What is the perimeter of a rectangle with workings​

Answer:

23 Heads or Legs

Answer:

this question is incomplete

The correct statement is the first one:

f(0) = 2

g(-2) = 0

Here we can see the graph of two quadratic equations.

The orange one is g(x), and we can see that it has the vertex at (-2, 0).

And the blue one is f(x), we can see that the vertex is at (2, 0)

From, that, we coclude that:

g(-2) = 0

f(2) = 0

We also can see that the two have the sa,me y-intercept (0, 2), so:

f(0) = g(0) = 2

Then the correct statement is the first one:

f(0) = 2

g(-2) = 0

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The distance from point A to point B is approximately 16.64 units. None of the given options (A, B, C, D) match this value exactly, so there seems to be an error in the options provided.

To find the distance from point A to point B, we can use the distance formula in Euclidean geometry. The distance formula between two points (x1, y1) and (x2, y2) is given by:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, point A is (-8, -3) and point B is (6, 6). Plugging these values into the distance formula, we have:

distance = sqrt((6 - (-8))^2 + (6 - (-3))^2)

= sqrt((6 + 8)^2 + (6 + 3)^2)

= sqrt(14^2 + 9^2)

= sqrt(196 + 81)

= sqrt(277)

≈ 16.64

Thus, the distance between points A and B is roughly 16.64 units. Since none of the available options (A, B, C, or D) exactly match this value, there appears to be a problem with the options.

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Answer:

$6240

Step-by-step explanation:

given likelihoods:

sunny day = 14% = 0.14

cloudy day = 26% = 0.26

rainy day = 60% = 0.60

profits:

profit on a sunny day = $40,000

profit on a cloudy day = $14,000

Loss on a rainy day = -$5,000

expected profit = (probability of sunny day * profit on sunny day) + (probability of cloudy day * profit on cloudy day) + (probability of rainy day * loss on rainy)

expected profit = (0.14 * $40,000) + (0.26 * $14,000) + (0.60 * -$5,000)

=6240

Answer:

Step-by-step explanation:

Let's denote the length of the rectangle as 3x and the width as 2x, based on the given ratio.

The perimeter of a rectangle is given by the formula P = 2(length + width). In this case, we have:

P = 2(3x + 2x)

40 = 2(5x)

Now, let's solve for x:

40 = 10x

x = 40/10

x = 4

Now that we have the value of x, we can find the length of the rectangle:

Length = 3x = 3(4) = 12

Therefore, the length of the rectangle is 12.

The correct statement about the mean is:

The mean equals the sum of all observations divided by the number of observations.

The mean is a commonly used measure of central tendency. It is calculated by summing up all the observations and then dividing the sum by the total number of observations. It provides an average value that represents the typical value of the data set.

To calculate the mean, it is not necessary to order the observations from least to most. The order of the observations does not affect the mean calculation.

The mean is not necessarily a whole number. It can be a decimal or a fraction, depending on the data set and the values of the observations. The mean represents the balance point of the data set and can take on any real number value.

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The ordered pair given in the first row of the table can be written using function notation as (x, f(x)) = (-6, 8).

f(x) = -5 when x is 4.

In function notation, we represent the input value as 'x' and the corresponding output value as 'f(x)'.

Looking at the first row of the table, we see that when x is -6, the corresponding value of f(x) is 8.

Therefore, we can write this ordered pair as (-6, 8) in function notation.

Similarly, we can determine that f(x) = -5 when x is 4 by examining the second row of the table.

The value of f(x) is -5 when x is 4, so we can express it as f(4) = -5.

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(a) Starting at 12 and making 1/2 revolution clockwise, the hand stops at 6.

(b) Starting at 2 and making 1/2 revolution clockwise, the hand stops at 8.

(c) Starting at 5 and making 1/4 revolution clockwise, the hand stops at 8.

(d) Starting at 5 and making 3/4 revolution clockwise, the hand stops at 11.

To determine where the hand of a clock will stop, we need to consider the fractions of a revolution made by the hand starting from different positions.

(a) If the hand starts at 12 and makes 1/2 of a revolution clockwise, it will stop at 6.

This is because a half revolution corresponds to the hand moving from 12 to 6 on the clock face.

(b) If the hand starts at 2 and makes 1/2 of a revolution clockwise, it will stop at 8.

Again, a half revolution corresponds to the hand moving from 2 to 8 on the clock face.

(c) If the hand starts at 5 and makes 1/4 of a revolution clockwise, it will stop at 8.

A quarter revolution corresponds to the hand moving from 5 to 8 on the clock face.

(d) If the hand starts at 5 and makes 3/4 of a revolution clockwise, it will stop at 11.

A three-quarter revolution corresponds to the hand moving from 5 to 11 on the clock face.

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Answer:

  f(x +h) = 4x² +4h² +8xh +5x +5h +3

  (f(x+h) -f(x))/h = 4h +8x +5

  f'(x) = 8x +5

Step-by-step explanation:

For f(x) = 4x² +5x +3, you want the simplified expression f(x+h), the difference quotient (f(x+h) -f(x))/h, and the value of that at h=0.

Put (x+h) where h is in the function, and simplify:

  f(x+h) = 4(x+h)² +5(x+h) +3

  = 4(x² +2xh +h²) +5x +5h +3

  f(x +h) = 4x² +4h² +8xh +5x +5h +3

The difference quotient is ...

  (f(x+h) -f(x))/h = ((4x² +4h² +8xh +5x +5h +3) - (4x² +5x +3))/h

  = (4h² +8xh +5h)/h

  (f(x+h) -f(x))/h = 4h +8x +5

When h=0, the value of this is ...

  f'(x) = 4·0 +8x +5

  f'(x) = 8x +5

__

Additional comment

Technically, the difference quotient is undefined at h=0, because h is in the denominator, and we cannot divide by 0. The limit as h→0 will be the value of the simplified rational expression that has h canceled from every term of the difference. This will always be the case for difference quotients for polynomial functions.

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Answer:

Step-by-step explanation:

To recover your investment in 5 years or less, you would need to earn enough to cover the cost of going to school ($30,000) as well as make up for the lost salary over the 2 years of schooling ($45,000/year * 2 years = $90,000).

Therefore, the minimum salary you would need to earn upon earning your degree is the sum of the cost of going to school and the lost salary:

Minimum salary = $30,000 + $90,000 = $120,000.

In order to recover your investment in 5 years or less, you would need to earn a minimum salary of $120,000 per year.

To recuperate the total cost of $120,000 ($30,000 tuition + $90,000 forgone salary) over 5 years, you would need to earn $24,000 more per year on top of your original $45,000 salary. This implies that the minimum salary you need to earn after graduating is $69,000 per annum.

To determine the minimum salary, we first need to calculate your total forfeiture over the 2 years of school, which equates to real costs and opportunity costs. Firstly, the real cost is the tuition of $30,000. Secondly, the opportunity costs are the 2 years of salary you're forgoing, best understood as the wages you would've made if you hadn't gone to school. Assuming the salary of $45,000 per year, the total opportunity cost for the 2 years would be $90,000.

Therefore, the total investment is calculated as the sum costs of tuition and forgone salary i.e. $30,000 (tuition) + $90,000 (forgone salary) = $120,000. So to recover this investment in 5 years, you would need to earn an addition of $120,000 above your original salary. Meaning, you will have to recover $120,000 / 5 years = $24,000 per year on top of your initial salary to recover your total costs in the stated timeframe.

Therefore, the minimum salary you need to earn after earning your degree is equal to your original salary plus recovered investment per year: $45,000 (original salary) + $24,000 (increase) = $69,000. Hence, upon completion of your degree, you will have to earn at least $69,000 per year to recover your total investment within 5 years.

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The tangent line at that point is:

y = (-3/25)*x + 6/5

so m = -3/25, and b = 6/5

To find the slope at that point, we need to evaluate the derivative at that point.

y = 3/x

The derivative is:

y' = -3/x²

When x = 5, we have:

y' = -3/5² = -3/25

So that is the slope, m.

Now let's find the line.

The line must pass trhough the point (5, 3/5), then:

3/5 = (-3/25)*5 + b

3/5 = -3/5 + b

3/5 + 3/5 = b

6/5 = b

The equation of the line is:

y = (-3/25)*x + 6/5

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Answer:

See attachment for the graph of the hyperbola.

Step-by-step explanation:

Given equation:

[tex](x-7)^2-\dfrac{(y-4)^2}{9}=1[/tex]

As the x²-term of the given equation is positive, the transverse axis is horizontal, and so the hyperbola is horizontal (opening left and right). Note, if the y²-term was positive, the hyperbola would have been vertical.

The general formula for a horizontal hyperbola (opening left and right) is:

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Standard equation of a horizontal hyperbola}\\\\$\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1$\\\\where:\\\phantom{ww}$\bullet$ $(h,k)$ is the center.\\ \phantom{ww}$\bullet$ $(h\pm a, k)$ are the vertices.\\\phantom{ww}$\bullet$ $(h\pm c, k)$ are the foci where $c^2=a^2+b^2.$\\\phantom{ww}$\bullet$ $y=\pm \dfrac{b}{a}(x-h)+k$ are the asymptotes.\\\end{minipage}}[/tex]

Comparing the given equation with the standard equation:

To find the value of c, use c² = a² + b²:

[tex]\begin{aligned}c^2&=a^2+b^2\\c^2&=1+9\\c^2&=10\\c&=\sqrt{10}\end{aligned}[/tex]

The center is (h, k). Therefore, the center is (7, 4).

The formula for the loci is (h±c, k). Therefore:

[tex]\begin{aligned}\textsf{Loci}&=(h \pm c, k)\\&=(7 \pm \sqrt{10}, 4)\\&=(7- \sqrt{10}, 4)\;\;\textsf{and}\;\;(7 +\sqrt{10}, 4)\end{aligned}[/tex]

The formula for the vertices is (h±a, k). Therefore:

[tex]\begin{aligned}\textsf{Vertices}&=(h \pm a, k)\\&=(7 \pm 1, 4)\\&=(6, 4)\;\;\textsf{and}\;\;(8, 4)\end{aligned}[/tex]

The asymptotes are:

[tex]\begin{aligned}y&=\pm \dfrac{b}{a}(x-h)+k\\\\y&=\pm \dfrac{3}{1}(x-7)+4\\\\y&=\pm 3(x-7)+4\\\\\implies y&=3x-17\\\implies y&=-3x+25\end{aligned}[/tex]

Therefore:

The graph of the hyperbola (x - 7)² - (y - 4)²/9 = 1 is attached below

The graph of a hyperbola is a curve that consists of two separate branches, each resembling a symmetrical curve. The general equation for a hyperbola in standard form is:

[(x - h)² / a²] - [(y - k)² / b²] = 1

The center of the hyperbola is represented by the coordinates (h, k). The parameters a and b determine the size and shape of the hyperbola.

Based on the standard form equation, there are two types of hyperbolas:

1. Horizontal Hyperbola:

When the major axis is parallel to the x-axis, the hyperbola is horizontal. The equation in this case is:

[(x - h)² / a²] - [(y - k)² / b²] = 1

The graph of a horizontal hyperbola opens left and right. The branches are symmetric about the x-axis and the center (h, k) is the midpoint between the branches.

2. Vertical Hyperbola:

When the major axis is parallel to the y-axis, the hyperbola is vertical. The equation in this case is:

[(y - k)² / b²] - [(x - h)² / a²] = 1

The graph of a vertical hyperbola opens up and down. The branches are symmetric about the y-axis and the center (h, k) is the midpoint between the branches.

The graph of the given hyperbola is attached below.

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The width of the house on the plan is 0.615 meters.

To find the scale of the plan in the form 1:n, we can compare the measurements on the plan to the actual measurements of the house.

Length of the rectangle on the plan = 78.5 cm

Actual length of the house = 15.7 m

We need to convert the actual length of the house to the same unit as the length on the plan, which is centimeters.

1 meter = 100 centimeters

So, the actual length of the house in centimeters = 15.7 m [tex]\times[/tex] 100 cm/m = 1570 cm

Now, we can find the scale of the plan by dividing the length on the plan by the actual length of the house:

Scale = Length on the plan / Actual length of the house

= 78.5 cm / 1570 cm

Simplifying this fraction, we get:

Scale = 1/20

Therefore, the scale of the plan is 1:20.

To find the width of the house on the plan, we can use the same scale.

Width of the house in actual measurements = 12.3 m.

Width of the house on the plan = (Width of the house in actual measurements) / Scale

= 12.3 m / 20

= 0.615 m.

So, the width of the house on the plan is 0.615 meters.

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The inverse of the original statement is: "If the sum of the interior angles of a polygon is not more than 180°, then the polygon is a triangle."

The inverse of the conditional statement "If the sum of interior angles of a polygon is more than 180°, then the polygon is not a triangle" is: "If the sum of the interior angles of a polygon is not more than 180°, then the polygon is a triangle."
To find the inverse, we need to negate both the hypothesis and the conclusion of the original statement.
The hypothesis of the original statement is "the sum of the interior angles of a polygon is more than 180°". To negate this, we say "the sum of the interior angles of a polygon is not more than 180°".
The conclusion of the original statement is "the polygon is not a triangle". To negate this, we say "the polygon is a triangle".
In summary, the inverse of the original statement is "If the sum of the interior angles of a polygon is not more than 180°, then the polygon is a triangle."

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There are 70 ways a person can order a two-course meal from the given restaurant.

To determine the number of ways a person can order a two-course meal from a restaurant that offers 10 appetizers and 7 main courses, we can use the concept of combinations.

First, we need to select one appetizer from the 10 available options.

This can be done in 10 different ways.

Next, we need to select one main course from the 7 available options. This can be done in 7 different ways.

Since the two courses are independent choices, we can multiply the number of options for each course to find the total number of combinations.

Therefore, the number of ways a person can order a two-course meal is 10 [tex]\times[/tex] 7 = 70.

So, there are 70 ways a person can order a two-course meal from the given restaurant.

It's important to note that this calculation assumes that a person can choose any combination of appetizer and main course.

If there are any restrictions or limitations on the choices, the number of combinations may vary.

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Answer:

Step-by-step explanation:

12

Answer:

[tex]\textsf{The parabola has a vertex at $\left(\:\boxed{-3}\:,\boxed{-7}\:\right)$, has a p-value of $\boxed{-1}$ and it}[/tex]

[tex]\textsf{$\boxed{\sf op\:\!ens\;to\;the\;left}$\:.}[/tex]

Step-by-step explanation:

The given directrix of the parabola is x = -2, which is a vertical line.

The directrix is perpendicular to the axis of symmetry. Therefore, this means that the parabola has a horizontal axis of symmetry.

The focus of a parabola is a fixed point located inside the curve. The x-coordinate of the given focus is x = -4. As this is to the left of the directrix, it means that the parabola opens to the left.

The standard form of a horizontal parabola is:

[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]

where:

As the focus is (-4, -7), then:

[tex]\begin{aligned}(h+p, k)&=(-4,-7)\\\\\implies k&=-7\\\implies h+p&=-4\end{aligned}[/tex]

As the directrix is x = -2, then:

[tex]h - p=-2[/tex]

To find the value of h, sum the equations involved h and p to eliminate p:

[tex]\begin{array}{crcccr}&h &+& p& =& -4\\+&h& -& p& = &-2\\\cline{2-6}&2h&&& =& -6\\\cline{2-6}\\\implies &h&&&=&-3\end{array}[/tex]

To find the value of p, substitute the found value of h into one of the equations:

[tex]\begin{aligned}-3 - p&=-2\\p&=-3+2\\p&=-1\end{aligned}[/tex]    

Therefore, the values of h, k and p are:

The parabola has a vertex at (-3, -7), has a p-value of -1 and it opens to the left.

The parabola has a vertex at (-3, y), has p-value of 1 and it equation is

(x + 3)² = 4y.

To find the equation of the parabola with the given focus and directrix, we can use the standard form equation of a parabola:

(x - h)² = 4p(y - k)

where (h, k) is the vertex of the parabola and "p" is the distance from the vertex to the focus (and also from the vertex to the directrix).

Given:

Focus: (-4, -7)

Directrix: x = -2

1. Finding the vertex:

Since the directrix is a vertical line, the vertex lies on the line that is equidistant from the focus and directrix. In this case, it lies on the line x = (-4 + (-2))/2 = -3.

Therefore, the vertex of the parabola is (-3, y).

2. Finding the p-value:

The distance from the vertex to the focus (and also to the directrix) is the same. In this case, the distance is |-3 - (-4)| = 1.

Therefore, the value of "p" is 1.

3. Writing the equation of the parabola:

Using the vertex (-3, y) and the p-value of 1, we can write the equation of the parabola:

(x - h)² = 4p(y - k)

(x - (-3))² = 4(1)(y - y)

Simplifying, we get:

(x + 3)² = 4(y - y)

(x + 3)² = 4y

So, the equation of the parabola is (x + 3)² = 4y.

The vertex of the parabola is (-3, y) and the p-value is 1.

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33.) The volume of the given triangular prism would be= 36. That is option E.(NOTA)

To calculate the volume of a triangular prism, the formula that should be used is given as follows;

Volume= BH

where;

B= area of base = 1/2 × base×height

= 1/2×4×3

= 6

H= 6

Volume= 6×6= 36.

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The value of x in the right triangle using pthagorean theorem is 3√41.

The figure in the image is that of a right triangle with of its interior angle at 90 degrees.

Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c² = a² + b²

From the figure:

Hypotenuse c = 25

Leg a = 16

Leb b = x

Plug these values into the above formula and solve for x:

c² = a² + b²

25² = 16² + x²

625 = 256 + x²

x² = 625 - 256

x² = 369

Take the square root( we use the positive value because its dimension ).

x = √369

x = 3√41

Therefore, the value of x is 3√41.

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Common ratio of the geometric sequence 9/8, 3/4, 1/2,...,8/81 is 2/3 and the number of all terms in this sequence is 7.

As we know that,

Common ratio of any G.P. is a constant number that is multiplied by the previous term to obtain the next term.

So, r= (n+1)th term / nth term

where r ⇒ common ratio

          (n+1)th term⇒ succeeding term

          nth term⇒ preceding term

According to the given question, r = (9/8) / (3/4)

                                                       r = (2/3)

We also know,

Any term of a G.P. [nth term] can be obtained by the formula:

Tₙ= a[tex]r^{n-1}[/tex]

where, Tₙ= nth term

            a= first term of G.P.

            r=common ratio

Since last term of the G.P. is given to be 8/81; putting this in the above formula will yield us the total number of terms.

   Tₙ= a[tex]r^{n-1}[/tex]

⇒ (8/81) = (9/8) x ([tex]2/3^{n-1}[/tex])

⇒ (64/729)= ([tex]2/3^{n-1}[/tex])

⇒[tex](2/3)^{6}[/tex] = ([tex]2/3^{n-1}[/tex])

⇒ n-1 = 6

⇒ n = 7

∴ The total number of terms in G.P. is 7.

Therefore, Common ratio of the sequence 9/8, 3/4, 1/2,...,8/81 is 2/3 and the number of all terms in this sequence is 7.

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The Common Ratio for this geometric sequence is 2/3 and the total number of terms in the sequence is 6.

The given mathematical sequence appears to be a geometric sequence, which is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the Common Ratio. In a geometric sequence, you can find the Common Ratio by dividing any term by the preceding term.  

So in this case, the second term (3/4) divided by the first term (9/8) equals 2/3. Therefore, the Common Ratio for this geometric sequence is 2/3.

To find the total number of terms in this sequence we use the formula for the nth term of a geometric sequence: a*n = a*r^(n-1), where a is the first term, r is the common ratio, and n is the number of terms. This gives us: 8/81 = (9/8)*(2/3)^(n-1). Solving this for n gives us n = 6. Therefore, the total number of terms in this sequence is 6.

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The total number of times the digit "9" would have been written to number the entire photo album is 12 + 9 = 21 times.

To determine how many times the digit "9" would have been written to number all the pages of the photo album, we need to analyze the numbering pattern.

Since the album has 108 pages, we can observe that the numbers 1 to 9 are repeated 12 times (1-9, 10-19, 20-29, ..., 90-99) to cover the first 99 pages. Each repetition consists of ten numbers, and the digit "9" appears once in each repetition.

So, the digit "9" would have been written 12 times for the numbers 9, 19, 29, ..., 89 and 99.

However, we have an additional 9 pages to consider, which are 100, 101, 102, ..., 108. Each of these pages contains a single "9" in its numbering.

Therefore, the total number of times the digit "9" would have been written to number the entire photo album is 12 + 9 = 21 times.

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The true statement about the transformation is that the second trapezoid is a dilation of the first trapezoid with a scale factor of 2.

The given transformation involves two trapezoids with identical angle measures but different side lengths. Let's analyze the two trapezoids and determine the statement that is true about the transformation.

First Trapezoid:

Side lengths: 4, 2, 6, 2

Second Trapezoid:

Side lengths: 8, 4, 12, 4

To determine the relationship between the side lengths of the two trapezoids, we can compare the corresponding sides.

Comparing the corresponding sides:

4 / 8 = 2 / 4 = 6 / 12 = 2 / 4

We can observe that the corresponding sides of the two trapezoids have the same ratio. This indicates that the side lengths of the second trapezoid are twice the lengths of the corresponding sides of the first trapezoid. Therefore, the statement that is true about the transformation is:

The second trapezoid is a dilation of the first trapezoid with a scale factor of 2.

A dilation is a type of transformation that produces an image that is the same shape as the original figure but a different size. In this case, the second trapezoid is obtained by scaling up the first trapezoid by a factor of 2 in all directions.

This transformation preserves the shape and angle measures of the trapezoid but changes its size. The corresponding sides of the second trapezoid are twice as long as the corresponding sides of the first trapezoid.

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The direct labor cost included in the Preble Company's flexible budget for March is $819,000.

To find the direct labor cost included in the company's flexible budget for March, we shall estimate the actual direct labor cost incurred during the period.

Given:

Actual production and sales =n26,600 units

Actual direct labor rate = $13.00 per hour

Actual direct labor hours worked = 63,000 hours

Direct labor cost = Actual direct labor rate × Actual direct labor hours worked

Direct labor cost = $13.00/hour × 63,000 hours

Direct labor cost = $819,000

Hence, the direct labor cost included in the company's flexible budget for March would be $819,000.

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The systematic sample would be A. The city manager takes a list of the residents and selects every 6th resident until 54 residents are selected.

The random sample would be C. The botanist assigns each plant a different number. Using a random number table, he draws 80 of those numbers at random. Then, he selects the plants assigned to the drawn numbers. Every set of 80 plants is equally likely to be drawn using the random number table.

The cluster sample is C. The host forms groups of 13 passengers based on the passengers' ages. Then, he randomly chooses 6 groups and selects all of the passengers in these groups.

A systematic sample involves selecting items from a larger population at uniform intervals. A random sample involves selecting items such that every individual item has an equal chance of being chosen.

A cluster sample involves dividing the population into distinct groups (clusters), then selecting entire clusters for inclusion in the sample.

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In a sample of 5000 students, the mean GPA is 2.80 and their standard deviation is 0.35 and 1428 students score below 2.60.

To find the number of students scoring below 2.60, we need to calculate the area under the normal distribution curve to the left of this value.

First, we need to standardize the value of 2.60 using the z-score formula: z = (x - μ) / σ, where x is the value (2.60), μ is the mean (2.80), and σ is the standard deviation (0.35). Plugging in the values, we get z = (2.60 - 2.80) / 0.35 = -0.57.

Now, we can use a standard normal distribution table or a statistical calculator to find the area to the left of -0.57. Consulting a standard normal distribution table, we find that the area to the left of -0.57 is approximately 0.2857.

To calculate the number of students scoring below 2.60, we multiply this area by the total number of students in the sample: 0.2857 * 5000 ≈ 1428.5.

Since the number of students must be a whole number, we round down to 1428 students.

Therefore, approximately 1428 students score below 2.60 in the sample of 5000 students, assuming a normal distribution with a mean of 2.80 and a standard deviation of 0.35.

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a) The least squares regression line for the given data is y = -3.5358x + 87.2857.

b) The slope of -3.5358 indicates that for each additional day absent, the final grade is expected to decrease by approximately 3.5358 points on average.

c) The y-intercept of 87.2857 represents the estimated final grade when the number of absences is zero, implying that a student who did not miss any classes is expected to have a final grade of approximately 87.2857.

a) To find the least squares regression line, we need to determine the equation of the line in the form y = mx + b, where m represents the slope and b represents the y-intercept.

Let's calculate the necessary sums:

∑x = 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

∑y = 89.2 + 86.4 + 83.5 + 81.1 + 78.2 + 73.9 + 64.3 + 71.8 + 65.5 + 66.2 = 759.9

∑xy = (0 * 89.2) + (1 * 86.4) + (2 * 83.5) + (3 * 81.1) + (4 * 78.2) + (5 * 73.9) + (6 * 64.3) + (7 * 71.8) + (8 * 65.5) + (9 * 66.2) = 5079.6

∑[tex]x^2[/tex] = [tex](0^2) + (1^2) + (2^2) + (3^2) + (4^2) + (5^2) + (6^2) + (7^2) + (8^2) + (9^2)[/tex] = 285

[tex]\sum y^2 = (89.2^2) + (86.4^2) + (83.5^2) + (81.1^2) + (78.2^2) + (73.9^2) + (64.3^2) + (71.8^2) + (65.5^2) + (66.2^2) = 59718.63[/tex]

Using the formulas for the slope (m) and y-intercept (b):

m = (n∑xy - (∑x)(∑y)) / (n∑x^2 - (∑x)^2)

b = (∑y - m(∑x)) / n

Substituting the calculated values:

m = (10 * 5079.6 - (45 * 759.9)) / (10 * 285 - (45)^2)

b = (759.9 - m(45)) / 10

Calculating the values:

m ≈ -3.5358

b ≈ 87.2857

Therefore, the least squares regression line is y = -3.5358x + 87.2857.

b) The slope (-3.5358) represents the change in the final grade (y) for each additional day absent (x). This means that on average, for each additional day a student is absent, their final grade is expected to decrease by approximately 3.5358 points.

c) The y-intercept (87.2857) represents the estimated final grade when the number of absences (x) is zero. In other words, it is the predicted final grade for a student who did not miss any classes.

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Question

The following data represents the number of days absent, x, and the final grade, y, for a sample of college students at a community college.

No.of absences, x | 0 1 2 3 4 5 6 7 8 9

Final Grade, y | 89.2 86.4 83.5 81.1 78.2 73.9 64.3 71.8 65.5 66.2

a) Find the least squares regression line treating the number of absences as the explanatory variable and the final grade as the response variable.

b) Interpret the slope using complete sentences.

c) Interpret the y intercept using complete sentences.

Answer:

180 meters

Step-by-step explanation:

To find the perimeter of the actual swimming pool, you need to first find the length and width of the actual swimming pool by multiplying the length and width of the pictured swimming pool by the scale factor of 1200 cm.

Now that we know that the perimeter of the actual pool is 18000 centimeters, we need to convert that to meters! Keep in mind that:

Now we can divide 18000 by 100:

18000 cm ÷ 100 = 180 m

Therefore, the perimeter of the actual swimming pool is 180 m.

Answer:

17.5

Step-by-step explanation:

The triangle is an equilateral triangle since all sides are equal

Area of a equilateral triangle is:

[tex]ar(triangle) = \frac{a^2\sqrt{3} x}{4}[/tex]

[tex]=\frac{5^2\sqrt{3} }{4} \\\\=\frac{25\sqrt{3} }{4} \\[/tex]

the sde of the square = diameterof the circle(d)

d = 6

r = d/2 = 3

ar(circle) = πr²

= π * 3²

= 9π

= 9*22/7

= 198/7

ar(shaded region) = ar(circle)-ar(triangle)

[tex]= \frac{198}{7} - \frac{25\sqrt{3} }{4}[/tex]

= 17.5