[tex]25 \div 2 [/tex]
How to solve this?​

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:

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

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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[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]

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¢).

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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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.

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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The area of the shaded portion is given by the difference between the area of the outer circle and the area of the inner circle.

First, let's find the areas of the circles:

Outer Circle: Area = πr^2 = π (2)^2 = 4π square meters

Inner Circle: Area = πr^2 = π (0.75)^2 = 0.5625π square meters

Area of shaded portion = Area of outer circle - Area of inner circle = 4π - 0.5625π = 3.4375π square meters

So the area of the shaded portion is approximately 10.8 square meters.

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 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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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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According to the information, we can infer that there are 20 games left. To solve this problem we have to use a linear equation.

To calculate how many games do the Rockets have left to play we have to use a linear equation. Additionally, we have to take into account the information that we have:

Also, we know that if the rockets loses all the remaining games, and the rangers win all the remaining games, both will win the same number of games. Finally, to solve this problem we have to make the following equation:

In this equation, X is equal to the number of games won by both teams.

(100 - X)*(7/20) + X = (100 - X)*(3/5)

X = (100 - X)*(3/5) - (100 - X)*(7/20)

X = (100 - X)*(3/5 - 7/20)

X = (100 - X)*(12/20 - 7/20)

X = (100 - X)*(5/20)

(20/5)*X = 100 - X

4*X = 100 - X

4*X + X = 100

5*X = 100

X = 100/5

X = 20

According to the above, the number of games won by both teams is 20.

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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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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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The cost of one hundred kilowatt-hours of electricity is $16.4

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

Given that, the formula for calculating the cost per one thousand kilowatt-hours of electricity is twice the sum of 36 and 4 times the difference of 7 and 2 dollars per thousand kilowatt-hours.

The cost for 1000 kilowatt-hours of electricity =

2(36+36) + 4(7-2)

= 2(72) + 4(5)

= 144 + 20

= $164

Since, 1000 kilowatt-hours of electricity costs $164

Then, 1 kwh will cost = $164 / 1000

And, 100 KWh will cost = $164 / 1000 × 100

= $16.4

Hence, The cost of one hundred kilowatt-hours of electricity is $16.4

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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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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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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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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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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: 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:

   20 miles

Step-by-step explanation:

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

Answer:

a) To find out how much money is added to the account each year, we use the simple interest formula: I = Prt, where I is the interest, P is the principal (initial deposit), r is the annual interest rate (expressed as a decimal), and t is the number of years.

In this case, P = 1800, r = 0.03, and t = 1 (because we are finding the interest added for 1 year)

So the formula becomes:

I = 1800 * 0.03 * 1 = 54

Therefore, £54 is added to the account each year.

b) To find out how much money will be in the account after two years, we add the original deposit to the total interest earned over two years.

We know that the interest added each year is £54, and since we are trying to find the balance after 2 years, we will multiply it by 2 to find the total interest earned over 2 years:

Interest = 54 * 2 = £108

Now we add the original deposit and the total interest to find the total amount in the account after 2 years:

Total = 1800 + 108 = £1908

So the amount of money in the account after two years will be £1908.

The account will have £1909.62 after two years.

Simple interest is the amount of interest charged on a specific principal amount at a specific interest rate. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.

a) The amount of money added to the account each year is determined by multiplying the principal amount (initial amount) by the interest rate. So, the amount added to the account each year is:

Interest = Principal x Rate

Interest = £1800 x 0.03

Interest = £54

Therefore, £54 will be added to the account each year.

b) To find the amount of money in the account after two years, we need to add the interest earned in each year to the principal amount. After one year, the account will have:

Amount after 1 year = £1800 + £54 = £1854

After the second year, the account will have earned another 3% interest on the new balance of £1854. So, the interest earned in the second year is:

Interest = £1854 x 0.03

Interest = £55.62

Therefore, the total amount of money in the account after two years is:

Amount after 2 years = £1854 + £55.62 = £1909.62

So, the account will have £1909.62 after two years.

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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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Answer:

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

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

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.