What is the solution to this system of linear equations yx 6 y x =- 10 O (- 2 8 O (- 8 2 O 6/10 O (- 10 6?.

amount of white fabric to coloured fabric a a ratio of it implet form is given by 1/2

2cm = 2 * 10 mm

2 cm = 20 mm

for every 50 mm of colored fabric, Gavyn uses 100 mm of white fabric.

The ratio is expressed as white fabric to colored fabric.

Ratio white to colored = 50/100 =  1/2

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The equation of line which passes through point (5,1) and having slope ½ is (y-1) = ½ (x-5).

What is the equation of a line?

The equation of a line is given as:

y = mx + c

The equation for the point on slope line is given as:

y - y1 = m ( x - x1 )

Substituting the above given values and the slope:

y - 1 = [tex]\frac{1}{2}[/tex] ( x - 5)

Hence, the equation of line which passes through point (5,1) and slope ½ is (y-1) = ½ (x-5).

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Answer:

[tex](-1.3,-3.69)[/tex]

Step-by-step explanation:

Take the derivative of the function and set it equal to 0.

[tex]f(x)=x^2+2.6x-2[/tex]

[tex]f'(x)=2x+2.6 = 0[/tex]

Solve for x.

[tex]2x+2.6=0\\2x=-2.6\\x=-1.3[/tex]

Find [tex]f(-1.3)[/tex]

[tex]f(-1.3)=(-1.3)^2+2.6(-1.3)-2[/tex]

[tex]f(-1.3)=-3.69[/tex]

Mrs. Ibanez is experiencing symptoms of a potentially serious condition and should be evaluated by a medical professional as soon as possible.

Any medical disease that has the potential to get worse or be life-threatening if it is not treated quickly and effectively qualifies as potentially serious. Infections, wounds, and long-term medical issues like diabetes or heart disease or profound dehydration are a few examples of potentially catastrophic illnesses. These illnesses can range in severity from moderate to severe, and they might need to be treated right once to avoid long-term harm or other consequences. If you think you may have a dangerous issue, it's crucial to speak with a doctor right away so you can get the proper care and stop the problem from becoming worse.

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Approximately 7 bags of soil are needed to fill the land.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is garden that needs 5 3/6 pounds of soil. The bag of soil contains only 5/6 of soil.

The total number of bags of soil you need to buy are -

n = (33/6)/(5/6)

n = 33/6 x 6/5

n = 33/5

n = 6.6

n = 7 (approx.)

Therefore, approximately 7 bags of soil are needed to fill the land.

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The overall MSE for the time series would be (0 + 0 + 0.0289 + 0.0144 + 0.0044 + 0.0144)/6 = 0.0119. This value indicates that the forecasted values are close to the actual time series values, with a small error.

Mean squared error (MSE) is a standard measure of the average squared difference between predicted and actual value. Regression analysis frequently use it to assess a model's performance pattern. The sum of squared discrepancies between the predicted and actual values is multiplied by the number of observations in the dataset to derive the MSE. A lower MSE signifies a better match between the model and the data. In regression analysis, MSE is generally compared to the variance of the response variable, which is a measure of data dispersion. The MSE reveals how well the model fits the data when it is less than the variance.

How to solve?

To construct a time series plot for the given data, we can plot the values of the data against the weeks on the x-axis.

Week 1 | |

Week 2 | |

Week 3 | |

Week 4 | |

Week 5 | |

Week 6 | |

The three-week moving average for each week would be as follows:

Week 1: 16

Week 2: 11

Week 3: 12.67

Week 4: 11.33

Week 5: 12

Week 6: 11.33

The MSE for each week would be as follows:

Week 1: 0

Week 2: 0

Week 3: 0.0289

Week 4: 0.0144

Week 5: 0.0044

Week 6: 0.0144

The overall MSE for the time series would be (0 + 0 + 0.0289 + 0.0144 + 0.0044 + 0.0144)/6 = 0.0119. This value indicates that the forecasted values are close to the actual time series values, with a small error.

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Sum of logarithm is [tex]\left(\log _3(5)+\log _3(a)\right) b$$[/tex]

The exponent or power that must be added to a base to produce a given number is called the logarithm. If bx = n, then the mathematical expression for x is x = logb n, where x is the logarithm of n to the base b.

For instance, since 23 = 8, 3 is the logarithm of 8 in base 2, or 3 = log2 8. In a similar manner, since 102 = 100, 2 = log10 100. Those of the latter type (base 10-based logarithms) are referred to as common, or Briggsian, logarithms and are denoted by the letter log n.

The time needed to multiply numbers with many digits was significantly reduced thanks to the development of logarithms in the 17th century, which was done to speed up calculations.

Simplifying [tex]$\log _3(5 a) b: \quad\left(\log _3(5)+\log _3(a)\right) b$$\log _3(5 a) b$[/tex]

[tex]\log _3(5 a) b[/tex]

Simplifying we get

[tex]$\log _3(5 a): \quad \log _3(5)+\log _3(a)$$$=\left(\log _3(5)+\log _3(a)\right) b$$[/tex]

Therefore the sum of logarithm is [tex]\left(\log _3(5)+\log _3(a)\right) b$$[/tex]

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The number of outstanding shares that BBQ Corp. will have post-split, given the number of outstanding shares is, 4, 050, 000 shares

A stock split refers to when the number of outstanding shares that a company has, are divided into a certain number of shares which is based on the split ratio.

For a 3:1 stock split ratio, the number of outstanding shares will be split into three shares each.

BBQ Corp. has 1. 35 million shares so post - split, they will have:

= Outstanding shares x  3

= 1, 350, 000 x  3

= 4, 050, 000 shares

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The annual growth rate in the expenses is 0.08035 or 8.03 % and with the same rate the expenses after 4 years will be equal to $24,642.

How annual growth rate is calculated?

Annual growth rates are calculated by taking the average revenue for a particular time period into account. The yearly growth rate formula divides the final value of an investment or asset by its original value. When you subtract one from this amount, you are left with a decimal point that can be translated into a percentage. You may determine the percentage by simply moving the decimal point two spaces to the right.

The growth in the 4 years is = 18,500 – 14,000 = 4,500

Growth = initial amount (rate) (time)

4500 = x(4)(14,000) = 0.08035

It means the annual growth rate is 8.03 %

To know the expenses after 4 years, lets take initial value = 18,500, rate = 8.03% = 0.083, time = 4 years,

Increase = 18500(0.083)(4) = 6,142

So, the expenses after 4 years,

Expenses = 18,500 + 6,142 = 24,642

Therefore, the expenses after 4 years are $24,642

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The Prime Factorization of 54 in exponential form is 2¹ × 3³  .

The Exponential Form is a way of writing repeated multiplication that involves base and exponents . For Example : 5×5×5 = 5³ .

In the question ,

it is given that ,

the number is 54 ,

we have to find the prime factorization , and write it in the exponential form .

the number 54 can be expressed in factors as 2 × 3 × 3 × 3 .

which means 54 = 2 × 3 × 3 × 3 .

which can be written as 2 × 3³ .

So , the exponential form is 2¹ × 3³ .

Therefore , The Prime Factorization of 54 in exponential form is 2¹ × 3³  .

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The cost of the t-shirt is 3 and the cost of a hat is 2

Let the price of a t-shirt be x

and the price of a hat be y

cost of 5 t-shirt and a hat is 17

5x + y = 17 equation 1

cost of 2 t-shirt and a hat is 8

2x + y = 8   equation 2

subtracting equation 2 from equation 1

5x + y - (2x + y) = 17 - 8

5x + y - 2x - y = 9

3x = 9

x = 3

2x + y = 8

2 (3) + y = 8

y = 8 - 6

y = 2

Therefore, the cost of the t-shirt is 3 and the cost of a hat is 2

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Answer:

x = 90° + 180° × n, for all integers, n

Step-by-step explanation:

(sin x - 1)(sin x + 1) = 0

sin x = 1  or sin x = -1

The sine function has value 1 at 90° and all coterminal angles.

The sine function has value -1 at 270° and all coterminal angles.

Answer: x = 90° + 180° × n, for all integers, n

Using equations we know that the value of x needs to be (E) 4 to make HL congruent to AC.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

So, HL is a hypotenuse that will be congruent to the hypotenuse AC.

We know that HL is 3x + 3.

Ac is 15.

Then the equation will be:

3x + 3 = 15

Now, solve the equation to get x as follows:

3x + 3 = 15

3x = 15 - 3

3x = 12

x = 12/3

x = 4

Therefore, the value of x needs to be (E) 4 to make HL congruent to AC.

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Correct question:
For the triangles to be congruent by hl, what must be the value of x?

a. 8

b. 9

c. 17

d. 3

e. 4

The weight of the newborn baby in pounds is 7pounds

Proportion is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

The relationship between a pound and stone is

1 pound = 1/14stone

therefore 1stone = 14pounds

The weight of the newborn baby is 1/2 stone

in pounds ,the weight of the baby is 14/2= 7pounds

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Simplified value of given expression is 2x³√10x.

What is simplification?

In arithmetic,  simplification is reducing the expression / fraction problem during a less complicated type.

Main body:

Factor 40 into its prime factors

          40 = 2³ • 5

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

Factors which will be extracted are :

          4 = 2²

Factors which will remain inside the root are :

          10 = 2 • 5

To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :

          2 = 2

At the end of this step the partly simplified SQRT looks like this:

        2 • sqrt (10x7)

Rules for simplifing variables which may be raised to a power:

  (1) variables with no exponent stay inside the radical

  (2) variables raised to power 1 or (-1) stay inside the radical

  (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

     (3.1) sqrt(x⁸)=x4

    (3.2) sqrt(x-⁶)=x-3

     (4) variables raised to an odd exponent which is  >2  or  <(-2) , examples:

     (4.1) sqrt(x5)=x²•sqrt(x)

    (4.2) sqrt(x-7)=x³•sqrt(x-1)

Applying these rules to our case we find out that

    SQRT(x7) = x³ • SQRT(x)

 sqrt (40x7) =

       2² x³• sqrt(10x)

Hence the simplification to the value is as 2² x³ • sqrt(10x)

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The asset's value should be recognized on the balance sheet at $1.61 million.

Given,

On January 1st, 2006, Trekkers Footwear paid $2.3 million for a piece of equipment that will be depreciated at a rate of $230,000 per year for ten years. As of December 31, 2008, IT was worth $1.75 million in the market. The company's accountant is putting the finishing touches on the financial statement for the fiscal year that ends on December 31, 2008.

The balance sheet should reflect the asset's value at,

Cost of Asset = $2.3 million

Annual depreciation = $230000

Total no. of years depreciated till December 31, 2008, = 3 years

Hence, total depreciation = $230000 x 3 = 690000 = 0.69 million

Hence, book value as on 31 December 2008 = $2.3 million - $0.69 million = 1.61 million

Given Market Value on Dec 31, 2008, = $1.75 million.

But as per accounting conventions, Assets are recorded at Book value.

Hence $1.61 million is the right answer.

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In given proportinal relation , Maila need 204 yards for make 68 bow.

What is proportion?

   In mathematics, proportional means that two quantities or variables are linearly related. When one quantity doubles, the other quantity also doubles. When one of the variables decreases to 1/10th of its previous value, the other also decreases. A ratio is a comparison of two numbers, each representing a part of a whole. Essentially, percentages show that two fractions are equal, even if they are of different magnitudes. For example, 1/2 of 10 marbles has the same ratio as 1/2 of 50 marbles.

Here the relationship between ribbon and bow is proportional. Let us take ribbon as r and bow as b.

=> r ∝b

=> r= kb . Where k is constant.

Now put r=51 and b =17 then,

=> 51=k*17

=> k = 3

then the equation is r = 3b.

Now b=68 then ,

=> r = 3*68

=> r = 204 yard.

Therefore Maila need 204 yard ribbon to make 68 bow.

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The probability that the sample proportion is at least 0.60 is 0.0294.

Given data,

In a local university, 70% of the students live in dormitories. A random sample of 75 students is selected for a particular study The probability that the sample proportion (the proportion living in the dormitories) is at least 0.60 is,

The sample size in this case,

n = 75

The proportion of students living in dormitories p,

⇒ 70% = 0.7

Since we are taking a distribution of 75-sample samples from the given population into consideration, we have:

The mean, p = 0.7

The standard deviation, s = √p * (1 − p)/n

                                           = √0.7 * (1 − 0.7)/75

                                           = 0.0529

Now, by figuring out their respective Z-scores, we can calculate the probability values corresponding to the supplied proportion values.

The Z-score for a proportion value of 0.60;

Z₀.₆₀ = (0.6 - p)/s

        = (0.6 - 0.7)/0.0529

        = -1.890

The Standard Normal Distribution table can be used to determine the corresponding probability. Consequently, the overall likelihood value for,

Z₀.₆₀ = -1.890

P-value from Z-Table,

P(x < 0.6) = 0.029355 = 0.0294

Hence, there is a 0.0294 percent chance that the sample proportion is at least 0.60.

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Answer:

6

Step-by-step explanation:

for this I simply divided that numbers and I got my answer as 5.77 and I turned as 6

(-5, 8)

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

These are two rules to memorize

[tex]\text{x-axis reflection: } \ \ (\text{x},\text{y})\to (\text{x},-\text{y})\\\\\text{y-axis reflection: } \ \ (\text{x},\text{y})\to (-\text{x},\text{y})\\\\[/tex]

----------

I'll relabel the point X as point A.

We apply a y-axis reflection first.

So we have:

[tex](\text{x},\text{y})\to (-\text{x},\text{y})\\\\(5,-8)\to (-5,-8)\\\\[/tex]

after the y axis reflection is applied.

This is the location of point A'

----------

Then we apply an x-axis reflection.

[tex](\text{x},\text{y})\to (\text{x},-\text{y})\\\\(-5,-8)\to (-5,-(-8))\\\\(-5,-8)\to \boldsymbol{(-5,8)}\\\\[/tex]

This is the location of point A''

which points us to choice C as the final answer.

----------

Side note:

The composition of an x-axis reflection and y-axis reflection, in either order, is the same as a 180 degree rotation around the origin.

The rule for a 180 degree rotation is [tex](\text{x},\text{y})\to (-\text{x},-\text{y})\\\\[/tex]

The equation of the line that passes through the point (8,4) and has a slope of 0 is y = 4.

Given:

point (8,4) and has a slope of 0

slope m = 0

Standard line equation is y = mx + c

substitute (8,4) and m values in y = mx + c

4 = 0*8 + c

4 = 0 + c

c = 4

c , m values in y = mx + c

y = 0*x + 4

y = 0 +4

y = 4.

Therefore The equation of the line that passes through the point (8,4) and has a slope of 0 is y = 4.

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The decimal division of 18.92 by 11 gives us; 1.72

When dividing decimals,  we first have to convert the divisor to a whole number by moving the decimal point to the right. Thereafter, we now carry the dividend's decimal point up to the exact same number of places to the right and then divide the resultant numbers in the normal way, like in regular long division.

We want to divide 18.92 by 11. Thus, let us apply that rule described above to get;

18.92/11 = 1892/1100

= 1 + (1892 - 1100)/1100

= 1 + (792/1100)

= 1 + 0.72

= 1.72

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An equation to represent the proportional relationship between the number of hours and the distance in miles is k=y/x.

Given that, Percy rides his bike 11.2 miles in 1.4 hours at a constant rate.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

The number of hours Percy rides x, and the distance in miles, y, that he travels

So, the proportional relationship is speed = y/x

Thus, 11.2/1.4

= 8 miles per hour

Therefore, an equation to represent the proportional relationship between the number of hours and the distance in miles is k=y/x.

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Answer:

No

Step-by-step explanation:

The sum of two sides of a triangle should be greater than the size of the third side.

2 + 3 is not greater than 5, so it's impossible to construct a triangle using the given lengths for the sides.

Key expansion is most responsible for this delay.

A block cipher encrypts and decrypts a block of data with an algorithm and symmetric key. In order to expand the keyspace of a block cipher and make it more difficult to break the key through brute force, an initialization vector (IV) must be added to the plaintext that is being used as input. Key Expansion: In the initial stage, it uses just one key, but in later rounds, it expands to multiple keys. Data bytes: Instead of working with bit data, the AES encryption algorithm performs operations on byte data. Consequently, during the encryption process, it treats the size of the 128-bit block as 16 bytes.

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Answer:

4 - log3 (2)

Step-by-step explanation:

2log3 (9) = log3 (9^2)

log3 (27 * 9^2 / 54)

log3 ( 3^3 * 3^4 / 9 * 6)

log3 (3^7 / 3^2 * 3 * 2)

log3 (3^7 / 3^3 * 2)

log3 ( 3^4 /2)

log3 (3^4) - log3 (2)

4 - log3 (2)

0.769 minutes of the ride is spent higher than 17 meters above the ground.

What is the unit conversion in mathematics?

Unit conversion is a multi-step process that includes multiplying or dividing by a numerical factor, determining the appropriate number of significant digits, and rounding.

The given figure is a Ferris wheel we have to find the time spent on the ride higher than 17 m.

It means we have to find time spent riding from A to C through B (i.e., Arc ABC)

From the figure, in ΔAOD, we have

         OA = 12.5 m

         OD = 12.5 - 1 = 11.5 m

Now find 'θ'

           θ = [tex]cos^{-1}(\frac{11.5}{12.5})[/tex]

                = 23.07°

The total angle of arc ABC = 2θ

                                       = 2 * 23.07

                                       = 46.14°

It is given that, 1 full revolution is completed in 6 minutes.

so 46.14° will be completed in = 6/360 * 46.14

                                                  = 0.769 minutes.

Hence, 0.769 minutes of the ride is spent higher than 17 meters above the ground.

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Answer:

91.1 cm

Step-by-step explanation:

the formula to find circumferences is pi times diameter

29pi

91.1

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