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3 years ago

Which expression is equivalent -21.8-(-18.3)

Mathematics

2 answers:

navik [9.2K]3 years ago

3 0

<span> -21.8-(-18.3) (2 negative signs become positive)
=</span><span> -21.8 + 18.3
= - 3.5

Answer
- 3.5</span>

makkiz [27]3 years ago

3 0

Answer:

Step-by-step explanation:

The given expression is

$-21.8-(-18.3)$

To find a equivalent expression to the given one, we have to first eliminate the parenthesis by multiplying the negative sign with the number inside

$-21.8+18.3$

Now we eliminated the parenthesis, we have to subtract these numbers, because they have different signs, the result will be negative because they major absolute value is in the negative number

$-21.8+18.3=-3.5$

Therefore, the given expression is equal to -3.5

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An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 110 engines

slava [35]

Answer:

we will fail to reject the null hypothesis and conclude that the mean pressure is not different from 4.7 psi

Step-by-step explanation:

Let's first define the hypothesis;

Null hypothesis: H0: μ = 4.7

Alternative hypothesis: Ha: μ ≠ 4.7

We have;

Sample size; n = 110

Sample mean; x¯ = 4.6

Variance: σ² = 0.64

Standard deviation; σ = √0.64 = 0.8

Formula for test statistic is;

z = (x¯ - μ)/(σ/√n)

z = (4.6 - 4.7)/(0.8/√110)

z = -0.1/0.0763

z = -1.31

From online p-value from z-score calculator attached, using; z = -1.31, two tailed hypothesis, significance value of 0.1, we have;

P-value = 0.190196

The p-value is greater than the significance value and thus we will fail to reject the null hypothesis and conclude that the mean pressure is not different from 4.7

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3 years ago

Suppose x is a real number and epsilon > 0. Prove that (x - epsilon, x epsilon) is a neighborhood of each of its members; in

kaheart [24]

Answer:

See proof below

Step-by-step explanation:

We will use properties of inequalities during the proof.

Let $y\in (x-\epsilon,x+\epsilon)$ . then we have that $x-\epsilon$ . Hence, it makes sense to define the positive number delta as $\delta=\min\{x+\epsilon-y,y-(x-\epsilon)\}$ (the inequality guarantees that these numbers are positive).

Intuitively, delta is the shortest distance from y to the endpoints of the interval. Now, we claim that $(y-\delta,y+\delta)\subseteq (x-\epsilon,x+\epsilon)$ , and if we prove this, we are done. To prove it, let $z\in (y-\delta,y+\delta)$ , then $y-\delta$ . First, $\delta \leq y-(x-\epsilon)$ then $-\delta \geq -y+x-\epsilon$ hence $z>y-\delta \geq x-\epsilon$

On the other hand, $\delta \leq x+\epsilon-y$ then $z$ hence $z$ . Combining the inequalities, we have that $x-\epsilon$ , therefore $(y-\delta,y+\delta)\subseteq (x-\epsilon,x+\epsilon)$ as required.