By rounding each number to 1 significant figure estimate to 6235.1 x 21.5

The possible value of the expression is 5 > y > 3

The expression is given as

1/5 < 1/y < 1/3

Take the exponent of the sides of the inequality

(The inequality sign would change)

So, we have

5 > y > 3

Hence, the possible value of the expression is 5 > y > 3

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The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively

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

The graph

The above graph is an exponential function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (0, ∝)

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In this case, the first two components are multiples \((4 = -2 * -2, 6 = -3 * -2)\), so if h is \(-16 (8 * -2),\) the vectors are scalar multiples, and thus linearly dependent. For all other values of h, the vectors are linearly independent.

To find the transpose of a matrix, interchange its rows and columns. The standard matrix of a linear transformation T, which rotates points through 3/4 pi radians counterclockwise, can be given as:

\([cos(3/4 pi) -sin(3/4 pi)][sin(3/4 pi)  cos(3/4 pi)]\)

To find the matrix product AB, first check if the dimensions are compatible. If not, AB is undefined.

To find the inverse of a matrix, check if it is invertible. If not, the matrix does not have an inverse.

To determine if columns of a matrix form a linearly independent set, analyze the solutions of Ax = 0. If it has only the trivial solution, the columns are linearly independent. If it has more than one solution, they are not linearly independent.

For the vectors [-2 -3 8] and [4 6 h] to be linearly independent, they must not be scalar multiples of each other.

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3.25 • 5 + 2.50 • 3 + 2 • 3 = x

16.25 + 7.50 + 6 = x

29.75 = how much they spent all-together

Answer:

no

Step-by-step explanation:

2/6 simplifies to 1/3 and 2/4 simplifies to 1/3. 1/2 is greater than 1/3

12·C

Step-by-step explanation:

2 * 6 = 12·C

Answer:

It is the distribution of the statistic if we were to draw all possible samples of a given size from the population and calculate the statistic for each sample.

Step-by-step explanation:

The sampling distribution of a statistic refers to the range of all possible sample values of the statistic that could be drawn from the parent population under the specified sampling plan.

In other words, it is the distribution of the statistic if we were to draw all possible samples of a given size from the population and calculate the statistic for each sample.

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Answer:

77.5

Step-by-step explanation:

First, find the cost without delivery fees

$4.50*5=$22.50

Then, the fees. $10*5=$50

Then, $50+$22.5=$77.5!

Answer:

Hope it works for u

Step-by-step explanation:

its so simple first to find the total cost for 1 sandwich

for 1 sandwich+ delivery charges

total cost for 1 sandwich= delivery charges+ sandwich cost

                                          =$10+4.50 =$14.50

Now to get total cost for 5 sandwich and also delivery charges is on each sandwich hence simply multiply total cost by 5,we get

Total cost for 5 =  5*($14.50)=$72.5 Ans.....

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The compass needle always points north because it is magnetic north pole.

Earth has magnetic field due to magnetic elements present in Earth's core in molten form. They are assumed to be in the form of giant bar to ease the calculations concerning magnetic field and polarity. The assumptions are geographic south pole harbours magnetic north pole and vice versa for the opposite pole.

So, we know that like poles attract each other and unlike poles repel each other. The north end of magnetic needle will point towards the magnetic south pole which is geographic north pole. Thus, we see compass needle directed to North pole.

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Answer:

y = (2/5) x

Step-by-step explanation:

hope this helps!

Triangle pairs are similar polygons if they have the same shape but not necessarily the same size. In order for two triangles to be similar, they must satisfy the following conditions:

They must have the same angles. This means that the measures of the angles in one triangle must be the same as the measures of the corresponding angles in the other triangle.

The lengths of the sides must be in the same ratio. This means that if you divide the lengths of the corresponding sides of one triangle by the lengths of the corresponding sides of the other triangle, you must get the same ratio for all pairs of sides.

For example, if triangle ABC is similar to triangle DEF, the ratios of AB/DE, AC/DF, and BC/EF must all be the same.

To determine if two triangles are similar, you can use one of several theorems and postulates, such as the Side-Side-Side (SSS) Similarity Theorem, the Side-Angle-Side (SAS) Similarity Theorem, or the Angle-Angle (AA) Similarity Postulate. These theorems and postulates provide different sets of conditions that must be satisfied in order for two triangles to be similar.

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Uranium-238 has a half-life of 4.5 billion years. Therefore, half of the original number of uranium atoms decay in 4.5 billion years. After another 4.5 billion years, half of the remaining atoms will decay.

The number of remaining uranium atoms after a specific amount of time can be found using the following formula:N = N0 x (1/2)t/Twhere:N0 is the initial number of atomsN is the number of atoms after time t has passedT is the half-life of the element is the amount of time that has passedIn this problem, we know that the sample initially contained 1.9 x 10^18 uranium-238 atoms when the universe was formed 13.8 billion years ago. We want to find out how many uranium-238 atoms it contains today, which is 13.8 billion years after it was formed. Since the half-life of uranium-238 is 4.5 billion years, we can calculate the number of remaining atoms as follows:\(N = N0 x (1/2)t/TN = (1.9 x 10^18) x (1/2)^(13.8/4.5)N = 6.58 x 10^17\)Therefore, the sample of uranium-238 would contain \(6.58 x 10^17\)atoms today.

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Answer:

5,809 m^2

Step-by-step explanation:

50/2=25 m

25^2 times 3.14=1,962.5 m^2

70/2=35 m

35^2 times 3.14=3,846.5 m^2

1,962.5+3,846.5=5,809 m^2

Answer:

Flip the fraction that you are applying the exponent to, if it's a whole number, just imagine it's over one and flip it that way.

Explanation:

If you have 3/5 ^-3

You would flip the fraction to 5/3, then the exponent turns to positive 3

So 5/3 ^3

For a whole number, for example, 6, ^-2

In other words, it's 6/1 ^2, so you would make it 1/6, then the exponent turns positive.

So 1/6 ^2

Hope this helped :)

To change a negative exponent to a positive one, a flip it into a reciprocal.

Here,

We have to explain, change a negative exponent to a positive one.

What is Reciprocal?

The inverse of a number is called Reciprocal.

Now,

Let a number is,  \(5^{-2}\)

Then change it into positive exponent as;

Take reciprocal of \(5^{-2}\), we get;

⇒ \((\frac{1}{5} )^2\)

Hence,  reciprocal of \(5^{-2}\) = \((\frac{1}{5} )^2\)

So, To change a negative exponent to a positive one, a flip it into a reciprocal.

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The five-number summary is:

Minimum: 9

First Quartile: 16.5

Median: 25.5

Third Quartile: 39

Maximum: 51

3. Range = 42

4. Interquartile range = 22.5

Given the data for the lengths as, 36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20, to find the five-number summary of the data set, we would follow the steps below:

1. The numbers in ordered from the smallest to the largest would be:

9, 14, 15, 18, 20, 22, 29, 36, 36, 42, 45, 51

2. The five-number summary for the lengths in minutes would be:

3. Range of the data = max - min = 51 - 9 = 42

4. The interquartile range for the data set = Q3 - Q1 = 39 - 16.5

Interquartile range for the data set = 22.5

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To find the coefficients of the parabola that passes through the given points, we need to solve for a, b, and c using a system of equations.

First, let's substitute the coordinates of the points into the equation of the parabola:

y = ax²+ bx + c

When x=0, y=2:
2 =  a(0)²+ b(0) + c
2 = c

When x=1, y=8:
8 =  a(1)²+ b(1) + c
8 = a + b + c

When x=2, y=16:
16 = a(2)² + b(2) + c
16 = 4a + 2b + c

Now we have a system of three equations with three unknowns:

2 = c
8 = a + b + c
16 = 4a + 2b + c

Substituting c=2 into the second equation:

8 = a + b + 2
a + b = 6

Subtracting the second equation from the third equation:

16 - 8 = 4a + 2b + c - (a + b + c)
8 = 3a + b

Now we have two equations with two unknowns:

a + b = 6
3a + b = 8

Solving this system of equations gives us:

a = 3
b = 1
c = 2

Therefore, the correct answer is A: a=3, b=1, c=2.

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The solution to the equation is x = 8, and it is non-extraneous. (D)

To solve the equation, we start by cross-multiplying to eliminate the denominators. This gives us 6(x) - 4 = 4(x).

Expanding the equation, we have 6x - 4 = 4x.

Next, we simplify the equation by moving all the x terms to one side and the constant terms to the other side. This gives us 6x - 4x = 4.

Combining like terms, we get 2x = 4.

Dividing both sides by 2, we find x = 2.

Therefore, the solution to the equation is x = 2.

To determine if the solution is extraneous, we substitute it back into the original equation: 6/2 - 4 = 4/2.

Simplifying, we have 3 - 4 = 2.

This simplifies further to -1 = 2, which is false.

Since the equation becomes false when x = 2, the solution x = 2 is extraneous which is option D.

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the complete question is:

Solve 6 over x minus 4 equals 4 over x for x and determine if the solution is extraneous or not.

A) x = −8, extraneous

B) x = −8, non-extraneous

C) x = 8, extraneous

D) x = 8, non-extraneous

To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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A. It should be noted that although Plant 2 clearly grew 2 cm per day as per the graph, Plant 1 still outgrew Plant 2 by 4 cm.

B. Guillermo claims that Plant 2 grows 4 cm per day is false, as shown by the graph, which contradicts Winston's claim, and Plant 2 actually grows 2 cm per day.

The relationship between lines and points is described by a graph, which is a mathematical representation of a network. A graph is made up of some points and connecting lines.

In the graph, we can clearly see that Plant 2 grew 2 cm per day, but still, Plant 1 grows more than plant 2 by 4 cm.

From the above part, we know that the error is statement that Plant 2 grows 2 cm per day, but according to the graph Plant, 2 grows by 2 cm per day.

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She must deposit approximately \($826,920.01\) at the end of each quarter, and the interest earned will be approximately \($673,079.99\).

Desired accumulated amount (A) = \($1,500,000\)

Annual interest rate (r) = 8% or 0.08

Number of compounding periods per year (n) = 4 (quarterly compounding)

Number of years (t) = 10

To find the deposit amount (P), we can use the formula:

\(\[ P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}} \]\)

Let's substitute the given values and calculate P:

\(\[ P = \frac{1,500,000}{\left(1 + \frac{0.08}{4}\right)^{4 \times 10}} \]\)

Simplifying further:

\(\[ P = \frac{1,500,000}{(1.02)^{40}} \]\)

\(\[ P \approx \frac{1,500,000}{1.818446957} \approx 826,920.01 \]\)

The deposit amount (P) is approximate \($826,920.01\).

To calculate the interest earned, we can subtract the total deposit amount from the desired accumulated amount:

\(\[ \text{Interest Earned} = A - \text{Total Deposit} = 1,500,000 - 826,920.01 \approx 673,079.99 \]\)

The interest earned is approximate \($673,079.99\).

Therefore, she must deposit approximately \($826,920.01\) at the end of each quarter to accumulate \($1,500,000\) after 10 years. The interest earned will be approximately \($673,079.99\).

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The first three nonzero terms of the Maclaurin series for f are 0, 0, and x^5/10.

To find the series, we use the Maclaurin series formula, which is a way to represent functions as an infinite sum of terms derived from their derivatives evaluated at a particular point. In this case, we evaluate the function's zeroth, first, and fifth derivatives at x=0 and obtain the first three nonzero terms of the series, which are 0, 0, and x^5/10.

The Maclaurin series is a powerful tool in mathematics and physics, and it is widely used in many areas such as calculus, differential equations, and quantum mechanics. By expressing functions as a series of terms, we can study their behavior and properties in greater detail, and make accurate predictions about their values for different inputs.

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Answer:

x=4   : y = -8

Step-by-step explanation: happy to help let me know if you have any more questions.

The equation which can be used to represent each situation, in terms of x, is;

A = 80 + 2x

B = 45 + 3x

The interval of miles driven, x, for which Company A is cheaper than Company B is when x = 35 miles

Let

Company A:

A = 80 + 2x

Company B:

B = 45 + 3x

Company B > Company A:

45 + 3x > 80 + 2x

collect like terms

3x - 2x > 80 - 45

x > 35

In conclusion, the interval of miles driven, x, for which Company A is cheaper than Company B is 35 miles.

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Step-by-step explanation:

1)4+9 = 13

2)9+16 = 25

3)4+16 = 18

4)9+25 = 34

Answer:

i) 13    ii) 25   iii) 20     iv) 34

Step-by-step explanation:

they are all exponents of 2 so you multiply each number by itself once.

i) 2x2 +  3x3

ii) 3x3 + 4x4

iii) 2x2 + 4x4

iv) 3x3 + 5x5

(next time you can use a calculator lol)

If V be a subspace of \(R^n\) with dim(V) = n - 1 (such a subspace is called a hyperplane in \(R^n\)) then, there exists a nonzero vector (u_n) orthogonal to every vector in the subspace V, which is a hyperplane in \(R^n\).

To prove this, follow these steps:

Step 1: Since dim(V) = n - 1, we know that V has a basis {v1, v2, ..., v(n-1)} consisting of n - 1 linearly independent vectors in \(R^n\)

Step 2: Extend this basis to a basis of \(R^n\) by adding an additional vector, say w, to the set. Now, the extended basis is {v1, v2, ..., v(n-1), w}.

Step 3: Apply the Gram-Schmidt orthogonalization process to the extended basis. This will produce a new set of orthogonal vectors {u1, u2, ..., u(n-1), u_n}, where u_n is orthogonal to all the other vectors in the set.

Step 4: Since u_n is orthogonal to all other vectors in the set, it is also orthogonal to every vector in the subspace V. This is because the vectors u1, u2, ..., u(n-1) form an orthogonal basis for V.

Therefore, we have proven that there exists a nonzero vector (u_n) orthogonal to every vector in the subspace V, which is a hyperplane in \(R^n\).

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Answer:

X=1

POQ= 1/3x+1/3= 1/3(1)+1/3=2/3

QOR= 2x +4/3= 2(1)+4/3= 10/3

POR= 5x-1= 5(1)-1= 4

Step-by-step explanation: