A small liberal arts college in the Northeast has 200 freshmen. Sixty of the freshmen are education majors. Suppose thirty freshmen are randomly selected (without replacement).
Find the standard deviation of the number of education majors in the sample. Round your answer to two decimal places, if necessary.

Answer:

  see below

Step-by-step explanation:

You want the piecewise function that gives straight line segments between domain boundary points (-8, 5), (-2, -9), (1, -2), (8, 4).

The two-point equation for the slope of a line is ...

  m = (y2 -y1)/(x2 -x1)

For the first pair of points, the slope is ...

  m = (-9 -5)/(-2 -(-8)) = -14/6 = -7/3

The attached calculator image shows the computation of slope for the other two segments. Those slopes are 7/3 and 6/7.

The slope-intercept form of the equation for a line can be rearranged to give the y-intercept:

  y = mx + b

  b = y - mx

In the attached, we used the (x1, y1) point for each segment. For the first segment, the y-intercept is ...

  b = 5 -(-7/3)(-8) = -41/3

The other two y-intercepts are computed to be -13/3 and -20/7.

The piecewise function that models the given data is ...

  [tex]\boxed{y=\begin{cases}-\dfrac{7}{3}x-\dfrac{41}{3}\quad&-8\le x\le-2\\\\\dfrac{7}{3}x-\dfrac{13}{3}\quad&-2 < x\le1\\\\\dfrac{6}{7}x-\dfrac{20}{7}\quad&1 < x\le8\end{cases}}[/tex]

__

Additional comment

There is nothing in this problem statement that requires the function be continuous. However, we have made it so this function is continuous in the region where it is defined.

The same repetitive computations are handled nicely by a spreadsheet.

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Answer:

7) No

8) Yes

9) Yes

Step-by-step explanation:

Plug each possible solution into the inequality and see if it holds true:

If x=1 (Not a solution)

[tex]\displaystyle 3(1)-2\stackrel{?}{ < }2-2(1)\\3-2\stackrel{?}{ < }2-2\\1\nless0[/tex]

If x=1/2 (Is a solution)

[tex]\displaystyle 3\biggr(\frac{1}{2}\biggr)-2\stackrel{?}{ < }2-2\biggr(\frac{1}{2}\biggr)\\\frac{3}{2}-2\stackrel{?}{ < }2-1\\\\\frac{1}{2} < 1[/tex]

If x=1/3 (Is a solution)

[tex]\displaystyle 3\biggr(\frac{1}{3}\biggr)-2\stackrel{?}{ < }2-2\biggr(\frac{1}{3}\biggr)\\1-2\stackrel{?}{ < }2-\frac{2}{3}\\\\-1 < \frac{4}{3}[/tex]

In the linear equation, the values of x and y are  10 and 5

A linear equation is an algebraic equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.  The standard form of a linear equation in one variable is of the form Ax + B = 0, where x is a variable, A is a coefficient, and B is a constant.

the given equation is 2x+4y = 20

to find the value of x, make y to be zero first

2(0) + 4y = 20

0+4y = 20

4y = 20 making y the subject of the relation to have

y = 5

Then when y = 0

2x +4(0) = 20

2x = 20 therefore making x the subject of the relation,

x = 10

Therefore the values of x and y are 10 and 5 respectively

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To find the previous population, we need to determine the population before the 27% decrease. Here's how we can calculate it:

Let's assume the previous population is P.

According to the problem, the current population is 7300, which represents 100% - 27% of the previous population:

(100% - 27%) * P = 7300

To simplify the equation, convert 27% to decimal form:

(100% - 0.27) * P = 7300

Simplifying further:

0.73P = 7300

Divide both sides of the equation by 0.73:

P = 7300 / 0.73

P ≈ 10000

Therefore, the previous population was approximately 10,000.

~~~Harsha~~~

Vector g is from the red jet ski to the green boat. The magnitude is √26 and the direction angle is 248.7°, the component form of vector g is approximately (-3.8, -1.4).

To write the component form of vector g, we need to determine the horizontal and vertical components of the vector.

Given:

Magnitude of g = √26

Direction angle = 248.7°

To find the horizontal component (g_x) and vertical component (g_y) of vector g, we can use the following trigonometric formulas:

g_x = magnitude * cos(angle)

g_y = magnitude * sin(angle)

Substituting the given values:

g_x = √26 * cos(248.7°)

g_y = √26 * sin(248.7°)

Now, let's calculate the values:

g_x = √26 * cos(248.7°) ≈ -3.8

g_y = √26 * sin(248.7°) ≈ -1.4

Therefore, the component form of vector g is approximately (-3.8, -1.4).

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Answer:

[tex]\dfrac{7}{9}[/tex]

Step-by-step explanation:

Let x be the denominator.

If the numerator is 2 less than the denominator, then the expression for the numerator is (x - 2):

[tex]\dfrac{x-2}{x}[/tex]

If 3 is added to both the numerator and the denominator, and the answer is 5/6, then:

[tex]\dfrac{x-2+3}{x+3}=\dfrac{5}{6}[/tex]

Now we can solve the equation for x.

Simplify the numerator in the fraction on the left of the equation:

[tex]\dfrac{x+1}{x+3}=\dfrac{5}{6}[/tex]

Cross mutliply:

[tex]6(x+1)=5(x+3)[/tex]

Expand the brackets:

[tex]6 \cdot x +6 \cdot 1 = 5 \cdot x + 5 \cdot 3[/tex]

[tex]6x+6=5x+15[/tex]

Subtract 5x from both sides of the equation:

[tex]6x+6-5x=5x+15-5x[/tex]

[tex]x+6=15[/tex]

Subtract 6 from both sides of the equation:

[tex]x+6-6=15-6[/tex]

[tex]x=9[/tex]

Therefore, the value of x is 9.

Now substitute the found value of x into the original rational expression:

[tex]\dfrac{x-2}{x}=\dfrac{9-2}{9}=\dfrac{7}{9}[/tex]

Therefore, the original fraction is:

[tex]\boxed{\dfrac{7}{9}}[/tex]

Answer:

$27.01

Step-by-step explanation:

100% + 19.3% = 119.3%.

$32.22 = 119.3%

divide both sides by 119.3:

(32220/1193) = 1

multiply by 100 to get 100% ie the bill before the tip:

$27.01 = 100%

$27.01 is bill to nearest cent

Hello!

men = 10/26 = 5/13

women = 2/29

P = 5/13 x 2/29 = 10/377

Answer:

The distance from each chord to the center of the circle is approximately 12.09 inches.

Step-by-step explanation:

To find the distance from each chord to the center of the circle, we can use the following formula:

[tex]d = \sqrt{r^2-(l/2)^2}[/tex]

Where:

- "d" is the distance from the chord to the center of the circle,

- "r" is the radius of the circle, and

- "l" is the length of the chord.

Given that the diameter of the circle is 29 inches, we can find the radius by dividing the diameter by 2:

[tex]r = 29/2 = 14.5[/tex] Inches

Now, let's calculate the distance from each chord to the center of the circle:

For the first chord with a length of 16 inches:

[tex]d_{1} =\sqrt{14.5^2-(16/2)^2} = \sqrt{210.25-64} = \sqrt{146.25} = 12.09[/tex] Inches

For the second chord with a length of 16 inches:

[tex]d_{2} = \sqrt{14.5^2-(16/2)^2} = \sqrt{210.25-64} = \sqrt{146.25} = 12.09[/tex] Inches

Therefore, the distance from each chord to the center of the circle is approximately 12.09 inches.

Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{14.5}\\ a=\stackrel{adjacent}{8}\\ o=\stackrel{opposite}{x} \end{cases} \\\\\\ x=\sqrt{ 14.5^2 - 8^2}\implies x=\sqrt{ 210.25 - 64 } \implies x=\sqrt{ 146.25 }\implies x\approx 12.09[/tex]

Answer:

Multiplicative identity for any real number is 1.

Step-by-step explanation:

The probability that either event A or B will occur is equal to 0.89 to the nearest hundredth

The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.

The total possible outcome = 20 + 12 + 4 = 36

probability of A = P(A) = 20/36

probability of B = P(B) = 12/36

probability that either event A or B will occur = 20/36 + 12/36

probability that either event A or B will occur = (20 + 12)/36

probability that either event A or B will occur = 32/36

probability that either event A or B will occur = 0.89

Therefore, the probability that either event A or B will occur is equal to 0.89 to the nearest hundredth

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Julia's total cost for the car purchase, including the negotiated price, rebate coupon deduction, optional stereo and accessories, and financing, amounts to $16,531.05 + $380 = $16,911.05 (excluding title fees, license plate charges, and sales taxes).

Let's break down the information given and calculate the various costs and payments involved in Julia's car purchase:

1. Dealer's Cost:

The dealer's cost is 11.7% lower than the sticker price of $17,350.

Dealer's Cost = $17,350 - (11.7% * $17,350) = $15,320.95

2. Negotiated Price:

Julia negotiated a price that left the dealer with a 9.5% profit margin over the invoice price.

Negotiated Price = Dealer's Cost + (9.5% * Dealer's Cost) = $15,320.95 + (9.5% * $15,320.95) = $16,781.05

3. Rebate Coupon:

Julia has a rebate coupon of $250, which will be deducted from the negotiated price.

Negotiated Price after Rebate = Negotiated Price - $250 = $16,781.05 - $250 = $16,531.05

4. Optional Stereo and Accessories:

Julia ordered a $300 stereo unit and other accessories costing $80.

Total Additional Cost = $300 + $80 = $380

5. Financing:

Julia will finance 83% of the total cost at an APR of 9 ¼ % over 4 years.

Loan Amount = 83% * Negotiated Price after Rebate = 83% * $16,531.05 = $13,711.48

APR = 9.25%

Loan Term = 4 years

6. Title Fees, License Plate Charges, and Sales Taxes:

The costs for title fees, license plate charges, and sales taxes will be paid later at the Registry of Motor Vehicles and are not included in the calculations above.

In summary, Julia's total cost for the car purchase, including the negotiated price, rebate coupon deduction, optional stereo and accessories, and financing, amounts to $16,531.05 + $380 = $16,911.05 (excluding title fees, license plate charges, and sales taxes).

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Answer:

66 inches²

Step-by-step explanation:

Area of 1 triangle = ½ × base × height = ½ × 7 × 4 = 14 in²

Area of 2 triangles = 14 × 2 = 28 in²

Area of outer rectangles = (6 × 2) × 2 = 24 in²

Area of inner rectangle = 2 × 7 = 14 in²

Total surface area = 28+24+14 = 66 in²

The shepherd could put 7 sheep in the second pen and 49 sheep in the third pen.

We have,

Let's solve the problem step by step.

-Let's assume that the number of sheep in the second pen is 7x, where x is a positive integer representing the number of multiples of 7.

Similarly, let's assume that the number of sheep in the third pen is 7y, where y is a positive integer representing the number of multiples of 7.

According to the given information, the shepherd placed a total of 63 sheep in the pens:

7 + 7x + 7y = 63

We can simplify this equation by dividing both sides by 7:

1 + x + y = 9

Now we need to find positive integer values for x and y that satisfy this equation.

Since we know that there were more sheep in the third pen, y should be greater than x.

Let's try different values for x and y:

If x = 1, then y = 9 - (1 + 1) = 7

If x = 2, then y = 9 - (2 + 1) = 6

If x = 3, then y = 9 - (3 + 1) = 5

If x = 4, then y = 9 - (4 + 1) = 4

We can see that when x = 1, y = 7, which satisfies the condition that there were more sheep in the third pen.

Therefore, the number of sheep in the second pen (7x) is 7 x 1 = 7, and the number of sheep in the third pen (7y) is 7 x 7 = 49.

Thus,

The shepherd could put 7 sheep in the second pen and 49 sheep in the third pen.

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The complete question:

A shepherd put sheep in pens. In a corral he placed 7 sheep, in the

second and in the third pen he placed multiples of 7. If in total he placed 63

sheep, knowing that where more sheep, was in the third corral.

How many sheep could he put in pens 2 and 3?

Answer:

shaded area ≈ 69.53 cm²

Step-by-step explanation:

the shaded area (A) is calculated as

A = area of square - area of circle

area of square = 18² = 324

area of circle = πr² ( r is the radius )

the diameter of the circle = 18 , so r = 18 ÷ 2 = 9

area of circle = π × 9² = 81π

then

A = 324 - 81π ≈ 69.53 cm² ( to 2 decimal places )

All the values of x, y and z are,

z = 12.99

y = 7.01

x = 28.3 degree

We have to given that;

In a triangle,

Two angles are, 61.7 degree and 90 degree

And, One side is, 14.76.

Now, We can formulate;

sin 61.7° = Perpendicular / Hypotenuse

sin 61.7° = z / 14.76

0.88 = z / 14.76

z = 0.88 x 14.76

z = 12.99

And, By Pythagoras theorem we get;

14.76² = z² + y²

14.76² = 12.99² + y²

217.85 = 168.74 + y²

y² = 217.85 - 168.74

y² = 49.1

y = 7.01

And, By sum of all the angles in triangle, we get;

x + 61.7 + 90 = 180

x + 151.7 = 180

x = 180 - 151.7

x = 28.3 degree

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The length and width of the wall of the barn are 2 feet and 12 feet

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

The area of a rectangle is calculated as

Area  = Length * Width

Using the above as a guide, we have the following:

x * (2x + 8) = 24

Express 24 as 2 * 12

So, we have

x * (2x + 8) = 2 * 12

This means that

x = 2 and 2x + 8 = 12

Evaluate

x = 2

Hence, the length of the rectangle is 2 feet

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The complete statements are;

m<Y = 90 degrees

m<M = 56.3 degrees

m<Z = 57 degrees

XY = 8

YZ = 12

To determine the values, we need to know the following;

From the image shown, we have that;

1. The measure of <Y is 90 degrees; angle at right angle

2. For m<M , we have;

Using the tangent identity, we have;

tan M = 12/8

tan M = 1.5

M = 56. 3 degrees

3. For m<Z, we have;

33 + m<Y + m<Z = 180

collect like terms

m<Z = 57 degrees

4. NM = XY

XY = 8

5, YZ = 12

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The equation in standard form for the circle with center (0, 9) passing through (15/2, 5) is x²+y²-18y-54.25=0.

The given coordinate points are (0, 9) and (15/2, 5).

The standard equation of a circle with center at (x₁, y₁) and radius r is (x-x₁)²+(y-y₁)²=r²

Here, (0-7.5)²+(9-5)²=r²

56.25+16=r²

r=8.5

Now, the equation is (x-0)²+(y-9)²=8.5²

x²+y²-18y+18=72.25

x²+y²-18y+18-72.25=0

x²+y²-18y-54.25=0

Therefore, the equation in standard form for the circle with center (0, 9) passing through (15/2, 5) is x²+y²-18y-54.25=0.

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The number that belongs in the green box is 130.4 units.

In Mathematics and Geometry, the sum of the angles in a triangle is equal to 180. This ultimately implies that, we would sum up all of the angles as follows;

a + c + b = 180°

12° + 27° + b = 180°

39° + b = 180°

b = 180° - 39°

b = 141°

In Mathematics and Geometry, the law of sine is modeled or represented by this mathematical equation:

sinA/a = sinB/b

sin141/a = sin12/43

a = 43sin141/sin12

a = 27.108/0.2079

a = 130.4 units.

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A full circle has [tex]360^{\circ}[/tex].

[tex]\dfrac{4}{9}\cdot 360^{\circ}=160^{\circ}[/tex]

The mark angle is [tex]160^{\circ}[/tex].

1)

The trigonometric functions :

sinA = 5/13 , cosA = 13/12 , tanA = 5/13

Given,

Right angled triangle with:

P = 5

B = 12

H = 13

Then trigonometric ratios,

sinA = P/H

cosA = B/H

tanA = P/B

Hence the ratios can be defined as,

sinA = 5/13

cosA = 12/13

tanA = 5/12

2)

The value x in the radical form 10.77

Given,

Right angled triangle,

Perpendicular = 4

Base = 10

Hypotenuse = x

Apply pythagora's theorem,

P² + B² = H²

4² + 10² = H²

16 + 100 = H²

H = 10.77

Hence the value of x is 10.77 .

3)

The value of x in radical form

Given,

P = 56

B = x

H = 106

Apply pythagora's theorem,

P² + B² = H²

56² + x² = 106²

x = 90

Hence the value of x is 90 .

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The total number of data values (games played) represented in the table is 14.

To determine the total number of data values (games played) represented in the frequency table, we need to sum up the frequencies for each category (number of goals scored).

The frequency represents the number of games in which a particular number of goals was scored.

Let's calculate the total number of games played by summing up the frequencies:

Total number of games played =

Frequency of 0 goals + Frequency of 1 goal + Frequency of 2 goals + Frequency of 3 goals + Frequency of 4 goals + Frequency of 7 goals + Frequency of 9 goals

Total number of games played = 1 + 3 + 2 + 4 + 2 + 1 + 1

Total number of games played = 14

We must add the frequencies for each category (number of goals scored) to get the total number of data values (games played) reflected in the frequency table.

The number of games with a specific amount of goals scored is the frequency.

Let's add up the frequencies to determine the total number of games played:

Total games played = Frequency of 0 goals, Frequency of 1, Frequency of 2, Frequency of 3, Frequency of 4, Frequency of 7, and Frequency of 9 goals.

Total games played: 1 plus 3 plus 2 plus 4 plus 2 plus 1 plus 1

14 games were played in total.

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Hello!

Event A:

is a 5 or 6 = 2 numbers on 6 = 2/6 = 1/3

EventB:

is not a 1 = 2,3,4,5,6 = 5/6

P(A and B) = 1/3 x 5/6 = 1x5/3x6 = 5/18 ≈ 0.28

The answer is 0.28.

Answer:

Step-by-step explanation:

3.14 . 11= 150/360

The regression equation that correctly models the data is B. y = 2.87x + 11.85

The regression equation is calculated using the following formula:

y = a + bx

where:

y is the dependent variable (daily food costs)

x is the independent variable (number of children in attendance)

a is the y-intercept

b is the slope of the line

The slope of the line is calculated using the following formula:

b = (∑xy - ∑x ∑y / n) / (∑x2 - (∑x)² / n)

Using the data from the table, we can calculate the y-intercept and slope of the line as follows:

a = 411 / 5 = 82.2

b = (13,393 - (143)(411) / 5) / (4,573 - (143)² / 5) = 2.87

Substituting the y-intercept and slope into the regression equation, we get the following equation:

y = 11.85 + 2.87x

Simplifying, we get the following equation:

y = 2.87x + 11.85

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Answer:

c=19

Step-by-step explanation:

11=c-8

+8  +8

19=c

11=c-8

move the variable to the left - hand side and change it sign: 11-c= -8

move the constant to the right-hand side and change its sign: -c= -8-11

calculate the difference: -c = -19

change the signs on each side c=19

The statement "an n-ary relation R is a set of n-tuples" refers to a mathematical concept in which an n-ary relation R is defined as a collection or set of n-tuples.

In this context, an n-ary relation refers to a relationship or connection between n elements or entities. It represents a logical association between these elements based on certain criteria or conditions.

An n-tuple, on the other hand, is an ordered sequence or collection of n elements, where the order and position of each element in the sequence are important.

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