As a result, the following is the system of equations' solution as 12x - 2y = 20 in the calculation, x = 7/4 and y = 1/2.
what is equation ?A mathematical assertion proving the equality of two expressions is known as an equation. It has two sides—a left side and a right side—that are divided by the equal symbol (=). Variables, constants, and mathematical processes may be used in the expressions on either side of the equal sign. For instance, the expression 2x + 3 on the left is equivalent to the expression 7 on the right, as shown by the equation 2x + 3 = 7.
given
We can use the technique of elimination to solve this system of equations by adding or removing one of the variables from the equations. In this instance, by combining the two equations, we can remove y:
12x - 2y = 20
16x + 2y = 29
28x = 49
We can now find the value of x by multiplying both parts by 28:
28x/28 = 49/28
x = 7/4
We can solve for y by substituting this value of x into either of the initial equations. Let's employ the initial equation:
12x - 2y = 20
12(7/4) - 2y = 20
21 - 2y = 20
-2y = -1
y = 1/2
As a result, the following is the system of equations' solution as 12x - 2y = 20 in the calculation, x = 7/4 and y = 1/2.
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a spinner has 4 equal sections colored red, blue, yellow, and green. after 18 spins, lucy lands on blue 8 times. what is the experimental probability of landing on blue?
The experimental probability of landing on blue is found by dividing the number of times blue was landed on by the total number of spins.
Experimental probability of landing on blue = Number of times blue was landed on / Total number of spins
In this case, Lucy spun the spinner 18 times and landed on blue 8 times.Experimental probability of landing on blue = 8 / 18Experimental probability of landing on blue = 4 / 9Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Therefore, the experimental probability of landing on blue is 4/9 or approximately 0.444 or 44.4% (rounded to the nearest tenth or percentage).
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Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures whenever appropriate. (Do this on paper. Your instructor may ask you to turn in this work.)
(a) P(0Image for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneveZImage for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneve2.74)
(b) P(0Image for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneveZImage for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneve1)
(c) P(-2.40Image for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneveZImage for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneve0)
(d) P(-2.40Image for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneveZImage for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneve+2.40)
(e) P(ZImage for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneve1.63)
(f) P(-1.74Image for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneveZ)
(g) P(-1.4Image for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneveZImage for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneve2.00)
(h) P(1.63Image for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneveZImage for Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wheneve2.50)
(a) To find P(0 < Z < 2.74), you'll want to look up the z-score for 2.74 in a standard normal table or use a calculator with a built-in normal distribution function. The probability is the area under the curve between 0 and 2.74.
(b) To find P(0 < Z < 1), you'll look up the z-score for 1 in a standard normal table or use a calculator. The probability is the area under the curve between 0 and 1.
(c) To find P(-2.40 < Z < 0), you'll look up the z-score for -2.40 in a standard normal table or use a calculator. The probability is the area under the curve between -2.40 and 0.
(d) To find P(-2.40 < Z < 2.40), you can first calculate the probability for P(-2.40 < Z < 0) and P(0 < Z < 2.40), and then sum the two probabilities.
(e) To find P(Z > 1.63), look up the z-score for 1.63 in a standard normal table or use a calculator. The probability is the area under the curve to the right of 1.63.
(f) To find P(Z < -1.74), look up the z-score for -1.74 in a standard normal table or use a calculator. The probability is the area under the curve to the left of -1.74.
(g) To find P(-1.4 < Z < 2.00), first look up the z-scores for -1.4 and 2.00 in a standard normal table or use a calculator. Subtract the smaller probability from the larger probability to find the area under the curve between these two values.
(h) To find P(1.63 < Z < 2.50), first look up the z-scores for 1.63 and 2.50 in a standard normal table or use a calculator. Subtract the smaller probability from the larger probability to find the area under the curve between these two values.
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I am struggling… find the domain and range of the polynomial function. Write your answer in interval notation!
f(x) = 3x2 + 4x − 9, the coefficient of x2 is 3, the coefficient of x is 4, and the constant is -9. This can be written in interval notation as [−9, ∞).
What is interval notation?Interval notation is a mathematical notation used to express the range of a variable. It is used to represent intervals on the number line, either on the real line or on the complex plane.
In this case, the domain of f(x) = 3x2 + 4x − 9 is all real numbers. The range of this function is all real numbers greater than or equal to -9. This can be written in interval notation as [−9, ∞).
The function is a quadratic polynomial of the form ax2 + bx + c. The domain of a polynomial function is all real numbers (i.e. any x-value). The range of the function is the set of all y-values that it can produce.
Here the coefficient of x2 is 3, the coefficient of x is 4, and the constant is -9. This means that the minimum y-value that the function can produce is -9. This means that the range of the function is all real numbers greater than or equal to -9.
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A scientist put 14.7 grams of a substance on a scale. She then put another 7.12 grams of the substance on the scale.
How many grams of the substance are on the scale?
iona discovers that the lifespan of cats is normally distributed with mean 12 years and standard deviation 2 years. what is the best estimate for the probability of a cat living more than 16 years?
The probability of a cat living more than 16 years can be estimated using the normal distribution. This can be calculated using the following equation: P(X>16) = 1-P(X<16) = 1- Φ((16-12)/2) = 0.1587. This means that the probability of a cat living more than 16 years is approximately 15.87%.
The normal distribution is a continuous probability distribution often used to represent real-world phenomena, such as the lifespan of cats. The distribution is characterized by two parameters, the mean and the standard deviation. The mean is the average value of the data, and the standard deviation is a measure of how spread out the data is around the mean.
To calculate the probability of a cat living more than 16 years, we need to find the cumulative probability of a value less than 16 years. This is done using the normal cumulative probability distribution. We subtract the mean (12 years) from the desired value (16 years) and divide the result by the standard deviation (2 years). We then use this value to calculate the cumulative probability using the cumulative probability function (Φ). The result is 0.1587, meaning that the probability of a cat living more than 16 years is approximately 15.87%.
In conclusion, the probability of a cat living more than 16 years is approximately 15.87%.
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in a pain clinic, the mean depression score on a sample of patients is 78 with a standard deviation of 8. what is the probability that a petient would have a depression score greater than 60.
The probability that a patient would have a depression score greater than 60 is 0.9878.
The probability that a patient would have a depression score greater than 60 in a pain clinic when the mean depression score on a sample of patients is 78 with a standard deviation of 8 can be calculated using z-score.
Z-score formula
Z-score = (x - μ) / σ
Where,
x = the value to be standardized
μ = the mean of the population
σ = the standard deviation of the population
Given data,
Mean = 78
Standard deviation, σ = 8
Let x be the depression score.
To find the probability that a patient would have a depression score greater than 60, we need to find the z-score first.
Using the formula,
z-score = (x - μ) / σ = (60 - 78) / 8 = -2.25
Now, the probability can be calculated using the z-score table which gives the probability that a value will be less than z.
To find the probability that a value will be greater than z, subtract the probability from 1.
Probability of Z < -2.25 = 0.0122
Probability of Z > -2.25 = 1 - 0.0122 = 0.9878
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Write the equation of the line that is parallel to y=- 3/2and passes through
point (2,3).
Answer:
[tex]y-3=-\frac{3}{2}(x-2)[/tex]
Step-by-step explanation:
In order to find an equation that is parallel, it must have the same slope. This means the y intercept could literally be anything.
By equation of the line, we can write it in point slope form
[tex]y-y1=m(x-x1)[/tex]
where y1 and x1 are points on the coordinate plane and m is the slope.
We are already given the slope, so we just plug in the numbers.
[tex]y-3=-\frac{3}{2}(x-2)[/tex]
find the value of x?
Answer: x is equal to 1
Step-by-step explanation:
Find the are 22ft 37ft 38. 09ft 109degrees 138degrees
Answer:
B.
Step-by-step explanation:
I just took the test
The measure of the angle turns through 3/5 of 360°, true or false
Answer:
false, 216° turns 3/5 in a 360° rotation
GIVING BRAINLIEST FOR RIGHT ANSWER (provide proof please i need to know how you got the answer)
Makers of generic drugs are required to show that their generic drugs do not differ significantly from the "reference" or brand name drugs that they imitate. One aspect in which the generic drugs might differ is their extent of absorption in the blood. Twelve subjects were available for the study. Six were randomly selected to receive the generic drug first and then, after a washout period, receive the "reference" drug. The remaining six received the "reference" drug first, followed by the generic drug after the washout period. Assume that all conditions are met. The mean of the differences was 1.33 and the standard deviation of those differences was 2.90. What is the test statistic for this procedure? a. 5.50 b. 2.35 c. 1.59 d. 1.90
The mean of the differences was 1.33 and the standard deviation of those differences was 2.90. The test statistic for this procedure is 1.90. The correct option is D.
Makers of generic drugs are required to show that their generic drugs do not differ significantly from the "reference" or brand name drugs that they imitate. One aspect in which the generic drugs might differ is their extent of absorption in the blood. Twelve subjects were available for the study. Six were randomly selected to receive the generic drug first and then, after a washout period, receive the "reference" drug. The remaining six received the "reference" drug first, followed by the generic drug after the washout period. Assume that all conditions are met.
The mean of the differences was 1.33 and the standard deviation of those differences was 2.90.
A t-test statistic for a paired sample is to be calculated to find out whether or not there is a statistically significant difference between the two treatments. The formula for a t-test statistic is given below:
t= x¯d/sd / √n
where x¯d is the mean difference,
sd is the standard deviation of the differences, and
n is the number of subjects.
Using the given values, we can substitute in the formula and solve for t as follows:
t=1.33/2.90 / √12t=1.90
Hence, the test statistic for this procedure is 1.90.
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please help quick
6d = 54
answer
6 divided by 54 is equal to 9
therefore
answer = d=9
What is the relationship between the mean and median? a. the mean is approximately the same as the median. b. the mean is greater than the median. c. the mean is less than the median.
The relationship between the mean and median depends on the shape of the distribution of the data, therefore correct options are
(a) The mean is approximately the same as the median
(b) The mean is greater than the median
(c) The mean is less than the median.
The relationship between the mean and the median depends on the shape of the distribution of the data. In a symmetric distribution, the mean and median will be approximately the same. In a skewed distribution, the mean will be pulled in the direction of the skew, and the median will be a better representation of the "typical" value.
If the distribution is symmetrical (i.e., evenly distributed around the center), the mean and median will be approximately the same.
If the distribution is positively skewed (i.e., has a long tail on the right side), the mean will be greater than the median.
If the distribution is negatively skewed (i.e., has a long tail on the left side), the mean will be less than the median.
Therefore, correct options are
(a) The mean is approximately the same as the median
(b) The mean is greater than the median
(c) The mean is less than the median.
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hirty five discrete math students are to be divided into seven discussion groups, each consisting of five students. in how many ways can this be done?
Answer:76904685 ways
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Fill in the blanks so the left side is a perfect square trinomial. That is, complete the square.
a. x^2+5/6x+___=(x+___)^2
b. x^2-11x+___=(x-__)^2
ANSWERS:
A ) x^2 + 5/6x + 25/144 = (x + 5/12)^2
B ) x^2 - 11x + 121/4 = (x - 11/2)^2
EXPLANATION:
a. To complete the square for the equation x^2 + 5/6x + ___,
first divide the coefficient of the linear term (5/6) by 2,
which gives you 5/12.
Then, square the result:
(5/12)^2 = 25/144.
So, the equation becomes:
x^2 + 5/6x + 25/144 = (x + 5/12)^2
b. To complete the square for the equation x^2 - 11x + ___,
first divide the coefficient of the linear term (-11) by 2,
which gives you -11/2.
Then, square the result:
(-11/2)^2 = 121/4.
So, the equation becomes:
x^2 - 11x + 121/4 = (x - 11/2)^2
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What is the constant (k) in this inverse variation?
y = 400/x
* x
* Not enough information given
* y
* 400
The constant (k) in this inverse variation y = 400/x is 400.
The correct answer choice is option D.
What is the constant (k) in this inverse variation?Inverse variation refers to the relationship that exists between two variables, such that the increase in the value of one variable decreases the value of the other variable.
It is written as;
y = k/x
Where,
k = constant of proportionality
x and y = the given variables
So,
y = 400/x
Therefore, it can be concluded that the constant of the inverse variation is 400
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8) What is the lower quartile of the numbers
4, 6, 7, 8, 10, 12, 20?
(a) 4
(b) 6
(c) 7
(d) 8
The lower quartile of the given set of numbers 4, 6, 7, 8, 10, 12, 20 is 6. So, correct option is B.
To find the lower quartile of a set of numbers, we first need to arrange them in ascending order. The given numbers are: 4, 6, 7, 8, 10, 12, 20.
Next, we divide the data set into four equal parts. The lower quartile is the median of the lower half of the data set. In this case, the lower half is 4, 6, and 7.
To determine the median of the lower half, we need to find the middle value. Since we have an odd number of data points in the lower half, the middle value is the single value between the two extremes. In this case, the median is 6.
This corresponds to option (b) in the given choices: 6.
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Which expression best represents the difference between triple a number and double a number
Answer: 3x-2x or (3x)-(2x)
Write an expression that best represents the difference between triple and double a number?
Step-by-step explanation: HOPE THIS HELPS!
Answer:
3x-2x
Step-by-step explanation:
I hope you this is it
f scores are normally distributed with a mean of 35 and a standard deviation of 10, what percent of the scores is: (a) greater than 34?
The percentage of scores greater than 34 is 0.5398 or 53.98%.
Given that the mean of scores (μ) = 35 and the standard deviation (σ) = 10. We need to find the percentage of scores greater than 34. Since the scores are normally distributed, we can standardize the variable by using the z-score formula.
z = (x - μ) / σ
Here, x = 34, μ = 35 and σ = 10z = (34 - 35) / 10z = -0.1
We need to find the area to the right of the z-score line on the standard normal distribution table. The standard normal distribution table provides the probabilities corresponding to the z-scores, i.e. the area under the curve to the right or left of the z-score line on the distribution table. The area to the right of the z-score line represents the percentage of scores that are greater than the given value. Using the standard normal distribution table, the area to the right of the z-score line -0.1 is 0.5398.
The percentage of scores greater than 34 is 0.5398 or 53.98%.
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A random sample of dogs at different animal shelters in a city shows that 10 of the 70 dogs are puppies. The city's animal shelters collectively house 1,960 dogs each year. About how many dogs in all of the city's animal shelters are puppies?
280 dogs in all of the city's animal shelters are puppies. The solution has been obtained by using ratios.
What is ratio?
The ratio between two amounts of the same unit can be used to determine how much of one quantity is included in the other.
We are given that different animal shelters in a city shows that 10 of the 70 dogs are puppies and the city's animal shelters collectively house 1,960 dogs each year.
So, from this we get the ratio as
⇒ [tex]\frac{10}{70}[/tex] = [tex]\frac{x}{1960}[/tex]
Now, by cross multiplying, we get
⇒ 19,600 = 70x
⇒ x = 280
Hence, 280 dogs in all of the city's animal shelters are puppies.
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A train travelling at 120 km/h goes through a tunnel 155m long. Calculate in seconds, the time a passenger on a train spends in the tunnel
passenger on the train spends approximately 4.65 seconds in the tunnel.
First, we need to convert the speed of the train from km/h to m/s (meters per second) since the length of the tunnel is given in meters. We can do this by dividing the speed in km/h by 3.6, which is the conversion factor from km/h to m/s:
Speed of the train = 120 km/h = (120/3.6) m/s = 33.33 m/s
Next, we can use the formula for time:
time = distance ÷ speed
where distance is the length of the tunnel, and speed is the speed of the train.
Plugging in the given values, we get:
time = 155 m ÷ 33.33 m/s ≈ 4.65 s
Therefore, a passenger on the train spends approximately 4.65 seconds in the tunnel.
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What are carbon compounds
Answer:
Carbon compounds are defined as chemical substances containing carbon i'd say.
find the closed formula for each of the following sequences by relating them to a well known sequence. assume the first term given is a1. (a) 2; 5; 10; 17; 26; : : : (b) 0; 2; 5; 9; 14; 20; : : : (c) 8; 12; 17; 23; 30; : : : (d) 1; 5; 23; 119; 719; :
a) an = 3n-1 · 2
b) an = 2·n
c) an = 5·n + 8
d) an = 4n-1 · 1
Let's dive deeper into the details below.
(a) The sequence 2, 5, 10, 17, 26 is a geometric sequence with common ratio 3 and a1 = 2. Therefore, the closed formula is an = 3n-1 · 2.
(b) The sequence 0, 2, 5, 9, 14 is an arithmetic sequence with common difference 2 and a1 = 0. Therefore, the closed formula is an = 2·n.
(c) The sequence 8, 12, 17, 23 is an arithmetic sequence with common difference 5 and a1 = 8. Therefore, the closed formula is an = 5·n + 8.
(d) The sequence 1, 5, 23, 119 is a geometric sequence with common ratio 4 and a1 = 1. Therefore, the closed formula is an = 4n-1 · 1.
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do these 2 equations show growth or decay pls i need help. Y = 2x^2 + 9, and
y = 3/2 + .45x
I used desmos to graph the equations and this is what I got. Let me know if I've done a typo.
1.
A boy throws a rock from his bedroom window. The height of the rock is a function of time and can be
modeled by the equation h(t) = 15 + 7t - 16t2. Height is measured in feet and time is measure in
seconds. The graph of this function is shown.
a. Evaluate h(0) and explain what it means in context.
b. Estimate the value of h(t) = 0 and explain what it means in context.
c. What does the equation h(1) = 6 mean?
height (ft)
d. Estimate and state the vertex h(t)and explain its meaning in context.
time (sec)
shift
(intel
Inside
The vertex of the parabola is approximately (7/32, 17.2), which represents the highest point the rock reaches during its flight.
What is parabola?A parabola is a symmetrical, U-shaped curve that is formed by the graph of a quadratic function. The equation of a parabola in standard form is y = ax² + bx + c, where "a", "b", and "c" are constants, and "x" and "y" are variables.
According to question:a. To evaluate h(0), we substitute t=0 in the equation:
h(0) = 15 + 7(0) - 16(0)² = 15
This means that at the instant the boy throws the rock (t=0), the height of the rock is 15 feet above the ground.
b. To estimate the time when the rock hits the ground, we need to find the value of t when h(t) = 0. We can solve the equation 15 + 7t - 16t² = 0 for t, using the quadratic formula:
t = (-7 ± √(7² - 4(-16)(15))) / (2(-16))
t ≈ 1.28 s or t ≈ 1.97 s
This means that the rock will hit the ground approximately 1.28 seconds or 1.97 seconds after it is thrown.
c. The equation h(1) = 6 means that one second after the rock is thrown, its height above the ground is 6 feet.
d. The vertex of the parabola h(t) = 15 + 7t - 16t² can be found by using the formula t = -b/2a, where a=-16 and b=7.
t = -7 / (2(-16)) = 7/32
Substituting t=7/32 into the equation, we get:
h(7/32) = 15 + 7(7/32) - 16(7/32)² ≈ 17.2
Therefore, the vertex of the parabola is approximately (7/32, 17.2), which represents the highest point the rock reaches during its flight.
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The Computer has labeled the lines you graphed a and b. What are the equations of the lines? Enter them into the table below
The equation of the line is 9x+8y + 19 = 0 and 5x - 4y+ 19 = 0 According to the given graphs, these are the equations of the graph.
Consider two points on the blue line.
The points are (5, -8) and ( -3,1 ).
Equation of the blue line is:
y - 1 = [tex]\frac{-8-1}{5+3} (x+3)[/tex]
8 (y - 1) = -9 ( x + 3)
8y - 8 = -9x -27
9x + 8y + 19 = 0
Therefore, the Equation of the blue line is 9x + 8y + 19 = 0.
Consider two points on the red line.
The points are (-3, 1) and ( 1,6 ).
Equation of the red line is:
y - 1 = [tex]\frac{6-1}{1+3} (x+3)[/tex]
4 (y - 1) = 5 (x + 3)
4y - 4 = 5x + 15
5x - 4y+ 19 = 0
Therefore, the Equation of the red line is 5x - 4y+ 19 = 0.
Hence, the equations for the given blue and red lines are completed.
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t is known that amounts of money spent on clothing in a year by college students follow a normal distribution with a mean of $310 and a standard deviation of $50. what is the probability that a randomly chosen student will spend between $300 and $400 on clothing in a year?
The probability that a randomly chosen college student will spend between $300 and $400 on clothing in a year is approximately 0.6645 or 66.45%.
To solve this problem, we need to standardize the given range of values using the z-score formula:
z = (x - μ) / σ
where x is the value of interest, μ is the mean, and σ is the standard deviation. For x = 300:
z = (300 - 310) / 50 = -0.2
For x = 400:
z = (400 - 310) / 50 = 1.8
Using a standard normal distribution table or calculator, we can find the probability of the z-score being between -0.2 and 1.8:
P(-0.2 ≤ z ≤ 1.8) = 0.6645
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two angles are supplementary. if one angle is two times the sum of other angle and 3, find the two angle
The answer of the given question based on the supplementary angle is the two angles are 58° degrees and 122° degrees.
What is Angle?An angle is a geometric figure that is formed by two rays or lines that share a common endpoint, called the vertex. The rays or lines are called sides or arms of angle. Angles are typically measured in the degrees or the radians.
The measure of an angle is determined by the amount of rotation needed to bring one of its sides into coincidence with the other side. A full rotation is 360° degrees, so an angle that is half of a full rotation is 180 degrees, an angle that is a quarter of a full rotation is 90° degrees, and so on.
Let's call the two angles "x" and "y". We know that they are supplementary, which means that their sum is 180° degrees:
x + y = 180
We also know that one angle (let's say "x") is two times the sum of the other angle (y) and 3:
x = 2(y + 3)
Now we can substitute the second equation into the first equation to eliminate "x":
(2(y + 3)) + y = 180
Simplifying the equation, we get:
3y + 6 = 180
Subtracting 6 from both sides, we get:
3y = 174
Dividing both sides by 3, we get:
y = 58
Now that we know "y", we can substitute it back into the equation for "x" to find its value:
x = 2(y + 3) = 2(58 + 3) = 122
Therefore, the two angles are 58° degrees and 122° degrees.
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the student body of a large university consists of 60% female students. a random sample of 8 students is selected. what is the probability that among
The probability of selecting 8 female students from a sample of 8 students from a student body with 60% female students is 0.2187, or 21.87%.
The probability of selecting a sample of 8 students from a student body of 60% female students is calculated using binomial probability. The binomial probability formula is used to calculate the probability of a certain number of successes in a certain number of independent trials. In this case, the probability of selecting 8 students, with 60% being female students, can be calculated using the binomial probability formula.
The probability can be calculated using the following equation:
[tex]P(x=8) = (n!/((n-x)!x!)) * p^x * q^{(n-x)}[/tex]
Where:
In this case, n = 8, x = 8, p = 0.6, and q = 0.4. Plugging these values into the equation gives us a probability of 0.2187. This means that there is a 21.87% chance of selecting 8 female students out of a sample of 8 students from a student body with 60% female students.
It is important to remember that binomial probability is only used when there are two possible outcomes in each trial (i.e. success or failure). Additionally, it is important to remember that the equation only applies when the trials are independent of each other.
In conclusion, the probability of selecting 8 female students from a sample of 8 students from a student body with 60% female students is 0.2187, or 21.87%.
See more about binomial probability at: https://brainly.com/question/14984348
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