The volume of the figure is 18 cubic units
How to determine the volume of the figureFrom the question, we have the following parameters that can be used in our computation:
The figure
The figure can be divided into two 3-D figures represented below
Cube: side length = 2
Cuboid: 2 by 5 by 1
The volume of the figure is then calculated as
Volume = Volume of cube + Volume of cuboid
So, we have
Volume = 2 * 2 * 2 + 2 * 5 * 1
Evaluate
Volume = 18
Hence, the volume is 18 cubic units
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the teacher of a class of third graders records the height of each student. indicate which level of measurement is being used in this scenario
In this situation, interval measurement is being employed as the measurement level.
As the height of each student can be measured on a continuous scale with equal intervals between the values. It's important to note that the teacher may have rounded the measurements to the nearest unit, which would make it a discrete measurement.
Interval measurement is a level of measurement in which the values are measured on a continuous scale and have equal intervals between them, but there is no true zero point. This means that the difference between any two values on the scale is meaningful and consistent, but it is not possible to say that one value is "zero" or has no quantity of the measured attribute.
For example, measuring temperature in degrees Celsius or Fahrenheit is an example of interval measurement. In this case, the difference between 10 and 20 degrees is the same as the difference between 20 and 30 degrees, but there is no true zero temperature - a temperature of 0 degrees does not mean the absence of heat.
Another example of interval measurement is measuring time in minutes or hours. The difference between 10 minutes and 20 minutes is the same as the difference between 20 minutes and 30 minutes, but there is no "zero" point in time - even if nothing is happening, time continues to pass.
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what was the first standard metric unit of mass?
Answer:
Gram.
Step-by-step explanation:
If the roots of x²-7x+k=0 are m and m-1,find the value of the constant k
The value of the constant k is 12.
By Vieta's formulas, the sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a, and the product of the roots is c/a. Therefore, we have:
m + (m-1) = 7 (sum of the roots)
m(m-1) = k (product of the roots)
Expanding the first equation, we get:
2m - 1 = 7
Solving for m, we get:
m = 4
Substituting m = 4 into the second equation, we get:
4(4-1) = k
Simplifying, we get:
12 = k
Therefore, the constant k is equal to 12.
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A bag has 12 red, 6 blue, and 7 yellow marbles, what is the probability of drawing a red
marble then a yellow marble out of the bag
Answer:
The probability of drawing a red marble then a yellow marble out of the bag is probably 0.48(Decimal) or 12/25(Fraction).
i need help with math i don't understand this
Answer:A
Step-by-step explanation:
they are alternate exterior angles so, x+y=180
Simplify this please
Answer:
15m3 + 16m5
Step-by-step explanation:
3m3 + 3m3 + 9m3 = 15m3
11m5 + m5 = 16m5
Answer:
-10m^5-3m^3
Step-by-step explanation:
3m^3+3m^3=6m^3-9m^3=-3m^3
-11m^5+m^5=-10m^5
Mover the larger exponent first so -10m^5-3m^3
For a large order of brownies. Ms. Perry made 8/8 kg of fudge in her kitchen. She then got 1/6 kg from Mrs. Marshall. If she needs a total of 1 1/8kg for brownies, how much more fudge does she needs to make?
Answer:
Ms. Perry needs to make an additional 1/24 kg of fudge.
Step-by-step explanation:
Ms. Perry has a total of 8/8 + 1/6 = 13/6 kg of fudge. She needs 1 1/8 kg of fudge for the brownies, which is equivalent to 9/8 kg. To find how much more fudge she needs to make, we can subtract the amount of fudge she already has from the amount she needs:
9/8 - 13/6 = 27/24 - 26/24 = 1/24
Therefore, Ms. Perry needs to make an additional 1/24 kg of fudge.
Choose the equation that correctly shows the Commutative Property of Multiplication.
10 x3/10 = 10 x 3/10
10 +3/10 = 3/10x 10
10 x 3/10 = 3/10 x 10
10 x3/10 = 3/10 ÷ 10 IL GIVE BRAINLIEST!!!
He equation that rightly shows the Commutative Property of addition is
10 x3/10 = 3/10 x 10
The Commutative Property of Multiplication states that changing the order of the factors doesn't change the product. In other words, when you multiply two figures, it doesn't count which number comes first. The equation 10 x3/10 = 3/10 x 10 is an illustration of this property, as both sides of the equation represent the same value, indeed though the order of the factors is different.
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I need some help with this I don't really understand this.
Answer: 31.5
Step-by-step explanation:
6*4=24 (Shaded Rectangle)
3*5=15 15/2=7.5 (Shaded Triangle)
7.5 + 24 = 31.5
Find the solution to the linear system of differential equations {x′= 22x + 60y, y′= -6x - 16y
satisfying the initial conditions satisfying the initial conditions x(0)=5 and y(0)=3:
The solution to the system of differential equations that satisfies the initial conditions x(0)=5 and y(0)=3 is:
x(t) = (29/3) [tex]e^{\frac{22t}{3} }[/tex] - (4/3) [tex]e^{\frac{-16t}{3} }[/tex]
y(t) = (-13/3) [tex]e^{\frac{22t}{3} }[/tex] + (2/3) [tex]e^{\frac{-16t}{3} }[/tex]
To solve the system of differential equations, we can use matrix exponential. The system can be written in matrix form as follows:
X' = AX, where X = [x y], A = [22 60; -6 -16]
The matrix exponential of A can be calculated as follows:
[tex]e^{(At)}[/tex] = I + At + [tex]\frac{(At)^{2}}{2!}[/tex] + [tex]\frac{(At)^{3}}{3!}[/tex] + ...
where I is the identity matrix and t is the variable of integration.
We can substitute A and t = 1 into the formula to get:
[tex]e^{A}[/tex]= I + A + [tex]\frac{(A)^{2}}{2!}[/tex] + [tex]\frac{(A)^{3}}{3!}[/tex]+ ...
= [1 0; 0 1] + [22 60; -6 -16] + [44 192; -36 -104]/2! + [ -256 -768; 96 272]/3! + ...
= [1 + 22 + [tex]\frac{44}{2!}[/tex] - [tex]\frac{256}{3!}[/tex]*60 + [tex]\frac{192}{2!}[/tex] - [tex]\frac{768}{3!}[/tex];
-6 + [tex]\frac{(-6)}{2!}[/tex] + [tex]\frac{96}{3!}[/tex] - 16 + [tex]\frac{(-104)}{2!}[/tex]+ [tex]\frac{272}{3!}[/tex]]
= [[tex]\frac{29}{3}[/tex] [tex]\frac{102}{3}[/tex];
[tex]\frac{-13}{3}[/tex] [tex]\frac{-4}{3}[/tex] ]
Now we can use the initial conditions to find the constants of integration. We have:
X(0) = [x(0) y(0)] = [5 3]
So,
[[tex]e^{A}[/tex]] [[tex]c_{1}[/tex]] = [5]
[[tex]c_{2}[/tex]] [3]
Multiplying both sides by the inverse of [tex]e^{A}[/tex], we get:
[[tex]c_{1}[/tex]] = [29/3 102/3]^(-1) [5]
[[tex]c_{2}[/tex]] [-13/3 -4/3] [3]
Solving this system of linear equations, we get:
[tex]c_{1}[/tex] = -4/3
[tex]c_{2}[/tex] = 2/3
Therefore, the solution to the system of differential equations that satisfies the initial conditions x(0)=5 and y(0)=3 is:
x(t) = (29/3) [tex]e^{\frac{22t}{3} }[/tex] - (4/3) [tex]e^{\frac{-16t}{3} }[/tex]
y(t) = (-13/3) [tex]e^{\frac{22t}{3} }[/tex] + (2/3) [tex]e^{\frac{-16t}{3} }[/tex]
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Transcribed image text: From a population of size 500, a random sample of 50 items is selected. The mode of the sample a. can be larger, smaller or equal to the mode of the population. b. must be equal to the mode of population, if the sample is truly random. c. must be equal to the mean of the population, if the sample is truly random. d. must be 500.
The mode of the sample can be larger, smaller, or equal to the mode of the population.
The correct answer is A.
The mode is the most frequent value in a dataset. In a random sample, the mode can differ from the mode of the population because random sampling is subject to sampling variability. In other words, each random sample is likely to have different sample statistics than the population parameters. Therefore, it is possible for the mode of the sample to be larger, smaller, or equal to the mode of the population.
However, as the sample size increases, the mode of the sample becomes more likely to approach the mode of the population. This is because larger samples provide more information about the population and therefore reduce the impact of sampling variability.
Option B is incorrect because even if the sample is truly random, it is still subject to sampling variability, which means that the mode of the sample may not be equal to the mode of the population.
Option C is also incorrect because the mean of the population is a different statistic than the mode, and it is not necessarily related to the mode of the sample.
Option D is clearly incorrect, as the mode of a sample cannot be equal to the population size.
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What is the binomial probability formula used for?
The binomial probability formula calculates the probability of obtaining a specific number of successes in a fixed number of independent trials, each with the same probability of success
The binomial probability formula is used to calculate the probability of obtaining a certain number of successes in a fixed number of independent trials, each with the same probability of success.
The formula is:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where:
P(X=k) is the probability of obtaining k successes
n is the total number of trials
p is the probability of success in each trial
(n choose k) represents the number of ways to choose k successes from n trials, and is calculated as n! / (k! * (n-k)!)
Therefore, the uses of binomial probability formula has been explained
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The binomial probability formula is widely used in various fields, including statistics, probability theory, and genetics, to analyze and predict outcomes in situations with binary events.
The binomial probability formula is used to calculate the probability of obtaining a specific number of successes in a fixed number of independent Bernoulli trials. In other words, it helps us determine the likelihood of achieving a certain outcome in a series of experiments, where each experiment can result in one of two possible outcomes (success or failure).
The formula is given by P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where P(X=k) represents the probability of getting exactly k successes, n is the total number of trials, p is the probability of success in a single trial, and (n choose k) is the binomial coefficient.
For example, let's say you flip a fair coin 10 times and want to know the probability of getting exactly 7 heads. In this case, n = 10 (number of trials), k = 7 (number of successes), and p = 0.5 (probability of heads). Plugging these values into the binomial probability formula will give you the desired probability.
The binomial probability formula is widely used in various fields, including statistics, probability theory, and genetics, to analyze and predict outcomes in situations with binary events.
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The ratio of triangle BOY to triangle GRL is 1:2. If BO=x+3 and GRL=3x-1, then the length of GR is
explain the math behind it please and thank you
A.5
B.7
C.10
D.20
Answer: B. 7
The ratio of the two triangles indicates that BOY is 1/2 the size of GRL. Therefore, the ratio of the sides of the triangles is also 1:2. Since the length of BO is given as x + 3, this means that the length of GR must be 2(x + 3) - 1 = 2x + 5. Therefore, the length of GR is 7.
suppose that the probability that someone in nyc who has covid in fact has the xbb.1.5 variant is 70%. (a) find the probability that at most 12 out of 20 randomly chosen people in nyc who have covid have this specific variant. (b) in order to run a first trial of a new vaccine, suppose that scientists must find five patients with this new variant. find the probability that one must test 8 or more covid patients in order to find (exactly) 5 that have the new variant.
The probability that at most 12 out of 20 randomly chosen people in NYC who have COVID have the XBB.1.5 variant is approximately 0.2277 and the probability that one must test 8 or more COVID patients in order to find exactly 5 that have the XBB.1.5 variant is approximately 0.9987.
What is the probability that at most 12 out of 20 have this specific variant(a) Let X be the number of people out of 20 who have the XBB.1.5 variant. X follows a binomial distribution with parameters n=20 and p=0.7. We need to find the probability that at most 12 out of 20 randomly chosen people in NYC who have COVID have this specific variant, which can be expressed as P(X ≤ 12).
Using a binomial distribution table or a calculator, we can calculate:
P(X ≤ 12) = ΣP(X=k), for k=0 to 12
P(X ≤ 12) = 0.2277
Therefore, the probability that at most 12 out of 20 randomly chosen people in NYC who have COVID have the XBB.1.5 variant is approximately 0.2277.
(b) Let Y be the number of patients tested until exactly 5 are found to have the XBB.1.5 variant. Y follows a negative binomial distribution with parameters r=5 and p=0.7. We need to find the probability that one must test 8 or more COVID patients in order to find exactly 5 that have the new variant, which can be expressed as P(Y ≥ 8).
Using the negative binomial distribution formula, we can calculate:
P(Y ≥ 8) = ΣP(Y=k), for k=8 to infinity
P(Y ≥ 8) = Σ [(k-1) choose (r-1)] p^r (1-p)^(k-r), for k=8 to infinity
This is a tedious calculation to do by hand, but we can use a calculator or software to find that P(Y ≥ 8) ≈ 0.99872
Therefore, the probability that one must test 8 or more COVID patients in order to find exactly 5 that have the XBB.1.5 variant is approximately 0.9987.
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Find a coordinate distance calculator
The distance between two points in a coordinate plane can be found by the formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
To calculate the distance between two points in a coordinate plane, you can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.
For example, if you want to find the distance between the points (2, 3) and (5, 7), you would plug in the values as follows:
d = sqrt((5 - 2)^2 + (7 - 3)^2)
d = sqrt(3^2 + 4^2)
d = sqrt(9 + 16)
d = sqrt(25)
d = 5
Therefore, the distance between two points is d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
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How much is 4 5 euros in dollars?
The official currency of 20 of the EU's 27 member states is the euro (symbol: €; code: EUR) (EU).
4 5 euros in dollars is equivalent to about 53.10 US dollars (45 x 1.18).
The euro and the US dollar are among the world's most popular currencies. On the other hand, the EUR to USD conversion asks you to get familiar with specific pointers such as the exchange rate today. The US dollar is widely accepted as a kind of currency in many places. As a result, foreign currency values are calculated by comparing them to the US dollar. Take a look at this comprehensive guide to help you convert EUR to USD. As of my current knowledge cutoff date of September 2021, one euro was approximately equal to 1.18 US dollars. Based on that exchange rate.
However, please note that exchange rates can fluctuate and the actual value of 45 euros in US dollars may be different depending on the current exchange rate.
45 euros would be equivalent to about 53.10 US dollars (45 x 1.18).
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5. Let a and b be two independent events with p (a) = 0. 4 and p (a ∪ b) = 0. 64. What is p (b)?
Let a and b be two independent events, if p (a) = 0. 4 and p (a ∪ b) = 0. 64 then the value of the p(b) = 0.4
In this question, we will utilise the notion of independent events and the probability addition rule to determine the probability of event B. The product of the individual probabilities will represent the intersection of independent events.
p(a) = 0.4
p(a∪b) = 0.64
p (a ∩ b) = p(a) x p(b)
p (a ∪ b) = p(a) + p(b) - p(a) x p(b)
0.64 = 0.4 + p(b) - 0.4 x p(b)
p(b) = 0.4
Therefore, the value of the p(b) = 0.4
Independent occurrences are ones whose occurrence is unrelated to any other event. For example, suppose we flip a coin in the air and receive the result Head, then we flip the coin again and obtain the result Tail. The occurrences occur independently of one another in both circumstances. It is one of the several kinds of occurrences in probability.
Let us now look at the whole description of independent events, including a Venn diagram, examples, and how they vary from mutually exclusive events.
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It is assumed that approximately​ 15% of adults in the u.s. are​ left-handed. consider the probability that among 100 adults selected in the​ u.s., there are at least 30 who are​ left-handed. given that the adults surveyed were selected without​ replacement, can the probability be found by using the binomial probability formula with x counting the number who are​ left-handed? why or why​ not?
a. Yes, because the 100 adults represent less than 5% of the U.S. adult population, the trials can be treated as independent.
b. No, because the 30 adults represent more than 5% of the sample size, the trials are dependent.
c. No, because the 100 adults were selected without replacement, the selections are dependent.
d. No, because the probability of being right-handed is greater, x must count the number of right-handed adults.
No, the probability be found by using the binomial probability formula with x counting the number who are left-handed. The correct option is (c) No, because the 100 adults were selected without replacement, the selections are dependent.
The binomial distribution assumes that the trials are independent, meaning that the outcome of one trial does not affect the outcome of any other trial. However, in this case, the 100 adults were selected without replacement, which means that the outcome of one selection affects the probability of the next selection. Therefore, the trials are dependent, and the binomial probability formula cannot be used.
Instead, we can use the hypergeometric distribution to calculate the probability of at least 30 left-handed adults in a sample of 100 adults selected without replacement from the U.S. population. The hypergeometric distribution takes into account the fact that the selections are dependent and is appropriate for this type of problem.
Therefore, the correct option is (c) No, because the 100 adults were selected without replacement, the selections are dependent.
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37 dollars an hour is how much a year
The required number of dollars in a year per 37 dollars in an hour equals 324,120 dollars.
Number of dollars in one hour is equal to 37 dollars.
Relation between year and hour .
1 year = 12 months
1 month = 31, 30 or 28 days
Total number of days in a year = 365 days
Number of hours in 1 day = 24 hours
Number of hours in 365 days = ( 365 × 24 ) hours
= 8760 hours
In 1 hour = 37 dollars
⇒ 8760 hours = ( 37 × 8760 ) dollars
⇒ 8760 hours = ( 324,120 ) dollars
⇒ 1year = ( 324,120 ) dollars
Therefore, the number of dollars in a year is equal to 324,120 dollars.
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find the volume of the solid generated when the region bounded by and is revolved about the x-axis.
The volume of the solid generated when the region bounded by and is revolved about the x-axis is (32/5)π units and 8π units.
Volume of the solid:
The volume of a solid is a measure of the space occupied by an object. It is measured by the number of unit cubes needed to fill a solid. If we count the unit cube in a solid, we have 30 unit cubes, so the volume is: 2 units 3 units 5 units = 30 cubic units
According to the Question:
The rose region is revolving about the x-axis and y-axis:
1)Volume = [tex]\pi \int\limits^2_0 {x^4} \, dx[/tex]
= [tex]\pi \int\limits^2_0 {y^4} \, dx[/tex]
= π{ (32/5)-0}
= (32/5)π units.
2)Volume = [tex]\pi \int\limits^4_0 {[(2^2)_2 - (\sqrt{y^2)_1 } } \, dy[/tex]
= [tex]\pi \int\limits^4_0 {[4 -y] } } \, dy[/tex] = 8π dy
Complete Question:
How do I find the volume of the solid generated by revolving the region bounded by y = x², y=0, and x = 2 about the x-axis?
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Theden went on three day hike up a 40 mile trail he decided to hike 12.8 miles the first day and 16.9 miles the second day how many miles does he need to hike on the third day to finish the trail
To determine how many miles Theden needs to hike on the third day to finish the trail, we can subtract the distance he hiked on the first two days from the total trail distance:
Total trail distance = 40 miles
Distance hiked on first day = 12.8 miles
Distance hiked on second day = 16.9 miles
Total distance hiked on first two days = 12.8 + 16.9 = 29.7 miles
Distance left to hike on the third day = 40 - 29.7 = 10.3 miles
Therefore, Theden needs to hike 10.3 miles on the third day to finish the trail.
A test of H0: p = 0. 6 versus Ha: p > 0. 6 has the test statistic z = 2. 27. Part A: What conclusion can you draw at the 5% significance level? At the 1% significance level? (6 points)
Part B: If the alternative hypothesis is Ha: p ≠ 0. 6, what conclusion can you draw at the 5% significance level? At the 1% significance level? (4 points)
A sample's null hypothesis indicates that no statistical relationship exists in a set of provided single observed variables. The null hypothesis is rejected for both parts A and B of the question.
A sample's null hypothesis indicates that no statistical relationship exists in a set of provided single observed variables.
Part A: The conclusion to be reached at the 5% level of significance-
The p value for the z score in the right tailed or upper test can be obtained from the z table, which is,
p-value=0.125=0.125
The p value of 0.125 is greater than the significance level of 0.06. As a result, the effect is not significant, and the null hypothesis cannot be rejected.
Part B: If the alternative hypothesis is Ha: p 0.6, the conclusion to reach at the 5% level is-
The unequal sign 2-test is carried out here. The p value for the 2-test is as follows:
The p-value is 0.25=0.25.
In this case, the p value of 0.25 is greater than the significance level of 0.05. As a result, the effect is not significant, and the null hypothesis cannot be rejected.
As a result, the null hypothesis fails to be rejected for both parts A and B of the question.
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What are the solutions to the equation cosine of the quantity x plus 3 times pi over 2 end quantity equals radical 2 over 2 on the interval [0, 2π]?
Answer:
The solutions to the equation cos(x + 3π/2) = √2/2 on the interval [0, 2π] are x = π/4 + 2kπ, k ∈ {0, 1, 2, 3}.
a soft-drink manufacturer bottles drinks with a machine that produces normally distributed weights. state law requires that no more than .3% (.003) of the bottles can have contents below the advertised weight (12 fluid ounces). the standard deviation of the content weight distribution is historically 0.04 fluid ounces. a mean setting of 12 ounces will result in 50% of the bottles having less than the advertised weight. a. true b. false.
The standard deviation of the content weight distribution is historically 0.04 fluid ounces. a mean setting of 12 ounces will result in 50% of the bottles having less than the advertised weight. This statement is false.
What is standard deviation?
The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.
Since the weight of the contents in the bottles follows a normal distribution, we can use the standard normal distribution to calculate the proportion of bottles that have contents below the advertised weight.
Let's define the random variable X as the weight of the contents in a bottle.
Then, we can standardize X by subtracting the mean weight (12 fluid ounces) & dividing by the standard deviation (0.04 fluid ounces):
Z = (X - μ) / σ
where μ = 12 and σ = 0.04.
We want to find the proportion of bottles that have contents below 12 fluid ounces, which is equivalent to finding the probability that Z is less than 0 -
P(Z < 0) = 0.5
This means that 50% of the bottles will have contents below the advertised weight if the mean setting is 12 ounces.
However, the problem states that state law requires that no more than 0.3% of the bottles can have contents below the advertised weight.
This means that we need to find the probability that Z is less than some value such that the area under the standard normal distribution to the left of that value is 0.003.
We can find this value using a standard normal distribution table or calculator -
P(Z < z) = 0.003
z ≈ -2.88
Therefore, the mean setting needs to be adjusted such that the mean weight of the contents is at least 12 + (-2.88) x 0.04 = 11.856 fluid ounces to ensure that no more than 0.3% of the bottles have contents below 12 fluid ounces.
Therefore, the statement in false.
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How to convert 9 into cm?
9 inches is equal to 22.86 centimeter
To convert 1 inches to cm, we can use the following formula:
1 inch = 2.54 cm
The conversion factor is 2.54
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
Therefore,
The length in cm = conversion factor × The length in inches
Substitute the values in the equation
9 inches = 9 × 2.54 cm
Multiply the numbers
= 22.86 cm ( rounded to two decimal places )
Therefore, 9 inch is 22.86 cm
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a mug slides across a horizontal counter with initial speed v. it slides off the 0.86 m high counter and lands 1 m from the base. what was its initial speed?
slides off the 0.86 m high counter and lands 1 m from the base. what was its initial speed ⇒ Ø = 56.87˚ beneath the horizontal
A. Suppose the horizontal component of the velocity is vx and the vertical is vy.
At first at t=0 (as the mug leaves the counter) the components are v0x and v0y.
v0y = 0 since the customer slides it horizontally so applied force is in the x component as it were.
The equations for horizontal and vertical shot movement are:
x = x0 + v0x t
y = y0 + v0y t - 1/2 g t^2 = y0 - 1/2 g t^2
Setting the beginning to be the end corner of the counter so that x0=0 and y0=0, thus:
x = v0x t
y = - 1/2 g t^2
Given esteem are: x=1.50m and y=-1.15m (y is negative since mug is going down)
1.50m = v0x t - - - - > v0x= 1.50/t
-1.15m = - (1/2) (9.81) t^2 - - - - - > t =0.4842 s
Working out for v0x:
v0x = 3.10 m/s
B. v0x is constant since there could be no other horizontal forces so, v0x=vx=3.10m/s
vy can be calculated from the recipe:
vy = v0y + at where a=-g (negative since going down)
vy = - gt = - 9.81 (0.4842)
vy = - 4.75 m/s
Presently to get the point beneath the horizontal, tan(90-Ø) = - vx/vy
tan(90-Ø )= 3.1/4.75
Ø = 56.87˚ beneath the horizontal
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Pick all 4 of the right answers for 100 points and brainliest
The the rectangular prisms have their volumes as:
1). 175 cubic feet
2). 60 cubic metres
3). 140 cubic metres
4). 216 square inches.
How to evaluate for the volume of the rectangular prismvolume for a rectangular prism is calculated using:
length × width × height
the rectangular prisms can be divided into bigger and smaller prism and their volumes calculated separately and then added to get the total volume as follows:
1). volume of bigger rectangular prism = 7ft × 7ft × 3ft = 147ft³
volume of smaller rectangular prism = 7ft × 2ft × 2ft = 28ft³
volume of object = 147ft³ + 28ft³ = 175ft³
2). volume of bigger rectangular prism = 6m × 3m × 3m = 54m³
volume of smaller rectangular prism = 3m × 3m × 1m = 6m³
3). volume of bigger rectangular prism = 7m × 6m × 3m = 126m³
volume of smaller rectangular prism = 7m × 2m × 1m = 14m³
volume of object = 126m³ + 14m³ = 140m³
4). volume of bigger rectangular prism = 12in × 4in × 4in = 192in²
volume of smaller rectangular prism = 4in × 3in × 2in = 24in³
volume of object = 192in³ + 24in³ = 216³
Therefore, the rectangular prisms have their volumes as:
1). 175 cubic feet
2). 60 cubic metres
3). 140 cubic metres
4). 216 square inches
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During lunch, Dasia drinks 2 3/4 cups of milk. Taniya drinks 1 1/6 cups of milk, Calixte drinks 8/8 cups of milk. How much milk do the 3 students drink?
The amount of milk the 3 students drink is 4 11/12 cups of milk
How much milk do the 3 students drink?From the question, we have the following parameters that can be used in our computation:
Dasia = 2 3/4
Taniya = 1 1/6
Calixte = 8/8
The amount of milk the 3 students drink is calculated as
Total = 2 3/4 + 1 1/6 + 8/8
Evaluate the sum
Total = 4 11/12
Hence, the total is 4 11/12 cups of milk
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Suppose you are driving. You notice that after driving for 4 hours, you are 215 miles from Seattle. You continue driving, and calculate that after driving 8 hours you are 415 miles from Seattle. What is your rate?
Your rate is 52.5 miles per hour, calculated by dividing the total distance traveled (200 miles) by the total time taken (4 hours).
To calculate this, take the total distance traveled (415 miles) and subtract the distance from Seattle at the start of the journey (215 miles). This gives you the total distance traveled, which is then divided by the total time taken (8 hours), giving you a rate of 52.5 miles per hour.
415-215/8=52.5To better understand this concept, imagine driving from Seattle to Los Angeles. You know that Los Angeles is 800 miles from Seattle, and if you drive for 16 hours, you will reach your destination. In this case, your rate would be
800/16 = 50 miles per hour.The same principle applies here, which is why you can use the same formula to calculate your rate.
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5√180 +4√/18 - √50.
Simply
Answer:
30√5 + 7√2
Step-by-step explanation:
To simplify this expression, we can first use the fact that the square root of a product is equal to the product of the square roots. We can also simplify any perfect squares under the square root sign.
5√180 + 4√18 - √50
= 5√(36 × 5) + 4√(9 × 2) - √(25 × 2)
= 5√36 × √5 + 4√9 × √2 - √25 × √2
= 5 × 6√5 + 4 × 3√2 - 5√2
= 30√5 + 12√2 - 5√2
= 30√5 + 7√2
Therefore, the simplified form of the expression is [30√5 + 7√2.]