What is the missing length?

There are 80 different combinations of 3 cupcakes are there if order does not matter

The given parameters are:

Flavors = 10

Flavors to choose = 3

The number of combination is calculated using:

\(^nC_r = \frac{n!}{(n - r)!r!}\)

This gives

\(^{10}C_3 = \frac{10!}{7!3!}\)

Expand

\(^{10}C_3 = \frac{10 * 9 * 8 * 7!}{7!3 * 2 * 1}\)

Evaluate quotient

\(^{10}C_3 = 80\)

Hence, there are 80 different combinations of 3 cupcakes are there if order does not matter

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Answer:

(1, -4)

Step-by-step explanation:

if you rotate from quadrant 3 to 4, x=-y and y=x

After the rotation of 90° clockwise about the origin, the coordinates become P'(- 1, - 4).

Given is the coordinate of point as (-4, - 1). It is rotated by 90° clockwise about the origin.

When we rotate a figure 90 degrees clockwise about the origin, then the new coordinates will be -

A(x, y) → A(y, - x)

Then, we can write the new coordinates according to the rule as -

P(-4, - 1) → P'(- 1, - 4)

Therefore, after the rotation of 90° clockwise about the origin, the coordinates become P'(- 1, - 4).

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Answer:

Income tax amount: $5047.50

Step-by-step explanation:

89172.5 is the total amount with income tax added.

The normal value is $84,125 so you can do this in your calculator in the future it's like this:

84,125 * .06 = 5047.5

This is close to the target volume of 733.6ml, but not exactly the same.

The given extract provides a conversion factor for the change in volume of water when it freezes. Using this information, we can determine the amount of ice needed to produce 733.6ml of liquid water at room temperature as follows:

Determine the change in volume of 500ml of water when it freezes.

The extract states that 500ml of water at room temperature will increase to 545.25cm³ when it freezes. This means that the change in volume is 545.25cm³ - 500ml = 45.25cm³.

Determine the volume of ice needed to produce 45.25cm³ of liquid water.

Since the density of ice is 0.92g/cm³ and the density of water is 1g/cm³, we know that 1g of ice will melt to produce 1cm³ of water. Therefore, the mass of ice needed to produce 45.25cm³ of water is 45.25g (which is also equal to 45.25cm³ since the density of ice is 0.92g/cm³).

Determine the volume of liquid water produced from melting 800cm³ of ice.

Using the conversion factor from step 1, we know that 1ml of water at room temperature is equal to 1.181/2000 cm³ of water when frozen. Therefore, 800cm³ of ice will produce 800 x 1.181/2000 = 472.48ml of water when it melts.

However, we need to take into account that the water will not be at 0°C when it melts. To simplify this, let's assume that the ice starts at a temperature of -10°C and that the final liquid water is at room temperature, which is approximately 20°C. The heat required to melt the ice and then warm the resulting water from -10°C to 20°C is:

Q = (800cm³) x (0.92g/cm³) x (80°C) + (800cm³) x (1g/cm³) x (30°C)

where 80°C is the difference between the final and initial temperatures of the ice, and 30°C is the difference between the final and initial temperatures of the water.

Simplifying this equation gives:

Q = 59,840g x °C

Determine the mass of ice needed to produce 733.6ml of water at room temperature.

Using the density of water (1g/cm³), we can convert the volume of water to its mass:

m = (733.6ml) x (1g/cm³) = 733.6g

To melt this amount of ice, we need to use the same amount of heat that was calculated in step 3. Therefore, the mass of ice needed is:

59,840g x °C / 733.6g = 81.5g

Check the answer

We can check this answer by calculating the volume of liquid water produced from melting 81.5g of ice and comparing it to the target volume of 733.6ml. The volume of liquid water produced is:

V = (81.5g) / (0.92g/cm³) = 88.59cm³

This is equivalent to:

88.59cm³ x 1ml / 1.181/2000cm³ = 74.93ml

This is close to the target volume of 733.6ml, but not exactly the same. The difference could be due to rounding errors in the calculations or the assumption of a constant density for water over the range of temperatures considered.

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Set up a ratio of height over shadow length:

3.2/1.29 = X/39.25

Cross multiply:

1.29x = 3.2 * 39.25

Simplify:

1.29x = 125.6

Divide both sides by 1.29:

x = 97.364 meters

Round to the nearest meter = 97 meters

\(x = \frac{15}{10} \times y\)

.

The product of (3 + 2√5)(2 + 4√5) is 46 + 16√5.

To find the product of (3 + 2√5)(2 + 4√5), we can use the distributive property.

Expanding the expression, we multiply each term from the first parentheses with each term from the second parentheses:

(3 + 2√5)(2 + 4√5) = 3(2) + 3(4√5) + 2√5(2) + 2√5(4√5)

Simplifying further, we have:

= 6 + 12√5 + 4√5 + 8(5)

= 6 + 12√5 + 4√5 + 40

= 46 + 16√5

Therefore, the product of (3 + 2√5)(2 + 4√5) is 46 + 16√5.

In this case, we end up with a simplified expression of the form a + b√5, where a and b are real numbers. The term 46 represents the constant part of the product, while 16√5 represents the radical part.

It's worth noting that the product (3 + 2√5)(2 + 4√5) cannot be simplified any further because the terms involving the square root of 5 cannot be combined or simplified with other terms. Therefore, the expression 46 + 16√5 is the final form of the product.

It's important to be cautious when dealing with radical expressions as they can often result in irrational numbers or expressions with square roots that cannot be simplified exactly.

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To find the rate at which the diameter of the circle is changing, we'll first need to determine the relationship between the area of the circular ripple and its radius.

The area of a circle is given by the formula A = πr². In this problem, the area is increasing at a constant rate of 5 m²/second (dA/dt = 5).

Now, we'll use implicit differentiation with respect to time (t) to find the rate of change of the radius:

dA/dt = d(πr²)/dt

5 = 2πr(dr/dt)

Since we're interested in the rate of change of the diameter (D) when the radius (r) is 4 m, and D = 2r, we'll differentiate D with respect to time:

dD/dt = 2(dr/dt)

Now, we can solve for (dr/dt) when r = 4:

5 = 2π(4)(dr/dt)

5/(8π) = dr/dt

Finally, we find dD/dt:

dD/dt = 2(5/(8π))

dD/dt = 5/(4π)

So, when the radius of the circular ripple in the pond is 4 m, the diameter is changing at a rate of 5/(4π) meters per second.

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a. a² - 26 = a² + 4b² + 2ab√2 - 26 = a² + 4b² is an element of Q(√2). Hence, we have proven that a² - 26 ∈ Q(√2) for any non-zero a ∈ Q(√2).

b. We can conclude that √2 is not an element of Q(√3).

c. Since 2φ(√2) ≠ 2√3, φ cannot preserve the addition operation. Therefore, there cannot exist a function φ: Q(√2) → Q(√3) that is a group isomorphism.

(a) To prove that a² - 26 is an element of Q(√2), we first express a non-zero element a in Q(√2) as a = a + b√2. By squaring a, we obtain a² - 26 = a² + 4b², which shows that a² - 26 is an element of Q(√2). The key point is that 2ab√2 must be irrational unless ab = 0, which leads to the conclusion.

(b) In order to demonstrate that √2 is not an element of Q(√3), we assume the opposite and suppose that √2 ∈ Q(√3). By squaring both sides of the equation √2 = a + b√3, we arrive at 2 = a² + 2ab√3 + 3b². Since √3 is irrational, the only way for 2ab√3 to be rational is if ab = 0. However, this contradicts the assumption that a and b are non-zero rational numbers, implying that √2 cannot belong to Q(√3).

(c) To prove that there cannot exist a function φ: Q(√2) → Q(√3) that preserves the group structure, we consider the element √2 + √2 in Q(√2). If φ is a group isomorphism, it should preserve addition. However, evaluating φ(√2 + √2) and φ(√2) + φ(√2) leads to a contradiction. Hence, there is no function φ that simultaneously preserves the group structures of Q(√2) and Q(√3).

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The value of p is 1.5 for which the table shows inverse relation.

For inverse relation between x and y we assume any function then check it with the given values and find the variable in the equation.

so let the equation is:

y = \(\frac{k}{x^n}\)    ------(i)

where k and n are variables which we have to find using the given data

for case 1 y=5 and x=3

after assigning the values in equation (i) we get

5 = \(\frac{k}{3^n}\)  ------(ii)

for case 3 ,  y= 15 and x=1;

after assigning the values in equation 1 we get:

  15 =\(\frac{k}{1^n}\)   -------(iii)

dividing equation (ii) and (i) we get

 3 = \(3^n\)

=> n=1

so equation (i) reduces to

y= \(\frac{k}{x}\)

putting y=3 and x=5 in the above equation we get

3 = k/5

=> k = 15

so the final equation we got is :

y = \(\frac{15}{x}\) -------(iv)

now in case 2 we are given y=p and x=10

after assigning the values in equation (iv) we get

p = 15/10

=> p= 1.5

so the value of p =1.5

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Answer:

There are 7 handshakes.

Step-by-step explanation:

The profesor is shaking hands with 7 people, so there are 7 handshakes between them.

The number of handshakes that take place are  \(^nC_{k}\)= \(\frac{n!}{k!(n-k)!}$\)  i.e 28

In mathematics, permutation relates to the act of arranging all the members of a set into some sequence or order. The combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter. The formula for permutation is nPr = (n!) / (n-r)! and combination formula is  nCr = n!/[r! (n-r)!]

Given here Prof. Anne Bishon has a meeting with 7 other academics, they all shake hands before sitting down thus

\(^8C_{2}\)   = \(\frac{8!}{2!(8-2)!}$\)

\(^8C_{2}\) = 28

Hence, The number of handshakes that takes place is equal to 28

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Answer:

1.2(3x)+3.75(2y)

Step-by-step explanation:

multiply 1.2 by what you know for number of people

multiply 3.75 by what you know for number of hours

The probability that a student who has an A is a male is 60%.

To find the probability that a student who has an A is a male, we need to calculate the ratio of the number of male students with an A to the total number of students with an A.

Given that there are 19 students in total, and 6 of them are female, we can determine that there are 19 - 6 = 13 male students. Out of these male students, 7 do not have an A. Therefore, the number of male students with an A is 13 - 7 = 6.

Now, we know that there are 10 students in total who have an A. Therefore, the probability that a student with an A is a male can be calculated as the ratio of the number of male students with an A to the total number of students with an A:

Probability = Number of male students with an A / Total number of students with an A

Probability = 6 / 10

Probability = 0.6 or 60%

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The correct Mathematical phrases of the English phrases would be j+4, 16c, 3(z+1), ef+8, and v/17 respectively and the solution of given linear equations (part B) will be -105, -291, 270, -48, and -30 respectively.

In part A, the translation of mathematical phrases gives rise to certain equations of linear nature. It helps in easy understanding of the relations between variables and numerical values. In part B, the values of x, b and c are already given for the sake of simplicity. Substituting these values in given linear equations gives the following results:

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Answer: \(y=\dfrac12 x\) .

Step-by-step explanation:

We know that \(a f (x)\)  compresses f(x) vertically such that

If we vertically compress the linear parent function, F(x) = x, by multiplying by \(\dfrac12\).

Then, the equation of the new function is \(y=\dfrac12 F(x)=\dfrac12 x\) .

i.e. \(y=\dfrac12 x\) .

Answer:

£8884.10625

Step-by-step explanation:

15% of £20,000:

20000x15/100=£3000

20000-3000=£17000

15% of £17000:

17000x15/100=£2550

17000-2550=£14450

15% of £14450:

14450x15/100=£2167.5

14450-2167.5=£12282.5

15% of £12282.5:

12282.5x15/100=£1842.375

12282.5-1842.375=£10440.125

15% of £10440.125:

10440.125x15/100=£1556.01875

10440.125-1556.01875=£8884.10625

Since the car loses 15% of it's value each year, it retains 85% of the value.

Value after 1 year = 85% of original value.

Value after 2 years = 85% of value after year 1

Value after 3 years = 85% of value after year 2

and so on...

We could calculate this year by year or we could do a single calculation to obtain the value.  We need to take 85% of the original value a total of 5 times, since we're wondering about the value in 5 years.

value after 5 years = 20000(0.85)(0.85)(0.85)(0.85)(0.85)

value after 5 years = 20000(0.85)^5

value after 5 years ≈ 8874.10625

So the value will be 8874.11 pounds in 5 years.

Answer:

.309

.34

.4

.46

.97

.98

Step-by-step explanation:

Hope this helped. Do not be shy to give Brainlist.

Answer:

0.4, 0.309, 0.34, 0.46, 0.97, 0.98

Step-by-step explanation:

Answer: ive had a question for many years and still no answered

Step-by-step explanation:

Answer:

Step-by-step explanation:

The first one is equal to.  203/203 is equal to 1.  1 times any number is itself.

The second on is less than.  9/37 is a proper fraction and when a number is multiplied by a proper fraction, it gets smaller.

To find the horizontal and vertical asymptotes of the function f(x) = (3x^2 - 13x + 4)/(2x - 3x - 4), we need to analyze the behavior of the function as x approaches positive or negative infinity.

Horizontal Asymptote:

To determine the horizontal asymptote, we compare the degrees of the numerator and denominator. Since the degree of the numerator is 2 and the degree of the denominator is 1, we have an oblique or slant asymptote instead of a horizontal asymptote.

To find the slant asymptote, we perform long division or polynomial division of the numerator by the denominator. After performing the division, we get:

f(x) = 3/2x - 7/4 + (1/8)/(2x - 4)

The slant asymptote is given by the equation y = 3/2x - 7/4. Therefore, the function approaches this line as x approaches infinity.

Vertical Asymptote:

To find the vertical asymptote, we set the denominator equal to zero and solve for x:

2x - 3x - 4 = 0

-x - 4 = 0

x = -4

Thus, the vertical asymptote is x = -4.

In summary, the function has a slant asymptote given by y = 3/2x - 7/4 and a vertical asymptote at x = -4.

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Answer:

5

Step-by-step explanation:

(3-8)²+(0+0)²

25+0

25----> The square root of 25 is 5

a. the direction of the acceleration is approximately 78.4° counterclockwise from the +x-axis. b. the mass of the object is approximately 12.1 kg. c. the initial speed of the object is 0 m/s. d. the velocity components after 21.0 s based solely on the given information.

To solve this problem, we will use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:

ΣF = m * a

Given:

F₁ = (-1.85i + 6.75) N

F₂ = (-5.50i - 2.35) N

F₃ = (-43i) N

Acceleration magnitude (a) = 3 m/s²

(a) Direction of the acceleration:

To determine the direction of the acceleration, we need to find the net force acting on the object and then calculate the angle between the net force vector and the positive x-axis.

Net force (ΣF) = F₁ + F₂ + F₃

Net force = (-1.85i + 6.75) + (-5.50i - 2.35) + (-43i)

         = (-1.85i + 6.75 - 5.50i - 2.35 - 43i)

         = (-7.35i - 35.6)

The magnitude of the net force can be calculated using Pythagorean theorem:

|ΣF| = sqrt(Re² + Im²) = sqrt((-7.35)² + (-35.6)²) ≈ 36.3 N

The angle (θ) between the net force vector and the positive x-axis can be found using trigonometry:

θ = atan(Im/Re) = atan((-35.6)/(-7.35)) ≈ 78.4°

Therefore, the direction of the acceleration is approximately 78.4° counterclockwise from the +x-axis.

(b) Mass of the object:

From Newton's second law, we know that ΣF = m * a. Since we have the acceleration magnitude and the net force, we can solve for the mass (m):

|ΣF| = m * a

36.3 = m * 3

m = 36.3 / 3

m ≈ 12.1 kg

Therefore, the mass of the object is approximately 12.1 kg.

(c) Initial speed:

Given that the object is initially at rest (v₀ = 0 m/s), we can use the formula for final velocity (v) in terms of initial velocity (v₀), acceleration (a), and time (t):

v = v₀ + a * t

Since v₀ = 0 m/s and a = 3 m/s², we have:

v = 0 + 3 * 0

v = 0 m/s

Therefore, the initial speed of the object is 0 m/s.

(d) Velocity components after 21.0 s:

The problem does not provide information about the time evolution of the forces acting on the object, so we cannot determine the velocity components after 21.0 s based solely on the given information.

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The given matrix is in row-echelon form, but it is not in reduced row-echelon form. The given matrix is:

2 0 0 0

0 1 1 6

0 0 0 0

To determine if it is in row-echelon form, we need to check the following conditions:

1. All rows consisting entirely of zeros are at the bottom: In the given matrix, the third row consists entirely of zeros and is located at the bottom, so this condition is satisfied.

2. The first nonzero entry in each row, called a leading entry, is always strictly to the right of the leading entry in the row above it: In the given matrix, the leading entry in the second row is 1, which is to the right of the leading entry in the first row (which is 2). So this condition is satisfied.

3. Any rows of all zeros are at the bottom: Again, in the given matrix, the third row consists entirely of zeros and is located at the bottom, satisfying this condition.

Therefore, the given matrix is in row-echelon form.

To determine if it is also in reduced row-echelon form, we need to check one additional condition:

4. Each leading entry is 1, and each leading 1 is the only nonzero entry in its column: In the given matrix, the leading entries are 2 and 1, which are not equal to 1. Therefore, the matrix is not in reduced row-echelon form.

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This month's forecast using exponential smoothing with alpha = 0.2, if August's forecast was 145 is  148..

The exponential window function is a general method for smoothing time series data known as exponential smoothing. In contrast to the ordinary moving average, which weights previous data equally, exponential functions use weights that decrease exponentially with time.

The exponential smoothing with an alpha of .2 can be expressed as

F(t) = α*D(t) + (1-α)*F(t-1)

α = 0.2

F(t) = forecast for this month (October)

D(t) = actual demand for the last month (September) = 160

F(t-1) = forecast for last month (August) = 145

Then this can be expressed as ;

0.2*160 + (1-0.2)*145

= 32 + 116

= 148

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complete question;

The owner of Darkest Tans Unlimited in a local mall is forecasting this month's (October's) demand for the one new tanning booth based on the following historical data: col1 Month April May June July August September col2 Number of Visits 100 140 110 150 120 160 What is this month's forecast using exponential smoothing with alpha =. 2, if August's forecast was 145? a. 163b. 142 c. 148 d. 140 e. 144

The radius of convergence of the Taylor series for the exponential function, e^x, centered at x = 0, is infinite.

The Taylor series expansion for the exponential function, \(e^x\), around x = 0 is given by the formula:

\(e^x = 1 + x + (x^2)/2! + (x^3)/3! + (x^4)/4! + ...\)

This series converges for all values of x because the terms in the series decrease in magnitude as the exponent increases. This means that as x approaches infinity or negative infinity, the terms in the series approach zero.

The convergence of a power series is determined by the ratio test or the root test. In the case of the exponential function, both tests yield a radius of convergence of infinity. This indicates that the series converges for all values of x. Therefore, the Taylor series expansion of e^x around x = 0 is valid for all real numbers x.

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Answer:

x^2 + 4x + 6.5 = 0

Step-by-step explanation:

The discriminant = b^2 - 4ac = -10.

Lets let a = 1, then:

b^2 - 4c = -10

4^2 - 4(6.5)

= 16 - 26 = -10.

so b = 4 and c = 6.5.

- so we can write our equation as

x^2 + 4x + 6.5 = 0 would fit the requirement.

Answer:

One goal that I would like to accomplish over the next twenty months is to become a better person. Academically and personally. As cliché as it sounds, I would love to get better grades. Personally, I would like to get better at my emotional regulation when working on school. I would love to discover better study habits.

Answer:

x = 5

Step-by-step explanation:

15 / 3 =5