can someone help me solve this equation
7-1/2x=3

Answer:208

Step-by-step explanation:

Midpoint formula:

(X1+x2)/2, (y1+y2)/2

Midpoint: (-12+7)/2 , (5+9)/2

=( -5/2,7)

The answer is a.

The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

From the question, we have the following parameters that can be used in our computation:

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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Answer:

7

Step-by-step explanation:

The middle 2 numbers are 6 and 8. Add them both up and divide them by 2. Gets you 7.

An equation having variables on both sides can be solved by bringing all variables to one side.

An equation with all variables on one side can be solved by simply keeping the variables on the left and simplifying the value on the right. For example,

5x = 6 + 2x;

3x = 6;

x = 2.

For an equation with variables on both sides, just bring all variables on one side. After that, the same process like above is to be followed. For example,

5y - 3 - 3y = 3y + 5 - 3y;

5y - 3y - 3y + 3y = 5 + 3;

2y = 8;

y = 4;

Thus, methods for solving both kinds of equations is similar.

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An equation having variables on both sides can be solved by bringing all variables to one side.

An equation with all variables on one side can be solved by simply keeping the variables on the left and simplifying the value on the right. For example,

5x = 6 + 2x;

3x = 6;

x = 2.

For an equation with variables on both sides, just bring all variables on one side. After that, the same process like above is to be followed. For example,

5y - 3 - 3y = 3y + 5 - 3y;

5y - 3y - 3y + 3y = 5 + 3;

2y = 8;

y = 4;

Thus, methods for solving both kinds of equations is similar.

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The midpoint of the line segment formed by joining P₁ = (0.3, -2.7) and
P₂ = (5.5, -8.1) is (2.9, -5.4). This is determined by taking the average of the x-coordinates and y-coordinates of the two endpoints.

To find the midpoint of the line segment formed by joining P₁ = (0.3, -2.7) and P₂ = (5.5, -8.1), we can use the midpoint formula.

The midpoint formula states that the coordinates of the midpoint (M) are given by the average of the coordinates of the two endpoints.

For the x-coordinate of the midpoint:

x-coordinate of midpoint (M) = (x-coordinate of P₁ + x-coordinate of P₂) / 2

Plugging in the values:

x-coordinate of midpoint (M) = (0.3 + 5.5) / 2 = 5.8 / 2 = 2.9

For the y-coordinate of the midpoint:

y-coordinate of midpoint (M) = (y-coordinate of P₁ + y-coordinate of P₂) / 2

Plugging in the values:

y-coordinate of midpoint (M) = (-2.7 + (-8.1)) / 2 = -10.8 / 2 = -5.4

Therefore, the midpoint (M) of the line segment formed by joining P₁ = (0.3, -2.7) and P₂ = (5.5, -8.1) is (2.9, -5.4).

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Answer:

recessions

Step-by-step explanation:

The probability that the largest of n random samples is greater than the population median M is bounded above by\(1 - F(M)^(n-1) \times F(X(n))\).

Assumptions about the population and the sampling method.

Let's assume that the population has a continuous probability distribution with a well-defined median, and that we are taking independent random samples from this population.

Let \(X1, X2, ..., Xn\) be the random samples that we take from the population, where n is the sample size.

Let M be the population median.

The probability that the largest of these random samples, denoted by X(n), is greater than M.

Cumulative distribution function (CDF) of the population distribution to calculate this probability.

The CDF gives the probability that a random variable takes on a value less than or equal to a given number.

Let F(x) be the CDF of the population distribution.

Then, the probability that X(n) is greater than M is:

\(P(X(n) > M) = 1 - P(X(n) < = M)\)

Since we are assuming that the samples are independent, the joint probability of the samples is the product of their individual probabilities:

\(P(X1 < = x1, X2 < = x2, ..., Xn < = xn) = P(X1 < = x1) \times P(X2 < = x2) \times ... \times P(Xn < = xn)\)

For any x <= M, we have:

\(P(Xi < = x) < = P(Xi < = M) for i = 1, 2, ..., n\)

Therefore,

\(P(X1 < = x, X2 < = x, ..., Xn < = x) < = P(X1 < = M, X2 < = M, ..., Xn < = M) = F(M)^n\)

Using the complement rule and the fact that the samples are identically distributed, we get:

\(P(X(n) > M) = 1 - P(X(n) < = M)\)

= \(1 - P(X1 < = M, X2 < = M, ..., X(n) < = M)\)

=\(1 - [P(X1 < = M) \times P(X2 < = M) \times ... \times P(X(n-1) < = M) \times P(X(n) < = M)]\)

\(< = 1 - F(M)^(n-1) \times F(X(n))\)

Probability depends on the sample size n and the distribution of the population.

If the population is symmetric around its median, the probability is 0.5 for any sample size.

As the sample size increases, the probability generally increases, but the rate of increase depends on the population distribution.

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a) The solution to this equation is the trivial solution x = (0,0,0)T, which means that the kernel of L is the zero vector.

The range of L is all of R3.

b) The kernel of L is the set of all vectors of the form (0,y,z)T.

The range of L is the set of all vectors of the form (a,a,a)T, where a is any constant.

To find the kernel and range of a linear operator on R3, we need to first understand what these terms mean. The kernel of a linear operator is the set of all vectors that are mapped to the zero vector by the operator, while the range is the set of all possible output vectors that can be obtained from the operator.

a) L(x) = (x3,x2, x1)T

To find the kernel, we need to solve the equation L(x) = 0, which gives us the system of equations:

x3 = 0

x2 = 0

x1 = 0

The only solution to this system is the trivial solution x = (0,0,0)T, which means that the kernel of L is the zero vector.

To find the range, we need to determine all possible output vectors that can be obtained from L. Since L maps a vector x to a vector with its components reversed, we can see that any vector in R3 can be obtained by applying L to a vector of the form (a,b,c)T, where a, b, and c are arbitrary constants. Therefore, the range of L is all of R3.

b) L(x) = (x1,x1, x1)T

To find the kernel, we need to solve the equation L(x) = 0, which gives us the system of equations:

x1 = 0

The solution to this system is x = (0,y,z)T, where y and z are arbitrary constants. Therefore, the kernel of L is the set of all vectors of the form (0,y,z)T.

To find the range, we can see that L maps any vector x in R3 to a vector of the form (x1,x1,x1)T. Therefore, the range of L is the set of all vectors of the form (a,a,a)T, where a is any constant.

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Answer:

r = C ÷ 2π

Step-by-step explanation:

Given

C = 2πr ( isolate r by dividing both sides by 2π )

C ÷ 2π = r

Answer:

6/10 or 3/5

Step-by-step explanation:

Answer:

Midpoint are 4,10

Step-by-step explanation:

x midpoint - 4

y midpoint - 10

midpoint formula (x1 + x2)/2 , (y1 + y2)/2

(2+8)/2, (7+13)/2

4,10

Full Explanation

\( M = (x_M, \; y_M) \)

\( M = \left(\dfrac{x_1 + x_2}{2}, \; \dfrac{y_1 + y_2}{2}\right) \)

\( M = \left(\dfrac{2 + 6}{2}, \; \dfrac{7 + 13}{2}\right)\)

\( M = \left(\dfrac{8}{2}, \; \dfrac{20}{2}\right)\)

\( M = (4, \; 10)\)

Therefore, the appropriate percent in the pie chart to represent the preference for Klean laundry detergent is 15%.

Percent is a way of expressing a fraction or a ratio as a portion of 100. The word "percent" means "per hundred." It is denoted by the symbol "%". Percentages are commonly used to express rates, proportions, or parts of a whole in various fields, such as mathematics, science, finance, and statistics. For example, an interest rate of 5% per annum means that for every 100 units of money, the lender will receive 5 units of interest each year.

Here,

To find the appropriate percent in the pie chart to represent the preference for Klean laundry detergent, we need to calculate the fraction of people who prefer Klean detergent, and then convert it to a percentage.

The fraction of people who prefer Klean detergent is:

75/500 = 0.15

To convert this fraction to a percentage, we can multiply by 100:

0.15 x 100 = 15%

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Answer:

A=2

B=-1

Step-by-step explanation:

a=(23−25)⋅ (4−5)=2

b=(97−123)/(18+8)=−1

Answer:

21 and 16

Step-by-step explanation:

x= big number

x`-5 = small number

x + x-5 = 37

2x-5 =37

2x= 42

x = 21

       21-5 = 16

21+16 = 37

3 exponent 2 × 5 exponent 1 × 7 exponent 1

One of the operation under which the given set is closed is "Modulus operation".

\(\{..., -3, -1, 1, 3, ... \}\)

Definition: A set is closed under an operation if the operation returns a member of the set when evaluated on members of the set.

Many operations can be defined. But some of the standard  operations are known.

From such operations, one operation for which the given set is closed under is modulus operation.

Proof:

\(Let \\\\S = \{.., -3, -1, 1,3,...\}\\\\Then \: \forall \: x \in S, \exists -x \in S.\\\\\)

Now let y be any value belonging to S.

Then two cases:

\(y < 0:\\ |y| = -y \: which \in S\)

or

\(y > 0:\\|y| = y \: which \in S\\\\\)

Thus under modulus operation, the given set is closed.

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Using a system of equations, it is found that:

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given by:

A rented and filled 14 vans and 5 buses with 442 students, hence:

14x + 5y = 442.

High School B rented and filled 5 vans and 5 buses with 280 students, hence:

5x + 5y = 280.

Simplifying by 5:

x + y = 56.

y = 56 - x.

Hence:

14x + 5(56 - x) = 442.

9x = 162

x = 162/9

x = 18.

Then:

y = 56 - x = 56 - 18 = 38.

Hence:

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Answer: I don't know  all of it but I know the power is -5^5, the base is -5, the exponent is 5 and I think the standard form is -3125  I think that's what it  is I don't remember all of it

The fraction is 5000/3.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is primarily used to compare and determine ratios and is represented by the symbol %.

Given:

166 2/3 percent as a fraction

Now, converting it into fraction

= 500/3 x 100

= 50000/3

Hence, the fraction is 5000/3

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A common everyday counting unit that is used to mean 12 of an object is a Dozen

Dozen is derived from the Old French word "douzaine" which means twelve each. In most situations, a dozen is used to refer to a group of twelve items. The term dozen is also used in informal situations to refer to a very large number of objects. For example, one might say "I have dozens of friends!" to mean that they have a lot of friends.

Dozen is a useful term when counting items. It allows for large numbers to be easily broken down into manageable groups. For example, if you have 120 pencils, you could easily count them by saying that you have 10 dozen pencils. It can also be useful when talking about fractions. For example, instead of saying "one and a half of an item," one could say "one and a half dozen of an item."

Dozen is a common everyday counting unit that is used to mean 12 of an object. It is a useful term when counting items and when talking about fractions, and can be used in both formal and informal settings.

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Answer:

60

Step-by-step explanation:

I divided 36 by 3 got 12 then mutiplyed 12 by 5

Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

3x - 2y = 4 ................(1)

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

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Answer:

i think its D because fun isn't 25%. food is 25% and fun is smaller than food

Answer:

B

The blue plus the yellow makes the half mark all the way across the circle. Just for example the red, green, and purple make the other half.

Hope that helps!! Have a good day!! :)

The volume of this prism = 2 × 3 × 9 units³.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

from the given figure we get,

A rectangular prism made up of unit cubes.

There are 3 layers, and each layer is 9 units long and 2 units wide.

i.e. l = 9

w = 2

h = 3

so, the volume = V

we know, V= l.w.h

so, V = 9.2.3

Hence, The volume of this prism = 2 × 3 × 9 units³.

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The given partial differential equation is u^x 2u^y. The general solution to this equation is in the form u = ke^cxy, where k and c are constants. To find the general solution of the partial differential equation u^x 2u^y, we can assume a solution of the form u = ke^cxy, where k and c are constants to be determined.

Taking the partial derivative of u with respect to x, we get u^x = ckye^cxy. Similarly, taking the partial derivative of u with respect to y, we get u^y = cxe^cxy.

Substituting these partial derivatives back into the given equation, we have ckye^cxy - 2cxe^cxy = 0.

Factoring out the common term cye^cxy, we get cye^cxy (k - 2x) = 0.

For this equation to hold for all values of x and y, we must have cye^cxy = 0 and k - 2x = 0.

Since e^cxy is always positive and nonzero, we have cye^cxy = 0 if and only if cy = 0, which implies c = 0.

Therefore, the general solution to the partial differential equation is u = ke^cxy, where k is a constant.

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For a vertical cylindrical water tank where the rate of flowing is 5 cubic metre per minute. The rate at which the height of the water is rising is equals to the \( \frac{5}{9π }\) metre per minute.

We have, water flowing into a vertical cylinder. Let the radius, height and volume of cylindrical tank be r metre, h metre and V cubic metre respectively. Now, Rate of water flow in tank, \( \frac{dV}{dt}\) = 5 cubic m /min

Radius of cylindrical tank, r = 3 m

We have to determine rate at which height of the water is rising, i.e., dh/dt. As we know, Volume of cylindrical water tank, V = πr²h --(2)

Differentiating equation (2) with respect to time t,

=> \( \frac{ dV}{dt }= π(r)²\frac{dh}{dt}\)( since, radius of cylinder is constant)

=> \(5 = π(3)² \frac{ dh}{dt}\)

=> \(5 = 9π \frac{dh}{dt}\)

=> \( \frac{ dh}{dt} = \frac{5}{9π }\)

Hence, the required rate is \( \frac{5}{9π }\)m/min.

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Answer:

The first line

Step-by-step explanation:

Answer:

the system has infinitely many solutions

Step-by-step explanation:

Given the expressions

y - 2x = 4 .... 1

2x -y - 4 = 0 .... 2

We are to find the solution to the equation as shown

From equation 1: y = 4+2x

Substitute into 2:

2x - (4+2x) - 4 = 0

2x - 4 - 2x - 4 = 0

0 = 0

This shows that the equation has infinite number of solutions

Let y = k

Get x

Substitute y = k into equation 2

From 2: 2x -y - 4 = 0

2x - k - 4 = 0

2x = k+4

x = (k+4)/2 where k is any integer

Hence the system has infinitely many solutions

The shell method, we integrate 2πrh*dx, where r is the distance from the axis of revolution to the shell,

The volume of the solid generated by revolving the region bounded by the line y = f(x), where f(x) is a function, using the shell method, we integrate 2πrh*dx, where r is the distance from the axis of revolution to the shell, h is the height of the shell, and dx represents an infinitesimally small change in x.

The limits of integration are determined by the intersection points of the line y = f(x) with the x-axis. We evaluate the integral from the lower limit to the upper limit to obtain the volume of the solid.

The shell method allows us to calculate the volume by considering infinitesimally thin cylindrical shells perpendicular to the axis of revolution.

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