8.<br> x Х<br> -1<br> 0<br> 1<br> 2<br> -2<br> -1<br> о<br> у<br> 1<br> 1

One terameter equals 1012 meters. One micrometer equals 10 meter.

Butoxors [25]

Answer:

<h2>a) 10⁶metres</h2><h2>b) 10¹⁸metres</h2>

Step-by-step explanation:

Given One terameter equals 10¹² meters. One micrometer equals 10⁻⁶ meter, one nanometer equals 10⁻⁹meter;

a) The product of one terameter and one micrometer will be expressed as;

10¹² * 10⁻⁶

Since the both have the same base, we will add their power according to one of the law in indices as shown

10¹² * 10⁻⁶ = 10⁻⁶⁺¹²

= 10⁶metres

b) The quotient of one terameter and one micrometer can be gotten by taking their ratio as shown below;

Note that when taking the quotient, the power are subtracted

$= \frac{10^{12} }{10^{-6} } \\= 10^{12-(-6)} \\= 10^{12+6} \\= 10^{18}metres$

3 0

3 years ago

A box contains 24 transistors,4 of which are defective. If 4 are sold at random,find the following probabilities. i. Exactly 2 a

zavuch27 [327]

SOLUTION

This is a binomial probability. For i, we will apply the Binomial probability formula

i. Exactly 2 are defective

Using the formula, we have

$\begin{gathered} P_x=^nC_x\left(p^x\right?\left(q^{n-x}\right) \\ Where\text{ } \\ P_x=binomial\text{ probability} \\ x=number\text{ of times for a specific outcome with n trials =2} \\ p=\text{ probability of success = }\frac{4}{24}=\frac{1}{6} \\ q=probability\text{ of failure =1-}\frac{1}{6}=\frac{5}{6} \\ ^nC_x=\text{ number of combinations = }^4C_2 \\ n=\text{ number of trials = 4} \end{gathered}$

Note that I made the probability of being defective as the probability of success = p

and probability of none defective as probability of failure = q

Exactly 2 are defective becomes the binomial probability

$\begin{gathered} P_x=^4C_2\times\lparen\frac{1}{6})^2\times\lparen\frac{5}{6})^{4-2} \\ P_x=6\times\frac{1}{36}\times\frac{25}{36} \\ P_x=\frac{25}{216} \\ =0.1157 \end{gathered}$

Hence the answer is 0.1157

(ii) None is defective becomes

$\begin{gathered} \lparen\frac{5}{6})^4=\frac{625}{1296} \\ =0.4823 \end{gathered}$

hence the answer is 0.4823

(iii) All are defective

$\begin{gathered} \lparen\frac{1}{6})^4=\frac{1}{1296} \\ =0.00077 \end{gathered}$

(iv) At least one is defective

This is 1 - probability that none is defective

$\begin{gathered} 1-\lparen\frac{5}{6})^4 \\ =1-\frac{625}{1296} \\ =\frac{671}{1296} \\ =0.5177 \end{gathered}$

Hence the answer is 0.5177

3 0

8 months ago

Add.<br><br> (6x3+3x2−2)+(x3−5x2−3)<br><br> Express the answer in standard form.

sergiy2304 [10]

Answer:

$7x^3-2x^2-5$

Step-by-step explanation:

We need to add the two terms.

$(6x^3+3x^2-2)+(x^3-5x^2-3)$

Solving,

Combine the like terms and adding those terms

$(6x^3+3x^2-2)+(x^3-5x^2-3)\\=6x^3+3x^2-2+x^3-5x^2-3\\=6x^3+x^3+3x^2-5x^2-2-3\\=7x^3-2x^2-5$

So, the answer is:

$7x^3-2x^2-5$

6 0

3 years ago

Can someone please help me with this?

jonny [76]

I need to know if you where are you gonna is the day you

4 0

3 years ago

Humberto evaluates the expression 4t2 for t=3. He correctly substitutes 3 for t in the expression, but then says that the value

AveGali [126]

Answer:

36

Step-by-step explanation:

He multiplied the four and the three first when he multiplied the equation together. However, according to the order of the operations, he was supposed to square three first. 3^2 = 9. Then multiplied 9*4 = 36.

4 0

2 years ago

8. x Х -1 0 1 2 -2 -1 о у 1 1