To earn full credit for this question use your own sheet of paper to solve the problem, showing all steps of your work in order to get full credit. A random sample of 30 male college students was selected, and their heights were measured. The heights (in inches) are given below. 73 68 72 74 6773 69 66 66 68 67 68 73 72 67 71 69 71 70 6769 68 7366 67 66 66 72 72 70 (a) Complete the frequency distribution for the data. Make sure to enter your answers for the relative frequency as decimals, rounded to t Height Frequency Relative Frequency 66 67 58 69 70 71 72 73 74 (b) Compute the (weighted) sample mean. Make sure to enter your answer rounded to the ni (c) Interpret the sample mean obtained in question (b) in the context of the problem.

a) To find the number of students getting more than 45 marks, we count the students whose marks are greater than 45 in the given list.

In the given list, the students with marks greater than 45 are: 50, 49, 47, 48, 49, 48, 47, 49, 48, 50, 47, 49, 48, 46, 47, 48, 47.

Counting these numbers, we find that there are 17 students who obtained more than 45 marks.

b) To find the number of students getting less than 45 marks, we count the students whose marks are less than 45 in the given list.

In the given list, the students with marks less than 45 are: 44, 44, 42, 41, 41, 42, 41, 44, 44, 42, 45, 45, 45, 44, 45.

Counting these numbers, we find that there are 15 students who obtained less than 45 marks.

c) To find the maximum number of students getting the same marks, we look for the mark that appears most frequently in the given list.

In the given list, the marks obtained by the students are: 44, 50, 44, 49, 42, 47, 45, 42, 44, 48, 49, 48, 47, 49, 47, 41, 45, 48, 41, 48, 41, 42, 47, 49, 49, 48, 50, 47, 49, 48, 46, 44, 45, 45, 46, 44, 42, 47, 48, 45.

Counting the frequency of each mark, we find that the marks 47 and 48 appear most frequently, with a count of 6 each. Therefore, the maximum number of students getting the same marks is 6.

d) To find the average marks obtained by the students in the class, we sum up all the marks and divide by the total number of students.

Total marks = 44 + 50 + 44 + 49 + 42 + 47 + 45 + 42 + 44 + 48 + 49 + 48 + 47 + 49 + 47 + 41 + 45 + 48 + 41 + 48 + 41 + 42 + 47 + 49 + 49 + 48 + 50 + 47 + 49 + 48 + 46 + 44 + 45 + 45 + 46 + 44 + 42 + 47 + 48 + 45

           = 1912

Total number of students = 40

Average marks = Total marks / Total number of students

                 = 1912 / 40

                 = 47.8

Therefore, the average marks obtained by the students in the class is 47.8.

e) To find the number of students getting more than the average marks, we count the students whose marks are greater than 47.8.

In the given list, the students with marks greater than 47.8 are: 50, 50, 49, 48, 49, 48, 49, 48, 50, 49, 49, 48, 48, 50, 49, 49, 48, 48, 47, 49, 49, 48, 50, 47,

49, 49, 48, 50, 47, 49, 49, 48, 48, 49, 48, 47, 48, 49, 49, 48, 50, 49.

Counting these numbers, we find that there are 40 students who obtained more than the average marks.

Answer:

B.1 1/4

Step-by-step explanation:

Answer:

20%is the increase in the amount

Answer:

- \(\frac{9}{10}\) > - \(\frac{10}{10}\)

Step-by-step explanation:

Which number is closer to 0, meaning that number is bigger.

-9/10 = -0.9

-10/10 = -1

We see -0.9 is closer to 0, meaning it is bigger.

So,  - \(\frac{9}{10}\) > - \(\frac{10}{10}\)

The unknown angle in the cyclic quadrilateral is as follows:

∠R = 86 degrees

The diagram above is cyclic quadrilateral. A cyclic quadrilateral is a four sided shape that can be inscribed into a circle.

The sum of angles in a cyclic quadrilateral is 360 degrees. The opposite angles in a cyclic quadrilateral is supplementary.

Hence, let's find the unknown angle.

∠R = 1 / 2 (92 + 80)

∠R = 1 / 2 (172)

∠R = 86 degrees

Therefore, the unknown angle is 86 degrees.

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Answer: I believe b and d

Step-by-step explanation:

Answer:

A is true  b is true

Step-by-step explanation:

A.if u add a postive to a negative that is the same number u get 0

b. negative plus negative is positive

have a great day

Answer: 5.25 inches cubed

Joey's actual speed is 143.59 mph, and his actual direction is slightly west of northwest.

Given that Joey's aircraft speed: 188 mph

Wind speed: 60 mph

Wind direction: 150 degrees (measured clockwise from due north)

We can consider the wind as a vector, which has both magnitude (speed) and direction.

The wind vector can be represented as follows:

Wind vector = 60 mph at 150 degrees

We convert the wind direction from degrees to a compass bearing.

Since 150 degrees is measured clockwise from due north, the compass bearing is 360 degrees - 150 degrees = 210 degrees.

Joey's aircraft speed vector = 188 mph at 0 degrees (due northwest)

Wind vector = 60 mph at 210 degrees

To find the resulting velocity vector, we add these two vectors together. This can be done using vector addition.

Converting the wind vector into its x and y components:

Wind vector (x component) = 60 mph × cos(210 degrees)

= -48.98 mph (negative because it opposes the aircraft's motion)

Wind vector (y component) = 60 mph×sin(210 degrees)

= -31.18 mph (negative because it opposes the aircraft's motion)

Now, we can add the x and y components of the two vectors to find the resulting velocity vector:

Resulting velocity (x component) = 188 mph + (-48.98 mph) = 139.02 mph

Resulting velocity (y component) = 0 mph + (-31.18 mph) = -31.18 mph

Magnitude (speed) = √((139.02 mph)² + (-31.18 mph)²)

= 143.59 mph

Direction = arctan((-31.18 mph) / 139.02 mph)

= -12.80 degrees

The magnitude of the resulting velocity vector represents Joey's actual speed, which is approximately 143.59 mph.

The direction is given as -12.80 degrees, which indicates the deviation from the original northwest direction.

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Answer:

One solution

Step-by-step explanation:

I easily searched it up! :)

Answer: No es porque el número podría ser 35

Answer:

1. \(\dfrac{dy}{dt}=4-\dfrac{3y(t)}{100+2t}\)

2. \(y(40) = 110.873 \ kg\)

Step-by-step explanation:

Given that:

A very large tank initially contains 100 L of pure water.

Starting at time t = 0 a solution with a salt concentration of 0.8kg/L is added at a rate of 5L/min.

. The solution is kept thoroughly mixed and is drained from the tank at a rate of 3L/min.

As 5L/min is entering and 3L/min is drained out, there is a 2L increase per minute. Therefore, the amount of water at any given time t = (100 +2t) L

t = (50 + t ) L

Since it is given that we should  consider y(t) to be the  amount of salt (in kilograms) in the tank after t minutes.

Then , the differential equation that  y satisfies can be computed as follows:

\(\dfrac{dy}{dt}=rate_{in} - rate_{out}\)

\(\dfrac{dy}{dt}=(0.8)(5) -\dfrac{y(t)}{100+2t} \times3\)

\(\dfrac{dy}{dt}=(0.8)(5) -\dfrac{3y}{100+2t}\)

\(\dfrac{dy}{dt}=4-\dfrac{3y(t)}{100+2t}\)

How much salt is in the tank after 40 minutes?

So,

suppose : \(e^{\int \dfrac{3}{100+2t} \ dt} = (t+50)^{3/2}\)

Then ,

\(( t + 50)^{3/2} y' + \dfrac{3}{2}(t+50)^{1/2} y = 4(t+50)^{3/2}\)

\(( t + 50)^{1.5} y' + \dfrac{3}{2}(t+50)^{0.5} y = 4(t+50)^{3/2}\)

\([y\ (t + 50)^{1.5}]' = 4(t+ 50)^{1.5}\)

Taking the integral on both sides; we have:

\([y(t + 50)^{1.5}] = 1.6 (t + 50)^{2.5} + C\)

\(y = 1.6 (t+50)+C(t+50)^{-1.5}\)

\(y(0) = 0 = 1.6(0+50) + C ( 0 + 50)^{-1.5}\)

\(0 = 1.6(50) + C ( 50)^{-1.5}\)

\(C= -1.6(50)^{2.5}\)

\(y(40) = 1.6 (40 + 50)^1 - 1.6 (50)^{2.5}(50+40)^{-1.5}\)

\(y(40) = 144 - 1.6 \times 17677.66953 (90)^{-1.5}\)

\(y(40) = 144 - 1.6 \times 17677.66953 \times 0.001171213948\)

\(y(40) = 144 - 33.12693299\)

\(y(40) = 110.873 \ kg\)

The systems of equations to solve for this quadratic function to model the values in the table is y =  -2x^2 + 4x - 2

The general form of a quadratic function is --> y = ax2 + bx + c

-2 = a(0)2 + b(0) + c

-2 = 0 + 0 + c

-2 = c

substitute c value

(-1 , -8) substitute

-8 = a ( -1 )2 + b ( -1 ) - 2

-8 = a - b - 2

-6 = a - b

( 3 , -8)

-8 = a ( 3 )2 + b ( 3 ) - 2

-8 = 9a + 3b - 2

-6 = 9a + 3b

a - b = -6

9a + 3b = -6

on solving :

9 ( b - 6 ) + 3b = -6

9b - 54 + 3b = -6

12b - 54 = -6

12b = 48

b = 4

a - 4 = -6

a = -2

The quadratic equation for this table is y = -2x^2 + 4x - 2

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Full question:

set up the systems of eqautions to solve for this quadratic function to model the values in the table.

x | y

-1 | -8

0 | -2

3 | -8

Step-by-step explanation:

-2(-3+2)2

(-2×-3)+(-2×2)2

(6-4)2

2(6-4)

(2×6)+(2×-4)

12-8=4

Answer:

its a right angle and a its an acute angle as well so it be 5

Answer:

A dynamic environment is a business environment that is rapidly changing. In a dynamic market, businesses have to adapt quickly to changes and develop new ideas, products and services to keep up with technology and new trends.

Step-by-step explanation:

11:59 AM is midday not midnight

Answer:1.325

Step-by-step explanation:

Answer:

32 degrees.

Step-by-step explanation:

The three angles in a triangle always add up to 180 degrees.

To find the third angle, \(180-50-98=32\).

Answer:

True

Step-by-step explanation:

Answer:

\( \huge\purple{TRUE}\)

Step-by-step explanation:

The absolute value of any number is always positive.

The equation shows that the number of toys that must be bought for them to have equal profit will be 212 toys.

From the information, it should be noted that the equation that can be used to represent the information about Jaclyn company will be:

= 2125 + (49.99 × x)

= 2125 + 49.99x

The equation that can be used to represent the information about Richie company will be:

= (39.95 × x)

= 39.95x

Therefore, we will equate both equations:

2125 + 49.99x = 39.95x

49.99x - 39.95x =2125

10.04x = 2125

x = 212

Therefore, the number of toys that must be bought for them to have equal profit will be 212 toys.

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The correct option for the given sum is option B. The point (2,-9) paired with (2, 3), will make a side equal to this length.

Let the other point of the pentagon will be M(n, o).

The given point be A (a, b)

Also given one of the sides of a pentagon has length 12.

Now, we need to find the distance between the two points,

Distance between two points: |AM| = √\((a-n)^2+(b-o)^2\)

Now,

\(12 = \sqrt{(2-n)^2+(3-o)^2}\)

\((12)^2\) = \((2-n)^2+(3-o)^2\)

\((2-n)^2+(3-o)^2\) = 144 ----------------------------- eq (1)

Now, check every point for the values to match with equation (1)

Option A: \((2-14)^2+(3-15)^2\) = 288. So the option is false.

Option B:

\((2-2)^2+(3-(-9))^2\) =114

0+114 =114

Therefore option B is correct. The other point is (2,-9).

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The rational function graphed in this problem is defined as follows:

y = -2(x - 1)/(x² - x - 2).

The vertical asymptotes of the rational function for this problem are given as follows:

x = -1 and x = 2.

Hence the denominator of the function is given as follows:

(x + 1)(x - 2) = x² - x - 2.

The intercept of the function is given as follows:

x = 1.

Hence the numerator of the function is given as follows:

a(x - 1)

In which a is the leading coefficient.

Hence:

y = a(x - 1)/(x² - x - 2).

When x = 0, y = -1, hence the leading coefficient a is obtained as follows:

-1 = a/2

a = -2.

Thus the function is given as follows:

y = -2(x - 1)/(x² - x - 2).

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Answer:

Step-by-step explanation:

You can use the equations:

x = 2y

where x is the number of $10 bills and y the number of $5 bills and:

10x+5y = 125

Solving gives x=10 and y = 5, or in other words there are 10 $10 bills and 5 $5 bills

Answer: 4*4= 16

Step-by-step explanation:

if Neha is 4 years older than her son, so she will be sixteen.

The logarithm expression can be simplified to:

In(6x^9)-In(x^2) =7·ln(6x)

There are some logarithm properties we can use here.

log(a) - log(b) = log(a/b)

log(a^n) = n*log(a)

(these obviously also apply to the natural logarithm)

Now let's look at our expression, it says that:

In(6x^9)-In(x^2)

Using the first rule, we can rewrite this as.

In(6x^9)-In(x^2) = ln(6x^9/x^2)

Now solving the quotient in the argument:

ln(6x^9/x^2) = ln(6x^7) = 7·ln(6x)

That is the expresison simplified.

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