In an inventory of standardized weights, 8% of the weights are found to exceed 10.282 grams and 6% weighs below 9.69 grams. If weight is a continuous random variable distributed normally, find the mean and standard deviation for this distribution.

Answer:  geometric series

Step-by-step explanation:

If it is arithmetic, the difference from each term to the next will always be the same.

4096 - 1024 = 3072; 1024 - 256 = 768

3072 ≠ 768. so not arithmetic

If it is geometric, the ratio of each term to the next will always be the same.

4096/1024 = 4

1024/256 = 4

256/64 = 4

64/16 = 4

This is a geometric series. Each term (after the first) is (1/4) of the term before.

Hope this helps.

The rest wavelength of the emission line observed at 2148 nanometers in the galaxy 100 million light-years away is approximately 2103 nanometers.

The rest wavelength of an emission line can be determined by applying the concept of redshift, which is a phenomenon observed in astrophysics where light from distant objects is shifted towards longer wavelengths due to the expansion of the universe.

In this case, the emission line is observed at 2148 nanometers (or 2.148 micrometers) in a galaxy located 100 million light-years away. To calculate the rest wavelength, we need to consider the redshift factor. Redshift, denoted by z, is defined as the observed wavelength divided by the rest wavelength minus 1.

Given that the observed wavelength is 2.148 micrometers and the galaxy is located 100 million light-years away, we need to convert the distance into a redshift factor using the cosmological relationship between redshift and distance. Assuming a standard cosmological model, we can use the Hubble constant to estimate the redshift.

The Hubble constant represents the rate at which the universe is expanding. Taking a typical value of the Hubble constant as 70 kilometers per second per megaparsec, we find that the redshift factor, z, is approximately 0.021.

To determine the rest wavelength, we rearrange the redshift equation as \((observed wavelength) = (1 + z) \times (rest wavelength)\). Substituting the values, we get \((2.148 micrometers) = (1 + 0.021) \times (rest wavelength).\)

Simplifying the equation, we find the rest wavelength to be approximately 2.103 micrometers or 2103 nanometers.

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The first three terms of the arithmetic sequence are -97, -63, and -29.

The value of x = -14.

To find the value of x and the first three terms of the arithmetic sequence, we can equate the differences between consecutive terms:

The common difference (d) is the same between all consecutive terms.

So, we have:

(5x + 7) - (7x + 1) = (2x - 1) - (5x + 7)

Simplifying the equation:

5x + 7 - 7x - 1 = 2x - 1 - 5x - 7

-2x + 6 = -3x - 8

Now, let's solve for X:

-2x + 3x = -8 - 6

x = -14

Substituting the value of X back into the expressions, we can find the first three terms:

First term: 7x + 1 = 7(-14) + 1 = -97

Second term: 5x + 7 = 5(-14) + 7 = -63

Third term: 2x - 1 = 2(-14) - 1 = -29

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The two main purposes of all businesses are earning revenue and maximizing profits, the correct option is B and E.

We are given that;

The four options

Now,

Earning revenue means generating income from selling goods or services to customers. Revenue is the lifeblood of a business, as it covers the costs of production, operation, and growth. Without revenue, a business cannot survive or fulfill its other purposes.

Maximizing profits means increasing the difference between revenue and costs. Profits are the reward for creating value for customers and stakeholders. Profits can be reinvested in the business to improve quality, efficiency, innovation, and competitiveness. Profits can also be distributed to shareholders, employees, or society as dividends, wages, or donations.

Therefore, by unitary method the answer will be earning revenue and maximizing profits.

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Answer: 0.00923521

Step-by-step explanation:

Given : The probability U.S households play video or computer games=69%=0.69

here, the probability of each U.S household play video or computer games is fixed as 0.69

Then, the probability of each U.S household not play video or computer games= 1-0.69=0.31

For independent events the probability of their intersection is product of probability of each event.

Now, the probability that none play video/computer games will be :-

\((0.31)^4=0.00923521\)

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer:

\(\boxed {x = -1}\)

Step-by-step explanation:

Solve for the value of \(x\):

\(15 + 3x = 3(2 - 2x)\)

-Use Distributive Property:

\(15 + 3x = 3(2 - 2x)\)

\(15 + 3x = 6 - 6x\)

-Take \(6x\) and add it to \(3x\):

\(15 + 3x + 6x = 6 + 6x - 6x\)

\(15 + 9x = 6\)

-Subtract both sides by \(15\):

\(15 - 15 + 9x = 6 - 15\)

\(9x = -9\)

-Divide both sides by \(9\):

\(\frac{9x}{9} = \frac{-9}{9}\)

\(\boxed {x = -1}\)

Therefore, the value of \(x\) is \(-1\).

Step-by-step explanation:

75 = 3 x 5 x 5    in prime factorization

Answer:

Step-by-step explanation:

3x5x5

Answer:

1) no traceable sources

3) too many pie slices

4) exploding 3D slices distort proportion being graphed.

7) no units of measurement.

Step-by-step explanation:

The job order costing is a way in which cost and expenses are allocated based on the no of jobs and its degrees of completion. In the given scenario the there is no traceable source for the allocation of the cost on the job. There are too many pie slices which are difficult to understand when analyses is done. The unit measurement is not assigned which is crucial for job order costing.

Answer:  A  129

Step-by-step explanation:

Because the 2 chords are the same (lines in the circle), the 2 arcs are the same  create an equation that makes them equal

3x+24 = 4x -11             >bring x to one side by subtracting both sides by 3x

24 = x -11                     > add both sides by 11

35 = x

Now that we have solved for x you need to plug that back into the equation for BC

BC= 4x-11

BC = 4(35) - 11

BC =  140 - 11

BC = 129                   >A

Answer: 5/3a + 4/2b

Step-by-step explanation:

\(\dfrac{4}{3} a-\dfrac{1}{2} b+\dfrac{1}{3} a+\dfrac{5}{2} b\)

Rearrange:

\(\dfrac{4}{3} a+\dfrac{1}{3} a-\dfrac{1}{2} b+\dfrac{5}{2} b\)

Combine Like Terms:

\(\dfrac{4}{3} a+\dfrac{1}{3} a=\dfrac{5}{3} a\\-\dfrac{1}{2}b+\dfrac{5}{2} b=\dfrac{4}{2} b\)

\(\fbox{$\dfrac{5}{3}$a + $\dfrac{4}{2}$b}\)

Answer:

A) 0.028

Step-by-step explanation:

Given:

Sample size, n = 115

Population parameter, p = 0.1

The X-Bin(n=155, p=0.1)

Required:

Find the standard deviation of the normal curve that can be used to approximate the binomial probability histogram.

To find the standard deviation, use the formula below:

\(\sigma = \sqrt{\frac{p(1-p)}{n}}\)

Substitute figures in the equation:

\(\sigma = \sqrt{\frac{0.1(1 - 0.1)}{115}}\)

\(\sigma = \sqrt{\frac{0.1 * 0.9}{115}}\)

\(\sigma = \sqrt{\frac{0.09}{115}}\)

\( \sigma = \sqrt{7.826*10^-^4}\)

\( \sigma = 0.028 \)

The Standard deviation of the normal curve that can be used to approximate the binomial probability histogram is 0.028

The actual distance represented by 23.7 cm on the map is 355.5 km.

To find the ratio of the amount of money Mabaso has to the amount of money Thabo has and the amount of money Ally has, we can divide each amount by the smallest amount (which is R35) to simplify the ratio.

Mabaso has R140, Thabo has R70, and Ally has R35.

The ratio of Mabaso's money to Thabo's money is:

R140 ÷ R35 = 4

The ratio of Mabaso's money to Ally's money is:

R140 ÷ R35 = 4

Therefore, the ratio of the amount of money Mabaso has to the amount of money Thabo has and to the amount of money Ally has is 4:1:1.

To calculate the percentage discount of a steel table, we need to find the difference between the original price and the discounted price, and then divide it by the original price. Finally, we multiply the result by 100 to get the percentage.

Original price: R750

Discounted price: R600

Discount: R750 - R600 = R150

Percentage discount: (R150 ÷ R750) × 100 = 20%

So, the table has a 20% discount on Black Friday.

To convert 125 grams to kilograms, we divide the amount in grams by 1,000 (since there are 1,000 grams in a kilogram).

125 g ÷ 1,000 = 0.125 kg

Therefore, 125 grams is equal to 0.125 kilograms.

If a green grocer packs 12 apples in a plastic bag and has 285 apples, we divide the total number of apples by the number of apples per bag to determine the number of bags needed.

Number of bags needed: 285 apples ÷ 12 apples/bag = 23.75 bags

Since we can't have a fraction of a bag, we round up to the nearest whole number. Therefore, the green grocer would need 24 bags.

If the scale of a map is 1,500,000 and the measurement on the map is 23.7 cm, we can use the scale to determine the actual distance.

1 cm on the map represents 1,500,000 cm in reality.

23.7 cm on the map represents x cm in reality.

x = 23.7 cm × 1,500,000 cm = 35,550,000 cm

To convert cm to km, we divide by 100,000 (since there are 100,000 cm in a kilometer).

35,550,000 cm ÷ 100,000 = 355.5 km

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Answer:

y = 5x - 6

Step-by-step explanation:

y - 9 = 5 ( x - 3 )

y = 5x - 15 + 9

y = 5x - 6

The volume of the solid whose base is a triangle with vertices (0,0), (0,3), and (5,0) is 25π/12 cubic units.

What is a triangle?

A triangle is a closed geometric shape that is formed by connecting three line segments. These line segments are called sides, and the points where they meet are called vertices. A triangle has three sides, three angles, and three vertices.

To start, let's graph the triangle to get a better understanding of the problem:

(0,3)   *

       |\

       | \

       |  \

       |   \

       |    \

(0,0)   *-----*-----> x

        (5,0)

The height of this slice is given by the line from the point (x,0) to the point (0,3), which has equation y = 3/5 * x + 0. The radius of the semicircle is half the height of the slice, which is given by the equation r = 3/10 * x.

The area of a semicircle is πr²/2, so the volume of this slice is:

V(x) = π * (3/10 * x)² / 2 * dx

To find the total volume of the solid, we need to integrate this expression over the range of x values that covers the entire base of the solid, which is from x=0 to x=5:

V = ∫₀₅ π * (3/10 * x)² / 2 dx

V = π/20 * ∫₀₅ x² dx

V = π/20 * [x³/3] from 0 to 5

V = π/20 * (5³/3)

V = π/4 * (25/3)

V = 25π/12

Therefore, the volume of the solid is 25π/12 cubic units.

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Madeline's school building model is 5.33 meter.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Given that, Madeline walks a distance of 9.45 meters from the building, then places a mirror flat on the ground, marked with an X at the center.

Use corresponding parts of similar triangles.

Madeline's eyes height/Madeline's distance from x = Buildings height/Buildings distance from X

1.55/2.75 = x/9.45

2.75x=1.55×9.45

2.75x=14.6475

x=14.6475/2.75

x=5.33

Therefore, Madeline's school building model is 5.33 meter.

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9514 1404 393

Answer:

  126 in²

Step-by-step explanation:

The area can be found using the formula ...

  A = 1/2bh

where b is the base length of the triangle, and h is its height.

Using the numbers shown, we find the area to be ...

  A = 1/2(12 in)(21 in) = 126 in²

Answer:

15 cubic inches

Step-by-step explanation:

I took an i-ready quiz also

The equation is rewritten in slope-intercept form as y = -3x + 5.

Slope = -3; y-intercept = 5.

The equation of any given line, when written in the slope-intercept form is expressed as y = mx + b, where:

Given the equation in standard form as 6x + 2y = 10, rewrite the equation in slope-intercept form as explained in the steps below:

6x + 2y = 10

2y = -6x + 10 [subtraction property of equality]

Divide both sides by 2

2y/2 = -6x/2 + 10/2

y = -3x + 5

The equation is y = -3x + 5, Destinee didn't rewrite the equation correctly because he subtracted 2y from both sides rather.

The slope of y = -3x + 5 is -3.

The y-intercept of the equation is 5.

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Answer:

false because simplifying it would be 2(square root 10) so it will be an irrational number

The reflection of the points P(-1, 4), Q(8, -3) and R(2, -6) across the line y = x are P'(1, -4), Q'(-8, 3) and R'(-2, 6).

First, let us understand the reflection of a point:

The reflection of a point or set of points across the line y = x results in a point or set of points whose coordinates are the interchange of the x-value and the y-value of the original point or set of points.

We are given:

The vertices of a triangle are P(-1, 4), Q(8, -3) and R(2, -6).

We need to find the reflection of the points across the line y = x.

So,

P(-1, 4) = P'(1, -4)

Q(8, -3) = Q'(-8, 3)

R(2, -6) = R'(-2, 6)

Thus, the reflection of the points P(-1, 4), Q(8, -3) and R(2, -6) across the line y = x are P'(1, -4), Q'(-8, 3) and R'(-2, 6).

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The rental cost in dollars per square foot is $11,00

Cost of renting 1.250 square feet = $13, 750 per month

Rental cost per square foot = Total renting cost / total renting area

= $13, 750 per month / 1.250 square feet

= $11,000

Hence, $11,000 is the rental cost in dollars per square foot.

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Matrices A and B are non-invertible matrices that can be added together to form an invertible matrix. To find these matrices, we can use the following steps:

Step 1: Choose a matrix A that is not a diagonal matrix and is not invertible. One example of such a matrix is

\(A = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]\)

Step 2: Choose a matrix B that is not a diagonal matrix, is not invertible, and is not a scalar multiple of matrix A. One example of such a matrix is
\(B = \left[\begin{array}{ccc}0&0\\1&1\end{array}\right]\)

Step 3: Add the matrices A and B together to form the matrix A+B. This matrix will be invertible, as shown below:

\(A+B = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]+\left[\begin{array}{ccc}0&0\\1&1\end{array}\right]=\left[\begin{array}{ccc}1&1\\1&1\end{array}\right]\)

Step 4: Verify that the matrix A+B is invertible by finding its determinant. The determinant of a 2x2 matrix is given by:

det(A+B) = (1)(1) - (1)(1) = 0

Since the determinant of the matrix A+B is not equal to zero, the matrix is invertible.

Therefore, the matrices \(A = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]\) and \(B = \left[\begin{array}{ccc}0&0\\1&1\end{array}\right]\) are non-invertible matrices that can be added together to form an invertible matrix \(A+B =\left[\begin{array}{ccc}1&1\\1&1\end{array}\right]\).

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Answer:

The answer is c

Step-by-step explanation:

If the area of the two triangles are similar, then Area of ∆ 1 : Area of ∆ 2 =

(Side of ∆ 1)² : (Side of ∆ 2)²

____________________________

Since the area of each triangle is equal to the corresponding side squared.

Area of ∆ = (Side of ∆)² →

√(Area of ∆) = Side of ∆ →

Side of ∆ = √(Area of ∆).

Therefore:

9 : 4 → √9 : √4 = 3 : 2

The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

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Answer:  \(\frac{\sqrt[4]{10xy^3}}{2y}\)

where y is positive.

The 2y in the denominator is not inside the fourth root

==================================================

Work Shown:

\(\sqrt[4]{\frac{5x}{8y}}\\\\\\\sqrt[4]{\frac{5x*2y^3}{8y*2y^3}}\ \ \text{.... multiply top and bottom by } 2y^3\\\\\\\sqrt[4]{\frac{10xy^3}{16y^4}}\\\\\\\frac{\sqrt[4]{10xy^3}}{\sqrt[4]{16y^4}} \ \ \text{ ... break up the fourth root}\\\\\\\frac{\sqrt[4]{10xy^3}}{\sqrt[4]{(2y)^4}} \ \ \text{ ... rewrite } 16y^4 \text{ as } (2y)^4\\\\\\\frac{\sqrt[4]{10xy^3}}{2y} \ \ \text{... where y is positive}\\\\\\\)

The idea is to get something of the form \(a^4\) in the denominator. In this case, \(a = 2y\)

To be able to reach the \(16y^4\), your teacher gave the hint to multiply top and bottom by \(2y^3\)

For more examples, search out "rationalizing the denominator".

Keep in mind that \(\sqrt[4]{(2y)^4} = 2y\) only works if y isn't negative.

If y could be negative, then we'd have to say \(\sqrt[4]{(2y)^4} = |2y|\). The absolute value bars ensure the result is never negative.

Furthermore, to avoid dividing by zero, we can't have y = 0. So all of this works as long as y > 0.

The degree of the polynomial is 14

The polynomial is given as:

y^2+7x^14-10x^2

Here, we assume that the variable of the polynomial is x

The highest power of x in the polynomial y^2+7x^14-10x^2 is 14

Hence, the degree of the polynomial is 14

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Answer:

a) FKR and F'KR form supplementary angles

b) FK = F'K

   EF = E'F'

(They are reflected by mirror)