The world's largest fruitcake was made by Dr.Fabrizio Sepe of Italy.It was 4,353kg.If each serving size was 200 grams.How many people could the fruitcake serve?

The rate of change of the average price of the new car is $274.50 per year.

The rate of change of the average price of the new car is a function of the change in average price over the years and the change in the number of years.

Rate of change = change in the average price / change in the number of years

Rate of change = (price in 2002 - price in 1994)  / difference in the number of years

Rate of change = (19,126 - 16,930) / (2002 - 1994)

Rate of change = 2196 / 8

Rate of change = $274.50

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if you mean 90 × 10⁴

then the answer would be, 900000.

but if you mean 9 × 10⁴ then the answer would be, 90000.

hope it helps.

Bye.

Answer:D

Step-by-step explanation:

Answer:

This problem is same as finding the least common multiple (LCM) of 3 and 4.

3 = 3

4 = 2 x 2

=> LCM = 3 x 2^2 = 12 (3 appears once, 2 appears twice)

=> After 12 hours, two bell P and Q ring simultaneously.

Hope this helps!

:)

Answer:

Step-by-step explanation:

a) If a driver uses a full tank of gas every day, the fraction of a tank he will use in 3 days is 3/1, or 3/1 of a tank.

b) If a driver uses a full tank of gas every day, the fraction of a tank he will use in 1 week is 7/1, or 7/1 of a tank.

It's worth noting that tanks of gas come in different sizes, so the amount of gas consumed in a day, week, or any other period of time will depend on the size of the tank, and the consumption of the car, so this answer is based on the assumption that a full tank is used every day.

Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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[(2, 2), (4, 4), (6, 6), (8, 8)] is the only function among the options.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
(2, 2), (4, 4), (6, 6), (8, 8)  = Function   [relation ship is linear]

(0, 3), (3, 5), (5, 6),(8, 4)  = not function [relationship cannot be justified]

(1,2), (3, 3), (4, 8), (6, 3) = not function [relationship cannot be justified]

(3, 4) (5, 2), (5, 6), 7.3)  = not function [relationship cannot be justified]

Thus, (2, 2), (4, 4), (6, 6), (8, 8) is the only function among the options.

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Answer:

7 x 8 x 3 = 56 x 3 = 56 + 56 +56 = 168

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The equation of the line that is parallel to the given line and has an x-intercept of -3 is y= 2/3x + 2.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

We have a graph.

So, slope of line in graph is

= (-1-1)/ (0.-3)

= -2/ (-3)

= 2/3

and, we know that two parallel line have same slope.

so, the slope of parallel line is 2/3 and the x intercept is -3.

So, the Equation line is y= 2/3 x  + b

0 = 2/3 (-3) +b

b= 2

Thus, the required equation is y= 2/3x + 2.

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Answer:

x>-5

Step-by-step explanation:

5x + 6 > 2x – 9

3x > -15

x>-5

Answer:

2. dM/dt = -0.11M

Step-by-step explanation:

Differential equations for proportional amouts:

A differential equation for proportional amounts is given by:

\(\frac{dx}{dt} = ax\)

In which a is the constant rate. If the amount increases, a is positive. If it decays, b is positive.

In this question:

Decays, so a < 0.

Proportional to the amount of the substance present at a given time, which means that a multiplies the amount M.

This means that the correct answer is given by option 2.

Answer: No it does not

Well, first you can search up a picture of the Louisiana State Flag if you don't know what it looks like. In case you don't, it looks like this.

The Louisiana State Flag does not have a line of symmetry because the bird's  head is facing in one direction. If you split the state flag in half, both sides would not be similar.

Answer: Shade 6 pieces

Step-by-step explanation:

Because 2/5 of 15 is 6

Answer:8z+5

Step-by-step explanation: Add 3z to 5z  which equals 8z and do 9-4 which equals 5 .Lastly add together.

Option (B) is correct. Thus, percentage of students with scores between 70 and 130 is 95% .

The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. The average degree of variability in your data set is represented by the standard deviation.

It reveals the average deviation of each score from the mean. Think about the following data: 2, 1, 3, 2, 4. The average and the total square of the observations' departures from the mean will be 2.4 and 5.2, respectively. This means that √(5.2/5) = 1.01 will be the standard deviation.

Here:

μ = 100, σ = 15

Thus we have

30 μ - kσ = 70

= 100 – k(15) = 70

= k= 30/15 = 2

Also we have, μ + Ασ: = 130

100+ k(15) = 130

k = 30/15 = 2

Now, the percentage of students with scores between 70 and 130 is same as the percentage of students between μ - 2σ, μ+ 2σ  and by empirical rule the area between μ (+-) 2σ  is 95%. Thus, percentage of students with scores between 70 and 130 is 95%

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3. The volume of the Pringle Chips container is approximately 2034.72 cubic inches.

4. The cake takes up approximately 7317 cubic inches of space.

5. The volume of foam in the model of the volcano is approximately 7234.08 cubic centimeters.

1. The units for Volume are always cubed.

2. Volume is the amount of space an object takes up. True.

3. To calculate the volume of the Pringle Chips container, we need to find the volume of a cylinder. The formula for the volume of a cylinder is V = πr^2h, where π is a constant (approximately 3.14), r is the radius, and h is the height. Given that the diameter is 9 inches, the radius would be half of that, which is 4.5 inches. Substituting the values into the formula, we have:

V = 3.14 * (4.5)^2 * 32

V = 3.14 * 20.25 * 32

V ≈ 2034.72 cubic inches

4. To find the volume of the 3-tier cake, we need to find the volume of each tier separately and then add them together. Since all the tiers are cylinders, we can use the formula V = πr^2h.

Tier 1:

V1 = 3.14 * (12)^2 * 10 = 4521.6 cubic inches

Tier 2:

V2 = 3.14 * (8)^2 * 10 = 2010.4 cubic inches

Tier 3:

V3 = 3.14 * (5)^2 * 10 = 785 cubic inches

Total volume:

Total V = V1 + V2 + V3

Total V = 4521.6 + 2010.4 + 785

Total V ≈ 7317 cubic inches

5. To find the volume of the Styrofoam model of the volcano, we can use the formula for the volume of a cone, V = (1/3)πr^2h. Given that the diameter is 48 centimeters, the radius would be half of that, which is 24 centimeters. Substituting the values into the formula, we have:

V = (1/3) * 3.14 * (24)^2 * 12

V = (1/3) * 3.14 * 576 * 12

V ≈ 7234.08 cubic centimeters

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The slope of Function A is less than the slope of Function B.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

given two function A and B

For Function A:

General formula of Slope:

Slope = (y₂ -y₁)/(x₂ - x₁)

in our case,

at x₂ = 4 , y₂= 2

at x₁ = 0 , y₁=0

Thus,

Slope = (2-0)/(4-0)

Slope = 1/2

For Function B:

General formula of Slope:

Slope = (y₂ -y₁)/(x₂ - x₁)

in our case,

at x₂ =-1  , y₂= -1

at x₁ = 3 , y₁=11

Thus,

Slope = (11+1)/(3+1)

Slope = 12/4

Slope = 3

Therefore, The slope of Function A is less than the slope of Function B.

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Answer:

367 meters

Step-by-step explanation:

(220.2÷60)x100

9514 1404 393

Answer:

  72

Step-by-step explanation:

The difference of 45 means the difference of digits in the number is 45/9 = 5. So, the ones digit is 7-5 = 2, and the number is 72.

__

If you want an equation, you can use x for the ones digit.

  70 +x = 45 +(10x +7)

  18 = 9x . . . . . . . . . . . . . subtract 52+x from both sides

  2 = x

The ones digit is 2, so the number is 72.

_____

Further explanation

If you start with the two digits xy in a number and reverse them, the difference between the numbers xy and yx is ...

  (10x +y) -(10y +x) = 9(x -y)

This tells you the difference between the digit-reversed numbers is 9 times the difference between the digits.

Answer:

the answer is 72

Step-by-step explanation:

:))))))

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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When the outer diameter of the ball with ice on it is 24 cm then the outer surface area of ice changes at the rate of 1/90cm²/sec.

As given in the question,

Spherical ball is coated with uniform thickness.

Ice melts at the rate of 8ml/min

= (8/60)cm³/sec

Consider r as the  radius of given spherical ball

Diameter = 24cm

⇒Radius 'r' =12cm

Volume 'V' = (4/3)πr³

⇒ dV /dt = (4/3)π(3r²r')

⇒-(8/60) = (4/3)π(3 ×12²×r')

⇒r' =-(8/60)×(1/576π)

⇒r' = - 1/ 4320π

Rate at which change in surface area

A =4πr²

⇒A' = 4πrr'

⇒A' = 4π (12) ( - 1/ 4320π)

      = -1/90 cm²/sec.

Decrease in surface area = 1/90 cm²/sec.

Therefore, when the outer diameter of the ball with ice on it is 24 cm then the outer surface area of ice changes at the rate of 1/90cm²/sec.

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Answer:

It’s b

Step-by-step explanation:

Which is point g

Answer:

Z

Step-by-step explanation:

The calculated value of y when x = 8 is 10.125

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

y varies inversely as the square of x

Mathematically, this can be expressed as

y = k/x²

So, we have

k = x²y

Given that x = 6 when y = -18, we have

k = 6² * -18

So, we have

k = -648

When x = 8, we have

y = -648/8²

Evaluate

y = -10.125

Hence, the value of y is 10.125

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Answer:

Step-by-step explanation:

The growth rate of the investment is represented by the constant multiplier in the exponential term of the formula y = 20000(1.035)x. In this case, the constant multiplier is 1.035, which represents the annual growth rate of the investment account.

To calculate the growth rate as a percentage, we can subtract 1 from the constant multiplier, and then multiply the result by 100.

So, the growth rate of the investment is:

1.035 - 1 = 0.035

0.035 * 100 = 3.5%

Therefore, the growth rate of the investment is 3.5%.

The power series representation of f(x) is, f(x) = 1/4 - 1/16 + (1/64)*x - (1/256)*x² + ...

Geometric progression is a sequence of series whose ratio with adjacent values remains the same.

Here,
The function f(x) = x/(4+x) can be expressed as a power series using partial fraction decomposition and geometric series expansion. Here's how,

First, we can decompose f(x) as:

f(x) = x/(4+x) = x/(4(1+x/4)) = (1/4) - (1/16)/(1+x/4)

Next, we can use the formula for the geometric series:

1/(1-z) = 1 + z + z² + z³ + ...

to write the second term as a power series,

(1/16)/(1+x/4) = (1/16) * (1 - x/4 + x²/16 - x³/64 + ...)

Putting it all together, we get:

f(x) = (1/4) - (1/16)/(1+x/4)

= (1/4) - (1/16) * (1 - x/4 + x²/16 - x³/64 + ...)

= (1/4) - (1/16) + (1/64)*x - (1/256)*x²+ ...

Therefore, the power series representation of f(x) is,

f(x) = 1/4 - 1/16 + (1/64)*x - (1/256)*x² + ...

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Answer:

D

Step-by-step explanation:

Base area = (leg 1 x leg 2)/2 = (9 x 12)/2 = 54 ft^2

Base perimeter = leg 1 + leg 2 + hypotenuse = 9 + 12 + 15 = 36 ft

LA= base perimeter x 24 = 36 x 24 = 864 ft^2

SA = 2 x base area + LA = 54 x 2 + 864 = 972 ft^2

After handling raw meat the food preparer should: wash hands with soap.

It is important that after handling raw meat the food preparer should endeavor to wash his/her with soap and water and  dry your hand with a clean towel.

Washing of hand with soap will help to prevent bacteria based on the fact that  raw meats can contaminate the area you place your hands on which is why it is advisable to wash your hands after handling raw meat.

Therefore after handling raw meat the food preparer should: wash hands with soap.

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Answer:

6 inches

Step-by-step explanation:

6 inches is the only feasible answer because if the length is 6 inches, you have 6 + 6  which equals 12. This leaves 2 more units for the perimeter so the width would be 1 unit. The other choices could not exist, because 7 x 2 is 14 (no units left for width, and the width of a rectangle cannot be 0), 8 x 2 is 16, and 9 x 2 is 18.

Answer:

Yes, Uncle Sonny is correct.

Step-by-step explanation:

If two figures are related by a dilation, then corresponding lines or line segments in the figures will be congruent. In a dilation, the ratio of the lengths of corresponding lines or line segments remains constant, which means they will have the same length. Therefore, they are congruent.