ken spent $4.50 without tax on 6 can of dog food. what is the unit rate or constant of proportionality for each can of dog food

Answer:

V=1582.56 cubic cm

Step-by-step explanation:

it's 490 because when you get a zero or less it takes 10 points off your grade which leaves 490 students with good grades.

Writing linear equations given two points can be a useful skill when graphing linear equations.

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The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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Answer:

2 yards

Step-by-step explanation:

1+3=4

4-6=2

Check the picture below.

the solution to the given difference equation is y(k) = \(0.2^k\) - 2.4 * \(1.2^k\)

To solve the given difference equation, we can use the Z-transform method. Let's denote the Z-transform of a function y(k) as Y(z), and the Z-transform of x(k) as X(z).

Applying the Z-transform to the given equation and using the properties of linearity, time shifting, and the Z-transform of the unit step function, we have:

z²Y(z) - zY(z) + 0.24Y(z) = (z + 1)X(z)

Next, we can rearrange the equation to solve for Y(z):

Y(z)(z² - z + 0.24) = (z + 1)X(z)

Dividing both sides by (z² - z + 0.24), we get:

Y(z) = (z + 1)X(z) / (z² - z + 0.24)

Now, we need to find the inverse Z-transform of Y(z) to obtain the time-domain solution y(k). To do this, we can use partial fraction decomposition and lookup tables to find the inverse Z-transform.

The denominator of Y(z), z² - z + 0.24, can be factored as (z - 0.2)(z - 1.2). We can then rewrite Y(z) as:

Y(z) = (z + 1)X(z) / [(z - 0.2)(z - 1.2)]

Now, we perform partial fraction decomposition to express Y(z) as:

Y(z) = A / (z - 0.2) + B / (z - 1.2)

To find the values of A and B, we can multiply both sides of the equation by the common denominator:

(z - 0.2)(z - 1.2)Y(z) = A(z - 1.2) + B(z - 0.2)

Expanding and equating coefficients, we have:

z²Y(z) - 1.4zY(z) + 0.24Y(z) = Az - 1.2A + Bz - 0.2B

Now, we can equate the coefficients of corresponding powers of z:

Coefficient of z²: 1 = A

Coefficient of z: -1.4 = A + B

Coefficient of z⁰ (constant term): 0.24 = -1.2A - 0.2B

Solving these equations, we find A = 1, B = -2.4.

Substituting these values back into the partial fraction decomposition equation, we have:

Y(z) = 1 / (z - 0.2) - 2.4 / (z - 1.2)

Now, we can use the inverse Z-transform lookup tables to find the inverse Z-transform of Y(z):

y(k) = Z⁻¹{Y(z)} = Z⁻¹{1 / (z - 0.2) - 2.4 / (z - 1.2)}

The inverse Z-transform of 1 / (z - 0.2) is given by the formula:

Z⁻¹{1 / (z - a)} = \(a^k\)

Using this formula, we get:

y(k) = \(0.2^k\) - 2.4 * \(1.2^k\)

Therefore, the solution to the given difference equation is y(k) = \(0.2^k\) - 2.4 * \(1.2^k\)

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Answer:

infinitely many solutions

There are ''Infinitely many solutions'' in this system of equations.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The system of equations are,

⇒ y = -2x + 2  .. (i)

⇒ 2y + 4x = 4  .. (ii)

Now, Solve the expression as;

Multiply by 2 in (i);

⇒ 2y = 2 (-2x + 2)  

⇒ 2y = -4x + 4

⇒ 2y + 4x = 4

Clearly., Both equations are same.

Hence, There are ''Infinitely many solutions'' in this system of equations.  

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Answer:

Step-by-step explanation:

As always, set the function equal to zero and solve for x:

x - 1 = 0 results in x = 1.  Thus, (1, 0) is one of the x-intercepts.

x + 6 = 0 results in x = -6.  (-6, 0) is the other x-intercept.

Answer:

1/4w + 3

Step-by-step explanation:

Answer:

30,70,110

Step-by-step explanation:

12. acute

13. acute

14. obtuse

The equation is in the form of the linear line: y = mx +b where m is the slope.

Thus the slope is 1/6

Hope that helps!

To determine if the series Σ(n/(n^2 + 30)) from n=1 to infinity is convergent or divergent, we can use the limit comparison test.

Let's compare the given series with the series Σ(1/n) from n=1 to infinity.

Taking the limit as n approaches infinity of the ratio of the terms of the two series, we have:

lim(n→∞) [(n/(n^2 + 30))/(1/n)]

= lim(n→∞) [n/(n^2 + 30)] * [n/1]

= lim(n→∞) (n^2)/(n^2 + 30)

= 1

Since the limit is a finite positive value (1), and the series Σ(1/n) is a well-known divergent harmonic series, we can conclude that the given series Σ(n/(n^2 + 30)) also diverges.

Therefore, the statement "The series Σ(n/(n^2 + 30)) is divergent by using Limit Comparison with the series Σ(1/n)" is true.

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Answer:

Step-by-step explanation:

Just think how many times each two number goes into the first two numbers

Answer:

\(y=\frac{3}{7} x-\frac{9}{7}\)

Step-by-step explanation:

To find the equation of a line in slope-intercept form, we need to first find the slope of the line. To do this, we can use the formula:

slope = (y2 - y1) / (x2 - x1)

In this case, we have the points (–7, –3) and (–14, –6), so our formula becomes:

slope = (-6 - (-3)) / (-14 - (-7)) = -3 / -7 = 3/7

We can now use the point-slope formula to find the equation of the line:

y - y1 = m * (x - x1)

where m is the slope and (x1, y1) is a point on the line. In this case, we have m = 3/7 and (x1, y1) = (-7, -3), so our equation becomes:

y - (-3) = (3/7) * (x - (-7))

We can now rearrange this equation to put it into slope-intercept form:

y = (3/7) * x + (3 * (-7) / 7) = (3/7) * x - 9/7

Therefore, the equation of the line in slope-intercept form is y = (3/7) * x - 9/7.

Answer:

He can buy no more than 3 gallons

Step-by-step explanation:

Let c = cookies and m = milk

1.5c + 6m

This is how much he is going to spend

it must be less than or equal to 30

1.5c + 6m≤ 30

He is going to buy 8 cookies

1.5*8 + 6m≤ 30

12 + 6m ≤ 30

Subtract 12 from each side

12+6m -12 ≤ 30-12

6m ≤ 18

Divide by 6

6m/6 ≤ 18/6

m≤ 3

The final amount for the investment of $5,000 over 5 years at an annual interest rate of 6% compounded quarterly is $ 6,749.29.

To find the final amount for an investment P over t years at an annual interest rate of r compounded quarterly, we can use the formula for compound interest:  

\({\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}\)

Where:

A = Final amount

P = Principal (initial investment)

r =  Annual interest rate (as a decimal)

n = Number of times the interest is compounded per year

t = Time period in years

Here we have

P = $5,000,

r = 6% = 0.06,

n = 4 (since the interest is compounded quarterly), and

t = 5 years.  

Using the above formula

\(A = 5000(1 + 0.06/4)^{(4*5)\)

\(A = 5000(1.015)^{20}\)

\(A = 5000(1.34985711)\)

\(A = $6,749.29\)

Therefore,

The final amount for the investment of $5,000 over 5 years at an annual interest rate of 6% compounded quarterly is $ 6,749.29.

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Answer:

y = 2.5

Step-by-step explanation:

if y = 0

x= 2.5

u do the y as 0 and x as 2.5

and then draw a straight line

The acceleration produced by a car will decrease as its mass rises. Less acceleration will be recorded by the computer system, which will cause a drop in the acceleration value on the graph.

Graph:

An organized visual representation of any data in mathematics is called a graph. The graph shows the correlation between the variable values. In graph theory, a graph is used to represent the collection of objects that are somehow connected to one another. In essence, the objects' vertices or nodes are mathematical concepts, and the connections between the nodes are represented by the edges. Different types of graphs are used in mathematics and statistics to visually display data. The discipline of graph theory is the study of points and lines. It is a field of mathematics that specializes in the study of graphs. This image visually illustrates the mathematical truth. The graph theory is used to study relationships.

Complete question:

Use the image to answer the question. Students are using the experimental setup shown in the image in which the two ends of a string are attached to a car and to a hanger. The students conduct three trials in which they place metal discs on the hanger to manipulate the force applied to the car. As a result, the car accelerates along the table while two photogate probes collect motion data. On the fourth trial of this experiment, a student places some discs on the car by mistake. In 1-2 sentences, explain how this mistake will affect the graphs produced by the computer.

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The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.

To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.

However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.

Therefore, the dog can run at approximately 3.125 mi/hr.

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Answer:

g=130 h=22

Step-by-step explanation:

bxh÷2

hope this helps

Answer:

2 1/10

Step-by-step explanation:

convert the decimal number to a fraction by placing the decimal number over a power of ten. since there is 1 number to the right of the decimal point, place the decimal number over 10^1 (10). next, add the whole number to the left of the decimal.

hope this helps

Step-by-step explanation:

please mark me as brainlest

The dimensions of the can that minimize the cost of the material are approximately:

Radius (r) ≈ 6.324 cm

Height (h) ≈ 3.984 cm

To determine the dimensions of the can that minimize the cost of the material, we need to find the dimensions that minimize the surface area of the can.

Let's assume the can has a height of h and a radius of r.

The volume of a cylinder is given by:

V = πr²h

Given that the can should hold 500 cubic centimeters of liquid, we have:

500 = πr²h

We want to minimize the cost, which depends on the surface area of the can.

The surface area of the can is the sum of the areas of the top, bottom, and side surfaces.

The cost of the top and bottom surfaces is twice as expensive per square centimeter as the sides.

Let's assume the cost per square centimeter of the sides is c, so the cost per square centimeter of the top and bottom surfaces is 2c.

The surface area of the sides of the cylinder is given by:

A_sides = 2πrh

The surface area of the top and bottom surfaces (each) is given by:

A_top_bottom = 2πr²

The total surface area (cost) is given by:

Cost = 2(2c)A_top_bottom + cA_sides

= 4cπr² + 2c(2πrh)

= 4cπr² + 4cπrh

To minimize the cost, we need to minimize the surface area. To do this, we can express the surface area in terms of a single variable, such as the radius (r) or the height (h).

From the volume equation, we have:

h = 500 / (πr²)

Substituting this value of h into the surface area equation, we get:

Cost = 4cπr² + 4cπr(500 / (πr²))

= 4cπr² + 2000c/r

Now, we can take the derivative of the cost function with respect to r, set it equal to zero, and solve for r to find the critical points:

dCost/dr = 8cπr - 2000c/r² = 0

8cπr = 2000c/r²

8πr³ = 2000

r³ = 250 / π

r ≈ 6.324

Now, we can substitute this value of r back into the equation for h:

h = 500 / (π(6.324)²)

≈ 3.984

So, the dimensions of the can that minimize the cost of the material are approximately:

Radius (r) ≈ 6.324 cm

Height (h) ≈ 3.984 cm

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Answer: B

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since there are 985 square feet to cover, and it costs 12.50 per square foot, you multiply 12.50 by 985 to get 12,312.50, the total cost and answer.

Answer:

Step-by-step explanation:

Figure 1

Figure 2

Figure 3

The function is:

The statements that were found to be true in a study by the American Press Institute concerning reader comprehension are:

B. For sentences longer than 20 words, comprehension fell to 80% or less comprehension.

D. The sentences that people understood most easily had no more than 10 words.

In a statement by the American Press Insitute, certain facts were seen to be true. For instance, it was believed that for sentences longer than 20 words, comprehension typically fell to 80% r less.

Also, it was discovered that the sentences that most people understood had no more than 10 words. So, the correct options are B and D.

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