Question 5 of 26 fi Time Remaining: 00:34:35 6 Points A random sample of 20 marks from an A scores in STAT 111 is listed as: 25. 26. 13. 23. 23. 25. 17. 22. 17. 19. 12. 26. 30. 30. 18. 14. 12. 26. 17. 18. The mean and the standard deviation are 20.65 and 5.71 respectively. The lecturer decided to add 5 marks to each student's mark Calculate the sample mean and sample standard deviation of the new marks O A 101.75.25.71 OB. 25.65, 10.71 OC 25.65.5.71 OD 20.65.5.71 O E. 20.65, 10.71​

Answer:

30

Step-by-step explanation:

25+35= 60

60/2=30

Answer: 30

Step-by-step explanation:

The term average has a number of different meanings. Most generally, it is a single number that is used to represent a collection of numbers. In the context of mathematics, "average" refers to the mean, specifically, the arithmetic mean. It is a relatively simple statistical concept that is widely used in many areas.

The equation below is one of the more commonly understood definitions of the average: \(Average =\) \(\frac{Sum}{Count}\)

Use the following property:

Express:

as:

so:

we would expect m to be positive.

In this case, we're considering a formula of the form y = mx + b, where y represents the cost of a four-year college x years after 2010. The variable m represents the coefficient of x, which determines the slope of the line.

Since we're discussing the cost of college, it's reasonable to expect that it generally increases over time. Therefore, we would expect the coefficient m to be positive. A positive value of m indicates that as the number of years after 2010 increases (x), the cost of college (y) will also increase.

If m were negative, it would imply a decreasing cost over time, which is less likely for a four-year college. If m were zero, it would indicate that the cost remains constant regardless of the number of years after 2010, which is also unlikely given the rising trend in college costs.

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The integral is ln|x + cos(x)| + C, where C represents the constant of integration.

To find the integral of the function 1/(x + cos(x)), we can employ a combination of algebraic manipulation and the use of standard integration techniques. Here's the solution:

First, let's rewrite the integral in a slightly different form to simplify the process:

∫(1/(x + cos(x))) dx

We notice that the denominator, x + cos(x), is not amenable to direct integration. To overcome this, we employ a substitution. Let's set u = x + cos(x). Now, differentiate u with respect to x: du/dx = 1 - sin(x).

Rearranging this equation, we get dx = du/(1 - sin(x)).

Substituting these values, the integral becomes:

∫(1/(u(1 - sin(x)))) du

Next, we simplify further by factoring out 1/(1 - sin(x)) from the integral:

∫(1/(u(1 - sin(x)))) du = ∫(1/u) du = ln|u| + C

Replacing u with its original expression, we have:

ln|x + cos(x)| + C

Therefore, the answer to the integral is ln|x + cos(x)| + C, where C represents the constant of integration.

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Answer:

Step-by-step explanation:

Given the height of the drone modelled by the equation:

h(t)=-3t^2+12t+96

a) Rewriting this in a factored form.

From the equation, we can see that -3 is the greatest common factor. The equation therefore becomes:

h(t)= -3(t^2-4t-32)

Hence the function can also be written as h(t)= -3(t^2-4t-32)

b) The drone landed on the ground at when h(t) = 0. Substitute h(t) = 0 into the expression  h(t)= -3(t^2-4t-32)

0 = -3(t^2-4t-32)

Divide through by -3

(t^2-4t-32) = 0

Factorize

t²+8t-4t-32 = 0

t(t+8)-4(t+8) = 0

(t-4)(t+8) = 0

t-4 = 0 and t+8 = 0

t = 4 and t = -8

Time can't be negative:

t = 4minutes

Hence it took the drone 4 minutes take off to land on the ground

Answer: 1) h(t)= -3 (t-8) (t+4)

2) 8 mins.

Step-by-step explanation: This is the correct answer. I tried.

Answer:

1. $ 193.2

2. 840 apples

Step-by-step explanation:

For number 1 add 30 and 26 then multiply 56 by 3.45 to get number 1

For number 2 add 30 and 26 then multiply 15

The inequality that describes the base length of the triangle is b ≤ 28/h

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

The area of a triangle can be calculated using the following formula

Area = 1/2 * Base * Height

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * b * h

Evaluate the products

Area = 1/2bh

Recall that

Area = At most 14 square feet

This means that

Area ≤ 14

So, we have

1/2bh ≤ 14

Multiply through by 2

bh ≤ 28

Divide both sides by h

b ≤ 28/h

Hence, the inequality is b ≤ 28/h

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Answer:

-9>2x+15

Step-by-step explanation:

Answer:

Step-by-step explanation:

slope=y2-y1/x2-x1

here x1=2 , y1=-4 , x2=-6 , y2=1

=1-(-4)/2-(-6)

=1+4/2+6

=5/8

-5/8  fraction shows a correct way to set up the slope formula for the line containing (2, -4) and (-6, 1)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

the slope formula for the line containing (2, -4) and (-6, 1) we calculate by plugging the values to the slope formula.

m=1-(-4)/-6-2

m=1+4/-8

m=-5/8

Hence, -5/8  fraction shows a correct way to set up the slope formula for the line containing (2, -4) and (-6, 1)

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The missing angle is <B= 40 degree and missing side length is AB = 12.25 and AC = 19.068.

To find the missing angle and side measures of ΔABC, we can use the properties of a triangle.

Given:

∠A = 50°

∠C = 90°

CB = 16

We can start by finding the measure of ∠B:

∠A + ∠B + ∠C = 180° (Sum of angles in a triangle)

50° + ∠B + 90° = 180°

∠B + 140° = 180°

∠B = 180° - 140°

∠B = 40°

Now, using Sine law

CB/ sin A = AB / sin C

16 / sin 50 = AB / sin 90

16 / 0.766044 = AB

AB = 12.25

Again 12.25 = AC/ sin B

12.25 = AC / sin 40

AC = 19.068

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x = 7.26

1. Add 11.24 to both sides

-3.98 = x - 11.24

-3.98 + 11.24 = x - 11.24 + 11.24

2. Simplify

Add the numbers:

-3.98 + 11.24 = x - 11.24 + 11.24

7.26 = x - 11.24 + 11.24

Add the numbers:

7.26 = x - 11.24 + 11.24

7.26 = x

Move the variable to the left:

7.26 = x

x = 7.26

x = 7.26

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer:

x = 7.26

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other.

First, add 11.24 to both sides of the equation:

-3.98 = x - 11.24

-3.98 (+11.24) = x - 11.24 (+11.24)

Next, simplify.

11.24 - 3.98 = x

x = 7.26

x = 7.26 is your answer.

~

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Answer:

1.5 per hour.

Step-by-step explanation:

By proportion that is 5.4 / 3.6

= 1.5 per hour.

The coordinate of point R after the rotation is determined as = ( - 4, 7).

option A.

A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction.

You can turn a figure 90°, a quarter turn, either clockwise or counterclockwise. When you spin the figure exactly halfway, you have rotated it 180°. Turning it all the way around rotates the figure 360°.

When a figure is rotated 180 degrees, each point of the figure is moved to a new position that is exactly opposite its original position with respect to a fixed center of rotation.

The initial coordinate of point R = ( 4, 7),

The new coordinate of point R after the rotation = ( - 4, 7)

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We need to add a volume of 39.69 fluid ounces of gasoline to the mixture to bring it to 50 parts gasoline and 1 part oil.

Mensuration is the branch of mathematics concerned with the measurement of geometric figures and parameters such as length, volume, shape, surface area, and lateral area. 

According to information in the question:

The mixture is 40 parts gasoline and 1 part oil, there are 40 + 1 = 41 parts in total.

Let, the amount of oil in the mixture "x".

We know that there are 2 and 1/2 gallons of the mixture, which is the same as 2.5 * 128 = 320 fluid ounces.

So, the equation which can be formed is

x/41 * 320 = the amount of oil in the mixture (in fluid ounces)

Solving for "x":

x/41 * 320 = x/41 * 50 + 320 - (x/41 * 50)

Multiplying both sides by 41:

x * 320 = 50x + 41(320 - 50x)

Simplifying:

320x = 41(320)

x = 41 * 10 = 410 (fluid ounces of oil in the mixture)

Thus, amount of gasoline in the mixture is

40 parts gasoline / 41 parts total * 320 fluid ounces = 311.22 fluid ounces of gasoline.

Let the gasoline we need be "y", so a equation can be formed as follows

(311.22 + y)/(41 + y) * 320 = 410

Solving for y:

(311.22 + y)/(41 + y) = 410/320

Multiplying both sides by (41 + y) * 320:

311.22 + y = 410/320 * (41 + y) * 320

Simplifying:

311.22 + y = 205.625 * (41 + y)

311.22 + y = 8434.375 + 205.625y

Solving for y:

204.625y = 8123.155

y = 39.69 (fluid ounces of gasoline to add)

Therefore, we need to add 39.69 fluid ounces volume of gasoline to the mixture to bring it to 50 parts gasoline and 1 part oil.

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Answer:

line 3 and 4 I believe

Step-by-step explanation:

Look at the bootom numbers. Look at the one and follow it up, the only lines that are not over two and are still above one are lines 3 and 4.

Answer:

Lines 3 and 4

Step-by-step explanation:

A slope is rise over run. So you have to determine how many you rise (go up) and run (go over). This is represented in a fraction form (such as 1/2 is up 1 and over 2). A slope greater than one would be 1/1 (go up more than one and over more than 1), and less than two (go up less than 2 and over less than 1).

Line 1 goes up 3 and over 1 (3/1 = a slope of 3)

Line 2 goes up 2 and over 1 (2/1= a slope of 2)

Line 3 goes up 3 and over 2 (3/2 = a slope of 1.5 )

Line 4 goes up slightly more than 1 and slight over 1

Line 5 goes up 1 and over 1 (1/1 = a slope of 1)

after four passes through the filtration system, 99.19% of the original contaminants will have been removed from the water sample

How to solve the question?

Each time the water passes through the filtration system, 70% of the contaminants are removed, which means that 30% of the contaminants remain in the water. After the first pass, 30% of the original contaminants are left in the water. After the second pass, 30% of the remaining 30% is left, which is equivalent to 9% of the original contaminants. After the third pass, 30% of the remaining 9% is left, which is equivalent to 2.7% of the original contaminants. Finally, after the fourth pass, 30% of the remaining 2.7% is left, which is equivalent to 0.81% of the original contaminants.

Therefore, after four passes through the filtration system, 99.19% of the original contaminants will have been removed from the water sample. This calculation can be obtained by subtracting the final percentage of contaminants left (0.81%) from 100%.

It's important to note that while passing the water through the filtration system multiple times increases the overall percentage of contaminants removed, it's not a substitute for regular maintenance and replacement of the filtration system's components. Over time, the filtration system's effectiveness can diminish, and it's crucial to follow the manufacturer's instructions for proper maintenance and replacement to ensure that the system continues to function optimally.

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Answer:

Let the length of the rectangle be L. Then we can use the formula for the area of a rectangle:

Area = Length x Width

Substituting the given values, we get:

16 1/3 = L x 4 2/3

To solve for L, we can first convert the mixed numbers to improper fractions:

16 1/3 = 49/3

4 2/3 = 14/3

Substituting these values, we get:

49/3 = L x 14/3

To solve for L, we can multiply both sides by the reciprocal of 14/3:

49/3 ÷ 14/3 = L

Simplifying, we get:

L = 49/3 x 3/14

L = 7/1

L = 7

Therefore, the length of the rectangle is 7 inches.

Step-by-step explanation:

Therefore , the solution of the given problem of unitary comes out to be 105 different meal combos that could be made.

By combining the information obtained using this variable technique with all supplementary data from two individuals who used a specific tactic, the job can be completed. This mean that, if indeed the desired outcome materialises, either the stated person will be recognized or, in actuality, the colour by both huge processes will be skipped. For forty pens, a refundable charge of Rupees ($1.01) might be required.

Here,

b. The following formula can be used to determine the total interest charged over the loan's term:

=>  total interest = (monthly payment X n) - P .

There have been a total of:

=>  120 = ten years times one year.

The entire interest paid is thus:

=>  ($3,943.80) (total monthly installments * n) - P

=>  (131.19 * 120) - 9900 (rounded to the nearest dollar)

So, rounded to the closest dollar, Reh will pay about $3,944 in interest for the duration of his loan.

=>  7 entree choices, 5 drink options, and 3 dessert options are available.

We must add the number of drink options, entree options, and dessert options together to get the total number of potential meal combinations:

=> 5 x 7 x 3 = 105

There are 105 different meal combos that could be made.

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Answer:

2362 dollars for all the students

Step-by-step explanation:

my big brain

Answer:

ya you are right okokgudcv

Answer:

To solve the equation:

2/3x - 1/5x = x - 1

First, we need to find a common denominator for 2/3 and 1/5, which is 15. So we can rewrite the equation as:

(10/15)x - (3/15)x = 15/15 x - 1

Simplifying the left side:

(7/15)x = 15/15 x - 1

Multiplying both sides by 15:

7x = 15x - 15

Subtracting 7x from both sides:

-8x = -15

Dividing both sides by -8:

x = 15/8 or 1.875

Therefore, the solution to the equation is x = 1.875.

Answer:

Question 2. 12% of 650 = 78

Step-by-step explanation:

100% = 1 in decimal form.

This is because finding 100% of something is the same as multiplying it by 1:

E.g. 100% of 10=10,  10x1 = 10

Therefore to find a percentage of something, we simply need to multiply it by the decimal form of that percentage. For example, if we were finding 50% of 10 (half), 50% in decimal form is 0.5, 10x0.5 = 5

The percentage here is 12%, we can find the decimal form by dividing it by 100, 12/100 = 0.12

So, in order to find 12% of 650, we just need to multiply 650 by 0.12:

650x0.12 = 78

12% of 650 = 78

Hope this helped!

Answer:

5.5

Step-by-step explanation:

\( \frac{1}{6 - d} = \frac{1}{d - 5} \\ \\ \therefore \: 6 - d = d - 5 \\ \\ 6 + 5 = d + d \\ \\ 11 = 2d \\ \\ d = \frac{11}{2} \\ \\ d = 5.5\)

A system of inequalities that can be used to model the scenario is d + a ≤ 300 and 10d ≥ 1,200.

A system of inequalities is two or more inequalities that must be proved simultaneously.

A system of inequalities contains at least two linear inequalities in the same variables.

Systems of inequalities are applied when there are a range of solutions and more than one constraint.

Inequalities may include greater than, less than, not equal to, equal to but less than, and equal to but greater than.

The total capacity of people the auditorium can hold = 300

The cost per ticket at the door = $10

The cost per ticket in advance = $7.50

Tickets cannot exceed 300

Door tickets must generate at least $1,200

Let the number of tickets sold at the door = d

Let the number of tickets sold in advance = a

10d + 7.5a ≤ 300

10d ≥ 1,200

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Answer:

$886.47

Step-by-step explanation:

Answer:

301.59

Step-by-step explanation:

if f is a bijection, then f-cube is also a bijection, and the inverse of f-cube is f^-1(y1/3). These results are important for understanding the properties of functions and their inverses.

Finding the inverse of the cube of a bijective function is an important step in understanding the properties of functions. To prove that f-cube is a bijection if f is a bijection, we can use the fact that for any two real numbers x and y, if x = y, then x1/3 = y1/3. This means that if f(x) = f(y), then (f(x))3 = (f(y))3, or f-cube(x) = f-cube(y). Since f is a bijection, this means that x = y, so f-cube is also a bijection.

To find the inverse of f-cube, we can use the fact that for any real number x, x1/3 is a well-defined real number. This means that if we have f-cube(x) = y, we can take the cube root of both sides to get f(x) = y1/3. Since f is a bijection, it has an inverse function f^-1, so we can apply this inverse to both sides to get x = f^-1(y1/3). This means that the inverse of f-cube is f^-1(y1/3).

In conclusion, if f is a bijection, then f-cube is also a bijection, and the inverse of f-cube is f^-1(y1/3). These results are important for understanding the properties of functions and their inverses.

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We have the following:

let x cost of a box of candy

let y cost of a box of peanuts

resolving the system of equations:

now, for y

Therefore the cost of the box of candy is $ 2 and the cost of the box of peanuts is $ 25

Answer:

Yes

Step-by-step explanation: