PLEASE HELP EASY A fair number cube is rolled twice. Determine whether each event is more or less likely than rolling the same number both times.
Select the correct button in the table to show the likelihood of each event.
Answers
Event A and Event B are less likely than rolling the same number both times
What is probability?
The chance of an event can be calculated using the probability formula by simply dividing the favorable number of possibilities by the total number of outcomes. The likelihood of an event occurring can be anything between 0 and 1, as the favorable number of outcomes can never exceed the total number of outcomes.
The probability of rolling a 1 on the first roll is 1/6, and the probability of rolling a 2 on the second roll is also 1/6. Therefore, the probability of rolling a 1 on the first roll and a 2 on the second roll is (1/6) x (1/6) = 1/36.
The probability of rolling an even number on the first roll is 3/6 (or 1/2), and the probability of rolling an odd number on the second roll is also 3/6 (or 1/2). Therefore, the probability of rolling an even number on the first roll and an odd number on the second roll is (1/2) x (1/2) = 1/4.
This event is more likely than rolling the same number both times, because there are nine possible outcomes that result in this event (2-1, 2-3, 2-5, 4-1, 4-3, 4-5, 6-1, 6-3, 6-5), while there are only six possible outcomes that result in rolling the same number both times.
Hence, Event A and Event B are less likely than rolling the same number both times
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Related Questions
An island is located 48 miles N23°38'W of a city. A
freighter in distress radios its position as N11°26'E of the
island and N12° 16'W of the city. How far is the freighter
from the city?
Answers
The freighter is approximately 164.33 miles from the city.
How to determine how far is the freighter from the city?We can use the Law of Cosines to solve this problem. Let's label the distances as follows:
d: distance between the city and the freighter
x: distance between the city and the island
y: distance between the island and the freighter
First, we need to find x using the given coordinates:
N23°38'W is equivalent to S23°38'E, so we have:
cos(23°38') = x/48
x = 48cos(23°38') ≈ 42.67 miles
Next, we can use the coordinates of the freighter to find y:
N11°26'E is equivalent to E11°26'N, and N12°16'W is equivalent to S12°16'E. This means that the angle between the island and the freighter is:
23°38' + 11°26' + 12°16' = 47°20'
cos(47°20') = y/d
We can rearrange this equation to solve for y:
y = dcos(47°20')
Now we can use the Law of Cosines to solve for d:
d² = x² + y² - 2xy cos(90° - 47°20')
d² = 42.67² + (d cos(47°20'))² - 2(42.67)(d cos(47°20')) sin(47°20')
d² = 1822.44 + d² cos²(47°20') - 2(42.67)(d cos(47°20')) sin(47°20')
d² - d² cos²(47°20') = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')
d² (1 - cos²(47°20')) = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')
d² sin²(47°20') = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')
d² = (1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')) / sin²(47°20')
d ≈ 164.33 miles
Therefore, the freighter is approximately 164.33 miles from the city.
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Erythropoietin (EPO) is a banned drug used by athletes to increase the oxygen-carrying capacity of their blood. New tests for EPO were first introduced prior to the 2000 Olympic Games held in Sydney, Australia. Chance (Spring 2004) reported that of a sample of 830 world-class athletes, 159 did not compete in the 1999 World Championships (a year prior to the new EPO test). Similarly, 133 of 82:5 potential athletes did not compete in the 2000 Olympic Games. Was the new test effective in deterring an athlete's participation in the 2000 Olympics? If so, then the proportion of nonparticipating athletes in 2000 will be greater than the proportion of nonparticipating athletes in 1999, Use a 98% confidence interval to compare the two proportions and make the proper conclusion.
Answers
Answer:
Step-by-step
The null and the alternative hypothesis can be define as follows,
Null Hypothesis; There is no significance difference between the proportions of non participating athletes in 1999 and 2000
\(H_0:(p_1-p_2)\neq 0\)
Alternative Hypothesis: The proportion of non participating athletes in 2000 will be more than the proportion of non participating athletes in 1999
\(H_1:(p_1-p_2)<0\)
The proportion of nonparticipating athletes in 1999 is given by
\(\hat p_1 = \frac{x_1}{n_1} \\\\=\frac{159}{830} =0.1916\)
The proportion of nonparticipating athletes in 2000 is given by
\(\hat p_2 =\frac{x_2}{n_1} \\\\=\frac{133}{825} =0.1612\)
The pooled proportion can be calculated using the following formula
\(\hat p = \frac{x_1+x_2}{n_1+n_2} \\\\=\frac{159+133}{830+825} =0.1764\)
under the null hypothesis, the test statistics can be calculated as follows
\(Z=\frac{\hat p_1 - \hat p_2}{\sqrt{\hat p \hat q(\frac{1}{n_1}+\frac{1}{n_2} ) } }\)
\(=\frac{0.1916-0.1612}{\sqrt{(0.1764)(0.8236)(\frac{1}{830} +\frac{1}{825} )} } \\\\=1.6257\)
Determine the P-value using the following formula
P-value = Normdist(1.6257)
=0.947993
Here, it can be observed that the P-value is greater than the level of the significance,
Hence, the null hypothesis fails to be rejected
Therefore it can be concluded that there is insufficient evidence to support that the proportions of non participating athletes in 2000 will be more than the proportions of non participating athletes in 1999
Without graphing, classify each system
independent, dependent, or inconsistent.
3y + 2x= 12
36 - 9y = -6x
Answers
Answer:
The solution to the system of equations be:
\(y=4,\:x=0\)
As the consistent system of equations has only one solution, it is independent.
Step-by-step explanation:
Given the system of equations
\(3y + 2x= 12\)
\(36 - 9y = -6x\)
solving the system of equations
\(\begin{bmatrix}3y+2x=12\\ 36-9y=-6x\end{bmatrix}\)
Arrange equation variables for elimination
\(\begin{bmatrix}3y+2x=12\\ -9y+6x=-36\end{bmatrix}\)
\(\mathrm{Multiply\:}3y+2x=12\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:9y+6x=36\)
\(\begin{bmatrix}9y+6x=36\\ -9y+6x=-36\end{bmatrix}\)
so
\(-9y+6x=-36\)
\(+\)
\(\underline{9y+6x=36}\)
\(12x=0\)
\(\begin{bmatrix}9y+6x=36\\ 12x=0\end{bmatrix}\)
solve 12x=0 for x
\(12x=0\)
Divide both sides by 12
\(\frac{12x}{12}=\frac{0}{12}\)
\(x=0\)
\(\mathrm{For\:}9y+6x=36\mathrm{\:plug\:in\:}x=0\)
\(9y+6\cdot \:0=36\)
\(9y=36\)
Divide both sides by 9
\(\frac{9y}{9}=\frac{36}{9}\)
\(y=4\)
Thus, the solution to the system of equations be:
\(y=4,\:x=0\)
As the consistent system of equations has only one solution, it is independent.
What is the value of csc 47° to the nearest thousandth?
Answers
Answer: 1.367
Step-by-step explanation:
csc47° = 1.3673 ≈ 1.367
The value of cosec 47° is 1.367.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
cosec 47°
The value of cosec 47°.
= 1.367334
Rounding to the nearest thousandth.
= 1.367
Thus,
The value of cosec 47° is 1.367.
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State the inequalities that satisfy the shaded region.
Answers
Answer:
Step-by-step explanation:
\(\Bigg\{ \begin{array}{ccc}2x-y+1&>&0\\x^2+2x-y-15&\leq &0\\\end {array} \right.\)
Hello, happy Friday, I am just here with some geometry questions.
Please only answer this if you know the answer. If you have a comment, please add it to the comment box. Only answer the question if you can explain your answer and why you think it is accurate. Thanks, good luck!
Please explain how you got it.
Answers
Answer:
\(x=4\)
Step-by-step explanation:
By the Triangle Proportionality Theorem:
\(\displaystyle \frac{x}{12}=\frac{x+1}{15}\)
By cross-multiplication:
\(\displaystyle 12(x+1)=15(x)\)
Distribute:
\(12x+12=15x\)
Subtract 12x from both sides:
\(12=3x\)
Hence:
\(x=4\)
Answer:
4
Step-by-step explanation:
The first thing you should notice is that the triangles (the smaller one and the larger one) are similar due to angle-angle similarity (the top angle equals itself, and because the bases are parallel lines cut by a transversal, the base angle of the bigger triangle is equal to the corresponding base of the smaller triangle.
Similar triangles' corresponding sides have equal ratios to one another. That means we can set up an equation: side of smaller triangle ÷ corresponding side of larger triangle = other side of smaller triangle ÷ corresponding side of larger triangle. We plug the values given to us and can change this equation to:\(\frac{x}{x + 12} = \frac{x + 1}{x + 16}\) **
We now multiply both sides of the above equation by \((x + 12)(x + 16)\) to get: \(x(x + 16) = (x + 1)(x + 12)\)
\(x^{2} + 16x = x^{2} + 13x + 12\)
\(3x = 12\)
\(x = 4\)
That means our answer, for the value of x, is 4
** Make sure you don't say \(\frac{x}{12} = \frac{x + 1}{15}\), because those aren't the sides of the larger square.
What is the range of this set of test scores?
My Science Test Scores:
82, 85, 87, 68, 74, 90, 92, 78, 89, 95, 94, 94
Science Test Scores
See
Leaf
6
1
48
3
2579
24.45
Xay 61 868
Answers
Answer:
range = 27
Step-by-step explanation:
the range is the difference between the largest and smallest values in the data set.
largest = 95 , smallest = 68
range = 95 - 68 = 27
Answer:
46
Step-by-step explanation:
PLZ HELP
1
9 in.
ALGEBRA
5 in.
15 in.
What is the volume of the shoebox shown above in cubic
inches (in.3)?
29
75
675
510
Answers
Answer:
675 in³
Step-by-step explanation:
The volume (V) of a cuboid is calculated as
V = lbh ( lis length, b is breadth and h the height )
Here l = 15, b = 5 and h = 9 , then
V = 15 × 5 × 9 = 675 in³
Which is equivalent to 5 x (7 x 4)
35
(5 x 7) x 4
5 x (4 x 4)
5 + (7 + 4)
Answers
Answer:
The answer is (5*7)*4 because they equal the same answer which is 140, u welcome
Answer:
(5x7) x 4.
Step-by-step explanation:
Both are equal to 140
36 slices from 4 cakes = slices per cake
Answers
Answer:
9 slices per cake
36 divided by 4 = 9
Step-by-step explanation:
Answer:
9 slices of cake per each cake
What is the value of S4 for
0 554
O
64
O
(J1
14
O 516
05/0
O
56
n-1
24 (1)
n=1
?
Answers
Answer: It's not entirely clear what is being asked for in the given question, as it is not clear what the numbers represent or what operation is being performed. If you could provide more information or context, I would be happy to try and help you.
Step-by-step explanation:
Every member of a population is assigned a label. A computer's random number generator selects 10 members of the population to be in the sample. This is an example of a
A. random sample
B. self-selecting sample
C. systematic sample
Answers
Answer:
A. Random sample.
Explanation:
This is an example of a random sample because each member of the population has an equal chance of being selected by the computer's random number generator, and the sample of 10 members is selected without any bias or preconceived notions about the population. This type of sampling technique is important in ensuring that the sample is representative of the population and that the results obtained from the sample can be generalized to the larger population.
If R is (-4, 7) and S is (-2, 12), what is the component form of the vector R.S?
(8,84)
(2,5)
(-6, 19)
(-3,9.5)
Answers
Answer:
(2, 5)
Step-by-step explanation:
Given:
R = (-4, 7)S = (-2, 12)To find the components of \(\overrightarrow{RS}\) we need to go from R to O and then O to S. Remember that \(\overrightarrow{RO}\) is the negative of \(\overrightarrow{OR}\). Therefore:
\(\begin{aligned} \displaystyle \overrightarrow{RS} & =\overrightarrow{RO}+\overrightarrow{OS}\\& = \overrightarrow{OS}-\overrightarrow{OR}\\& =\binom{-2}{12}-\binom{-4}{7}\\& =\binom{2}{5}\end{aligned}\)
Therefore, the component form (x, y) of the vector \(\overrightarrow{RS}\) is (2, 5)
What is 4+5 devices by two
Answers
The equation can be written as:
4 + 5 / 2
Remember to follow PEMDAS.
4 + 5 / 2
4 + 2.5
6.5
Best of Luck!
Answer:
If you mean whats 4+5/2 the answer is 6.5 because PEMDAS says to Divide first . So 4+(5/2). 5/2 is 2.5. so 4+(2.5) which equals 6.5
The analysis of total variability into between-treatments and within-treatments variability is the same for a repeated-measures ANOVA and an independent-measures ANOVA.TrueFalse
Answers
The given statement ,the analysis of total variability into between-treatments and within-treatments variability is the same for a repeated-measures ANOVA and an independent-measure ANOVA is true.
The first stage of the repeated-measures ANOVA is identical to the independent-measures analysis and splits the overall variability into two components: between-treatments and within-treatments
Measurements that are repeated ANOVA is the extension of the dependent t-test and is the equivalent of one-way ANOVA for related, rather than independent, groups.
A repeated measures ANOVA is often referred to as a within-subjects ANOVA or ANOVA for correlated samples. The term "responsibility" refers to the act of determining whether or not a person is responsible for his or her own actions.
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In a middle school of 80 students, 42 girls and 38 boys. What is the probability
that if two students were randomly chosen, the first is a boy and then a girl
sequentially?
Answers
Answer:
dont have idea
Step-by-step explanation:
have not studied that topic
Evaluate -5a if a = -4
a: 20
b: -20
c: -9
d: 9
Answers
Answer:
The answer is A 20!
Step-by-step explanation:
Hope This Helps
Have A Great Day
You can buy five cans for green beans at the village market for $2.20 you can buy 10 of the same cans of beans at Sam’s Club for $5.30 which place is better
Answers
Answer:
The village market is better than Sam's Club
Step-by-step explanation:
If you buy 5 more cans of green beans at the village, it will cost $4.40 in total. Therefore if you go buy the beans at Sam's club, the village one will be cheaper.
3 1/8 divided by (x - 4 7/28) = 17/18 + 1 5/6
(Key on how to write the mixed numbers: Three is a whole number and then the fraction is 1/8, 4 is the whole number and 7/28 is the fraction, 1 is the whole number and 5/6 is the fraction)
Please provide the work and the answer! :)
Answers
x = 301/56
Algebraic expressionsAlgebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.
Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.
For example, d + d = 2d
This is an example of an algebraic expression
Given the algebraic expression,
\(3\frac{1}{8} \div (x - 4 \frac{7}{28} ) = \frac{17}{18} + 1 \frac{5}{6} \)
Step 1:
Simplify the expression by converting the mixed numbers into improper fractions:
25/8 ÷ ( x - 119/28) = 17/18 + 11/6
Step 2: Simplify the right side of the equation
25/8 ÷( x - 119/28) = 17/18 + 33/18
25/8 ÷( x - 119/28) = 50/18
Step 3: Multiply both sides of the equation by (x - 119/28)
25/8 = 50/18 × (x - 119/28)
Step 4: Multiply both sides of the equation by (18/50)
25/8 × (18/50) = (x - 119/28)
Step 5: Simplify the left side of the equation
9/8 = (x - 119/28)
Step 6: Add 119/28 to both sides of the equation
9/8 + 119/28 = x
Step 7: Calculate the value of x:
x = 9/8 + 119/28
= 63/56 + 238/56
= 301/56
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The length of a rectangle is 10, and the width is x - 2. If the area of the rectangle is 80sq cm, find
the dimensions.
Answers
Answer:
Length = 10 cm
Width = 10-2 = 8 cm
Step-by-step explanation:
Area formula (L)(W)
80 = 10(x-2)
80 = 10x - 20
Add 20 to both side
100 = 10x
x= 10
Length = 10 cm
Width = 10-2 = 8 cm
PLEASE HURRY TAKING A TEST RN
Type the correct answer in each box.
An image of lines p and q parallel to each other. Lines m and n are not parallel to each other. Line m, p form an angle of one hundred two degrees and an angle marked y. Lines n, q form an angle marked x and an angle of one hundred fifteen degrees.Parallel lines p and q are cut by two non-parallel lines, m and n, as shown in the figure.
The value of x is
degrees, and the value of y is
degrees.
Answers
The value of angle x and angle y is determined as 78⁰ and 115⁰ respectively.
What is the value of angle x and angle y?The value of angle x and angle y is calculated by applying principle of angles formed by parallel lines as follows;
The value of angle adjacent x = 102⁰
The value of angle x is calculated as;
x = 180 - 102 ( sum of angles on a straight line)
x = 78⁰
The value of angle y is calculated as follows;
y = 115⁰ (corresponding angles are equal)
Thus, the value of angle x and angle y is determined as 78⁰ and 115⁰ respectively.
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Please help me with this problem
Answers
Answer:
1516
Step-by-step explanation:
hope can help you
2000x 2%=40
9000x 5%= 450
(30000-9000-2000) x 5.4% = 1026
total tas 40+450+1026=
Determine if the two triangles are similar, if so write a similarity statement for the triangles. D 53° G 60° -67° 160° C С E F Η not similar B yes, ACDE - AHFG yes, ACDE - AFGH yes, ACDE - AFHG
Answers
Answer:
add all that up and you will get your a
Step-by-step explanation:
What is the sum of the interior angles of a regular polygon with 9 sides?
1,260°
1,620°
1,800°
1,980°
Answers
The sum of the interior angles of a regular polygon with 9 sides will be 1260°. The correct option is A.
What is the angle of the polygons?An angle is defined in mathematics as the figure formed by joining two rays at their common endpoint. An interior angle is an angle that exists within a shape. Polygons are closed shapes with sides and vertices. All of the interior angles of a regular polygon are equal.
Given that the number of the sides of the polygon is 9. The sum of the interior angles of the polygons will be calculated as,
Sum = ( n - 2 ) 180°
Sum = ( 9 - 2 ) 180
Sum = 7 x 180
Sum = 1260°
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Question 1 of 10
Which expressions are equivalent to the one below? Check all that apply.
log 2-log 4
A. log(¹)
B. log 1
C. log(2) + log(¹)
D. log 2
Answers
"The correct option is C." The only expression that is equivalent to log 2 - log 4 is option C: log(2) + log(¹).
The expression "log 2 - log 4" can be simplified using logarithmic properties. Specifically, the property states that "log(a) - log(b) = log(a/b)." Applying this property to the given expression, we have "log 2 - log 4 = log(2/4) = log(1/2) = -log(2)."
The expression log 2 - log 4 can be simplified using logarithmic properties. Let's analyze each option:
A. log(¹): This expression is not equivalent to log 2 - log 4. The logarithm of 1 is 0, but it does not cancel out the terms log 2 and log 4.
B. log 1: This expression is equivalent to 0, but it does not cancel out the terms log 2 and log 4.
C. log(2) + log(¹): This expression is equivalent to log 2 + 0, which simplifies to just log 2. It is not equivalent to log 2 - log 4.
D. log 2: This expression is not equivalent to log 2 - log 4. It represents the logarithm of 2, but it does not account for the subtraction of log 4.
Option C, "log(2) + log(¹)," again uses an exponentiation notation without an exponent and is not a valid mathematical expression.
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3 · {(300 - 70 ÷ 5) - [3 · 23 - (8 - 2 · 3)]}
Answers
Answer:
(657)
Step-by-step explanation:
Simplify the following:
3 (300 - 70/5 - (3×23 - (8 - 2×3)))
The gcd of -70 and 5 is 5, so (-70)/5 = (5 (-14))/(5×1) = 5/5×-14 = -14:
3 (300 + -14 - (3×23 - (8 - 2×3)))
-2×3 = -6:
3 (300 - 14 - (3×23 - (-6 + 8)))
8 - 6 = 2:
3 (300 - 14 - (3×23 - 2))
3×23 = 69:
3 (300 - 14 - (69 - 2))
| 6 | 9
- | | 2
| 6 | 7:
3 (300 - 14 - 67)
300 - 14 - 67 = 300 - (14 + 67):
3 ((300 - (14 + 67)))
| 1 |
| 6 | 7
+ | 1 | 4
| 8 | 1:
3 (300 - 81)
| | 9 |
| 2 | | 10
| | |
- | | 8 | 1
| 2 | 1 | 9:
3 (219)
3 (219) = (3×219):
(3×219)
3×219 = 657:
Answer: (657)
At a local university, 40% of students are male and 60% are female. In the male group, 50% major in art, 40% major in science, and the rest major in other. In the female group, 70% major in art, 10% major in science, and the rest major in other.
A.) if a student who majors in science is randomly selected, what is the probability that this student is a female?
B.) if a student is randomly selected, what is the probability that this student is a male or majors in art?
Answers
According to the given question we can conclude that the probability that a student who majors in science is a female is approximately 0.375 and the probability that a student is male or majors in art is 0.78.
Explain probability?Probability is the research of probabilities, which also are based on the ratio of favourable events to likely circumstances. One of the areas of probability theory is the estimation of the chance of experiments occurring. With a probability, we can calculate any number of things, from the probability of obtaining a head or a tail when flipping a coin towards the likelihood of generating a research error, for example.
A.) To find the probability that a student who majors in science is a female, we need to use Bayes' theorem. Let F be the event that a randomly selected student is female, and S be the event that the student majors in science. Then we have:
P(F|S) = P(S|F) * P(F) / P(S)
We know that P(F) = 0.6 (since 60% of students are female), and P(S|F) = 0.1 (since 10% of female students major in science). To find P(S), we need to use the law of total probability:
P(S) = P(S|F) * P(F) + P(S|M) * P(M)
We know that P(S|M) = 0.4 (since 40% of male students major in science), and P(M) = 0.4 (since 40% of students are male). Therefore:
P(S) = 0.1 * 0.6 + 0.4 * 0.4 = 0.16
Now we can calculate P(F|S):
P(F|S) = 0.1 * 0.6 / 0.16 ≈ 0.375
Therefore, the probability that a student who majors in science is a female is approximately 0.375.
B.) To find the probability that a student is male or majors in art, we need to use the law of total probability again:
P(Male or Art) = P(Male) + P(Art) - P(Male and Art)
We know that P(Male) = 0.4 (since 40% of students are male), and P(Art|Male) = 0.5 (since 50% of male students major in art). We also know that P(Female) = 0.6 (since 60% of students are female), and P(Art|Female) = 0.7 (since 70% of female students major in art). Therefore:
P(Art) = P(Art|Male) * P(Male) + P(Art|Female) * P(Female)
= 0.5*0.4+0.7*0.6
= 0.58
To find P(Male and Art), we can multiply the probabilities of being male and majoring in art:
P(Male and Art) = P(Male) * P(Art|Male)
= 0.4 * 0.5
= 0.2
Now we can calculate P(Male or Art):
P(Male or Art) = 0.4 + 0.58 - 0.2
= 0.78
Therefore, the probability that a student is male or majors in art is 0.78.
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ANOTHA ONE LETS GOOOOOO
Answers
Answer:
1/560
Step-by-step explanation:
So the x input which is the top row the numbers increase by 1 so that is your top number of your slope (rate of change)
And your bottom row increases by 560 so that is your bottom number of your slope
So your rate of change is 1/560
How do I know where to get these numbers?
Well if you take the first 2 numbers from the top row (in your case 1 and 2) and subtract them from each other (2-1=1) you get your first number. Then you do the same for the bottom (in your case 560 and 1120) subtract them (1120-560=560) and get your bottom....If needed you can simplify your fraction but sometimes your slope can come out as a whole number instead of a fraction but in your case you have a fraction.
That is where you get 1/560
Hope this helped!
Two lines have the same slope and y-intercept. Describe the graph of the system of equations representing the two lines.
Answers
Answer:
Parallel lines.
Step-by-step explanation:
If the two linear equations have the same slope (and the SAME y-intercept), the equations represent the same line. Since a line intersects with itself everywhere, there will be an infinite number of solutions (intersecting everywhere.)
If two equations have the same slope and the same y-intercept, then they are the same line and an infinite solution .
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
We have three cases in terms of slope and intercept:
The system has precisely one solution if the slopes of the two lines differ (whether the lines have the same intercept or different intercepts).There exists an infinite number of solutions to the system if they share the same slope and intercept, making them the same line.If they are parallel and have different intercepts but the same slope, there is no solution.So, The identical numerical values used for x and y in the first solution will also work for the second because these lines have an infinite number of solutions.
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Answers
Answer:
43
Step-by-step explanation:
47 + 90 = 137
180 - 137 = 43
angle MNP and angle PNL are same
hence, angle PNL = 43