The ratio of black and white keys of piano give correct values of A, B, C as 9, 52, 130.
The ratio of black to white keys of Piano of different sizes are as follow,
Black A 36 63 90
White 13 B 91 C
From the table of black and white keys relation of proportionality is equal to,
( A / 13 ) = ( 36 / B ) = ( 63 / 91 ) = ( 90 / C )
This implies ,
( A / 13 ) = ( 63 / 91 )
⇒ A = ( 63 / 91 ) × 13
⇒ A = ( 9 / 13 ) × 13
⇒ A = 9
Similarly,
( 36 / B ) = ( 63 / 91 )
⇒ B = 36 × ( 91 / 63 )
⇒ B = 36 × ( 13 / 9 )
⇒ B = 52
And
( 63 / 91 ) = ( 90 / C )
⇒ C = 90 × ( 91 / 63 )
⇒ B = 90 × ( 13 / 9 )
⇒ B = 130
Therefore, the correct values of A , B, C using the ratio of black and white keys of the piano is equal to 9, 52, 130.
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The above question is incomplete, the complete question is:
The table below shows the ratios of black to white keys on pianos of various sizes.
Black A 36 63 90
White 13 B 91 C
Determine which table has the correct values for A, B, and C.
F(x)=1/x squared -3x +1 then iind the inverse
The inverse function for the given function F(x)=1/x² -3x +1 is given by
f⁻¹(x) =(3 ± √(9 + 4/(x - 1))) /2.
Function f(x) is equals to,
F(x)=1/x² -3x +1
Inverse of a function, we need to swap the positions of the x and y variables and then solve for y.
Let's start with the original function
f(x) = 1/x^2 - 3x + 1
Now we will swap x and y,
⇒ x = 1/y^2 - 3y + 1
Next, Solve for y in terms of x
⇒ x = 1/y^2 - 3y + 1
⇒ x - 1 = 1/y^2 - 3y
⇒ 1/(x - 1) = y^2 - 3y
⇒ 1/(x - 1) = y(y - 3)
⇒ y(y - 3) = 1/(x - 1)
⇒ y^2 - 3y - 1/(x - 1) = 0
Using the quadratic formula, solve for y to get inverse function we have,
y = (3 ± √(9 + 4/(x - 1))) / 2
Therefore, the inverse function of f(x) is equal to f⁻¹(x) =(3 ± √(9 + 4/(x - 1))) /2.
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The above question is incomplete, the complete question is:
F(x)=1/x squared -3x +1 then Find the inverse
Determine the area and perimeter of the figure below. Note that each square is 1 unit in length.
Answer:
area = 127[tex]units^{2}[/tex]
perimeter = 46 units
Step-by-step explanation:
count them
as a television executive, you have been given 24 shows to choose from to run during your prime time slots each week. if you have to choose 16 shows to run on your network, how many ways can you choose which shows to pick up?
As per the combination concept, there are 735,471 ways to choose 16 shows from a set of 24.
To find the number of ways to choose 16 shows from a set of 24, we can use the formula for combinations, which is:
ⁿCₓ = n! / x!(n-x)!
Where n is the total number of objects in the set (in this case, 24), and x is the number of objects we want to choose (in this case, 16). The exclamation mark (!) denotes the factorial function, which means multiplying the number by all positive integers less than itself.
Plugging in the numbers, we get:
²⁴C₁₆ = 24! / 16!(24-16)! = 735471
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One fifth less than the product of seven and a number
Answer:
Step-by-step explanation:
[tex]\frac{1}{5}[/tex] ∠ 7x
[tex]\frac{1/5}{7}[/tex] ∠ x
1/35 ∠x
x ≥ [tex]\frac{1}{35}[/tex]
What are the values of x and y? *
Pls help!
Answer:
x = 8
y = 12
Step-by-step explanation:
m∠A = sin⁻¹(9/15) = 36.87⁰
cos36.87 = y/15
y = 15(cos36.87) = 12
sin36.87 = 12/(12+x)
12 + x = 12/(sin36.87)
x = 12/(sin36.87) - 12 = 8
An environmental agency frequently samples the water in a region to ensure that the levels of a certain contaminant do not exceed 30 parts per billion (ppb). From 12 randomly selected samples of the water, the agency constructed the 99 percent confidence interval (22.5, 28.7). Assuming all conditions for inference are met, which of the following is a correct interpretation of the interval? A For all water in the region, 99 percent of the water contains a level of the contaminant between 22.5 ppb and 28.7 ppb. B We are 99 percent confident that the mean level of the contaminant in the sample is between 22.5 ppb and 28.7 ppb. We are 99 percent confident that the mean level of the contaminant in all the water in the region is between 22.5 ppb and 28.7 ppb. D There is a 0.99 probability that the mean level of the contaminant in the sample is between 22.5 ppb and 28.7 ppb. E There is a 0.99 probability that the mean level of the contaminant in all the water in the region is between 22.5 ppb and 28.7 ppb.
The correct interpretation of the 99 percent confidence interval (22.5, 28.7) is B: We are 99 percent confident that the mean level of the contaminant in the sample is between 22.5 ppb and 28.7 ppb.
This does not indicate that the mean level of the contaminant in all the water in the region is necessarily between 22.5 ppb and 28.7 ppb.
Confidence intervals provide an estimate of the population mean based on a sample. In other words, they indicate the range of values that are likely to include the true mean of the population. Therefore, the interval (22.5, 28.7) indicates that we are 99 percent confident that the mean of the sample (which is used to estimate the true population mean) lies between 22.5 ppb and 28.7 ppb. However, this does not guarantee that the true population mean (i.e., the mean of all the water in the region) lies between 22.5 ppb and 28.7 ppb.
The other answers are incorrect because they do not reflect the fact that the interval provides an estimate of the population mean based on a sample.
Answer A is incorrect because it states that all of the water in the region must contain a level of the contaminant between 22.5 ppb and 28.7 ppb, which is not necessarily true.
Answer D is incorrect because it states that there is a 0.99 probability that the mean of the sample is between 22.5 ppb and 28.7 ppb, when in reality the interval indicates that we are 99 percent confident that the mean of the sample is between 22.5 ppb and 28.7 ppb. Finally,
Answer E is incorrect because it states that there is a 0.99 probability that the true population mean (i.e., the mean of all the water in the region) is between 22.5 ppb and 28.7 ppb, which is not necessarily true.
In summary, the correct interpretation of the 99 percent confidence interval (22.5, 28.7) is that we are 99 percent confident that the mean level of the contaminant in the sample is between 22.5 ppb and 28.7 ppb.
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we have 45 m2 of material to build a box with a square base and no top. determine the dimensions of the box that will maximize the enclosed volume.
The dimensions of the box that will maximize the enclosed volume are l = √(45/2) m and h = (22.5 - l²)/2 m.
To determine the dimensions of the box that will maximize the enclosed volume if we have 45 m² of material to build a box with a square base and no top, we can use the following steps:
Step 1: Write the formula for the volume of the box.V = l²h
Step 2: Write the formula for the surface area of the box.S = 2l² + 4lh
Step 3: Substitute S = 45 m² and simplify.2l² + 4lh = 45 m²l² + 2lh = 22.5 m²h = (22.5 - l²)/2
Step 4: Substitute the value of h in the formula for the volume and simplify.V = l²[(22.5 - l²)/2]V = (22.5l² - l⁴)/2
Step 5: Take the derivative of V with respect to l.dV/dl = 45l - 2l³
Step 6: Set dV/dl = 0 and solve for l.45l - 2l³ = 0l(2l² - 45) = 0l = 0 or l = √(45/2)
Step 7: Determine if the critical point is a maximum or a minimum by taking the second derivative of V with respect to l.d²V/dl² = 45 - 6l²d²V/dl² > 0 for l = √(45/2)
Therefore, the dimensions of the box that will maximize the enclosed volume are l = √(45/2) m and h = (22.5 - l²)/2 m.
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For the given figure, can you conclude mlln? Explain.
the doctor has ordered 1.25 mg/kg of a medication im. it the patient weighs 175 lbs. the drug on hand is available is a vial with 100 mg/2ml. (1) how many mg will be given? (2) calculate the amount to be injected.
1. The amount of medication to be given is 99.25 mg.
2.The amount of 1.985 mL medication should be injected.
To answer the given question, let's follow the steps mentioned below.
Determine the amount of medication to be given:1. Convert the weight of the patient from pounds to kilograms.
175 pounds = 79.4 kilograms
2. Multiply the patient's weight in kilograms by the ordered dosage.
1.25 mg/kg × 79.4 kg = 99.25 mg
Therefore, 99.25 mg of medication is required
Calculate the amount to be injected1. Find the number of milliliters (mL) required to deliver the medication dosage.
The concentration of the drug is 100 mg/2 mL.
100 mg/2 mL ÷ 1 = 50 mg/m
2. Divide the total amount of medication required by the concentration of the drug.
99.25 mg ÷ 50 mg/mL = 1.985 mL
Therefore, 1.985 mL of the medication should be injected.
Note:
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Consider the system of equations
below. What is the solution of the
system?
y=4x-8
4x + 2y = 20
Answer:
x = 3, y = 4
Step-by-step explanation:
Substitute 4x - 8 in for y and then solve for x:
4x + 2(4x - 8) = 20
Then, 4x + 8x - 16 = 20 --> 12x = 36 --> x = 3.
Once you have x, you can solve for y.
y = 4x - 8 = 4(3) - 8 = 12 - 8 = 4
So, x = 3, y = 4
you're playing a game in which the probability of winning each round is .20. if you play five times, what is the probability of winning exactly 2 of the 5 times?
the probability of winning exactly 2 of the 5 times is 0.2048, or approximately 20.48%
define probabilityProbability refers to the measure of the likelihood or chance of a particular event occurring. It is represented by a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certainty.
The formula for the binomial distribution can be used to resolve this issue:
P(X=k) = (n choose k) × pᵇ×(1-p)ⁿ⁻ˣ
where:
The number of trials, n, is five in this instance.
bis the number of successes we want (in this case, b = 2)
p is the probability of success on each trial (in this case, p = 0.20)
So, plugging in the values:
P(X=2) = (5 choose 2) ×0.20² × (1-0.20)⁵⁻²
= 10 × 0.04×0.512
= 0.2048
Therefore, the probability of winning exactly 2 of the 5 times is 0.2048, or approximately 20.48%.
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the sum of the numbers (20cba)16 and (a02)16 is ( (click to select) )16 and their product is ( (click to select) )16.
To solve this problem, we need to convert the hexadecimal numbers (20cba)16 and (a02)16 to decimal form, add them together, and then convert the result back to hexadecimal form.
(20cba)16 = 2x16^4 + 12x16^3 + 11x16^2 + 10x16^1 = 131402
(a02)16 = 10x16^2 + 0x16^1 + 2x16^0 = 256
Adding the two decimal numbers together gives us:
131402 + 256 = 131658
To convert this decimal number back to hexadecimal form, we can use the repeated division method.
131658 / 16 = 8228 remainder 10 (A)
8228 / 16 = 514 remainders 4 (4)
514 / 16 = 32 remainder 2 (2)
32 / 16 = 2 remainder 0
2 / 16 = 0 remainder 2
Therefore, (20cba)16 + (a02)16 = (131658)10 = (2002A)16.
To find their product, we can multiply the two decimal numbers together and then convert the result to hexadecimal form.
131402 x 256 = 33559552
Converting this decimal number to hexadecimal form gives us:
33559552 / 16 = 2097472 remainder 0
2097472 / 16 = 131092 remainder 0
131092 / 16 = 8193 remainder 4 (4)
8193 / 16 = 512 remainders 1 (1)
512 / 16 = 32 remainder 0
32 / 16 = 2 remainder 0
2 / 16 = 0 remainder 2
Therefore, the product of (20cba)16 and (a02)16 is (33559552)10 = (2011004)16.
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A particle of mass 1. 2 kg is moving with speed of 8 ms inn a straight line on a horizontal table. A resistance force is app. Lied to the particle in the direction of the motion. The magnitude of the force is proportional to the square of the speed, ao that F=0,3v^2
The speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2[/tex], or 19.2 N.
A particle of mass 1.2 kg is moving with a speed of 8 m/s in a straight line on a horizontal table. A resistance force is applied to the particle in the direction of the motion. The magnitude of the force is proportional to the square of the speed, such that [tex]F=0.3v^2[/tex]
The force of resistance is an opposing force that acts to reduce the speed of the particle. As the particle moves faster, the resistance force increases. The force is proportional to the square of the speed, meaning that if the speed doubles, the force is multiplied by four. The force is also in the same direction as the motion, meaning that it will reduce the speed of the particle.
The equation for the force of resistance is [tex]F=0.3v^2[/tex], where v is the speed of the particle. Therefore, if the speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2,[/tex] or 19.2 N. This means that the force of resistance acting on the particle is 19.2 N.
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suppose you have 4 pairs of socks and 4 pairs of shoes. if you can wear any combination of socks and shoes, including mismatched pairs, how many different possible footwear choices can you make
There are a total of 32 different possible footwear choices that we can make.
Given, The number of pairs of socks = 4
The number of pairs of shoes = 4
We are to find out the number of possible footwear choices we can make if we can wear any combination of socks and shoes, including mismatched pairs.
So, We can wear any pair of socks with any pair of shoes including a mismatch.
Thus, for each pair of socks, there are 4 possible pairs of shoes.
And for each pair of shoes, there are 4 possible pairs of socks.
Therefore, we can form,
Total number of possible footwear choices = 4 pairs of socks * 4 pairs of shoes * 2 (considering the case of mismatched pairs) = 32 pairs.
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alexis puts dimes and quarters aside for the parking meter. she has a total of 20 coins and they are worth $3.80. how many quarters does alexis have?
Alexis has 12 quarters and 8 dimes.
Let's use d to represent the number of dimes and q to represent the number of quarters. We know that Alexis has a total of 20 coins, so d + q = 20.
We also know that the value of these coins is $3.80. Since dimes are worth $0.10 and quarters are worth $0.25, we can write an equation for the total value in cents:
10d + 25q = 380
To make things easier, let's divide both sides of the equation by 5:
2d + 5q = 76
Now we can use the first equation to solve for d in terms of q:
d + q = 20
d = 20 - q
Substituting this into the second equation gives:
2(20 - q) + 5q = 76
Expanding the parentheses and simplifying, we get:
40 - 2q + 5q = 76
3q = 36
q = 12
Therefore, Alexis has 12 quarters. We can check this by plugging q back into the first equation to find that she has 8 dimes as well:
d + q = 20
d + 12 = 20
d = 8
The total value of 12 quarters and 8 dimes is:
12 quarters x $0.25 per quarter + 8 dimes x $0.10 per dime = $3.00 + $0.80 = $3.80
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Graph the line passing through (−4,−1) whose slope is m=−45
Step-by-step explanation:
y=mx+b
let(-4,-1)
x. y
then lets fill it with the formula
-4=-45(-1)+b
-4=45+b
-b=45+4
-b=49
b=-49
Find the volume of a right circular cone that has a height of 20 ft and a base with a radius of 18 ft. Round your answer to the nearest tenth of a cubic foot
Answer:
The answer should be 20,365.714 but I am not sure
Step-by-step explanation:
What are the integer solutions to the inequality below?
−
1
≤
x
≤
3
Answer:
i don't know i haven't done integers in a long time
Step-by-step explanation:
Help meee plssssss!!!!!!11
Write an explicit formula that can be used to find the number of bacteria cells after each generation. Then use the formula to find how many cells there are after 10 generations.
Answer:
N = N0 x 2^n
Step-by-step explanation:
The formula for calculating the number of bacteria cells after n generations is N = N0 x 2^n, where N is the total number of cells after n generations, N0 is the initial number of cells, and 2^n represents the number of times the population doubles after n generations. Assuming an initial population of 100 cells, there will be approximately 102,400 cells after 10 generations.
Answer:
The explicit formula for the number of bacteria cells after each generation can be written as:
N = N0 * r^n
Where:
N is the number of bacteria cells after n generations
N0 is the initial number of bacteria cells (at n=0)
r is the growth rate (how many new cells are produced per existing cell)
Assuming that each bacteria cell doubles in number with each generation (i.e. r=2), the formula can be simplified to:
N = N0 * 2^n
To find the number of cells after 10 generations, we can substitute n=10 into the formula:
N = N0 * 2^10
Since we don't have a specific value for N0, we can't find the exact number of cells after 10 generations. However, we can make some assumptions. For example, if we assume that there are initially 100 bacteria cells (N0=100), we can calculate:
N = 100 * 2^10 = 102,400
So, if each bacteria cell doubles in number with each generation and there were initially 100 cells, there will be 102,400 cells after 10 generations.
please thank me by marking my answer as brainlest!
What is the volume of the cone expressed in terms of pi?
1 7/8 hours every wednesday
2 3/8 hours every friday
What is total number of hours?
The total number of hours is 30 hours as the sum of 7/8 and 3/8 comes out to be 30 hours.
1) We know that there is a total of 24 hours in a day.
therefore, 7/8 hours of Wednesday =
number of hours in a day = 24
number of hours every Wednesday = 7/8
= 7/8 x 24 hours
= 7 x 3 hours
= 21 hours
7/8 hours every Wednesday means 21 hours every Wednesday.
2) We know that there are a total of 24 hours in a day;
therefore, 3/8 hours of Friday =
number of hours in a day = 24
number of hours every Friday = 3/8
= 3/8 x 24 hours
= 3 x 3 hours
= 9 hours
3/8 hours every Friday means 9 hours every Friday.
therefore, the total number of hours = 21 + 9 = 30
The total number of hours is 30 hours as the sum of 7/8 and 3/8 comes out to be 30 hours.
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Find the missing of dimension of the cone. Round you answer to the nearest tenth. Volume=13. 4m³
Radius=3. 2m
Height=h
The missing dimension of the cone is its height, which is approximately 2.5 m when rounded to the nearest tenth.
We can use the formula for the volume of a cone, which is:
Volume = (1/3)πr²h
where r is the radius of the base and h is the height of the cone.
We are given the volume of the cone as 13.4 m³ and the radius as 3.2 m. Substituting these values into the formula, we get:
13.4 = (1/3)π(3.2)²h
Multiplying both sides by 3 and dividing by π(3.2)², we get:
h = 3 × 13.4 / π(3.2)²
h ≈ 2.5 m
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Help Please
m-6=50
i need to find the value of m
please urgent
Answer:
m = 50 + 6
m= 56
lol easy ques
This one is easy. All you have to do is add 6 to both sides to get the value of m
m-6=50
m=50+6
m=56
Bennie is calculating the density of books in a box. He knows the number of books in the box and the volume of the box. Which of the following formulas can be used to calculate the density of books in the box? Density = number of books over volume of box Density = volume of box over number of books Volume of shelf = density over number of books Number of books = density over volume of box
Answer:
Density = number of books over volume of box
Step-by-step explanation:
The formula that can be used to calculate the density of books in the box is:
Density = number of books / volume of box
This formula relates the number of books in the box to the volume of the box, and calculates the density of books per unit volume.Therefore, the correct formula to calculate the density of books in the box is the first one given in the options:
Density = number of books over volume of box
Answer:
Density = number of books over volume of box
Step-by-step explanation:
Pls help ASAP. Will mark BRAINLIEST if answered CORRECTLY!
Diameter = 16 mm
Radius = Diameter/2
= 16/2
= 8 mm
Total height of figure = 32 mm
Height of cylinder = 19 mm
Height of cone = 32 - 19
= 13 mm
Volume of cylinder = πr²h
Substituting the values of r and h in above formula,,
[tex] \longrightarrow \sf \pi \times {(8)}^{2} \times 19 \\ \\ \longrightarrow \sf \pi \times 64 \times 19 \\ \\ \longrightarrow \sf 1216 \pi \\ \\ \longrightarrow \sf 3820.17 \: mm^{3}\\ \\ [/tex]
Hence, Volume of cylinder is 3820.17 mm³
Now,
Volume of cone = 1/3 πr²h
[tex] \longrightarrow \sf \dfrac{1}{3} \times \pi \times {(8)}^{2}\times 13 \\ \\ \longrightarrow \sf \dfrac{1}{3} \times \pi \times 64 \times 13 \\ \\ \longrightarrow \sf 871.26~ mm^3 \\ \\ [/tex]
Hence, Volume of the cone is 871.26 mm³
Volume of composite figure = Volume of cylinder + Volume of cone.
= 3820.17 + 871.26
= 4691.43 mm³
Therefore, Volume of the composite figure is 4691.43 mm³.
Find a power series representation for the function. (Center your power series representation at x = 0.) f(x) = 1/5 + x f(x) = sigma^infinity_n = 0 ((1/5 + x)^n) Determine the interval of convergence.
a) The power series representation of f(x) = 1/5 + x f(x) centered at x = 0 is f(x) = sigma^infinity_n = 0 ((x/5)^n)
b) The interval of convergence is (-5, 5)
To find the power series representation of f(x), we can use the formula for the geometric series
1 / (1 - r) = sigma^infinity_n = 0 (r^n)
where r is a constant.
In this case, we have
f(x) = 1/5 + x f(x)
We can solve for f(x) to get
f(x) = 1/5 / (1 - x)
Using the formula for the geometric series with r = x/5, we have
f(x) = sigma^infinity_n = 0 ((x/5)^n)
Multiplying both sides by 5, we get
5f(x) = sigma^infinity_n = 0 (x^n
So the power series representation of f(x) centered at x = 0 is
f(x) = sigma^infinity_n = 0 ((x/5)^n)
To determine the interval of convergence, we can use the ratio test
| (x/5)^(n+1) | / | (x/5)^n | = |x/5|
The series converges if the limit of |x/5| as n approaches infinity is less than 1. This is true when |x| < 5, so the interval of convergence is (-5, 5).
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help please image attached
The first inequality -4 ≤ x ≤ 3 represents the values of x that fall between the two vertical lines, while the second inequality 1 ≤ y ≤ 6 represents the values of y that fall between the two horizontal lines.
Describe Inequality?An inequality is a mathematical statement that compares two quantities or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).
Inequalities can involve variables or constants, and can be expressed in one variable or multiple variables. The solution to an inequality is the set of values that satisfy the inequality.
For example, the inequality 2x + 3 > 7 is true for values of x that are greater than 2, since if we substitute x = 2, we get 2(2) + 3 = 7, which is not greater than 7. On the other hand, if we substitute x = 3, we get 2(3) + 3 = 9, which is greater than 7, so the inequality is true for x > 2.
Inequalities have many applications in mathematics and other fields, such as economics, physics, and engineering. They are used to represent constraints in optimization problems, to model relationships between variables, and to describe ranges of possible values for a quantity or variable.
To determine the double inequalities that define the shaded region, we need to find the equations of the two boundary lines that form the sides of the shaded region.
The two vertical lines are x=-4 and x=3. The two horizontal lines are y=1 and y=6.
The shaded region is enclosed by these four lines, so the double inequalities that define it are:
-4 ≤ x ≤ 3 and 1 ≤ y ≤ 6
The first inequality -4 ≤ x ≤ 3 represents the values of x that fall between the two vertical lines, while the second inequality 1 ≤ y ≤ 6 represents the values of y that fall between the two horizontal lines. Together, they define the rectangular shaded region with vertices (-4,1), (-4,6), (3,6), and (3,1).
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Rolling a Die If a die is rolled one time, find these probabilities. Enter your answers as fractions or as decimals rounded to 3 decimal places.Part 1 of 3 (a) Getting an even number. P(an even number)= ___Part 2 of 3 (b) Getting a number less than or equal to 4. P(a number less than or equal to 4)=___ Part 3 of 3 (c) Getting a number greater than 5 and an even number. P(a number greater than 5 and an even number) = ___
P(a number greater than 5 and an even number) = 1/6 or 0.167
Part 1 of 3 (a) To find the probability of getting an even number, divide the number of favorable outcomes (rolling a 2, 4, or 6) by the total possible outcomes (rolling any number between 1 and 6). There are 3 even numbers and 6 total possible outcomes.
P(an even number) = [tex]3/6 = 1/2 or 0.500[/tex]
Part 2 of 3 (b) To find the probability of getting a number less than or equal to 4, count the favorable outcomes (rolling a 1, 2, 3, or 4) and divide by the total possible outcomes (6). There are 4 favorable outcomes and 6 total possible outcomes.
P(a number less than or equal to 4) =[tex] 4/6 = 2/3 or 0.667[/tex]
Part 3 of 3 (c) To find the probability of getting a number greater than 5 and an even number, count the favorable outcomes (rolling a 6) and divide by the total possible outcomes (6). There is 1 favorable outcome and 6 total possible outcomes.
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4in 5in 6in 6in 8in 7in triangular prism surface area
the surface area of the given triangular prism with sides of 4in, 5in, 6in, 6in, 8in, and 7in is 146 square inches.
To calculate the surface area of a triangular prism, you need to find the area of each of the faces and add them up.
First, let's find the area of the two triangular faces. To do this, we need to find the base and height of each triangle. Since the prism is isosceles, the base of each triangle is 6 inches (the length of one of the sides of the equilateral triangle). The height of each triangle can be found using the Pythagorean theorem. We have two sides of the triangle: 4 inches and 5 inches. Using the Pythagorean theorem, we can find the height:
[tex]h^2 = 5^2 - 4^2\\h^2 = 25 - 16\\h^2 = 9\\h = 3[/tex]
So the height of each triangular face is 3 inches. Now we can find the area of each triangular face:
Area of one triangular face = (1/2) x base x height
= (1/2) x 6 x 3
= 9 square inches
Since there are two triangular faces, the total area of the triangular faces is:
Total area of triangular faces = 2 x 9 = 18 square inches
Next, let's find the area of the three rectangular faces. We have two rectangles with sides of 6 inches by 8 inches, and one rectangle with sides of 4 inches by 8 inches. The area of each rectangular face is:
Area of rectangular face = length x width
So the area of the rectangular faces are:
Area of rectangular face 1 = 6 x 8 = 48 square inches
Area of rectangular face 2 = 6 x 8 = 48 square inches
Area of rectangular face 3 = 4 x 8 = 32 square inches
Therefore, the total surface area of the triangular prism is:
Total surface area = 18 + 48 + 48 + 32 = 146 square inches
So the surface area of the given triangular prism with sides of 4in, 5in, 6in, 6in, 8in, and 7in is 146 square inches.
To know more about Pythagorean theorem click here:
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Answer:
16/5
Step-by-step explanation:
We can see that the new triangle is larger than the original triangle so we know the scale factor is greater than 1.
The scale factor can be found by calculating the ratio of the length of any two corresponding sides. The length of the bottom side of the original triangle is 5. The length of the bottom side of the new triangle is 16. We can calculate the ratio which is 16:5 or 16/5.