A store sells ice cream with assorted toppings. They charge $3.00 for an ice cream, plus 50 cents per ounce of toppings. How much does an ice cream cost with 4 ounces of toppings?

The graph of each function in the piecewise function is added as an attachment

The equation of the piecewise function is given as

f(n) = n/2 if n is even

        3n + 1 if n is odd

In the above definition of the piecewise function, we have the following functions and the domains

Note that:

The domain of the function is the set of input values of the graph

This in other words mean the domain of a function is the set of x values of the graph.

Next, we plot the graph of each function in the piecewise function in their respective domain

See attachment for the graph of each function in the piecewise function,

On the graph, the blue line represents f(n) = n/2 while the other line represents f(n) = 3n + 1

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Answer:

D) 1 3/4 x 4 1/6= 7 7/24

C) 7/9 x 5 2/5= 4 1/5

Done by NeighborhoodDealer

Answer:

twice as many residents use techy than use upstart

Step-by-step explanation:

edg 2023

Answer:

Step-by-step explanation:

Which cyclist lives closest to the park?

I'll rewrite both equations as y = mx + b so that they are more clearly understood.

A(x)=  - 9.2x + 36.8

B(x)=  - 13.8x + 41.4

The negative slopes represent the fact that both boys are headed toward the park from their homes, so as time increases, their distance from the park decreases.  The y-intercept represents their starting points from the park (at time = 0, they are still at home, doing homework).

Distance from home:  A:  36.8 miles;  B:  41.4 miles.  Boy A lives closest to the park.

Who will be the first to arrive at the park?

The slopes are their speeds.  Boy B cycles faster, but has to cover a greater distance.  A(x) and B(x) are 0 when they reach the park,  Find the time, x, for each by setting that distance to 0.

A(x)=  - 9.2x + 36.8

0 = - 9.2x + 36.8

9.2x = 36.8

x = 4 hours

B(x)=  - 13.8x + 41.4

0 = - 13.8x + 41.4

13.8x = 41.4

x = 3 hours

Boy B arrives first.

How much earlier will that cyclist arrive?

From above, Boy B arrives one hour before Boy A.  He uses that time flirting with a classmate while waiting.

Is there a time when both cyclists are the same distance from the orchard?

This is asking is there a time, x, in which both equations are wequal to each other:

A(x)= b(x) ?

A(x)=36.8 - 9.2x

B(x)= 41.4 - 13.8x

36.8 - 9.2x = 41.4 - 13.8x

4.6x = 4.6

x = 1 hour

At one hour they are both the same distance from the park.

The orthogonal trajectories of the family of curves x² + 2y² = k² are given by the equation x² = K²y⁴.

To find the orthogonal trajectories of the family of curves x² + 2y² = k², follow these steps:

1. Write the given equation as a function: x² + 2y² = k².
2. Differentiate the equation implicitly with respect to x: 2x + 4y(dy/dx) = 0.
3. Solve for dy/dx: dy/dx = -2x / (4y) = -x / (2y).
4. Replace dy/dx with -dx/dy to obtain the orthogonal trajectory: -dx/dy = -x / (2y).
5. Simplify the equation: dx/dy = x / (2y).
6. Separate the variables: dx/x = 2dy/y.
7. Integrate both sides: ∫(1/x)dx = 2∫(1/y)dy.
8. Obtain the integrals: ln|x| = 2ln|y| + C.
9. Remove the natural logarithm by raising e to the power of both sides: |x| = \(|y|^2 * e^C\).
10. Introduce a new constant K, where K = \(e^C: |x| = K|y|^2\).
11. Eliminate the absolute values by squaring both sides: x² = K²y⁴.

The orthogonal trajectories of the family of curves x² + 2y² = k² are given by the equation x² = K²y⁴.

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Answer:

I think the answer you're looking for is 86400

Step-by-step explanation:

Answer:

No, but if it was how many studens school like math then yes

in Step-by-step explanation:

Answer:

I think it's the third one.

The solution is 19.8x - 11.1y

Net yardage for these four plays is given by the equation A = 19.8x - 11.1y

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The number of plays = 4 plays

On the first play , it gains = 25x yards

On the second play , it gains = 0.9y yards

On the third play , it loses = -12y yards

On the fourth play , it loses = -5.2x yards

So , the net yardage of plays A = 25x + 0.9y - 12y - 5.2x

On simplifying the equation , we get

A = 25x + 0.9y - 12y - 5.2x

A = 19.8x - 11.1y

Therefore , the value of A is 19.8x - 11.1y

Hence , the equation is A = 19.8x - 11.1y

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Answer:

1,400,000,000

Step-by-step explanation:

We can express the value \(1.4\times 10^9\) in standard form by moving the decimal point of the coefficient (1.4) to the right 9 times because 9 is the exponent of the 10 term:

1,400,000,000.

Hence, 15 people out of 3 people can be chosen in 35 ways.

It is given that:

The total number of people in a race, n = 15

The number of finalists, r = 3.

Hence, the number of ways in which 3 people out of the 15 people can be finishers are:

\(^{15}C_{3} }\) = \(\frac{15!}{(15-3)!3!}\) = \(\frac{15!}{12!3!}\) = 35.

Hence, 15 people out of 3 people can be chosen in 35 ways.

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We have shown that the log of the geometric mean of two numbers is the arithmetic mean of the logs of those two numbers.

We can use the properties of logarithms to show that the log of the geometric mean of two numbers is the arithmetic mean of the logs of those two numbers.

First, recall that the arithmetic mean of two numbers is half their sum:
arithmetic mean = (v + w)/2

And the geometric mean is the square root of their product:
geometric mean = √(v*w)

Now, let's take the log of the geometric mean:
log(geometric mean) = log(√(v*w))

Using the property of logarithms that log(a*b) = log(a) + log(b), we can expand the expression:
log(√(v*w)) = log(√v) + log(√w)

Using the property of logarithms that log(a^b) = b*log(a), we can simplify the expression:
log(√v) + log(√w) = (1/2)*log(v) + (1/2)*log(w)

Now, we can see that the log of the geometric mean is the arithmetic mean of the logs of the two numbers:
log(geometric mean) = (log(v) + log(w))/2

So, if we let p = log(v) and q = log(w), we can see that the log of the geometric mean of v and w is the arithmetic mean of p and q:
log(geometric mean) = (p + q)/2

Therefore, we have shown that the log of the geometric mean of two numbers is the arithmetic mean of the logs of those two numbers.

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Answer:

12 square in

Step-by-step explanation:

In the diagram, the diameter is 4 in. Radius is half the length of diameter, so the radius of the yellow circle is 2 in. Using the given formula, A = pi*r*r, we can calculate the approximate area of the circle.

A = pi*r*r = 3*2*2 = 12 square in

Answer:

12 in^2

Step-by-step explanation:

Since the formula to find the area of a circle is already up, we can use that to solve the question.

In the image, we can see that the diameter of the circle is 4inches. Since two radii equal one diameter, one radius is 2 inches.

--> The reason why we found the radius is because the 'r' in the formula means radius. We need the value of the radius to find the area of the circle.

Now, we can just replace r with 2.

--> A = 4\(\pi\)

Since the question told us to replace \(\pi\) with 3, we can do that.

--> A = 4 x 3

--> A = 12

We can conclude that the area of the circle is 12 in^2.

The correct answer is the fourth option: "On a coordinate plane, parallelogram R prime S prime T prime U prime has points (3.2, 4.8), (5.5, 2.5), (5.5, negative 0.5), (3.2, 1.8)."

we can follow the steps outlined in the previous response. First, we plot the vertices of parallelogram RSTU: (2, 3), (5, 3), (7, 1), (4, 1). Then, we apply the rotation transformation to each vertex using the formulas provided, and obtain the coordinates of R', S', T', and U': (3.2, 4.8), (5.5, 2.5), (5.5, -0.5), (3.2, 1.8). Finally, we plot these transformed vertices to obtain parallelogram R'S'T'U'. This parallelogram corresponds to the fourth option in the answer choices.

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Complete question is :

Parallelogram RSTU is rotated 45° clockwise using the origin as the center of rotation. On a coordinate plane, parallelogram R S T U has points (2, 3), (5, 3), (7, 1), (4, 1). Which graph shows the image of RSTU? On a coordinate plane, parallelogram R prime S prime T prime U prime has points (negative 1, 4), (1, 6), (4, 6), (2, 4). On a coordinate plane, parallelogram R prime S prime T prime U prime has points (3.5, 1), (5.5, negative 1), (5.5, negative 4), (3.5, negative 2). On a coordinate plane, parallelogram R prime S prime T prime U prime has points (2, negative 3), (5, negative 3), (7, negative 1), (4, negative 1). On a coordinate plane, parallelogram R prime S prime T prime U prime has points (3.2, 4.8), (5.5, 2.5), (5.5, negative 0.5), (3.2, 1.8).

The value of the inverse function at x = 4 is:

\(y = g^-^1^(^4^) =-5\)

From the attachment of graph :

Points available on the graph 'g' are (-5, 4), (-2, 1), (0, -1), (4, -2).

Since, rule to get the points lying on the graph of the inverse of the given function is,

(x, y) → (y, x)

And, (x, y) is the function of g and (y , x) is the inverse function of the g.

By the given rule, points on \(g^-^1^(^x^)\)  will be,

(4, -5), (1, -2), (-1, 0), (-2, 4)

Therefore, value of the inverse function at x = 4 will be:

\(y = g^-^1^(^4^) =-5\)

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Answer:

239 miles per gallon for a round trip.

Step-by-step explanation:

you'd need to achieve 238,900 / 2000 = 119.5 miles per gallon for a one way trip,

Answer:

The first one

\( log_{11} \: (x)\)

Step-by-step explanation:

f(x) = 11^x

Here are the steps to find the inverse of a function:

1. Let f(x)=y

2. Make x the subject of formula.

3. Replace y by x.

\(11 {}^{x} = y \\ \: log(11 {}^{x} ) = log(y) \\ x log(11) = log(y) \\ x = \frac{ log(y) }{ log(11) } = log_{11}(y) \\ f {}^{ - 1} (x) = log_{11}(x) \)

Answer:

156.25

Step-by-step explanation:

8x2 (2 years) = 16. 2500 / 16 = 156.25

Answer:

they are both natural numbers

So, the given system of equations has no solutions.

The system of equations 2x + 4y = 10 and 3x + 6y = 12 can be written in matrix form as:

| 2 4 | | x | | 10 |

| 3 6 | | y | = | 12 |

To find the number of solutions, we can use the concept of the determinant of a matrix. The determinant of a matrix is a scalar value that can be calculated from the elements of a square matrix. If the determinant of the matrix is non-zero, the system of equations has a unique solution. If the determinant is zero, the system may have either no solutions or infinitely many solutions.

To find the determinant of the matrix, we can use the formula:

| 2 4 |

| 3 6 | = (26) - (43) = 12 - 12 = 0

Since the determinant of the matrix is zero, the system of equations has either no solutions or infinitely many solutions.

To determine which case applies, we can use the concept of the rank of a matrix. The rank of a matrix is the number of linearly independent rows or columns in the matrix. If the rank of the matrix is less than the number of variables, then the system has no solutions. If the rank of the matrix is equal to the number of variables, then the system has a unique solution.

The rank of the matrix can be found by converting it into the row echelon form or reduced row echelon form.

| 2 4 | | 2 4 |

| 3 6 | = | 0 0 |

The rank is 1, which is less than 2, the number of variables. Therefore, the system of equations has no solutions.

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9514 1404 393

Answer:

  A.  $4006

Step-by-step explanation:

The total tax due is the sum of the amounts due in each applicable bracket.

  $970 +3,036 = $4,006

_____

Additional comment

There are easier ways to compute the tax, but this is the way shown on many tax forms.

Based on the data in the table, if a cow is randomly selected from farm B, the probability that its feed includes seaweed is 0.597 (Option D) and without is 0.57

Note that the total number of feed with sea weed is 74.
And the total number of cows on the farm B is 124.

Thus, the cows whose feed includes seaweed is 74/124

= 0.59677419354

≈ 0.597

The Probability of those whose feed is without sea weed is

Note that the total number of feed without sea weed is 40.
And the total number of cows on the farm B is 76.

Thus, the probability is 40/70
= 0.5714285714

≈ 0.571

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The required requirement of the density curve is should be equal to 1 and the ordinate should not be zero.

Given that,
Two requirements of a density curve are to be determined.

A density curve is defined as a curve on a graph that represents the distribution of values in a dataset.

Here,

The two requirements of a density curve should be,

a. The area under the density curve should be equal to 1.

b. The ordinate of the curve should not be zero i.e. they should always have the vertical height.

Thus, the required requirement of the density curve is mentioned above.

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Answer: 20

Step-by-step explanation:

18/20 %90

The probability that exactly one of the coins is a 10p piece is 1/2.

To find the probability that exactly one of the coins is a 10p piece, we can consider the possible outcomes.

There are two coins, and each coin can be either a 10p piece or a non-10p piece. Let's consider the four possible outcomes:

1. Erin's coin is a 10p piece, and Jack's coin is a non-10p piece.

2. Erin's coin is a non-10p piece, and Jack's coin is a 10p piece.

3. Both Erin's and Jack's coins are 10p pieces.

4. Both Erin's and Jack's coins are non-10p pieces.

Since the total amount of the two coins is less than 50p, we can eliminate the third possibility (both coins being 10p pieces).

Now, let's calculate the probability for each of the remaining possibilities:

1. Erin's coin is a 10p piece, and Jack's coin is a non-10p piece:

The probability of Erin having a 10p piece is 1/2, and the probability of Jack having a non-10p piece is also 1/2. Therefore, the probability of this outcome is (1/2) * (1/2) = 1/4.

2. Erin's coin is a non-10p piece, and Jack's coin is a 10p piece:

This is the same as the previous case, so the probability is also 1/4.

3. Both Erin's and Jack's coins are non-10p pieces:

The probability of Erin having a non-10p piece is 1/2, and the probability of Jack having a non-10p piece is also 1/2. Therefore, the probability of this outcome is (1/2) * (1/2) = 1/4.

Now, we sum up the probabilities of the two cases where exactly one of the coins is a 10p piece:

1/4 + 1/4 = 2/4 = 1/2.

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There are 144 possible sequences of chip colors.

We can solve this problem by counting the number of possible sequences of chip colors that can be drawn from the bag until the total value of the chips is at least $7.

Let's consider all the possible sequences of chips that can be drawn from the bag. The first chip can be any of the 6 chips in the bag. For each chip color, there are different scenarios that can happen after drawing the first chip:

Therefore, the total number of possible sequences of chip colors that can be drawn from the bag until the total value of the chips is at least $7 is: 2 x 32 + 1 x 32 + 3 x 16 = 144

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The estimated area of the circle is then: Estimated area = 0.7 x 4r²= 2.8r²

To estimate the area of a circle with the center at origin and radius r, there are various methods you can use.

One of them is Monte Carlo Integration.

Monte Carlo Integration is a numerical technique used to calculate an estimate of an area by performing a probability simulation. In this case, the simulation involves generating a random sample of points within the circle, and then counting the number of points that lie within it.

Here is a simple method for using Monte Carlo Integration to estimate the area of a circle with center at origin and radius r:

Step 1: Create a square of side length 2r centered at the origin, with vertices (r, r), (r, -r), (-r, r), and (-r, -r). This square completely encloses the circle.

Step 2: Generate a large number of random points within the square, using a uniform distribution. For example, you could use a computer program to generate 10,000 random points with x and y coordinates between -r and r.

Step 3: Count the number of points that lie within the circle. To do this, you can use the Pythagorean theorem to check if each point is inside or outside the circle. If a point has coordinates (x, y), then it lies within the circle if x^2 + y^2 ≤ r^2.

Step 4: Estimate the area of the circle by multiplying the proportion of points that lie within the circle by the area of the square. The proportion of points that lie within the circle is equal to the number of points within the circle divided by the total number of points generated.

The area of the square is 4r^2.

The estimated area of the circle is then:

Estimated area = Proportion of points in circle x Area of square

= Number of points in circle / Total number of points x 4r²

For example, if 7,000 of the 10,000 random points lie within the circle, then the proportion of points within the circle is 0.7.

The estimated area of the circle is then:

Estimated area = 0.7 x 4r²

= 2.8r²

This method is easy to use, and it becomes more accurate as the number of random points generated increases.

For best results, you should generate at least 10,000 points.

The estimated area may not be precise like the known formula, but the result would be quite close to the actual area of the circle.

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Answer:

2 days

Step-by-step explanation:

To eliminate the ys in the system of equations, we need to add the equations

From the question, we have the following parameters that can be used in our computation:

5x + 3y = 9

4x - 3y = 9

To eliminate the ys in the system of equations, we multiply the equations by 1

So, we have

5x + 3y = 9

4x - 3y = 9

Next, we add the equations

9y = 18

Hence, the new equation is 9y = 18

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Answer:

77 C

Step-by-step explanation:

To find the mean add all the numbers together then divide by the total amount of numbers

Answer:    54

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