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4 years ago

10

N a division problem, the divisor is twenty times the quotient and five times the remainder. If remainder is 16, the number will

be:
Option 1 : 3360 Option 2 : 336 Option 3 : 1616 Option 4 : 20516

1 answer:

strojnjashka [21]4 years ago

6 0

The reminder: r = 16
The divisor: d = 16 * 5 = 80
The quotient : q = 80 : 20 = 4
N = d q + r
N = 80 * 4 + 16
N = 320 + 16 = 336
Verification: 336 : 80 = 4 ( r =16 )
Answer:
Option 2 : 336

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Answer: It is D

Step-by-step explanation:

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3 years ago

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at 10a.m. you consume an energy drink containing 800mg of caffeine. if the half-life of caffeine is 5.7 hours, how much caffeine

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Answer:

268 mg

Step-by-step explanation:

Let A₀ = the original amount of caffeine

The amount remaining after one half-life is ½A₀.

After two half-lives, the amount remaining is ½ ×½A₀ = (½)²A₀.

After three half-lives, the amount remaining is ½ ×(½)²A₀ = (½)³A₀.

We can write a general formula for the amount remaining:

A =A₀(½)ⁿ

where n is the number of half-lives .

n = t/t_½

Data:

A₀ = 800 mg

t₁ = 10 a.m.

t₂ = 7 p.m.

t_½ = 5.7 h

Calculations:

(a) Calculate t

t = t₂ - t₁ = 7 p.m. - 10 a.m. = 19:00 - 10:00 = 9:00 = 9.00 h

(b) Calculate n

n = 9.00/5.7 = 1.58

(b) Calculate A

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3 years ago

These are Questions/answers for #1, 2, 3, 17, 18, 19 & 20 if you can't see what it says in the picture (Please answer all qu

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Answer:

See below for answers and explanations (along with a graph for #3)

Step-by-step explanation:

<u>Problem #1</u>

Applying scalar multiplication, $-4w=-4\langle-96,-180\rangle=\langle384,720\rangle$ .

Its magnitude would be $||-4w||=\sqrt{384^2+720^2}=816$ .

Its direction would be $\displaystyle\theta=tan^{-1}\biggr(\frac{720}{384}\biggr)\approx61.927^\circ\approx62^\circ$ .

Thus, B) 816; 62° is the correct answer

<u>Problem #2</u>

Find the time it takes for the ball to cover 13ft:

$x=(24\cos48^\circ)t\\13=(24\cos48^\circ)t\\t\approx0.8095$

Find the height of the ball at the time it takes for the ball to cover 13ft:

$y=6.1+(24\sin48^\circ)t-16t^2\\y=6.1+(24\sin48^\circ)(0.8095)-16(0.8095)^2\\y\approx10.053$

Thus, A) 10.053 is the correct answer

<u>Problem #3</u>

We have $u=\langle0,-8\rangle$ and $v=\langle6,0\rangle$ as our vectors. Thus, $u+v=\langle0+6,-8+0\rangle=\langle6,-8\rangle$ . Attached below is the correct graph. You can also solve the problem visually by using the parallelogram method where the resultant vector is the diagonal of the parallelogram.

<u>Problem 4 (#7)</u>

<u /> $\displaystyle t \cdot v=(7)(-10)+(-3)(-8)=-70+24=-46$

Thus, C) -46 is the correct answer

<u>Problem 5 (#8)</u>

Find $r$ and $\theta$ :

$r=\sqrt{x^2+y^2}=\sqrt{2^2+(-8)^2}=\sqrt{4+64}=\sqrt{68}=2\sqrt{17}\approx8.246$

$\displaystyle\theta=tan^{-1}\biggr(\frac{y}{x}\biggr)=tan^{-1}\biggr(\frac{-8}{2}\biggr)\approx-75.964^\circ$

Find the true direction angle accounting for Quadrant IV:

$\theta=360^\circ-75.964^\circ=284.036^\circ$

Write the complex number in polar/trigonometric form:

$z=8.246(\cos284.036^\circ+i\sin284.036^\circ)$

Thus, C) 8.246(cos 284.036° + i sin 284.036°) is the correct answer

<u>Problem 6 (#12)</u>

Eliminate the parameter and find the rectangular equation:

$x=3t\\\frac{x}{3}=t\\ \\y=t^2+5\\y=(\frac{x}{3})^2+5\\y=\frac{x^2}{9}+5\\9y=x^2+45\\0=x^2-9y+45\\x^2-9y+45=0$

Thus, D) x^2-9y+45=0 is the correct answer

<u>Problem 7 (#13)</u>

Find the magnitude of the vector:

$||v||=\sqrt{(-77)^2+36^2}=85$

Find the true direction of the vector accounting for Quadrant II:

$\displaystyle \theta=tan^{-1}\biggr(\frac{36}{-77}\biggr)\approx-25^\circ=180^\circ-25^\circ=155^\circ$

Write the vector in trigonometric form:

$w=85\cos155^\circ i+85\sin155^\circ j$

Thus, D) w=85cos155°i+85sin155°j is the corrwect answer

<u>Problem 8 (#15)</u>

$\frac{z_1+z_2}{2}=\frac{(3-7i)+(-9-19i)}{2}=\frac{-6-26i}{2}=-3-13i=(-3,-13)$

Thus, C) (-3,-13) is the correct answer

<u>Problem 9 (#16)</u>

Treat the golf ball and wind as vectors:

$u=\langle1.3\cos140^\circ,1.3\sin140^\circ\rangle$ <-- Golf Ball

$v=\langle1.2\cos50^\circ,1.2\sin50^\circ\rangle$ <-- Wind

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$u+v=\langle1.3\cos140^\circ+1.2\cos50^\circ,1.3\sin140^\circ+1.2\sin50^\circ\rangle\approx\langle-0.225,1.755\rangle$

Find the magnitude of the resultant vector:

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Thus, B) 1.769 m/s; 97° is the correct answer

<u>Problem 10 (#17)</u>

Identify the vectors and add them:

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Find the magnitude of the resultant vector:

$||u+v+w||=\sqrt{53.062^2+(-4.367)^2}\approx53.241$

Find the true direction of the resultant vector accounting for Quadrant IV:

$\displaystyle \theta=\tan^{-1}\biggr(\frac{-4.367}{53.062}\biggr)\approx-4.705^\circ\approx-5^\circ=360^\circ-5^\circ=355^\circ$

Thus, A) 53.241, 355° is the correct answer

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We observe that $z_1=-8-6i$ and $z_2=4-4i$ , hence, $z_1+z_2=(-8-6i)+(4-4i)=-4-10i$

Thus, Q is the correct answer

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Find the dot product of the vectors:

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Find the magnitude of each vector:

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Find the angle between the two vectors:

$\displaystyle \theta=\cos^{-1}\biggr(\frac{F_1\cdot F_2}{||F_1||||F_2||}\biggr)\\ \theta=\cos^{-1}\biggr(\frac{139000000}{(1000\sqrt{193})(500\sqrt{941})}\biggr)\\\theta\approx49.282^\circ\approx49^\circ$

Thus, C) 49° is the correct answer

<u>Problem 13 (#20)</u>

Using scalar multiplication, $7v-2w=7\langle8,-3\rangle-2\langle-12,4\rangle=\langle56,-21\rangle-\langle-24,8\rangle=\langle56-(-24),-21-8\rangle=\langle80,-29\rangle=80i-29j$

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2 years ago

An online survey company wants to know if customer age is important in deciding to subscribe. The company has gathered a random

aleksley [76]

Answer:

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Step-by-step explanation:

The appropriate statistical test to adopt for the above problem is the Chisquare test.

The hypothesis :

H0 : service subscription and age are independent

H1 : service subscription and age are not independent

Observed values :

Under 18 18-34 35 and Over Total

Yes__ 120 __262 __237__ 619

No___ 41 ___103 __237 __381

Total 161 365 574 1000

χ² = (Observed - Expected)²/Expected

Expected Values:

99.659 __ 225.935 __ 293.406

61.341 ___ 139.065 __ 180.594

The Chisquare values :

4.15172__ 5.7569__ 10.8438

6.74518_ 9.35307 __ 17.6176

χ² = 4.15172 + 5.7569 + 10.8438 + 6.74518 + 9.35307 + 17.6176 = 54.46827

Degree of freedom = (row-1)*(column-1) = (2-1)*(3-1) = 1*2 = 2

Pvalue at df = 2 ; Pvalue = 0

α = 0.05

Pvalue < Α ; Hence, we reject H0 ; and conclude that service subscription and age are not independent

3 0

3 years ago