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3 years ago

How to convert 120 barrels to quarts

Mathematics

1 answer:

umka21 [38]3 years ago

4 0

The conversion factors are 42 gallons in a barrel

4 quarts = 1 gallon. I use unit analysis to get answers for questions like these.

$\dfrac{120barrels}{1} * \dfrac{42 gallons}{1 barrel} * \dfrac{4 quarts}{1 gallon}$

All the units are in the numerator. There are 120 * 42* 4 = 20160 quarts in 120 barrels.

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Describe and correct the error in finding csc θ, given that θ is an acute angle of a right triangle and cos θ =7/11

a_sh-v [17]

Answer:

<h2>cosecθ = 1/sinθ = 11/6√2</h2>

Step-by-step explanation:

Given that cos θ =7/11, cosec θ = 1/sinθ in trigonometry.

Based on SOH, CAH, TOA;

cosθ = adjacent/hypotenuse = 7/11

adjacent = 7 and hyp = 11

Since sinθ = opp/hyp, we need to get the opposite to be able to calculate sinθ.

Using pythagoras theorem to get the opposite;

$hyp^{2} = adj^{2} + opp ^{2} \\opp = \sqrt{hyp^{2} - adj^{2} } \\opp = \sqrt{11^{2} - 7^{2}} \\opp = \sqrt{72} \\opp = 6\sqrt{2}$

sinθ = 6√2/11

cosecθ = 1/sinθ = 1/( 6√2/11)

cosecθ = 1/sinθ = 11/6√2

Note the error; cscθ $\neq$ 1/cosθ but cscθ = 1/sinθ

6 0

3 years ago

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 434 gram setting. It is

yan [13]

Answer:

No, there is not sufficient evidence to support the claim that the bags are underfilled

Step-by-step explanation:

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 434 gram setting.

This means that the null hypothesis is:

$H_{0}: \mu = 434$

It is believed that the machine is underfilling the bags.

This means that the alternate hypothesis is:

$H_{a}: \mu < 434$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

434 is tested at the null hypothesis:

This means that $\mu = 434$

A 9 bag sample had a mean of 431 grams with a variance of 144.

This means that $X = 431, n = 9, \sigma = \sqrt{144} = 12$

Value of the test-statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{431 - 434}{\frac{12}{\sqrt{9}}}$

$z = -0.75$

P-value of the test:

The pvalue of the test is the pvalue of z = -0.75, which is 0.2266

0.2266 > 0.01, which means that there is not sufficient evidence to support the claim that the bags are underfilled.

7 0

2 years ago

A store sells packages of comic books with a poster. A poster and 5 comics cost $15.75 A poster and 11 comics cost $27.75 Writ

Vanyuwa [196]

Answer:

y=x+5.99

Step-by-step explanation:

A poster and 2 comics cost $7.99

(2,7.99)

A poster and 11 comics cost $16.99.

(11,16.99)

Let y be the cost of package and x be the no. of comics

We will use two point slope form :

(x1,y1) = (2,7.99)

(x2,y2) = (11,16.99)

Formula :

y-y1 = y2-y1/x2-x1(x-x1)

Substitute the values:

Hence a linear function rule that models the cost y of a package containing any number x of comic books is y=x+5.99

8 0

2 years ago

Question 1

PilotLPTM [1.2K]

answer: where is the question?

5 0

3 years ago

What is the solution set of the equation using the quadratic formula?

oee [108]

(1)

we are given

$x^2+6x+10=0$

we can use quadratic formula

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

now, we can compare and find a , b and c

we get

$a=1,b=6,c=10$

now, we can plug these values into quadratic formula

$x=\frac{-6\pm \sqrt{6^2-4(1)(10)}}{2(1)}$

$x=\frac{-6+\sqrt{6^2-4\cdot \:1\cdot \:10}}{2\cdot \:1}$

we can simplify it

$x=-3+i$

$x=\frac{-6-\sqrt{6^2-4\cdot \:1\cdot \:10}}{2\cdot \:1}$

$x=-3-i$

so, we will get solution

{−3+i, −3−i}.........Answer

(2)

we are given equation as

$x^2-8x+14=0$

Since, Jamal solve this equation by completing square

so, firstly we will move constant term on right side

so, subtract both sides by 14

$x^2-8x+14-14=0-14$

$x^2-8x=-14$

we can write

$-8x=-2\times 4\times x$

so, we will add both sides by 4^2

$x^2-8x+4^2=-14+4^2$

we get

$x^2-8x+16=-14+16$ ..............Answer

4 0

2 years ago