Two systems of equations are given below.
For each system, choose the best description of its solution.
If applicable, give the solution.

Solving the following expression (4x4-7x3+7x2-12x+15)/(x-1) yields the result -7x2 + 4 + 19/ in the form q(x)+r(x)/b(x) (x-1).

It is permissible to multiply, divide, add, or subtract in mathematics. The following is how an expression is put together: Number, term, and mathematical operator Three components of a numerical method include numbers, variable, and processes (such as addition, subtraction, multiplication or division etc.) It is possible to oppose expressions and words. An expression, often known as an analytical form, is any mathematics statement that contains variables, values, and an arithmetic procedure between them. For instance, the word m in the balanced formula is separated from the terms 4m and 5 by that of the arithmetic symbol +, as is the term m in the expression 4m + 5.

given

Given expression  is (4x⁴-7x³+7x²-12x+15)/(x-1)

then dividing this

=4x⁴/x-1-7x³/x-1+7x²/x-1-12x/x-1+15/x-1

=4x³-3x²+4x-8+7/x-1  in form of  q(x)+r(x)/b(x)

= 4x⁴/x-1-7x³/x-1+7x²/x-1-12x/x-1+15/x-1

= -7x² + 4 + 19/(x-1)

Solving the following expression (4x4-7x3+7x2-12x+15)/(x-1) yields the result -7x2 + 4 + 19/ in the form q(x)+r(x)/b(x) (x-1).

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The correct measure of variation for best to describe this distribution is,

⇒ interquartile range

Option B is true.

For a data set has outliers and variability is often summarized by a statistic called the interquartile range, which is the difference between the first and third quartiles.

Given that;

The dot plot shows the ages of the 20 people currently in Ms. Jens classroom.

Hence, To describe this distribution we can use the interquartile range.

Thus, The correct measure of variation for best to describe this distribution is,

⇒ interquartile range

Option B is true.

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As a result, the answers to the above quadrilateral issue are A.5, B.2, 3, C.-1/5, and D.2/3.

In terms of the geometry, a quadrilateral is really a four-sided polygon with four corners and four corners. Its origins originate from the Latin terms tetra and latus (meaning "side"). A rectangle is a this double form with four sides, 4 vertices, with four corners. Two main types of convex and convex exist. Convex bedbugs or bed bug also have a number of subclasses, such as trapezoids, parallelograms, quarters, rhombuses, and squares. Corresponding points come in many irregular configurations, such as quadrilaterals, trapezoids, rectangles, kites, square, and rhombuses.

given

The vertices of the quadrilateral ABCD are A(-4, -5), B(-3, 0), C(0, 2), and D. (5, 1).

We need to determine whether ABCD is a trapezoidal shape or not.

We are known that a trapezoid has one set of parallel opposed sides, making it a quadrilateral. Moreover, the slopes of two parallel lines are equal.

To start, the slopes of sides AB, BC, CD, and DA will be calculated.

It has

The incline for

AB =0+5/ -3+4

5. In the first step.

Step 2: The slope in BC is

=> 2-0 / 0+3

=> 2/3.

Step 3: The CD's gradient is

1-2/5-0 is equivalent to -1/5.

The gradient of DA is equal to in step four.

=>-5.1/-4.4/2.3

=>2/3.

As a result, the answers to the above quadrilateral issue are A.5, B.2, 3, C.-1/5, and D.2/3.

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The length of the shorter pipe will be 1.065 meters.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that a plumber had two pipes. The ratio of the length of the longer pipe to the shorter pipe was 9:2.

When he cut 1.65m from the longer pipe, the remaining length was 3 times that of the shorter pipe.

L / S = 9 / 2

L - 1.65 = 3S

4.5S - 1.65 = 3S

1.5S = 1.65

S = 1.065 meters

Hence, the measure of the short pipe will be 1.065 meters.

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The required answers are

i) -65.6

ii) -64.8

iii) -64

iv) -64

The pace at which an object's position changes in relation to a frame of reference and time is known as its velocity.

Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction.

Its SI equivalent is the metre per second (ms-1). A body is considered to be accelerating if its velocity changes, either in magnitude or direction.

Now in the given question,

1. Average velocity

When t=2

i. [2, 2.1]

= y(2.1) - y(2) / 2.1 - 2

= 205 - 16(2.1)^2 - 205 + 16(2)^2 / 0.1

= 205 - 16*4.41 - 205 +16(4) / 0.1

= -70.56 +64 / 0.1

= -6.56 /0.1

= -65.6

ii. [2, 2.05]

= y(2.05) - y(4) / 4.05 - 4

= 205 - 16(2.05)^2 - 205 +16(2)^2 / 0.05

= 205 - 16*4.2025 - 205 + 16(4) / 0.05

= -3.24 / 0.05

= -64.8

iii. [2, 2.01]

= y(2.01) - y(2) / 2.01 - 2

= 205 - 16(2.01)^2 - 205 + 16(2)^2 / 0.01

= 205 - 16*4.0401 - 205 + 16(4) / 0.01

= -64.64 + 64 / 0.01

= -0.64 / 0.01

= -64

iv. Instantaneous velocity

y = 205 - 16t^2

dy/dx = -32t

Considering t = 2

Instantaneous velocity after 2 seconds = -32(2)

Instantaneous velocity after 2 seconds = -64

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Step-by-step explanation:

The definite integral of (sin(x))^3 from 0 to π can be evaluated using a trigonometric identity.

∫_0^π (sin(x))^3 dx = -cos(x)(sin(x))^2 |_0^π

Using the fact that sin(0) = 0 and sin(π) = 0, we have:

-cos(x)(sin(x))^2 |_0^π = -cos(π)(sin(π))^2 + cos(0)(sin(0))^2

= 0 - (-1)(0)^2 = 0

Therefore, the definite integral of (sin(x))^3 from 0 to π is equal to 0.

Part A: β₂ = β₁ + 10 log₁₀ (f)

Part B: Δβ = 20 log10 (d₁/d₂)

This can be solved using the concept of sound intensity.

While amplitude is the distance between a wave's resting position and its crest, sound intensity is defined as the sound power per unit area. The power carried by sound waves per unit area in a direction perpendicular to that region is known as sound intensity or acoustic intensity. The watt per square metre is the SI measure of intensity that includes sound intensity.

Part A:

β₂ - β₁ = 10 log₁₀ (I₂/I₁)

given that : I₂ = f × I₁

hence, I₂/I₁ = f

so the equation becomes:

β₂ - β₁ = 10 log₁₀ (f)

β₂ = β₁ + 10 log₁₀ (f)

Part B:

P = Power by the source

I₁= intensity at distance d1 = P/(4πd₁²)

I₂ = intensity at distance d2 = P/(4πd₂²)

Δβ = β₂ - β₁ = 10 log₁₀ (I₂/I₁)

β₂ - β₁ = 10 log₁₀ ((P/(4πd₂²))/(P/(4πd₁²)))

Δβ = 10log₁₀  ((d₁/d₂)²)

Δβ = 20log₁₀ (d₁/d₂)

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The probability that a randomly selected Atlantic cod has a length of 53.68 cm or less is given by the equation P ( x < 53.68 ) = 0.8439

The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.

The Z-score is calculated using the formula:

z = (x - μ)/σ

where z: standard score

x: observed value

μ: mean of the sample

σ: standard deviation of the sample

Given data ,

Let the probability that a randomly selected Atlantic cod has a length of 53.68 cm or less be represented as P

Now , the equation will be

The observed value of x = 53.68 cm

The mean of the sample μ = 49.9 cm

The standard deviation of the sample σ = 3.74 cm

Now , z-score is calculated using the formula:

z = (x - μ)/σ

Substituting the values in the equation , we get

z = ( 53.68 - 49.9 ) / 3.74

z = 1.0107

Now ,the p value from the z table is

P ( x < 53.68 ) = 0.84392

And , the probability is P ( x < 53.68 ) = 84.392 %

Hence , the probability is 84.392 %

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Let the point of A be (x,y)Then, (2x−4,2y+19)=(2,8)2x−4=2,2y+19=8x=8,y=−3So, the point A is (8,−3)(b) Let the point B be (x,y)Then,  (2x−1,2y+2)=(−2,4)2x−1=−2,2y+2=4x=−3,y=6So, point B is (−3,6)

I hope it helps mate

Have a nice day

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Answer:

What I did was:

Number of possible outcomes when three science papers are together: 3!×16!

Number of possible outcomes when two science papers are together: 2!×17!

Therefore, the answer is 18!−3!×16!−2×17!

I feel like there's some faulty logic in the second line. Correct answer is 4.39×10 15th

.

Answer:

it takes 0.30769 days or 7.3846 hours for the light bulb to consume 5850 watt-hours.

Step-by-step explanation:

To solve for the time, we can set up a proportion:

1800 watt-hours / day = X / 5850 watt-hours

Cross-multiplying, we get:

1800 watt-hours * 1 day = X * 5850 watt-hours

Simplifying, we get:

X = (1800 watt-hours * 1 day) / 5850 watt-hours

X = 0.30769 days

To convert to hours, we can multiply by 24:

X = 0.30769 days * 24 hours/day

X = 7.3846 hours

Therefore, it takes 0.30769 days or 7.3846 hours for the light bulb to consume 5850 watt-hours.

The range of possible side lengths that satisfy the these conditions is given as follows:

34.5 < s < 46.5.

The perimeter of a square of side length s is given by the multiplication of 4 by s, as follows:

P = 4s.

Hence, for a square with perimeter of 138 inches, the side length is given as follows:

4s = 138

s = 138/4

s = 34.5 inches.

For a square with perimeter of 186 inches, the side length is given as follows:

4s = 186

s = 186/4

s = 46.5.

Hence the interval is given as follows:

34.5 < s < 46.5.

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A: The reasonable domain to plot the growth function would be all positive integers for the number of days, d, since the growth occurs over time.

B: The y-intercept of the graph of the function f(d) represents the initial radius of the algae when d = 0. In this case, the y-intercept is 9 mm.

C: To find the average rate of change of the function from d = 3 to d = 9, we need to find the difference in the radius of the algae at d = 9 and d = 3 and divide by the difference in the number of days.

f(9) = 9(1.04)^9 = 12.81 mm

f(3) = 9(1.04)^3 = 10.46 mm

Average rate of change = (12.81 - 10.46) / (9 - 3) = 0.71 mm/day

The average rate of change represents the average amount by which the radius of the algae increases each day from d = 3 to d = 9.

In the polynomial f(x) = 3x² - 2x + 5, f(0) is solved to get -2

From the equation of the tangent line

m= -2

b = 5

The derivative of the polynomial f(x) = 3x² - 2x + 5 is solved to be

f'(x) = 2(3)x - 1(2)

f'(x) = 6x - 2

f(0) = -2

Equation of the tangent to the parabola f(x) = 3x² - 2x + 5

f'(x) = 6x - 2 at x = 0, f'(x) = -2 hence the slope, m is -2

Using the point slope formula for (0, 5)

(y - 5) = m (x - 0)

y - 5 = -2x - 0

y = -2x + 5

comparing with y = mx + b

m = -2 and b = 5

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Answer:

330

Step-by-step explanation:

the actual answer is 328.77. 15% was 42.88

Answer:

330$

Step-by-step explanation:

the actual answer is 330$ it is true if you not believe then go

The area of the shaded region is 13.76 square meters.

Basically, we have the area of a square minus 4 times the area of the quarter of a circle of radius of 4m.

Remember that for a square of side length S the area is:

A = S^2

And the area of a quarter of a circle of radius R is:

A' = pi*R^2/4

Then the area of the shaded region is:

area = (8m)^2 - 4*(3.14*(4in)^2/4)

area = 64 m^2 - 50.24 m^2

area = 13.76 m^2

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The volume of a sphere of radius 5 yd is 523.33 yd³.

What is the volume?

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.

We have given,

the radius of a sphere is 5 yd,

To Find: the volume of the sphere solid

So,

Sphere volume = 4/3 πr³

= 4/3 * 3.14 * (5)³

= 4/3 * 3.14 * 125

= 523.33 yd³

Hence, the volume of a sphere of radius 5 yd is 523.33 yd³.

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Answer:

2

Step-by-step explanation:

To find the slope when given two points, we can use the formula

m = ( y2-y1)/ (x2-x1)

    = ( 3- -9)/( 5 - -1)

   = ( 3+9) / ( 5+1)

    = 12/6

     = 2

The slope is 2.

the volume of a sphere:

V=[tex]\frac{4\pi r^3}{3} =\frac{4*3.14*13^3}{3}[/tex]≈9198.106

Note that:
a) This is a cross-sectional observational study because the data was collected from a single point in time and the observations were made without any manipulation of the variables by the researchers.

b) The explanatory variable in the study is the method of delivery (Caseload midwifery, Standard hospital care, Private obstetric care).

c) The two response variables in the study are the rate of vaginal deliveries (58.5%, 48.2%, 30.8%) and the cost of delivery ($3903.78, $5279.23, $5413.69). The rate of vaginal deliveries is a qualitative variable as it is a categorization of the type of delivery, while the cost of delivery is a quantitative variable as it is a measure of the amount of money spent on delivery.

It is to be noted that a cross-sectional observational study is a type of study in which data is collected from a single point in time without any manipulation of variables by the researchers.

The data collected provides a snapshot of the variables at that point in time.

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So, the growth rate for each year, x%, can be calculated using the above formula if the population of Nashville for a specific year, f(x)= (ln(f(x) / 10,000) / ln(1.15)) * 100, is known.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

Here,

The expression f(x)=10,000(1.15)^x represents the population of Nashville each year, where x is the number of years after a certain reference point. The growth rate for each year can be found by taking the natural logarithm of the factor (1.15) in the expression:

ln(1.15^x) = ln(f(x) / 10,000)

x ln(1.15) = ln(f(x) / 10,000)

x = ln(f(x) / 10,000) / ln(1.15)

The value of x represents the growth rate as a percentage, so we need to multiply it by 100 to get the percentage:

x = (ln(f(x) / 10,000) / ln(1.15)) * 100

So, the growth rate for each year, x%, can be calculated using the above formula if the population of Nashville for a specific year, f(x)= (ln(f(x) / 10,000) / ln(1.15)) * 100, is known.

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Answer:

1. See below.

2. See attachment.

3. See below.

Step-by-step explanation:

Definition of variables:

A rectangle has two pairs of parallel sides of equal length.

Therefore, the equation for the perimeter of a rectangle is:

[tex]P=2(w+l)[/tex]

If the perimeter is 20 meters then:

[tex]\implies 2(w+l)=20[/tex]

[tex]\implies w+l=10[/tex]

If the side lengths are whole numbers, then the length and width are restricted to whole numbers from 1 to 9 (inclusive).

The equation for the area of a rectangle is:

[tex]A =w\cdot l[/tex]

Table

[tex]\begin{array}{|c|c|c|}\cline{1-3}\vphantom{\dfrac12}\textsf{width, m}&\textsf{length, m}&\textsf{Area, m$^2$}\\\cline{1-3}\vphantom{\dfrac12}1&9&9\\\cline{1-3}\vphantom{\dfrac12}2&8&16\\\cline{1-3}\vphantom{\dfrac12}3&7&21\\\cline{1-3}\vphantom{\dfrac12}4&6&24\\\cline{1-3}\vphantom{\dfrac12}5&5&25\\\cline{1-3}\vphantom{\dfrac12}6&4&24\\\cline{1-3}\vphantom{\dfrac12}7&3&21\\\cline{1-3}\vphantom{\dfrac12}8&2&16\\\cline{1-3}\vphantom{\dfrac12}9&1&9\\\cline{1-3}\end{array}[/tex]

To create a graph of the data, plot the length along the x-axis and the area along the y-axis.  Plot the following points:

The shape of the graph is a parabola that opens downwards.

Its vertex is (5, 25) and its axis of symmetry is x = 5.

This step pattern of  7, 5, 3, 1, ... is apparent in the graph; as you move away from the vertex in the x-direction, the graph goes down by 7, then 5, then 3, etc.  This is the step pattern of a parabola that opens downwards.

There is an axis of symmetry on the graph at the side length value when the width and length are the same (x = 5).

The required individual functions are given as g(x) = x⁴- 6 and f(x) = [tex]\sqrt[7]{x}[/tex].

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given funciton
h(x) = (f o g) (x)

Where g(x) = x⁴- 6 and h(x) = [tex]\sqrt[7]{x^4-6}[/tex]

Since, put h(x) ⇒ f(x) and  g(x) = x⁴- 6
f(x) =  [tex]\sqrt[7]{g(x)}[/tex]

Again put g(x) ⇒ x
f(x) = [tex]\sqrt[7]{x}[/tex]

Thus, the required individual functions are given as f(x) = x⁴- 6 and g(x) = [tex]\sqrt[7]{x}[/tex].

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The lion is right. When a preimage has parallel lines, these lines will remain parallel under a rotation, translation, and reflection transformation.

This property is known as parallelism preservation. A rotation preserves parallelism because it does not change the orientation of the lines. A translation preserves parallelism because it moves all the points on the lines by the same distance and in the same direction. A reflection preserves parallelism because it flips the preimage across a line, which does not change the relative distances between points on the parallel lines.

Therefore, the image of a preimage with parallel lines under a combination of rotation, translation, and reflection transformations will also have corresponding parallel lines.

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The unit vector with positive first component that is orthogonal to the plane passing through the points is 63i - 63j + 0k.

What is a unit vector?

A measurement that combines magnitude and direction is called a vector. A vector having magnitude 1 is referred to as a unit vector.

We are given three points P, Q and R.

The two vectors PQ and PR will lie on the plane through the three given points P(3, 0, 1), Q(4, -2, 1) & R(5, 3,-1).

The vector PQ = (9, 9, 9) and PR = (9, 9, 16) .

Therefore, the required vector is

N = PQ × PR

N = 63i - 63j + 0k

Hence, the unit vector with positive first component that is orthogonal to the plane passing through the points is 63i - 63j + 0k.

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The probability that a person lives with another person, given that they live in an apartment, is approximately 0.664.

We need to utilise conditional probability to determine the likelihood that a person lives with another person given that they reside in an apartment.

Let's define the subsequent occasions:

A: at least one other person lives with the individual.

B: The resident is an apartment dweller.

The probability that a person shares a home with at most one other person, assuming that they reside in an apartment, is P(A|B).

We are aware of:

The probability that someone resides in an apartment is P(B) = 329/837.

The probability that a person shares a home with at most one other person, given that they reside in an apartment, is given by P(A|B) = 218/329.

P(A|B) can be calculated using Bayes' theorem as follows:

P(A|B) equals P(B|A)*P(A)/P (B)

We may calculate P(B|A), the probability that an individual resides in an apartments given that they share a residence with at most one other person, using the following formula:

P(A and B) = P(B|A) (A)

We are aware of:

The probability that someone lives in an apartment with at most one other person is P(A and B) = 218/837.

The probability that someone lives with at most one other person is P(A) = 629/837.

By entering these values, we obtain:

P(B|A) = (218/837) / (629/837) = 218/629

Now that all the numbers have been entered, we can calculate P(A|B):

P(A|B) = (218/629) * (629/837) / (329/837) = 0.664

Given that they reside in an apartment, the probability that a person lives with another individual is roughly 0.664.

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The test static value for the stocks is obtained as 3.482.

What is proportion?

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.

It is given that -

The number of stocks n = 76

X = Number of stocks that got increased in price = 36

p = Proportion of stocks that got increased in price.

The formula for p is p = X/n.

Substitute the values in the equation -

p = 76/36 = 2.11111

Now find the value for q -

q = 1 - p

= 1 - 2.11111

= -1.11111

P=0.3

Q = 1 - P

= 1 - 0.3

= 0.7

Now, the values for H0 and H1 are -

H0 : P = 0.3

H1 : P > 0.3

Under H0, the test statistic is given by -

Z = (p - P)/√(PQ/n)

Substitute the values in the equation -

Z = (2.11111 - 0.3)/√(0.3 × 0.7/76)

Z = 1.81111 /√0.002763

Z = 1.81111 /0.052

Z = 3.482

Therefore, test statistic is 3.482.

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Answer:

Step-by-step explanation:

0