Possible triangles that satisfy the given conditions are:
Triangle 1: a = 36, b = 43.5, c = 44, A = 31, B = 63.5, C = 85.5
Triangle 2: a = 36, b = 27.5, c = 44, A = 31, B = 116.5, C = 33.5
What are the possible triangles that satisfy the given conditions?Generally, To use the Law of Sines to solve for the possible triangles that satisfy the given conditions, we need to know at least one additional angle or side length of the triangle. The Law of Sines states that:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the side lengths of the triangle and A, B, and C are the corresponding angles opposite those sides. Therefore, we need to know at least one additional angle or side length in order to use the Law of Sines to solve for the remaining sides and angles of the triangle.
If we let B1 and B2 be the two possible values of angle B, then we can use the Law of Sines to find the corresponding values of angles A1 and A2 and sides a1 and a2 as follows:
a1/sin(A) = c/sin(B1) a2/sin(A) = c/sin(B2)
Solving these equations for a1 and a2, we get:
a1 = c * sin(A) / sin(B1) a2 = c * sin(A) / sin(B2)
Since we are given that a = 36 and c = 44, we can substitute these values into the above equations to find the values of a1 and a2.
a1 = 44 * sin(31) / sin(B1) a2 = 44 * sin(31) / sin(B2)
Now, we can use the Law of Sines to find the corresponding values of angles A1 and A2.
A1 = arcsin(a1 * sin(B1) / c) A2 = arcsin(a2 * sin(B2) / c)
Substituting the values of a1 and a2 that we found earlier and the given value of c, we get:
A1 = arcsin(36 * sin(B1) / 44) A2 = arcsin(36 * sin(B2) / 44)
To find the possible values of angles B1 and B2, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Therefore, we have:
B1 + A1 + C1 = 180 degrees B2 + A2 + C2 = 180 degrees
Substituting the values of A1 and A2 that we found earlier, we get:
B1 + arcsin(36 * sin(B1) / 44) + (180 - 31 - B1) = 180 degrees B2 + arcsin(36 * sin(B2) / 44) + (180 - 31 - B2) = 180 degrees
Solving these equations for B1 and B2, we find that the possible values of B1 and B2 are:
B1 = 63.5 degrees B2 = 116.5 degrees
Therefore, the possible triangles that satisfy the given conditions are:
Triangle 1: a = 36, b = 43.5, c = 44, A = 31, B = 63.5, C = 85.5
Triangle 2: a = 36, b = 27.5, c = 44, A = 31, B = 116.5, C = 33.5
Note that these values should be rounded to one decimal place as requested.
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Suppose that in an election voter preference is sharply divided along gender lines. 60% of women will vote for Candidate J, the rest will vote for Candidate K; 30% of men will vote for Candidate J, the rest for Candidate K. Which of the following represents the lowest percentage of voters that must be women on election day, in order that Candidate J wins the election?
* 65%
* 67%
* 69%
* 71%
* 73%
By using proportions, it is discovered that 67% of voters who are female and vote for Candidate J to win.
What exactly is a ratio ?A percentage is a component of a total amount, and the three-step rule is used to relate the measurements.
The percentage of voters who select Candidate J is:
60% of x are voters are female
30% of (1 - x), who vote are male
If the total of these percentages is larger than 50% = 0.5, Candidate J will be elected; therefore:
0.6x + 0.3(1 - x) > 0.5
0.6x + 0.3 - 0.3x > 0.5
0.3x > 0.2
x > 2/3
x > 0.667
x > 67%
By using proportions, it is discovered that 67% of voters who are female and vote for Candidate J to win.
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Can someone please explain step by step on how I stole this problem?
-1 - ( -0.25 )
The final answer of the problem is -0.75.
What is the order of operations?
The order of operations is also known as the hierarchy of operations. The order of operations tells us the order in which we should perform mathematical operations in order to get the correct result. The order of operations is usually represented by the acronym PEMDAS:
P: Parentheses first
E: Exponents (ie Powers and Square Roots, etc.)
MD: Multiplication and Division (left-to-right)
AS: Addition and Subtraction (left-to-right)
We have,
-1 - (-0.25)
Using the order of operations, we can solve this problem as follows:
Parentheses: The first step is to perform any calculations inside parentheses. In this case, there are no parentheses, so we can move on to the next step.
Exponents: There are no exponents in this problem, so we can move on to the next step.
Multiplication and Division: There is no multiplication or division in this problem, so we can move on to the next step.
Addition and Subtraction: Finally, we can perform addition and subtraction in the problem. We start from left to right, so we start with the first operation: -1 - (-0.25). To subtract a negative number, we can use the rule that subtracting a negative number is the same as adding a positive number.
Therefore, we have -1 + 0.25.
The final step is to simplify the expression by performing the addition: -1 + 0.25 = -0.75.
Therefore, the final result of the problem is -0.75.
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Leon Starr purchased 55 shares of stock at
$41.09 per share. His online stockbroker charged him
a $15.99 commission. What is the total amount that he
paid for the stock?
Total amount paid for the stock:
Answer: $2,275.94
Step-by-step explanation: First, we need to find how much he pays for the stocks alone. So, we would use this equation:
41.09(55)
41.09 x 55
That would get us to $2,259.95. Now, we have to add the $15.99, bc he had to pay a fee. So $2,259.95 + 15.99 = $2,275.94. I hope this helped!
What is the rate of change of the linear function whose graph includes the points (5, 2) and (10, 0)?
help!!
find the measures of each angle
The measures of angles x, y and z are 40°, 50° and 130° and measures of the segments are AY = 16, IY = 9, FG = 30, AP = 24
What is centroid?Centroid is the point in a triangle where all the medians of the triangle intersects.
Given are two triangles, in first we have to find the missing angles and in the second one we need to find the asked segments,
1) We know that, in a right triangle, one angle is 90° and the sum of other two sides is 90°,
Therefore, 40°+y = 90°
y = 50°
x+y = 90°
x = 90°-50°
x = 40°
z = 180°-50° (linear pair)
z = 130°
2) we know that, the centroid divides the medians into 2:1
AY = 2YP
AY = 16
IY = TY/2
IY = 9
FG = GY+YF (segment addition postulate)
GY = YF/2
GY = 10
FG = 10+20 = 30
PA = AY+YP (segment addition postulate)
PA = 8+16
PA = 24
Hence. the measures are x, y and z are 40°, 50° and 130° and AY = 16, IY = 9, FG = 30, AP = 24
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60 POINTS!!! As a special promotion for its 12-ounce cans of cold coffee, a coffee drink company printed a message on the bottom of each can. Some of the bottoms read, "Better luck next time!" whereas others read, "You won!" The company advertised the promotion with the slogan "One in five wins a prize!" Suppose the company is telling the truth and that every 12-ounce can of coffee has a one-in-five chance of being a winner. Six friends each buy one 12-ounce can of coffee at a local convenience store. Let X equal the number of friends who win a prize.
Part A: Explain why X is a binomial random variable.
Part B: Find the mean and standard deviation of X. Interpret each value in context.
Part C: The store clerk is surprised when two of the friends win a prize. Is this group of friends just lucky, or is the company's one-in-five claim inaccurate? Compute P(X ≥ 2) and use the result to justify your answer.
A) Yes, X is a binomial random variable because all of the requirements for a binomial distribution have been established
B) The mean and standard deviation are respectively; 1.2 and 0.6
C) The probability given as P(X ≥ 2) is 0.34464
How to solve binomial probability distribution?The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.
The general formula of binomial probability distribution is;
P(X = x) = nCr * p^(x) * (1 - p)^(n - x)
where;
p = probability of "success"
n = number of trials, or the sample size
x = the number of "successes" in the probability we are trying to calculate.
A) We are told that 6 friends each buy one 12-ounce bottle of the soda at a local convenience store. Let X = the number who win a prize.
Probability of success; p = 1/5
Number of events; n = 6 which is the random variable being binomial random variable:
There are two types of accomplishments: successes and failures.
Candies are unrelated to one another.
There is a set number of buddies available.
In addition, the chance of success is fixed.
Because all of the requirements for a binomial distribution have been established, then it is a binomial probability distribution.
B) The formula for the mean here is;
μ = np
Plugging in the relevant values gives;
μ = 6(1/5) = 1.2
Formula for the standard deviation is;
σ = √(np(1 - p))
Thus;
σ = √(6 * 1/5)(1 - (1/5)))
σ = 0.6
C) The probability P(X ≥ 2) calculated with online binomial probability calculator gives;
P(X ≥ 2) = 0.34464
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Which points have a distance of 6 units between them?
Select all that apply.
A-(-12,2) and B-(-6,2)
B-(-6,2) and C-(-6-4)
C-(-6-4) and D-(6,2)
D-(6.2) and E=(6,4)
E-(64) and F=(-12.4) please help me with this
The points that have a distance of 6 units between them are A(-12, 2) and B(-6, 2); B(-6, 2) and C(-6, -4).
Distance between two points:The distance between two points P(x₁, y₁) and Q(x₂, y₂) is given by
Distance PQ = [tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2} - y_{1})^{2} }[/tex]Here we have
A (-12, 2) and B(-6, 2)
B (-6, 2) and C(-6, -4)
C (-6, -4) and D(6, 2)
D (6, 2) and E(6, 4)
E (6, 4) and F(-12, 4)
Here we will find the distance between given points to find the point which has 6 units between them.
As we know Distance = [tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2} - y_{1})^{2} }[/tex]
For Option A
A (-12, 2) and B(-6, 2)
Distance = √(-6 + 12)² + (2 - 2)²
= √[(6)² + (0)²] = √36 = 6
For Option B
For B (-6, 2) and C(-6, -4)
Distance = √(-6 - (-6))² + ( - 4 - 2)²
= √[(0)² + (-6)²] = √36 = 6
For Option C
For C (-6, -4) and D(6, 2)
Distance =√(6 - (-6))² + (2 - (-4))²
= √(12)² + (6)² = √180 = 6√5
For Option D
For D (6, 2) and E(6, 4)
Distance = √(4 - 2)² + ( 6 - 6)²
= √[(2)² + (0)²] = √4 = 2
For Option E
For E (6, 4) and F(-12, 4)
Distance = √(-12 - 6)² + (4 - 4)²
= √[(18)² + (0)²] = √18² = 18
Therefore,
The points that have a distance of 6 units between them are A(-12, 2) and B(-6, 2); B(-6, 2) and C(-6, -4).
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Awnser if this is a function or not yes or no please.
Answer: NO
Step-by-step explanation:
This is not a function, since there are multiple outputs for ONE input.
Answer:
no
Step-by-step explanation:
to be a function, the x's can only have one partner. Here, 7 has two partners (7 goes to 20 and also to 18) and the 11 has two partners also. This relation is not a function.
determine the number of different sets of quantum numbers possible for each of the following shells. n2
Answer:
Step-by-step explanation:
Explanation:
As you know, each electron that's part of an atom has its own unique set of four quantum numbers that describes its position and spin.
This means that looking for the number of unique sets of quantum numbers is equivalent to looking for the number of electrons that can occupy the third energy level.
As you know, the number of orbitals you get per energy level is given by the equation
no. of orbitals
=
n
2
, where
n
- the principal quantum number, the ones that gives the energy level.
So, if you're dealing with the third energy level, you can say that it will contain a total of
no. of orbitals
=
3
2
=
9
distinct orbitals.
Now, each orbital can contain a maximum of
2
electrons of opposite spins. This means that the third energy level will contain a maximum number of
no. of electron
=
9
⋅
2
=
18 e
−
So, if each electron is described by an unique set of quantum numbers, you can conclude that
18
sets of quantum numbers are possible for the third energy level.
ok maybe that will help!
Use the data{1,1,1,3,3,5,7,7,9,11,13,14} to create a histogram with 5 bins.
The information needs to be divided into class intervals in order to make a histogram. Following that, make a tally to display the frequency (or relative frequency) of the data within each interval.
How do you make a histogram with data?A frequency histogram or a relative frequency histogram can be used to depict data if there are several data points and we want to examine how they are distributed.A histogram resembles a bar chart in appearance, but it displays numerical data. The data must be divided into class intervals in order to make a histogram. Then make a tally to display the frequency (or relative frequency) of the data within each interval. The frequency in a given class divided by the overall number of observations is the relative frequency. The bars are the same width as the class interval and the same height as the frequency (or relative frequency).Histogram Illustration
Jessica has been self-weighing every Saturday for the past 30 weeks. She was weighed in pounds, as shown in the table below.135 137 136 137 138 139
140 139 137 140 142 146
148 145 139 140 142 143
144 143 141 139 137 138
139 136 133 134 132 132
Her weight should be a histogram.
Answer
Usually, we want histograms to have intervals between 5 and 20. With a class of width 2, which will offer us 9 intervals given that the data ranges from 132 to 148, it is practical to have.131.5-133.5
133.5-135.5
135.5-137.5
137.5-139.5
139.5-141.5
141.5-143.5
143.5-145.5
145.5-147.5
147.5-149.5
To eliminate any doubt about whether the end point belongs to the interval to its left or to its right, we chose the end points to be.5, which is why. The endpoint convention specification is a substitute. The left end point, for instance, is included by Minitab but the right end point is not.To Learn more About histogram refer to:
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The sampling distribution of the sample mean is formed from random samples of size 16 taken from a population with mean μ = 64 and standard deviation σ = 10. What are the mean and standard deviation of the sampling distribution of ?
mean = 64, standard deviation = 0.625
mean = 8, standard deviation = 2.5
mean = 64, standard deviation = 2.5
The mean and standard deviation of the sampling distribution include the following: C. mean = 64, standard deviation = 2.5.
What is the Central Limit Theorem?In Mathematics and statistics, the Central Limit Theorem states that the sampling distribution of means would always be normally distributed, as long as the sample size is large enough.
This ultimately implies that, the sampling distribution of means would always be normally distributed as the sample size gets larger in accordance with the Central Limit Theorem.
Mathematically, the standard deviation of a sampling distribution can be calculated by using this mathematical expression:
Standard deviation, σy = σ/√n
Where:
σ represents the standard deviation.n represents the sample size or number of items.Substituting the given parameters into the formula, we have;
Standard deviation, σy = 10/√16
Standard deviation, σy = 10/4
Standard deviation, σy = 2.5.
In conclusion, the mean of an original population is expected to be equal to the mean of the sampling distribution of means i.e 64.
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Please help me with this question
The average rate change of the function is -4.
What is a function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given function is f(x) = 1x² + 1x - 8.
Find the average rate change of the function in the interval [-4, -1]
For this compute the value of f(x) at x = -4 and x = -1.
Then find the difference the value of f(x) and divide it by the difference the value of x.
The average rate change of function f(x) in the interval [a,b] is [f(b) - f(a)]/(b-a).
Putting x = -4 in the given function:
f(-4) = 1(-4)² + 1(-4) - 8
f(-4) = 4
Putting x = -1 in the given function:
f(-1) = 1(-1)² + 1(-1) - 8
f(-1) = -8.
The rate change of x is -1 - (-4) = 3
The average rate change of the function is
[f(-1) - f(-4)] /3
= -8 - 4/3
= - 12/3
= -4
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Suppose that the daily number of miles driven per school bus driver in the United States is normally distributed with a mean of 300 mi and standard deviation equal to 26 mi. A local school bus budget committee believes the daily number of miles driven per bus driver in their community is different from 300 mi, but they are not sure if it is greater than or less than the national average.
To test their hypothesis, the committee chooses a random sample of 40 school bus drivers and records how many miles each of them drives per day during a typical week. On average, the bus drivers from the sample drive 309 mi per day. To test the hypothesis that the average number of miles driven by local bus drivers is different from the national average, the budget committee calculates the z-statistic to be 2.19 standard deviations above the population mean.
Use the standard normal z-distribution table to calculate the P-value that represents the probability of mistakenly rejecting the claim that the daily number of miles driven by local bus drivers is not statistically different from the national average. Give your answer as a decimal rounded to four places.
P-value:
The p-value for the z-distribution table is 0.4854.
What is z-distribution?
A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution. By transforming the values of any normal distribution into z scores, it is possible to standardise it. Z scores provide the number of standard deviations from the mean that each value falls within.
Given that the z statistic to be 2.19 standard deviation above the population mean.
2.19 can be written as 2.1 + 0.09
Z₂.₁₉ = Z₂.₁₊₀.₀₉ = 0.4854
Therefore p-value is 0.4854.
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A bi-weekly visit to your favorite restaurant. Say on average you spend $25 each visit.
A bi-weekly visit to your favorite restaurant. Say on average you spend $25 each visit.
You will spend an average of $50 a week at this restaurant.
Forest Fires and Acres Burned Numbers (in thousands) of forest fires over the year and the number (in hundred thousands) of acres burned for 7 recent years are shown. Number of fires x 69 58 47 84 62 57 72 Number of acres burned y 64 53 42 79 57 52 67 The correlation coefficient for the data is r=1 and α=0.05. Should regression analysis be done? The regression analysis should not be done. The regression analysis should be done. Find the equation of the regression line. y′=a+bx a= Find y' when x=50
The equation of the regression line is y = 4 + x and the regression analysis of the given data need not be done.
Straight line equation is y = a + bx.
The normal equations are
∑y = a·n + b ∑x ∑ xy = a ∑x + b∑x² Hence the regression analysis of the data :
The values are calculated using the following table
x y x² x⋅y
58 62 3364 3596
47 51 2209 2397
84 88 7056 7392
62 66 3844 4092
57 61 3249 3477
72 76 5184 5472
69 73 4761 5037
hence :
∑x = 449
∑y = 477
∑x² = 29667
∑x⋅y = 31463
Substituting these values in the normal equations
7a+449b=477
449a+29667b=31463
Solving these two equations using Elimination method,
7a+449b=477
and 449a+29667b=31463
7a+449b=477→(1)
449a+29667b=31463→(2)
equation(1)×449
⇒3143a+201601b=214173
equation(2)×7
⇒3143a+207669b=220241
Substracting
⇒-6068b = -6068
⇒6068b = 6068
⇒b = 1
Putting b = 1 in equation (1), we have
7a+449(1) = 477
⇒7a = 477 - 449
⇒7a = 28 or a = 4.
Now Estimate y for x=50
y = a + bx , we get
y = 4 + 1×50
y = 4 + 50
y = 54
At x equals 50 we get the value of y as 54 .
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3. Which of the following is the solution to lx + 12| = 3x.
A. x = 3
C. x = 6
b. x = -6
d. x = - 3
Dae and Eric are working together on a paper. Dae typed 333 words in 9 minutes, and Eric typed 252 words in 6 minutes. How many more words per minute did Eric type?
Eric typed 15 words more than Dae per minute.
What is a Linear Equation?Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line. A nonlinear equation is an equation whose highest power of the variables is not 1 and the graph is not a straight line.
To find the amount of words typed in 1 minute for both;
Dae = 333/9
Dae = 27 words per minute
Eric = 252/6
Eric = 42 words per minute
Therefore 42 - 27 = 15 words per minute
Eric typed 15 more words per minute.
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I'm not sure what the reasoning is
The reasons that complete the statements are:
Statement 2: GivenStatement 4: SAS congruence propertyHow to determine the reasons that complete the statementsFrom the question, we have the following parameters that can be used in our computation:
Triangles = RST, and TUR
From the question, we have the following given parameters
∠SRT ≅ ∠UTR
This means that
Statement 2: ∠SRT ≅ ∠UTR ------ Given
At this point, we have
RS ≅ TU --- Congruent side (S)
∠SRT ≅ ∠UTR ------ Congruent angle (A)
RT ≅ TR --- Congruent side (S)
When these congruent sides and angles are combined, we have
SAS congruence property
The SAS congruent theorem implies that the corresponding sides of the triangles in question are congruent and the angles between the corresponding sides are also congruent
Hence, the additional information on the congruency of the triangles are Given and SAS congruence property
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Select the correct symbol.
9.48 ? 9.480
The 2 3/4 is greater than 1 5/6, hence 1 1/4 × 2 1/5 > 5/6 × 2 1/5
What is meant by Inequality expressions?An algebraic inequality is a mathematical statement that uses the inequality sign to connect an expression to a value, a variable, or another expression.
Relationships between two expressions that aren't equal to one another are known as inequalities. Inequalities are represented by the symbols, >,,, and. has the connotation "7 is greater than" (or "is less than 7," when read left to right).
Given the incomplete expression
1 1/4 × 2 1/5 _ 5/6 × 2 1/5
We are to fill it with the necessary inequality sign
For the expression:
1 1/4 × 2 1/5 = 5/4 * 11/5
1 1/4 × 2 1/5 = 55/20
1 1/4 × 2 1/5 = 2 3/4
For the expression 5/6 × 2 1/5
5/6 × 2 1/5 = 5/6 * 11/5
5/6 × 2 1/5 = 55/30
5/6 × 2 1/5 = 1 25/30
Since 2 3/4 is greater than 1 5/6, hence 1 1/4 × 2 1/5 > 5/6 × 2 1/5
The complete question is : Select the correct symbol to compare the expressions below.
1 1/4 × 2 1/5 _ 5/6 × 2 1/5
Symbols: <, >, =
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52% of 70
what is the answer
Answer: 36.4
Step-by-step explanation:
Just convert the percentage to decimal and multiply.
70 x 0.52 = 36.4
A random sample of 115 observations results in 46 successes. Use Table 1.
a. Construct a 90% confidence interval for the population proportion of successes. (Round intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answers to 3 decimal places.)
Confidence interval to
b. Construct a 90% confidence interval for the population proportion of failures. (Round intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answers to 3 decimal places.)
Confidence interval to
Option a) 90% confidence interval for the population proportion of successes = 0.402
Option b) 90% confidence interval for the population proportion of failures = 0.598
According to the question given,
Critical values of Standard deviations are to be used to construct the proportions for the confidence interval.
The formula of a confidence interval that we will be using for the solution will be,
p = [tex]z_{a} * \sqrt{\frac{p(1-p)}{n} }[/tex]
In the above expression,
p = observed population.
n = sample size
[tex]z_{a}[/tex] = critical value of confidence interval
Now the given observations in question = 115
That result in success = 46
The resultant sample proportion = [tex]\frac{46}{115}[/tex]
⇒ 0.40 and it is for both success and failure
Here we can see that the answer for both parts will be identical.
The critical value of z at 90% confidence = 1.64
a) Lower bound = [tex]0.4 - 1.64 * \sqrt{\frac{0.4(1-0.4)}{90} }[/tex]
⇒ 0.402
b) Upper bound = [tex]0.4 + 1.64 * \sqrt{\frac{0.4(1-0.4)}{90} }[/tex]
⇒ 0.598
Confidence interval = 0.402 to 0.598
Therefore,
Option a) 90% confidence interval for the population proportion of successes = 0.402
Option b) 90% confidence interval for the population proportion of failures = 0.598
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Does the point (4, 7) satisfy the equation y = x + 3?
Data is collected from the US Geologic Survey about the flow rate of the Poudre river. After some study, and unit conversions, a scientist makes a first model of the historical flow rate data as F(t) = 1.5 + 1.2 cos(2 t) in billions of cubic feet per year, while t is measured in fractions of a year since May 1, 2000. Use the Fundamental Theorem of Calculus to find the net amount of water from t = 0) to t = using this flow rate F"(t).First, F(t) = +C The model predicts the net amount of water discharged from the Poudre is F112 -Filo 0.75 What does the model predict the net discharge will be from t = 0 to t = 12 Net discharge = 1.5 Billions of ft 3
The model predicts that the net discharge will be -0.8 + 1.2 cos(24) billions of cubic feet from t = 0 to t = 12.
The net amount of water discharged from the Poudre river from t = 0 to t = 12 can be found using the Fundamental Theorem of Calculus, which states that the net change in a function over an interval is equal to the function evaluated at the endpoints of the interval minus the function evaluated at the beginning of the interval.
In this case, the net discharge from t = 0 to t = 12 can be calculated as follows:
Net discharge = F(12) - F(0)
= (1.5 + 1.2 cos(212)) - (1.5 + 1.2 cos(20))
= 1.5 + 1.2 cos(24) - 1.5 - 1.2
= -0.8 + 1.2 cos(24)
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When you are testing hypotheses by using proportions, what are the necessary requirements? OA. np 25 and nq 25 ?B.np < 5 and nq < 5 C. The population standard deviation is unknown. D. p
The following conditions must be met in order to test hypotheses using proportions: np ≥ 5 and nq ≥ 5
To test hypotheses using proportions, the following requirements are necessary:
np ≥ 5 and nq ≥ 5: It is necessary to have a sufficient number of samples in each group being compared.
The rule of thumb is to have at least 5 observations in each group, where n is the sample size and p is the proportion in that group.
This ensures that the sampling distribution of the proportion is approximately normal, which is necessary for hypothesis testing.
Hence, the correct answer would be an option (A).
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A student completes ⅘ of a math project in ⅔ hour. If the student continues at the same rate, how long will it take the student to complete the project?
The number of hours it will take the student to complete the project is 5 / 6 hours.
How to find the time the project will be completed?A student completes ⅘ of a math project in ⅔ hour. If the student continues at the same rate, the time it will take the student to complete the project can be calculated as follows:
Therefore,
let
x = time it will take the student to complete the project
Hence
if 4 / 5 x = 2 / 3 hours
x = ? hours
cross multiply
Therefore,
number of hours to complete the whole math project = x × 2 / 3 ÷ 4 / 5 x
number of hours to complete the whole math project = 2 / 3 x × 5 / 4x
number of hours to complete the whole math project = 10x / 12x
number of hours to complete the whole math project = 10 / 12
number of hours to complete the whole math project = 5 / 6 hours
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2. Of the total pounds, x, of fudge at the fudge shop on Monday morning, {3}/{4} contain nuts. Helena works at the fudge shop and prepares 12 {3}/{4} more pounds of fudge containing nuts to fulfill a special order Monday afternoon. With this additional amount of fudge, there are at least 29 {5}/{8} pounds of fudge containing nuts at the fudge shop on Monday.
(a) Write an inequality that represents the scenario. Begin by defining your variable.
(b) Solve your inequality from Part (a). Show all work.
(c) Fudge is packaged into 1-pound boxes. What is the fewest number of boxes of fudge at the fudge shop Monday morning?
Answer:
At least means less than or equal to.
Fewest means the smallest number of boxes.
12 3/4 +x ≥ 29 5/8
x ≥ 16 7/8
The fewest number of boxes would be almost ≅ 42 boxes
Part A:
Let x denote the amount of fudge at the shop.
Helena prepares 12 3/4 pounds of fudge containing nuts.
Mathematically, the total amount of fudge on Monday will be
12 3/4 +x
Of this amount of fudge there are at least 29 5/8 pounds of fudge containing nuts at the fudge shop on Monday
12 3/4 +x ≥ 29 5/8
Part B:
The inequality can be solved
12 3/4 +x ≥ 29 5/8
x ≥ 29 5/8- 12 3/4
x ≥ 29- 12 5/8- 3/4
The whole numbers are subtracted and the fractions are solved separately to avoid long calculations.
x ≥ 17 (5-6)/8
x ≥ 17 - 1/8
x ≥ (136-1)/8
x ≥ (135)/8
x ≥ 16 7/8
Part C :
To find the number of boxes we divide the equal number of pounds .
12 3/4 + 29 5/8
12 + 29 3/4 + 5/8
41 11/8
42 3/8
The fewest number of boxes would be almost ≅ 42 boxes
At least problem can be understood by the following link.
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Drag and drop the choices into the boxes to correctly complete the table.
corresponding alternate interior alternate exterior none of these
Definitions:
Corresponding angles are the angles at matching corners.Alternate interior angles lie on the inner side of the parallel lines but on the opposite side of the transversal.Alternate exterior angles lie on the outer side of the parallel lines but on the opposite side of the transversal.The given angles are:
Top left figure ⇒ Alternate interiorTop middle figure ⇒ CorrespondingTop right figure ⇒ CorrespondingBottom left figure ⇒ Alternate exteriorBottom right figure ⇒ None of thesegravel is being dumped from a conveyor belt at a rate of 40 cubic feet per minute. it forms a pile in the shape of a right circular cone whose base diameter and height are always equal. how fast is the height of the pile increasing when the pile is 16 feet high? recall that the volume of a right circular cone with height h and radius of the base r is given by v=(1/3)xpix(r^2)xh
The height of the pile increasing when the pile is 16 feet high is 5/32 ft/min.
We are given dV/dt=10 cubic ft/min and we want to find dh/dt. Therefore, first we need to write a formula relating v and h.
V=pi*r^2*h/3 since d=h at any moment, we know that r=h/2 at any moment and if we substitute h/2 for r, we get
V=pi(h/2)^2*h/3 and if we simplify this, we get
V=pi*(h^3)/12
Now we need to take the derivative of both sides with respect to t
dV/dt = pi * ( 3 * h^2 ) */12 * dh/dt
= pi * h^2 / 4 * dh/dt, substitute 40 for dV/dt and 16 for h and solve for dh/dt and we get
40 = pi * 16^2/4*dh/dt
dh/dt = 40 * 4 / ( 256 * pi )
= 40/(256*pi) ft/min,
= 10/64
= 5/32 ft/min
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From a hot-air balloon, Violet measures a 24° angle of depression to a landmark
that's 806 feet away, measuring horizontally. What's the balloon's vertical distance
above the ground? Round your answer to the nearest tenth of a foot if necessary.
The balloon's vertical distance above the ground is 358.9 feet.
An angle is said to be that of depression when it is measured downwards with respect to the horizontal plane.
So that applying the appropriate trigonometric function to solve the question, we have;
Tan θ = Opposite side/ Adjacent side
But,
θ = 90 - 24
= 66
θ = [tex]66^{o}[/tex]
Let the vertical distance of the balloon be represented by x.
Tan 66 = 806/ x
x = 806/ Tan 66
= 806/ 2.246
= 358.86
x = 358.9 feet
The balloon's vertical distance above the ground is 358.9 feet.
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Andreas has $18. Bonnie has 1 2/3 times as much as Andreas. Cheryl has 1 3/5 times as much as Bonnie.
How much money do
they have altogether?
