The points on this graph represent a relationship between x- and y-values. Which statement about the relationship is true?

Line graph where line does not start at (0, 0) but further up y axis. 4 points are plotted in a line on graph.
CLEAR CHECK

It cannot be proportional because the straight line through the points does not go through the origin.


It cannot be proportional because no values are given.


It must be proportional because each time x increases by 3 units, y increases by 1 unit.


It must be proportional because the points lie in a straight line.

Answer:

an obtuse angle is an angle that is wider than 90⁰, 100⁰ for example is an obtuse angle

Answer:   width=8, length=24

Step-by-step explanation:

2(x+3x)=64

2x+6x=64

x=8

width (x)=8

length (3x)=24

perimeter=2(x+3x)=64

The 14th value in the ordered set is 21, not 89. Therefore, the student's claim is incorrect. The value 89 does not correspond to the 70th percentile in this set of values.

The 70th percentile is a measure that indicates the value below which 70% of the data falls. To determine the 70th percentile, we need to arrange the given set of values in ascending order.

The given set of values: 1 1 1 1 1 1 2 3 5 8 13 21 34 55 89 89 89 89 89 89

When we arrange the values in ascending order, we get: 1 1 1 1 1 1 2 3 5 8 13 21 34 55 89 89 89 89 89 89

To find the value at the 70th percentile, we calculate the index position by multiplying the percentile (70) by the total number of values (20) and dividing by 100:

70 * 20 / 100 = 14

The student's claim that 89 is at the 70th percentile is incorrect.

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Answer:

672 had dark hair, 592 had blond hair, and 48 had red hair

Step-by-step explanation:

To solve this problem, we need to first find the total number of people for each hair color based on the given ratio.

Let's start by finding the common factor that we can use to scale the ratio up to the total number of people, which is 1,312:

42 + 37 + 3 = 82

We can then divide 1,312 by 82 to get the scaling factor:

1,312 ÷ 82 = 16

This means that for every 16 people, there are 42 with dark hair, 37 with blond hair, and 3 with red hair.

To find the actual number of people with each hair color in the town meeting, we can multiply the scaling factor by the number of people for each hair color in the ratio:

Dark-haired people: 42 × 16 = 672

Blond-haired people: 37 × 16 = 592

Red-haired people: 3 × 16 = 48

Therefore, there are 672 people with dark hair, 592 people with blond hair, and 48 people with red hair at the town meeting.

Answer:

17 cans

Step-by-step explanation:

18 cans

7 are taken away

18-7 =11

Then we put 6 back on

11+6 = 17

There are now 17 cans

The required probability = 4/10 = 2/5. Answer: 2/5.

Given: A box contains five balls numbered 1, 2, 3, 4, and 5. Three balls are randomly selected without replacement.To find: Probability that the median of the values on the selected balls is less than 4.

Solution:The sample space for this experiment is given by the number of ways of selecting 3 balls out of 5, which is: `5C3 = 10`.

Possible outcomes of this experiment are: (1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 3, 4), (1, 3, 5), (1, 4, 5), (2, 3, 4), (2, 3, 5), (2, 4, 5), (3, 4, 5).

Now we need to find out the cases where the median is less than 4.

So, the median of (1, 2, 3) is 2, and the median of (1, 2, 4), (1, 3, 4), (2, 3, 4) is 3.

So, there are 4 cases where the median is less than 4.

So, the required probability = 4/10 = 2/5. Answer: 2/5.

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To answer this question, re-arrange the terms to be on one side of the equation.

Thus, the value of x is 1.

Answer:

x=1

Step-by-step explanation:

when x from -∞ to 2, it starts at a value close to -3( >-3) and increase until y = 5 and decrease from the too gradually approaching (>1)

How would you define range?

The difference between the highest and lowest values in statistics for a particular data collection is called the range. The range, for instance, will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, 3. The difference between the greatest and lowest observation might therefore also be used to determine the range.

f(x) = { 2ˣ⁺¹ -3                        

         {(-x+3)(x+1)/(x-2)(x-3)

      =  -(x-3)(x + 1)/(x-3)(x-2)

      = (x +1)/(x-2)

      = x- 2+ 3/x -2

      = 1 + 3/x - 2

a) range = (-3 , +∞ )

b) 2ˣ⁺¹  always  > 0  so   2ˣ⁺¹ - 3 > -3 ,  y = -3

        and x - 2 ≠0 , x≠2  , if  x>2 ,  1+ 3/x-2 > 1   ,  y = 1

c) when x from -∞ to 2, it starts at a value close to -3( >-3) and increase until y = 5 and decrease from the too gradually approaching (>1)

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According to the given information, the equation of the tangent line to f(x) at x = 1 is y = 4 + 5(x - 1). The value of h'(1) is 1.

In order to find h'(1), we need to differentiate the function h(x) = √f(x) with respect to x and then evaluate it at x = 1. Since h(x) is the square root of f(x), we can rewrite it as h(x) = f(x)^(1/2).

Applying the chain rule, the derivative of h(x) with respect to x can be calculated as h'(x) = (1/2) * f(x)^(-1/2) * f'(x).

Since we are interested in finding h'(1), we substitute x = 1 into the derivative expression. Therefore, h'(1) = (1/2) * f(1)^(-1/2) * f'(1).

According to the given information, the equation of the tangent line to f(x) at x = 1 is y = 4 + 5(x - 1). From this equation, we can deduce that f(1) = 4.

Substituting f(1) = 4 into the derivative expression, we have h'(1) = (1/2) * 4^(-1/2) * f'(1). Simplifying further, h'(1) = (1/2) * (1/2) * f'(1) = 1 * f'(1) = f'(1).

Therefore, h'(1) is equal to f'(1), which is given as 1.

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a) The equation for the directrix of the given parabola is y = -5.

b) The equation for the parabola is (y + 1) = -2/2(x - 5)^2.

a) To find the equation for the directrix of the parabola, we observe that the directrix is a horizontal line equidistant from the vertex and focus. Since the vertex is at (5, -1) and the focus is at (5, -3), the directrix will be a horizontal line y = k, where k is the y-coordinate of the vertex minus the distance between the vertex and the focus. In this case, the equation for the directrix is y = -5.

b) The equation for a parabola in vertex form is (y - k) = 4a(x - h)^2, where (h, k) represents the vertex of the parabola and a is the distance between the vertex and the focus. Given the vertex at (5, -1) and the focus at (5, -3), we can determine the value of a as the distance between the vertex and focus, which is 2.

Plugging the values into the vertex form equation, we have (y + 1) = 4(1/4)(x - 5)^2, simplifying to (y + 1) = (x - 5)^2. Further simplifying, we get (y + 1) = -2/2(x - 5)^2. Therefore, the equation for the parabola is (y + 1) = -2/2(x - 5)^2.

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The answer is that 84% of women are taller than 62 inches .

The given problem is a problem of normal distribution in mathematical statistics. This distribution is a continuous univariate distribution. Its density function is given by -

f(x)= \(\frac{1}{σ\sqrt{2\pi } }\)\(e^{\frac{-1}{2} }\)(\({\frac{x-u}{σ}}^{2}\))

Now the actual question is  what proportion of women are taller than the height at one standard deviation below the mean since that is the first quartile range.  

Following the statistical rules of the normal distribution, we know that 50% of women are taller than the mean height of 64.5 inches.

In addition to this, we know that 34% of women will have heights of between minus 1 standard deviation and the mean (62 and 64.5 inches). Adding these percentages together, we can determine that 84% of women are taller than 62 inches or minus 1 standard deviation.

Hence, 84% of women are taller than 62 inches or minus 1 standard deviation.

Please find the attached image.

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Answer:

SAS, because vertical angles are congruent.

Answer:

Domain: \(0\leq x\leq 6\)

Range: \(\{0, 12, 24, 36, 48, 60, 72\}\)

Step-by-step explanation:

Let \(y\) or \(f(x)\) be equal to the amount of plant food that remains after each day.

\(x\) be the number of days that have passed.

Total amount of plant food used is 72 mm.

Number of days the experiment goes on is 6 days.

Plant food used each day is \(\dfrac{72}{6}=12\ \text{mm}\).

So, the function will be

\(y=f(x)=72-12x\)

at

\(x=0,y=72\)

\(x=1,y=72-12\times 1=60\)

\(x=2,y=72-12\times 2=48\)

\(x=3,72-12\times 3=36\)

\(x=4,72-12\times 4=24\)

\(x=5,72-12\times 5=12\)

\(x=6,72-12\times 6=0\)

Value of \(x\) is the domain which is \(0\leq x\leq 6\).

Value of \(y=f(x)\) is the range which is \(\{0, 12, 24, 36, 48, 60, 72\}\).

A quadrilateral is a polygon with four sides. It is a two-dimensional shape formed by connecting four non-collinear points. The perimeter of the quadrilateral is 20 units.

The angles of a quadrilateral can vary, and it can have sides of different lengths. Examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses.

Quadrilaterals have certain properties and characteristics. Some common properties include:

Interior angles: The sum of the interior angles of a quadrilateral is always equal to 360 degrees.

Diagonals: A quadrilateral has two diagonals, which are line segments connecting opposite vertices. The diagonals of some quadrilaterals are perpendicular, while in others they intersect at a point inside the shape.

To find the perimeter of a quadrilateral with vertices at c (-2, 1), d (2, 4), e (5, 0), and f (1, -3), you can use the distance formula. The distance formula is given by:

d = √((x2 - x1)² + (y2 - y1)² )

So, let's calculate the distances between the vertices:

Distance between c and d:
d_cd = √((2 - (-2))² + (4 - 1)² )

Distance between d and e:
d_de = √((5 - 2)²  + (0 - 4)² )

Distance between e and f:
d_ef = √((1 - 5)² + (-3 - 0)² )

Distance between f and c:
d_cf = √((-2 - 1)²  + (1 - (-3))² )

Now, we sum the lengths of all four sides to find the perimeter:

Perimeter = CD + DE + EF + FC = 5 + 5 + 5 + 5 = 20

Therefore, the perimeter of the quadrilateral is 20 units.

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Answer:

75 % of the items lie.

Step-by-step explanation:

Upper quartile is the point below which 75 % of the items lie.

Answer:

-12

Step-by-step explanation:

Answer:

w = -12

Step-by-step explanation:

Given: w/-2 = 6

Rewriting to make it easier to see what is going on: \(\frac{w}{-2}\) = 6

Multiplying both sides by -2: w = -12

Have a nice day!

    I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

49 degrees could be an interpolation.

Step-by-step explanation:

For an interpolation, the data point in question needs to be in the middle of the given data points of the graph. Only the value 49 is in between all the points in our graph. The rest of the choice fall outside of the points.

Answer:

Step-by-step explanation:

First of all, I have a strong feeling that that is supposed to be

\(log_2(32)=y\) so I'm going to go with that. We can solve for y by rewriting that in exponential form. Exponential form and log form are inverses of each other. If the log form of an equation is

\(log_b(x)=y\), the exponential form of it is

\(b^y=x\). We will apply that here to solve for y:

\(2^y=32\)

which is asking us, "2 to the power of what equals 32?". We can use our calculator to raise 2 to consecutive powers til we reach the one that gives us a 32, or we could solve it by writing the 32 in terms of a 2:

\(2^y=2^5\)

Since both bases are the same, 2, then the exponents are equal to one another. y = 5. This is an important rule to remember while solving either log or exponential equations.

The constant of proportionality in table four is -1/3

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".

In each of the table, we can check if proportionality exists.

In the first table, there's no proportionality.

In the second table, there's no proportionality

In the third table, there's no proportionality

In the fourth table, proportionality exist here which we can find the constant of proportionality.

When x = 6, y = -2

y = ax

a = constant of proportionality

-2 = a(6)

a = -1/3

The constant of proportionality is -1/3

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The reciprocal (inverse or indirect quote) for the given exchange rates is as follows:

USO/DKK: The reciprocal exchange rate is 0.1557 DKK/USO.

GBP/NZD: The reciprocal exchange rate is 0.4898 NZD/GBP.

USO/INR: The reciprocal exchange rate is 0.0226 INR/USO.

To calculate the reciprocal quote, we take the reciprocal of the given exchange rate. For example, for USO/DKK with an exchange rate of 6.4270 DKK per USO, the reciprocal is 1 divided by 6.4270, which equals 0.1557 DKK per USO.

Similarly, for GBP/NZD with an exchange rate of 2.0397 NZD per GBP, the reciprocal is 1 divided by 2.0397, which equals 0.4898 NZD per GBP.

Finally, for USO/INR with an exchange rate of 44.333 INR per USO, the reciprocal is 1 divided by 44.333, which equals 0.0226 INR per USO.

These reciprocal quotes represent the inverse of the original exchange rates.

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Complete question: Calculate the reciprocal (inverse or indirect quote) for the following currency pairs:
1. USO/DKK: 1/6.4270 or DKK/USO: 1/350
2. GBP/NZD: 1/2.0397 or NZD/GBP: 1/0.7000
3. USO/INR: 1/44.333 or INR/USO: 1/44.333

Part A: Approximation of f(2) using Euler's method with two steps of equal size is (1 + 9k) + k(1 + 9k)(1 - 9k). Part B: f "(0) in terms of k and y is 8k.

Part A: To approximate f(2) using Euler's method with two steps of equal size, we need to find the values of f(x) at x = 0, x = 1, and x = 2.

Given the differential equation:

y' = ky(10 - y)

Using Euler's method with a step size of h, the approximation formula is:

f(x + h) ≈ f(x) + hf'(x)

Let's calculate the values using two steps of equal size (h = 1):

x = 0, f(0) = 1 (given initial condition)

f'(0) = k(1)(10 - 1) = 9k

f(1) ≈ f(0) + hf'(0) = 1 + 1(9k) = 1 + 9k

x = 1, f(1) ≈ 1 + 9k

f'(1) = k(1 + 9k)(10 - (1 + 9k)) = k(1 + 9k)(1 - 9k)

f(2) ≈ f(1) + hf'(1) = (1 + 9k) + 1(k)(1 + 9k)(1 - 9k) = (1 + 9k) + k(1 + 9k)(1 - 9k)

Therefore, the approximation of f(2) in terms of k using Euler's method with two steps is (1 + 9k) + k(1 + 9k)(1 - 9k).

Part B: To find f "(0) in terms of k and y, we need to differentiate the given differential equation with respect to x.

Differentiating y' = ky(10 - y):

y" = k(10 - y) + ky(-1)

Simplifying:

y" = 10k - ky - ky

y" = 10k - 2ky

Substituting the initial condition f(0) = 1 into the equation:

f "(0) = 10k - 2k(1) = 10k - 2k = 8k

Therefore, f "(0) in terms of k and y is 8k.

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Answer:

1/2

Step-by-step explanation:

It's a reduction; the scale factor is 1/3. It's a reduction; the scale factor is 1/2.

a. To find the Maclaurin series for f(x) = 5e^-2x, we first need to find the derivatives of the function.

f(x) = 5e^-2x

f'(x) = -10e^-2x

f''(x) = 20e^-2x

f'''(x) = -40e^-2x

The Maclaurin series for f(x) can be written as:

f(x) = Σ (n=0 to infinity) [f^(n)(0)/n!] x^n

The first four nonzero terms of the Maclaurin series for f(x) are:

f(0) = 5

f'(0) = -10

f''(0) = 20

f'''(0) = -40

So the Maclaurin series for f(x) is:

f(x) = 5 - 10x + 20x^2/2! - 40x^3/3! + ...

b. The power series using summation notation can be written as:

f(x) = Σ (n=0 to infinity) [f^(n)(0)/n!] x^n

f(x) = Σ (n=0 to infinity) [(-1)^n * 10^n * x^n] / n!

c. To determine the interval of convergence of the series, we can use the ratio test.

lim |(-1)^(n+1) * 10^(n+1) * x^(n+1) / (n+1)!| / |(-1)^n * 10^n * x^n / n!|

= lim |10x / (n+1)|

As n approaches infinity, the limit approaches 0 for all values of x. Therefore, the series converges for all values of x.

The interval of convergence is (-infinity, infinity).

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Answer:

52.22

Step-by-step explanation:

→ Write down which length is not given

Hypotenuse

→ Identify a formula without hypotenuse in it

T = O ÷ A

→ Rearrange formula to find assigned length

Opposite = Tan ÷ Adjacent

→ Substitute in the numbers

tan ( 43 ) ÷ 56 = 52.22

To find \(\( (4 \sqrt{3}+4i)^3 \)\) using De Moivre's Theorem, we can first express the complex number in trigonometric form. The given complex number is\(\( 4 \sqrt{3}+4i \)\), which can be written as \(\( 8(\frac{\sqrt{3}}{2} + \frac{1}{2}i) \)\).

In trigonometric form, the complex number \(\( a+bi \)\) can be expressed as\(\( r(\cos(\theta) + i\sin(\theta)) \)\), where \(\( r \)\) is the magnitude of the complex number and \(\( \theta \)\) is its argument or angle.

For \(\( 8(\frac{\sqrt{3}}{2} + \frac{1}{2}i) \)\), the magnitude \(\( r \)\) can be calculated as \(\( \sqrt{(\frac{\sqrt{3}}{2})^2 + (\frac{1}{2})^2} = 1 \)\) and the argument \(\( \theta \)\) can be determined as \(\( \tan^{-1}(\frac{1}{\sqrt{3}}) = \frac{\pi}{6} \)\).

Now, we can use De Moivre's Theorem, which states that\(\( (r(\cos(\theta) + i\sin(\theta)))^n = r^n(\cos(n\theta) + i\sin(n\theta)) \)\).

Applying De Moivre's Theorem, we have\(\( (4 \sqrt{3}+4i)^3 = 8^3(\cos(3\cdot\frac{\pi}{6}) + i\sin(3\cdot\frac{\pi}{6})) \)\).

Simplifying the expression, we get  \(\( 512(\cos(\frac{\pi}{2}) + i\sin(\frac{\pi}{2})) \)\).

In standard form, the answer is \(\( 512i \)\).

In summary, using De Moivre's Theorem, we found that \(\( (4 \sqrt{3}+4i)^3 \) is equal to \( 512i \)\). By expressing the complex number in trigonometric form, applying De Moivre's Theorem, and simplifying the expression, we determined the final answer.

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In a linear regression model, the variable (or variables) used for predicting or explaining values of the response variable are known as the  independent variable. It(they) is(are) denoted by x.

The correct answer is an option (d)

For given question,

The variable that researchers are trying to explain or predict is called the

response variable. It is also sometimes called the dependent variable

because it depends on another variable.

The variable which is used to predict the response variable is known as the explanatory variable. It is also called as an independent variable because it does not depend on another variable.

In regression, the order of the variables is very important.

The explanatory variable (or the independent variable) always belongs on the x-axis. The response variable (or the dependent variable) always belongs on the y-axis.

Therefore, in a linear regression model, the variable (or variables) used for predicting or explaining values of the response variable are known as the  independent variable. It(they) is(are) denoted by x.

The correct answer is an option (d)

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