Five friends are splitting a package of 30 lemon drops if they divide the candy evenly how many lemon drops will each friend get

Answer:its b

Step-by-step explanation:

Ax=b has a solution for infinitely many b in R3, but Ax=b does not have a solution for all b in R3.

Consider the matrix A:

```
A = [1 2 3;
    4 5 6;
    7 8 9]
```

To find the solutions of Ax=b, we need to solve the system of linear equations:

```
x1 + 2x2 + 3x3 = b1
4x1 + 5x2 + 6x3 = b2
7x1 + 8x2 + 9x3 = b3
```

We can rewrite this system as:

```
x1 + 2x2 + 3x3 - b1 = 0
4x1 + 5x2 + 6x3 - b2 = 0
7x1 + 8x2 + 9x3 - b3 = 0
```

This is an homogeneous system of linear equations, and we can solve it using Gaussian elimination. We find that the rank of A is 2, since the third row is a linear combination of the first two rows. Therefore, the system has either one or infinitely many solutions.

If we solve for x1, x2, and x3 in terms of b1, b2, and b3 using Gaussian elimination, we get:

```
x1 = -b1 + 2b2 - b3
x2 = b1 - b2
x3 = (1/3)b1 - (2/3)b2 + (1/3)b3
```

These expressions show that the solution of Ax=b depends on the values of b1, b2, and b3. If we choose b1 = 1, b2 = 0, and b3 = 0, then we find that Ax=b has a solution. Similarly, if we choose b1 = 0, b2 = 1, and b3 = 0, then we find that Ax=b has a solution. In fact, for any values of b1, b2, and b3 such that b1 - b2 + b3 = 0, the system Ax=b has a solution.

However, if we choose b1 = 1, b2 = 1, and b3 = 1, then we find that Ax=b does not have a solution, since the equation b1 - b2 + b3 = 1 - 1 + 1 = 1 is not satisfied. Therefore, Ax=b has a solution for infinitely many b in R3, but Ax=b does not have a solution for all b in R3.

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The conclusion about p using an absolute value inequality would be that |p - 72| ≤ 4. This means that the difference between the true proportion p and the estimated proportion 72% is no more than 4%.

In other words, p is most likely to fall within the range of 68% to 76%, as determined by the margin of error in the statistical polling calculation. This emphasizes the importance of recognizing and accounting for the potential for error and uncertainty in estimating percentages and proportions in various fields, including politics and marketing.
To describe the conclusion about the percentage (p) in statistical polling using an absolute value inequality, you can use the margin of error (4% in this example) as a way to create the inequality.
In this case, we have a poll result of 72% and a margin of error of 4%. So, the absolute value inequality would be:
|p - 72%| ≤ 4%
This inequality shows that the difference between the true percentage (p) and the poll result (72%) should be less than or equal to the margin of error (4%). In other words, the true percentage (p) is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%).

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240 wooden cubes can fit in box.

We have,

Volume of wooden cube= 1/2 cubic foot

Dimension of box = 5ft x 8 ft x 3 ft

So, the Volume of Box

= l w h

= 5 x 8 x 3

= 120 ft³

Now, the number of wooden cubes fit in box

= 120/ 0.5

= 240

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The formula for the curvature of a smooth curve in three-dimensional space, parameterized by arc length, in terms of its unit tangent vector T(t) and unit tangent vector N(t), is given by: k = |dT/ds| = |dT/dt| / |dr/dt| where s is the arc length parameter and r(t) is the position vector of the curve.

While it is true that the magnitude of the rate of change of the unit tangent vector with respect to time, |dT/dt|, is related to the curvature, it is not equal to the curvature unless the curve is parameterized by arc length. If the curve is parameterized by some other parameter, such as time or a parameter that does not correspond to arc length, then the curvature formula will involve an additional factor related to the rate of change of the parameter with respect to arc length.

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The probability that the cycle time exceeds 65 minutes given that it exceeds 55 minutes is 1/3.

To solve this problem, we can use conditional probability. We know that the cycle time for trucks hauling concrete is uniformly distributed between 50 to 70 minutes. Let X be the cycle time in minutes.

So, P(X > 65 | X > 55) = P(X > 65 and X > 55) / P(X > 55)

We can simplify the numerator as P(X > 65 and X > 55) = P(X > 65) since if X is greater than 65, it is also greater than 55. Using the formula for the uniform distribution, we get:

P(X > 65) = (70 - 65) / (70 - 50) = 1/4

Similarly, we can calculate the probability of X being greater than 55:

P(X > 55) = (70 - 55) / (70 - 50) = 3/4

Putting these values in the conditional probability formula, we get:

P(X > 65 | X > 55) = (1/4) / (3/4) = 1/3

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Cosx, -sinx, -cosx + C, sinx + C are the derivative answers to the question.

The derivative of sin x with respect to x is cos x.
The derivative of cos x with respect to x is -sin x.
The antiderivative of sin x with respect to x is -cos x + C, where C is the constant of integration.
The antiderivative of cos x with respect to x is sin x + C, where C is the constant of integration.

1. The derivative of sin(x) with respect to x is cos(x).
2. The derivative of cos(x) with respect to x is -sin(x).
3. The antiderivative of sin(x) with respect to x is -cos(x) + C, where C is the constant of integration.
4. The antiderivative of cos(x) with respect to x is sin(x) + C, where C is the constant of integration.

A derivative in mathematics is a measurement of how much a function alters as its input alters. It refers to how quickly a function alters in relation to its input variable. The slope of the tangent line to the function at a certain point is what it is, in other words.

The limit of the ratio of the change in the output to the change in the input, as the change in the input approaches zero, is known as the derivative of a function, indicated by the symbols f'(x) or [tex]dy/dx[/tex].

The opposite of differentiation is an antiderivative, usually referred to as an indeterminate integral. It is a function that yields the original function when differentiated. In other words, f(x) follows if [tex]f'(x) = g(x)[/tex].

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Answer:

Step-by-step explanation:

The equation of the absolute value function y = |x| is a V-shaped graph centered at the origin. To translate this graph left 4 units, we need to replace x with (x + 4) in the equation. Also, since the question asks for y = -|x|, we need to reflect the graph across the x-axis by multiplying the entire equation by -1. Therefore, the equation of the translated absolute value function is:

y = -|x + 4|

This equation represents a V-shaped graph that is centered at x = -4 and opens downward (since it is multiplied by -1), with the vertex at (-4,0).

Answer: y = -|x+4|

Step-by-step explanation:

the formula for absolute value is

y = a|x-h| +k    

(h, k), is your vertex

h, is your shift left or right

k, is your shift up or down

a, is your stretch and negative in front indicates a reflections.

if you want to shift he function left for that's -4 so substitut in your  equations for h -4

y= -|x-(-4)|

y = -|x+4|

Answer:

Step-by-step explanation:

1 plus 2 equals 3

3 plus 3 equals 6

6 plus 4 equals 10

10 plus 5 equals 15.       did this help?

Based on the information, the most appropriate graph for this situation would be option A.

To identify the most appropriate graph for this situation we must analyze the data. In this case we have the relationship of the toppings with the number of customers who prefer each variety.

Now, We get;

Due to the above, we could affirm that the best option is A because it shows the number of people who prefer each topping in the order in which the table organizes them.

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The value of the fraction -5/7 and -4/7 added and subtracted from the fraction -21/2 added to 1/22 is 64/77.

The sum of 1/2 and -21/22 can be found by finding a common denominator,

1/2 = 11/22 (since 11 x 2 = 22)

-21/22 = -21/22

Therefore, the sum of 1/2 and -21/22 is,

= 11/22 - 21/22

= -10/22 = -5/11

The sum of -4/7 and -5/7 is,

-4/7 - 5/7 = -9/7

Now, subtracting as asked in the question.

= (-5/11)-(-9/7)

= (-5/11)+(9/7)

Finding common denominator to add the fractions,

7 x 11 = 77

(-5x7)/(11x7)+(9x11)/(7x11)

= -35/77 + 99/77

Now, we can combine the numerators,

-35/77 + 99/77 = 64/77

Therefore, the final answer is 64/77.

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Answer:

look the picture for the representation

thank you

The volume of the box is given as follows:

V = 199.5 in³.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions for this problem, in inches, are given as follows:

10.5, 9.5 and 2.

Hence the volume of the box is given as follows:

V = 10.5 x 9.5 x 2

V = 199.5 in³.

The problem asks for the volume of the box.

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Based on the given information, we can conclude that f(2) is an analytic function in a deleted neighborhood of infinity. This means that f(z) has a Laurent expansion in the form of

[tex]f(z) = ..._c-2/z^2 + _c-1/z + c0 + c1z + ... + cnz^n + ...,[/tex]

where the coefficients

[tex]_c-2, _c-1, c0, c1, ...,[/tex]

cn are constants.

The point morc is a singular point of f(z) that can be either removable, a pole of order m, or an essential singular point. The type of singular point depends on the behavior of the Laurent expansion of f(z).

If the Laurent expansion of f(z) contains no positive powers of z, then the point morc is a removable singular point. This means that the singularity can be "filled in" or removed, and the function can be defined at that point.

If the Laurent expansion of f(z) contains only a finite number of positive powers of z, with the highest positive power being m, then the point morc is a pole of order m. This means that the singularity is a simple pole, double pole, triple pole, or higher order pole, depending on the value of m.

If the Laurent expansion of f(z) contains infinitely many positive powers of z, then the point morc is an essential singular point. This means that the singularity cannot be removed or "filled in", and the behavior of the function at that point is very complex.

In summary, the type of singular point at the point morc depends on the behavior of the Laurent expansion of f(z) at that point.

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The scientific notation of mass 6,200,000 is 6.2 × 10⁶kg and 6.2 × 10⁹g

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form, since to do so would require writing out an unusually long string of digits.

It can be referred to as scientific form or standard index.

A mass of 6,200,00 kg can be written to index form by putting it to base of 10.

6200000/1000000

= 6.2 × 1000000 = 6.2 × 10⁶kg

1 kg = 10³ g

therefore;

6.2 × 10⁶kg = 6.2 × 10⁶kg × 10³

= 6.2 × 10⁹g

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Answer:5/14

Step-by-step explanation:

you have 5 red and 14 total so your probability is 5/14 and 5/14 is the simplest terms

Answer:

The answer for x is 20

Step-by-step explanation:

a=1

b=10

<C=60°

cos 60=b/hyp

let hyp be x

cos 60=10/x

x=10/cos 60

x=10/0.5

x=20

The given fraction, 6/2 can be written as a multiple of units fraction, which is calculated out to be is 3/1.

When we write a fraction as a multiple of units fraction, we express it in the form of a fraction whose numerator is a whole number and denominator is 1.

To write 6/2 as a multiple of units fraction, we need to find a fraction which is equivalent to 6/2, but with a denominator of 1.

To do this, we can simplify the fraction 6/2 by dividing the numerator and denominator by their greatest common factor, which is 2.

So, 6/2 = (6 ÷ 2)/(2 ÷ 2) = 3/1

Here, we have divided both numerator and denominator by 2, which gives us an equivalent fraction of 3/1.

Therefore, 6/2 as a multiple of units fraction is 3/1.

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We need a sample size of at least 62 to detect the alternative hypothesis with power of at least 0.80 at a 5% significance level.

To answer this question, we need to use power analysis. Power is the probability of rejecting the null hypothesis when it is false. In this case, the null hypothesis is m = 0 and the alternative hypothesis is m > 0. We want to detect the alternative hypothesis with power of at least 0.80 at a 5% significance level.

Assuming that s is 20 and we want to detect the alternative m > 4, we can use the following formula to calculate the sample size:

n = (Zα/2 + Zβ)² * σ² / δ²

where:
- Zα/2 is the critical value for the significance level α/2 (α = 0.05, so Zα/2 = 1.96)
- Zβ is the critical value for the power (power = 0.80, so Zβ = 0.84)
- σ is the standard deviation (σ = 20)
- δ is the difference between the null hypothesis and the alternative hypothesis (δ = 4)

Substituting these values into the formula, we get:

n = (1.96 + 0.84)² * 20² / 4²
n = 61.61

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To minimize the cost of the package, we need to find the dimensions that minimize the cost function.

The cost function is the sum of the cost of the side and bottom (made of syrofoam) and the cost of the top (made of paper). Let r be the radius and h be the height of the cylinder. Then the cost function is:

C(r, h) = 0.02(2πrh + πr^2) + 0.05(πr^2)

We need to find the values of r and h that minimize this function subject to the constraint that the volume of the cylinder is 600 cubic centimeters. That is:

V = πr^2h = 600

We can solve for h in terms of r from the volume equation:

h = 600/(πr^2)

Substituting this expression for h in the cost function, we get:

C(r) = 0.02(2πr(600/(πr^2)) + πr^2) + 0.05(πr^2)

= 0.04(600/r) + 0.05πr^2

To minimize C(r), we take the derivative with respect to r and set it equal to zero:

dC/dr = -0.04(600/r^2) + 0.1πr = 0

Solving for r, we get:

r = (300/π)^(1/3) ≈ 5.17 cm

Substituting this value of r into the volume equation, we get:

h = 600/(πr^2) ≈ 2.17 cm

Therefore, the dimensions of the cylinder that minimize the production cost are r ≈ 5.17 cm and h ≈ 2.17 cm, and the minimum cost is:

C(r, h) ≈ $1.24

So, the minimum cost of producing a microwaveable cup-of-soup package in the shape of a cylinder with a volume of 600 cubic centimeters is about $1.24, with a radius of about 5.17 cm and a height of about 2.17 cm.

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The slope and y-intercept are 4.5 and 25 respectively.

A graph of the equation for the total shipping charges is shown below.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided about this freight company, the total shipping charges are given by;

C = 4.5n + 25

By comparison, we have the following:

Slope, m = 4.5.

y-intercept = 25.

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To sketch and describe the locus of points in a plane in the interior of a right triangle with sides of 6 in., 8 in., and 10 in. and at a distance of 1 in. from the triangle, we need to first understand what a locus of points is.

A locus of points refers to the set of points that satisfy a given condition.
In this case, the given condition is that the points must be located at a distance of 1 in. from the right triangle with sides of 6 in., 8 in., and 10 in. To visualize this, we can imagine a circle with a radius of 1 in. drawn around each of the three vertices of the triangle.
The locus of points that we are interested in is the region that is enclosed by these three circles. This is because any point that is located within all three circles is at a distance of 1 in. from each of the three sides of the right triangle.
We can see that this region takes the shape of a smaller triangle that is located in the interior of the original right triangle. This smaller triangle has sides that are each 2 in. shorter than the corresponding sides of the original triangle.
To summarize, the locus of points in a plane in the interior of a right triangle with sides of 6 in., 8 in., and 10 in. and at a distance of 1 in. from the triangle is a smaller triangle that is located in the interior of the original triangle. This smaller triangle has sides that are each 2 in. shorter than the corresponding sides of the original triangle.

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Answer:

$4853

Step-by-step explanation:

Since there are 12 months in 1 year, the monthly salary is 1/12 of the yearly salary. We divide the annual salary by 12 to calculate the monthly salary.

$58236/12 = $4853

Using distributive property, the simplification of the expression shows that the given expression is already simplified.

To simplify expressions first expand any brackets, next multiply or divide any terms and use the laws of indices if necessary, then collect like terms by adding or subtracting and finally rewrite the expression.

t - 2 / v - 3

Let's combine the numerator with the denominator

(t - 2)(v - 3) / (v - 3)

Expand the expression using distributive property

tv - 3t - 2v + 6 / (v - 3)

We can factor as;

(t - 2)(v - 3) / (v - 3)

Cancel both sides

(t - 2) / (v - 3)

The expression has already been simplified

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The number of white marbles in the bag is w = 7

Given data ,

Let's write "w" for the quantity of white marbles in the bag. Four of the twelve marbles in the bag are blue, as shown by the information provided. This indicates that "12 - 4 = 8" applies to the remaining white marbles.

Now , when a marble is randomly selected and returned to the bag, the probability of selecting a white marble is w/12, where "w" is the number of white marbles and 12 is the total number of marbles in the bag.

Similarly, when a second marble is randomly selected (with replacement), the probability of selecting a blue marble is 4/12, since there are 4 blue marbles out of 12 marbles in total.

So , the probability is given by

(w/12) x (4/12) = 7/36

On simplifying , we get

4w/144 = 7/36

Cross-multiplying:

144 x (4w/144) = 144 x (7/36)

4w = 28

Dividing both sides by 4:

w = 28/4

w = 7

Hence , the number of white marbles in the bag is 7

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Answer: 512 feet^3

Step-by-step explanation:

The volume of a cube is x^3, where x is the sidelength.  8^3 is equal to 512 and since its in the 3rd dimension it's feet^3 or feet cubed.

Answer:

Approximately 243.917

Step-by-step explanation:

The cube has a volume of 8³ = 512.

The sphere has a volume of   [tex]\frac{4}{3}\pi r^3[/tex].

The volume inside the cube but outside the sphere is:

[tex]512-\frac{4}{3}\pi r^3[/tex] (1)

The radius of the sphere is equal to the sidelengths of the cube divided by 2 as seen by the picture.

So r = 8/2 = 4.

Substituting r into (1):

[tex]512-\frac{4}{3}\pi 4^3=512-\frac{256\pi }{3}=243.917[/tex]

The measure of the shorter base is approximately 28.85.

To solve this problem, we need to use the fact that the line segment joining the midpoints of the diagonals of a trapezoid is parallel to the bases and has a length equal to half the sum of the bases. Let's call the shorter base "x".

We know that the longer base is 97, so the sum of the bases is x + 97.

We also know that the line segment joining the midpoints of the diagonals has a length of 3. Since this line segment is parallel to the bases, it divides the trapezoid into two smaller trapezoids that are similar to the original trapezoid.

Using the similar triangles, we can set up the following equation:

3/x = (x + 97)/97

Cross-multiplying and simplifying, we get:

3*97 = x^2 + 97x

Multiplying out the right side and rearranging, we get:

x^2 + 97x - 291 = 0

Now we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac))/2a

Plugging in a=1, b=97, and c=-291, we get:

x = (-97 ± sqrt(97^2 - 4(1)(-291)))/2(1)

x = (-97 ± sqrt(9429))/2

x = (-97 ± 97)/2 or x = (-97 ± sqrt(9429))/2

Since we're looking for the shorter base, we can discard the negative solution:

x = (-97 + sqrt(9429))/2

x ≈ 28.85

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