean weight of 1467lbs, and a standard deviation of 93lbs. What is the probability t

krok68 [10]

Answer:

0.5034 = 50.34% probability that the mean weight of the sample of horses would differ from the population mean by less than 9lbs if 49 horses are sampled at random from the stable

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 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.

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.

In this problem, we have that:

$\mu = 1467, \sigma = 93, n = 49, s = \frac{93}{\sqrt{49}} = 13.2857$

What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 9lbs if 49 horses are sampled at random from the stable?

This is the pvalue of Z when X = 1467 + 9 = 1476 subtracted by the pvalue of Z when X = 1467 - 9 = 1458.

X = 1476

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

By the Central Limit Theorem

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

$Z = \frac{1476 - 1467}{13.2857}$

$Z = 0.68$

$Z = 0.68$ has a pvalue of 0.7517

X = 1458

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

$Z = \frac{1458 - 1467}{13.2857}$

$Z = -0.68$

$Z = -0.68$ has a pvalue of 0.2483

0.7517 - 0.2483 = 0.5034

0.5034 = 50.34% probability that the mean weight of the sample of horses would differ from the population mean by less than 9lbs if 49 horses are sampled at random from the stable

5 0

3 years ago

Angelica says the tangent is the ratio of the length of the leg opposite angle A ∠ A over the length of the leg adjacent to angl

Tpy6a [65]

Based on the trigonometry ratios and the Pythagorean theorem both of them were incorrect.

Cos A = 4/5; Sin A = 3/5

<h3>What is the Trigonometry Ratios?</h3>

The Trigonometry ratios relates the length of the sides of a right triangles. They are given as:

Sine ratio, sin ∅ = opp/hyp
Cosine ratio, cos ∅ = adj/hyp
Tangent ratio, tan ∅ = opp/adj.

<h3>What is the Pythagroean Theorem?</h3>

If two sides of a right triangle are known the third side can be determined using the Pythagorean theorem, which is given as, c² = a² + b², where and b are legs, and c is the hypotenuse of the right triangle.

1. Given that tan A = 3/4, it is not necessarily true that BC MUST have a length of 3 units, and AC MUST have a length of 4 units, because:

If BC = 9 units and AC = 12 units, the it will give us the same tangent ratio as:

tan A = 9/12 = 3/4.

Therefore, Angelica's mistake is stating that BC MUST be 3 units, and AC MUST be 4 units.

2. Knowing two length of the sides of a right triangle is enough information needed to find the length of the third side using the Pythagorean theorem, so Graceilla is incorrect.

3. Find AC using the Pythagorean theorem:

AB = √(3² + 4²)

AB = 5 units.

Cos A = adj/hyp = AC/AB

Cos A = 4/5

Sin A = opp/hyp = BC/AB

Sin A = 3/5

Learn more about the trigonometry ratios on:

brainly.com/question/10417664

3 0

2 years ago

Redondear a 100,000 el numero 5,370,288