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konstantin123 [22]
3 years ago
9

4.

Mathematics
1 answer:
zubka84 [21]3 years ago
3 0

Answer:

See Explanation Below

Step-by-step explanation:

Given

(sin x - cos x)^2 = sec^2x - tan^2x - 2sinx.cos x.

Required

Prove

To start with; we open the bracket on the left hand side

(sin x - cos x)^2 = (sin x - cos x)(sin x - cos x)

(sin x - cos x)^2 = (sin x )(sin x - cos x)- (cos x)(sin x - cos x)

(sin x - cos x)^2 = sin^2 x -sinx cos x - sin xcos x + cos^2 x

(sin x - cos x)^2 = sin^2 x -2sinx cos x + cos^2 x

Reorder

(sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x

From trigonometry;

sin^2x + cos^2x = 1

So;

(sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x

becomes

(sin x - cos x)^2 = 1 - 2sinx cos x

Also from trigonometry;

sec^2x - tan^2x = 1

So,  

(sin x - cos x)^2 = 1 - 2sinx cos x

becomes

(sin x - cos x)^2 = sec^2x - tan^2x  - 2sinx cos x

Proved

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A quality control engineer at a potato chip company tests the bag filling machine by weighing bags of potato chips. Not every ba
Ahat [919]

Answer:

z=\frac{0.21 -0.15}{\sqrt{\frac{0.15(1-0.15)}{100}}}=1.68  

Step-by-step explanation:

Information provided

n=100 represent the random sample taken

X=21 represent the number of bags overfilled

\hat p=\frac{21}{100}=0.21 estimated proportion of overfilled bags

p_o=0.15 is the value that we want to test

z would represent the statistic

Hypothesis

We need to conduct a hypothesis in order to test if the true proportion of overfilled bags is higher than 0.15.:  

Null hypothesis:p =0.7  

Alternative hypothesis:p > 0.15  

The statistic for this case is:

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

And replacing the info given we got:

z=\frac{0.21 -0.15}{\sqrt{\frac{0.15(1-0.15)}{100}}}=1.68  

5 0
3 years ago
A water tank is in the shape of a right rectangular prism. Its dimensions are 6 feet by 4 feet by 7 feet. What is the surface ar
Norma-Jean [14]

Answer:

\LARGE{ \underline{\underline{ \sf{\pink{ Required\: answer:}}}}}

<h2><u>GIVEN</u><u> </u>- </h2>

  • Water tank which is in a shape of right rectangular prism

Dimensions = 6 feet × 4 feet × 7 feet

<h3><u>TO</u><u> </u><u>FIND</u><u> </u><u>-</u><u> </u> </h3>

  • Surface area of tank

<h2><u>SOLUTION</u> - </h2>

<em><u>Using</u></em><em><u> </u></em><em><u>formula</u></em><em><u> </u></em><em><u>of</u></em><em><u> </u></em><em><u>surface</u></em><em><u> </u></em><em><u>area</u></em><em><u> </u></em><em><u>of</u></em><em><u> </u></em><em><u>right</u></em><em><u> </u></em><em><u>rectangular</u></em><em><u> </u></em><em><u>prism</u></em><em><u> </u></em><em><u>-</u></em><em><u> </u></em>

Surface area =

2(wl  + hl + hw)

L = length

w = width

h = height

( assumimg 6 feet = L , 4 feet = W , 7 feet = h)

Putting value of L, W and H in the equation. we get,

=2(4 × 6 + 7 × 6 + 7× 4)

= 2(24 + 42 + 28)

= 2( 94)

= 2 × 94

= 188

7 0
3 years ago
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HELP! I put the formula but I don’t know the radius
ahrayia [7]

Answer:

C. 8,624

Step-by-step explanation:

recall that the formula for circumference is

Circumference = 2πr  ( = given as 85 meters)

hence,

85 = 2πr

r = 85/(2π)

given h = 15m

volume of cylinder

= πr²h

= π (85/2π)² 15  (using calculator and assuming π = 3.14)

= 8628.58

Comparing with the choices, the closest choice (within rounding error) is C. 8,624

8 0
3 years ago
Susan wants to buy cherries for a party. She has $8.00 to spend. Cherries are $2.75/kg. How many kilograms of cherries can Susan
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Answer:you would have to divide $8.00/$2.75 and it would equal $2.90

Step-by-step explanation:This may help and if it does please thank me in the comments.

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3 years ago
Whats 2.13×0.197 as a decimal
Tcecarenko [31]

Answer:

It's 0.41961.

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