Answers
Answer: 68
Step-by-step explanation:
Angles in a triangle add to [tex]180^{\circ}[/tex], meaning that [tex]m\angle TRS +m\angle TSR=136^{\circ}[/tex].
Furthermore, since [tex]\triangle TSR[/tex] is isosceles, [tex]m\angle TRS=m\angle TSR[/tex].
Therefore, [tex]m\angle TSR=68^{\circ}[/tex].
Related Questions
Find x and y -- if your answer is not a whole number, round to the tenths!
x =
y =
Answers
Answer: x = 10.57 and y = 15 degree
Step-by-step explanation:
Answer: x= 10 degrees
y= 15 degrees
Step-by-step explanation:
In 2012, the population of a city was 6.51 million. The exponential growth rate was 2.75% per year. a) Find the exponential growth function. b) Estimate the population of the city in 2018. c) When will the population of the city be 10 million? d) Find the doubling time.
Answers
The exponential growth function is P = 6.51 (1.0275)^t. The population of the city in 2018 will be 7.66 million. The population of the city will be 10 million in 15.82258467 years and the doubling time is 25.55035862 years
How to find the exponential growth function?The exponential growth function is of the form P = P₀(1+r)^t
where P₀ is the current population, r is the growth rate and t is the time
Given: P₀ = 6.51 million, r = 2.75% per year
a) The exponential growth function
P = 6.51 (1+0.0275)^t
P = 6.51 (1.0275)^t
b) The population of the city in 2018
t = 2018-2012 = 6 years
P = 6.51 (1.0275)^t
P = 6.51 (1.0275)⁶ = 7.66 million
c) When the population of the city will be 10 million
P = 6.51 (1.0275)^t
10 = 6.51 (1.0275)^t (Solve for t)
(1.0275)^t =10/6.51
log (1.0275)^t = log(10/6.51)
t × log (1.0275) = log(10/6.51)
t = [log(10/6.51)] / [log (1.0275)]
t = 15.82258467 years
d) The doubling time
P = 6.51 (1.0275)^t will become:
2 = 1 (1.0275)^t
1.0275^t = 2
log(1.0275)^t = log 2
t log(1.0275) = log 2
t = log 2 / log 1.0275
t = 25.55035862 years
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an anova procedure is used for data that were obtained from five sample groups each comprised of six observations. the degrees of freedom for the critical value of f are . a. 5 and 26 b. 4 and 29 c. 4 and 25 d. 4 and 30
Answers
The correct option 4 and 25; the degrees of freedom for the critical value of f.
Explain the term degrees of freedom?The number of separate bits of information required to construct a statistic is called the degrees of freedom, which is frequently denoted by the letters v or df. It is determined by subtracting the number of constraints from the sample size. The greatest number of logical manner independent variables is, values with the freedom to change—in the data sample is referred to as the degree of freedom.The essential value F's degrees of freedom are (k-1,n-k).
Four sample groups are provided to us, so,
k = 5.
Additionally, we know that each of the five groups has six observations, therefore
n = 5*6
n = 30
The crucial factor F can vary in freedom.
(k-1,n-k)
(5-1, 30 - 5)
(4,25).
Its degrees of freedom again for critical F value are as a result (4,25).
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Each problem describes the relationship between two variables. Use the equation that models the relationship to complete the table. Then plot the points from the table on the graph. Draw the line connecting the points to represent the equation on the coordinate plane.
1. Andre uses 2 scoops of lemonade mix for each batch of lemonade he makes. The equation that models the total scoops of lemonade mix Andre uses, s, for b batches is s=2 b.
Answers
The completed table and the graph of the proportional relationship are given by the image shown at the end of the answer.
What is the proportional relationship?The proportional relationship in this problem is defined as follows:
s=2 b.
The variables are defined as follows:
The output s is the number of lemonade mixes used.The input b is the number of batches of lemonade made.Then the graph of the proportional relationship is that of a linear function with these following features:
Slope of 2, hence when b increases by one, s increases by two.Intercept of zero, as when b = 0, s = 0.Then the numeric values that complete the table are calculated as follows:
b = 0: s = 2(0) = 0.b = 1: s = 2(1) = 2.b = 2: s = 2(2) = 4.b = 3: s = 2(3) = 6.More can be learned about proportional relationships at https://brainly.com/question/10424180
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solve this on graph paper
Answers
The graphs of the equations are drawn ad attached here.
What is the slope-intercept form of a line?The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.
The given equations are (i) y = x-4, (ii) y = 2x-4, (iii) y = 3x-4.
The equations are given in the slope-intercept form.
(i) The given equation is y = x-4.
the y-intercept of the equation is (0,-4).
Now, substitute y = 0 into the given equation:
0 = x - 4
x = 4
Hence, the line y = x-4 passes through points (0,-4) and (4,0).
Now, draw a line passing through the points (0,-4) and (4,0).
Using the same procedure, the graphs of the other two equations are also drawn.
Hence, the graphs of the equations are drawn ad attached here.
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In the diagram below, UV is parallel to RS. If UV is 12 less than UT, RT = 42,
and RS = 21, find the length of UT. Figures are not necessarily drawn to scale.
State your answer in simplest radical form, if necessary.
Answers
The length of UT if, The line UV || RS, UV is 12 less than UT, RT = 42, and RS = 21 is,24.
What are parallel lines?Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.
Given:
The line UV || RS,
UV is 12 less than UT,
RT = 42, and RS = 21,
Write the equation for the UV and UT,
UV = UT - 12
Calculate the value of UT as shown below,
UT / RT = UV / RS (For parallel lines, the ratio should be the same)
UT / 42 = (UT - 12) / 21
21 × UT / 42 = (UT - 12)
UT / 2 = (UT - 12)
UT = 2UT - 24
2UT - UT = 24
UT = 24
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The point (2, 90) represents the value that after 2 weeks, Paul's math average is a 90. The point (4, 50) represents the value that after 4 weeks, Paul's grade has dropped to a 50 because he doesn't do homework and doesn't know how to log into Quizlet. What equation represents the line of Paul's grade downfall?
Answers
The equation that represents the line of Paul's grade downfall is y = -20x + 130.
How to find the equation represents the line of Paul's grade downfall?To find the equation of the line that represents Paul's grade downfall, we need to use the two points given: (2, 90) and (4, 50).
We can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope of the line, we can use the formula: slope (m) = (y2 - y1)/(x2 - x1).
Plugging in the values from the two points we have:
m = (50 - 90)/(4 - 2) = -40/2 = -20.
y = mx+b [Using (x= 2, y = 90)]
90 =-20(2) + b
90 = -40
b = 130
Plugging these values into the slope-intercept form, we get:
y = -20x + 130.
Thus, the equation is y = -20x + 130
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( (-2)³)²
help me solve please
Answers
The answer is 64
If you need a breakdown I don't know how to help.
So, the order of operations requires you do the inside parentheses first. -2^3 is -8. Then, (-8)^2 means -8 • -8 = 64. (negative times negative is positive). Peace.
|-10-2| • 3(2x+7) -25+2y
x=2
y=3
Answers
Answer:
377 is answer
Step-by-step explanation:
12.33-25 +6
396-25+6
377
A machine is designed to dispense 20 mg of d-desoxyephedrine into each capsule of a medicine. 13
pills are tested, and it's found that they have a mean drug content of 20.2 mg, with a standard
deviation of 2.4 mg. To a 1% level of significance, can it be asserted that the standard deviation of
the process (in general) is over 2 mg?
[Assume that the drug contents of all the pills are normally distributed.]
Answers
There is no enough evidence to assert that the standard deviation of the process (in general) is over 2 mg
How to determine if it can be asserted that the standard deviation of the process (in general) is over 2 mg?To determine whether the standard deviation of the process (in general) is over 2 mg to a 1% level of significance, you can perform a hypothesis test.
In this case, the null hypothesis is that the standard deviation of the process is equal to or less than 2 mg, and the alternative hypothesis is that the standard deviation of the process is greater than 2 mg.
To perform the hypothesis test, you can first calculate the test statistic. That is:
test statistic = (sample mean - hypothesized mean) / (standard error of the mean)
test statistic = (20.2 - 20) / (2.4 / √(13))
= 0.2 / 0.67
= 0.3
Next, you can look up the critical value for the test statistic in a table of critical values for a one-tailed test with a 1% level of significance and 12 degrees of freedom (df = 13 - 1).
The critical value for the test statistic is 2.6. Since the test statistic (0.3) is less than the critical value (2.6), you cannot reject the null hypothesis.
This means that you do not have enough evidence to assert that the standard deviation of the process (in general) is over 2 mg to a 1% level of significance.
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A pilot flew a jet from City A to City B, a distance of 2400 mi. On the return trip, the average speed was 20% faster than the outbound speed. The round-trip took 5 h 30 min. What was the speed from City A to City B?
Answers
The speed from City A to City B is 873.33 mi/h.
What is the speed, distance and time?
That is speed = distance ÷ time. Or to put it another way, distance divided by speed will give you the time. Provided you know two of the inputs you can work out the third.
Let's call the speed from City A to City B x. The speed on the return trip was 1.2x. The total distance traveled was 2400 + 2400 = 4800 mi. The total time taken was 330 minutes, which is 330/60 = 5.5 hours. The average speed is the total distance traveled divided by the total time taken, so:
4800 mi / 5.5 h = 873.33 mi/h
The total speed for both legs of the trip is 873.33 + 873.33 = 1746.66 mi/h
The speed for just one leg of the trip is half of the total speed, so the speed from City A to City B is 1746.66/2 = 873.33 mi/h.
Hence, the speed from City A to City B is 873.33 mi/h.
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the dimension of an eigenspace of a symmetric matrix is sometimes less than the multiplicity of the corresponding eigenvalue.
a. true
b. false
Answers
True, The dimension of the eigenspace for each eigenvalue equals the multiplicity.
What is eigen value?Eigenvalues are a unique set of scalar values connected to a set of linear equations that are most likely seen in matrix equations. The characteristic roots are another name for the eigenvectors. It is a non-zero vector that, after applying linear transformations, can only be altered by its scalar factor.
What is an Eigenspace?When a linear transformation is done to an eigenvector, a set of eigenvectors called an eigenspace is created for each eigenvalue. In many cases, the linear transformation uses a square matrix (a matrix that has the same number of columns as it does rows).
yes, it is true that the dimension of an eigenspace of a symmetric matrix is sometimes less than the multiplicity of the corresponding eigenvalue.
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A company produces shotgun shells in batches of 350. A sample of 5 is tested from each batch, and if more than one defect is found, the entire batch is tested. (Round your answers to five decimal places.) (a) If 1% of the shells are actually defective and we assume independence, what is the probability of 0 defective shells in the sample?
(b) If 1% of the shells are actually defective and we assume independence, what is the probability of 1 defective shell in the sample?
(c) If 1% of the shells are actually defective and we assume independence, what is the probability of more than 1 defective shell in the sample?
Answers
a. The probability of defective shells from the given samples are:
a. Probability of zero defective shells of samples is equal to 0.9510.
b. Probability of one defective shells of samples is equal to 0.04803
c. Probability of more than 1 defective shells of samples is equal to 0.00107.
As given in the question,
Total number of batches = 350
Sample size used to test for each batch 'n' = 5
Actual defective shells (success) 'p' = 1%
= 0.01
Actual non-defective shells ' 1 - p ' = 1 - 0.01
= 0.99
a. Probability of zero defective shells from the given samples is
= ⁵C₀ × ( 0.01 )⁰ × (0.99)⁵⁻⁰
= [ (5!)/(5-0)!0! ] × 1 × ( 0.99)⁵
= 0.9510
b. Probability of 1 defective shells from the given samples is
= ⁵C₁ × ( 0.01 )¹ × (0.99)⁵⁻¹
= [ (5!)/(5-1)!1! ] × 0.01 × ( 0.99)⁴
= 5 × 0.01 × 0.9606
=0.04803
c. Probability of more than 1 defective shells from the given samples is
= P(2) + P(3) + P(4) + P(5)
= ⁵C₂ × ( 0.01 )²× (0.99)⁵⁻² + ⁵C₃ × ( 0.01 )³ × (0.99)⁵⁻³ + ⁵C₄× ( 0.01 )⁴ × (0.99)⁵⁻⁴+ ⁵C₅× ( 0.01 )⁵× (0.99)⁵⁻⁵
= 0.00097 + 0.000098 +0.000000044 +0.0000000001
=0.00107
Therefore, the probability of following conditions are as follow:
a. Probability of zero defective shells of samples is equal to 0.9510.
b. Probability of one defective shells of samples is equal to 0.04803
c. Probability of more than 1 defective shells of samples is equal to 0.00107.
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What is the difference in the things shown on the photo
Answers
option c) 4x⁴ -2x³ -2x² +3x -10
On subtracting we will get
(3x²₋ 2x + 4x⁴) - (5x²+2x³-5x+10)
= 3x²- 5x²- 2x -2x³+ 4x⁴+ 5x -10
= -2x² + 3x -2x³ + 4x⁴- 10
= 4x⁴ -2x³- 2x² + 3x - 10
The given sum belongs to quadratic equation
Quadratic equation definition:
When a, b, and c are real-world coefficients, a second-order equation is said to be quadratic if it is represented as ax²+ bx + c = 0.
The Characteristics of Quadratic Equations' Roots
The discriminant of the quadratic equation ax2+bx+c=0 is (b2-4ac), which determines whether or not the equation has real roots.
The quadratic equation ax2+ bx + c= 0 hence
If b2-4ac >0, two different real roots
If b2-4ac= 0, there are two equal real roots.
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Drag each tile to the correct box.
Arrange the numbers as they appear from left to right on a horizontal number line.
Answers
The numbers as they appear from left to right on a horizontal number line is Horizontal number line.
This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically. As we move towards the right side of a horizontal number line, the numbers increase; as we move towards the left, the numbers decrease.
What's the equation of a horizontal line?
Horizontal lines have a slope of 0. Thus, in the slope-intercept equation y = mx + b, m = 0. The equation becomes y = b, where b is the y-coordinate of the y-intercept.
-2.76
-2.57
-2.5
-1.85
-1.58
2.5
2.85
On a number line, we have this horizontal line, meaning it moves left and right, and zero is placed in the middle.
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Part A
In the story "Life on the Sea," how does the captain mostly feel when he is on the sea?
Responses
miserable
miserable
proud
proud
guilty
guilty
confident
confident
Question 2
Part B
Which excerpts from the story best support the answer in Part A?
Select the two correct answers.
Responses
"He gave his job two weeks’ notice and was back on the sea right away."
"The calmness that he felt when the water was placid wasn’t like any stillness that he experienced on land."
"He had spent most of his life on the sea; he knew the habits and nuances of the water like it was his closest friend."
"The storm roiled on the horizon as rough waves rocked the helm of the boat."
"
Answers
Confident, In contrast to any stillness he had ever felt on land, he felt a sense of calm when the water was calm. and "He gave two weeks' notice at his job and immediately sailed off again."
What is a fishing vessel?fishing vessel Place on list Share. fishing boat definitions. a fishing vessel with a well for preserving the catch. A boat and a fishing smack are potential candidates. both sorts of draggers and trawlers. Fishing ships or boats are used to remove aquatic creatures from bodies of water.
A trawl is a type of fishing net that is currently dragged along or through the ocean floor at specific depths. Since trawlers are frequently bigger than fishing boats and struggle to maneuver when necessary, they are given special qualities in ror.
Thus, options A and A, B are correct.
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Answer:
Part a: confident
Part b: "The calmness that he felt when the water was placid wasn’t like any stillness that he experienced on land." and "He had spent most of his life on the sea; he knew the habits and nuances of the water like it was his closest friend."
Step-by-step explanation: I took the test :)
d(x) = 3x²-x
Find d(-4).
Answers
Answer:
52
Step-by-step explanation:
Substitute the value -4 into the expression and simplify:
3(-4)^2 - (-4)
3(16) + 4
48 + 4
52
Solve the following and find Q R
Answers
Answer:
QR = 49
Step-by-step explanation:
QR = QP
3x + 22 = 10x - 41
x = 9
10(9) - 41
= 49
Please help me with this.
Answers
1. Parallel
2. Perpendicular
3. Skew
4. Parallel
5. Perpendicular
6. ↔QW, ↔SW, ↔TZ
7. ↔YZ, ↔ST
8. ↔RQ, ↔QW, ↔ST, ↔TZ
9. Plane TQW, plane SRX, plane ZWX
10. Plane WXY
11. Corresponding
12. Alternate exterior
13. Alternate interior
14. Consecutive interior
15. Alternate exterior
16. Alternate interior
17. ↔OL ║↔VN
18. ↔VN ⊥ ↔RT
19. No; the markings do not indicate that the lines are parallel
y=3x-8- here is it’s the right answer
Answers
Given is the equation of a line with slope of m = 3 and [y] intercept of c = -8.
What is the general equation of a Straight line?
The general equation of a straight line is -
y = mx + c[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.Other possible equations of lines are -
(y - y₁) = m(x - x₁) {Point - slope form}(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}x/a + y/b = 1 {intercept form}x cos(β) + y sin(β) = L {Normal form}We have the equation of line as -
y = 3x - 8
The given is the equation of a line with slope of m = 3 and [y] intercept of c = -8.
Therefore, given is the equation of a line with slope of m = 3 and [y] intercept of c = -8.
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When you calculate In (10), you would be finding the value of which of the following expressions?
O log (10)
O log₁0(e)
O log(10)
O 10 In(e)
Answers
Answer: Given the log function ln(100), this can therefore be written as loge(100)
Step-by-step explanation: Logarithmic functions
Logarithmic functions are inverse of exponential functions. There are different ways to write log function;
Some are written as a exponent base
Some to the base of 10
Loga is also written as log10(a)
lna is written as loge(a)
Given the log function ln(100), this can therefore be written as loge(100)
Answer: C log(10).
Step-by-step explanation: When you calculate In (10), you would be finding the value of log(10).
In mathematics, the logarithm function is used to express the exponent to which a base must be raised in order to produce a given number. The base of the logarithm is usually denoted by "b" and the number whose logarithm is being taken is denoted by "x". The logarithm of x to base b is denoted as logb(x).
For example, the logarithm of 10 to base 10 is denoted as log10(10), which is equal to 1. The logarithm of 100 to base 10 is denoted as log10(100), which is equal to 2.
In general, the logarithm of x to base b can be calculated as follows:
logb(x) = y
This equation states that b raised to the power of y is equal to x.
The natural logarithm, denoted as In, is a special case of the logarithm function where the base is the mathematical constant e (approximately 2.718). The natural logarithm of x, denoted as In(x), is equal to the logarithm of x to base e.
Therefore, when you calculate In (10), you are finding the value of the natural logarithm of 10, which is the logarithm of 10 to base e.
Option A log (10) is incorrect because it is missing the base of the logarithm (e).
Option B log₁0(e) is incorrect because it is the logarithm of e to base 10, which is not the same as the natural logarithm of 10.
Option D 10 In(e) is incorrect because it is the value of 10 raised to the power of the natural logarithm of e, which is not the same as the natural logarithm of 10.
Option C log(10) is correct because it is the natural logarithm of 10, which is the value we are trying to find. Therefore, the correct answer is C log(10).
Which term is −20,155,392 for the following sequence, assuming that the pattern continues?
2, −12, 72, −432, ...
a
a9
b
a10
c
a11
d
a12
Answers
The term that is the −20,155,392 in the sequence is a₁₀.
What is sequence?A sequence is defined as an arrangement of numbers in a particular order.
The given sequence is 2, -12, 72, -432
a = first term
n = number of terms
r = common ratio
r = -12 / 2 = 72 / -12 = -432 / 72 = -6
a = 2
Therefore, nth term = arⁿ⁻¹
−20,155,392 = 2 × -6ⁿ⁻¹
−20,155,392 / 2 = -6ⁿ⁻¹
- 10077696 = -6ⁿ⁻¹
6ⁿ⁻¹ = 10077696
6ⁿ⁻¹ = 6⁹
n - 1 = 9
n = 9 + 1
n = 10
Hence, it's the 10th term.
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solve for x:ax=bx+c , a≠b
Answers
The solution for x in the equation ax = bx + c is x = c/(a - b)
How to determine the solution for x in the equationFrom the question, we have the following parameters that can be used in our computation:
ax=bx+c
Also, from the question, we have the following variable to solve
Variable = x
Rewrite the given equation as
ax = bx + c
Using the above as a guide, we have the following:
Subtract bx from both sides of the equation
So, we have the following representation
-bx + ax = bx + c - bx
Evaluate the like terms
ax - bx = c
So, we have
x(a - b) = c
Divide by a - b
x = c/(a - b)
Hence, the solution is x = c/(a - b)
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What is the perimeter of WXYZ?
I need the answer please help me
Answers
Answer: 48
Step-by-step explanation:
Using isosceles triangle [tex]XWZ[/tex], we know that [tex]WZ=11[/tex].
Using equilateral triangle [tex]XYZ[/tex], we know that [tex]YZ=XY=11[/tex].
So, the perimeter is [tex]WX+WZ+ZY+XY=11+11+11+15=48[/tex].
The Riddler earns $18 per hour at the Gotham Police Station. He regularly works 40 hours per week. He is paid time-and-a-half for each hour of overtime work. Last week he worked 47 hours. What was his gross pay for the week?
Answers
The gross pay for Riddler for working 47 hours will be $783.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the Riddler earns $18 per hour at the Gotham Police Station. He regularly works 40 hours per week. He is paid time-and-a-half for each hour of overtime work. Last week he worked 47 hours.
The overtime cost = 1/2 x 18
The overtime cost = $9
The gross pay will be calculated as,
Gross pay = ( 40 x 18 ) + ( 7 x 9 )
Gross pay = 720 + 63
Gross pay = $783
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For those who are on Plato and have done this tutorial,please tell me the answer to this question. And it can't be equilibrium,because I tried that and it didn't work.
Answers
By using the concept of demand and supply, it can be concluded that-
The price at which the quantity demanded is equal to the quantity supplied is the equilibrium price.
What is demand and supply?
Demand is the amount of good which the customer wants to purchase during a particular time at a particular price.
Supply is the total amount of goods made available to the customer at a particular time
Equilibrium price is the price at which the quantity demanded is equal to the quantity supplied
So the price at which the quantity demanded is equal to the quantity supplied is the equilibrium price.
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You roll two fair 6-sided dice with sides labeled 1, 2, 3, 4, 5, 6. What is the probability of rolling a sum that is at most 7
Answers
The probability of rolling a sum that is at most 7 = 1/6
What is probability and example?
Probability = the number of ways of achieving success. the total number of possible outcomes.For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail).P(heads) = ½ .sample space (S) = 36
The probability of rolling a sum that is at most 7
No of sample space = { (1,6) ,(2,5) ,(3,4), (4,3),(5,2),(6,1)}
n(s)/ total sample space = 6/36
= 1/6
Therefore, he probability of rolling a sum that is at most 7 = 1/6
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The C major key, starting with the middle C, consists of seven notes (white keys on the piano) with the following frequencies. Note C D E F G A B Frequency(Hz) 261.6 293.7 329.6 349.2 392.0 440.0 493.9 Determine the ratio of the note B to middle C
Answers
Answer:
Step-by-step explanation:
To determine the ratio of the note B to middle C, we can divide the frequency of B by the frequency of C. Using the information provided, the frequency of B is 493.9 Hz and the frequency of C is 261.6 Hz. The ratio of B to C is therefore 493.9 / 261.6, which is approximately equal to 1.89. This means that the note B is approximately 1.89 times higher in pitch than the note C.
What is the solution to this system of equations?
8a−4b=20
5a−8b=62
a=
b=
Answers
Answer:
Hello there, I think this is the answer
a = - 2
b = - 9
Consider the following general triangle.
C = 60.0°, c = 151 m, b = 181 m
(a)
Determine the number of solutions.
(b)
Solve the triangle, if possible, using the labels as shown in the figure below. (Round lengths in m to three significant digits and angles to the nearest tenth of a degree. If there is no solution, enter NO SOLUTION in all unused answer blanks. If there is more than one solution, enter your answers as a comma-separated list.)
A °=
B °=
a=
Answers
To solve this problem, we can use the Law of Cosines. The Law of Cosines states that for a triangle with sides a, b, and c and the angle C opposite side c, the following equation holds:
c^2 = a^2 + b^2 - 2abcos(C)
In this problem, we are given the measure of angle C and the lengths of sides b and c. We can use this information to find the length of side a and the measures of angles A and B.
First, we can use the Law of Cosines to find the length of side a. Plugging in the given values, we get:
a^2 = c^2 - b^2 + 2bc cos(C)
Substituting in the given values, we get:
a^2 = 151^2 - 181^2 + 2 * 151 * 181 * cos(60.0°)
Solving this equation gives us a = 143 m.
Now that we have the length of side a, we can use the Law of Sines to find the measures of angles A and B. The Law of Sines states that for a triangle with sides a, b, and c and angles A, B, and C opposite these sides, the following equation holds:
a/sin(A) = b/sin(B) = c/sin(C)
We are given the lengths of sides a and b and the measure of angle C. We can use this information to find the measures of angles A and B.
First, we can use the Law of Sines to find the measure of angle A. Plugging in the given values, we get:
a/sin(A) = b/sin(B)
Solving for sin(A), we get:
sin(A) = a * sin(B) / b
Substituting in the given values, we get:
sin(A) = 143 m * sin(B) / 181 m
To find the measure of angle A, we can use the inverse sine function (sin^-1). This gives us:
A = sin^-1(sin(A))
= sin^-1(143 m * sin(B) / 181 m)
Similarly, we can use the Law of Sines to find the measure of angle B:
B = sin^-1(143 m * sin(A) / 181 m)
Since we have two unknowns (A and B) and two equations, there is a unique solution for this triangle.
Therefore, the number of solutions is 1, and the measures of angles A and B are A = 38.5° and B = 101.5°. The length of side a is 143 m.