A box contains 12 tickets labeled with numbers. The number on the tickets are -9, -9, -8, -8, -5, -5, -4, 3, 6, 6, 6, 7 . The expected value of the sample sum of the ticket labels in 11 independent random draws with replacement from the box is

The gradient vector field ∇f of f(x, y) = 7 x2 + y2 is ∇f(x, y) = <14x, 2y>.

The gradient vector field ∇f of a scalar function f(x, y) is given by the vector function

∇f(x, y) = <∂f/∂x, ∂f/∂y>.

In this case, the function f(x, y) = 7x^2 + y^2 and we can find the gradient vector field as follows:

∇f(x, y) = <∂f/∂x, ∂f/∂y> = <14x, 2y>

This vector field points in the direction of steepest ascent at each point in the xy-plane, and its magnitude at each point is equal to the rate of change of f in that direction.

To sketch the gradient vector field, we can plot the vector <14x, 2y> at various points in the xy-plane. The direction of the vector at each point will be the direction of steepest ascent of the function f, and the length of the vector will indicate the rate of change of f in that direction.

We can notice that for the function f(x,y) = 7x^2+y^2, the function is always increasing as we move along the direction of the vector <14x,2y> and the vectors are always pointing away from the origin, which means that the origin is a local minimum of the function.

It's important to note that this is a paraboloid. The direction of steepest ascent is the direction of the tangent of the paraboloid at any point, which is pointing upwards from the vertex of the paraboloid.

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[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=7 \end{cases}\implies V=\cfrac{\pi (3)^2(7)}{3} \\\\\\ V=21\pi \implies {\Large \begin{array}{llll} V\approx 65.97 \end{array}} ~in^3 ~~ \approx 66~in^3[/tex]

Answer:

20

Step-by-step explanation:

Given the function:

[tex]p(x)=3x^3-x^2[/tex]

We need to find p(2)

This means we need to find the value of the function when x is 2

[tex]p(2)=3*2^3-2^2=3*8-4=24-4=20[/tex]

Hope this helps :)

Have a great day!

Answer:

Step-by-step explanation:

Brad's solution to find the surface area of the composite figure is not correct.

In his solution, Brad adds the surface areas of the triangular prism and the rectangular prism separately,

but it's not taking into account that the two prisms share a face that is 14 by 20.

When finding the surface area of a composite figure, it's important to take into account any shared faces.

Since the two prisms share a face that is 14 by 20, Brad should subtract this area from one of the prisms,

otherwise he will be counting it twice in the final result.

The correct method would be:

Rectangular prism: (2 * 8 * 14) + (2 * 14 * 20) + (2 * 8 * 20) = 1,104 cm^2

Triangular prism: (1/2 * 14 * 12) + (1/2 * 13 * 15) + (3 * 14 * 20) = 1,008 cm^2

Subtracting shared area: 1,104 cm^2 + 1,008 cm^2 - (14 * 20) = 2,096 cm^2.

So Brad's solution is incorrect, the correct surface area of the composite figure is 2,096 cm^2.

Answer:90x567

Step-by-step explanation:

Using the addition operation, the position of the salmon currently relative to the surface is 8 feet below the surface.

The addition operation is one of the four basic mathematical operations, including subtraction, division, and multiplication.

The addition operation involves adding two or more addends to get a result known as the sum or total, using the equal symbol (=) and the addition operand (+).

The initial position of the school of salmon below the surface = 5 feet

The depth they went down further to escape the bear = 3 feet

The current position = 8 feet (5 + 3) below the surface.

Thus, based on the addition operation, the school of salmon can be located 8 feet below the surface as they attempted to escape the hungry bear.

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The function expressing the volume of water t minutes after the plug was pulled is V(t) = -2.4t^2 + 11.2t + 46,b)tub had 46 liters of water when the plug was pulled and will be empty at 2.16 minutes,c) the least amount of water predicted by the model is -52.6667 liters which is not reasonable as the volume of water can't be negative.

What is parabola ?

A parabola is a symmetric, U-shaped geometric shape.

a)V(1) = 38.4 = a(1)^2 + b(1) + c

V(2) = 21.6 = a(2)^2 + b(2) + c

V(3) = 9.6 = a(3)^2 + b(3) + c

Solving the system of equations, we get ,

a = -2.4 , b = 11.2 , c = 46 , V(t) = -2.4t^2 + 11.2t + 46.

b)We can find the initial volume of water in the tub by plugging in t = 0 into the function V(t) = -2.4t^2 + 11.2t + 46. This gives us V(0) = 46 liters, so the tub had 46 liters of water when the plug was pulled.

c)t = (-11.2 +/- sqrt(11.2^2 - 4*(-2.4)46))/(2(-2.4))

t = (11.2 +/- sqrt(124.48 + 552.8))/-4.8

t = (11.2 +/- sqrt(677.28))/-4.8 = (11.2 +/- 26.16)/-4.8 = -14.96 or 2.16

d)V(4.6667) = -2.4*(4.6667)^2 + 11.2*(4.6667) + 46 = -2.4*21.778 + 46.4 + 46 = -52.6667. So the least amount of water the model predict is -52.6667 liters. This number is not reasonable as the volume of water can't be negative.

e) The graph of the function V(t) = -2.4t^2 + 11.2t + 46 is a parabola that opens downward and has its vertex at (4.6667, -52.6667). Any portion of the graph for t < 0 or t > 2.

The function expressing the volume of water t minutes after the plug was pulled is V(t) = -2.4t^2 + 11.2t + 46,b)tub had 46 liters of water when the plug was pulled and will be empty at 2.16 minutes,c) the least amount of water predicted by the model is -52.6667 liters which is not reasonable as the volume of water can't be negative.

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Observational data that contains a numerical value or amount is called Quantitative observation.

What is observational data?

An observational study draws conclusions from a sample to a population in disciplines like epidemiology, social sciences, psychology, and statistics when the independent variable is not under the researcher's control due to ethical considerations or logistical limitations.

Observational data in market research refers to information gathered without the research subject (such as a specific client, patient, employee, etc.) having to be explicitly involved in documenting what they are doing.

An objective collection of data, quantitative observation refers to "associated to, of or depicted in terms of a quantity" and is primarily focused on numbers and values.

Methods of statistical and numerical analysis are used to derive the results of quantitative observation.

Hence, observational data that contains a numerical value or amount is called Quantitative observation.

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The correlation coefficient having -negative value means inverse correlation and +positive value means direct relationship.

An analytical way to gauge how strongly two variables are linearly related is to use the correlation coefficient. Anywhere between -1 and 1 can be its value. A correlation coefficient of -1 indicates a perfect negative, inverse, or inverse-correlation, where values in one series increase as those in the other decline and vice versa. An exact positive correlation or direct relationship is indicated by a coefficient of 1, or 1. In the absence of a linear relationship, a correlation coefficient of 0 indicates.

When evaluating the level of association between two variables, factors, or data sets, scientists and financiers alike use correlation coefficients. Assuming, for instance, that there is a strong positive correlation between oil prices and forward returns on oil stocks given that high oil prices are advantageous for crude producers

Now,

For

A. r = 0.921 -Direct relationship.

B. r= -0.873 -Inverse relationship.

C. r = -0.281 -Inverse relationship.

D. r = 0.303 -Direct relationship.

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Joel needs 1.5 gallons of blue paint.

Joel needs a total of 10 gallons of paint to paint the outside of his house. Since the ratio is 3 parts blue paint to 2 parts yellow paint, we can use proportions to solve for the amount of blue paint needed.

We can set up the proportion like this:

3/2 = x/10

We can solve for x (the amount of blue paint) by cross-multiplying:

3*10 = 2*x

3*10 = 20x

20x = 30

x = 30/20

x = 1.5

Joel needs 1.5 gallons of blue paint.

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Sry I thought I knew the answer and posted it, and do not know how to delete it so I leave u with this.

The number of revolutions per minute made by the wheel of a car with a diameter of 50 cm travelling at an average speed of 36 km/hr is 226.7 revolutions per minute.

Number of revolutions per minute = (36 x 1000) / (50 x 3.14) = 226.7 revolutions per minute

1. Convert the speed from kilometers to meters per hour

36 km/hr = 36 x 1000 m/hr

2. Calculate the circumference of the wheel

Circumference of wheel = Diameter x π

Circumference of wheel = 50 cm x 3.14 = 157 cm

3. Calculate the number of revolutions per minute

Number of revolutions per minute = (Speed in m/hr) / (Circumference of wheel in cm)

Number of revolutions per minute = (36 x 1000) / (50 x 3.14) = 226.7 revolutions per minute

The number of revolutions per minute made by the wheel of a car with a diameter of 50 cm travelling at an average speed of 36 km/hr is 226.7 revolutions per minute.

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Hope it helps.

If you have any query, feel free to ask.

Answer: Hello how are you doing today?

Step-by-step explanation: How may I help you?

No the relation doesn't necessarily represent a function.

The term function is known as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Here we have given that you record the number x of runs scored by the winning team and the number y of runs scored by the losing team for each softball game in a team's season.

As we all know that in any two games here we have given that if the winning teams had the same numbers of runs while the losing teams had different numbers of runs then the given relation is not a function.

Here we have to remember that for a relationship to be a function then it must be fulfilled and it is possible for every input value there must be only one output value

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Yes, the conditions for constructing a 90% confidence interval for the difference in the true mean growth of all large- and small-cap stocks for the last 60 days are met.

Shares of businesses having a market value between $300 million and $2 billion are considered small-cap stocks. Small-cap firms have the potential for rapid development, which makes them attractive investment targets even if their stocks may be more volatile and carry greater risks for buyers.

Large-cap stocks, commonly referred to as large caps, are stocks that are traded for businesses with a market value of at least $10 billion. Because investors gravitate toward quality and stability and become more risk-averse during challenging markets, large-cap companies often exhibit lower volatility.

Thus, the conditions for constructing a 90% confidence interval for the difference in the true mean growth of all large- and small-cap stocks for the last 60 days are met.

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Check the picture below.

notice, times where he stops, is time where distance is not added however time elapses, meaning we get a straight line, when chatting with his friend, it went from 10 minutes to 15 minutes over the same 800 meters, in other words, he never moved, time kept on going for 5 minutes.  When he gets back home, distance goes from 2000 meters to 0 meters, 0 meters because he's back at 0 distance after 90 minutes.

This is the answer above mentioned

The outcome Asher needs to win the game are 2, 3, 4, 5, 6, 7, 8, 9, 10.

We get the above answer following the given method.

We have been given the information that there are 2 six-sided number cubes and Eitan needs to roll a sum of 11 or more.

The possible outcomes for rolling two six-sided number cubes are the integers from 2 to 12. In order for Asher to have a better probability of winning than Eitan, Asher's winning outcome must be a lower number than Eitan's winning outcome of 11. The possible winning outcomes for Asher are therefore 2, 3, 4, 5, 6, 7, 8, 9, 10. So the possible outcomes that Asher needs to win the game are 2, 3, 4, 5, 6, 7, 8, 9, 10.

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Answer:

A) The money spent on a phone plan can be represented by the inequality:

50 + 25x > 100

B) The total spent on the phone service exceeds the amount of the gift card after the 2nd month.

Step-by-step explanation:

A. The inequality represents the total cost of the phone plan, where x represents the number of months for which the service is used.

The first part of the inequality, 50$, represents the initial cost of the phone.

The second part, 25x, represents the monthly cost of the service, 25$ per month.

So, the inequality represents the total cost of the phone plan as the sum of the initial cost of the phone and the monthly cost of the service for x number of months.

50 + 25x > 100

It states that the total cost (50 + 25x) of the phone plan is greater than 100$.

It's the total cost you have to pay for the phone and the service.

It's used to know when the total cost exceeds 100$, which is the gift card's value.

B. To find out when the total spent on the phone service exceeds the amount of the gift card, we can substitute in the inequality with the given values and solve for x.

50 + 25x > 100

x > (100-50)/25

x > 2

So, the total spent on the phone service exceeds the amount of the gift card after the 2nd month.

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The element X will take 7.3 minutes to decay to 26 grams.

Radioactive radiations are the radiations that an atom nucleus releases.

It is a sequence of numbers that have common differences.

The decaying acts like an arithmetic progression in which a=670,d=-30.45 (per minute decaying), and n we have to find with the value of 26 grams.

So, the formula of the nth term of an arithmetic progression is

nth term=a+(n-1)d

26=220+(n-1) x (-30.45)

-194=-30.45n+30.45

-224.45 =-30.45n

n=7.3 (after rounding off)

Hence the element X would take 22.10 minutes to decay to 26 grams.

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The radius of the circle, in inches, is (2√6)/π.

The perimeter of an equilateral triangle is equal to 3 times its side length. We know that the area of a circle is equal to πr2, where r is the radius of the circle. Therefore, the radius of the circle, in inches, is equal to the square root of (3*s2)/π, where s is the length of the side of the triangle.

For example, if the length of the side of the triangle is 8 inches, then the radius of the circle is equal to the square root of [(3*82)/π] = (24/π) inches. Simplifying this into simplest radical form, we get (2√6)/π inches. Thus, the radius of the circle, in inches, is (2√6)/π.

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The measure of minor arc RS, in degrees, will be approximately 86.66

Call the intersection of BT and circle A.

And we have that angle measurement. RTB =(1/2) (a measure of minor arc RB - a measure of minor arc SA) (a measure of minor arc RB - the measure of minor arc SA)

But angle SOT equals the measure of angle SOA.

Moreover, because SOA is a central angle, its measure is the same as that of minor arc SA.

ROB has the same measure as minor arc RB since it is also a central angle.

The measure of minor arc SA= angle SOT= angle SOA=M

The measure of minor arc RB= angle ROB=4M

So we have this equation

28=(1/2)(4M-M)

56=3 M

[56/3]=M

So, minor arc S A=[tex](56 / 3)^{\circ}[/tex]

And minor arc RB =[tex]4(56/3)=(224/3)^{\circ}[/tex]

And minor arc RS =[180-(56/3)-(224/3)]=[tex](260/3)^{\circ} \approx 86.66^{\circ}[/tex]

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The complete question should be like this:

In the figure, point O is the centre of the circle, the measure of angle RTB  is 28 degrees, and the measure of angle ROB  is four times the measure of angle SOT. What is the measure of minor arc RS, in degrees?

The needed diagram is attached below:

Answer: 7

Step-by-step explanation:

[tex]g(3)=5 \implies f(g(3))=f(5)=2(5)-3=7[/tex]

The difference of length of Tom's pencil from Ellen's pencil is given by the equation A = 3x + 1/5 cm

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 difference of length be represented as A

Now , the equation will be

The length of Ellen's pencil is p = 2x + 1/5 cm

The length of Tom's pencil is q = 5x + 2/5 cm

Now , the difference of length A = q - p

Substituting the values in the equation , we get

The difference of length A = 5x + 2/5 cm - 2x + 1/5 cm

On simplifying the equation , we get

The difference of length A = ( 5x - 2x ) + ( 2/5 - 1/5 ) cm

The difference of length A = 3x + 1/5 cm

Therefore , Tom's pencil is longer than Ellen's pencil by 3x + 1/5 cm

Hence , the equation is A = 3x + 1/5 cm

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The infinite series for the given indefinite integral will be as [tex]\int\ {\frac{cos(x) - 1}{x} } \, dx[/tex] Σ[infinity]n=1  [tex](-1)^n \frac{x^{2n}}{(2n)} . \frac{1}{(2n)!} + C[/tex].

We know that the infinite series also called as Maclaurin series

the Maclaurin series for cos(x)

cos(x) = Σ[infinity]n=0  [tex](-1)^n \frac{x^{2n}}{(2n)!}[/tex]

cos(x) = [tex]1 - \frac{x^2}{2!} + \frac{x^4}{4!} - .. + (-1)^n \frac{x^{2n}}{(2n)!}[/tex]

cos(x) - 1 = Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n}}{(2n)!}[/tex]

Now, divide both sides by x

cos(x) -1/x = Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n-1}}{(2n)!}[/tex]

[tex]\int\ {\frac{cos(x) - 1}{x} } \, dx =[/tex] [tex]\int { } \,[/tex] Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n-1}}{(2n)!} dx[/tex]

or [tex]\int\ {\frac{cos(x) - 1}{x} } \, dx =[/tex] Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n}}{(2n)} . \frac{1}{(2n)!} + C[/tex]

Therefore, [tex]\int\ {\frac{cos(x) - 1}{x} } \, dx =[/tex] Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n}}{(2n)} . \frac{1}{(2n)!} + C[/tex]

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The required expression is x(x - 1)/5 which is determined by multiplication.

The expression is given in the question, as follows:

(x² - 1)/5xy × x²y/(1 + x)

We have to determine the solution to the given expression by multiplication.

As per the given expression, we have

⇒ (x² - 1)/5xy × x²y/(1 + x)

Cancel out the equivalent terms in the above expression,

⇒ (x - 1)(x + 1)/5 × x/(1 + x)

Reduce the same in the above expression,

⇒ x(x - 1)/5

The required expression is x(x - 1)/5.

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round off 987 416 to the nearest 5 mean the 6 turns into 5 so the answer is 987 415.If the 6 was 2 the 2 will turn into 0 and if the 6 was 9 the 9 will turn into 10

In the given figure, where triangle QPS = triangle SRQ, the value of

a. x = 47°

b. ∠PQS = 32°

c. ∠PSR = 74°

A triangle is a 3-sided polygon that is occasionally (though not very frequently) referred to as the trigon. Every triangle has three sides and three angles, some of which might be the same.

In a right triangle, the two sides opposite the right angle are referred to as the hypotenuse, and the other two sides are referred to as the legs. All triangles are bicentric and convex. The triangle's interior is that part of the plane it encloses; the exterior is the rest.

Given that  ∆QPS ≈ ∆SRQ

a) ∠QPS = ∠QRS

106° = 2x + 12

106° - 12 = 2x

2x = 94°

x = 47°

b) ∠RSQ = ∠PQS

∠SQR + ∠SRQ + ∠RSQ = 180°

42° + 2(47°) + 12 + ∠RSQ = 180°

148 + ∠RSQ = 180°

∠RSQ = 180° - 148°

∠RSQ = 32°

∠PQS = 32°

c) ∠PSR = ∠PSQ + ∠RSQ

[ ∠PSQ = 42° = ∠SQR ; ∠RSQ = 32°]

∠PSR = 42° + 32°

∠PSR = 74°

Thus, In the given figure, where triangle QPS = triangle SRQ, the value of x = 47°, ∠PQS = 32°, ∠PSR = 74°.

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Answer:

(x - 2)(x + 2)

Step-by-step explanation:

x² - 4 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

x² - 4

= x² - 2²

= (x - 2)(x + 2) ← in factored form

The values of Z and X, considering the normal curve, are given as follows:

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 120, \sigma = 4[/tex]

The p-value is of 0.12, hence the z-score is given as follows:

-1.175.

Then the value of X is obtained as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

-1.175 = (X - 120)/4

X - 120 = -1.175 x 4

X = 115.3.

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