Answer:
Robert can read the books in 129,600 different ways.
Step-by-step explanation:
The order in which the book are read is important, which means that the permutations formula is used to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
Top shelf:
4 books from a set of 6. So
[tex]P_{(6,4)} = \frac{6!}{2!} = 360[/tex]
Middle shelf:
2 books from a set of 3. So
[tex]P_{(3,2)} = \frac{3!}{2!} = 3[/tex]
Bottom shelf:
3 books from a set of 6. So
[tex]P_{(6,3)} = \frac{6!}{3!} = 120[/tex]
Total:
360*3*120 = 129,600
Robert can read the books in 129,600 different ways.
question in pictures
Answer:
V = 252 m³
Step-by-step explanation:
Formula for volume of a triangular prism = base area × height of prism
We are given the height (H) of the prism = 9 m
Let's find the base area using the figure of the base that is shown above with the dimensions:
Base area = ½*bh
b = 14 m
h = 4 m
Base area = ½*14*4
= 28 m²
✅Volume of the triangular prism = 28 × 9
= 252 m³
please draw out the rectangular prism parts
PLEASE HELP
Answer:
280
Step-by-step explanation:
Angle Relationships
When solving for x, the sine of 33° is used. What other angle and trigonometric function could be used to solve for x?
a. cos 57°
b. tan 33°
c. tan 57°
d. cos 33°
Please select the best answer from the choices provided
Answer:
A. cos 57°
Step-by-step explanation:
I calculated it logically
Answer:
The answer correct A. Cos 57
Step-by-step explanation:
90-33=57
Plz help me well mark brainliest if correct.....????
Answer:
The answer would be C. 31
Step-by-step explanation:
Answer:
Hello There!!
Step-by-step explanation:
15 Girls like fantasy books and 16 boys like fantasy books so in total the students that like fantasy books are 31.
hope this helps,have a great day!!
~Pinky~
How many solutions exist for the given equation?
1/2(x + 12) = 4x - 1
zero
one
two
O infinitely many
Answer: X = 2
Step-by-step explanation:
Step 1: Simplify both sides of the equation!
Step 2: Subtract 4x from both sides.
Step 3: Subtract 6 from both sides.
Step 4: Multiply both sides by 2/(-7).
Which of the following grids correctly graphs the points A (3, 1), B (0, 3), and C (1, 3)?
First quadrant grid with points A, B, and C labeled
First quadrant grid with points A, B, and C labeled
First quadrant grid with points A, B, and C labeled
First quadrant grid with points A, B, and C labeled
Answer:
First quadrant grid with points A, B, and C labeled
Step-by-step explanation:
Because that is the only option and I also don't see the graph
in desperate need of help please :/
Answer:
since 13 miles is 68640 i wood say 189 inches long from bumper to bumper. A mile is 5,280 feet (or 63,360 inches).
If 335 of these cars were parked with their bumpers touching, they would be almost exactly a mile long.
If your question refers to traffic jams, the answer will be a bit different, since cars in traffic jams don’t get that close together. I’m going to take a wild guess here, but let’s assume that there is a 4-foot gap between cars in our hypothetical traffic jam. now put that in to 13 miles
Step-by-step explanation:
R.
A circle has a diameter of 6 inches.
Show your work to find the following (use
3.14 for pi):
A) Area of the circle
B) Circumference of the circle
FIND THE VALUES FOR ANGLES A, B, C,
CuOUL/CYPLAIN YOUR
Answer: A IS CORRECT
Step-by-step explanation:
A ranger spots a forest fire while on a 30-meter observation tower. The angle of depression from the tower to the fire is 14°. To the nearest meter, how far is the fire from the base of the tower?
a. 7 meters
b. 4 meters
c. 124 meters
d. 120 meters
The fire from the base of the tower is at 120 m and Option D is the correct answer.
What is Angle of Depression ?The angle of depression is an angle formed between the horizontal line and the line of sight when an observer looks downwards at an object is known as an angle of depression.
The formula is
[tex]\rm sin\;\theta = y/z\\\\\\cos\; \theta = x/z\\\\\\tan\; \theta = y/x[/tex]
where x is the distance between the point of the ground and the object , horizontally,
y is the perpendicular distance between the surface to the object
and z is the measure of line of sight
[tex]\rm \theta[/tex] is the angle of depression = 14°
It is given in the question that y= 30 m
x= ?
To determine we will substitute the value
[tex]\rm tan\; \theta = y/x\\\\\\tan \;14^{o} = 30/ x\\\\\\0.25 = 30/x\\\\\\\x= 30/0.25\\\\\\x= 120 m\\[/tex]
Therefore the fire from the base of the tower is at 120 m and Option D is the correct answer.
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Find the volume of the solid
Answer:
V = 2784 mm^3
Step-by-step explanation:
The base of this prism is a right triangle. We can use the formula:
A = bh/2
to find the area of the base. A is area, b is base, and h is height. We can substitute what we have:
A = 16 * 12 / 2
A = 96
The volume of a prism is represented by the formula:
V = Bh
Where V is the volume, B is the base, and h is the height.
We have the area of the base as 96 and the height as 29, so we can substitute them in:
V = 96 * 29
V = 2784 mm^3
Marcie Ann Weber, age 32, takes out $15,000 of a term insurance for a ten year term.
annual premium: $
quarterly premium: $
Answer:
Annual premium = $1,500 per year
Quarterly premium = $375 per quarter
Step-by-step explanation:
Given:
Insured amount of term insurance plan = $15,000
Number of year = 10 year
Find:
Annual premium
Quarterly premium
Computation:
Annual premium = Insured amount of term insurance plan / Number of year
Annual premium = $15,000 / 10
Annual premium = $1,500 per year
Quarterly premium = Insured amount of term insurance plan / Number of quarter in 10 year
Quarterly premium = 15,000 / (10 x 4)
Quarterly premium = 15,000 / 40
Quarterly premium = $375 per quarter
How far from the base of the house do you need to place an 18’ ladder so that it exactly reaches the top of a 14’ wall?
Answer:
Length of Ladder(Hypotenuse)=18
Height of wall(Opposite) =14
How far from the base... This talks about the adjacent or distance between the wall and the base.
You can get your answer from Pythagoras theorem
Which states
The square of the hypotenuse is = to the squares of the adjacent and Opposite sides
H² = O² + A²
We're looking for the adjacent "A"
Making A the subject
A² = H² - O²
A= √H² - O²
A= √18² - 14²
A=√128
A= 8√2'
122333444455555666666777777788888888
what is the patern
Answer:
each number it being counted that number of times
hope this helps
have a good day :)
Step-by-step explanation:
Gary's stock dropped 3 points in value every day for 4 days. Find the integer that represents the change in value of his stock during that time.
Answer:
- 12 points
Step-by-step explanation:
He's dropping three points each day for four days, ie 4 * 3 , which is equal to 12.
What is an equation of the line that passes through the point(-1,-3) and is perpendicularly to the line x-2y=14
Answer:
the equation will be
Step-by-step explanation:
2x+y+5=0
Answer:
2x + y + 5 = 0
Step-by-step explanation:
The equation of line is x-2y = 14 and we need to find the equⁿ of line which passes through (-1,-3) and is perpendicular to given line.
Find the slope of given line by converting it into slope intercept form.=> x - 2y = 14
=> 2y = x - 14
=> y = x-14/2
=> y = x/2 - 7
Comparing to y = mx + c ,=> Slope (m) = 1/2 .
Now the slope of line perpendicular to it , will have a slope ,
=>[tex] m_{perp}[/tex] = -1/m
=>[tex] m_{perp}[/tex] = -1/½
=> [tex] m_{perp}[/tex] = -2
Using point slope form ,=> m = (y - y₁) / ( x - x₁)
=> -2 = { y - (-3) } / { x - (-1) }
=> -2 = y + 3/x + 1
=> -2(x + 1) = y + 3
=> -2x -2 = y + 3
=> y + 2x +3+2 = 0
=> 2x + y + 5 = 0
Hence the equation of line perpendicular to it is 2x + y + 5 = 0 .Last exam question for the day And im finally off!
No LINKS
Answer:
A1: a=4
A2: a=12
A3: p=18
Step-by-step explanation:
a= 1/2 4 * 2
= 4
a = 1/2 6 * 4
= 12
to find p add all sides
P= 6 + 6 + 6 = 18
please help me (no links or you are reported)
Answer:
whats the qestion??
Step-by-step explanation:
What is the solution to the inequality below?
√x>5
O A. No solutions
O B. O< x< 25
O C. x> 25
O D. x>10
Answer:
Quadratic Equations
A quadratic equation is one of the form ax2 + bx + c = 0, where a, b, and c are numbers, and a is not equal to 0.
Factoring
This approach to solving equations is based on the fact that if the product of two quantities is zero, then at least one of the quantities must be zero. In other words, if a*b = 0, then either a = 0, or b = 0, or both. For more on factoring polynomials, see the review section P.3 (p.26) of the text.
Example 1.
2x2 - 5x - 12 = 0.
(2x + 3)(x - 4) = 0.
2x + 3 = 0 or x - 4 = 0.
x = -3/2, or x = 4.
Analyze the table below and complete the instructions that follow.
A. A = 11, B = 39, C = 3, D = 8, E = 54
B. A = 22, B = 11, C = 5, D = 28, E = 54
C. A= 32, B= 17, C = 3, D= 8, E = 54
D. A = 22, B = 39, C = 3, D = 8, E = 54
You go to the ice cream shop and you can choose from 3 different flavors and 2 different toppings? What is the
probability that you will pick an ice cream with sprinkles?
Answer:
I Think C is correct
what is the answer to x+2y=2 and
3x+4y=-4
Answer:
x = − 8 and y = 5 or (-8, 5)
Step-by-step explanation:
what is 1+1-(3x3)-(1x9)
pls, be honest. 20 points
Answer:
it is 5.7 so it should be in between the 5 and 6 but closer to the 6.
Step-by-step explanation:
Hope this helps have a great day! :)
Answer: 5.7
Step-by-step explanation:
Because it’s closer to six but still In the 5 range.
A rectangle is removed from a right triangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct unit in
your answer.
00
alyd
yd
yde
yoo
3yd
х
3
?
2yd
4yd
2yd
Josie makes fruit punch by mixing fruit juice and lemonade in the ratio 1:3
She needs to make 28 litres of punch for a party,
How much of each ingredient does she need?
Fruit juice = 7 litres Lemonade = 21 litres [4]
During the party Josie decides to make some more.
She has 3 litres of fruit juice left and plenty of lemonade,
How much extra punch can she make?
litres
To make the second batch of punch go further Josie
adds 3 more litres of lemonade,
What is the ratio of fruit juice to
lemonade in the second batch?
4 When Janelle was born, her grandmother put $200 into a college savings account for her.
Each month, her grandmother adds $50 to the account. Which inequality can be used to find
m, the number of months it will take for Janelle's savings account to have more than $1,250
in savings?
A 200m + 50 > 1,250
B 200 + 50m > 1,250
C 200 + 50m < 1,250
D 200m + 50 < 1,250
Answer:
B
Step-by-step explanation:
200+50m >1250
This means that for every month her grandmother gives 50 for an unknown amount of months along with the first 200 dollars.
The greater than 1250 shows that until she is greater than 1250 she'll keep getting money
which of these fractions is greater and by how much? 3/5 or 3/8
Answer:
3/5
Step-by-step explanation:
Answer:
Step-by-step explanation:
3/5 is greater than 3/8 I’m not sure by how much tho
2x+y=3
x-y= 1
solve the equation
Answer:
x = 4/3
y = 1/3
Step-by-step explanation:
System of equations! This is set up really well to make the second equation equal x then substitute.
x - y = 1
x = 1 + y
and then our substitution:
2 (1+y) + y = 3
and solve:
2 + 2y + y = 3
3y + 2 = 3
3y = 1
y = 1/3
And now we can substitute that value into one of our equations:
x - (1/3) = 1
x = 4/3
Next we should check by substituting these values into both of our equations:
2 (4/3) + (1/3) = 3
9 / 3 does equal 3 !
(4/3) - (1/3) does equal 1 !
Therefore, x = 4/3 , and y = 1/3
A square has an area of 49in^2. If the same amount is added to the length and removed from the width, the resulting rectangle has an area of 45in^2. Find the dimensions of the rectangle Round your answer to the nearest tenth, when appropriate
The area of a rectangle is given as:
Area = Length x width
The dimensions of the rectangle are 9 inches and 5 inches.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
Area of a square = 49 in²
Area of a square = side²
This means the side of the square is 7 inches.
Now,
Let the same amount be x.
The area of the rectangle = 45 in²
The length of the rectangle = 7 + x
The width of the rectangle = 7 - x
The area of the rectangle = Length x Width
45 in² = (7 + x)(7 - x)
45 = 49 - 7x + 7x - x²
45 = 49 - x²
x² = 49 - 45
x² = 4
x = 2
Now,
The dimensions of the rectangle are:
Length = 7 + x = 7 + 2 = 9 inches
Width = 7 - x = 7 - 2 = 5 inches
Thus,
The dimensions of the rectangle are 9 inches and 5 inches.
Learn more about rectangles here:
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The identity (x^2 + y^2)^2 = (x^2 - y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples. What Pythagorean triple could be generated using x = 8 and y = 3?
Answer:
The triple are: 48, 55 and 73
Step-by-step explanation:
Given
[tex](x^2 + y^2)^2 = (x^2 - y^2)^2 + (2xy)^2[/tex]
[tex]x = 8; y=3[/tex]
Required
The Pythagorean triple
We have:
[tex](x^2 + y^2)^2 = (x^2 - y^2)^2 + (2xy)^2[/tex]
Substitute: [tex]x = 8; y=3[/tex]
[tex](8^2 + 3^2)^2 = (8^2 - 3^2)^2 + (2*8*3)^2[/tex]
[tex](64 + 9)^2 = (64 - 9)^2 + (48)^2[/tex]
[tex](73)^2 = (55)^2 + (48)^2[/tex]
[tex]5329 = 5329[/tex]
Hence, the triple are: 48, 55 and 73