There was 7L punch for the birthday party. How many mL punch was there?

sin(x - 20)° = cos(5x - 10)°

Expand 5x - 10 in terms of x - 20:

5x - 10 = 5x - 100 + 90

… = 5 (x - 20) + 90

and recall that for all θ, cos(θ + 90)° = - sin(θ)°, so

sin(x - 20)° = cos(5 (x - 20) + 90)°

sin(x - 20)° = - sin(5 (x - 20))°

Replace (x - 20)° = y ° to make this a bit easier to read:

sin(y °) = - sin(5y )°

Expand the right side in terms of powers of sin:

sin(5θ) = 5 sin(θ) - 20 sin³(θ) + 16 sin⁵(θ)

so the equation becomes

sin(y °) = -5 sin(y °) + 20 sin³(y °) - 16 sin⁵(y °)

16 sin⁵(y °) - 20 sin³(y °) + 6 sin(y °) = 0

Replace z = sin(y °) to get a polynomial equation:

16z ⁵ - 20z ³ + 6z = 0

Factorize the left side:

2z (8z ⁴ - 10z ² + 3) = 0

2z (2z ² - 1) (4z ² - 3) = 0

Solve for z :

• 2z = 0   →   z = 0

• 2z ² - 1 = 0   →   z ² = 1/2   →   z = ± 1/√2

• 4z ² - 3 = 0   →   z ² = 3/4   →   z = ± √3/2

Solve for y in each case above:

• z = sin(y °) = 0   →   y = 0 + 360n   or   y = 180 + 360n

(where n is any integer)

These solutions can be combined into one family, y = 180n.

• z = sin(y °) = -1/√2   →   y = 225 + 360n   or   y = 315 + 360n

• z = sin(y °) = 1/√2   →   y = 45 + 360n   or   y = 135 + 360n

These solutions can also be combined, y = 45 + 90n.

• z = sin(y °) = -√3/2   →   y = 240 + 360n   or   y = 300 + 360n

• z = sin(y °) = √3/2   →   y = 60 + 360n   or   y = 120 + 360n

These can be combined as y = 60 + 180n or y = 120 + 180n.

Solve for x in each case:

• y = x - 20 = 180n   →   x = 20 + 180n

• y = x - 20 = 45 + 90n   →   x = 65 + 90n

• y = x - 20 = 60 + 180n   →   x = 80 + 180n

• y = x - 20 = 120 + 180n   →   x = 140 + 180n

Answer:

The correct answer would be 6000.

Step-by-step explanation:

To round decimal numbers to the nearest thousand, consider the last four digits that should be modified to the nearest thousandth number.

Answer:

[tex]H'I = 48[/tex]

Step-by-step explanation:

Given

See attachment for complete question.

From the attachment, we have:

[tex]GH=16.5[/tex]

[tex]HI =24[/tex]

[tex]IJ = 17[/tex]

[tex]JG =32.2[/tex]

[tex]k = 2[/tex] --- Scale factor

Required

Find H'I

The corresponding side of H'I is HI.

So:

H'I is calculated as:

[tex]H'I = k * HI[/tex]

This gives:

[tex]H'I = 2 * 24[/tex]

[tex]H'I = 48[/tex]

Answer I to j is 42

Step-by-step explanation:

theres no diagram given

Answer:

C)

Step-by-step explanation:

You can download answer here

tinyurl.com/wpazsebu

Answer is in the photo. I can't attach it here, but I uploaded it to a file hosting. link below! Good Luck!

tinyurl.com/wpazsebu

Answer:

the answer is 30

Step-by-step explanation:

(6+4) * 3

Do what is in the parenthesis!

(6+4) = 10

Then do the *3

10*3 = 30!

Hope this help! Goodluck!

Answer:

None

Step-by-step explanation:

2(x + 10) - 17 = 2x - 2

simplify:

2x + 20 - 17 = 2x - 2

2x + 3 = 2x - 2

subtract 3 from both sides of the equation:

2x = 3x -5

no solution

Answer: 20% of 90 = 18

Answer:

90%

Step-by-step explanation:

i hope this helps:)

Answer:

the answer is 144

Step-by-step explanation:

just multiply 12 by 12.

Answer:

144 ft.

Step-by-step explanation:

It is 12 x 12 which is 144 so it is 144 ft.

Step-by-step explanation:

60°+(7x-12)°+90° = 180°. (angle sum property of triangle)

(7x-12) + 150° = 180°

(7x-12) = 180° - 150°

7x-12 = 30°

7x = 30 + 12

7x = 42°

x = 42°/7

x = 6°

Length = 80

Breadth = 30  

Height = 30

Total surface area of a cuboid is=

2 ( lb + bh + hl )

Putting the values in the formula,

We get,

= 2 [ (80 x 30) + (30 x 30) + (30 x 80)]

= 2 (2400 + 900 + 2400)

= 8100 cm²

THANK YOU!!

∝ Sidhdi

Answer:

Try photo math, it will explain it all to you

Answer:

still stuck but when i get the correct answer i will tell u

Step-by-step explanation:

d or b

Answer:

(x + 6)(x - 4)

Step-by-step explanation:

x² + 2x - 24

(x + 6)(x - 4)

-4 and +6 multiply to 24 and add to +2.

Answer:

any how there are three consecutive positive numbers

Answer:

B and e

Step-by-step explanation:

The shape is a square.

'A square pyramid is a  three-dimensional geometric shape having a square base and four triangular faces/sides that meet at a single point (called vertex) is called a square pyramid.'

According to the given problem,

If a square pyramid is cut along the plane, then the cross-section of the solid is square. Because it is a square pyramid.

Hence, we concluded that square could be formed by slicing the square pyramid by a plane.

Learn more about square pyramid here: https://brainly.com/question/27350043

#SPJ2

Answer:

SA of the sphere is 1333.17 and SA of the circle is 333.29

Step-by-step explanation:

Answer:

if you want the answer us photo math I think !

Answer:

rotational symmetry of 60 degrees around the origin - yes

rotational symmetry of 120 degrees around the origin - yes

Step-by-step explanation:

A regular hexagon has 6 congruent angles

the the angles created on the line of symmetry are equal to 60 so the angle of rotational symmetry is 60 degrees.

The regular hexagon, like stated before, has 6 congruent angles so the order of symmetry is 6

Here is a visual from basic-matematics

Answer:

1. 60, 122 feet

2. a + s = 12

6a + 4s = 59

Step-by-step explanation:

I can't do all of them but I'll do the first 2:

1.

let w be the width of the rectangle

Then the length would be 2w + 2

Using those, the perimeter would be:

2w + 2 + 2w +2 + w + w = 364

solving:

[tex]6w + 4 = 364\\6w = 360\\w = 60[/tex]

This means the length would be:

[tex]2(60)+2\\120 + 2\\122[/tex]

2.

let a be the number of adult tickets

let s be the number of student tickets

Then:

The total number of tickets is 12, so:

a + s = 12

And the total cost is 59, so:

6a + 4s = 59

Answer:If we compare the p value and the significance level assumed we see thatso we can conclude that we have enough evidence to FAIL reject the null hypothesis, so we can conclude that the true mean is not different from the specification at 1% of signficance.  

Step-by-step explanation:

The machine is working properly based on the convincing evidence provided by the sample.

For the null hypothesis, we would test that:

H0 : p = 2

For the alternate hypothesis, we would test that:

Ha > p = 2

In Mathematics, the test statistics of a given sample is calculated by using this formula:

[tex]Z=\frac{x\;-\;u}{\frac{\sigma}{\sqrt{n} } }[/tex]

Where:

Substituting the given parameters into the formula, we have;

[tex]Z=\frac{2.024\;-\;2}{\frac{0.205}{\sqrt{200} } }\\\\Z=\frac{0.024}{\frac{0.205}{14.14} }\\\\Z=\frac{0.024}{0.0145 }[/tex]

Z = 1.66.

For the p-value:

P(Z > Zo) = P(Z > 1.66)

P(Z > 1.66) = P(Z < -1.66)

P(Z < -1.66) = 0.0485.

From the z-table, a z-score of 1.66 corresponds has a p-value of 0.0485. Therefore, the p-value for this test is 0.0485 < 2 while assuming a confidence level of 95%.

In conclusion, we fail to reject the null hypothesis because 0.0485 < 2.

Read more on null hypothesis here: https://brainly.com/question/14913351

Answer:

5/6

Step-by-step explanation:

Because there are 6 sides, and it's saying we need a greater number than 1. And there are 5 other numbers.

The answer is:

[tex] \frac{14}{59} [/tex]Decimal form is 0.2372 is infinity

Explication:

7(2x +2 )= 73x (Remove the parentheses and sort out 7 and solve for each number that is in the parentheses)

14x+14=73x

14x=73-14

-59x=-14

Both sides are divided by -59 but the -59 / -59 is canceled

Answer:

0.0001

Step-by-step explanation:

The computation of the probability of experiencing such a drop in water pressure is shown below:

Given that

mean = 519,645 gallons

Standard deviation = 71,564 gallons

Now the probability is

= 1 - p (x - mean ÷ standard deviation <  782,238 - 519,645 ÷ 71,564)

= 1 - p(z<3.67)

= 1 - 0.9999

= 0.0001

Answer:

24 in

Step-by-step explanation:

5in + 4in + 9in + 5in + (4in - 3in) = 24in