In the figure below ABCDE A’B’C’D’E’
Which transformation maps figure ABCDE onto figure A’B’C’D’E’?

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

An explicit formula for aₙ, the nth term of the arithmetic sequence is aₙ = 3 + 5(n - 1)..

Mathematically, the nth term of an arithmetic sequence can be calculated by using this mathematical expression:

aₙ = a₁ + (n - 1)d

Where:

From the information provided, we have the following parameters:

First term, a₁ = 3

Second term, a₂ = 8

Next, we would determine the common difference as follows:

Common difference, d = a₂ - a₁

Common difference, d = 8 - 3

Common difference, d = 5

Substituting the parameters into the mathematical expression, we have;

aₙ = 3 + (n - 1)(5)

aₙ = 3 + 5(n - 1).

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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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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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This test batch can be chosen is 455 ways. (Option A).

The problem is asking for the number of ways to choose 3 batteries out of a box of 15.

This is a combination problem and the number of ways to choose k items out of a set of n items, without regard to the order of selection, is given by the binomial coefficient:

C(n,k) = n!/(k!(n-k)!)

where ! denotes factorial.

So in this case, we have:

C(15,3) = 15!/(3!(15-3)!) = 151413/(321) = 455

So, the answer is 455.

Therefore, This test batch can be chosen is 455 ways. (Option A).

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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!

So, on solving the provided question, we can say that, here  by differential equations So, 2(400)(25) = 2(500)(dy/dt) => [tex]dy/dt = 20 ft/sec[/tex]

Sequences in which the difference between succeeding terms is constant are known as arithmetic progressions. For instance, an arithmetic progression with a tolerance of 2 is the sequence 5, 7, 9, 11, 13, and so on. An arithmetic progression (A.P.) is a progression where the tolerance between two succeeding numbers is always the same.

Let x be the girl's distance from the kite at time t and y be the length of the string at that same moment.

The right triangle at time t has a hypotenuse of length y, a hypotenuse of length 300, and a hypotenuse of length x.

[tex]dx/dt = 25[/tex]

By the Pythagorean Theorem,

[tex]x2 + 3002 = y2[/tex]

[tex]2x(dx/dt) = 2y(dy/dt)[/tex]

Since [tex]x2 + 3002 = y2 and y = 500, x = 400[/tex]

So, 2(400)(25) = 2(500)(dy/dt)

[tex]dy/dt = 20 ft/sec[/tex]

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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 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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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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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.

Hope it helps.

If you have any query, feel free to ask.

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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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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Answer: Hello how are you doing today?

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

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

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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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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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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Answer: Apples $0.18 (18 Cents) Bananas $0.14 (14 cents)

Step-by-step explanation:

Math knowledge would give the cost for each item. We have:

4 apples + 6 bananas = $1.56

and

9 apples + 7 bananas = $2.60

To find a cost, we encode an apple as 'a', and a banana as 'b' in the following two main equations:

4a+6b=1.56

9a+7b=2.6

The following formula represents the situation by using elimination method to find, let's say, the banana value:

4a+6b=1.56 , 9a+7b=2.6

9×4a+9×6b=9×1.56, 4×9a+4×7b=4×2.6

36a+54b=14.04, 36a+28b=10.4

36a−36a+54b−28b=14.04−10.4

54b−28b=14.04−10.4

26b=14.04−10.4

26b=3.64

b=3.64÷26

b=0.14

That is a banana costs $0.14 (14¢).

Now we have found the value of a banana, we substitute this new value in one of the main equations above to reduce variables so that we can find the value of an apple as follows:

4a+6b=1.56

4a+(6×0.14)=1.56

4a+0.84=1.56

4a=1.56-0.84

4a=0.72

a=0.72÷4

a=0.18

Simply enough, an apple costs $0.18 (18¢), and a banana costs $0.14 (14¢).

Answer: 3ml:4ml:7ml

Step-by-step explanation: To simplify ratios you have to find the highest number that you can divide all the parts in the ratio by (AKA as highest common factor)

In this case the common factor of 18,24 and 42 is 6.

so now divide all the parts by 6:

18/6=3

24/6=4

42/6=7

finally put these numbers back into the correct ratio format and for this question put on the units.

final answer= 3ml:4ml:7ml

Answer:

I think the answer is A. I hope this is helpful

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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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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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

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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[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:

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:

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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This is the answer above mentioned