Answers
the initial speed with which the particle was projected is approximately 29.7 m/s.
How to solve?
We can solve this problem using the equations of motion for a particle moving under constant acceleration due to gravity.
Let v be the initial velocity with which the particle was projected, and let θ be the angle of projection with respect to the horizontal. Since the particle is launched from a height of 15m, its initial vertical velocity is v sin(θ), and its initial horizontal velocity is v cos(θ).
The time taken for the particle to hit the ground can be found by using the equation:
y = y0 + v0t + 1/2at²
where y is the vertical displacement, y0 is the initial vertical position, v0 is the initial vertical velocity, a is the acceleration due to gravity (-9.8 m/s²), and t is the time taken.
Since the particle starts and ends at the same vertical position (15m), we have:
y - y0 = 0
Substituting the values, we get:
0 = 15 + v sin(θ)t - 1/2(9.8)t²
Simplifying and rearranging, we get:
4.9t² - vt - 30 = 0
Using the quadratic formula, we get:
t = (v ±√(v² + 4(4.9)(30))) / (2(4.9))
Since we want the time taken for the particle to hit the ground, we take the positive root:
t = (v + √(v² + 588)) / 9.8
Now, we can use the horizontal displacement to find the initial speed v. Since the particle travels a horizontal distance of 30m in time t, we have:
x = v cos(θ) t
Substituting the values, we get:
30 = v cos(θ) [(v +√(v² + 588)) / 9.8]
Simplifying and rearranging, we get:
v² - 882 = 0
Using the quadratic formula again, we get:
v = ±√(882)
Since the initial velocity must be positive, we take the positive root:
v ≈ 29.7 m/s
Therefore, the initial speed with which the particle was projected is approximately 29.7 m/s.
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Related Questions
Assume a jar has five red marbles and four black marbles. Draw out two marbles with and without replacement. Find the requested probabilities. (Enter the probabilities as fractions.)
(a) P(two red marbles)
with replacement without replacement (b) P(two black marbles)
with replacement without replacement (c) P(one red and one black marble)
with replacement without replacement (d) P(red on the first draw and black on the second draw)
with replacement without replacement
Answers
The probability of selecting another black marble is 3/7. As a result, the probability of drawing two black marbles in a row without replacement
(a) P(two red marbles) with replacement:The probability of drawing a red marble from a jar with five red marbles and four black marbles is 5/9, as there are five red marbles and nine total marbles. As a result, the probability of selecting two red marbles in a row with replacement is:P(two red marbles with replacement) = (5/9) × (5/9) = 25/81without replacement:When the first marble is removed, there are now only eight marbles remaining in the jar. Because there are only four black marbles in the jar, the probability of drawing a red marble is now 5/8. Therefore, the probability of selecting two red marbles in a row without replacement is:P(two red marbles without replacement) = (5/9) × (5/8) = 25/72(b) P(two black marbles)with replacement:For the first draw, there are four black marbles in the jar and a total of nine marbles. Therefore, the probability of drawing a black marble on the first draw is 4/9. Since the first marble was not removed, there are now eight marbles in the jar, including three black ones, and there are a total of nine marbles. Therefore, the probability of selecting another black marble is 3/9 or 1/3.
The probability of drawing two black marbles in a row with replacement is:P(two black marbles with replacement) = (4/9) × (1/3) = 4/27without replacement:Since the first marble was removed, there are only eight marbles in the jar, and there are four black ones. Therefore, the probability of selecting a black marble is 4/8 or 1/2. When the first black marble is removed, there are only seven marbles left, including three black ones. Therefore, the probability of selecting another black marble is 3/7. As a result, the probability of drawing two black marbles in a row without replacement is:P(two black marbles without replacement) = (4/9) × (3/7) = 12/63(c) P(one red and one black marble)with replacement:When one red and one black marble are selected with replacement, there are nine marbles in the jar for each draw. The probability of selecting one red and one black marble in a row is:P(one red and one black marble with replacement) = 2 × (5/9) × (4/9) = 40/81without replacement:Since there are five red and four black marbles in the jar, the probability of selecting a red marble first is 5/9. Once the red marble has been drawn and removed, there are only eight marbles remaining, including four black ones. As a result, the probability of selecting a black marble is 4/8 or 1/2.
As a result, the probability of drawing one red and one black marble without replacement is:P(one red and one black marble without replacement) = (5/9) × (4/8) + (4/9) × (5/8) = 20/36 + 20/36 = 10/18 = 5/9(d) P(red on the first draw and black on the second draw)with replacement:There are nine marbles in the jar for each draw. The probability of selecting a red marble first is 5/9. When the red marble is returned to the jar, there are still nine marbles in the jar, but now there are only four black marbles. The probability of selecting a black marble on the second draw is 4/9. As a result, the probability of drawing a red marble first and a black marble second with replacement is:P(red on the first draw and black on the second draw with replacement) = (5/9) × (4/9) = 20/81without replacement:Since there are five red and four black marbles in the jar, the probability of selecting a red marble first is 5/9. Once the red marble has been drawn and removed, there are only eight marbles remaining, including four black ones. As a result, the probability of selecting a black marble is 4/8 or 1/2. As a result, the probability of drawing a red marble first and a black marble second without replacement is:P(red on the first draw and black on the second draw without replacement) = (5/9) × (4/8) = 5/18
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Data and statistics:
what is each students favorite restaurant at my school
Answers
Therefore, we estimate that about 7 sixth graders should be chosen to create a representative sample, given that 9 seventh graders were chosen.
What is statistics?Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data. It provides methods for summarizing and describing data, making inferences about populations based on samples, and testing hypotheses. Statistics is used in many fields, such as business, economics, health care, social sciences, engineering, and more, to make decisions and draw conclusions based on data. Some common techniques used in statistics include descriptive statistics (e.g., mean, median, mode, standard deviation), probability theory, hypothesis testing, regression analysis, and sampling methods.
Here,
To estimate the number of sixth graders that should be chosen to create a representative sample, we can use the proportion of seventh graders in the sample and assume that the proportions of each grade in the sample should match the proportions in the population. We know that the sample contains 9 seventh graders, but we don't know the total size of the sample yet. We can use the following formula to estimate the sample size:
sample proportion = population proportion
where
sample proportion = number of seventh graders in the sample / total sample size
population proportion = number of seventh graders in the population / total population size
We can plug in the values we know:
9 / total sample size = 180 / (160 + 180 + 140)
Simplifying the right-hand side:
9 / total sample size = 0.4
Multiplying both sides by total sample size and simplifying:
total sample size = 9 / 0.4
total sample size ≈ 22.5
This means that the sample size should be about 22.5 students. Since we can't choose a fractional number of students, we should round up to the nearest whole number, giving a total sample size of 23 students.
To estimate the number of sixth graders in the sample, we can use the proportion of sixth graders in the population and assume that the proportion should be the same in the sample:
number of sixth graders in the sample / total sample size = 160 / (160 + 180 + 140)
Simplifying the right-hand side:
number of sixth graders in the sample / total sample size = 0.32
Multiplying both sides by total sample size and simplifying:
number of sixth graders in the sample = 0.32 * 23
number of sixth graders in the sample ≈ 7
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Complete question:
A population of middle school students contains 160 sixth graders, 180 seventh graders, and 140 eighth graders. Nine seventh graders were part of a random sample of the population chosen to participate in a survey. For the sample to accurately represent the population, about how many sixth graders should be chosen for each students favorite restaurant at my school?
Make x the subject
3x² + 4y = 4
Answers
3x² + 4y = 4
Subtract 4y from both sides:
3x² = 4 - 4y
Divide both sides by 3:
x² = (4 - 4y) / 3
Take the square root of both sides, remembering to include both the positive and negative roots:
x = ±sqrt((4 - 4y) / 3))
Therefore, x can be expressed as:
x = sqrt((4 - 4y) / 3)) or x = -sqrt((4 - 4y) / 3))
what is (2x+45)° x° = what?
Answers
Answer:
x = 45.
Step-by-step explanation:
Given a straight line with the equation.
First collect like terms:
2x + x = 180 - 45
Then calculate:
3x = 135
Finally after dividing both sides by 3:
x = 45
Determine the number of 15 boxes in kilograms
Answers
Answer:
Step-by-step explanation:
150
answer pls pls pls pls
Answers
Therefore, 0.02 times 100 is equal to 2.
What is multiplication?Multiplication is a mathematical operation that involves combining two or more quantities to find their product. The quantities being multiplied are called factors, and the result of the multiplication is called the product. Multiplication is denoted by the "×" or "*" symbol, and is read as "times" or "multiplied by". Multiplication has many applications in mathematics and everyday life. It is used for calculating areas and volumes, scaling objects, calculating distances and speeds, and much more. It is also a fundamental operation in algebra, calculus, and other branches of mathematics.
Here,
To find out what number is equal to 0.02 times 100, we can use the formula:
0.02 * 100 = x
where "x" is the number we want to find. To solve for "x", we can multiply 0.02 and 100 using the distributive property of multiplication, which states that:
a * (b + c) = a * b + a * c
Using this property, we can write:
0.02 * 100 = 0.02 * (50 + 50)
Then, we can distribute the 0.02 to each term inside the parentheses:
0.02 * 100 = 0.02 * 50 + 0.02 * 50
Next, we can simplify each multiplication:
0.02 * 100 = 1 + 1
Finally, we can add the two numbers to get the result:
0.02 * 100 = 2
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(Do not use a calculator for this question) Given f(x)-73-12x + 5 answer the following: Is the function increasing or decreasing at x-3? List the interval A=B=where f(x) is decreasing. a F At what X-value does f(x) have a relative maximum?
Answers
The function is a set of ordered pairs (x, y), where x is an element of the domain and y is the corresponding element of the range. The notation f(x) is commonly used to denote the output value of the function for a given input value x.
The function is decreasing at x=3. The interval where f(x) is decreasing is (3,∞). The x-value at which f(x) has a relative maximum is x= -4.The derivative of the function f(x) is f'(x)=-12.At x=3, the derivative is negative, f'(3)=-12, so the function is decreasing at x=3.
The function is always decreasing since its derivative is constant and negative. Therefore, the interval where f(x) is decreasing is the entire real line, or (-∞, ∞).
Since the function is always decreasing, it does not have a relative maximum.
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Which of the following is a factor of x³ + 343?
Ox-7
Ox² - 14x +49
Ox² + 7x +49
Ox+7
Answers
x³ + 343 = (x + 7) (x² - 7x + 49) is the function.
What are functions?A relation is any subset of a Cartesian product.
As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."
A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.
Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).
A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).
Every function, as you can see from these definitions,
is a relation from X
Hence, x³ + 343 = (x + 7) (x² - 7x + 49) is the function.
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Suppose you roll a special 37-sided die. What is the probability that one of the following numbers is rolled? 35 | 25 | 33 | 9 | 19 Probability = (Round to 4 decimal places) License Points possible: 1 This is attempt 1 of 2.
Answers
Answer:
5/37
Step-by-step explanation:
There are 37 possible outcomes when rolling a 37-sided die, so the probability of rolling any one specific number is 1/37.
To find the probability of rolling any of the given numbers (35, 25, 33, 9, or 19), we need to add the probabilities of rolling each individual number.
Probability of rolling 35: 1/37
Probability of rolling 25: 1/37
Probability of rolling 33: 1/37
Probability of rolling 9: 1/37
Probability of rolling 19: 1/37
The probability of rolling any one of these numbers is the sum of these probabilities:
1/37 + 1/37 + 1/37 + 1/37 + 1/37 = 5/37
So the probability of rolling any of the given numbers is 5/37, which is approximately 0.1351 when rounded to four decimal places.
Stats... I need help please
Answers
Answer:
.
Step-by-step explanation:
...................
CONNAIS TU LES LIMITES ?
Answers
Answer:
yes
Step-by-step explanation:
what percentage of 23 miles is 27 miles? round your answer to the nearest hundredth of a percentage point.
Answers
The percentage of 27 miles in 23 miles is 117.39%.
Percentage is a way of expressing a fraction or a portion of a whole number in relation to 100. It is denoted by the symbol "%". A percentage is calculated by dividing the part (numerator) by the whole (denominator) and multiplying the result by 100. A percentage can also be used to represent a rate or a percentage change over time.
In this case, we are asked to find what percentage of 23 miles is 27 miles. The part is 27 miles and the whole is 23 miles. Therefore, the percentage is:
% = part/whole = 27/23 x 100 = 117.39%
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Does anyone know the what all of the y's are
Answers
Step-by-step explanation:
You need solve for y:
[tex]y-4=3(x-1)\\y-4=3x-3\\y=3x-3+4\\\therfore \quad y=3x+1[/tex]
now, evaluate in each x's value, for example:
[tex]y=3(-2)+1\\\therefore \quad y=-5[/tex]
This, is the value of [tex]y[/tex], when [tex]x=-2[/tex]
Therefore:
[tex]\begin{tabular}{|c|c|} \cline{0-1}x & y \\ \cline{0-1}-2 & -5 \\ -1 & -2\\ 0& 1 \\ 1& 4\\ 2& 7\\ \cline{0-1}\end{tabular}[/tex]
[tex]\text{-B$\mathfrak{randon}$VN}[/tex]
A) 4 x + 7 = 2 x + 13 ;
b) x – 2 = 10 + 5 x ;
c) – 3 x – 8 = – 7 x – 4 ;
d) 2 t + 5 = 5 t + 12 ;
e) 7 x – 6 = 6 x + 3
f) 15 x = 7 x + 4
Answers
For equation a, x = 3
For equation b, x = -11/4.
For equation c, x = 1.
For equation d, x = -7/3.
For equation e, x = 9.
For equation f, x = 1/2.
To solve this equation, we need to isolate the variable x on one side of the equation.
7x - 6 = 6x + 3
Subtracting 6x from both sides:
x - 6 = 3
Adding 6 to both sides:
x = 9
Therefore, the solution to the equation is x = 9.
In the other equations:
a) 4x + 7 = 2x + 13
Subtracting 2x from both sides:
2x + 7 = 13
Subtracting 7 from both sides:
2x = 6
Dividing by 2:
x = 3
Therefore, the solution to the equation is x = 3.
b) x - 2 = 10 + 5x
Subtracting x from both sides:
-2 = 9 + 4x
Subtracting 9 from both sides:
-11 = 4x
Dividing by 4:
x = -11/4
Therefore, the solution to the equation is x = -11/4.
c) -3x - 8 = -7x - 4
Adding 7x to both sides:
4x - 8 = -4
Adding 8 to both sides:
4x = 4
Dividing by 4:
x = 1
Therefore, the solution to the equation is x = 1.
d) 2t + 5 = 5t + 12
Subtracting 2t from both sides:
5 = 3t + 12
Subtracting 12 from both sides:
-7 = 3t
Dividing by 3:
t = -7/3
Therefore, the solution to the equation is t = -7/3.
f) 15x = 7x + 4
Subtracting 7x from both sides:
8x = 4
Dividing by 8:
x = 1/2
Therefore, the solution to the equation is x = 1/2.
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Complete Question:
Find X for each equation.
A) 4 x + 7 = 2 x + 13 ;
b) x – 2 = 10 + 5 x ;
c) – 3 x – 8 = – 7 x – 4 ;
d) 2 t + 5 = 5 t + 12 ;
e) 7 x – 6 = 6 x + 3
f) 15 x = 7 x + 4
The shedding frequency based on the analysis of Question 3 is to be determined through the use of a small-scale model to be tested in a water tunnel. For the specific bridge structure of interest D=20 cm and H=300 cm, and the wind speed V is 25 m/s. Assume the air is at MSL ISA conditions. For the model, assume that Dm =2 cm. (a) Determine the length of the model Hm needed for geometric scaling. (b) Determine the flow velocity Vm needed for Reynolds number scaling. (c) If the shedding frequency for the model is found to be 27 Hz, what is the corresponding frequency for the full-scale structural component of the bridge? Notes: Refer to the eBook for the properties of air. Assume the density of water
rhoH2O = 1000 kg/m3 and the dynamic viscosity of water μH2O =1×10^−3 kg/m/s
Answers
Answer:
Step-by-step explanation:
Let $ABCD$ be a parallelogram. Extend $\overline{DA}$ through $A$ to a point $P,$ and let $\overline{PC}$ meet $\overline{AB}$ at $Q$ and $\overline{DB}$ at $R.$ Given that $PQ = 735$ and $QR = 112,$ find $RC.$
Answers
The x ≤ 32Putting x = 24 in the expression we get RC = 96Therefore, the value of RC is 96.
In order to find RC, we will make use of the given information in the following manner: Given that ABDC is a parallelogram. Hence, AB = DC. We have also been given that PQ = 735 and QR = 112.Now, extend PQ to meet DC at S.Let PS = x; then DS = DC - x = AB - x. (Since AB = DC)We have that PS/SP = QR/RB (Since PQR is similar to DBR)Therefore, we getx/SP = 112/(AB - x)We can cross multiply and simplify to getSP = (112* x)/(AB - x)......(1)Further, we have that AQ/QB = SP/BR (Since PQR is similar to AQB)Therefore, we getx/(AB - x) = SP/BROn substituting the value of SP from equation (1) above, we getx/(AB - x) = (112* x)/(BR*(AB - x))Therefore, we getBR = (x*(AB - x)*QR)/[PQ*(AB - 2*x)]BR = (x*(32 - x)*112)/(735*(32 - 2*x))BR = (56*x*(16 - x))/(245*(16 - x))BR = (56*x/245)Since the sum of all sides of a parallelogram is equal to the sum of its opposite sides, we have thatRC + QR = AB + AQ - QBRearranging the terms we getRC = AB + AQ - QB - QR......(2)Now, AQ = PQ - APSubstituting the values of PQ and AP we get AQ = 735 - (DC - x) = 735 - 32 + x = x + 703Also, QB = AB - AQ = (32 - x) - (x + 703) = -x - 671Substituting the values of AQ and QB in equation (2) above we getRC = 32 + (x + 703) + (x + 671) - 112RC = 48 + 2xRC = 2(x + 24)We know that AB = 32, hence, x ≤ 32Putting x = 24 in the expression we get RC = 96Therefore, the value of RC is 96.
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5 ft
8 ft
6:ft
Find the area.
10 ft
5 ft
Remember: A = πr²
A = [?] ft²
Round to the nearest
hundredth.
Use 3.14 for T.
Answers
The area of the composite figure with the given subshapes is 99.13 square feet
How to determine the area of the composite figureGiven the following parameters:
The composite figure with the following shapes
Semi-circle with diameter 8 ft
Triangle with base of 8 ft and height of 6 feet
Rectangle of 10 by 5 feet
The area of the composite figure is the sum of the individual areas
So, we have
Area = 1/2 * π(8/2)² + 1/2 * 8 * 6 + 10 * 5
Evaluate
Area = 99.13
Hence, the area is 99.13 square feet
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1. school a's graduation rate is 10 points higher than school b's. how much higher do we expect a's giving rate to be? 2. how does the answer to question 1 change if we learn that a and b have identical student-to-faculty ratio? why would the answer to question 1 change? 3. which of the 123 schools has the most (least) giving rate? please elaborate on your finding as to what other variables (s) might have contributed to the differences in giving rates? 4. consider a school similar to ours. we have a 67% graduation rate and a student-to-faculty ratio of 17:1, 34% of the classes have fewer than 20 students, 23% of the classes have more than 50 students, and we have a freshman retention rate of 77%. should this school's giving rate be greater than or less than 8%?
Answers
To estimate the difference between the giving rates of school A and school B, we must first identify the missing value. It is not given in the statement.
1. However, it can be assumed that the giving rate of school B is 0%, as the difference between the two figures should be expressed as a percentage.
If school A has a graduation rate of 90%, we can estimate its giving rate as follows: Given that school A's graduation rate is 10 points higher than school B's graduation rate, the Giving rate of school A = (90 + 10)% = 100%Thus, school A's giving rate is expected to be 100%.2. If we learn that schools A and B have identical student-to-faculty ratios, the answer to the previous question would not change. The student-to-faculty ratio has no bearing on the graduation and giving rates of the school.
The student-to-faculty ratio is a measure of class size and may be used to determine how well the school is prepared to manage the educational needs of its students.3. The question does not provide a list of 123 schools to choose from. It is not possible to determine the school with the highest or lowest giving rate without this information.
4. To calculate whether the school's giving rate is greater or lesser than 8%, we must first estimate the value of the giving rate. The problem statement does not provide a clue to the school's giving rate.
Nonetheless, we can estimate that the giving rate of a school with a 67% graduation rate and a freshman retention rate of 77% would be relatively lower than 8%. Schools with a higher graduation rate are more likely to have a higher giving rate because their alumni are more inclined to contribute to the institution.Therefore, it is not possible to calculate the school's giving rate without more information.
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Suppose two students from Georgia State University, working as interns for Select one answer the American National Elections Studies agency (ANES), are both 10 points assigned to survey a random sample of registered voters and ask whether or not they will vote for a certain candidate. The first intern plans to select 500 voters and the second intern plans to select 1500 voters. If each intern conducted the study repeatedly selecting different samples of people each time... but using the same sample size), which one of the following would be true regarding the resulting sample proportion, p, of "yes" responses for each intern? A. For either sample size, using the same size each time, as long as the sampling is done with replacement, their mean would be o. B. Different sample proportions, p, would result for each intern, but for either sample size, they would be centered (have their mean) at the true population proportion, P. C. Different sample proportions, p, would result for each intern, but for the intern using a sample size of 1500 they would be centered (have their mean) at the true population proportion, P, whereas for sample size 500 they would not. D. Different sample proportions, p, would result for each intern, but for sample size 500 they would be centered (have their mean) at the true population proportion, P, whereas for sample size 1500 they would not.
Answers
Answer: Different sample proportions, ^p, could result for each intern, but for either sample size, they would be centered (have their mean) at the true population proportion, p.
Step-by-step explanation:
Hank bought 5 meters of ribbon for $4. Use the drop-down menus to complete the sentence. The ribbon costs per .
Answers
Answer:
the ribbon costs $0.80 per meter.
Step-by-step explanation:
To calculate the cost per meter of ribbon, we can divide the total cost of the ribbon by the length of the ribbon:
Cost per meter = Total cost of ribbon / Length of ribbon
In this case, the total cost of the ribbon is $4, and the length of the ribbon is 5 meters:
Cost per meter = $4 / 5 meters = $0.80/meter
To determine the cost of each meter of the ribbon, we divide the cost for 5 meters of ribbon by 5. That is,
[tex]x = \$4 / 5[/tex]
where x is the cost of each meter. Simplifying will give us an answer of $0.8/m. Converting this to per mm.
[tex]($0.8/m) \times (1 m/ 1000 mm)[/tex]
[tex]= \$0.0008/mm[/tex]
The null hypothesis is rejected whenever:A. past studies prove it wrong. B. there is a low probability that the obtained results could be due to random error.C. the independent variable fails to have an effect on the dependent variable.D. the researcher is convinced that the variable is ineffective in causing changes in behavior.
Answers
The null hypothesis is rejected whenever "there is a low probability that the obtained results could be due to random error." The correct answer is Option B.
What is the null hypothesis?The null hypothesis is a statistical hypothesis used to test the difference between two sample data groups. The null hypothesis is the hypothesis that the sample statistics are not significantly different. Any significant differences between the sample data are seen as supporting the alternative hypothesis.
A null hypothesis is often expressed as "no difference," "no correlation," or "no significant effect." For example, the null hypothesis for an experiment comparing two groups of people could be "there is no difference between the two groups." When the null hypothesis is rejected, it means that the results of the experiment are statistically significant, and the alternative hypothesis is supported.
Therefore, the null hypothesis is rejected whenever there is a low probability that the obtained results could be due to random error.
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Help please I dont know how to do this.
Answers
[tex]0.000000778\implies \stackrel{ \textit{rounded up} }{0.000000800} ~\hfill 0.00000000155\implies \stackrel{ \textit{rounded up} }{0.00000000200} \\\\[-0.35em] ~\dotfill\\\\ 0.\underset{ 6~zeros }{\underline{000000}}800\implies 8.00\times 10^{-6}\implies \boxed{8\times 10^{-6}} \\\\\\ \underset{ 8~zeros }{0.\underline{00000000}200}\implies 2.00\times 10^{-8}\implies \boxed{2\times 10^{-8}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{\stackrel{ \textit{dust particle} }{8\times 10^{-6}}}{\underset{ \textit{grain of pollen} }{2\times 10^{-8}}}\implies \cfrac{8}{2}\times\cfrac{10^{-6}}{10^{-8}}\implies 4\times10^{-6}10^{8}\implies 4\times 10^2\implies \boxed{400}[/tex]
What is the area of this polygon in square units
Answers
The area of the polygon is 80 units².
What is a Polygon?
A polygon is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides.
Dividing the polygon into parts marked in the attached figure so as to calculate the area easily.
For triangle, DEF
Area = [tex]\frac{1}{2} bh[/tex]
= [tex]\frac{1}{2}[/tex] × 3 × 4
= 6 units²
For triangle BCD
Area = [tex]\frac{1}{2}bh[/tex]
= [tex]\frac{1}{2}[/tex] × 2 × 4
= 4 units²
For trapezoid ABFG,
Area = [tex]\frac{1}{2} (a + b) h[/tex]
= [tex]\frac{1}{2}[/tex] × (5.5 + 12) × 8
= 70 units²
Hence, total area = 6 + 4 + 70
= 80 units².
Therefore, the total area of the polygon is 80 units².
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anyone know the answer?
Answers
The required value of the base of the triangle is [tex]\frac{7\sqrt{3} }{3}[/tex].
What is right angled triangle?Right-angle triangles are formed when the angle formed by two of their edges is exactly 90 degrees. Obtuse angle triangle: An obtuse angle triangle is one in which the angle formed by two sides is larger than 90 degrees.
According to question:In the given triangle, we will use tangent function to find the value of x.
tan(∅) = Perpendicular/ base
tan(60°) = 7/x
x = 7/tan(60°)
x = 7/√3 ∴ (tan(60°) =√3 )
On rationalizing
x = [tex]\frac{7\sqrt{3} }{3}[/tex]
Thus, required value of x is [tex]\frac{7\sqrt{3} }{3}[/tex].
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How to do matrix multiplication in MIPS?
Answers
To perform matrix multiplication in MIPS, we can use nested loops to iterate over the rows and columns of the matrices.
The outer loop iterates over the rows of the first matrix, while the inner loop iterates over the columns of the second matrix. We then perform the dot product of the corresponding row and column, which involves multiplying the elements and summing the products.
To perform multiplication efficiently, we can use MIPS registers to store intermediate values and avoid accessing memory unnecessarily. We can also use assembly instructions like "lw" and "sw" to load and store values from memory, and "add" and "mul" to perform arithmetic operations.
In summary, matrix multiplication in MIPS involves nested loops, efficient use of registers and assembly instructions, and arithmetic operations.
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The table below shows the number of gold, silver and bronze medals won by
some countries in the 2016 Paralympic Games.
Work out the ratio of gold to silver to bronze medals won by Belarus.
Give your answer in its simplest form.
Country
Cuba
Malaysia
Belarus
Spain
Gold
8
3
8
9
Silver
1
0
0
14
Bronze
6
1
2
8
Answers
The ratio of gold to silver to bronze medals won by Belarus in its simplest form is 4:0:1, which means that Belarus won four times as many gold medals as bronze medals, and no silver medals.
What is simplest form ?In mathematics, the simplest form refers to the most reduced or compact form of an expression.
The simplest form can be achieved by simplifying, reducing, or condensing a mathematical expression or ratio to its smallest possible form using various techniques such as factorization, cancellation, and distribution.
To find the ratio of gold to silver to bronze medals won by Belarus, we need to look at the row corresponding to Belarus in the table:
Country Gold Silver Bronze
Belarus 8 0 2
The ratio of gold to silver to bronze medals won by Belarus is: 8:0:2
However, this ratio is not in its simplest form, because we can simplify it by dividing all of the numbers by the greatest common factor of the three numbers. In this case, the greatest common factor of 8, 0, and 2 is 2, so we can simplify the ratio by dividing each number by 2:
8 ÷ 2 : 0 ÷ 2 : 2 ÷ 2
4 : 0 : 1
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a researcher wishes to study railroad accidents. he wishes to select 3 railroads from 10 class i railroads, 2 railroads from 6 class ii railroads, and 1 railroad from 5 class iii railroads. how many different possibilities are there for his study?
Answers
There are, 6300 different possibilities for the researcher’s study.
How do we calculate the different possibilities?Total number of class I railroads = 10Number of class I railroads selected = 3Total number of class II railroads = 6Number of class II railroads selected = 2Total number of class III railroads = 5Number of class III railroads selected = 1Number of different possibilities for selecting 3 class I railroads from 10 class I railroads = 10C3 = (10 x 9 x 8)/(3 x 2 x 1) = 120
Number of different possibilities for selecting 2 class II railroads from 6 class II railroads = 6C2 = (6 x 5)/(2 x 1) = 15Number of different possibilities for selecting 1 class III railroad from 5 class III railroads = 5C1 = 5Total number of different possibilities for selecting 3 class I railroads from 10 class I railroads, 2 class II railroads from 6 class II railroads, and 1 class III railroad from 5 class III railroads = 10C3 x 6C2 x 5C1= 120 x 15 x 5= 6300Therefore, there are 6300 different possibilities for the researcher’s study.
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Joan has a credit limit of $900. Her new balance is $450. What is Joan's available credit?
Answers
Hi!
Let's write this out.
Her limit is $900, and she's used $450. So, we subtract 450 from 900.
900-450 = 450.
So, she has $450 available credit left.
Hope this helps!
~~~PicklePoppers~~~
Answer: your credit utilization ratio on that card would be 50% but the answer is 450
Step-by-step explanation:
900-450 = 450
4/7+1/8+1/3 prime number
Answers
Since 7 is the smallest integer that divides 173/168, we can conclude that the sum is not a prime number.
How to solve?
To add the fractions 4/7, 1/8, and 1/3, we need to find a common denominator.
The prime factorization of 7 is 7, the prime factorization of 8 is 2²3, and the prime factorization of 3 is 3. The least common multiple (LCM) of these three numbers is 7× 2²3× 3 = 168.
So, we can rewrite the fractions with the common denominator of 168:
4/7 = 96/168
1/8 = 21/168
1/3 = 56/168
Now we can add these fractions:
96/168 + 21/168 + 56/168 = 173/168
To check if this sum is a prime number, we can use trial division by checking all the integers between 2 and the√ of 173/168 (which is approximately 1.053):
2 does not divide 173/168
3 does not divide 173/168
4 does not divide 173/168
5 does not divide 173/168
6 does not divide 173/168
7 divides 173/168 (24 times)
8 does not divide 173/168
9 does not divide 173/168
...
Since 7 is the smallest integer that divides 173/168, we can conclude that the sum is not a prime number.
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Complete question:
What is the result of adding 4/7, 1/8, and 1/3, and is the sum a prime number?
there exists a complex number $c$ such that we can get $z 2$ from $z 0$ by rotating around $c$ by $\pi/2$ counter-clockwise. find the sum of the real and imaginary parts of $c$.
Answers
The sum of the real and imaginary parts of $c$ is$$\operatorname{Re}(c) + \operatorname{Im}(c) = \frac{\operatorname{Re}(2c)}{2} + \frac{\operatorname{Im}(2c)}{2}$$$$= \frac{\operatorname{Re}(z_0+z_2)}{2} - \frac{\operatorname{Im}(z_0)}{2}(1-\cos(\theta/2)) - \frac{\operatorname{Re}(z_0)}{2}\sin(\theta/2)$$$$+ \frac{\operatorname{Im}(z_0+z_2)}{2} - \frac{\operatorname{Re}(z_0)}{2}(1-\cos(\theta/2)) + \frac{\operatorname{Im}(z_0)}{2}\sin(\theta/2).$$
The given problem can be solved using algebraic and geometric methods. We can use algebraic methods, such as the equations given in the problem, and we can use geometric methods by visualizing what the problem is asking. To start, let's translate the given problem into mathematical equations. Let $z_0$ be the original complex number. We want to rotate this point by 90 degrees counter-clockwise about some complex number $c$ to get $z_2$. Thus,$$z_2 = c + i(z_0 - c)$$$$=c + iz_0 - ic$$$$= (1-i)c + iz_0.$$We also know that this transformation will rotate the point $z_1 = (z_0 + z_2)/2$ by 45 degrees. Thus, using similar logic,$$z_1 = (1-i/2)c + iz_0/2.$$Now let's use the formula for rotating a point about the origin by $\theta$ degrees (where $\theta$ is measured in radians) to find a relationship between $z_1$ and $z_0$.$$z_1 = z_0 e^{i\theta/2}$$$$\implies (1-i/2)c + iz_0/2 = z_0 e^{i\theta/2}$$$$\implies (1-i/2)c = (e^{i\theta/2} - 1)z_0/2.$$We can solve for $c$ by dividing both sides by $1-i/2$.$$c = \frac{e^{i\theta/2} - 1}{1-i/2}\cdot\frac{z_0}{2}.$$We can now use the information given in the problem to solve for the sum of the real and imaginary parts of $c$. We know that rotating $z_0$ by 90 degrees counter-clockwise will result in the complex number $z_2$. Visually, this means that $c$ is located at the midpoint between $z_0$ and $z_2$ on the line that is perpendicular to the line segment connecting $z_0$ and $z_2$. We can use this geometric interpretation to solve for $c$. The midpoint of the line segment connecting $z_0$ and $z_2$ is$$\frac{z_0+z_2}{2} = c + i\frac{z_0-c}{2}.$$Solving for $c$, we get$$c = \frac{z_0+z_2}{2} - \frac{i}{2}(z_0-c)$$$$\implies 2c = z_0+z_2 - i(z_0-c)$$$$\implies 2c = z_0+z_2 - i(z_0- (e^{i\theta/2} - 1)(z_0/2)/(1-i/2)).$$We can now find the real and imaginary parts of $c$ and add them together to get the desired answer. Let's first simplify the expression for $c$.$$2c = z_0+z_2 - i(z_0 - (e^{i\theta/2} - 1)\cdot(z_0/2)\cdot(1+i)/2)$$$$= z_0 + z_2 - i(z_0 - z_0(e^{i\theta/2} - 1)(1+i)/4)$$$$= z_0 + z_2 - i(z_0 - z_0e^{i\theta/2}(1+i)/4 + z_0(1-i)/4)$$$$= z_0 + z_2 - i(z_0(1-e^{i\theta/2})/4 + z_0(1-i)/4)$$$$= z_0 + z_2 - i(z_0/4(1-e^{i\theta/2} + 1 - i))$$$$= z_0 + z_2 - i(z_0/2(1-\cos(\theta/2) - i\sin(\theta/2)))$$$$= z_0 + z_2 - i(z_0(1-\cos(\theta/2)) + z_0\sin(\theta/2) - i(z_0\cos(\theta/2))/2.$$Now we can find the real and imaginary parts of $2c$ and divide by 2 to get the real and imaginary parts of $c$. We have$$\operatorname{Re}(2c) = \operatorname{Re}(z_0+z_2) - \operatorname{Im}(z_0)(1-\cos(\theta/2)) - \operatorname{Re}(z_0)\sin(\theta/2)$$$$\operatorname{Im}(2c) = \operatorname{Im}(z_0+z_2) - \operatorname{Re}(z_0)(1-\cos(\theta/2)) + \operatorname{Im}(z_0)\sin(\theta/2).$$Thus, the sum of the real and imaginary parts of $c$ is$$\operatorname{Re}(c) + \operatorname{Im}(c) = \frac{\operatorname{Re}(2c)}{2} + \frac{\operatorname{Im}(2c)}{2}$$$$= \frac{\operatorname{Re}(z_0+z_2)}{2} - \frac{\operatorname{Im}(z_0)}{2}(1-\cos(\theta/2)) - \frac{\operatorname{Re}(z_0)}{2}\sin(\theta/2)$$$$+ \frac{\operatorname{Im}(z_0+z_2)}{2} - \frac{\operatorname{Re}(z_0)}{2}(1-\cos(\theta/2)) + \frac{\operatorname{Im}(z_0)}{2}\sin(\theta/2).$$
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