Evaluate the expression. −6−(−8)+6=

Answer:

The answer is the first one

Step-by-step explanation:

The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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Answer:

2y=13x−3

divide everything by 2 and then  that  will be your final answer

The company will use approximately 7 trucks.

to separate into two or more parts or pieces. : to separate into classes or categories. : cleave entry 2, part.

To calculate the number of trucks needed, divide the total number of bicycles by the number of bicycles that can fit in each truck:

328 bicycles / 50 bicycles per truck = 6.56 trucks.

Since you can't have a fraction of a truck, the company will need to round up to the nearest whole number. Therefore, the company will use 7 trucks to ship the 328 bicycles across the country.

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Answer: 160 degrees

Step-by-step explanation:

(18-2)180 = 2880

2880/18 = 160

Answer:

a choro m isi ihe

Step-by-step explanation:

Answer:

Step-by-step explanation:

I'll just write log for log base 10.  The important rules about logarithms we need to know are:

\( a \log b = \log( b^a) \)

\( \log a + \log b = \log( ab) \)

and at the end we'll need something like

\(\log a = \log b \implies a=b\)

Suitably armed we can begin,

\( \left( 1 + \dfrac{1}{2x} \right) \log 3 + \log 2 = \log (27 - 3^{1/x}) \)

First rule,

\( \log 3^{ 1 + 1/2x}  + \log 2 = \log (27 - 3^{1/x}) \)

Second rule,

\( \log 2(3^{ 1 + 1/2x})  = \log (27 - 3^{1/x}) \)

Third rule,

\( 2(3^{ 1 + 1/2x})  = 27 - 3^{1/x} \)

We can rewrite this to be a quadratic equation in \(y=3^{1/2x}\).

\(  6 (3^{1/2x})  = 27 -  (3^{1/2x})^2 \)

\(y^2 +6y - 27 =0\)

\((y - 3)(y+9)=0\)

\(y=3 \textrm{ or } y=-9\)

First solution:

\(3^{1/2x} = 3 = 3^{1}\)

\(1/2x = 1\)

\(1=2x\)

\(x = 1/2\)

Second solution,

\(3^{1/2x} = -9\)

No real powers of 3 will be negative, no solution here.

Answer: x=1/2

Check:  

1 + 1/2x = 2 so the left side is log 2(3²) = log 18

Right side, log(27-3^2) = log 18  √

Answer:

The ship travels approximately 10.261 meters to the East.

Step-by-step explanation:

At first we introduce a graphical description of the statement as an attachment below. Let suppose that bearing is respect to the North-direction, then the change in position in the East direction is modelled by the following Trigonometric formula:

\(x = r\cdot \sin \theta\) (1)

Where:

\(r\) - Distance travelled by the ship, measured in kilometers.

\(\theta\) - Bearing angle, measured in sexagesimal degrees.

\(x\) - Distance component in the east direction, measured in kilometers.

If we know that \(r = 30\,km\) and \(\theta = 20^{\circ}\), then the distance in the East direction is:

\(x = (30\,km)\cdot \sin 20^{\circ}\)

\(x \approx 10.261\,m\)

The ship travels approximately 10.261 meters to the East.

The bearing is the angle measured relative to or from the Northern

direction.

The ship's distance East from its starting point is approximately 10.26 km.

Reasons:

The given bearing of the ship's path, θ = 020°

The distance the ship has travelled = 30 km.

Required:

The ship's distance East from its starting position

Solution:

By using trigonometric ratios, we have;

\(sin(\theta) = \dfrac{Ship's \ distance \ East \ from \ its \ starting \ point}{The \ distance \ the \ ship \ has \ sailed}\)

Which gives;

\(sin(20^{\circ}) = \dfrac{Ship's \ distance \ East \ from \ its \ starting \ point}{30 \ km}\)

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The best description of the geometric construction of the quotient z/w on the complex plane is; Option A; z is scaled by a factor of One-fifth and rotated 90 degrees clockwise

We are given;

z = 3(cos(15°) + i sin(15°))

w = 5(cos(90°) + i sin(90°))

Now, if we want to find the quotient z/w, it is clear that in geometric construction, the procedure will be to scale z by a factor of 1/5 and thereafter we will rotate by 90° clockwise.

Thus, option A is the correct answer.

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The most important cell in your body is the red blood cell.

Cells are the fundamental components of life. Every item you observe contains cells. Organelles are structures found inside cells that allow the cell to function.

Red blood cells are the most frequent form of blood cell and the vertebrate's primary mechanism of distributing oxygen to bodily tissues via blood flow through the circulatory system.

Blood cell activity is essential to life, from delivering oxygen throughout the body to battling infection. Bone marrow is responsible for the production of blood cells. Red blood cells, white blood cells, and platelets are the three major types of blood cells.

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Answer:

x = 2 , y = 1

Step-by-step explanation:

For the triangles to be congruent then the hypotenuse and leg must be congruent, that is

x = y + 1 → (1)

4y = x + 2 → (2)

Substitute x = y + 1 into (2)

4y = y + 1 + 2

4y = y + 3 ( subtract y from both sides )

3y = 3 ( divide both sides by 3 )

y = 1

Substitute y = 1 into (1)

x = y + 1 = 1 + 1 = 2

Answer:

domain = ( 3, 11, 121, 34, 23)

range = ( 21, 34, 1, 23)

Answer:  Choice B

Writing k ≤ 1 means "either k = 1, or k < 1"

The closed filled in endpoint at 1 shows us that it is part of the solution set. You would use an open hole if you had k < 1 without the "or equal to".

Answer:

Step-by-step explanation:

Marco is incorrect because a function is a relation for which each input has a different output. An example of a function is y=2x each input x has a different output y.

Answer:

The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²vvvThe diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²v

Step-by-step explanation:

its E and A

Answer:

The solutions to the inequality are B, E, and F: 25, 36, and 9.

Step-by-step explanation:

The solutions to the inequality √x < 10 are the values of x that make the inequality true when plugged in. To find these values, we can square both sides of the inequality:

√x < 10

x < 10^2 = 100

So, the values of x that make the inequality true are those that are less than 100. The options that satisfy this condition are:

A. 100 (not a solution)

B. 25 (solution)

C. -100 (not a solution)

D. 105 (not a solution)

E. 36 (solution)

F. 9 (solution)

The determinant of the transpose of A is equal to the determinant of A. And since the transpose of a skew-symmetric matrix is its negative, this implies that the determinant of A should also be equal to its negation. The only possible value that satisfies this condition is zero. Therefore, det(A) = 0 when "n" is an odd number.

We can use the property of skew-symmetric matrices, which states that the determinant of a skew-symmetric matrix of odd order is always 0. This means that for the given matrix A, which is skew-symmetric and of order n, where n is odd, det(A) = 0. In order to prove this property, we can use the fact that the determinant of a matrix is equal to the product of its eigenvalues. Since A is skew-symmetric, all its eigenvalues are imaginary and come in pairs of the form λ and -λ. Since n is odd, there is at least one eigenvalue that is equal to 0, and therefore det(A) = 0. The answer to problem 4 is that the determinant of the skew-symmetric n x n matrix A, where n is an odd number, is equal to 0.

When dealing with a skew-symmetric matrix "A" of odd order "n" (n x n matrix), the determinant of A is always zero.
In a skew-symmetric matrix, the elements below the main diagonal are the negation of the elements above the main diagonal, and the elements on the main diagonal are zero. Mathematically, this can be represented as A(i,j) = -A(j,i) for all i and j.  Since "n" is an odd number, multiplying an odd number of negative pairs will result in a negative value for the determinant.

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Answer:

b

Step-by-step explanation:

The height of the tree is 6.4m

the difference is that in one case the shadow of the tree is 60 - 20 = 40 m, and in the other case it is 60 + 20 = 80 m long.

anyway, for a certain angle of the sunlight we know the shadow of the pole is 60 m long, which creates with the 4.8 m height a right-angled triangle, with the line of sight from the top of the pole to the ground end of the shadow being the Hypotenuse or radius for or trigonometric triangle in a circle.

the shadow length (60 m) is sine of the sunshine angle multiplied by the radius.

the height (4.8 m) is cosine of that sunshine angle multiplied also by that radius.

Pythagoras gets us the radius for the pole triangle :

radius² = 60² + 4.8² = 3600 + 23.04 = 3623.04

radius = sqrt(3623.04) = 60.19169378... m

sin(angle) × radius = 60

sin(angle) = 60/radius = 0.996815279...

angle = 85.42607874...°

the sunshine creates with the tree also a right-angled triangle with the same sunshine angle (the sun is so far away, that the tiny, tiny difference is irrelevant, we can simply assume the angles are equal).

but the shadow is of different length (sin(angle)×radius), which means also the radius for the tree triangle has to be different. and that defines the height of the tree (cos(angle)×radius).

but now we know the angle, and we can reverse calculate the side lengths.

but the question is (as mentioned at the beginning) : is the tree shadow 40 m or 80 m long.

we have therefore 2 solutions for the height of the tree.

1. the shadow is 40 m long.

sin(angle) × radius = 40

radius = 40/sin(angle) = 40.12779585... m

tree height = cos(angle)×radius = 3.2 m

2. the shadow is 80 m long.

sin(angle) × radius = 80

radius = 80/sin(angle) = 80.25559171... m

tree height = cos(angle)×radius = 6.4 m

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If 1500 g can be divided evenly into batches of bread that are 70 g each, then the baker should choose the 1500 g package.

To check this, we can divide 1500 g by 70 g to see how many batches of bread can be made:

1500 g / 70 g = 21.428571428571427

Since this is a non-whole number, it means that some of the dough would be wasted if the baker chooses a package of 1500 g. The baker should choose the 1500 g package, as it can be divided evenly into batches of bread that are 70 g each.

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Answer:

  the graph of f has 3 turning points

Step-by-step explanation:

The graph of a function has a turning point (local extreme) where the derivative is zero and changes sign.

The derivative of a function tells you the slope of that function's graph. When the derivative is positive, the function is increasing. When the derivative is negative, the function is decreasing.

Where the derivative changes sign from positive to negative, the graph of the function changes direction from increasing to decreasing. At the point where the derivative is zero (between positive and negative), the graph is neither increasing nor decreasing. A tangent to the function at that point is a horizontal line, and the function itself is at a local maximum, a turning point.

The reverse is also true. When the derivative changes sign from negative to positive, the function changes from decreasing to increasing. The turning point where that occurs is a local minimum.

If the derivative crosses the x-axis (changes sign) 3 times, then there are three local extremes in the graph of f. The graph of f has 3 turning points.

__

Additional comment

In the attached graph, we have constructed a derivative function (red) that crosses the x-axis 3 times. It is the derivative of f(x), which is shown in blue. The purpose is to show the local extremes of f(x) match the zero crossings of the derivative.

Answer:

Below

Step-by-step explanation:

Follow this rule:

● if the numbers multiplied together have the same signs, the product is a positive number.

● if the nupbers multiplied togethers have different signs, the product is a negative number.

Answer:

Step-by-step explanation:

anytime you multiply a positive+Positive= it equals a positive number  if you multiplying a negative + positive it will equal a negative even if the positive number is bigger for example 4 x -9= -36           9 x 4= 36      -9 x -4 = 36

The probability that a die will land on an even number at least once when rolled twice is 3/4.

To find the probability that a die will land on an even number at least once when rolled twice, we can use complementary probability.

Step 1: Identify the complementary event.
The complementary event to landing on an even number at least once is that the die lands on odd numbers both times.

Step 2: Calculate the probability of the complementary event.
There are 3 odd numbers (1, 3, and 5) on a standard 6-sided die. So, the probability of landing on an odd number in one roll is 3/6 or 1/2.
For two rolls, the probability of landing on odd numbers both times is (1/2) * (1/2) = 1/4.

Step 3: Calculate the probability of the original event using complementary probability.
The probability of landing on an even number at least once is 1 - the probability of the complementary event,

which is 1 - 1/4 = 3/4.

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-14 is the value of the expression b - 3a at a =6 and b = 4.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression b - 3a

For this expression given,

a = 6 and b = 4

Thus the value of expression at given values

=> b - 3a

=> 4 - 3 * 6

=>4 - 18

=> -14

Therefore, the value of the expression b - 3a at a =6 and b = 4 is -14.

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t3(x)  = f(a) + f'(a)(x-a) + (1/2)f''(a)(x-a)^2 + (1/6)f'''(a)(x-a)^3.

To find t3(x) we need to find the coefficient of polynomials by using the formula for nth degree taylor polynomial.

what is taylor polynomials?

This are approximations of a function, which become generally better as n increases. It is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point.

using the nth degree taylor polynomial formula:

tn(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...... + f^(n)(a)(x-a)^n/n!

where f^(n)(a) is the nth derivative of f evaluated at x=a.

By calculating we get t3(x) as

t3(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3!

       = f(a) + f'(a)(x-a) + (1/2)f''(a)(x-a)^2 + (1/6)f'''(a)(x-a)^3.

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Given:

AD = 7x - 5

CB = 5x - 2

We are asked to find x.

recall, in polygon, diagonal are equal.

Since AD and CB are diagonals, therefore they are equal.

So,

AD = CB

7x - 5 = 5x - 2

let's collect like terms:

7x - 5x = 5 - 2

carry out both the addition and subtraction operations:

2x = 3

Divide both sides by 2

2x/2 = 3/2

x = 3/2

Therefore, the correct option is D, which is 3/2.

Answer:

I can't see it

Step-by-step explanation:

you should zoom in a little bit please

(a) The chance that the sum of the draws will be more than 1,500

(b) The chance that there will be fewer than 90 occurrences of the number 3.

(a) To estimate the chance that the sum of the draws will be more than 1,500, we need to consider the possible combinations and their probabilities. Since there are four numbers in the box, each with an equal chance of being drawn, we can calculate the mean and standard deviation of the draws. With this information, we can use statistical methods such as the normal distribution to estimate the probability of the sum exceeding 1,500.

(b) To estimate the chance that there will be fewer than 90 occurrences of the number 3, we need to calculate the probability of drawing a 3 in each individual draw and then consider the distribution of the number of 3's over the 400 draws. Using statistical techniques such as the binomial distribution, we can estimate the probability of having fewer than 90 occurrences of 3 in the 400 draws.

Both estimations involve applying statistical methods to analyze the probabilities of specific events occurring in the random drawing process. The precise calculations and estimations would require detailed information about the probabilities of drawing each number and the distribution of these numbers in the box.

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Answer:

c. 15

Step-by-step explanation: 15 is divisible by 3

Answer:

D. x=1

Step-by-step explanation:

Solve  :    x-1 = 0

Add  1  to both sides of the equation :

                     x = 1

x = 1 for equation 5x - ( 4x - 1) = 2.

An equation is a mathematical statement that shows that two mathematical expressions are equal. It may have one variable, two, three and so on.

For given equation,

5x - ( 4x - 1) = 2

This is a equation in one variable which can be solved by transposing the terms.

Firstly, Solving the parenthesis,

5x-4x+1=2

Then, Solving the like terms.

x+1=2

To calculate the value of x, subtract 1 from both the sides.

x+1-1=2-1

x=1

Thus, the value of x is 1. So, option d) is correct.

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