Hello! Can someone help me, please? Thank you so much!!!
Nick has 5, 10, 20, 50 cent coin in his pocket.
He accidentally takes 2 coins out of his pocket. Calculate the possibility of the sum of the two coins that he has taken out being 25 cents.

Answer:

1st option

2,4,8,16

Step-by-step explanation:

1st option is not an Arithmetic sequence, it is geometric sequence. Because, the common ratio is 2

the 2nd option has a common difference of 7, so it is arithmetic

the 3rd option has a common difference of 0.5,  so it is arithmetic

and 4th option has a common difference of -4.  so it is arithmetic

The polar coordinates of this same point is (-8, -2π).

The point (-10, 2π) can be plotted on a graph with polar coordinates by beginning at the origin (0,0) and moving -10 units along the θ axis and then 2π units along the r axis.

To find other polar coordinates (r, θ) of this same point for which r > 0 and -2π ≤ θ < 0, we can move the point along the θ axis and then along the r axis in the opposite direction. This will result in a new point (r, θ) where r > 0 and -2π ≤ θ < 0.

For example, we can move the point along the θ axis to (-10, -2π), and then move it along the r axis to (-8, -2π).

This would result in the new point (r = -8, θ = -2π), which satisfies the given conditions.

Therefore, the polar coordinates of this same point is (-8, -2π).

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Answer:

The vertex is option C: (-6, -2)

Step-by-step explanation:

The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)

Pls mark brainliest.

Answer:

41m, 30m, 15m

Step-by-step explanation:

A triangle can only be formed if the sum of any 2 side lengths adds up to be greater than the length of the other side.

The combination 41m, 30m, 15m is the only one where any 2 side lengths adds up to be greater than the other side.

We can test this:

41 + 30 > 15

30 + 15 > 41

The solution is Option C.

The sides of the triangles are 15 m , 30 m and 45 m

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the triangle be represented as ABC

Now , the measure of the sides of the triangle are

a)

AB = 8 m

BC = 10 m

AC = 20 m

Now , for a triangle AC < AB + BC

So , substituting the values in the equation , we get

20 < 10 + 8

20 < 18 which is FALSE

b)

AB = 2.5 m

BC = 2.5 m

AC = 8 m

Now , for a triangle AC < AB + BC

So , substituting the values in the equation , we get

8 < 2.5 + 2.5

8 < 5 which is FALSE

c)

AB = 15 m

BC = 30 m

AC = 41 m

Now , for a triangle AC < AB + BC

So , substituting the values in the equation , we get

41 < 30 + 15

41 < 45 which is TRUE

So , triangle ABC with sides 15 m , 30 m and 41 m is a triangle

d)

AB = 25 m

BC = 25m

AC = 75 m

Now , for a triangle AC < AB + BC

So , substituting the values in the equation , we get

75 < 25 + 25

75 < 50 which is FALSE

Hence , the triangle is with sides 15 m , 30 m and 41 m

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Answer:

cos(2x)

Step-by-step explanation:

The simplified expression is

How to evaluate trigonometric expression?

A Trigonometric expression consists of sin, cos and various other parameters which can be simplified using identities.

Given expression:

cos(x){cos(x)-tan(x)sin(x)}

Evaluation:

\(cos(x)(cos(x)-\dfrac{ sin(x)*sin(x)}{cos(x)})\)

\(cos(x)(\frac{cos^{2} x-sin^{2}x}{cos(x)} )\)

\(cos^{2}x-sin^{2}x\)

\(cos2x\)

Therefore, the given expression simplifies to cos2x.

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Answer:

∠ O = 61°, ∠ N = 119°

Step-by-step explanation:

In a parallelogram

Consecutive angles are supplementary

Opposite angles are congruent, thus

x + 2x - 3 = 180

3x - 3 = 180 ( add 3 to both sides )

3x = 183 ( divide both sides by 3 )

x = 61°

Thus

∠ O = ∠ M = x = 61°

∠ N = ∠ P = 2x - 3 = 2(61) - 3 = 122 - 3 = 119°

The price of a dozen eggs rose by approximately 90% between December 2000 and December 2017. The average wage for workers in private industries increased by approximately 56% during the same period. In order to earn enough to buy a dozen eggs, a worker had to work a certain number of minutes in December 2000 and a different number of minutes in December 2017. The change in workers' purchasing power in terms of eggs between 2000 and 2017 can be assessed based on these price and wage changes.

To calculate the percentage change in the price of a dozen eggs, we use the formula:

Percentage change = ((New value - Old value) / Old value) * 100

Substituting the values:

Percentage change = ((1.82 - 0.96) / 0.96) * 100 ≈ 89.58%

Therefore, the price of a dozen eggs rose by approximately 90%.

Similarly, to calculate the percentage change in the average wage, we use the formula:

Percentage change = ((New value - Old value) / Old value) * 100

Substituting the values:

Percentage change = ((22.31 - 14.28) / 14.28) * 100 ≈ 56.22%

Therefore, the average wage for workers in private industries increased by approximately 56%.

To determine the number of minutes a worker had to work in order to buy a dozen eggs, we can use the ratio of wages to the price of eggs. Let's calculate the number of minutes:

Minutes worked in December 2000 = (Price of a dozen eggs / Average wage) * 60

Substituting the values:

Minutes worked in December 2000 = (0.96 / 14.28) * 60 ≈ 4.03 minutes

Minutes worked in December 2017 = (Price of a dozen eggs / Average wage) * 60

Substituting the values:

Minutes worked in December 2017 = (1.82 / 22.31) * 60 ≈ 4.90 minutes

Therefore, in December 2000, a worker had to work approximately 4.03 minutes to earn enough to buy a dozen eggs, whereas in December 2017, a worker had to work approximately 4.90 minutes. This indicates that workers' purchasing power in terms of eggs decreased during this period.

Answer:

The price of a dozen eggs rose by approximately 90%.

The average wage for workers in private industries increased by approximately 56%.

In December 2000, a worker had to work approximately 4.03 minutes to earn enough to buy a dozen eggs, while in December 2017, a worker had to work approximately 4.90 minutes. Therefore, workers' purchasing power in terms of eggs decreased between 2000 and 2017.

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Answer:

The answer is 2.)

Step-by-step explanation:

Given initial velocity=135 ft/s

& cliff=76 foot

Given quadratic equation

⇒                      (let h=0 it is given)

⇒  

⇒  

⇒    t=8.96≈9 s (the other root is negative)

Hence, rocket will take 9 s to hit the ground after launched.

Answer:  Choice D

0 = 16t^2 + 135t + 76;  9 s

==============================================

Explanation:

The equation we start with is

\(h = -16t^2 + vt + c\\\\\)

where v is the starting or initial velocity, and c is the starting height.

We're told that v = 135 and c = 76

We let h = 0 to indicate when the object hits the ground, aka the height is 0 ft.

That means the equation updates to \(0 = -16t^2 + 135t + 76\\\\\)

Based on that alone, the answer is between A or D

-------------------

We'll use the quadratic formula to solve for t

We have

So,

\(t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\t = \frac{-135 \pm \sqrt{135^2 - 4(-16)(76)}}{2(-16)}\\\\t = \frac{-135 \pm \sqrt{23,089}}{-32}\\\\t \approx \frac{-135 \pm 151.9506}{-32}\\\\t \approx \frac{-135 + 151.9506}{-32} \ \text{ or } \ t \approx \frac{-135 - 151.9506}{-32}\\\\t \approx \frac{16.9506}{-32} \ \text{ or } \ t \approx \frac{-286.9506}{-32}\\\\t \approx -0.52971 \ \text{ or } \ t \approx 8.96721\\\\\)

We ignore the negative t value because a negative time duration makes no sense.

The only practical solution here is roughly 8.96721 which rounds to 9.0 or simply 9 when we round to the nearest tenth (one decimal place).

In short, the object will hit the ground at the 9 second mark roughly. Or put another way: the object is in the air for about 9 seconds.

From this, we can see that the final answer is choice D.

Keep in mind that we aren't accounting for any wind resistance. Considering this variable greatly complicates the problem and requires much higher level mathematics. So we just assume that there is no wind at this moment.

To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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The average value of the function on the closed interval 1≤x≤3 is approximately 0.281.

1. Determine the length of the closed interval. The interval is from x=1 to x=3, so the length is (3-1) = 2.

2. Integrate the function over the closed interval. To do this, you need to find the integral of sin(2x)cos(x) with respect to x from 1 to 3:
∫[1,3] sin(2x)cos(x) dx

3. Divide the result of the integration by the length of the closed interval to find the average value:
(1/2) * ∫[1,3] sin(2x)cos(x) dx

Now, let's calculate the integral:

∫ sin(2x)cos(x) dx = (1/4) * sin^2(x) + C (using integration by parts)

Now, we evaluate the definite integral from 1 to 3:

[(1/4) * sin^2(3)] - [(1/4) * sin^2(1)]

Finally, divide the result by 2 to find the average value:

(1/2) * {[(1/4) * sin^2(3)] - [(1/4) * sin^2(1)]}

After calculating the values, the average value of the function on the closed interval 1≤x≤3 is approximately 0.281.

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The frequency tells us how many times the integer appears in the set of numbers.

The integer tells us the numbers that appear in the set of numbers.

To find the mean, we add up all the numbers in the set and divide the sum by the number of integers.

Let's write the information on the graph as a list of numbers:

0, 1, 2, 3, 3, 3, 4, 4, 6, 7, 8, 10

Find the sum:

51

Divide the sum by the number of integers (which is 12):

51/12

= 4.25

The mean is 4.25.

Answer:

80

Step-by-step explanation:

10*16=160 160 is the area of the square so you have to divide it by 2 and then you get 80

Answer:

Average rate of change = 31

Step-by-step explanation:

Average rate of change: [f(b) - (f(a)] / (b - a)

a = 1 and b = 5

f(x) = x^3 - 50

[(-50 + 5^3 - (-50 + 1^3)] / 5 - 1

= (75+49)/4

= 31

Answer:

J

Step-by-step explanation:

Answer:

The answer is J

Step-by-step explanation:

The letters are corresponding with each other.

HOPE IT HELPS YOU

MARK AS BRAINLIEST

Answer:

15-20%

Step-by-step explanation:

can u make me brainiest thanks

Start by putting the inequality in the form

in this case c wil be how much he has sold, and d will be how much he needs to sell, and a is the price for the bar.

it would look like this

solve it like a regular equation

He will have to sell over 54 bars to win the prize.

Answer:

\((-\infty, -1)\ \cup\ (0, 2)\)

Step-by-step explanation:

So if you expand out the two binomials (k-2)(k+1), you'll get: \(k^2+k-2k-2\). which simplifies to: \(k^2-k-2\). Multiplying this by the k gives you: \(k^3-k^2-2k\). As you can see the degree is odd, this means that this polynomial will have two opposite end behaviors. And as you can see the leading coefficient is positive, meaning that this function will go towards positive infinity as k goes towards positive infinity. Also we if look at the original equation given, it's in factored form, with the zeroes as k=0, k=2, and k=-1. So given this we can draw a simple graph to see when the value of the equation is negative. If you look at the graph I drew you'll see that it's negative from (-infinity, -1) and then negative from (0, 2)

Answer:

-1

Step-by-step explanation:

this is really simple.

a = 5 ? great, then we put that 5 into every place, where there is "a" on the expression.

b = 1 ? then we put 1 into every place , where there is "b" in the expression.

that is what variables are for : placeholders for actual values.

and now we just calculate.

remember the priorities of operations :

1. brackets, functions

2. exponents

3. multiplications, divisions

4. additions, subtractions

so

12 + (2 - (4×a²))÷7 + b = 12 + (2 - (4×5²))÷7 + 1 =

= 12 + (2 - (4×25))÷7 + 1 =

= 12 + (2 - 100)÷7 + 1 =

= 12 + -98÷7 + 1 =

= 12 - 14 + 1 = -2 + 1 = -1

so, the point has to be made at -1.

Greetings from Brasil...

Here is the graphical explanation in the annex.

A = (-4; 3)

B = (3; 2)

(segment BLUE)

After reflection on F(X) we will get the segment GREEN

note that the length M = M and N = N

Answer:

equilateral triangle is the answer

Answer:

256

1.  2^3=8       2^6=64      2^5=32

2.  8/64=0.125

3. 32/0.125=256

Answer:

275.4cm

Step-by-step explanation:

A = pi*r^2

r = 9

A = 3.14 * 9^2

A = 3.14 * 81

A = 275.4

Hope this helps!

The missing number in the sequence is 22.

To find the missing number, we need to look for a pattern in the given numbers.

If we subtract each number from the next number in the sequence, we get the following:

5-4 = 1

7-5 = 2

10-7 = 3

15-10 = 5

So, the differences between the consecutive numbers are increasing by 1 each time.

Using this pattern, we can find the next number in the sequence by adding 6 to the last number (since the difference between the last two numbers is 5, we add 1 to get the next difference and add 6 to get the next number).

15 + 6 = 21

Therefore, the missing number should be 22, not D-23D-23.

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Find the interest amount.

\(I=1740-1200=540\)

Use the formula for simple interest.

\(I=prt/100\)

Solve for t.

\(540=1200 \times 15\% \times t\)

\(540=1200 \times \frac{15}{100} \times t\)

\(540=180t\)

\(t=\frac{540}{180}\)

\(t=3\)

The number of years will be 3 for Rs.1200 at the rate of 15% interest amounting to Rs. 1740​.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific amount of time.

Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to calculate interest, the principal amount in simple interest remains constant.

Given that Rs.1200 at the rate of 15% interest amount to Rs. 1740​. The number of years will be calculated as:-

SI = ( P x R x T ) / 100

1740 - 1200 = ( 1200 x 15 x T ) / 100

T = ( 540 x 100 ) / ( 1200 x 15)

T = 3 years

Hence, the time will be 3 years.

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The first step in finding the surface area of the box in terms of only x is to express the height of the box in terms of x. The volume of the box with a square base is given by;V = l × w × hV = x × x × hV = x² × h And, we are told that the volume of the box is 340736 cm³;V = 340736 cm³ .

Substituting x²h in V;340736 cm³ = x²hHence, h = 340736 / x²

Now that we have expressed h in terms of x, we can proceed to find the formula for the surface area of the box.

We know that the box has a square base. Therefore, the surface area of the square is given by the formula;

S₁ = x² . There are four rectangular sides to the box, which all have the same dimensions, x by h.

Therefore, the total surface area for all the rectangular sides can be found by the formula;

S₂ = 4xhReplacing h with 340736 / x²;S₂ = 4x(340736 / x²)S₂ = (1362944 / x) cm²Adding the two surface areas gives the formula for the surface area of the box;

A(x) = x² + (1362944 / x)We can simplify this by taking the common denominator as follows;

A(x) = (x³ + 1362944) / x

Now, to find the derivative A′(x);A(x) = (x³ + 1362944) / xA′(x) = [(3x² × x) - (x³ + 1362944) × 1] / x²A′(x) = (3x² - x³ - 1362944) / x²Setting A′(x) = 0;A′(x) = 0(3x² - x³ - 1362944) / x² = 0.

Solving for x;3x² - x³ - 1362944 = 0x³ - 3x² + 1362944 = 0

This can be solved using the cubic formula;ax³ + bx² + cx + d = 0x = -b ± √(b² - 4ac) / 2a

For our equation, a = 1, b = -3, c = 0 and d = 1362944.

Substituting in the cubic formula; x = -(-3) ± √((-3)² - 4(1)(0)(1362944)) / 2(1)x = 3 ± √(9 - 0) / 2x = 3 ± √9 / 2x = (3 ± 3) / 2x = 6 / 2 or x = 0 / 2x = 3 or x = 0

The value of x is 3 because x cannot be 0, or else there will be no box.

Secondly, we will perform the second derivative test to confirm that this value of x gives a minimum value for the surface area.

To do that, we need to find A′′(x);A′(x) = (3x² - x³ - 1362944) / x²A′′(x) = [(6x × x²) - (2x × (3x² - x³ - 1362944))] / x⁴A′′(x) = (6x³ - 6x³ + 2x⁴ + 2725888) / x⁴A′′(x) = (2x⁴ + 2725888) / x⁴

Evaluating A′′(x) at x = 3;A′′(3) = (2(3)⁴ + 2725888) / (3)⁴A′′(3) = (4374 + 2725888) / 81A′′(3) = 33712.69Since A′′(3) > 0, this means that the graph of A(x) is concave up around that value, so the zero of A′(x) at x = 3 must indicate a local minimum for A(x).

Therefore, the dimensions of the box that minimize the amount of material used are;

Length = x = 3 cm

Width = x = 3 cm

Height = h = 340736 / x² = 12646.67 cm³

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Answer:

To create groups that are as similar as possible so the main difference between the groups is the treatment

Step-by-step explanation: got it right on khan