Find the fraction of the prime numbers in the range from 1 to 32.Write your answer in the simplest form.

Answer:

Step-by-step explanation:

Y=7 enjoy

Answer:

y = 7

Step-by-step explanation:

For every x input, one that hits a spot on x, the spot that is on y is the output.

Take a look at the graph, and you see that x = -1 is the output of y = 7

Answer:

probability = 6/7

Step-by-step explanation:

a+b+c= 30 students

there are 35 students in total.

=30/35

30/35 fully simplified = 6/7

the probability that a student earns a grade of A, B, or C is 6/7.

also, 6/7 as a decimal rounded the nearest hundreth is 0.86, FYI.

A vertical 1-meter stick casts a shadow of 0.4 meters , then the height of the tree is 30 meters , the correct option is (c) .

We use the concept of proportions to find the height of the tree .

We know that , A vertical stick of 1 meter casts a shadow of 0.4 meters.

We have to find the height of tree which casts a shadow of 12 meter at the same time ,

Let x =  the height of the tree in meters.

So , we can write ,

⇒ 1/0.4 = x/12 ,

Simplifying this proportion:

We get ,

⇒ 0.4x = 12 ,

⇒ x = 12/0.4

⇒ x = 30

Therefore, the height of the tree is Option(c) 30 meters.

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The given question is incomplete , the complete question is

A vertical 1-meter stick casts a shadow of 0.4 meters. If a tree casts a shadow of 12 meters at the same time, how tall is the tree?

(a) 13.4 meters

(b) 12.6 meters

(c) 30 meters

(d) 4.8 meters.

Answer:

Step-by-step explanation:

145+c>380 subtract 145 from each side

c>235 so the answer is

145+c>380; c>235

The correct option would be "None of these" since the projection is an ellipse and not any of the given options (2, 4, 16, or "This option").

To determine the projection of the region D onto the xy-plane, we need to find the intersection curve of the two paraboloids.

First, let's set the two equations equal to each other:

3x² + (12/24)y² = 16 - x²

Next, we simplify the equation:

4x² + (12/24)y² = 16

Multiplying both sides by 24 to eliminate the fraction:

96x² + 12y² = 384

Dividing both sides by 12 to simplify further:

8x² + y² = 32

Now, we can see that this equation represents an elliptical shape in the xy-plane. The equation of an ellipse centered at the origin is:

(x²/a²) + (y²/b²) = 1

Comparing this with our equation, we can deduce that a² = 4 and b² = 32. Taking the square root of both sides, we have a = 2 and b = √32 = 4√2.

So, the semi-major axis is 2 and the semi-minor axis is 4√2. The projection of region D onto the xy-plane is an ellipse with a major axis of length 4 and a minor axis of length 8√2.

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Answer:

l = (3x+5)

Step-by-step explanation:

Given that,

The area of a room, \(A=3x^2-x-10\)

The width of the room, \(b=(x-2)\)

We need to find the length of the room.

The area of the room is given by :

A = lb

\(l=\dfrac{A}{b}\\\\l=\dfrac{3x^2-x-10}{x-2}\\\\l=\dfrac{(x-2)(3x+5)}{x-2}\\\\l=(3x+5)\)

So, the length of the room is equal to (3x+5).

a) \(x=2\)

b) see below

a) Since the first three terms are \(\sqrt{x}-1}\), 1 and \(\sqrt{x}+1}\), the middle term, 1, must be the geometric mean of the other two. Hence

\(1^2=(\sqrt{x} -1)(\sqrt{x} +1)\implies\)

\(1=x-1\implies x=2\)

b)

The common ratio is then \(\sqrt{2}+1\), and the first term is \(\sqrt{2} -1\).

Thus, the fifth term is

\((\sqrt{2} -1)\times(\sqrt{2} +1)^4=(\sqrt{2} +1)^3\)

    \(=(\sqrt{2} )3+3(\sqrt{2} )2+3(\sqrt{2} )+1\)

    \(=2\sqrt{2} +6+3\sqrt{2} +1\)

    \(=7+5\sqrt{2}\)

Answer:

If 1 m/s is 1 meter per second, then it would take 5 seconds.

Answer:

Step-by-step explanation:

I'm not sure how correct I am about these questions, but this is what I got:

13.x=-9

14.x=8

15.x=-2

16.x=5

17.x=-1

18.x=1.5

Therefore, the global maximum value of the function on the region B is 12, and the global minimum value is 4.

To find the global maximum and minimum values of the function f(x, y) = x² + y² + x²y + 4y² + x²y + 4 on the region B = {(x, y) ∈ R² | −1 ≤ x ≤ 1, -1 ≤ y ≤ 1}, we need to evaluate the function at its critical points within the given region and compare the function values.

1. Critical Points:

To find the critical points, we need to find the points where the gradient of the function is zero or undefined.

The gradient of f(x, y) is given by:

∇f(x, y) = (df/dx, df/dy) = (2x + 2xy + 2x, 2y + x² + 8y + x²).

Setting the partial derivatives equal to zero, we get:

2x + 2xy + 2x = 0          (Equation 1)

2y + x² + 8y + x² = 0      (Equation 2)

Simplifying Equation 1, we have:

2x(1 + y + 1) = 0

x(1 + y + 1) = 0

x(2 + y) = 0

So, either x = 0 or y = -2.

If x = 0, substituting this into Equation 2, we get:

2y + 0 + 8y + 0 = 0

10y = 0

y = 0

Thus, we have one critical point: (0, 0).

2. Evaluate Function at Critical Points and Boundary:

Next, we evaluate the function f(x, y) at the critical point and the boundary points of the region B.

(i) Critical point:

f(0, 0) = (0)² + (0)² + (0)²(0) + 4(0)² + (0)²(0) + 4

       = 0 + 0 + 0 + 0 + 0 + 4

       = 4

(ii) Boundary points:

- At (1, 1):

f(1, 1) = (1)² + (1)² + (1)²(1) + 4(1)² + (1)²(1) + 4

       = 1 + 1 + 1 + 4 + 1 + 4

       = 12

- At (1, -1):

f(1, -1) = (1)² + (-1)² + (1)²(-1) + 4(-1)² + (1)²(-1) + 4

         = 1 + 1 - 1 + 4 + (-1) + 4

         = 8

- At (-1, 1):

f(-1, 1) = (-1)² + (1)² + (-1)²(1) + 4(1)² + (-1)²(1) + 4

         = 1 + 1 - 1 + 4 + (-1) + 4

         = 8

- At (-1, -1):

f(-1, -1) = (-1)² + (-1)² + (-1)²(-1) + 4(-1)² + (-1)²(-1) + 4

          = 1 + 1 + 1 + 4 + 1 + 4

          = 12

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Answer:

It is the option c x=-3 x=-9

The equation y = x^2 + 5x - 6 can be factored as y = (x - 1)(x + 6). The x-intercepts of the equation are (1, 0) and (-6, 0).

To convert the equation y = x^2 + 5x - 6 to factored form, we factor the quadratic expression. The factored form is y = (x - 1)(x + 6).

To identify the x-intercepts, we set y = 0 and solve for x. Setting each factor equal to zero gives us x - 1 = 0, which leads to x = 1, and x + 6 = 0, which gives x = -6.

Therefore, the x-intercepts of the equation y = x^2 + 5x - 6 are (1, 0) and (-6, 0).

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Given a linear system of equations in unknowns x, y, and z with the following augmented matrix:{[1, -1, 0, 0, -7], [-2, 3, 0, 0, 2], [0, 0, 4, -2, 2]}Use Gauss-Jordan elimination to solve the system for x, y, and z.Solution:Step 1. The first step in solving this linear system of equations is to write the matrix in the form of an augmented matrix. In the following, we list the system of equations associated with the augmented matrix: 1x−1y=−72x+3y=24z−y=1  We begin by focusing on the first equation, which is:1x−1y=−7.

To get rid of the x-coefficient, we add one time the first equation to the second equation. This operation is written as follows:{[1, -1, 0, 0, -7], [-2, 3, 0, 0, 2], [0, 0, 4, -2, 2]}We add row1 to row2. -2r1 + r2 = r2{-2, 2, 0, 0, 14}r3 = r3This gives us the new augmented matrix.{[1, -1, 0, 0, -7], [0, 1, 0, 0, -5], [0, 0, 4, -2, 2]}Step 2Next, we focus on the second equation:0x+1y=−5.

The y-variable is isolated, and we now look at the third equation.4z−2y=1We can isolate the variable z by dividing the entire equation by 4 as follows:z−0.5y=0.25In order to eliminate y in the third row, we add 0.5 times the second row to the third row. This operation is written as follows:{[1, -1, 0, 0, -7], [0, 1, 0, 0, -5], [0, 0, 4, -2, 2]}We add 0.5 r2 to r3. r3 + 0.5r2 = r3{[1, -1, 0, 0, -7], [0, 1, 0, 0, -5], [0, 0, 4, -1, -1]}Step 3We can now solve for z using the third equation:4z−1y=−1z = (-1 + y) / 4.

Substituting this into the second equation gives:-2((1 - y) / 4) + 3y = 2y - 1 = 2y - 1Thus, y = 1/2.Substituting the value of y = 1/2 into the first equation gives:x - (1/2) = -7, so x = -13/2.Finally, we can substitute the values of x and y into the third equation to get the value of z: 4z - 1(1/2) = -1, so z = -3/2.The solution to the system of linear equations is: x = -13/2, y = 1/2, and z = -3/2.

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Comparing  with the estimated change in cost using differentials (dc = 7.5 dollars), we can see that the estimate is significantly larger than the actual change in cost.

We can use the differential of the function to approximate the change in cost (C) corresponding to an increase in sales (or production) of one unit (dx). The differential of the function C = 0.075x² + 6x + 7 is given by:

dC = (d/dx) (0.075x² + 6x + 7) dx

dC = (0.15x + 6) dx

At x = 10 dollars (which represents the initial sales or production level), we have:

dC = (0.15*10 + 6) dx = 7.5 dx

Therefore, an increase in sales or production of one unit (dx = 1) would lead to an approximate increase in cost of:

dc ≈ dC = 7.5 dollars

To find the actual change in cost (AC), we can calculate the cost at x = 11 dollars and subtract the cost at x = 10 dollars. This gives:

C(11) - C(10) = (0.07511² + 611 + 7) - (0.07510² + 610 + 7)

C(11) - C(10) ≈ 21.85 - 19.25 = 2.60 dollars

Comparing this with the estimated change in cost using differentials (dc = 7.5 dollars), we can see that the estimate is significantly larger than the actual change in cost. This is because the differential approximation assumes that the function is changing linearly at x = 10, whereas the actual function may be changing at a different rate.

However, the differential approximation can still provide a useful estimate of the change in cost for small changes in sales or production levels.

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Answer:

\(\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}\)

the question asks us to rationalise the given term ! thus , we'll just have to remove the √3 from th denominator anyhow !

let's start ~

\( \frac{2 \sqrt{5} }{7 - \sqrt{3} } \\ \\ \implies \: \frac{2 \sqrt{5} }{7 - \sqrt{3} } \: \times \: \frac{7 + \sqrt{3} }{7 + \sqrt{3} } = \frac{14 \sqrt{5} + 2 \sqrt{15} }{(7) {}^{2} - ( \sqrt{3) {}^{2} } } \\ \\ \implies \frac{14 \sqrt{5} + 2 \sqrt{15} }{49 - 3} \\ \\ \implies \frac{14 \sqrt{5} + 2 \sqrt{15} }{46} \\ \\ \implies \: \frac{\cancel{2}(7 \sqrt{5{} } \: + \sqrt{15} )}{\cancel{46} } \\ \\\bold\red{ \implies \: \frac{7 \sqrt{5} + \sqrt{15} }{23}}\)

hope helpful :D

The number that, when multiplied by ¼, results in 5 is 20.

Let's assume the unknown number is x.

According to the problem, when x is multiplied by ¼ (or 1/4), the result is 5.

We can express this situation as an equation: x * 1/4 = 5.

To find the value of x, we need to isolate it on one side of the equation.

Multiplying both sides of the equation by 4 gives us: (x * 1/4) * 4 = 5 * 4.

Simplifying the equation gives us: x = 20.

Therefore, the unknown number x is 20.

To verify our answer, we can substitute x with 20 in the original equation: 20 * 1/4 = 5.

This indeed gives us the desired result of 5, confirming that our answer is correct.

Hence, the number that, when multiplied by ¼, results in 5 is 20.

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Answer:

50 and 80

Step-by-step explanation:

two numbers are in ratio 5;8 which  is 5x + 8x

sum = 130

5x  + 8x  = 130

13x = 130   ( divide both sides by 13)

x = 10

to find the two numbers we multiply by x

5x  = 5 x 10   = 50

8x  =  8  x 10  = 80

Answer:

6 feet

Step-by-step explanation:

Because a 6 foot hole would be 6 feet deep

The depth of the hole is given by the equation A = 6 feet

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 equation be represented as A

Now , the value of A is

The depth of the hole dug by the person = 6 foot

So , the equation will be

The depth of the hole A = 6 feet

A = 72 inches

Therefore , the value of A = 6 feet or 72 inches

Hence , the equation is A = 6 feet

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The odds in favor of the event happening are 5 to 4.

We have,

To find the odds in favor of an event happening, we use the formula:

Odds in favor = Probability of the event happening / Probability of the event not happening

In this case,

The probability of the event happening is 5/9.

The probability of the event not happening is 1 - 5/9, which simplifies to 4/9. So the odds in favor of the event happening are:

Odds in favor

= 5/9 / 4/9

= 5/4

Therefore,

The odds in favor of the event happening are 5 to 4.

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Answer:

2.08

Step-by-step explanation:

12.48 ÷ 6

= 2.08

Answer:

Hi

Answer:

= 1.6

Answer:

For example, a scale factor of 2 means that the new shape is double the size of the original shape. When a scale factor is a fraction the shape decreases in size, but we still call this an enlargement. So a scale factor of ¼ means that the new shape is 4 times smaller than the original.

Answer:

Step-by-step explanation:

The given sequence an = sin(√n)/√n converges to limit 0 as n approaches infinity

The mentioned nth term of the sequence is an = sin(√n)/√n. To determine the convergence or divergence of the sequence and find its limit, we can use the limit comparison test, which is based on comparing the given sequence with a known sequence whose convergence or divergence is already known.Suppose bn is a known sequence whose convergence or divergence is already known. Then, by the limit comparison test, the given sequence converges or diverges according as the sequence bn converges or diverges.

To apply the limit comparison test, we need to find a suitable sequence bn whose convergence or divergence is known. For this, we observe that sin x ≤ x for all x > 0. Hence, we have 0 ≤ sin(√n)/√n ≤ 1/√n, where the inequality follows by dividing both sides of sin x ≤ x by √n and substituting x = √n. Also, we know that the sequence bn = 1/√n converges to 0 as n approaches infinity. Therefore, by the limit comparison test, the given sequence an = sin(√n)/√n also converges to 0 as n approaches infinity.

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Answer:

x=9+/-2i√3/2

Step-by-step explanation:

The number which is absent in the first 31 digits of pi = 0

We know that a number pi is nothing but the ratio of the circumference of a circle to its diameter.

It is represented by a symbol 'π'

pi is an irrational number. This means that it is not equal to the ratio of any two whole numbers.

Its digits do not repeat.

An approximation 3.14 or 22/7 is often used for everyday calculations.

To 31 decimal places, the value of pi is 3.1415926535897932384626433832795

The numbers present in the first 31 digits of pi are:

1, 2, 3, 4, 5, 6, 7, 8, 9

Only '0' is not present.

Therefore, the number which is absent in the first 31 digits of pi = 0

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Answer:

\(x {}^{2} \times + 4x\)

Step-by-step explanation:

\(f(x + 4) = (x + 4) {}^{2} - 3(x + 4) - 4 \\ = x {}^{2} + 8x + 16 - 3x - 12 - 4 \\ = x {}^{2} + 4x\)

-------------------------------------------------------------------------------------------------------------

Answer:  \(\textsf{(1, 1) is NOT a solution of the inequality}\)

-------------------------------------------------------------------------------------------------------------

Given:  \(y \le-3x + 1\)

Find:  \(\textsf{Determine if (1, 1) is a solution of the inequality}\)

Solution:  In order to determine if (1, 1) is a solution we need to plug in 1 for the x values and 1 for the y values and see if the equation evaluated to true.

Plug in the values

Simplify

As we can see the expression states that 1 is less than or equal to -2 which is false therefore (1, 1) is NOT a solution of the inequality.

Hey there!

Algebra I

Inequality

Ordered pair

y ≤ -3x+1

1 ≤ -3(1) + 1

1 ≤ -3 + 1

1 ≤ -2

The statement is NOT true as 1 is not less than or equal to -2.

Therefore, the ordered pair is not a solution of the inequality.

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w = 60 lb (amt. of walnuts needed)

100-w = 40 lb (amt. of peanuts needed)

For the first part, let’s create matrix A.

\(A = [183;476;769]\)

To replace the first and third column of matrix A with ones, you can use the following code:

\(A(:, [1, 3]) = ones(3, 2)b)\)

For the second part, let’s create matrix B. B = [66;39]To expand matrix B to a 4-by-4 matrix with a value of 6, you can use the following code: B

\(= ones(4) * 6c).\)

To combine matrix A and B, where B is to the right of A, you can use the following code:

\(C = [A, [B; zeros(1, 2)]]\)

Here, we are concatenating B with a 1-by-2 matrix of zeros to match the dimensions of A.

Then, we are concatenating the two matrices horizontally using square brackets) To reorder matrix C as a 9-by-2 matrix and save it into a new matrix F, you can use the following code

\(:F = reshape(C.', 18, 1)\)

This will transpose the matrix C, reshape it to a 18-by-1 column vector, and save it into matrix F.

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