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3 years ago

Please help @Nopinkiepie and @Oretummy

Mathematics

1 answer:

zubka84 [21]3 years ago

3 0

Easy peasy
the fastest way is to pretend we have 1 big rectangle with 2 smaller rectangles cut out
see attachment

the big one is 12 by 7
the smaller ones are 5 by6 and 5 by 6

big-smaller=area
big=12*7=84
smaller=5*6+5*6=30+30=60

big-smaller=84-60=24

answer is 24 in²

first choice

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Find the magnitude of the net electric field at the origin (created by charges q1 and q2).

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The direction of the net magnetic field is $167.36^{\circ}$

<h3>How to find the magnitude?</h3>

$q_1=-4 \mathrm{nC} \text { at }(0.6,0.8)$

$q_2=6 \mathrm{nC}$ at (0.6,0)

$r_1=$ Distance of $q_1$ from origin $=\sqrt{0.6^2+0.8^2}$

$r_2=$ Distance of $q_2$ from origin $=0.6$

$\mathrm{k}=$ Coulomb constant $$=9$ times $10^9 \mathrm{Nm}^2 / \mathrm{C}^2$$

Electric field is given by

$&E_1=\frac{k q_1}{r_1^2} \\$

$&\Rightarrow E_1=\frac{9 \times 10^9 \times 4 \times 10^{-9}}{\sqrt{0.6^2+0.8^2}} \\$

$&\Rightarrow E_1=36 \mathrm{~N} / \mathrm{C}$

$&\theta=\tan ^{-1} \frac{0.8}{0.6} \\$

$&\Rightarrow \theta=53.13^{\circ} \\$

$&E_1=36 \cos 53.13^{\circ} \hat{i}+36 \sin 53.13^{\circ} \hat{j} \\$

$&\Rightarrow E_1=21.6 \hat{i}+28.8 \hat{j}$

$&E_2=\frac{k q_2}{r_2^2} \\$

$&\Rightarrow E_2=\frac{9 \times 10^9 \times 6 \times 10^{-9}}{0.6^2} \\$

$&\Rightarrow E_2=150 \mathrm{~N} / \mathrm{C}$

The charge $q_2$ is on the $\mathrm{x}$ axis itself and it is pointing towards the origin (left side) so the sign will be negative

$E_2=-150 \hat{i}$

Resultant electric field

$&E=E_1+E_2 \\$

$&\Rightarrow E=21.6 \hat{i}+28.8 \hat{j}+(-150 \hat{i}) \\$

$&\Rightarrow E=-128.4 \hat{i}+28.8 \hat{j}$

Magnitude of electric field is given by

$&|E|=\sqrt{(-128.4)^2+28.8^2} \\$

$&\Rightarrow|E|=121.6 \mathrm{~N} / \mathrm{C}$

Magnitude of the net electric field is $121.6 \mathrm{~N} / \mathrm{C}$

Direction is given by

$\theta=\tan ^{-1} \frac{128.4}{28.8}=77.36^{\circ}$

From the -x axis

$(90+77.36)^{\circ}=167.36^{\circ}$

The direction of the net magnetic field is $167.36^{\circ}$

To learn more about magnetic field, refer to:

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2 years ago

A certain type of automobile battery is known to last an average of 1140 days with a standard deviation of 80 days. If 400 of th

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Answer:

Mean = $\mu = 1140$

Standard deviation = $\sigma = 80$

Find the probabilities for the average length of life of the selected batteries.

A)The average is between 1128 and 1140.

We are supposed to fidn P(1128<x<1140)

Formula : $Z=\frac{x-\mu}{\sigma}$

At x = 1128

$Z=\frac{1128-1140}{80}$

$Z=-0.15$

Refer the z table for p value

P(x<1128)=0.4404

At x = 1140

$Z=\frac{1140-1140}{80}$

$Z=0$

Refer the z table for p value

P(x<1140)=0.5

So,P(1128<x<1140)=P(x<1140)-P(x<1128)=0.5-0.4404=0.0596

Hence the probabilities for the average length of life of the selected batteries is between 1128 and 1140 is 0.0596

B)The average is greater than 1152.

P(x>1152)

At x = 1128

$Z=\frac{1152-1140}{80}$

$Z=0.15$

Refer the z table for p value

P(x<1152)=0.5596

So,P(x>1152)=1-P(x<1152)=1-0.5596=0.4404

Hence the probabilities for the average length of life of the selected batteries is greater than 1152 is 0.4404

C) The average is less than 940.

P(x<940)

At x = 940

$Z=\frac{940-1140}{80}$

$Z=-2.5$

Refer the z table for p value

P(x<940)=0.5596

Hence the probabilities for the average length of life of the selected batteries is less than 940 is 0.5596

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3 years ago

The conditional relative frequency table below was generated by column using data comparing gender and a person's favorite meal

Triss [41]

The answer is C.

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4 years ago

Read 2 more answers

What is the probability that he will hit fewer than 8 of the bottles?

torisob [31]

Using the binomial distribution, it is found that the probability that he will hit fewer than 8 of the bottles is of 0.012, given by option A.

<h3>What is the binomial distribution formula?</h3>

The formula is:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem, we have that:

The probability of a bottle being hit is of p = 0.95.

There are n = 10 bottles.

The probability that he hits fewer than 8 of the bottles is given by:

$P(X < 8) = 1 - P(X \geq 8)$

In which:

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)$

Then:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 8) = C_{10,8}.(0.95)^{8}.(0.05)^{2} = 0.0746$

$P(X = 9) = C_{10,9}.(0.95)^{9}.(0.05)^{1} = 0.3151$

$P(X = 10) = C_{10,10}.(0.95)^{10}.(0.05)^{0} = 0.5987$

Hence:

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.0746 + 0.3151 + 0.5987 = 0.988$

$P(X < 8) = 1 - P(X \geq 8) = 0.012$

The probability that he will hit fewer than 8 of the bottles is of 0.012, given by option A.

More can be learned about binomial distribution at brainly.com/question/24863377

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2 years ago

Consider the polynomial 2x5 + 4x3 - 3x8

almond37 [142]

Answer:

Step-by-step explanation:

Considering the polynomial 2x⁵ + 4x³ - 3x⁸. The polynomial is not yet in standard form. For a polynomial to be in standard form, the power of the variables must decrease as we progress to the right of the expression.

A) The polynomial in standard form is therefore<u> - 3x⁸ + 2x⁵ + 4x³</u>. <em>We can see that the power are reducing as we move through each terms i.e from 8 to 5 then to 3.</em>

<em />

B) The degree of a polynomial is the maximum degree among all the terms of the polynomial. The term that has the maximum degree is -3x⁸. Hence, the degree of the polynomial is 8

C) There are only 3 terms in the polynomial given. The terms are separated by mathematical signs. The terms if the polynomial are 2x⁵, 4x³ and - 3x⁸.

D) The leading term of the polynomial is the term that comes first after rewriting the polynomial in standard format. Given the standard from of the polynomial given as -3x⁸ + 2x⁵ + 4x³, the leading term will be - 3x⁸

E) Given the leading term to be - 3x⁸, the leading coefficient of the polynomial will be the coefficient of the leading term. The coefficient of -3x⁸ is -3

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3 years ago