__________ is a measure of how responsive one variable is to a change in another variable.

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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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

Answer:

x=54⁰ y= 43⁰ z= 83⁰

Step-by-step explanation:

z=180⁰-97⁰

83⁰ opposite angles add upto 180⁰

y= 43⁰

x= 83⁰+43⁰=126⁰

180⁰-126⁰= 54⁰ (alternate angles)

Answer:

The midpoint of AB is (-0.5, 0)

Step-by-step explanation:

( X1 plus X2 = -1/2 = -0.5, Y1 plus Y2 = 0

Answer:

D) 12/16 = 36/48

Step-by-step explanation:

They are equivalent fractions, unlike the other options. Both of these fractions simplify to 1/3 so they are indeed equivalent.

Answer:

12/16 = 36/48

Step-by-step explanation:

because 12/16 multiplyed by 3 is 36/48

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 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 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 correct expression for the Perimeter of the Rectangle will be  8w, 2w + 6w, and  2 (w + 3w).

The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.

Given, The length of a rectangle is 3 times the width, w

Since,

width of the rectangle = w

Length of the rectangle = 3w

From the general formula of the Perimeter of the Rectangle:

Perimeter = 2(Length + width)

Perimeter = 2 (w + 3w)

Perimeter = 2w + 6w

Perimeter =  8w

Therefore, the correct expression for the Perimeter of the Rectangle will be  8w, 2w + 6w, and  2 (w + 3w).

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1: The number of dogs is greater than 20

2: The temperature was less than 80°

3: The cost of the bike is atleast $100.

4: The grocery list does not exceed 15 items. The speed limit is not more than 40mph

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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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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The area of this region is equal to [tex]\pi \cdot (\sqrt{35})^2 = 35\pi[/tex]

The equation for the set of complex numbers z such that the real part of 1/z is equal to 1/6 is given by:

Re(1/z) = 1/6

Since 1/z = 1/x + i/y,

Where x and y are the real and imaginary parts of z, respectively,

we can write the equation as:

(1/x)=(1/6) and [tex]$\frac{y}{x^2 + y^2} = \frac{1}{6}$[/tex]

From the first equation,

we have x = 6.

Substituting this value into the second equation, we get:

[tex]$\frac{y}{36 + y^2} = \frac{1}{6}$[/tex]

Solving for y,

we find that [tex]$y = \pm \sqrt{35}$[/tex].

So, the set of complex numbers z that satisfies the equation forms a circle centred at 6 + 0i with radius [tex]$\sqrt{35}$[/tex].

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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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a) The initial population is [tex]N_0[/tex] = 125 / [tex]e^{(2k)}[/tex].

b) The exponential growth model for the bacteria population is N = [tex]N_0[/tex] × [tex]e^{(kt)}[/tex].

c) The number of bacteria after 8 hours is N = [tex]N_0[/tex] × [tex]e^{(8k)}[/tex].

d) After t = ln(25,000 / [tex]N_0[/tex]) / k hours the bacteria count will be 25,000.

(a) To calculate the beginning population, we must first establish the bacterium population's exponential growth rate. Assume that the initial bacterial population is [tex]N_0[/tex]. The exponential growth model is given by:

N = [tex]N_0[/tex] × [tex]e^{(kt)}[/tex]

Where N is the number of bacteria at time t, [tex]N_0[/tex] is the starting population, e is the natural logarithm base, k is the growth rate constant, and t is time in hours.

We have two data sets: N = 125 after two hours and N = 350 after four hours. We can solve using these two equations [tex]N_0[/tex] and k.

(125) = [tex]N_0[/tex] × [tex]e^{(2k)}[/tex]

(350) = [tex]N_0[/tex] × [tex]e^{(4k)}[/tex]

Dividing the second equation by the first equation:

(350/125) = [tex]e^{(2k)}[/tex]

Taking the natural logarithm of both sides:

ln(350/125) = 2k

Solving for k:

k = ln(350/125) / 2

Now that we have k, we can plug it into either equation and solve for it. [tex]N_0[/tex]:

[tex]N_0[/tex] = 125 / [tex]e^{(2k)}[/tex]

(b) The bacterium population's exponential growth model is:

N = [tex]N_0[/tex] × [tex]e^{(kt)}[/tex]

Where [tex]N_0[/tex] = 125 / [tex]e^{(2k)}[/tex] and k = ln(350/125) / 2

(c) To calculate the number of bacteria present after 8 hours, we use the exponential growth model with t = 8:

N = [tex]N_0[/tex] × [tex]e^{(8k)}[/tex]

(d) To calculate the time when the bacterium count reaches 25,000, enter N = 25,000 into the exponentially growing model and solve for t:

25,000 = [tex]N_0[/tex] × [tex]e^{(kt)}[/tex]

t = ln(25,000 / [tex]N_0[/tex]) / k

However, in the absence of a specified growth rate constant (k) and starting population ([tex]N_0[/tex]), we are unable to determine a precise value for t.

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The question is -

The number of bacteria in the culture is increasing according to the law of exponential growth. There are 125 bacteria in the culture after 2 hours and 350 bacteria after 4 hours.

(a) Find the initial population.

(b) Write an exponential growth model for the bacteria population. (Let t represent time in hours)

(c) Use the model to determine the number of bacteria after 8 hours.

(d) After how many hours will the bacteria count be 25,000?

The y intercept represents the amount of snow in inches on his lawn at noon

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

The standard form of a linear equation is:

Ax + By = C

Where A, B and C are constants

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope and b is the y intercept

If y represents the number of inches of snow on the lawn at x minutes past noon.

The y intercept represents the amount of snow on his lawn at noon

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Simple Random sampling  as each student is getting equal opportunity to get selected.

Describe random sampling.

A selection of participants from a community are chosen at random by the investigator using simple random sampling, a sort of sampling techniques. Every individual in the population has the same chance of being chosen. Then, information is gathered from as much of this randomly selected subgroup as possible.

Which four forms of random sampling are there?

Simple random sampling, systematic sampling, stratified sampling, and cluster sampling are the four main random (probability) sampling techniques.

What benefit may simple random sampling provide?

The benefits of a simple random sample include its simplicity and accuracy of depiction. Simple random sampling is the easiest way to select a study sample from a bigger population.

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Answer:

56.52cm

Step-by-step explanation:

2r = 18cm

r = 9cm

[tex]c = 2r\pi[/tex]

C = 2 × 9 × 3.14

C = 56.52cm

One roti costs $20.00 and one pie costs $3.33.

Let x be the cost of one roti. Then, the cost of one pie is (10 - 2x) / 3.

Since the total cost is $10.00, we can set up an equation:

2x + (10 - 2x) / 3 = 10

Expanding the right-hand side:

2x + 3.33 - 2x = 10

0.33x = 6.67

Finally, dividing both sides by 0.33:

x = 20.00

So, one roti costs $20.00 and one pie costs (10 - 2 * 20) / 3 = $3.33.

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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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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 probability that 3 individuals have conditions caused by outside factors is 0.1496

The proportion of heart failures due to outside factors, p = 11% = 0.11

Sample size, n = 15

The formula for binomial distribution is:

                    P(x) = ⁿCₓ pˣ (1 - p)ⁿ⁻ˣ

Here, x = Number of heart failures.

We are asked to determine the probability that 3 individuals have conditions caused by outside factors

So, here x = 3

                    P(3) = ¹⁵C₃ p³ (1 - p)¹⁵⁻³

                    P(3) = ¹⁵C₃ (0.11)³ (1 - 0.11)¹²

                    P(3) = ¹⁵C₃ (0.11)³ (0.89)¹²

                    P(3) = 455 (0.11)³ (0.89)¹²

                    P(3) = 0.1496

Hence, the probability that 3 individuals have conditions caused by outside factors is 0.1496

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The solution is, The value of x where f(x) = g(x) is 3.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

Functions and values

According to the given question, we are to find the value of x for which the function f(x) is equal to g(x)

From the given table, we need to find the point where the values of f(x) = g(x). The value of x at this point is the solution.

Therefore from the table, the value of x where f(x) = g(x) is 3

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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 )

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:

12 nickles and 9 dimes

Step-by-step explanation:

First, let's use the first equation, n + d = 21, to solve for d in terms of n:

n + d = 21     [Subtract n from both sides]

d = 21 - n

Now that we have found d in terms of n, let's plug d into the second equation, 0.05n + 0.1d = 1.5:

0.05n + 0.1d = 1.5     [Plug in d]

0.05n + 0.1(21 - n) = 1.5     [Distribute 0.1 to (21-n)]

0.05n + 2.1 - 0.1n = 1.5     [Combine like terms]

-0.05n + 2.1 = 1.5     [Subtract 2.1 from both sides]

-0.05n = -0.6     [Divide both sides by -0.05]

n = 12

Now that we have found the amount of nickles Donna had, let's use the first equation, n + d = 21, to solve for d, the amount of dimes she used.

n + d = 21     [Plug in n]

12 + d = 21     [Subtract 12 from both sides]

d = 9

So, Donna must have bought her candy bar using 12 nickles and 9 dimes.

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The expression 81xy^4 - yx cannot be simplified

From the question, we have the following parameters that can be used in our computation:

81xy4 - yx

Express properly

So, we have the following representation

81xy^4 - yx

This expression can be rewritten a

81xy^4 - xy

There are no like terms in the above expression

This means that the expression cannot be simplified

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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 values of n in -15<3n<6 are -4, -3, -2, 1, 0 and 1

From the question, we have the following parameters that can be used in our computation:

-15<3n<6

Divide through by 3

So, we have the following representation

-5 < n < 2

The values in this range are -4, -3, -2, 1, 0 and 1

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Answer:87

Step-by-step explanation: