cot²A=(1-sin²A)cosec²A​

Answer:Instructions below

Step-by-step explanation:

This is completing the square, so what happened was that -14 was divided, then squared, to find a perfect square. To find the third term, you have to divide it by two then square it, then add it to the other side to balance the equation out.

-14/2 = -7^2 = 49  This applies to every question in which you have to complete the square

Answer:

15 1/4

Step-by-step explanation:

16-3/4

64/4-3/4

61/4

15 1/4

Answer:

I think it is 16 cups in a gallon

Answer:

The probability that the sum is odd or a multiple of 5

P(E₁∪E₂) = 0.58 = 58%

Step-by-step explanation:

Step ( i ) :-    

Given the two dice are thrown ,The total number of  exhaustive cases

n(S) =  6² = 36

Let 'E₁' be the event of getting the sum is odd on two dice

E₁ = { (1,2)(1,4),(1,6),(2,1),(2,3),(2,5),(3,2)(3,4),(3,6),(4,1)(4,3),(4,5),(5,2),(5,4),(5,6),(6,1),(6,3),(6,5)}

n(E₁) = 18

Let 'E₂' be the event of getting the sum is multiple of 5 on two dice

E₂ = { (1,4),(2,3), (3,2),(4,1),(4,6),(5,5),(6,4)}  

n(E₂) = 7  

n(E₁∩E₂) = {(1,4),(2,3),(3,2),(4,1)} = 4

Step(ii):-

The probability that the event of getting the sum is odd on two dice

[tex]P(E_{1}) = \frac{n(E)}{n(S)} = \frac{18}{36}[/tex]

The probability that the event of getting the sum is multiple of '5' on two dice

[tex]P(E_{2}) = \frac{n(E_{2} )}{n(S)} = \frac{7}{36}[/tex]

The probability that the event of getting the sum is odd and multiple of '5' on two dice

[tex]P(E_{1} n E_{2}) = \frac{n(E_{1} n E_{2} )}{n(S)} = \frac{4}{36}[/tex]

The probability that the sum is odd or a multiple of 5

P(E₁∪E₂) = P(E₁) + p(E₂) - P(E₁ ∩ E₂)

              =    [tex]\frac{18}{36} + \frac{7}{36} - \frac{4}{36}[/tex]

              [tex]\frac{18+7}{36} - \frac{4}{36} = \frac{25-4}{36} = \frac{21}{36}[/tex]

P(E₁∪E₂) = 0.58 = 58%

Final answer:-

The probability that the sum is odd or a multiple of 5

P(E₁∪E₂) = 0.58 = 58%

The probability that the sum is odd or a multiple of 5 is 56 %.

When two dice are rolled, then

Total number of outcomes is [tex]=6^{2}=36[/tex]

Outcomes for  the sum is odd or a multiple of 5 ,

    [tex](1,2),(2,1),(2,3),(3,2),(1,4),(4,1),(1,6),(6,1),(2,5),(5,2),(3,4)\\\\(4,3),(3,6),(6,3),(4,5),(5,4),(6,5),(5,6),(4,6),(6,4)[/tex]

Number of favourable outcomes are [tex]=20[/tex]

the probability that the sum is odd or a multiple of 5 is,

                   [tex]P(E)=\frac{20}{36} =0.56[/tex]

Learn more about the probability here:

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Answer:

B, 12.48 is the answer

Step-by-step explanation:

Just took the test

Answer:

its b just took the quiz on edge 2020

Step-by-step explanation:

Answer:

  83.79 kJ

Step-by-step explanation:

The potential energy is the product of weight and height, where weight is in newtons.

  PE = Mgh = (190 kg)(9.8 m/s^2)(45 m) = 83,790 J

Answer:

Step-by-step explanation:

Answer:

∠NQR, ∠NRQ and side QR for ΔQNR is equivalent to ∠MRQ, ∠MQR and side QR, which defines the two triangles and proves that the two triangles are congruent

Step-by-step explanation:

Here, we have

ΔPQR is an isosceles triangle,

∠MRQ = ∠NQR

Therefore, since ∡R = ∡Q (Base angles of isosceles ΔPQR), then;

∠MRQ + ∡Q + ∠QMR = 180° = ∠NQR + ∡R + ∠RNQ (Sum of angles in a triangle)

Whereby ∠MRQ = ∠NQR and ∡R = ∡Q, we have;

∠MRQ + ∡Q  = ∠NQR + ∡R which gives;

∠QMR = ∠RNQ

Which gives;

∠NQR, ∠NRQ and side QR for ΔQNR is equivalent to ∠MRQ, ∠MQR and side QR, which defines the two triangles and proves that the two triangles are congruent.

Answer:

Step-by-step explanation:

This problem is about random experiments.

Random experiments are defined as experiments where the outcome can't be predicted. To ensure that result, the subjects are selected randomly. So, in this case, the right answer must be a situation where subjects are randomly present.

People taking the bus is a random experiment, because there's no the exact subjects in a bus at any time, it happens randomly.

Also, the winner of a sport league is also a random experiment, because it happens after several games which cannot be predicted.

Therefore, the right answers are a and c.

Answer:

157.48

Step-by-step explanation:

Answer:

Area of shaded region = 16π in² (D)

Step-by-step explanation:

The question is incomplete without the diagram if the circles. Find attached the diagram used in solving the question.

Area of the smaller circle = 8π in²

Area of a circle = πr²

πr² = 8π

r² =8

r = √8 = 2√2

From the diagram, there are two smaller circles in a bigger circle.

The radius of the bigger circle (R) is 2times the radius of the smaller circle (r)

R = 2r

Area of bigger circle = πR²

= π×(2r)² =   π×(2×2√2)²

= π×(4√2)² = π×16×(√2)²

Area of bigger circle = π×16×2

Area of bigger circle = 32π in²

Since there are two smaller circles in a bigger circle

Area of shaded region = Area of bigger circle -2(area of smaller circles)

Area of shaded region = 32π in² - 2(8π in²)

Area of shaded region = 32π in² - 16π in²

Area of shaded region = 16π in²

Answer:

D.

Step-by-step explanation:

X intercepts:

(-1/4,0),(3/2,0)

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Answer:

No it wont

Step-by-step explanation:

Answer:

1/5

Step-by-step explanation:

There are 3+5+2 = 10 marbles in the bottle

P(green) = number of green marbles/ total

               = 2/ 10 = 1/5

Answer:

b is about 25.5, c is about 18.7

Step-by-step explanation:

Using the law of sines, you can find the measure of side b with the following equation:

[tex]\dfrac{\sin 48}{19}=\dfrac{\sin 85}{b}[/tex]

[tex]b\approx 25.5[/tex]

Similarly, for c, you can do the following:

[tex]\dfrac{\sin 48}{19}=\dfrac{\sin 47}{c}[/tex]

[tex]c\approx 18.7[/tex]

Hope this helps!

Answer:

If events A and B are independent:

P(A|B) = P(A⋂B)/P(B) = (P(A) x P(B))/P(B) = P(A)

=> Option A is correct

Hope this helps!

:)

Answer:

ax=cz-by

Answer:

The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.

Step-by-step explanation:

Step-by-step explanation:

15 - 5n = 2n + 1

Bringing like terms on one side

15 - 1 = 2n + 5n

14 = 7n

14/ 7 = n

2 = n

Answer:

Step-by-step explanation:

First distribute. 5•3 and 5•n.

This gives you 15-5n=2n+1

Next add 5n to both sides.

This will give you 15=7n+1

Then you will subtract 1 from both sides.

14=7n

Finally you divide by 7 so you can get n by itself.

Your answer will be 2=n

You can always go back and plug your answer in to see if it works!

Answer:

Option (3).

Step-by-step explanation:

This question is incomplete; find the compete question in the attachment.

Equation (1):  q = d + n

"Total number of quarters is equal to the sum of number of dimes and nickels."

Equation (2): 0.25q + 0.10d + 0.05n = 6.05

"Total value of the coins in the jar is $36"

Equation (3) : q + d + n = 36

"There are a total of 36 coins in the jar."

By comparing the options given, we find the third option which matches with equation (3)

Therefore, option (3) is the correct answer.

Answer:

B) 9 cm

Step-by-step explanation:

Just look at the triangle and use Pythagoras theoreum.

a² + b² = c²

a = 9 9 - 4.9 = 5

b = ?

c = 10

5² + b² = 10²

b² = 100 - 25

b² = 75

b = + - SQRT( 75 )

{Only the positive term has a meaning here.}

b = 8.66 rounded that is 9, which is answer B.

Answer:

Answer:

B,C,E

Step-by-step explanation:

khan academy

Side length of the scaled copy of square is smaller than original.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Given,

Scale factor of scaled copy of square is less than 1.

Scale factor basically defines the ratio between the sides of the constructed square to that of the original square.

if scale factor is less than 1 then the sides of the constructed square is smaller than that of the original square.

Hence, side length of constructed square is smaller than the original square.

Learn more about scale factor here:

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#SPJ2

Answer: 5

Step-by-step explanation:

two negatives equal a positive, so if you are subtracting with two negatives it just like 7-2 if that makes sense :)

Answer:

5

Step-by-step explanation:

you have to multiply the 2 negative signs in between of 2 and 7 and then you will get a positive sign

since the 2 signs are different you will need to subtract.

so 7-2 equals 5 and you put the bigger number's sign which is positive

Answer:

18.0625 ft

Step-by-step explanation:

Greatest height is when:

t = -b/2a

t = -30/2(-16)

t = 15/16

Greatest height is:

-16t(15/16)² + 30(15/16) + 4 = 289/16

= 18.0625m

Answer:

g = j - 12

Step-by-step explanation:

Let's say Jessie installed j axles. Convert words to math:

- "12 more" = + 12

- "the number of engine blocks her friend Gus installed yesterday" = g

Put it together: g + 12. This is equal to j: j = g + 12. Solve for g:

j = g + 12

g = j - 12

Lets use the variables "a" and "g" to solve.

a =  number of axles

g =  number of engine blocks

If Jessie has 12 more axles than the number of engine blocks, this means we are adding (g + 12).

Now, we have the expression a = g + 12

Solve for g since we are finding the number of engine blocks Gus Installed.

a = g + 12

~Subtract 12 to both sides

a - 12 = g + 12 - 12

a - 12 = g

Therefore, the answer is [ a - 12 = g ]

Best of Luck!

Answer: i^2 = -1

Step-by-step explanation:

NVM Ignore this answer (:::::::

Answer:The distance around a rectangle or a square is as you might remember called the perimeter. The distance around a circle on the other hand is called the circumference (c).

circle diameter radius

A line that is drawn straight through the midpoint of a circle and that has its end points on the circle border is called the diameter (d)

Half of the diameter, or the distance from the midpoint to the circle border, is called the radius of the circle (r).

The circumference of a circle is found using this formula: so the answer is B

Step-by-step explanation:

Answer:

y= - 4/1x + 5

Step-by-step explanation:

Answer:

y=-4x+5

Step-by-step explanation:

4 equals the slope (rise over run) and 5 equals the y-intercept