A small liberal arts college in the Northeast has 200
freshmen. Eighty of the freshmen are education majors. Suppose fifty freshmen are randomly selected (without replacement).

Step 1 of 2 : Find the expected number of education majors in the sample. Round your answer to two decimal places, if necessary.

The value of x measure as 90 degree. the solution would be sinx = 1.

Since it is known that Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

WE are given the trigonometric functions as;

(sin2x)/(cosx)=2 for 0≤x≤2π

We know that sin 2x = 2 sinx cosx

Therefore,

(sin2x)/(cosx)=2

(2 sinx cosx)/(cosx)=2

sinx = 2/2

sinx = 1

Thus sin 90 = 1

x = 90 degree

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The side AC corresponds to the side AC in the other triangle and the length of BC is 15 units

For two triangles to be similar, the corresponding sides of the triangles must be in proportion

Having said  that

The side AC corresponds to the side AC in the other triangle

The length BC is calculated as

BC/9 = 25/15

Express as products

So, we have

BC = 9 * 25/15

Evaluate the products

BC = 15

Hence, the length of BC is 15 units

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Based on the figure, we can see that triangles OHJ and OIX are similar because they share the same angle at O and HI and HJ are tangent to the circle. Thus, we can set up the following proportion:

OH / OI = HJ / (HJ + 9)

Substituting the given values:

6.5 / 3.9 = HJ / (HJ + 9)

Cross-multiplying:

6.5(HJ + 9) = 3.9HJ

Distributing:

6.5HJ + 58.5 = 3.9HJ

Simplifying:

2.6HJ = -58.5

HJ = -22.5

However, this answer doesn't make sense in the context of the problem. Since HJ represents a length, it cannot be negative. Therefore, we need to re-examine our work.

Looking back at our proportion, we can see that the ratio of OH to OI is greater than 1, which implies that HJ is greater than 9. This makes sense since HJ is a chord of the circle and thus must be longer than the radius.

Let's try the problem again, but this time we'll rearrange the proportion to solve for HJ:

HJ / (HJ + 9) = OI / OH

Substituting the given values:

HJ / (HJ + 9) = 3.9 / 6.5

Cross-multiplying:

6.5HJ = 3.9HJ + 35.1

Simplifying:

2.6HJ = 35.1

HJ = 13.5

Therefore, HJ is equal to 13.5.

Answer:

∠ C = 84°

Step-by-step explanation:

A quadrilateral inscribed in a circle is a cyclic quadrilateral.

the opposite angles sum to 180° , that is

∠ A + ∠ C = 180 , then

x² + 60 + 8x + 36 = 180

x² + 8x + 96 = 180 ( subtract 180 from both sides )

x² + 8x - 84 = 0 ← in standard form

(x + 14)(x - 6) = 0 ← in factored form

equate each factor to zero and solve for x

x + 14 = 0 ⇒ x = - 14

x - 6 = 0 ⇒ x = 6

x > 0 , then x = 6 , so

∠ C = 8x + 36 = 8(6) + 36 = 48 + 36 = 84°

The sum of 3√5 and 4√25 is an irrational number.

First, simplify the expressions inside the square roots:

3√5 = 3√(5×1) = 3√5

4√25 = 4√(25×1) = 4×5 = 20

Now, we add them together:

3√5 + 4√25 = 3√5 + 20

This is the simplest form since 20 is already a rational number and we cannot simplify the square root of 5 any further.

To determine whether the result is rational or irrational.

Since 3√5 is irrational and cannot be simplified any further, the expression as a whole is also irrational.

Therefore, the sum of 3√5 and 4√25 is an irrational number.

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Answer:

5/2

Step-by-step explanation:

Slope is rise over run, or how far it goes in the y direction over how far it goes in the x direction. In this case, y increases by a value of 5 at the same time x is increasing by a value of 2. This makes the slope 5/2, and it is positive since the values are increasing. If there is a problem your stuck on like this try graphing the points, desmos has a good graphing calculator :)

1) Matrices that have determinants are square matrices

2) Due to the inverse matrix's calculation utilizing a matrix's determinant, the determinant and the inverse matrix are connected.

3) The determinant affects whether a matrix has an inverse.

A matrix is a collection of numbers that have been sorted into rows and columns to create a rectangular array. The elements, or entries, of the matrix are the integers.

If and only if the determinant of a square matrix A is nonzero, the matrix has an inverse. The matrix A is referred to as singular and devoid of an inverse if its determinant is zero.

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Answer: A,E or F.

Step-by-step explanation: That's the only ones that have X's and then x is 0

The most likely number of minutes of usage recorded by Jason is A . approximately 50.

We can see that initially, the temperature of the electronic system began to increase as the time increased. It then began to decrease from the 20 minute and ketp decreasing till the 40th minute.

Assuming that the temperature keeps decreasing, it would mean that at 50 minutes, the temperature would be more than the temperature at 40 minutes and so would most likely be 48 degrees.

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Answer:

12/2

Step-by-step explanation:

(x - h)^2 + (y - k)^2 = r^2

where (h,k) is the center of the circle and r is the radius.

Comparing this to the given equation, we see that the center of the circle is (-10,0) and the radius is sqrt(9) = 3.

The diameter of the circle is twice the radius, so:

diameter = 2(radius) = 2(3) = 6

Therefore, the diameter of the circle is 6.

We can write this in simplified, rationalized form as:

diameter = 6 = 6/1 = 12/2

The expected number of people over 70 years old in that country in 2050 is given as follows:

D) 5.40 million.

The expected number of people over 70 years old in that country in 2050 is obtained applying the proportions in the context of the problem.

The expected population of that country in 2050 is given as follows:

180 million.

Hence the expected population of the country over 70 years old, equivalent to a percentage of 3%, is obtained as follows:

0.03 x 180 million = 5.4 million.

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Answer:

The pattern of association between time and distance is positive and linear.

The requried equivalent fraction for the equivalent fraction to 3 3/4 and 1 2/3, is 45/12, and 20/12.

To find a common denominator for 4 and 3, we can multiply them together to get 12.

So, we can convert 3 3/4 as:

3 3/4 = 12/4 + 3/4 = 15/4

Similarly, we can convert 1 2/3 as:

1 2/3 = 5/3

Therefore, the equivalent fractions for 3 3/4 and 1 2/3 using a common denominator of 12 are:

15/4 = 45/12 and 5/3 = 20/12

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The missing angle C of the given triangle using law of cosine is: 62.1°

The Law of Cosines is defined as a numerical formula that relates the side lengths and points of any triangle. It expresses that the square of any side of a triangle is equivalent to the number of squares of the other different sides short two times the result of those sides and the cosine of the point between them.

Numerically, the Law of Cosines can be communicated as:

c² = a² + b² - 2abcos(C),

where c is the length of the side inverse to the point C, and an and b are the lengths of the other different sides.

Thus:

90² = 55² + 50² - 2(55 * 50)cos(C),

2575 = 5500 cos C

2575/5500 = cos C

cos C = 0.4682

C = cos⁻¹0.4682

C = 62.1°

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The solutions to the expressions are (m-8)² = m² - 16m + 64 and 2m²-16m + m²-8m+161 = 3m²- 24m + 161

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

(m-8)²

Expand

So, we have

m² - 16m + 64

Next, we have

2m²-16m + m²-8m+161

Evaluate the like terms

3m²- 24m + 161

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The height attained is 1290 feet

The time taken to reach the ground is 9s

The velocity on reaching the ground is  288 m/s.

We know that we can be able to handle the problems that we have here by the use of the equations of motion and that is what we shall do in the problems that follow.

h = ut - 1/2gt^2

h = height

u = initial velocity

g = acceleration due to gravity

t = time

Thus;

h = (18 * 5) - 1/2 * (-32) * 5^2

h =90 + 400

h = 490 feet

Thus the height after five seconds is 490 feet + 800 feet = 1290 feet

Using h = ut + 1/2gt^2

h = 1290 feet

u = 0 m/s when dropped

1290=  + 1/2 * (32) *t^2

1290 = 16t^2

Thus

t = 9s

The velocity when it hits the ground is;

v = u + gt

u = 0 m/s when dropped

v = 32 * 9

v = 288 m/s

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Answer:

To find how far above the water the lip balm will be after 3 seconds, we need to evaluate the polynomial -16t² + 220 when t = 3.

Substituting t = 3 into the polynomial, we get:

-16(3²) + 220 = -16(9) + 220 = -144 + 220 = 76

Therefore, after 3 seconds, the height of the lip balm above the water will be 76 feet.

The interest earned and the future value of an annuity with monthly payments of $200 for two years that pays 6% interest per year compounded monthly is $25.43 and $225.43

Principal,P = $200

Time, t = 6%

Number of periods, n = 12

Interest rate, r = 6%

= 6/100

= 0.06 rate per year,

FV = P(1 + r/n)^nt

FV = 200.00(1 + 0.06/12)^(12)(2)

FV = 200.00(1 + 0.005)^(24)

FV = $225.43

Therefore,

Principal = $200.00

Interest = $25.43

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Answer:

w=0,

w=-7

Step-by-step explanation:

Michel-Eugène Chevreul found that the greatest intensity came from placing complementary colors next to each other. The Option C is correct.

Chevreul made great contributions to the field of color theory as he made key findings was that placing complementary colors next to each other creates the greatest intensity.

These colors are opposite to each other on the color wheel such as red & green, blue & orange or yellow &  purple. When these color are placed next to each other, these colors create a visual contrast that makes them appear brighter and more intense.

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Answer:  C

Step-by-step explanation:

Think about y=[tex]x^{3}[/tex]     This is an odd function because the highest exponent(degree) is odd

A.  is wrong. Symmetry is where you can fold it and it would be the same.  If i folded y=[tex]x^{3}[/tex] along the y- axis it would not be the same.  

B is wrong. Transformations are where has it moved, which has nothing to do with odd functions in general

C.  is correct.  It is folded along y=x and flipped.

D. is wrong.  If folded y=x it's in the same quadrant but it's not the same, its' reversed.

The fourth term in the expanded form of (x - 1)⁶ is  -20x³.

The fourth term in the expanded form of (x - 1)⁶  using the binomial theorem is calculated as follows;

The expanded form of (x - 1)⁶ using the binomial theorem is;

(x - 1)⁶ = 1x⁶ + (-6)x⁵ + 15x⁴ + (-20)x³ + 15x² + (-6)x + 1

(x - 1)⁶ = x⁶ -6x⁵ + 15x⁴ -20x³ + 15x² -6x + 1

To find the fourth term, we look for the fourth term from the left side to right side, which is  -20x³.

Therefore, the fourth term in the expanded form of (x - 1)⁶ is  -20x³.

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A) The best graphical representatiοn tο display the data wοuld be a histοgram.

B) The resulting histοgram shοuld shοw the distributiοn οf the grades and allοw fοr easy cοmparisοn οf the frequency οf grades in different ranges.

A) The best graphical representatiοn tο display the data wοuld be a histοgram. This is because a histοgram is a bar graph-like representatiοn οf data that grοups a range οf values intο intervals called bins οr classes. The height οf each bar represents the frequency οr number οf data pοints that fall within that bin οr class. A histοgram is an apprοpriate display fοr the data because it shοws the distributiοn οf the grades and allοws fοr easy cοmparisοn οf the frequency οf grades in different ranges.

Part B: Tο create a histοgram οf the data, the steps are as follows:

Step 1: Chοοse a title fοr the histοgram, such as "Distributiοn οf 7th Grade Math Exam Grades".

Step 2: Determine the range οf the data by finding the minimum and maximum values. In this case, the minimum grade is 61 and the maximum grade is 98.

Step 3: Divide the range intο a suitable number οf bins οr classes. A cοmmοn rule οf thumb is tο use between 5 and 20 bins, depending οn the range and distributiοn οf the data. Fοr this data, we can use 10 bins, with a bin width οf 3 (rοunded up frοm 2.9).

Step 4: Label the x-axis with the range οf grades, and label the y-axis with the frequency οr number οf grades.

Step 5: Draw the histοgram by drawing a bar fοr each bin, with the height οf the bar representing the frequency οf grades in that bin. Fοr example, the first bin wοuld be fοr grades between 60 and 62, the secοnd bin wοuld be fοr grades between 63 and 65, and sο οn. Cοunt the number οf grades that fall within each bin, and draw a bar with that height οn the y-axis.

Therefοre, The resulting histοgram shοuld shοw the distributiοn οf the grades and allοw fοr easy cοmparisοn οf the frequency οf grades in different ranges.

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Answer:

y = [tex]\frac{-3}{8}[/tex]x - [tex]\frac{57}{8}[/tex]

Step-by-step explanation:

a perpendicular slope is the opposite reciprocal.  The slope will be [tex]\frac{-3}{8}[/tex]

Two write the equation, you need the slope and the y-intercept.  We have the slope ([tex]\frac{-3}{8}[/tex]).  We know need to find the y-intercept.

We will use the m or slope of [tex]\frac{-3}{8}[/tex], x value of -3 from the point (-3,-6)and the y value of -6 from the point (-3,-6)

y = mx + b

-6 = [tex]\frac{-3}{8}[/tex]([tex]\frac{-3}{1)}[/tex]) + b

-6 = [tex]\frac{9}{8}[/tex] + b  Subtract [tex]\frac{9}{8}[/tex] from both sides

[tex]\frac{-6}{1 }[/tex] - [tex]\frac{9}{8}[/tex] = [tex]\frac{9}{8}[/tex] - [tex]\frac{9}{8}[/tex] + b  Use the common denominator of 8

[tex]\frac{-48}{8}[/tex] - [tex]\frac{9}{8}[/tex] = b

[tex]\frac{-57}{8}[/tex] = b

y = [tex]\frac{-3}{8}[/tex]x - [tex]\frac{57}{8}[/tex]

The value of P(A∩B) rounding to the nearest thousandth, if necessary is:  0.086

The parameters given are:

P(A) = 0.12

P(B) = 0.3

P(A ∪ B) = 0.334

We want to find the probability P(A∩B)

The P(A∪B) probability formula is given as:

P(A∪B) = P(A) + P(B) - P(A∩B)

where:

P(A) is Probability of event A happening

P(B) is Probability of event B happening

P(A∩B) is Probability of happening of both A and B.

Thus:

0.334 = 0.12 + 0.3 - P(A∩B)

P(A∩B) = 0.12 + 0.3 - 0.334

P(A∩B) = 0.086

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The bearing of the cruise ship displacement from its initial position is 15.06°, which makes the second option correct

Bearing is usually measured in degrees, with 0° indicating the reference direction (usually North), and increasing clockwise to 360°. It refers to the direction or angle between a reference direction and a point or object.

We will get a right triangle from travels of the ship, such that we can call the initial position A, the point after 8 miles B and the point after 30 miles C

angle B = 30° + 60° = 90°

AB = 8

BC = 30

by Pythagoras rule;

AC = √(8² + 30²) = 31.04

using sine rule;

30/sinA = 31.04/sin90

A = sin⁻¹[(30 × sin90)/31.04]

A = 75.06°

bearing from initial position = (30° + 75.06°) - 90°

bearing from initial position = 105.06 - 90°

bearing from initial position = 15.06°

Therefore, the bearing of the cruise ship displacement from its initial position is 15.06°

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The drop down menu is used to match each situation as below.

1. The rocket reached its maximum  the x-value of the vertex

height in 5 s.

2. ground level                                    the y-intercept

3. The rocket launcher was                the y-value of the point containing

on the ground.                                     the x-intercept on the right

4. The rocket was in the air 10           the x-intercept on the right                                                                                    

5. The maximum height of the           the y-value of the vertex

rocket is 50 ft.

6. the time the rocket was                the x-value of the point containing the

launched                                          y-intercept

The key features of the curve such as the x intercept is the point the launcher and the rocket were on ground.

The vertex is the point the rocket had the maximum and height.

Generally, the curve traces a parabolic path

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The line that has the slope with the greatest value is determined as the: A. Blue line.

The slope of a line is the change in y over the change in x, which can also be calculated as:

Slope (m) = rise / run = y2 - y1 / x2 - x1.

Also, the steeper the slope, the greater the value of the slope that you will get, while the more gentle the slope, the smaller the value of the slope of the line we would get.

Out of the three lines shown in the graph, the steepest is the blue line, this means that it has the greatest slope value.

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