A rectangular solid has edges that are 10, 8, and 3 units long.
1. Draw the solid, showing the 10 x 8 face as the base. Find:
a. The lateral area
b. The total area
c. The volume
2. Repeat Exercise 1, but show the 10 x 3 face as the base.
a.
b.
c.
We are adjusting the original rectangular solid and here is what we have:
1. Rectangular solid showing 10x8 face as the base(a) The lateral area is the sum of the areas of the four sides, which are all rectangles. The two sides with dimensions 8 x 3 have an area of 8 x 3 = 24 square units each, and the two sides with dimensions 10 x 3 have an area of 10 x 3 = 30 square units each. Therefore, the lateral area is:
2(24) + 2(30) = 48 + 60 = 108 square units
(b) The total area is the sum of the areas of all six faces. The two faces with dimensions 10 x 8 have an area of 10 x 8 = 80 square units each, the two faces with dimensions 8 x 3 have an area of 8 x 3 = 24 square units each, and the two faces with dimensions 10 x 3 have an area of 10 x 3 = 30 square units each. Therefore, the total area is:
2(80) + 2(24) + 2(30) = 160 + 48 + 60 = 268 square units
(c) The volume is the product of the length, width, and height of the rectangular solid. Therefore, the volume is:
10 x 8 x 3 = 240 cubic units
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The diameter of a circle is 5 centimeters. What’s the radius? Give the exact answer in simplest form
Answer:
2.5cm
Step-by-step explanation:
you half the diameter to get the radius
Pls help with this question
The plane degrees off course is 6.79 degrees off at a speed of 541. 92 km / hr relative to the ground.
How to find the degrees off course ?To find the airplane's course deviation and its ground speed, we need to first determine the velocity vectors of the airplane and the wind.
W x = W x cos(225) = 90 x cos(225) = -63.64 km/hr
Wy = W x sin(225) = 90 x sin(225) = -63.64 km/hr
Magnitude: |R| = sqrt(Rx^2 + Ry^2) = √(536.36^2 + (-63.64)^2) = 541.92 km/hr
Direction: θ = arctan(Ry / Rx) ≈ arctan (-63.64 / 536.36) = -6.79 degrees
So, the airplane is 6.79 degrees off course, and its ground speed is 541.92 km/hr.
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If P(A)=0.3, P(B)=0.2 and P(A∩B)=0.2 determine the following probabilities:
(a) P(A')
(b) P(A∪B)
(c) P(A'∩B)
(d) P(A∩B')
(e) P[(A∪B)']
The probabilities are as follows:
(a) P(A')= 0.7
(b) P(A∪B) = 0.3
(c) P(A'∩B) = 0
(d) P(A∩B') = 0.1
(e) P[(A∪B)'] = 0.7
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
(a) P(A') = 1 - P(A) = 1 - 0.3 = 0.7
(b) P(A∪B) = P(A) + P(B) - P(A∩B) = 0.3 + 0.2 - 0.2 = 0.3
(c) P(A'∩B) = P(B) - P(A∩B) = 0.2 - 0.2 = 0
(d) P(A∩B') = P(A) - P(A∩B) = 0.3 - 0.2 = 0.1
(e) P[(A∪B)'] = 1 - P(A∪B) = 1 - 0.3 = 0.7
Note: P(A) represents the probability of event A occurring, P(B) represents the probability of event B occurring, and P(A∩B) represents the probability of both events A and B occurring simultaneously. The symbol '∪' represents the union of two events, and the symbol '∩' represents the intersection of two events. The complement of an event A is represented by A'.
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3√b in exponential form
Triangle PQR is rotated 180 degrees clockwise about the origin to produce the image Triangle P’Q’R’. Which of the following statements is TRUE abóyate Triangle P’Q’R’.
Answer:
Step-by-step explanation:
We get triangle PQR by plotting the point P (1, 4), Q (3, 1), R (2, -1) on the graph paper when rotated through 180° about the origin. The new position of the point is: P (1, 4) → P' (-1, -4) Q (3, 1) → Q' (-3, -1) R (2, -1) → R' (-2, 1) Thus, the new position of ∆PQR is ∆P’Q’R’.
Landon and Maria are meeting at the library to work on their history project. Maria walks 9 blocks east and 3 blocks north to get to the library from her house. Landon walks 5 blocks south and 7 blocks west to get to the library from his house. The map below shows the location of the library and Landon's and Maria's houses. To the nearest block, how far is Landon's house from Maria's house if Maria could walk in a straight line?
To the nearest block, Landon's house is at distance of 12 blocks away from Maria's house if Maria could walk in a straight line.
What is Pythagoras theorem?A basic mathematical theorem relating to the sides of a right-angled triangle is known as Pythagoras' theorem. The square of the length of the hypotenuse, the side that faces the right angle, is said to be equal to the sum of the squares of the lengths of the other two sides, known as the legs, in a right triangle.
This can be written in mathematical notation as:
c² = a² + b²
where c is the length of the hypotenuse, and a and b are the lengths of the legs of the right triangle.
In this case, we can consider the straight line between Maria's house and Landon's house as the hypotenuse of a right triangle, with the distances they walked as the other two sides. We can use the distance formula to find the lengths of those sides:
Distance walked by Maria = √(9² + 3²) = √90 ≈ 9.49 blocks
Distance walked by Landon = √(5² + 7²) = √74 ≈ 8.60 blocks
Now we can use the Pythagorean theorem to find the distance between their houses:
Distance between houses = √(9.49² + 8.60²) ≈ 12.46 blocks
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how can you tell if a quotient is less than 1'.
Answer:
Step-by-step explanation:
Okay so when a smaller number is divided by a larger number, the quotient is less than 1. Hope this helps Bye sisters slay.
1. You go to the ice cream shop with your friends and you can choose an ice cream, a topping
and sprinkles. How many different sundaes can you make when you order one flavor of ice
cream, one topping and one color of sprinkles from the chart below? Show all possible
outcomes in a tree diagram.
Ice Cream
Chocolate
Vanilla
Strawberry
Topping
Fudge
Marshmallow
Sprinkles
Chocolate
Rainbow
How many sample spaces are there? HINT: How many possible combinations?
b. P (Chocolate, Fudge, Rainbow)
Answer:
Step-by-step explanation:
Answer:
You can make 12 possible sundaes with these toppings.
Step-by-step explanation:
Chocolate, Vanilla, and Strawberry all have 4 possible outcomes:
1. Fudge & Chocolate Sprinkles
2. Fudge & Rainbow Sprinkles
3. Marshmallow & Chocolate Sprinkles
4. Marshmallow & Rainbow Sprinkles
-------------------------------------------------------------------------------------------------------------
4 x 3 will equal 12, the total possible sundaes you can make with these toppings and ice cream flavors.
^4√p7
in exponential form.
Answer:1111
Step-by-step explanation:
Brenda is fishing from a small boat. Her fishing hook is 12 feet below her, and a fish is swimming at the same depth as the hook, 16 feet away. How far away is Brenda from the fish?
Answer:
We can use the Pythagorean theorem to solve this problem. Let's call the distance Brenda is away from the fish "x". Then, we have a right triangle with legs of length 12 and x, and a hypotenuse of length 16. So:
x^2 + 12^2 = 16^2
Simplifying:
x^2 + 144 = 256
x^2 = 112
Taking the square root of both sides:
x ≈ 10.6 feet
Therefore, Brenda is approximately 10.6 feet away from the fish.
Can someone help me with this problem, and explain how to solve it?
Thus, the height of flagpole from the ground is found as 23.34 feet.
Explain about the angle of elevation:The measurement of the angle between a person's eyes' line of sight to anything above and the horizontal line is known as the angle of elevation.
The movement of the observer's eyes determines the elevation angle. The angle of elevation is the angle formed by the line of sight and the horizontal line when a viewer is looking up at an object.
Given data:
height of boy = 5 ftDistance of boy from flagpole = 30 ft angle of elevation = 35 degreesLet the height of pole above the boy be 'h'feet.Using the trigonometric ratios in the right triangle ABE.
tan 35 = h / 30
h = 30* tan(35)
h = 18.34
Height of flagpole = 18.34 + 5 = 23.34 feet
Thus, the height of the flagpole from the ground is found as 23.34 feet.
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There is a 25% chance that a vowel is drawn from a bag of random letter tiles. what is the probability of drawing a vowel, placing it back in the bag, and then drawing a consonant
The probability of drawing a vowel, placing it back in the bag, and then drawing a consonant is 0.1875 or 18.75%.
The probability of drawing a vowel from the bag of random letter tiles is 25%. Since the tile is replaced after drawing, the probability of drawing a vowel on the second draw is also 25%.
The probability of drawing a vowel and then a consonant can be calculated by multiplying the probabilities of each event:
P(vowel and consonant) = P(vowel) x P(consonant)
= 0.25 x 0.75
= 0.1875
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. (Adapted from Terence Blows, Northern Arizona University.) Classify as in Exercise 6 but for the following circumstances. a. The amount of caffeine in the bloodstream decreases by 50% every 5 hours or so after stopping drinking coffee. b. The amount of trash in a landfill increases by 350 tons per week. c. The amount of alcohol in the bloodstream decreases by 10 grams (the amount in a standard drink) per hour after stopping drinking. d. Your age increases every day.
The statements are classified as Exponential decay and Linear growth.
What are the classification of the statements?
a. Exponential decay: The amount of caffeine in the bloodstream decreases by 50% every 5 hours, which indicates an exponential decay process where the quantity decreases at a constant percentage rate over time.
b. Linear growth: The amount of trash in a landfill increases by 350 tons per week, which indicates a linear growth process where the quantity increases by a constant amount over time.
c. Exponential decay: The amount of alcohol in the bloodstream decreases by 10 grams (the amount in a standard drink) per hour after stopping drinking, which indicates an exponential decay process where the quantity decreases at a constant percentage rate over time.
d. Linear growth: Your age increases every day, which indicates a linear growth process where the quantity (age) increases by a constant amount (1 day) over time.
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1. All numbered streets runs parallel to each other. Both 3rd and 4th Streets are intersected by King Ave. as shown:
(a) Suppose a car is traveling east on 4th Street and turns onto King Avenue heading northeast. What is the measure of the angle created by the car's turning? Explain your answer.
(b) Suppose a car is traveling southwest on King Avenue and turns left onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer.
(c) Suppose a car is traveling northeast on King Avenue and turns right onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer.
When the car travels east on 4th Street and turns onto King Avenue heading northeast, the angle created by the car's turning is a 45-degree angle.
When the car travels southwest on King Avenue and turns left onto 3rd Street, the angle created by the car's turning is a 135-degree angle.
When the car travels northeast on King Avenue and turns right onto 3rd Street, the angle created by the car's turning is a 45-degree angle.
How to get the Angle?(a) When the car travels east on 4th Street and turns onto King Avenue heading northeast, the angle created by the car's turning is a 45-degree angle. This is because the intersection of 4th Street and King Avenue creates a right angle, and the car turns northeast, creating another 45-degree angle with the horizontal 4th Street.
(b) When the car travels southwest on King Avenue and turns left onto 3rd Street, the angle created by the car's turning is a 135-degree angle. This is because the intersection of King Avenue and 3rd Street creates a right angle, and the car turns left, creating an additional 90-degree angle. Therefore, the total angle is 90 degrees + 45 degrees = 135 degrees.
(c) When the car travels northeast on King Avenue and turns right onto 3rd Street, the angle created by the car's turning is a 45-degree angle. This is because the intersection of King Avenue and 3rd Street creates a right angle, and the car turns right, creating another 45-degree angle with the horizontal 3rd Street.
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coordinate plane with points at A 0 comma 2 and B 2 comma 0 intersected by line f Dilate line f by a scale factor of one half with the center of dilation at the origin to create line f′. Where are points A′ and B′ located after dilation, and how are lines f and f′ related? The locations of A′ and B′ are A′ (0, 2) and B′ (0, 0); lines f and f′ intersect at point A. The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel. The locations of A′ and B′ are A′ (0, 0) and B′ (2, 0); lines f and f′ intersect at point B. The locations of A′ and B′ are A′ (0, 2) and B′ (2, 0); lines f and f′ are the same line.
The answer of the given question based on the graph is , The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.
What is Scale factor?A scale factor is a number that scales, or multiplies, a quantity by some factor. It is used in mathematics to describe the relationship between corresponding measurements of two similar figures, such as triangles or rectangles.
To dilate line f by scale factor of one half with center of dilation at origin, we multiply coordinates of each point on line f by 1/2.
The equation of line f can be found by using the points A and B:
slope of line f = (0 - 2)/(2 - 0) = -1
y-intercept of line f = 2
Therefore, the equation of line f is y = -x + 2.
To find the coordinates of A' and B' after dilation, we can apply the dilation factor to each point:
A' = (0, 2)*1/2 =(0, 1)
B' = (2, 0)*1/2 =(1, 0)
So A' is located at (0, 1) and B' is located at (1, 0) after dilation.
Now let's analyze the relationship between lines f and f'. The dilation was centered at the origin, so the origin is a fixed point of the dilation. This means that the point where lines f and f' intersect must be the origin.
If we plug in x = 0 into the equation of line f, we get y = 2. This means that point A is located at (0, 2) and intersects with line f at y = 2. After dilation, point A' is located at (0, 1), which means that lines f and f' intersect at point A.
To determine the relationship between lines f and f', we can compare their equations. The equation of f' can be found by using the points A' and B':
slope of f' = (0 - 1)/(1 - 0) = -1
y-intercept of f' = 0
Therefore, the equation of f' is y = -x.
Comparing the equations of f and f', we can see that they have the same slope of -1, which means they are parallel. Therefore, the correct answer is: The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.
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Chef Lori uses 1 1/4 cup of milk for every 3/4 cup of broth in her soup recipe. This recipe will feed 4 people. Lori is making soup for a banquet that will feed 120 people. How many gallons of milk and broth combined does she need.
Answer: To make soup for 4 people, Lori needs 1 1/4 cups of milk for every 3/4 cup of broth. Therefore, the ratio of milk to broth is:
(1 1/4 cups milk) / (3/4 cup broth) = (5/4 cups milk) / (3/4 cups broth) = (5/3) cups milk per cup of broth
To make soup for 120 people, Lori needs to multiply the ratio by 30 (120/4) to get the total amount of milk and broth needed:
(5/3 cups milk per cup of broth) * 30 = 50 cups of milk per 30 cups of broth
To convert cups to gallons, we divide by 16 (since there are 16 cups in a gallon):
50/16 = 3.125 gallons of milk
30/16 = 1.875 gallons of broth
Therefore, Lori needs a total of 3.125 + 1.875 = 5 gallons of milk and broth combined.
Step-by-step explanation:
Hello, I am confused on how to answer this question.
Answer: x=14
Step-by-step explanation:
cb=10.
ac=14
The value of X will be 14.
This is a simple mathematics problem that can be solved by using ratios.
Given, AC : BC : AB = 7 : 5 : 8
AC = X ; BC = 10 ; AB = X + 2
AC/ BC = X/ 10 = 7/5 (Ratios can also be represented as fractions)
X/10 = 7/5
On Transposing,
5X = 70
X = 70/5
X = 14
Alternatively,
BC/AB = 5/8 = 10/ (X + 2)
5/8 = 10/ (X + 2)
On Transposing,
80 = 5X + 10
5X = 70
X = 14
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Ian has a deck that measures 20 feet by 10 feet. He wants to increase each dimension by equal lengths so that its area is tripled. By how much should he increase each dimension?
Answer:
10 feet
Step-by-step explanation:
Let's start by finding the current area of the deck:
Area = length x width = 20 ft x 10 ft = 200 sq ft
If Ian increases each dimension by the same amount, let's call this amount "x", then the new dimensions of the deck will be:
Length = 20 ft + x
Width = 10 ft + x
The new area of the deck will be:
New Area = (20 ft + x) x (10 ft + x)
We know that Ian wants the new area to be triple the original area of 200 sq ft, so:
New Area = 3 x 200 sq ft
New Area = 600 sq ft
Substituting this into the equation above and solving for "x", we get:
(20 ft + x) x (10 ft + x) = 600 sq ft
200 + 30x + x^2 = 600
x^2 + 30x - 400 = 0
(x + 40) (x - 10) = 0
We discard the negative solution, and we get:
x = 10 ft
Therefore, Ian should increase each dimension by 10 feet to triple the area of his deck.
To confirm, we can check the original area of the deck which is 20 ft x 10 ft = 200 sq ft.
If Ian increases each dimension by 10 feet, the new dimensions of the deck will be 30 ft x 20 ft. The new area of the deck will be 30 ft x 20 ft = 600 sq ft. This is triple the original area of the deck (200 sq ft), which is what we wanted to achieve.
Therefore, increasing each dimension by 10 feet will triple the area of the deck as required.
Ian should increase both the sides by 10 feet each.
This is a simple mathematics problems related to the topic of mensuration.
Firstly we calculate the current area of the deck:
Area of the deck (rectangle) = l x b
Area of the deck (rectangle) = 20 x 10
Area of the deck (rectangle) = 200 square feet
Since Ian wants to triple the area of the deck, the required area is 600 square feet.
We now look at pairs of numbers multiplying which will give us 600:
(1,600) (2,300) (3,200) (4,150) (5,120) (6,100) (8,75) (10,60) (12,50) (15,40) (20,30) (25,24)
Out of the above pairs only one pair fulfils Ian's criteria to increase the length and breadth of the deck by equal measure, i.e., (20,30). So, Ian should increase the length and breadth of his deck by 10 feet each.
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Matt can save $225 per month that he puts into a savings
account earning 5% annual interest. How much will he have
saved after 2 years?
Answer:
FV ≈ $5,673.56
Step-by-step explanation:
To calculate the total amount that Matt will have saved after 2 years of saving $225 per month at an annual interest rate of 5%, we can use the formula for the future value of an annuity:
FV = P * (((1 + r/12)^(n*12) - 1) / (r/12))
where:
FV is the future value of the annuity
P is the periodic payment (in this case, $225 per month)
r is the interest rate per year (in this case, 5%)
n is the number of years (in this case, 2)
Substituting the given values, we get:
FV = $225 * (((1 + 0.05/12)^(2*12) - 1) / (0.05/12))
Using a calculator, we get:
FV ≈ $5,673.56
Therefore, after 2 years of saving $225 per month at an annual interest rate of 5%, Matt will have saved approximately $5,673.56.
The table below shows the numbers of two to five bedroom houses in the Belmont Neighborhood. What is the mean number of bedrooms in a house in this neighborhood?
Number of bedrooms Frequency
2 7
3 35
4 56
5 27
The mean number of bedrooms in a house in this neighborhood will be: 3.824.
How to determine the mean number of bedroomsIn order to find the mean number of bedrooms in a house in the Belmont Neighborhood, we need to calculate the weighted mean by multiplying each number of bedrooms by their respective frequency.
Next, we will add the products, and then divide by the total frequency. So we can start as follows:
(2 * 7) + (3 * 35) + (4 * 56) + (5 * 27) = 14 + 105 + 224 + 135 = 478
Total frequency = 7 + 35 + 56 + 27 = 125
Therefore, the mean number of bedrooms = 478 / 125 approximately 3.824
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If you horizontally…
Check the picture below.
so following the template below, a shift 2 units to the left, means C=2
[tex]G(x)=\sqrt{x+2}[/tex]
Hurry help Greg plants a seed and as soon as the plant sprouts, he measures its height each day and records his data for two weeks. If the plant continues to grow the whole two weeks, what would a line graph of Greg's data look like?
It would be flat.
It would move downward.
It would go up and down.
It would move upward.
The line graph of Greg's data wood look like "It would move upward."
What is graph?A graph is a visual representation of data that shows the relationship between two or more variables. There are several types of graphs that can be used to display data
If Greg is measuring the height of the plant each day and the plant is continuing to grow for two weeks, then the line graph of his data would move upward. The graph would show an increasing trend as the plant grows taller each day. Therefore, the correct answer is "It would move upward."
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Find the area of a shaded region
Answer:
40 cm²
Step-by-step explanation:
you have to multiply the top of the triangle by the base(40) which is 80 then you divide by two since it's a triangle then you get 40 again since your finding the area you have to put the 2 above the cm
Given the figure below .find X and Y to three significant digits.Write your answer in the answer box provided below
Check the picture below.
Make sure your calculator is in Degree mode.
[tex]\cos(25^o )=\cfrac{\stackrel{adjacent}{x}}{\underset{hypotenuse}{12}}\implies 12\cos(25^o)=x\implies \boxed{10.876\approx x} \\\\[-0.35em] ~\dotfill\\\\ \sin(25^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{12}}\implies 12\sin(25^o)=z \\\\[-0.35em] ~\dotfill\\\\ \sin(50^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{y}}\implies y=\cfrac{z}{\sin(50^o)}\implies y=\cfrac{12\sin(25^o)}{\sin(50^o)}\implies \boxed{y\approx 6.62}[/tex]
(01.08)
Let f(x) = 3x² + x - 3 and g(x) = x² - 5x +
1. Find f(x) - g(x).
Answer:
f(x) - g(x) = 2x² + 6x - 4
Step-by-step explanation:
f(x) - g(x)
= 3x² + x - 3 - (x² - 5x + 1) ← distribute parenthesis by - 1
= 3x² + x - 3 - x² + 5x - 1 ← collect like terms
= 2x² + 6x - 4
Please help will mark Brainliest
Step-by-step explanation:
5 cos (307) = 3
5 sin (307) = -4
just plot the point ( 3, -4 ) Done.
Answer:
The point is (3, -4) because 5 cos [307] = 3 and 5 sin [307] = -4
i have 60 square feet of paper to wrap a box in the shape of a right rectangular prism the height of the box is 1 2/3 feet the width is 4 feet and the length is 5 1/2 feet what percent of the box will remain unwrapped if i use all the paper i has available
The percent of the box that will remain unwrapped by the 60 square feet of paper is about 20.70%
What is a percentage?A percentage is a proportion of a number expressed as fraction of a 100
The dimensions in mixed fractions can be expressed as follows;
Height of the box = 1 2/3 feet = 5/3 feet
Width of the box = 4 feet
Length of the box = 5 1/2 feet = 11/2 feet
Surface area of the box, A = 2 × (5/3) × 4 + 2 × 4 × 11/2 + 2 × (5/3) × 11/2 = 227/3 = 75 2/3 square inches
The percent of the box that will remain unwrapped is therefore;
Percentage = 60/(227/3) × 100 ≈ 79.3%
The percentage of the box that will remain unwrapped is about (100 - 79.3)% = 20.70%
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6. Two out of every five Canadians read at least 10 books a year. What percent of Canadians read at least 10 books a year?
Answer:
40%
Step-by-step explanation:
2/5=x/100
cross multiply and you get 5x=200
by isolation the variable you will get x=40
therefore, 40% of Canadians read at least 10 books a year
3. How many ways can you line up 7 books on a shelf?
Answer:
There are 5040 different ways to arrange the 7 books on a shelf.------------------------------
Use the formula for permutations:
n! = n × (n - 1) × (n - 2) × ... × 1, where n is the number of objects and ! denotes a factorial.The number of objects is n = 7 books.
Calculate the factorial:
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040