ms. young, a special education teacher, is teaching kim, a 13-year-old with multiple disabilities, how to identify each us coin (penny, nickel, dime, quarter). every day, ms. young gives kim 15 random coins to identify. with the help of a chart showing each coin and its name, kim is asked to identify each coin. the results after one week of instruction are shown below. day number of coins identified correctly monday 7 tuesday 4 wednesday 5 thursday 4 friday 2 based on this data, what should ms. young do next?

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 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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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 required value of the given function is (f ⋅ g)(4) = 130.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The functions are given in the question, as follows:

f(x)=3x+1 and g(x)=x²-6

(f ⋅g)(x) is the composition of the functions f and g, which means f(x) × g(x).

(f ⋅ g)(x) = f(x) × g(x)

So, substituting x = 4:

(f ⋅ g)(4) = f(4) × g(4)

= (3 × 4 + 1)×(4² - 6)

= 13 × 10

= 130

So, (f ⋅ g)(4) = 130.

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Hope it helps.

If you have any query, feel free to ask.

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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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:

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

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 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 only statements that is false is A. I only: 1. We use one-sample procedures when our samples are equal in size but aren't independent.

A one-sample procedure is used when we want to compare a sample mean to a known population mean or when we want to estimate a population mean using a sample mean. In a one-sample procedure, the sample is selected independently and is typically assumed to be random. So, independence of the sample is a requirement for one-sample procedure.

While statement II and III are true.

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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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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: 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: The system of equations to determine the number of each item sold would be:

4x + 5y = 340 (where x is the number of cakes and y is the number of pies)

and

x + y = 75 (where x and y is number of cakes and pies)

This system of equations can be solved using methods such as substitution or elimination.

Step-by-step explanation:

To find the height of a stack of 8x10^9 books, we need to calculate the total thickness of all the books.

The thickness of one book is 3.1x10^-4 meters. So, the total thickness of 8x10^9 books can be calculated by multiplying the thickness of one book by the number of books:

3.1x10^-4 meters/book * 8x10^9 books = 24.8 meters

Therefore, the height of a stack of 8x10^9 books, each with a thickness of 3.1x10^-4 meters, would be 24.8 meters.

It's equivalent to about 81 ft.

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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A poster is being designed that is to contain 2 150. In of printed material with margins of 2 inches at the top and bottom and 3 inches at each side. the dimensions that will minimize the amount of paper used is that should be 12 inches wide by 6 inches tall.

The margins are 2 inches at the top and bottom and 3 inches at each side. The margins are then added to the two 150s, making a total width of 12 inches and a total height of 6 inches. This is the minimum amount of paper that can be used for the poster.   In order to minimize the amount of paper used, it is important to consider the size of the margins.

The margins should be kept as small as possible in order to maximize the amount of space available for the printed material. Generally speaking, a margin of 1 inch is sufficient for most printed materials. If a larger margin is necessary, then the overall dimensions of the poster should be adjusted accordingly.

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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: 0.875 for decimal, 87.5 for percent.

Step-by-step explanation- Pretty easy, all you gotta do is divide the top by the bottom. So 7 divided by 8= 0.875!

For percent, divide 7 by 8 and then multiply by 100, it would be 87.5

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:

   20 miles

Step-by-step explanation:

first, draw a diagram. Then, use the pythagorean theorem to calculate.

0.05, fail to reject null hypothesis..

What is hypothesis in math

A proposition is considered to be a hypothesis if it is plausible given the available information but has not been proven true or wrong.

                  A statement on which hypothesis testing will be based is referred to as a hypothesis in statistics (also known as a statistical hypothesis).

Below are the null and alternative Hypothesis,

Null Hypothesis: μ = 9.2

Alternative Hypothesis: μ ≠ 9.2

Test statistic,

t = (xbar - mu)/(s/sqrt(n))

t = (8.25 - 9.2)/(5.1478/sqrt(8))

t = -0.522

P-value Approach

P-value = 0.6178

As P-value >= 0.05, fail to reject null hypothesis..

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W is an invariant sub-space under T if and only if all non-zero vectors in W are eigenvectors of T because T=αI,α∈F.

The vector is an entity with both magnitude and direction. The movement of an item between two points is described by a vector. The directed line segment can be used to graphically represent vector math.

Given that,

For each vector v ∈ V, there exists [tex]a_{v}[/tex] such that [tex]T_{v}=a_{v}v[/tex] (because [tex]T_{v}[/tex] ∈ span(v) ). Suppose there are vectors u, v∈V such that [tex]a_{u}\neq a_{v}[/tex]. Then

T(u+v)=Tu+Tv⇒[tex]a_{u+v}(u+v)=a_{u}u+a_{v}v[/tex]

which means (u,v) is linearly dependent (since both coefficients cannot be zero simultaneously, by assumption). Therefore, either [tex]a_{u}= a_{v}[/tex], and T is a scalar transformation, or V has a dimension of at most 1, which also implies Tx=αx, with constant α.

Hence, T=αI,α∈F

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[tex]\textit{Product to Sum Identities} \\\\ cos(\alpha)sin(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad -\quad sin(\alpha-\beta)] \\\\[-0.35em] ~\dotfill\\\\ cos(3x)sin(x)\implies \cfrac{1}{2}[sin(3x+x)~~ - ~~sin(3x-x)] \\\\\\ ~\hfill {\Large \begin{array}{llll} \cfrac{1}{2}[sin(4x)-sin(2x)] \end{array}}~\hfill[/tex]

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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It will take (miles / (mph eastbound + mph westbound)) hours for the two trains to be miles apart.

(miles / (mph eastbound + mph westbound)) * 60 minutes/hour = minutes

The time it takes for two trains to be a certain distance apart depends on the speed of each train and the distance between them. To calculate this, we can use the equation time = distance/speed. We can also use this equation to calculate the time for two trains traveling in opposite directions. To do this, we add the speed of the eastbound train (mph eastbound) and the speed of the westbound train (mph westbound) and divide the distance between the two trains (miles) by the total. This gives us the amount of time it will take for the two trains to be miles apart. After converting the answer to minutes, we get the amount of time it will take for the two trains to be miles apart.

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As per the unitary method, the number of matches produced in Oregon over the same period is 64

The term unitary method is known as the method of finding the value of a single unit from the value of multiple units

Here we have given that the increase in the number of matches produced in California from 1980 to 1990 exceeds.

Therefore, the number of increase is calculated as,

CA = 0.33(1.2) = 396

If the increase is calculated as,

=> 0.33(1.6) = 528

Then the difference is calculated as,

=> 528 - 396 = 132

Similarly the number of matches in Oregon is calculated as.

=>  0.17(1.2) =204 M

=> 0.17(1.6) = 272 M

Therefore, the difference is calculated as

=> 272 -204 = 68

Therefore the total difference between increases is written as,

=> 132-68 = 64

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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.