Answer:
x = 42.9
Step-by-step explanation:
We can let 34 represent the reference angle. Using this angle, we see that the side measuring 24 units is the opposite side and the side measuring x is the hypotenuse.
Thus, we can use the sine trig function which is
[tex]sin(angle)=\frac{opposite}{hypotenuse}[/tex]
We plug in what we have into the equation above and solve for x:
[tex]sin(34)=\frac{24}{x}\\ x*sin(34)=24\\x=\frac{24}{sin(34)}\\ x=42.9189996\\x=42.9[/tex]
how do you simplify 7/8 + 3/4?
Answer:
13/8
Step-by-step explanation:
You first find the lcm of 8 and 4 which is 8
Then make a dividing line (/) with the lcm as the numerator.
After which you start diviing the lcm by each denominator of the two terms, and then multiplying with their numerators:
8/8 x 7 + 8/4 x 3 all over the lcm which is 8
(1 x 7 + 2 x 3)/8
(7 + 6)/8
13/8
What is the coefficient of the fourth term in the expansion of (x - y)^4?
Answer: the distribution to the x and the 3 makes the solution 4
Step-by-step explanation: i got you broski
choose 5 objects without replacement from 17 objects
Answer:
6188 ways
Step-by-step explanation:
there ate 5 objects to be choosen and there is no replacement of the object therefore you got
17 choices for the first selection of the object and 16 objects for the selection of the second object and so on until you get 13 objects for the last selection
totally you have 5 selections also arrangement does not matter there fore you have 17!/12!5! which is 6188
note we used 5! cause there are 5 placed objects and 12! are unplaced objects
note
that you have used one so you have to deduct one every time you use one
it takes 6 painters 4 1/2 to paint these classroom. calculate how long 3 painters will take to complete the same job
Hi please help will get max points + brainliest!
The perimeter of the given figures is: Triangle = 4x - 2. Rectangle = 8x - 8, and square = 12x - 8y.
What is perimeter?The whole distance encircling a form is referred to as its perimeter. It is the length of any two-dimensional geometric shape's border or outline. Depending on the size, the perimeter of several figures can be the same. Consider a triangle built of an L-length wire, for instance. If all the sides are the same length, the same wire can be used to create a square.
The perimeter of a figure is the sum of all the segments of the figure.
The perimeter of triangle is:
P = 2x - 5 + x + x + 3 = 4x - 2
The perimeter of rectangle is:
P = 2(l + b)
P = 2(3x + 1 + x - 5)
P = 2(4x - 4)
P = 8x - 8
The perimeter of square is:
P = 4(s)
P = 4(3x - 2y)
P= 12x - 8y
Hence, the perimeter of the given figures is: Triangle = 4x - 2. Rectangle = 8x - 8, and square = 12x - 8y.
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If A B C are three matric such that AB=AC such that A=C then A is
Answer:
invertible
Step-by-step explanation:
If A is invertible then ∣A∣ =0
state the third congruence statement that is needed to prove that FGH is congruent to LMN using the ASA congruence therom
Answer:
a
Step-by-step explanation:
I need help with this
The line segment AB and CB are perpendicular to each other.
How to determine if a line is perpendicular?Check whether the slopes of the lines are the negative reciprocals of one another to see if they are perpendicular to one another. The steps are as follows:
Using the following formula, get the slope of the first line:slope is equal to (y-change) / (change in x)where the "change in y" refers to the difference between the y-coordinates of two points on the line, and the "change in x" refers to the difference between the x-coordinates of the same two places.Using the same formula, determine the slope of the second lineTake the first slope's negative reciprocal by turning it upside down and altering its sign. For instance, the negative reciprocal of the first line's slope of 2/3 is -3/2.Check if the second slope is equal to the negative reciprocal of the first slope. If it is, then the lines are perpendicular.Learn more about Coordinates here:
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show that if 16 people are seated in a row of 20 chairs, then some group of 4 consecutive chairs must be occupied.
The process to show that if 16 people are seated in a row of 20 chairs, then some group of 4 consecutive chairs must be occupied is shown below.
We prove this using the Pigeonhole Principle, which states that if n items are placed into m containers, and n > m, then at least one container must contain more than one item.
Let us consider the 16 people seated in a row of 20 chairs. Each person occupies one chair, so there are 20 - 16 = 4 empty chairs in the row.
We assume that empty chairs as containers, and people as items that need to be placed into containers.
Since there are more items (people) than containers (empty chairs), there must be at least one group of 2 or more consecutive empty chairs.
Now, let's consider the complement of this statement: Suppose there are no groups of 4 consecutive chairs that are occupied. Then, each group of 4 consecutive chairs contains at most 3 people.
We partition the row of chairs into groups of 4 consecutive chairs.
So, there are 20 - 3 = 17 such groups. By the statement above, each of these groups contains at most 3 people. Therefore, the total number of people seated in the row is at most 17×3 = 51.
But, we know that there are actually 16 people seated in the row. This is a contradiction, since 51 < 16. Therefore, our assumption that there are no groups of 4 consecutive chairs that are occupied must be false, and we have proved that some group of 4 consecutive chairs must be occupied.
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Please help me anyone please ?!!!?!!
Answer:
7. 23
8. (3 - 8) x 5
Step-by-step explanation:
I think the second one is right but I know the first one is.
-3+b> 7 OR b +9 <17.
The solution to the compound inequality -3+b> 7 OR b +9 <17 is given as follows:
b < 8 or b > 10.
How to solve the compound inequality?The inequality for this problem is defined as follows:
-3+b> 7 OR b +9 <17.
The or operation means that the we must solve each operation separately, and then the solution set to the compound inequality is given by the union of the solution set of each of the inequalities.
The solution set for the first inequality is given as follows:
-3+b> 7
b > 10.
The solution set for the second inequality is given as follows:
b + 9 < 17
b < 8.
Hence the solution for the entire inequality is of:
b < 8 or b > 10.
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Question 11 (2 points)
Among the seniors at a small high school of 150 total students, 80 take Math, 41
take Spanish, and 54 take Physics. 10 seniors take Math and Spanish. 19 take Math
and Physics. 12 take Physics and Spanish. 7 take all three.
How many seniors take Math and Spanish, but not Physics?
Note: Consider making a Venn Diagram to solve this problem.
3
10
27
121
There are 3 seniors who take Math and Spanish, but not Physics.
What is Venn Diagram?
A diagram representing mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle (the universal set), common elements of the sets being represented by the areas of overlap among the circles.
To solve this problem, we can use a Venn diagram to organize the information given about the students.
First, we know that there are 150 seniors in total, so we can label the outer rectangle of the Venn diagram as having a total of 150 students.
Next, we can label the three circles as Math, Spanish, and Physics, with the numbers given in the problem:
80 seniors take Math, so we label the Math circle with 80.
41 seniors take Spanish, so we label the Spanish circle with 41.
54 seniors take Physics, so we label the Physics circle with 54.
We also know that 10 seniors take Math and Spanish, 19 take Math and Physics, 12 take Physics and Spanish, and 7 take all three. We can label these overlaps in the Venn diagram as follows:
The overlap of Math and Spanish is 10.
The overlap of Math and Physics is 19.
The overlap of Physics and Spanish is 12.
The overlap of all three is 7.
To find the number of seniors who take Math and Spanish, but not Physics, we need to subtract the number of seniors who take all three (because they are counted in all three circles) and the number of seniors who take Math, Spanish, and Physics (because they are counted in the overlap of all three circles). Then we add the number of seniors who take only Math and Spanish (because they are not counted in the Physics circle).
Using the formula for the number of elements in the union of three sets, we have:
Math or Spanish or Physics = Math + Spanish + Physics - (Math and Spanish) - (Math and Physics) - (Spanish and Physics) + (Math and Spanish and Physics)
So, the number of seniors who take Math and Spanish, but not Physics is:
Math and Spanish - (Math and Spanish and Physics) + (Math or Spanish or Physics - (Math + Spanish + Physics) + (Math and Spanish and Physics))
= 10 - 7 + (80 + 41 + 54 - 2(10) - 2(19) - 2(12) + 7)
= 3
Therefore, there are 3 seniors who take Math and Spanish, but not Physics.
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On the 1st January 2014 Carol invested some money in a bank account.
The total amount of money Carol originally invested is £22,000 in the bank account.
What is compound intrest?Compound interest is interest that is calculated not only on the initial amount of money invested or borrowed, but also on any accumulated interest from previous periods.
This results in exponential growth or accumulation of interest over time.
Let X be the amount that Carol originally invested in the account.
After 1 year, the amount of money in the account will be X(1+0.025) = X(1.025).
After Carol withdrew £1000, the amount of money in the account will be X(1.025) - £1000.
After 2 years (i.e. on 1st January 2016), the amount of money in the account will be (X(1.025) - £1000)(1+0.025) = (X(1.025) - £1000)(1.025).
We know that the amount of money in the account on 1st January 2016 was £23,517.60, so we can write the equation:
(X(1.025) - £1000)(1.025) = £23,517.60
Expanding the left-hand side and simplifying, we get:
X(1.025)² - £1000(1.025) = £23,517.60
X(1.025)² = £24,567.63
Dividing both sides by (1.025)², we get:
X = £22,000 (rounded to the nearest pound)
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The complete question is -
On the 1st of January 2014, Carol invested some money in a bank account. The account pays 2.5% compound interest per year. On the 1st of January 2015, Carol withdrew £1000 from the account. On the 1st of January 2016, she had £23 517.60 in the account. Work out how much Carol originally invested in the account?
Can you guys help me?
Answer:
[tex]{ \sf{a = \frac{0.012}{0.633 -0.063 } }} \\ \\ { \sf{a = \frac{0.012}{0.57} }} \\ \\ { \sf{a = 0.021 \: (2 \: s.f)}}[/tex]
Martin has a spinner that is divided into four sections labeled A, B, C, and D. He spins the spinner twice. PLEASE ANSWER RIGHT HELP EASY THANK UU
Drag the letter pairs into the boxes to correctly complete the table and show the sample space of Martin's experiment.
Answer:
going from left to right:
AA
BD
CB
DC
Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs. y 0 1 2 3 4 ply) 0.60 0.20 0.15 0.03 0.02 (a) Calculate and interpret Hy My = 0.20 (b) In the long run, for what proportion of cartons is the number of broken eggs less than jy? (Round your answer to two decimal places). Enter a number. Does this surprise you? Yes O No 0 + 1 + 2 + 3 + 4 (c) Explain why sy is not equal to = 2.0. 5 This computation of the mean is incorrect because the value in the denominator should equal the maximum y value. This computation of the mean is incorrect because it does not take into account that the number of broken eggs are all equally like O This computation of the mean is incorrect because it includes zero in the numerator which should not be taken into account when O This computation of the mean is incorrect because it does not take into account the number of partially broken eggs.
a) The value of Hy = 1.15
b) The proportion of cartons with less than 1.15 broken eggs is 0.60
c) The answer is B)This computation of the mean is incorrect because it does not take into account that the number of broken eggs are not all equally like.
(a) Hy = 0.67, which means that on average, there are 0.67 broken eggs per carton.
Hy = (0*0.60 + 1*0.20 + 2*0.15 + 3*0.03 + 4*0.02)/1
= 0.67
(b) The proportion of cartons with less than 0.67 broken eggs is 0.60 which is probability of 0 broken eggs.. This may be surprising as the probability of having less than 0.67 broken eggs is only 0.60, but this is due to the fact that the distribution is skewed towards higher values.
(c) Hy is not equal to the simple average of 0, 1, 2, 3, and 4 because the distribution is not symmetrical. The probabilities are weighted towards higher values, which increases the mean. Additionally, the value of zero should be included in the calculation, as it represents a possible outcome. Therefore, the correct formula for Hy is (0*0.60 + 1*0.20 + 2*0.15 + 3*0.03 + 4*0.02)/1 = 0.67.
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--The question is incomplete, answering to the question below--
"Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs.
y 0 1 2 3 4
p(y) 0.60 0.20 0.15 0.03 0.02
(a) Calculate and interpret Hy
(b) In the long run, for what proportion of cartons is the number of broken eggs less than Hy? (Round your answer to two decimal places).
Does this surprise you?
Yes
No
(c) Explain why Hy is not equal to (0 + 1 + 2 + 3 + 4)/5 = 2.0.
A. This computation of the mean is incorrect because the value in the denominator should equal the maximum y value.
B. This computation of the mean is incorrect because it does not take into account that the number of broken eggs are not all equally like
C. This computation of the mean is incorrect because it includes zero in the numerator which should not be taken into account when
D. This computation of the mean is incorrect because it does not take into account the number of partially broken eggs."
plssss helpppppp!!!!
Answer:
2.
a) log base 10 of 100
b) The expression means that 10 to the 2nd power equals 100.
c) 2
3.
4. It would make sense that the value is between 1 and 2 because 10 to the 1st power is 10, and 10 to the 2nd power is 100. 50 is between 10 and 100 so the value would have to be between 1 and 2. This works because logs are the inverse function to exponentiation.
a) 2.6021
b) 3 and the value is exact because the base 10 in the log expression is technically the exponent when you convert it to exponent form. This works because logs are the inverse function to exponentiation. So 10 to the 3rd power would give you exactly 1000.
Instructions: Use the following data set to find the sample statistics for the
following data set. (Round answers to the nearest hundredth, if necessary.
{51, 48, 42, 43, 48, 48, 46, 15, 29, 45,
47, 55, 46, 35, 47, 48, 54, 26, 53, 42}
1.
2.
<<>>
11
4. Mode =
(>>
3. Median =
=
11
By using sample standard deviation - (1) N or n = 20
(2) X or μ = 43.4
(3) σ = 9.78 and s = 10.04
Why does sample standard deviation exist?
When we talk about a sample standard deviation, we're not talking about population standard deviation. The average amount by which a group of values deviates from their mean is shown by the statistical measure of variability known as the standard deviation.
We are given with the following data set below;
{51, 48, 42, 43, 48, 48, 46, 15, 29, 45, 47, 55, 46, 35, 47, 48, 54, 26, 53, 42}
(1) As we can see in the above data that there are 20 data values in our data set which means that the value of N or n (numner of observations) is 20.
(2) The formula for calculating Mean of the data, i.e. X or μ is given by;
Mean = 51 +48+ 42+ 43+ 48 + 48 + 46+ 15+ 29+ 45+ 47+ 55+ 46+ 35+ 47+ 48+ 54+ 26+ 53+ 42/20
= 868/20 = 43.4
So, the value of X or μ is 43.4.
(3) The formula for calculating population standard deviation () is given by;
Standard deviation, σ = √(51 - 43.4)² + (48 - 43.4)² + .........+(42 - 43.4)²/20
= 9.78
Similarly, the formula for calculating sample standard deviation (s) is given by;
Sample Standard deviation, s =
√(51 - 43.4)² + (48 - 43.4)² + .........+(42 - 43.4)²/20 - 1
= 10.04
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In each case either show that the statement is true, or give an example showing it is false. a. If a linear system has n variables and m equations, then the augmented matrix has n rows.
The given statements are true or false are shown below, about linear system has n variables and m equations, then the augmented matrix has n rows.
First, let's write how A and C look like.
A = [C|b], where b is the constant matrix.
(a) False.
Example
[tex]\left[\begin{array}{ccc}1&0&2\\0&1&3\\\end{array}\right][/tex]
We can see that z = t and so we have infinitely many solutions but there's no row of zeros.
(b) False.
Example
[tex]\left[\begin{array}{cc}1&0&0\1&1&0&0\\\end{array}\right][/tex]
Here; x1 = 1 and x2 = 1 is a unique solution and we have a row of zeros.
(c) True.
In the row-echelon form, the last row is either a row of zeros or a row that contains a leading 1. If the row has a leading 1, then there is a solution. Since we assume there is no solution, then the row must be a row of zeros.
(d) False.
Example
[tex]\left[\begin{array}{cc}1&3\\0&0\end{array}\right][/tex]
Here; x₁ = 1 − 3t and x2 = t. Thus, the system is consistent.
(e) True.
Suppose we have a typical equation in a system
а1x1 + A2X2 + ··· + anxn = b
Now, if b≠0 and x1 = x2 = ··· = x₂ = 0, then the system is Xn inconsistent. But, if b = 0, then we have a solution.
(f) False.
Example
[tex]\left[\begin{array}{cc}1&2&0&0\end{array}\right][/tex]
If a = 0, then it's consistent(infinitely many solutions) but if a 0, then it's inconsistent.
(g) Ture.
Since the rank would be at most 3 and this will lead to a free variable (4 columns in C and the rank is 3, so there is at leat 1 free variable). Thus, the system has more thatn one solution.
(h) True.
Because the rank is the number of leading 1's lying in different rows and A has 3 rows. Thus, the rank ≤ 3.
(i) False.
Because we could have a row of zeros in C and a leading 1 in A. In other words, a31 = a32 = A33 = A34 = 0 and c3 1. This makes the system inconsistent.
(j) True.
If the rank of C = 3, then there will be a free variable and this means the system is consistent.
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Complete question:
In each case either show that the statement is true, or give an example showing it is false. (a) If a linear system has n variables and m equations, then the augmented matrix has n rows. quations • ( *b) A consistent linear system must have infinitely many solutions. . (c) If a row operation is done to a consistent linear system, the resulting system must be consistent. (d) If a series of row operations on a linear system results in an inconsistent system, the original system is inconsistent.
Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch. I need help D:
Please !!!!
The length of the top of the bookcase should be approximately 25 inches to display the soap carving collection with an area of 300 in².
What is the length of the top of the bookcase?
To find the length of the top of the bookcase (which we'll call "b"), we need to know the area of the collection of soap carvings and the formula for the area of a rectangle:
Area = length x width
We're given the area of the soap carving collection (300 square inches), and we know that the soap carvings will be displayed on top of the bookcase, which is a rectangle.
Let's assume that the width of the bookcase is 1 unit (we can choose any unit we want, as long as we're consistent). Then we can write:
300 = b x 1
Simplifying this equation, we get:
b = 300/1
b = 300
So the length of the top of the bookcase should be 300 inches. However, this assumes that the width of the bookcase is only 1 inch, which is quite narrow.
If we assume a more reasonable width of, say, 12 inches, then we can write:
300 = b x 12
Simplifying this equation, we get:
b = 300/12
b = 25
So the length of the top of the bookcase should be 25 inches (if the width of the bookcase is 12 inches).
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Find the standard normal area for each of the following(round your answers to 4 decimal places
With four decimal places added, we have P(2.04 Z 3.04) 0.0189.
Two decimal places are what?To round a decimal value to two decimal places, use the hundredths place, which is the second place to the right of the decimal point.
Subtracting the area to the left of 1.25 from the area to the left of 2.15 will give us the standard normal area between 1.25 and 2.15.
The area to the left of 1.25 is 0.8944, and the area to the left of 2.15 is 0.9842, according to a conventional normal distribution table or calculator.
So, the standard normal area between 1.25 and 2.15 is:
P(1.25 < Z < 2.15) = 0.9842 - 0.8944 = 0.0898
Rounding to four decimal places, we get:
P(1.25 < Z < 2.15) ≈ 0.0898
We follow the same procedure as before to determine the standard normal region between 2.04 and 3.04:
P(2.04 < Z < 3.04) = P(Z < 3.04) - P(Z < 2.04)\
The area to the left of 2.04 is 0.9798, and the area to the left of 3.04 is 0.9987, according to a conventional normal distribution table or calculator.
So, the standard normal area between 2.04 and 3.04 is:
P(2.04 < Z < 3.04) = 0.9987 - 0.9798 = 0.0189
Rounding to four decimal places, we get:
P(2.04 < Z < 3.04) ≈ 0.0189
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Both descriptive statistics (mean, median, mode, and range) and probability (the likelihood that something will happen) can be useful in our academic, professional, and personal lives. • Determine which of the two (descriptive statistics or probability) you find to be the most useful in your life and explain why using two (2) specific examples.
Descriptive statistics are the most useful in life. Descriptive statistics provide information about a data set and can help to summarize and interpret data. Specifically, I find the mean and median to be the most useful.
What does Descriptive statistics mean?Descriptive statistics involves the use of measures such as the mean, median, mode, and range, as well as graphical representations of the data, such as histograms, box plots, and scatter plots.
The mean is the average of a set of data and is useful for summarizing and interpreting data. For example, when I am studying for a test, I often use the mean of my practice test scores to understand my overall performance.
The median is the middle value of a set of data and is useful for understanding the spread of the data. For example, when I am tracking my monthly expenses, I often use the median to understand how much I am spending each month. By taking the median of my monthly expenses, I can get an idea of which expenses are taking up the most of my budget.
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a) find the probability the chosen person is a woman
b) find the probability the chosen person favors pink or purple
c) if the chosen person favors turquoise, what is the probability this person is a man?
The probability that the person chosen is a woman is 0.51.
The probability that the person chosen favors pink or purple is 0.67.
The probability that a person that favors turquoise is a man is 0.66.
What are the probabilities?Probability is the odds that a random event would occur. The odds that the event occurs has a probability value that lies between 0 and 1. The more likely it is that the event would happen, the closer the probability value would be to 1.
The probability that the person chosen is a woman = number of women / total number of people = 152 / 300 = 0.51.
The probability that the person chosen favors pink or purple = (number of people who favor pink / total number of people) + (total number of people that favor purple / total number of people) = (50 /300) + (50 / 300) = 0.67.
The probability that a person that favors turquoise is a man = men who favor turquoise / total number of people who favor turquoise = 79/120 = 0.66
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How do you compute the sum of squared errors
Answer:
Relating SSE to Other Statistical Data
Variance = SSE/n, if you are calculating the variance of a full population.Variance = SSE/(n-1), if you are calculating the variance of a sample set of data.
please help me 60 points
Answer:
Matt would walk 8 miles in to hours.
Step-by-step explanation:
15 minutes is 1/4 of an hour, meaning it would be 1/8 of 2 hours.
1 mile times 8 = 8 miles
Hope that helps!
Which of the following conditions are sufficient to show that triangle ABC sim triangle QPR
Select all that apply.
A. m angle Q = 63
B. m angle R = 81
D. m angle P = 81
C. RP = 4.5
Answer:
C. RP = 4.5
Step-by-step explanation:
You want to know what condition is sufficient to show ∆ABC ~ ∆QPR, given three sides and 2 angles in ∆ABC, and 2 sides in ∆QPR.
SimilaritySimilarity can be shown if all three sides are proportional, or if two angles are congruent.
The offered answer choices only list one angle, so none of those will work. The answer choice that makes the third side of ∆QPR be in the same proportion as the corresponding side of ∆ABC is the condition of interest.
C. RP = 4.5
__
Additional comment
The side ratios in the two triangles are ...
AB : BC : CA = 10 : 9 : 6
QP : PR : RQ = 5 : PR : 3
For these ratios to be the same, PR must be half of BC, just as the other segments in ∆QPR are half their counterparts in ∆ABC.
find the slope of a line parallel to the line whose equation is 5x - 6y = 30. fully simplify your answer 
By answering the presented questiοn, we may cοnclude that Since a line equatiοn parallel tο this οne will have the same slοpe, the slοpe οf the parallel line is alsο 5/6.
What is equatiοn?When twο expressiοns are equal, a mathematical equatiοn is a statement stating that equality. Twο sides are jοined by the algebraic symbοl (=), and tοgether they make up an equatiοn. Fοr instance, the claim that "2x + 3 = 9" means that "2x plus 3" equals the number "9" is made in this argument. Finding the value(s) οf the variable(s) necessary fοr the equatiοn tο be true is the gοal οf sοlving equatiοns.
There are variοus types οf equatiοns, including regular and nοnlinear οnes with οne οr mοre elements. "x² + 2x - 3 = 0" is an equatiοn that raises the variable x tο the secοnd pοwer. Mathematical disciplines like algebra, calculus, and geοmetry all make use οf lines.
the given equatiοn:
[tex]$\begin{array}{c}{{5x-6y=30}}\\ {{-6y=-5x+30}}\\ {{y=(5/6)x-5}}\end{array}$[/tex]
Sο the slοpe οf the given line is 5/6.
Since a line parallel tο this οne will have the same slοpe, the slοpe οf the parallel line is alsο 5/6.
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Without an appointment, the average waiting time in minutes at the doctor's office has the probability density function f(t)=1/38, where 0≤t≤38
Step 1 of 2:
What is the probability that you will wait at least 26 minutes? Enter your answer as an exact expression or rounded to 3 decimal places.
Step 2 of 2:
What is the average waiting time?
The probability of waiting at least 26 minutes is 0.316. The average waiting time is 19 minutes.
Step 1:
The probability of waiting at least 26 minutes can be calculated by finding the area under the probability density function from 26 to 38:
P(waiting at least 26 minutes) = ∫26^38 (1/38) dt = [t/38] from 26 to 38
= (38/38) - (26/38) = 12/38 = 0.316
So the probability of waiting at least 26 minutes is 0.316 or approximately 0.316 rounded to 3 decimal places.
Step 2:
The average waiting time can be calculated by finding the expected value of the probability density function:
E(waiting time) = ∫0³⁸ t f(t) dt = ∫0³⁸ (t/38) dt
= [(t²)/(238)] from 0 to 38
= (38²)/(238) = 19
Therefore, the average waiting time is 19 minutes.
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Which of the following describes the transformation from Figure 1 to Figure 2?
On a coordinate plane, figure 1 has points (negative 2, 5), (negative 2, 4), (negative 3, 4), (negative 3, 2), (negative 5, 2), (negative 5, 5). Figure 2 has points (2, negative 5), (2, negative 4), (3, negative 4), (3, negative 2), (5, negative 2), (5, negative 5).
Initially, while maintaining the very same [tex]x-[/tex]coordinates, the negative reflect across the [tex]x-axis[/tex] modifies the signs of all locations' [tex]y-[/tex]coordinates.
Negative: Does it signify plus or minus?A negative value is one that always has a value lower than zero and is denoted by the minus (-) symbol. In a number line, negative values are displayed just left of zero.
What is the significance of both positive and negative values in math?If a number is higher than zero, it is considered positive. Or less zero numbers are referred to as negative numbers. If a number is bigger than that or equal to zero, it is not negative. If a number falls below or equal to zero, it is non-positive.
This transforms Figure [tex]1[/tex] into a new figure with points [tex](-2, -5), (-2, -4), (-3, -4), (-3, -2), (-5, -2), (-5, -5)[/tex].
Next, the [tex]180^{0}[/tex] rotation about the origin swaps the signs of both [tex]x[/tex] and [tex]y[/tex] coordinates of each point. This results in the final figure with points [tex](2, -5), (2, -4), (3, -4), (3, -2), (5, -2), (5, -5)[/tex].
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Parallelogram ABCD is a rhombus with measure EBC = 36. What is the measure of DAE?
picture below
Answer:
54°
Step-by-step explanation:
AB = BC = CD = AD (Because all sides of a rhombus are equal)
Let's consider the triangle DBC:
BC = DC => ∠DBC = 36°
The angle DCB is equal to:
180° - 36*2 = 180° - 72° = 108°
In a parallelogram, opposite angles are equal.
Then the angle DAB = DCB = 108°
Also, we know that the diagonals of a rhombus are the bisectors of the angles from which they come.
So, the angle DAE = EAB = 108° / 2 = 54°