find the volume pls help asap

Answer:

11.97 lb

Step-by-step explanation:

To find the force that the rope must exert on the cart to keep it from rolling down the ramp, we need to resolve the forces acting on the cart along the direction of the ramp and perpendicular to the ramp.

First, we resolve the weight of the cart into its components. The weight of the cart acting vertically downwards can be resolved into a component perpendicular to the ramp and a component parallel to the ramp.

The component perpendicular to the ramp is given by:

W_perp = W * cos(theta) = 40lb * cos(15°) = 38.6lb

The component parallel to the ramp is given by:

W_parallel = W * sin(theta) = 40lb * sin(15°) = 10.4lb

where W is the weight of the cart, and theta is the angle of inclination of the ramp.

Next, we resolve the force exerted by the rope into its components. The force exerted by the rope can be resolved into a component perpendicular to the ramp and a component parallel to the ramp.

The component perpendicular to the ramp is given by:

F_perp = F * cos(phi) = F * cos(60°) = 0.5F

The component parallel to the ramp is given by:

F_parallel = F * sin(phi) = F * sin(60°) = 0.87F

where F is the force exerted by the rope, and phi is the angle of inclination of the rope.

To keep the cart from rolling down the ramp, the force exerted by the rope must balance the weight of the cart along the direction of the ramp. That is,

F_parallel = W_parallel

0.87F = 10.4lb

Solving for F, we get:

F = 11.97lb

Therefore, the force that the rope must exert on the cart to keep it from rolling down the ramp is approximately 11.97lb.

The amount of chemical in the tank after 15 minutes is 154.14 grams.

To determine the amount of chemical in the tank after 15 minutes, we need to use the formula for the concentration of a solution:

C = m/V

Where C is the concentration of the solution, m is the mass of the chemical, and V is the volume of the solution.

Initially, the tank contains 12 litres of water and 24 grams of chemical A, so the initial concentration of the solution is:

C0 = 24/12 = 2 grams per litre

The solution flows into the tank at a rate of 4 grams per litre and 4 litres per minute, so the amount of chemical flowing into the tank per minute is:

4 grams per litre × 4 litres per minute = 16 grams per minute

The well-stirred mixture flows out of the tank at a rate of 2 litres per minute, so the amount of chemical flowing out of the tank per minute is:

C × 2 litres per minute = 2C grams per minute

The net change in the amount of chemical in the tank per minute is:

16 grams per minute - 2C grams per minute = 16 - 2C grams per minute

After 15 minutes, the net change in the amount of chemical in the tank is:

(16 - 2C) grams per minute × 15 minutes = 240 - 30C grams

The final amount of chemical in the tank is:

m = 24 + 240 - 30C = 264 - 30C grams

The final volume of the solution in the tank is:

V = 12 + 4 litres per minute × 15 minutes - 2 litres per minute × 15 minutes = 42 litres

The final concentration of the solution in the tank is:

C = m/V = (264 - 30C)/42

Solving for C, we get:

42C = 264 - 30C

72C = 264

C = 264/72 = 3.67 grams per litre

The final amount of chemical in the tank is:

m = C × V = 3.67 grams per litre × 42 litres = 154.14 grams

Therefore, the amount of chemical in the tank after 15 minutes is 154.14 grams.

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Answer:

Point D is the solution to the system of equations.

Step-by-step explanation:

When asked for a solution involving 2 equations, the goal is to find a point (x,y) that would be a solution to both equations.  Any point on a line that is defined by an equation is a solution to that equation.  For an equation of y = 2x + 2, possible solutions are (1,4), (2,6), (5,12) etc.  These points all lie on the line formed by that equation.  There are an infinite number of possible solutions.  If a second eqaution is added, there is now a constraint on the possible answers.  The goal is to find a point that satisfies both equations.

If a seond equation of y = 1x + 3 were matced with y=2x+2, both are straight lines, but with different slopes.  So they will intersect at some point.  One may either solve mathematically using substitution, or by graphing, as was done here.  

Matematically:

y = 2x + 2

y = 1x + 3

Rearrange either equation to isolate a variable, x or y.  These are already isolated (since I made them up) so go to the next step of substituting one expression of y into the other:

y = 1x + 3

2x + 2 = 1x + 3

x = 1

Now use this value of x to find y:

y = 2x + 2

y = 2*(1) + 2

y = 4

The point these two lines intersect is (1,4) and is the "solution" to this series of equations.

See the attached graph.

E|X|n < ∞

Let X and Y be independent random variables satisfying E|X+Y|n < ∞ for some a > 0. We can show that E|X|n < ∞ using the triangle inequality.

Let b = a/2. Since E|X+Y|n < ∞, we know that E|X+Y| < ∞. Then by the triangle inequality, we have E|X| < |X+Y| + |Y| < ∞.

Raising both sides of the inequality to the nth power gives us E|X|n < (|X+Y| + |Y|)n < ∞.

Therefore, E|X|n < ∞.

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Answer:

Let's assume that the price before adding the VAT is x.

We know that the VAT rate is 8%, which means that the VAT amount is 8% of x, or 0.08x.

The total price including VAT is the sum of the price before VAT and the VAT amount, so we can write:

Total price = price before VAT + VAT amount

or

2,700 = x + 0.08x

Simplifying this equation, we can combine like terms on the right-hand side to get:

2,700 = 1.08x

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 1.08:

x = 2,700 / 1.08

x = 2,500

Therefore, the price before VAT was added is 2,500.

The CRB (Cramér-Rao Bound) of variance estimation is a lower bound on the variance of an unbiased estimator of a parameter. The CRB of variance estimation for this system is (02 +0)^2/(02 +0 + (02 +0)^2). This is the minimum variance that an unbiased estimator of the parameter 8 can achieve.

In this case, the parameter we are trying to estimate is 8. To derive the CRB for estimating the parameter 8, we first need to find the Fisher Information matrix, which is defined as:
I(8) = E[(d log f(X; 8)/d8)^2]
where f(X; 8) is the probability density function of X and E is the expectation operator.

Since X~N(0,02 +0), the probability density function of X is:
f(X; 8) = (1/sqrt(2*pi*(02 +0)))*exp(-X^2/(2*(02 +0)))

Taking the derivative of the log of this function with respect to 8, we get:
d log f(X; 8)/d8 = -(1/(02 +0))*((X^2)/(02 +0) - 1)

Squaring this and taking the expectation, we get:
I(8) = E[(1/(02 +0))^2*((X^2)/(02 +0) - 1)^2]

Simplifying and using the fact that E[X^2] = 02 +0, we get:
I(8) = (1/(02 +0))^2*(02 +0 + (02 +0)^2)

Finally, the CRB for estimating the parameter 8 is given by the inverse of the Fisher Information matrix:
CRB(8) = 1/I(8) = (02 +0)^2/(02 +0 + (02 +0)^2)

Therefore, the CRB of variance estimation for this system is (02 +0)^2/(02 +0 + (02 +0)^2). This is the minimum variance that an unbiased estimator of the parameter 8 can achieve.

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The value of (f-g)(x)  is  x^(2)-6x-55.

Mathematical operations on a function involve the manipulation or transformation of the function, such as adding, subtracting, multiplying, dividing, and integrating the function. These operations can be done either to the function itself or to the domain or range of the function. This can be used to find the inverse of a function, calculate the area under the curve, or find the first or second derivative of a function.

To find (f-g)(x), we need to subtract the function g(x) from the function f(x).

(f-g)(x) = f(x) - g(x)

= (x^(2)-5x-50) - (x+5)

= x^(2)-5x-50 - x - 5

= x^(2)-6x-55

Therefore, (f-g)(x) = x^(2)-6x-55.

This is the final answer for the difference between the two functions f(x) and g(x).

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The value of h is 99.969.

The Esscher Premium Principle is a method of calculating insurance premiums that considers the risk of an event occurring and the potential severity of the loss. The formula for the Esscher Premium Principle is:

Ex = ln(∑eαx Px)/α

Where Ex is the Esscher premium, α is the parameter, x is the loss amount, and Px is the probability of the loss occurring.

In this case, we are given X (3, 0.02), meaning that the loss amount is 3 and the probability of the loss occurring is 0.02. We are also given that the Esscher premium is 300 and the parameter is 1. Plugging these values into the formula, we get:

300 = ln(∑e1(3) 0.02)/1

Simplifying the equation, we get:

300 = ln(0.02e3)

Taking the natural logarithm of both sides, we get:

e300 = 0.02e3

Dividing both sides by 0.02, we get:

e300/0.02 = e3

Taking the natural logarithm of both sides again, we get:

300 - ln(0.02) = 3

Solving for h, we get:

h = (300 - ln(0.02))/3

h = 99.969

Therefore, the value of h is 99.969.

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Our assumption is false

We can prove this statement by contradiction. Suppose a > b and c > 0 but ac < bc.

Since a > b, then a - b > 0. Multiplying both sides by c > 0 gives (a - b)c > 0.

We can then add bc to both sides to get (a - b)c + bc > bc.

Since we assumed that ac < bc, then (a - b)c < 0, and thus (a - b)c + bc < bc, which contradicts the previous result.

Therefore, our assumption is false, and we can conclude that for a, b, and c ∈ Z, a > b and c > 0 =⇒ ac ≥ bc.

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Answer:

The answer is -4

Step-by-step explanation:

The slot of the line can be calculated using the formula : y2 - y1/ x2 - x1.

So, you would plug in the values making the equation 5 - (-7)/ -1 - 2 and solve.

a)\( -9 \)

b)\( \left[\begin{array}{ccc}+18 & -18 & +9 \\ +9 & -9 & +4 \\ -4 & +4 & -1\end{array}\right] \).

(a) The determinant of \( A \) can be calculated using the Laplace expansion, which states that the determinant of a matrix can be found by multiplying the elements in the first row of the matrix by the determinant of the matrix formed by removing the elements of the first row and column of the original matrix, then subtracting the result from the elements in the second row multiplied by the determinant of the matrix formed by removing the elements of the second row and column of the original matrix, and so on.

Using the Laplace expansion, the determinant of \( A \) can be found as follows:

\( \operatorname{det}(A) = 0 \times \operatorname{det}\left[\begin{array}{cc}1 & -3 \\ 2 & 3\end{array}\right] - (-2) \times \operatorname{det}\left[\begin{array}{cc}-3 & -3 \\ 2 & 3\end{array}\right] + (-3) \times \operatorname{det}\left[\begin{array}{cc}-3 & 1 \\ -3 & 3\end{array}\right] \)

\( \operatorname{det}(A) = 0 \times 18 + 2 \times (-18) + 3 \times 9 \)

\( \operatorname{det}(A) = 0 - 36 + 27 \)

\( \operatorname{det}(A) = -9 \)

Therefore, the determinant of \( A \) is \( -9 \).

(b) The matrix of cofactors of \( A \) can be found by taking the determinant of the matrix formed by removing the elements of the first row and column of the original matrix and multiplying it by the sign of the elements of the first row and column, then subtracting the result from the elements in the second row multiplied by the determinant of the matrix formed by removing the elements of the second row and column of the original matrix and multiplying it by the sign of the elements of the second row and column, and so on.

Using this method, the matrix of cofactors of \( A \) can be found as follows:

\( \left[\begin{array}{ccc}C_{11} & C_{12} & C_{13} \\ C_{21} & C_{22} & C_{23} \\ C_{31} & C_{32} & C_{33}\end{array}\right] = \left[\begin{array}{ccc}+18 & -18 & +9 \\ +9 & -9 & +4 \\ -4 & +4 & -1\end{array}\right] \)

Therefore, the matrix of cofactors of \( A \) is \( \left[\begin{array}{ccc}+18 & -18 & +9 \\ +9 & -9 & +4 \\ -4 & +4 & -1\end{array}\right] \).

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The volume of the silo is approximately 9,685.73 cubic feet.

What is volume of a cylinder?

The volume of a cylinder can be calculated using the formula:

[tex]V = \pi r^2h[/tex]  where V is the volume, r is the radius of the base of the cylinder, and h is the height of the cylinder.

We are given that the diameter of the silo is 17 feet. The radius, which is half the diameter, is therefore:

r = 17/2 = 8.5 feet

We are also given that the height of the silo is 42 feet.

Using the formula for the volume of a cylinder, we can calculate the volume of the silo:

[tex]V = \pi r^2h[/tex]

[tex]= \pi(8.5)^2(42)[/tex]

≈ 9,685.73 cubic feet

Therefore, the volume of the silo is approximately 9,685.73 cubic feet.

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Answer:

OPTION C

Step-by-step explanation:

There are 3 sides in a triangle. 2 of them are legs, and one of them is the Hypotenuse. "Sin" refers to Opposite/Hypotenuse.

To find A given a sine value, we must use inverse sin. I would suggest using desmos for this, but you need to switch to degrees in the online caluclator.

So the Equation is: [tex]sin^{-1} (0.9659)[/tex]

After plugging that into desmos, we get 74.994 degrees. Because that is not one of the answer, I'm assuming we must round our answer to the nearest whole number. In that case, your answer is 75 degrees, or OPTION C

To find the percent of the original amount of Carbon-14 in the bone remains when found in 1968, we can use the following formula:
A = A0 * (1/2)^(t/h)
Where A is the final amount of Carbon-14, A0 is the original amount of Carbon-14, t is the time elapsed, and h is the half-life of Carbon-14.

Plugging in the given values, we get:
A = A0 * (1/2)^(12600/5730)
Simplifying the exponent, we get:
A = A0 * (1/2)^2.199
Using a calculator, we find that (1/2)^2.199 is approximately 0.153, so:
A = A0 * 0.153
This means that the final amount of Carbon-14 is 15.3% of the original amount of Carbon-14. Therefore, the percent of the original amount of Carbon-14 in the bone remains when found in 1968 is 15.3%.

As for the second part of the question, Sarah Anzick was a member of the team that did DNA sequencing on the remains in 2014. This allowed for further analysis and understanding of the remains and their significance in terms of human history and evolution.

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The missing side of the triangle is 16 mm.

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common uses for an angle in trigonometry.

As per the given diagram:

The sides and angles of the right-angled triangle is given:

To find v using the trigonometric ratio:

sinθ = (P/H) {P is perpendicular and H is hypotunese}

for θ = 30°

sin30° = (8/v)

1/2 = 8/v

v = 16 mm

Hence, the missing side of the triangle is 16 mm.

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Therefore, one possible way to write vector u as a linear combination of the vectors in set S is:

u = [2] + [3]

To write vector u as a linear combination of the vectors in set S, we need to find scalars a, b, and c such that:

u = a[1] + b[2] + c[-2]

Substituting the given values of u and the vectors in S, we get:

[3] = a[1] + b[2] + c[-2]

To solve for the scalars a, b, and c, we can set up a system of equations:

3 = a + 2b - 2c

Since we only have one equation and three unknowns, there are infinitely many solutions to this system. One possible solution is:

a = 1, b = 1, c = 0

Substituting these values back into the equation, we get:

[3] = 1[1] + 1[2] + 0[-2]

Therefore, one possible way to write vector u as a linear combination of the vectors in set S is:

u = [1] + [2]

Similarly, for the second set of vectors, we need to find scalars d, e, and f such that:

u = d[2] + e[3] + f[-5]

Substituting the given values of u and the vectors in S, we get:

[8] = d[2] + e[3] + f[-5]

To solve for the scalars d, e, and f, we can set up a system of equations:

8 = 2d + 3e - 5f

Since we only have one equation and three unknowns, there are infinitely many solutions to this system. One possible solution is:

d = 2, e = 2, f = 0

Substituting these values back into the equation, we get:

[8] = 2[2] + 2[3] + 0[-5]

Therefore, one possible way to write vector u as a linear combination of the vectors in set S is:

u = [2] + [3]

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The correct answer is option a. 1 - e^-2.

To find the probability of a random variable X with exponential distribution, we use the following formula:P[X > x] = e^(-λx)Where λ is the rate parameter and x is the value we are trying to find the probability of.

In this case, we are given that the mean of the distribution is 1, so we can use this information to find the rate parameter:λ = 1/mean = 1/1 = 1Now, we can plug in the values for λ and x into the formula to find the probability:P[X > 2] = e^(-1*2) = e^-2 = 0.1353Therefore, the correct answer is option a. 1 - e^-2.

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Hypothesis: The P-value for this test is 0.026251 which is less than the significance level of 0.05.

Hypothesis is a statement or explanation proposed to explain a phenomenon. It is a logical conjecture, based on observations or experiments, made in order to draw out and test its consequences. In scientific research, a hypothesis is used as a starting point for further investigation and is tested through the scientific method. A hypothesis must be testable and falsifiable, meaning it can be tested and disproved using scientific evidence.

Therefore, we can reject the null hypothesis that there is no difference in the proportions of almonds in the new and old recipes. This means that the proportion of almonds in the new recipe is greater than in the previous recipe.

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We can deduce that 3pi/4<5pi/3<2pi

The angle is in the 4th quadrant. To find the angle you just do:

[tex]2\pi -\frac{5\pi }{3}=\frac{\pi }{3}[/tex]

The answer to your question is B. I hope that this is the answer that you were looking for and it has helped you.

For matrix g : \(\displaystyle g^{-1}=\frac{1}{\left| g \right|}\left[\begin{array}{ccc}6 & 1 & -3 \\ -8 & -3 & 2 \\ 3 & -1 & -3\end{array}\right] \)
For matrix h : \(\displaystyle h^{-1}=\frac{1}{\left| h \right|}\left[\begin{array}{ccc}1 & 0 & -1 \\ 1 & -1 & 1 \\ 0 & 1 & -1\end{array}\right] \)

For matrix g, the inverse can be found using the following equation:

\(\displaystyle g^{-1}=\frac{1}{\left| g \right|}\left[\begin{array}{ccc}6 & 1 & -3 \\ -8 & -3 & 2 \\ 3 & -1 & -3\end{array}\right] \)



For matrix h, the inverse can be found using the following equation:

\(\displaystyle h^{-1}=\frac{1}{\left| h \right|}\left[\begin{array}{ccc}1 & 0 & -1 \\ 1 & -1 & 1 \\ 0 & 1 & -1\end{array}\right] \)



Where \(\left| g \right|\) is the determinant of the matrix g and \(\left| h \right|\) is the determinant of the matrix h.

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Hello there! To find f ∘ g, g ∘ f, and g ∘ g, let's first recall the definition of function composition: given two functions f and g, their composition f ∘ g is defined as the function that results from applying g to the result of applying f to its argument. Specifically, for a given input x, we can express the composition f ∘ g as follows: (f ∘ g)(x) = f(g(x)).

Given f(x) = x4 and g(x) = 1/x, we can find each composition as follows:

(a) f ∘ g = f(g(x)) = f(1/x) = (1/x)4

(b) g ∘ f = g(f(x)) = g(x4) = 1/(x4)

(c) g ∘ g = g(g(x)) = g(1/x) = 1/(1/x) = x

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Answer:

See below.

Step-by-step explanation:

We are asked to find the value of x.

We should know that these angles are Same-Side Interior Angles.

Same-Side Interior Angles are 2 angles that aren't equal, but supplementary. They're formed inside 2 parallel lines.

Supplementary angles are 2 angles that add up to 180°.

Since these 2 angles are Same-Side Interior Angles, both can be added to equal 180°.

[tex]4x+2x+12=180[/tex]

Combine Like Terms:

[tex]6x=168\\x = 28[/tex]

The value of x is 28.

a) The value of k is 0.04.

b) The value of E[X] is 3.3333 and the value of var[X] is 1.3889.

c) The standard deviation of G is 5.8916.

d) The standard deviation of H is 7.0711.

(a) To find the value of k that ensures that f(x) is a proper density function, we need to ensure that the integral of f(x) over its domain is equal to 1:

∫05 (0.1 + kx) dx = 1

0.5 + 12.5k = 1

12.5k = 0.5

k = 0.04

Therefore, the value of k is 0.04.


(b) To find E[X], we need to evaluate the integral of x*f(x) over its domain:

E[X] = ∫05 x(0.1 + 0.04x) dx

E[X] = 0.5 + 0.02(125/3) = 3.3333

To find var[X], we need to evaluate the integral of (x - E[X])2*f(x) over its domain:

var[X] = ∫05 (x - 3.3333)2(0.1 + 0.04x) dx = 1.3889


(c) If G = 5X - 6, then E[G] = 5E[X] - 6 = 11.6667 and var[G] = 52var[X] = 34.7225. The standard deviation of G is the square root of var[G], which is 5.8916.


(d) If H = 5 - 6X, then E[H] = 5 - 6E[X] = -14.9998 and var[H] = 62var[X] = 49.9994. The standard deviation of H is the square root of var[H], which is 7.0711.

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Check the picture below.

The linear speed of the circle is 2.125 cm/s and the angular speed of the circle is 0.1012 rad/s.

The linear speed of the circle can be found by calculating the length of the arc traveled in 25 seconds. The length of an arc is given by the formula L = rθ, where r is the radius of the circle and θ is the central angle in radians. Converting the given angle from degrees to radians, we have:

θ = 145 degrees * π/180 = 2.53 radians

Substituting the values into the formula, we get:

L = 21 cm * 2.53 = 53.13 cm

Therefore, the linear speed of the circle is:

v = L/t = 53.13 cm/25 s = 2.125 cm/s

The angular speed of the circle can be found by dividing the central angle by the time taken to travel that angle. Therefore, the angular speed of the circle is:

ω = θ/t = 2.53 radians/25 s = 0.1012 rad/s

Hence, the linear speed of the circle is 2.125 cm/s and the angular speed of the circle is 0.1012 rad/s.

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The correct option representing possible sum for the long chain is B. 13 3 4 + 15 2 4 = 29 1 4.

Firstly let us convert the mixed fraction to fraction. So, the length of first chain = (13×4)+3/4

Length of first chain = 55/4 inches

Length of first chain = 13.75 inches

Length of second chain = (15×4)+2/4

Length of second chain = 62/4

Second chain length = 15.5 inches

So, total length = length of first chain + length of second chain

Total length = 13.75 + 15.5

Total length = 29.25 inches

Converting the decimal back to mixed fraction -

Total length = 29 1/4 inches

Thus, the correct answer B. 13 3 4 + 15 2 4 = 29 1 4.

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The equatiοn οf the least squares regressiοn line which mοst clοsely matches the data set is y = 3.5 x + 43.8

Tο sοlve fοr the data set, lets lοοk at the table,

X            1190         1992          1994         1996           1998

Y             45             51               57            61               75

Let the equatiοn that shοws the abοve data be

y = b + a x ---------(1)

Where, a = Σy Σx² - Σx Σxy

And, b = (Σxy - Σx Σy) / n Σx² -(Σx)²

By the abοve table,

Σx=20

Σxy = 1296

Σx² = 120

Σy=289

By substituting these values in the abοve value οf a and b,

We get b = 43.8 and a = 3.5

Substitute this value in equatiοn (1)

We get, the equatiοn that shοws the given data is,

y = 3.5 x + 43.8

Therefοre, οptiοn 3 is cοrrect.

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Answer:  The total number of milkshakes sold is 7 + 18 = 25.

The number of milkshakes sold with whipped cream is 7.

To find the percentage of milkshakes with whipped cream, we can use the formula:

percentage = (part/whole) x 100

Substituting the values, we get:

percentage = (7/25) x 100

percentage = 28

Therefore, 28% of the milkshakes had whipped cream.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To calculate your new income after an increase of 8.2%, you can use the following formula:

New income = Old income + (Percentage increase * Old income)

Plugging in the values given in the problem, we get:

New income = 420,600,000 + (8.2% * 420,600,000)

New income = 420,600,000 + (0.082 * 420,600,000)

New income = 420,600,000 + 34,524,120

New income = 455,124,120

Therefore, your new income after an increase of 8.2% would be 455,124,120.