how many different possible options of combinations are available in binary code using eight bits?
1. 64
2. 16
3. 128
4. 256

The following pairs of equations have its second equation valid

7 + 5x= 3 - 2x and 7 + 7x = 3

1/(x - 5) = 10 and 1 = 10(x - 5)

The invalid equations are;

3(x - 4) = 15 and x - 4 = 15

x^2 = 6x and x = 6

1. 7 + 5x= 3 - 2x and 7 + 7x = 3

Add 2x to both sides

7 + 5x + 2x = 3

7 + 7x = 3

Valid

2. 3(x - 4) = 15 and x - 4 = 15

3x - 12 = 15

Invalid

3. x^2 = 6x and x = 6

find the square root of both sides

√x² = √6x

x = √6x

Invalid

4. 1/(x - 5) = 10 and 1 = 10(x - 5)

cross product

1 × 1 = 10(x - 5)

1 = 10(x - 5)

Valid

Therefore, 7 + 5x= 3 - 2x and 7 + 7x = 3;

1/(x - 5) = 10 and 1 = 10(x - 5) are the valid equations.

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Answer:8,5

Step-by-step explanation: look at where the dots are and see the numbers

Answer:

AC = 3[tex]\sqrt{5}[/tex] ≈ 6.71

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

AC² = AB² + BC² = 6² + 3² = 36 + 9 = 45 ( take square root of both sides )

AC = [tex]\sqrt{45}[/tex] = [tex]\sqrt{9(5)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex] = 3[tex]\sqrt{5}[/tex] ← exact value

AC ≈ 6.71 ( to the nearest hundredth )

Answer:87

Step-by-step explanation:

Answer:

Step 1: $5 to $6 is a $1 increase

Step 2: Divide by the old value: $1/$5 = 0.2

Step 3: Convert 0.2 to percentage: 0.2×100 = 20% rise.

Or you could do it this way:

Step 1: Divide new value by old value: $6/$5 = 1.2

Step 2: Convert to percentage: 1.2×100 = 120% (i.e. $6 is 120% of $5)

Step 3: Subtract 100%: 120% − 100% = 20%, and that means a 20% rise.

Answer:

20%

Step-by-step explanation:

$5 to $6 is a $1 increase

Divide by old value: $1/$5=.2=20%
To check: $5 times 1.2 (120%)=6

2nd Method:

Divide by new vlaue: $6/$5=1.2

1.2=120%

120%-100%=20%

The 96 % confidence interval for the cans, given the diameter and standard deviation, is (50.45, 53.55).

The 96% confidence interval for the mean diameter of soda cans manufactured by the company can be calculated using the following formula:

= Mean ± (critical value x standard deviation / square root of sample size)

The critical value for a 96 % confidence interval is 2. 33 so the lower bound of the interval is:

= 52 - ( 2.33 x 2. 3 / √12 )

= 50. 45

The upper bound of the interval is:

= 52 + ( 2.33 x 2. 3 / √12 )

= 53. 55

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The exterior angle adjacent to the largest interior angle in a triangle with a 2:2:4 angle ratio is 90 degrees.

The exterior angle adjacent to the largest interior angle in a triangle is equal to the sum of the other two interior angles.

Let's call the measures of the angles in the triangle x, x, and 2x. Then,

x + x + 2x = 180 degrees,

so 4x = 180 degrees, and

x = 45 degrees.

The largest interior angle is 2x, or 90 degrees. The exterior angle that is adjacent to this angle is equal to 180 degrees minus the interior angle, which is 180 - 90 = 90 degrees.

So the exterior angle adjacent to the largest interior angle in a triangle with a 2:2:4 angle ratio is 90 degrees.

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The factor is the variable that the experimenter will use to judge its impact on the response variable.

A dependent variable is one that is altered as a result of the modification of an independent variable. The outcome you're trying to measure "depends" on your independent variable. Response variables in statistics are another name for dependent variables (they respond to a change in another variable).

The coefficient of a variable term is that word's numerical factor.

The variable being measured or tested in an experiment is known as the dependent variable.

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The right answer is D.

Detailed explanation:

$35,000. Original cost of the vehicle

The car's current value is $28,500.

The residual worth of Sally's leased vehicle is equal to x.

Current Price x * 38,000 = 28,500 x = 28,500/38,000 x = 0.75 Residual value * Original Price

Since we must determine the proportion

Divide the residual value by 100, or 0.75 * 100, to get 75%.

The right answer is D.

A lease is a contract in which the owner of an asset (the lessor) agrees to let the lessee use it in exchange for a specific amount of money (the rent), which may or may not be based on any factors, for a specified amount of time (the lease term), which may or may not be flexible.

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Answer:

Factor 4 out of 12+4x 4(3+x)

Step-by-step explanation:

Answer:

5 StartRoot 10 EndRoot

Step-by-step explanation:

we know that

The legs of a 45°-45°-90° triangle are congruent

Let

x ---->  the length of one leg of the triangle

Applying the Pythagorean Theorem

where

c is the hypotenuse

a and b are the legs

we have

substitute

Simplify

5 StartRoot 10 EndRoot

The solution used to make 40% of salt solution is 12 grams and 70% of salt solution is 8 grams.

Let us consider 'a' represents the 40% of salt in water.

And 'b' represents the 70% of salt in water.

Total salt required to make 52% salt solution = 20 grams

Required equations is :

a + b = 20

⇒ a = 20 - b  ___( 1 )

40% of a + 70% of b = 52% of  20 grams

⇒ 0.40a + 0.70b = 10.4 ___( 2 )

Substitute the value of 'a' in equation ( 2 ) from (1) we get,

0.40( 20 - b ) + 0.70b = 10.4

⇒8 - 0.40b +  0.70b = 10.4

⇒ 0.30b = 10.4 - 8

⇒ b = 2.4 / 0.30

⇒ b = 8

⇒ a = 12

Therefore, the solution used by Serena for 40% is 12 grams and 70% solution is 8 grams.

The above question is incomplete , the complete question is:

Serena is making an experiment. For that, she needs 20 grams of a 52% solution of salt. She has two large bottles of salt water: one with 40% and the other with 70% of salt in them. How much of each must she use to make the solution she needs?

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Percentage increment means the part of original value is added to the value. The new length of the living room is 14.4 feet long and new width of the living room is 1.6 feet long. The option A is the correct option.

The length of the living room is 12 feet.

The width of the living room is 8 feet.

The owner increases the 20 percent of length and 20% width.

Suppose new length is feet long. As the owner increases the 20 percent of length. Thus the new length will be sum of original length and the 20 percent of it. Hence,

l=12+12/100*12

l=14.4

Thus the new length of the living room is 14.4 feet long.

Suppose new width is  feet long. As the owner increases the 20 percent of width. Thus the new width will be sum of original width and the 20 percent of it. Hence,

w=8+20/100*8

w=9.6

the new width of the living room is 1.6 feet long.

Hence the new length of the living room is 14.4 feet long and new width of the living room is 1.6 feet long.

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If line r through (1, 1) and (5, 7) is parallel to line s through (4, -2) and (x, y),

all the possible values of x and y are those values that  satisfy the equation 3x - 2y = 16.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Given:

If line r through (1, 1) and (5, 7) is parallel to line s through (4, -2) and (x, y),

then their slopes are equal.

(7 -1)/(5 - 1) = (y + 2)/(x-4)

3/2 = (y + 2)/(x-4)

3x - 12 = 2y + 4

3x - 2y = 16.

Therefore,  all the values that satisfy the equation 3x - 2y = 16.

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The quadratic equation can be written in vertex form as:

y = (x - 3)^2 - 7

A general quadratic equation with a leading coefficient a and a vertex (h, k) can be written as:

y = a*(x - h)^2 + k

If particularly we take a = 1 (we could take any value here, because the problem doesn't say anything about the leading coefficient).

And the vertex is (3, -7)

Then the quadratic equation can be:

y = (x - 3)^2 - 7

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The requried graph of the solution of a set of given inequality 13 > 5+ 4x is shown.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

here,
Given inequality,
13 > 5 + 4x

Simplify the above expression,
Subtract -5 from both sides,
13  - 5 > 5 - 5 + 4x
8 > 4x

Divide by 4 into both sides
2 > x

The graph of the solution to the given inequality is less than 2, and line x = 2 will be a dotted line [value no included in x < 2]

Thus, the graph of the inequality has been shown.

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Answer:

0.25

Step-by-step explanation:

You are finding the average of the two numbers by finding the halfway point. So you do 0.2+0.3 = 0.5 and then you divide by 2. 0.5/2 = 0.25

Hope this helped :)

Answer:

Answer is in attached photo.

Step-by-step explanation:

The solution is in the attached photo, do note that to solve this question, there are multiple ways (using Pythagoras' Theorem), this is only one of the ways.

According to the solving triangle proportion proves that cos ∠d = cos ∠a is

3/3.61 = 6/7.22

A triangle seems to be a three-sided polygon with three vertices. The angles of both the triangle are formed by the connection of the three sides end to end at a single point. The triangle's three angles add up to 180 degrees.

According to the given information:

Right angled triangles BAC and BDE are comparable to one another.

This is due to the fact that when a shape is dilated, then new shape would resemble the previous shape but be smaller. Both shapes' angles are the same if they both stay the same.

Scale factor = 2

BE = 3, BD = 2, DE = 3.61

Each of the corresponding sides of ∆BDE will be multiplied to get each of the corresponding sides of ∆ABC.

BC = 2×BE = 2×3 = 6

AB = 2×DE = 2×3.61 = 7.22

See second diagram

sin ∠D = opposite/hypotenuse = BE/DE

BE/DE = 3/3.61

sin ∠A = BC/AC

BC/AC =  6/7.22

Therefore sin ∠D = sin ∠A

3/3.61 = 6/7.22 (C)

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Answer:3/3.61 = 6/7.22

Step-by-step explanation:

got it right on the test

The number 5.634x10 to the 2nd power can be expressed as 563.4. The numbers between which 563.4 falls are 560 and 567.

The length of a football field, including the end zones, is 120 yards, which is equal to 4320 inches.

To calculate this, we can use the conversion rate of 1 yard equal to 3 feet and 1 foot equal to 12 inches. This means that 1 yard is equal to 36 inches. To convert 120 yards to inches, we can multiply 120 by 36, resulting in 4320 inches.

To explain this mathematically, we can use the formula:

where Inches/Foot = 12 and Feet/Yard = 3.

Plugging in the appropriate variables, we can calculate the number of inches in a football field as:

Inches = 120 x 3 x 12 = 4320 inches.

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The graph represents the inequality, the graph shows a dashed line, which crosses the y-axis at 1 and the x-axis at 3, with shading below the line.

According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. Any of the symbols for inequality, including greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).

Given the phrase, y is less than negative one-third times x plus 1

negative one-third times x plus 1,

-1/3x + 1

y < -1/3x + 1

to plot the coordinates consider,

y = -1/3x + 1

when x = 0, y = 1

and when y = 0,

0 = -1/3x + 1

-1/3x = -1

x = 3

x     0       3

y      1        0

and the graph says y is less than negative one-third times x plus 1,

so the shaded portion will be below the line, and the graph is attached for the condition.

Hence option D is correct.

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The 90% confidence interval is (2.76, 4.84).

The standard deviation is a measure of the amount of variation or dispersion of a set of values.  A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.

Standard deviation may be abbreviated SD and is most commonly represented in mathematical texts and equations by the lower-case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.

Mean [tex]$(\overline{\mathbf{x}})[/tex] =3.8, sample standard deviation [tex]$(\mathrm{s})[/tex] =1.8, sample size     [tex]$(\mathrm{n})[/tex] = 10

since population standard deviation [tex]$(\sigma)$[/tex] is unknown and the value of [tex]$\mathrm{n}$[/tex] is less than 30, use. [tex]$\mathrm{t}$[/tex] - distribution

degrees of freedom =10-1=9

for 90% confidence level with degrees of freedom = 9

[tex]$t_{\frac{\alpha}{2}}=1.833[/tex] (from t- table)

formula: confidence interval for population mean. [tex]$\mu=\bar{x} \pm t_{\frac{\alpha}{2}} *\left\{\frac{s}{\sqrt{n}}\right\}$[/tex]

= 3.8 ± 1.833×[tex]\left\{\frac{1.8}{\sqrt{10}}\right\}$[/tex]

= 3.8 ± 1.04

= (3.8 - 1.04, 3.8 + 1.04)

= (2.76, 4.84)

Therefore, the 90% confidence interval is (2.76, 4.84).

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Answer:

1183

Step-by-step explanation:

75th term of Arithmetic sequence is 1183 Given: -1, 15, 31,... is Arithmetic series To find: The 75th term of the arithmetic sequence -1, 15, 31

Answer:

It looks like you're trying to solve a problem involving geometry and algebra. To solve this problem, you need to use the information given in the statements to find the value of x and then use that value to find the lengths of the sides of the trapezoid.

Starting with the first statement, we have:

WH = 10x + 2.6

NH = 11x - 7.4

Next, we can use the information about Y being the midpoint of WT to find the value of WT:

WT = 2 * RY = 2 * (18x - 4.1) = 36x - 8.2

Using the information about R being the midpoint of HN, we can find the value of HN:

HN = 2 * RY = 2 * (18x - 4.1) = 36x - 8.2

Finally, using the information about TN, we can find the value of TN:

TN = 23x - 3.9

With these values, we can now find the lengths of the sides of the trapezoid. The length of the top side (WH) is 10x + 2.6, the length of the bottom side (TN) is 23x - 3.9, the length of the left side (NH) is 11x - 7.4, and the length of the right side (WT) is 36x - 8.2.

Note: To fully solve the problem, you will need to use the given equations to find the value of x.

To find the value of x, we need to equate the midpoint formula with the given expressions.

The midpoint formula is (x1 + x2)/2 = x and (y1 + y2)/2 = y.

We can use this formula to find the value of x.

For example, for the midpoint R:

x = (WT + NH)/2

x = (8x + 5.2 + 11x - 7.4)/2

x = (19x - 2.2)/2

x = 9.5x - 1.1

And for the midpoint Y:

y = (WH + TN)/2

y = (10x + 2.6 + 23x - 3.9)/2

y = (33x - 1.65)/2

y = 16.5x - 0.825

Now we have two equations:

9.5x - 1.1 = 16.5x - 0.825

7x = 0.725

x = 0.725/7

x = 0.104285714

So the value of x is approximately 0.104285714.

Answer:

Step-by-step explanation:0.1

The length of a training track running around the field is 334.7m.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

A semicircle is created when a circle is divided in half along its diameter. There is an equal distribution of each half. A semicircle is a circle that has been folded in half; it is sometimes referred to as a half-disk.

here, we have,

GIven that;

length of rectangle = 81m

width of rectangle = 55m

Length of track running around the field = 2 x length of field + circumference of two semicircles

= 2 x 81 +pi x 55

= 162 + 3.14 x 55

= 334.7m

∴ the length of a training track field is 334.7m

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si por qué si y si por qué obvio si

As a result, Company B is more likely to make you an offer of $33,000 or more than Company A.

The standard deviation in statistics is a measure of the degree of variation or dispersion in a set of values. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.

Here,

To determine which company you are more likely to receive an offer of $33,000 or more, we need to look at the standard deviations of each company's starting salary. Company B has a standard deviation of $5000, which is 5 times greater than Company A's standard deviation of $1000. This means that the salaries offered by Company B are spread out over a larger range, with a higher chance of extreme values.

We can calculate the z-score for an offer of $33,000 from each company using the formula:

z = (x - μ) / σ

For Company A:

z = ($33,000 - $31,000) / $1000 = 2

For Company B:

z = ($33,000 - $31,000) / $5000 = 0.4

A z-score of 2 for Company A indicates that an offer of $33,000 is 2 standard deviations above the mean, which is relatively rare. On the other hand, a z-score of 0.4 for Company B indicates that an offer of $33,000 is only 0.4 standard deviations above the mean, which is much more likely.

Therefore, you are more likely to receive an offer of $33,000 or more from Company B than Company A.

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There is a 50% chance that the person selected is female.

Let's assume that there are 50 students in the class and of them, 25 are female and 25 are male.

The probability that the person selected is female will be calculated by the formula P(Female) = 25/50 = 0.5

Therefore, the probability that the person selected is female is 0.5 or 50%. This means that if a person is randomly selected from the front, middle portion of the class, there is a 50% chance that the person selected is female.

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Complete question:

What is the gender ratio of the people in the class?

A vertical asymptote basically means of a graph on a  vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a.

In a graph a vertical asymptote  is a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a. And similarly the horizontal asymptote in a graph is a horizontal line y = b where the graph approaches the line as the inputs approach ∞ or –∞.

At x = a in a graph  where  a is a zero for a factor in the denominator the removable discontinuity occur that is common with a factor in the numerator.

Factor the numerator and denominator.

It is set it equal to zero and solve if any factors are common to both the numerator and denominator.

This is removable discontinuity type location.

In mathematics a graph is defined as a diagrametical or a pictorial representation  that helps to represents data or values in an organized manner. The points that are shown on the graph are use to mark of represent the various value or relation between two value .

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Answer:

1600 mL

Step-by-step explanation:

if 1L = 1000mL then:

2.8L is equal to 2800mL

2800 - 1200 = 1600