Anita states that in her experience, a jar can hold 288 marbles. How accurate is Anita’s statement? Explain.

Answer:

16

Step-by-step explanation:

Answer:

(0,0) is a saddle point

(-4,4) is a local maximum

Step-by-step explanation:

\(\displaystyle z=3x^3-36xy-3y^3\\\\\frac{\partial z}{\partial x}=9x^2-36y\\\\\frac{\partial z}{\partial y}=-36x-9y^2\)

Determine critical points

\(9x^2-36y=0\\9x^2=36y\\\frac{x^2}{4}=y\)

\(-36x-9y^2=0\\-36x-9(\frac{x^2}{4})^2=0\\-36x-\frac{9}{16}x^4=0\\x(-36-\frac{9}{16}x^3)=0\\\\x=0\\\\-36-\frac{9}{16}x^3=0\\-36=\frac{9}{16}x^3\\-64=x^3\\-4=x\)

When x=0

\(9x^2-36y=0\\9(0)^2-36y=0\\-36y=0\\y=0\)

When x=-4

\(9x^2-36y=0\\9(-4)^2-36y=0\\9(16)-36y=0\\144-36y=0\\144=36y\\4=y\)

So, we need to check what kinds of points (0,0) and (-4,4) are.

For (0,0)

\(\displaystyle H=\biggr(\frac{\partial^2 z}{\partial x^2}\biggr)\biggr(\frac{\partial^2 z}{\partial y^2}\biggr)-\biggr(\frac{\partial^2 z}{\partial x\partial y}\biggr)^2\\\\H=(18x)(-18y)-(-36)^2\\\\H=(18(0))(-18(0))-(-36)^2\\\\H=-1296 < 0\)

Therefore, (0,0) is a saddle point since \(H < 0\).

For (-4,4)

\(\displaystyle H=\biggr(\frac{\partial^2 z}{\partial x^2}\biggr)\biggr(\frac{\partial^2 z}{\partial y^2}\biggr)-\biggr(\frac{\partial^2 z}{\partial x\partial y}\biggr)^2\\\\H=(18x)(-18y)-(-36)^2\\\\H=(18(-4))(-18(4))-(-36)^2\\\\H=(-72)(-72)-1296\\\\H=5184-1296\\\\H=3888 > 0\)

Because \(H > 0\) and since \(\frac{\partial^2z}{\partial x^2}=-72 < 0\), then (-4,4) is a local maximum

Answer:

Equation D, y = 1.75x + 6.25

Step-by-step explanation:

We know that the common ratio is 1.75 which means that the data would go up by $1.75 each time and then an additional of 6.25 is also there. Hence, 1.75 would be the slope and 6.25 would be the intercept of the equation.

Hope this helps!

Internal validity explains the association between binge-watching tv and irritability.

In the context of a specific study, internal validity refers to how strongly a piece of evidence supports a claim regarding cause and effect. It is one of the most crucial characteristics of scientific research and a crucial idea when considering evidence more generally.

The extent to which alternative explanations for a study's findings (often, sources of systematic error or "bias") can be ruled out is a measure of its internal validity. In contrast, external validity measures how well data support judgments made regarding other situations (that is, the extent to which results can be generalized).

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Answer:

The value can be entered in the box to correctly make this conversion is 60 minutes. Hence, the value can be entered in the box to correctly make this conversion is 60 minutes.

Step-by-step explanation:

The growth rate of the bacterial colony after 3 hours is 32%, the population of a slowly growing bacterial colony after t hours is given by the function p(t) = 100 + 24t + 2t²

The growth rate of the colony is the rate of change of the population, which is given by the derivative of the function. The derivative of p(t) is p'(t) = 24 + 4t

The growth rate after 3 hours is p'(3) = 24 + 4 * 3 = 32. This means that the population of the colony is increasing by 32% after 3 hours.

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Answer:

The rate of function 1 is greater than function 2, the y intercept of function 1 is 3

Step-by-step explanation:

Approximately 5% of drivers have a reaction time of more than 2.14 seconds.

Standard deviation is a statistical measure that quantifies the amount of variability or dispersion in a dataset. It measures how spread out the values are from the mean (average) of the dataset. In other words, it provides an indication of the average distance between each data point and the mean.

The given mean is μ = 1.9 and standard deviation is σ = 0.12.

It is known that the reaction time is approximately symmetric and mound-shaped.

Suppose that the distribution follows normal distribution.

So, we need to find the percentage of drivers having a reaction time of more than 2.14 seconds.

The standardized value of x is:

z = (x - μ) / σ

Where x is the random variable, μ is the mean, and σ is the standard deviation of the distribution of x.

Plugging the given values, we have

z = (2.14 - 1.9) / 0.12 = 2.00

Using the 68-95-99.7 rule, the percentage of drivers having a reaction time of more than 2.14 seconds isP(z > 2) ≈ 0.05 (from the 99.7% section of the normal distribution curve)

Therefore, approximately 5% of drivers have a reaction time of more than 2.14 seconds.

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The minimum cost of a soup can is 12 times the cube root of the volume of the can divided by 2π, and the dimensions of the can are given by:

\(r = (V/(2\pi ))^{(1/3)}\\h = 2V/[(\pi (V/(2\pi ))^{(1/3))}]\)

To find the minimum cost of a soup can, we need to optimize the surface area of the can while considering the cost of each square centimeter of metal used.

Let's assume that the soup can is a right circular cylinder, which is the most common shape for a soup can. Let the radius of the can be "r" and the height be "h". Then, the surface area of the can is given by:

A = 2πr² + 2πrh

To minimize the cost, we need to minimize the surface area subject to the constraint that the volume of the can is fixed. The volume of a cylinder is given by:

V = πr²h

We can solve for "h" in terms of "r" using the volume equation:

h = V/(πr²)

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

A = 2πr² + 2πr(V/(πr²))

A = 2πr² + 2V/r

Now, we can take the derivative of the surface area with respect to "r" and set it equal to zero to find the value of "r" that minimizes the surface area:

dA/dr = 4πr - 2V/r² = 0

4πr = 2V/r²

r³ = V/(2π)

Substituting this value of "r" back into the equation for "h", we get:

h = 2V/(πr)

Therefore, the dimensions of the can that minimize the cost are:

\(r = (V/(2\pi ))^{(1/3)}\\h = 2V/[(\pi (V/(2\pi ))^{(1/3))]\)

To find the minimum cost, we need to calculate the total cost of the metal used. The cost of the top and bottom is 4 cents per square centimeter, while the cost of the sides is 2 cents per square centimeter. The area of the top and bottom is:

A_topbottom = 2πr²

The area of the sides is:

A_sides = 2πrh

Substituting the values of "r" and "h" we found above, we get:

\(A_topbottom = 4\pi (V/(2\pi ))^{(2/3)}\\A_sides = 4\pi (V/(2\pi ))^{(2/3)}\)

The total cost is:

\(C = 2(4\pi (V/(2\pi ))^{(2/3)}) + 4(4\pi (V/(2\pi ))^{(2/3)}) = 12(V/(2\pi ))^{(2/3)\)

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Answer:

----------------------------------------

The perimeter is:

If the perimeter is less than 20, then the inequality is:

Answer:

x < 4

Step-by-step explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside.

Therefore, from inspection of the triangle:

⇒ Perimeter = 4 + 9 + x + 3

⇒ Perimeter = x + 16

If the perimeter is less than 20 meters then:

⇒ x + 16 < 20

Solve the inequality:

⇒ x + 16 - 16 < 20 - 16

⇒ x < 4

"The correct answer is B) 7 toppings." The Carla's pizza had 7 toppings.

To find out how many toppings were on Carla's pizza, we need to solve the equation by setting the cost of the pizza equal to the amount Carla paid.

The given function is f(t) = 10.25 + 1.25t, where t represents the number of toppings on the pizza.

Carla paid $19.00 for the pizza.Setting up the equation, we have:

10.25 + 1.25t = 19.00

Subtracting 10.25 from both sides:

1.25t = 8.75

Dividing both sides by 1.25:

t = 7.

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Sale tax rate = 6.85%

To calculate the sale tax on a $14,000 Car, multiply 14,000 by the sale tax rate in decimal form ( divided by 100)

14,000 x (6.85/100) = 14,000 x 0.0685= $959

To find the final cost, add the sale tax amount to the price:

14,000 + 959 = $14,959

The advantages of the superposition theorem compared to other circuit theorems are its simplicity and modularity in circuit analysis, as well as its applicability to linear circuits.

Superposition theorem is a powerful tool in circuit analysis that allows us to simplify complex circuits and analyze them in a more systematic manner. When compared to other circuit theorems, such as Ohm's Law or Kirchhoff's laws, the superposition theorem offers several advantages. Here are two key advantages of the superposition theorem:

Simplicity and Modularity: One major advantage of the superposition theorem is its simplicity and modular approach to circuit analysis. The theorem states that in a linear circuit with multiple independent sources, the response (current or voltage) across any component can be determined by considering each source individually while the other sources are turned off. This approach allows us to break down complex circuits into simpler sub-circuits and analyze them independently. By solving these individual sub-circuits and then superposing the results, we can determine the overall response of the circuit. This modular nature of the superposition theorem simplifies the analysis process, making it easier to understand and apply.

Applicability to Linear Circuits: Another advantage of the superposition theorem is its applicability to linear circuits. The theorem holds true for circuits that follow the principles of linearity, which means that the circuit components (resistors, capacitors, inductors, etc.) behave proportionally to the applied voltage or current. Linearity is a fundamental characteristic of many practical circuits, making the superposition theorem widely applicable in real-world scenarios. This advantage distinguishes the superposition theorem from other circuit theorems that may have limitations or restrictions on their application, depending on the circuit's characteristics.

It's important to note that the superposition theorem has its limitations as well. It assumes linearity and works only with independent sources, neglecting any nonlinear or dependent sources present in the circuit. Additionally, the superposition theorem can become time-consuming when dealing with a large number of sources. Despite these limitations, the advantages of simplicity and applicability to linear circuits make the superposition theorem a valuable tool in circuit analysis.

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Answer:

F

Step-by-step explanation

If there is 4 months and every month $32 is added you count $32 for every month.

Answer:

Eric earnings equals $7

Step-by-step explanation:

Let amount earned by Robert = $10

Amount earned by Eric = $x

Robert earnings = 2x - 4

2x - 4 = 10

2x = 10 + 4

2x = 14

Divide both sides by 2

x = 14 / 2

= 7

x = 7

Eric earns $x which is equal to $7

Eric earnings equals $7

Answer:

5 shirts (read explanation)

Step-by-step explanation:

14x+29=100

14x=71

x=5.1

She can buy 5 shirts

Using the z-distribution, as we have the standard deviation for the population, it is found that it does not appear that there is a difference.

Given,

mean of 33.56

standard deviation of 5.20

So,

At the null hypothesis, it is tested that there is no difference, that is, the mean of the distribution of the differences is of 0, hence:

\(H_{0} : u = 0\)

At the alternative hypothesis, it is tested if there is a difference, hence:

\(H_{1} : u\) ≠ 0

Test statistic,

z = x - u /s

x is the mean of the distribution of differences.

u  is the value tested at the null hypothesis.

s is the standard error.

Here the parameters are as follows:

u = 1.11 , s = 4.28

Hence,

z = 1.11 - 0 / 4.28

z = 0.26

Now,

Decision:

Considering a two-tailed test, as we are testing if the mean is different of a value, with a standard significance level of 0.05, the critical value is of,

\(|z*| = 1.96\)

There does not appear to be any difference between Oven A and Oven B with respect to the mean percentages of defective chips produced .

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Answer:

6

Step-by-step explanation:

You know DF = 6 and EB = 6 too. Since E is the mid-point of AEB, EB and AB are equal.

DF = EB

     = AB

     = 6

Answer:

Step-by-step explanation:

Area of each face of a cube = 25 ft²

⇒ Side² = 25

Surface area of cube = 6side²

                                     = 6*25

                                      = 150 ft²

Answer:

For anyone who needs it the answer is 150 ft

Step-by-step explanation:

Answer:

B is the correct answer I believe (๑・ω-)～♥”

If I was right please mark me brainliest! (๑・ω-)～♥”

Answer:

There is no reminder as the answer will be an integer 131.

Thank you and please rate me as brainliest as it will help me to level up

Answer:

The first/top option

Step-by-step explanation:

First, we can find the inequality that the line is representing. X is the number of hours she has already done, and she has five hours more to do to fulfill the 12 or more hours of required service. The inequality would be x+5≥12.

The minimum that X has to be is 7 because any value lower than 7 would make the inequality false[ ex. 6 + 5 ≠ 12 ]. The arrow would be pointing to the right, because 7 is the minimum value, not the max, so any value higher than 7 would still make the inequality true. Lastly, the circle would be filled, because 7 is included in the set of values that make the inequality true[ 7 + 5 = 12 ].

So, the answer would be the first option.

Answer:

Step-by-step explanation:

-17+n/5 = 33

+17          +17

n/5 = 50

x 5    x 5

n = 250

-17+250/5 = 33

-17 + 50 = 33

y = 4x + 3

x=1 7 = 4(1) +3

x=2 11 = 4(2) +3

x=3 15 = 4(3) +3

x=4 19 = 4(4) +3

x=5 23 = 4(5) +3

Answer:

(The multiply and the x are the same, so I’m just letting you know that the first x is the letter x and the second is the multiply sign.)

x x 3 + 4 (equation)

x = 6 (solution)

Step-by-step explanation:

6 x 3 + 4

22 - 4 = 18 (which takes out the four, which means what number times 3 would get 18)

6 x 3 = 18

6 x 3 + 4 = 22

Answer:

D. 42

Step-by-step explanation:

The total angle by which the 60 sided polygon will have rotated after 7 minutes is; 42°

Exterior angle = 360/n

Thus,

Size of each exterior angle = 360/6

Size of each exterior angle = 6°

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Answer:

lateral surface area of cone =πrl

Answer:

1=65+72

=137 degrees,,,