Answer:
The volume of a rectangular prism is given by the formula V = l x w x h, where l is the length, w is the width, and h is the height.
The rectangular prism in question has the following dimensions:
Length (l) = 3 cm
Width (w) = 5 cm
Height (h) = 4 cm
Using the formula for volume, we get:
V = l x w x h
= 3 cm x 5 cm x 4 cm
= 60 cm³
Therefore, the volume of the rectangular prism is 60 cm³.
The answer is (d) 60 cm³.
I Hope This Helps!
1. Higher Order Thinking Sam made the shape at the right
from colored tiles. What is the area of the shape? Explain
how you found your answer.
1
square in
The area of the given shape is 22 square tiles. The given shape consists of two rectangles and a square.
To find the area of the shape, we need to find the area of each of these three shapes and then add them up.
First, we can see that the length of the longer rectangle is 6 tiles and the width is 2 tiles. Therefore, the area of this rectangle is 6 × 2 = 12 tiles.
Next, the length of the shorter rectangle is 3 tiles and the width is 2 tiles. Thus, the area of this rectangle is 3 × 2 = 6 tiles.
Finally, the square has a side length of 2 tiles, so its area is 2 × 2 = 4 tiles.
Adding up the areas of the three shapes, we get 12 + 6 + 4 = 22 tiles.
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a particular triangle has sides of length 14 cm, 8 cm and 9 cm. in centimeters, what is the perimeter of the triangle?
Answer:
31cm
Step-by-step explanation:
14 + 8 + 9 = 31
Make sure to add the cm on the end!
The perimeter of the triangle is 31cm.
The perimeter of the triangle with sides of length 14 cm, 8 cm and 9 cm is 31 cm. This can be calculated by simply adding up the length of each side. To explain, the perimeter of a triangle is the sum of the lengths of all three sides.
In this particular triangle, the length of side 1 is 14 cm, the length of side 2 is 8 cm and the length of side 3 is 9 cm. When we add these three lengths, we get the perimeter of the triangle: 14 cm + 8 cm + 9 cm = 31 cm.
In general, to calculate the perimeter of any triangle, we first have to identify the lengths of all three sides. Then, we simply add these lengths together to get the perimeter.
For example, if the triangle had sides of lengths 4 cm, 5 cm and 6 cm, then the perimeter would be 4 cm + 5 cm + 6 cm = 15 cm.
In conclusion, the perimeter of any triangle can be calculated by adding together the length of each side. In the case of the particular triangle in question, the perimeter is 31 cm.
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Find the sum of the first 48 terms of the following series, to the nearest integer.
5,9,13,. ???
The sum of the first 48 terms of the following series, to the nearest integer is 4632.
An computation progression( AP) is a sequence of figures where the differences between every two successive terms are the same. In this progression, each term, except the first term, is attained by adding a fixed number to its former term. This fixed number is known as the common difference and is denoted by'd'. The first term of an computation progression is generally denoted by' a' or' a1'.
We have series as,
5,9,13,....48
so we have
First term = a = 5
Last term T = 48
Interval between them as d = 9 - 5 = 4
To find the sum of the first 48 terms we have formula as,
[tex]S = \frac{n}{2} [a+(n-1)d]\\[/tex]
putting the value of the values in the equation,
[tex]S = \frac{48}{2} [5+(48-1)4]\\\\S = 24[5+188]\\\\S = 4632\\[/tex]
Therefore, the sum of the first 48 terms is 4632.
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Complete the statements about these similar pyramids. [picture of pyramids]two square base pyramids a and b are represented side-by-side. pyramid a has square base pqrs of side length 5 meters and t is the vertex. pyramid b has square base jklm of side length 25 meters and n is the vertex. the ratio of the heights is _____the ratio of the surface areas is ______the ratio of the volumes is ______
The ratio of the heights is 5, the ratio of the surface areas is 25, and the ratio of the volumes is 125
Step-by-step explanation:
We can use the fact that similar pyramids have the same shape, but possibly different sizes. Let's denote the height of pyramid a by h_a, the height of pyramid b by h_b, and the scale factor between the two pyramids by k. Then, we have:
The ratio of the heights is k, since the height is scaled up by the same factor as the base length. That is, k = h_b / h_a.
The ratio of the surface areas is k^2, since the surface area is proportional to the square of the base length and the height. That is, k^2 = (side length of b / side length of a)^2 = (25 / 5)^2 = 5^2 = 25.
The ratio of the volumes is k^3, since the volume is proportional to the cube of the base length and the height. That is, k^3 = (side length of b / side length of a)^3 = (25 / 5)^3 = 5^3 = 125.
Therefore, the ratio of the heights is 5, the ratio of the surface areas is 25, and the ratio of the volumes is 125.
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Answer:
height ratio- 1:5 surface area- 1:25 volume- 1:125
Step-by-step explanation:
a triangle has sides with lengths of 6 kilometers, 7 kilometers, and 10 kilometers. is it a right triangle?
Answer:
Step-by-step explanation:
no because 6 , 7 and 10 doesn't add up to 180 so it is not
A triangle has sides with lengths of 6 kilometers, 7 kilometers, and 10 kilometers is not a right triangle.
To determine if a triangle is a right triangle, you can use the Pythagorean Theorem. The Pythagorean Theorem states that "In a right-angled triangle, the sum of the square of the two shorter sides is equal to the square of the longest side." It can be written as:
a² + b² = c², where 'a' and 'b' are the lengths of the two legs of a right triangle, and 'c' is the length of the hypotenuse.
In this triangle, the two shorter sides have lengths of 6 kilometers and 7 kilometers and the longest side is 10 kilometers.
The square of 6 kilometers is 36 kilometers and the square of 7 kilometers is 49 kilometers.
The sum of 36 kilometers and 49 kilometers is 85 kilometers.
The longest side of the triangle has a length of 10 kilometers, and the square of 10 kilometers is 100 kilometers.
Since 85 kilometers is not equal to 100 kilometers, this triangle is not a right triangle.
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Which system of inequalities has the solution shown in the graph?
pLeAsE hElP
I need help solving this: 1+1
Answer:2
Step-by-step explanation:
1+1=2
two cyclists start from the same point and ride in opposite directions. one cyclist rides twice as fast as the other. in 2 hr, they are 72 mi apart. find the rate of each cyclist.
From the same starting point, two cyclists ride in different directions. The speed of one cyclist is twice that of the other. They will be 72 miles apart in 2 hours. The rate of each cyclist is 12 miles per hour and 24 miles per hour
Let’s call the rate of the slower cyclist “r”. Then, according to the problem, the rate of the faster cyclist is “2r”.
We can use the formula distance = rate x time to set up two equations, one for the distance traveled by the slower cyclist and one for the distance traveled by the faster cyclist. The sum of these distances is the total distance they are apart after 2 hours, which we know is 72 miles:
2r x 2+r x 2=72
Simplifying this equation, we get:
4r+2r=72
Combining like terms, we get:
6r=72
Dividing both sides by 6, we get:
R=12
So the rate of the slower cyclist is 12 miles per hour. Using the fact that the faster cyclist rides at twice the rate of the slower cyclist, we can find the rate of the faster cyclist:
2r=2 x 12=24
So the rate of the faster cyclist is 24 miles per hour.
Therefore, the two cyclists ride at rates of 12 miles per hour and 24 miles per hour, respectively.
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i hate math fr but pls help asap
Answer:
379.94
Step-by-step explanation:
Area of a circle given radius is really easy! The equation for area of a cicle is pi x r^2. So just plug in. Assuming pi is 3.14 your equation would be
3.14x11^2. 11 squared is 121. Then multiply by 3.14 and thats your answer.
When given a set of cards lying face down that spell M, A, T, H, C, L, U, B, determine the probability of randomly drawing a consonant.
six eighths
two sixths
six tenths
one third
Answer:
The answer is six eighths
There's 8 letters in all and 6 of them are consonants (M, T, H, C, L, B)
Step-by-step explanation:
so all you have to do is take out all the vowel and count the letters that are consonant then you make that your top number than you put that over the amount of numbers in total
the equation above relates the number of hours, a, kevin spends doing homework each week and the number of hours he spends watching television each week. if kevin spends a total of 15 hours doing homework and watching television each week, what does the variable b represent?
Variable b represents the number of hours Kevin spends watching television each week.
Define the term equation?A statement proving the equality of two mathematical expressions is known as an equation.
Given equation a + b = 15 relates the number of hours.
If here Kevin spends doing homework each week (represented by the variable "a") and the number of hours he spends watching television each week (represented by the variable "b").
Since the total number of hours Kevin spends doing homework and watching television each week is 15, we can write:
homework + watching television = 15 hours
a + b = 15
To find out what b represents, we can rearrange the equation to solve for b:
b = 15 - a
This means that b represents the number of hours Kevin spends watching television each week, given that he spends a hours doing homework each week and the total number of hours spent on both activities is 15.
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Complete question-
The equation is a + b = 15
the probability of drawing a diamond from a deck of cards is 1 4 ; what are the odds in favor of drawing a diamond from an ordinary deck of cards?
The probability of drawing a diamond from a deck of cards is 1/4. So, the odds in favor of drawing a diamond from an ordinary deck of cards are 1/3.
A deck of cards has 52 cards in it, and there are 13 cards of diamonds in it. So, the probability of drawing a diamond is 13/52. Simplifying 13/52, we get 1/4. The odds of an event happening are the ratio of the probability of an event happening to the probability of an event not happening. It's expressed in the form of x:y.
The probability of an event happening is the probability of success. The probability of an event not happening is the probability of failure. In the current scenario, the probability of drawing a diamond is 1/4. So, the probability of not drawing a diamond is 3/4. Therefore, the odds in favor of drawing a diamond are:
=1/3
The odds in favor of drawing a diamond from an ordinary deck of cards are 1/3.
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An app store opened in 2018, and consumers downloaded one million apps. The owner of the app store predicts that the number of app downloads (in millions) will increase at a rate of about 30% per year.
Write an exponential growth function f(x) that gives the number of app downloads (in millions) in year x
As a result, the app stοre's οwner prοjects that in its third year οf οperatiοn, there will be rοughly 2.197 milliοn app dοwnlοads.
What is expοnential functiοn ?A mathematical functiοn with the fοllοwing fοrmula is an expοnential functiοn: f(x) = [tex]a^x[/tex] where x is the expοnent and an is a cοnstant knοwn as the base. Expοnential functiοns have a distinctive structure where the value οf the functiοn rapidly rises (οr falls) as the expοnent x value rises. The rate οf increase οr decline is determined by the expοnential functiοn's base. If a > 1, the functiοn will quickly increase as x rises, and if 0 a 1, the functiοn will quickly decrease as x rises.
We can use the fοrmula: tο create an expοnential grοwth functiοn f(x) that prοvides the number οf app dοwnlοads (in milliοns) in year x.
[tex]f(x) = f(0) * (1 + r)^x[/tex]
where x is the number οf years since the app stοre first launched, r is the grοwth rate, and f(0) is the οriginal number οf dοwnlοads.
In this instance, there were 1 milliοn initial dοwnlοads, and the grοwth rate was 30%, οr 0.30. Thus, the fοllοwing is the expοnential grοwth equatiοn fοr the milliοns οf app dοwnlοads in year x:
[tex]f(x) = 1 * (1 + 0.30)^x[/tex]
[tex]f(x) = 1.3^x[/tex]
Therefοre, fοr instance, entering x=3 intο the functiοn will return the amοunt οf app dοwnlοads (in milliοns) fοr the third year.
[tex]f(3) = 1.3^3[/tex]
[tex]f(3) = 2.197[/tex]
As a result, the app stοre's οwner prοjects that in its third year οf οperatiοn, there will be rοughly 2.197 milliοn app dοwnlοads.
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LMNO id a parallelogram. If NM =c+30 and OL=4x +9, find the value of X NM AND OL
The value of x is 7, and NM and OL are both equal to 37.
Since LMNO is a parallelogram, its opposite sides must be parallel and equal in length. Therefore, we have,
NM = OL
We also have the following information:
NM = x + 30
OL = 4x + 9
Substituting the first equation into the second equation, we get:
x + 30 = 4x + 9
Simplifying this equation, we get:
3x = 21
Therefore, x = 7.
Substituting this value back into the original equations, we get:
NM = x + 30 = 7 + 30 = 37
OL = 4x + 9 = 4(7) + 9 = 37
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Place the steps of eukaryotic DNA replication in order, from when a germ cell enters gap 1 (G_1) phase to the cell cycle termination.
Answer:
The correct order of the steps of eukaryotic DNA replication from when a germ cell enters gap 1 (G1) phase to the cell cycle termination is : G1-> S Phase ->G2 ->Mitosis ->Cytokinesis ->Cell cycle termination
Step-by-step explanation:
The correct order of the steps of eukaryotic DNA replication from when a germ cell enters gap 1 (G1) phase to the cell cycle termination is as follows:
Step 1: G1 phase - During this phase, the germ cell is growing and preparing for DNA synthesis.
Step 2: S phase - DNA replication occurs during this phase. The chromosomes duplicate to form two identical chromatids, which remain attached at the centromere.
Step 3: G2 phase - During this phase, the cell checks for any errors in DNA replication and prepares for cell division.
Step 4: Mitosis - The cell divides its replicated DNA and organelles into two identical daughter cells. This process ensures that each daughter cell has the same amount of genetic material as the parent cell.
Step 5: Cytokinesis - The cytoplasm divides, creating two identical daughter cells.
Step 6: Cell cycle termination: After successful completion of mitosis and cytokinesis, the cell cycle is terminated, and the daughter cells may enter a new cycle or enter a non-dividing state (G0 phase).
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x=10
x-7y=-18 what is the answer
Answer: y=4
Step-by-step explanation:
you would plug in 10 wherever x would be so your new equation would be 10-7y=-18.
subtract 10 from both sides.
-7y=-28
then divide by -7
y=4
A square pyramid has a base with a side length of 4cm and triangular faces with a height of 7cm. Esther calculated the surface area as (4x4)+4(4x7) equals 128cm. Explain Esther's error and find the correct surface area
Esther missed including the surface area of the square sides of the pyramid. The correct surface area is found by adding the surface area of the four triangular faces, base, and sides. The total surface area is 104cm².
Esther's error was that she only considered the surface area of the triangular faces and the base of the pyramid. She failed to include the surface area of the pyramid's square sides.
To find the correct surface area of the pyramid, we need to add the surface area of the four triangular faces and the surface area of the square base and sides. The surface area of the square base is 4² = 16cm², and the surface area of each triangular face is (1/2)bh = (1/2)(4)(7) = 14cm². The surface area of each square side is 4 x 4 = 16cm².
Therefore, the correct surface area of the square pyramid is:
4 x 14cm² (for the four triangular faces) + 16cm² (for the base) + 4 x 16cm² (for the four square sides) = 104cm².
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Please answer with explanation!
The exact dimensions (in inches) of the cylindrical mailing tube that may be mailed using the postal service is 7 inches radius and a length of 14 inches.
How to calculate radius and length?To find the maximum volume of the mailing tube, maximize the function:
V = πr²L
subject to the constraint:
C = 2πr + L = 84
where C is the girth.
Using Lagrange multipliers, we need to solve the system of equations:
∇V = λ∇C
2πrL = λ(2π)
πr² = λ
2πr + L = 84
Taking the ratio of the first two equations:
L = 2r
Substituting this into the third equation:
4πr + 2r = 84
Simplifying:
r = 7
Substituting this into the equation L = 2r:
L = 14
Therefore, the cylindrical mailing tube of greatest volume that may be mailed using the postal service has a radius of 7 inches and a length of 14 inches.
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Image transcribed:
A package to be mailed using a certain postal service may not measure more than 84 inches in length plus girth. (Length is the longest dimension and girth is the largest distance around the package, perpendicular to the length.)
length
girth
Use Lagrange multipliers to find the exact dimensions (in inches) of the cylindrical mailing tube of greatest volume that may be mailed using the postal service.
radius ______ in
length ______ in
Ellie and Terrell are also putting new
carpeting in their family room,
which is a rectangle having length =
x + 3 and width = x + 1. What is
the area of the family room?
Answer:
x² +4x + 3
Step-by-step explanation:
Area = length x width
Area = (x + 3)( x + 1)
Area = x² + X + 3x +3
Area = x² + 4x +3
how many driving lessons do you need to do with a professioanl instructor before my parents could teach me
The number of driving lessons you need to take with a professional instructor before your parents can teach you varies depending on the regulations in your area. In some regions, a specific number of driving lessons is required by law before you can apply for your driver's license. As a result, you should check with your local Department of Motor Vehicles (DMV) or other regulatory agency to learn more about the specific requirements in your area.
In general, however, it is usually beneficial to take as many driving lessons as possible with a professional instructor. Professional driving instructors have been educated in how to teach driving skills safely and effectively. They have also assisted many other people in learning how to drive, and as a result, they have a wealth of knowledge and expertise to draw on.
The more driving lessons you take with a professional instructor, the more chances you'll have to learn and improve your driving abilities. You may be able to practice with your parents after only a few lessons, but it's generally a good idea to take as many as possible with an instructor before doing so. This will give you the best chance of success while you learn to drive safely and confidently.
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what does 4x^{3} ÷ 8 equal
Answer:
4x^{3} ÷ 8 = x^{3}/2
How to factor this so that it's in parenthesis? (Please use a detailed explanation thanks)
8n^2 -14n -15
Answer:
(4n+3)(2n-5)
Step-by-step explanation:
1) Split the second term [tex]8n^2-14n-15[/tex] into two terms.
1- Multiply the coefficient of the first term by the constant term.
[tex]8\times-15=-120[/tex]
2- Ask: Which two numbers add up to -14 and multiply to -120?
6 and -20
3- Split -14n as the sum of 6n and -20n.
[tex]8n^2+6n-20n-15[/tex]
2) Factor out common terms in the first two terms, then in the last two terms.
[tex]2n(4n+3)-5(4n+3)[/tex]
3) Factor out the common term [tex]4n+3[/tex].
[tex](4n+3)(2n-5)[/tex]
Find the area of a 2.5-by-2.5 square by splitting it into unit squares.
The area of 2.5 by 2.5 square is given as follows:
6.25 square units.
How to obtain the area of a square?The area of a square of side length s is given by the square of the side length, as follows:
A = s².
For this problem, we have 2.5 by 2.5 square, hence the side lengths are given as follows:
s = 2.5.
Then the area of 2.5 by 2.5 square is obtained applying the formula as follows:
A = 2.5²
A = 6.25 square units.
This means that the entire 2.5-by-2.5 square can be divided into 6.25 unit squares, in which each of them would have a side length of one unit.
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pls help me with both of them
The year that saw 164 billion dollars being spent on advertising, given the function for the advertising would be c. 1994
The dimensions of the rectangle, given the area of the rectangle would be:
Length : 12. 8 meters Width : 6.9 meters How to find the year ?The function is given by y = 0.93x² + 2.2x + 130, where y is the amount of money spent (in billions of dollars) and x is the number of years since 1990. We need to find the value of x when y = 164.
164 = 0.93x² + 2.2x + 130
0.93x² + 2.2x + 130 - 164 = 0
0.93x² + 2.2x - 34 = 0
x = 2.5
Now, we'll find the year by adding the value of x to 1990:
Year = 1990 + 2.5 = 1992.5
= 1994 which is the closest year in options
How to find the dimensions of the rectangle ?The area of the rectangle is given by:
Area = width × length
91 = (x + 2)(2x + 3)
91 = 2x² + 3x + 4x + 6
91 = 2x² + 7x + 6
2x² + 7x - 85 = 0
When solved differently:
x = 4.9
x = -3.5
Using the positive values:
Width = x + 2 ≈ 4.9 + 2 = 6.9 meters
Length = 2x + 3 ≈ 2(4.9) + 3 ≈ 9.8 + 3 = 12.8 meters
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Helppppppppppppppppp
a dance delegation of 4 people must be chosen from 5 pairs of dance partners. if 2 dance partners can never be together on the delegation, how many different ways are there to form the delegation?
There are 120 different ways to form the dance delegation from five pairs of dance partners if two dance partners can never be together on the delegation.
The total number of ways to form the delegation from five pairs of dance partners can be calculated using the combination formula. The combination formula is used to calculate the number of different combinations of n objects taken r at a time without repetition.
In this question, n is the total number of dance partners (5) and r is the number of people on the delegation (4).
Therefore, the calculation is as follows:
total number of ways = nCr
= 5C4
= 5! / 4!(5-4)!
= 5! / 4!1!
= 5 x 4 x 3 x 2 x 1 / 4 x 1 x 1
= 5 x 4 x 3 x 2
= 120
Hence, there are 120 different ways to form the dance delegation from five pairs of dance partners if two dance partners can never be together on the delegation.
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studies have shown that bats can consume an average of 10 mosquitoes per minute. what is the probability that a bat does not consume any mosquitoes in a 30-second interval?
The probability that a bat does not consume any mosquitoes in a 30-second interval is 0.0067379 or 0.67%.
In this case, the average rate of mosquitoes consumed by a bat is 10 per minute.
To find the rate for a 30-second interval, calculate the rate for 1 minute and then adjust it for the 30-second interval:
Average rate for 1 minute = 10 mosquitoes
Rate for 30 seconds = [tex]\dfrac{10 \,mosquitoes}{1 \,minute} \times \dfrac{1}{2}[/tex]
= 5 mosquitoes
The Poisson distribution probability mass function is given by:
[tex]\[ P(X = k) = \dfrac{e^{-\lambda} \cdot \lambda^k}{k!} \][/tex]
Where:
[tex]\(\lambda\)[/tex] is the average rate of events.
In this case, to find the probability that k = 0.
So, let's plug in the values:
[tex]\(\lambda = 5\)[/tex]
[tex]\(k = 0\)[/tex], back to the formula as
[tex]\[ P(X = 0) = \dfrac{e^{-5} \cdot 5^0}{0!} \][/tex]
Calculating the probability as
[tex]\[ P(X = 0) = e^{-5}[/tex]
[tex]= 0.0067379[/tex]
Therefore, the probability is 0.0067379 or 0.67%.
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the width of this rectangle is 1/3 of the length. Find the width of the rectangle
Answer:
length = 42 in , width = 14 in
Step-by-step explanation:
given the width is [tex]\frac{1}{3}[/tex] of the length , then
y - 4 = [tex]\frac{1}{3}[/tex] (2y + 6) ← multiply both sides by 3 to clear the fraction
3y - 12 = 2y + 6 ( subtract 2y from both sides )
y - 12 = 6 ( add 12 to both sides )
y = 18
then
length = 2y + 6 = 2(18) + 6 = 36 + 6 = 42 in
width = y - 4 = 18 - 4 = 14 in
11. To wrap gift boxes, Joelle uses 24 yards of ribbon, which is 86 of her total amount of ribbon. How many yards of ribbon does she have in all? A 32 B 192 C 300 D 1,920
Joelle has a total of 32 yards of ribbon in all, the correct option is A.
Let's use x to represent Joelle's total amount of ribbon. We know that 24 yards of the ribbon represent 86% of her total amount of ribbon, which can be expressed as:
24 = 0.86x
We can solve for x by dividing both sides by 0.86:
x = 27.91
The response options are all integers, thus we must round to the closest whole number because of this. Since 0.91 is greater than or equal to 0.5, we round up to 28.
Therefore, Joelle has a total of
x = 27.91 / 0.86
= 32.44 yards of ribbon.
Once again, we round to the nearest whole number, which is 32.
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The complete question is:
To wrap gift boxes, Joelle uses 24 yards of ribbon, which is 86 of her total amount of ribbon. How many yards of ribbon does she have in all?
A 32
B 192
C 300
D 1920
5 cards are drawn randomly from a regular deck of cards. how many ways can you draw 5 cards and get 4 hearts and 1 spade?
Answer:
There are 13 hearts in a deck of cards, so the probability of drawing a heart on the first draw is 13/52. After the first heart is drawn, there are 12 hearts left in the deck out of a total of 51 cards, so the probability of drawing another heart is 12/51. This process continues until we have drawn 4 hearts and 1 spade. Therefore, the total number of ways to draw 5 cards with 4 hearts and 1 spade is:
(13/52) x (12/51) x (11/50) x (10/49) x (13/48) x 5!
The factor of 5! accounts for the fact that the 5 cards can be drawn in any order. Simplifying the expression above, we get:
(13/52) x (12/51) x (11/50) x (10/49) x (13/48) x 120 = 0.000495 or approximately 1 in 2,020 ways.
Therefore, there are approximately 2020 ways to draw 5 cards from a regular deck of cards and get 4 hearts and 1 spade.
There are 54,145,200 ways to draw 5 cards and get 4 hearts and 1 spade from a regular deck of cards.
There are 13 hearts in a deck of cards, so the probability of drawing a heart on the first draw is 13/52 or 1/4. The probability of drawing another heart on the second draw, given that one heart has already been drawn, is 12/51. The same goes for the third and fourth draws. The probability of drawing a spade on the fifth draw is 13/50.
To calculate the number of ways to draw 4 hearts and 1 spade, we need to multiply the number of ways to choose 4 hearts from 13 (13 choose 4 or 715) by the number of ways to choose 1 spade from 13 (13 choose 1 or 13) and then multiply that by the number of ways to arrange those 5 cards (5!). So, the total number of ways is:
715 * 13 * 5! = 54,145,200
Therefore, there are 54,145,200 ways to draw 5 cards and get 4 hearts and 1 spade from a regular deck of cards.
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