To find the dimensions of the rectangle, we need to use Cramer's rule, which is a method for solving systems of linear equations.
Let's start by defining the variables:
Let x be the width of the rectangle in cm.
Let y be the length of the rectangle in cm.
According to the problem, we have two equations:
y = 3x - 6 (the length is 6cm less than three times the width)
2(x + y) = P (the perimeter of the rectangle is P)
We can rewrite the second equation as:
2x + 2y = P
To solve for x and y, we need to set up a matrix and apply Cramer's rule. The matrix is:
| 0 1 | | x | | -6 |
| 2 2 | x | y | = | P |
Using Cramer's rule, we can solve for x and y as follows:
x = (|-6 1| / |-2 1|) = 9
y = (|0 -6| / |-2 1|) = 12
Therefore, the width of the rectangle is 9 cm and the length of the rectangle is 12 cm.
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A trapezoid has bases of lengths 14 and 21. Find the trapezoid's height if it's area is 245
Answer: 8575/2
Step-by-step explanation:
A. Kiera is making charm bracelets
and uses 2 blue charms to every 3
yellow. How many yellow charms
will she use if she has 10 blue?
Answer:
Kiera will use 15 yellow charms
Step-by-step explanation:
The pattern would look like this:
BBYYYBBYYYBBYYYBBYYYBBYYY
B = Blue Charms
Y = Yellow Charms
What is the slope of 2/3 on a graph
Answer:
The slope is 0
Step-by-step explanation:
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
y = mx + b
Using the slope-intercept form, the slope is 0.
m = 0
(See the attachment below)
Hope this helps :)
Pls brainliest...
There are 20 students in a class. Everyone in the class scored 6 out of 10
in a test. What is the range of their scores?
Answer: 0
Step-by-step explanation:
Range = Highest number - lowest number
range = 6 - 6
range = 0
ruby company has an annual profit, in billions, that has a normal distribution with variance that is equal to the cube of its mean. the probability of an annual loss is 5%. calculate the company's expected annual profit.
Therefore, the expected annual profit of Ruby Company is 2.703 billion dollars using probability.
Let X be the annual profit of the company. We know that X follows a normal distribution with variance equal to the cube of its mean, i.e., Var(X) = (E[X])^3.
To find the expected annual profit, we need to find the mean of X, denoted as E[X].
We are given that the probability of an annual loss is 5%. This means that the probability of making a profit is 1 - 0.05 = 0.95.
Let Z be a standard normal random variable, then we have:
P(X < 0) = P((X - E[X]) / sqrt(Var(X)) < (0 - E[X]) / sqrt(Var(X)))
= P(Z < -E[X] / (E[X])^(3/2))
Since P(X < 0) = 0.05, we have:
0.05 = P(Z < -E[X] / (E[X])^(3/2))
Using a standard normal table or calculator, we can find that P(Z < -1.645) = 0.05, where -1.645 is the 5th percentile of the standard normal distribution.
Thus, we have:
-E[X] / (E[X])^(3/2) = -1.645
this equation, we get:
E[X]^(1/2) = 1.645
Taking the square of both sides, we get:
E[X] = 2.703
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Andrea is keeping track of how many calories she eats. On Friday, she ate 4 cookies at snack time and 1700 calories with her meals. On Saturday, she ate 5 cookies at snack time and 1650 calories with her meals. If Andrea ate the same amount of calories both days, how many calories are in each cookie?
If Andrea ate the same amount of calories both days, Each cookie has 100 calories.
To find out how many calories are in each cookie, we need to determine the total number of calories consumed and divide it by the total number of cookies.
On Friday, Andrea ate 4 cookies and 1700 calories with her meals, resulting in a total of 1700 + (4 * C) calories, where C represents the calories per cookie.
On Saturday, Andrea ate 5 cookies and 1650 calories with her meals, resulting in a total of 1650 + (5 * C) calories.
Since Andrea ate the same amount of calories both days, we can set up an equation:
1700 + (4 * C) = 1650 + (5 * C)
Simplifying the equation, we get:
50 = C
Therefore, each cookie has 50 calories.
It's worth noting that the solution assumes that the calorie content of the meals on both days is the same and only the calorie content from the cookies varies.
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Solve for x. Assume that lines which
appear tangent are tangent.
5
3x+1
6
2x
The value of x in the circle is 3.
We have,
In geometry, a secant is a line that intersects a circle at two distinct points.
The formula for two secant segments on a circle states that the product of the lengths of one secant segment and its external segment is equal to the product of the lengths of the other secant segment and its external segment.
We will use the formula for two secants on a circle.
So,
There are two secant segments on the circle.
This means,
5 x (5 + 3x + 1) = 6 x (6 + 2x)
Now,
Solve for x.
5 x (5 + 3x + 1) = 6 x (6 + 2x)
Distributive property.
5 x (6 + 3x) = 6 x (6 + 2x)
Adding like terms
30 + 15x = 36 + 12x
15x - 12x = 36 - 30
2x = 6
Divide 2 on both sides.
x = 3
Thus,
The value of x in the circle is 3.
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The intersection of a right cylinder and a plane makes an oval cross section. Which option is true about the plane of intersection?
1.The right cylinder is cut with a plane that is neither parallel nor perpendicular to the base.
2.The right cylinder is cut with a plane perpendicular to the base and passing through the center.
3.The right cylinder is cut with a plane parallel to the base.
4.The right cylinder is cut with a plane perpendicular to the base but not passing through the center.
An answer option that is true about the plane of intersection include the following: 1. The right cylinder is cut with a plane that is neither parallel nor perpendicular to the base.
What is a plane?In Mathematics and Geometry, a plane is sometimes referred to as a two-dimensional surface and it can be defined as a flat, two-dimensional surface with zero curvature and zero thickness, that extends indefinitely (infinitely). Additionally, two (2) planes generally intersect at a line.
In order to have an intersection of a right cylinder and a plane that would make an oval cross section, the right cylinder must be cut with a plane that is neither parallel nor perpendicular to its base.
However, if the right cylinder is cut with a plane that is parallel to its base, then, the shape of cross section that would be formed is a circle.
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Kevin makes muffins. It takes 8 minutes to mix the batter. The muffins bake for 17 minutes. The muffins then cool for 5 minutes. What is the total amount of time, in minutes, Kevin spends mixing, baking, and cooling the muffins? Enter your answer in the box.
Answer:
8+17+5=30
Step-by-step explanation:
Kevin spends mixing, baking, and cooling the muffins. If you add 7 and 8 you get 15 and add another 5 you get 20+10 = 30
volume of cones and spheres questions
The volume of the cone is 57.44 cubic cm
The volume of the cone and sphere is 229.88 cubic cm
The height of the square pyramid will be 115.03 cm
How to find the volume of the coneThe volume of a cone can be calculated using the formula:
V = (1/3)πr²h
where
V = volume of the cone
π = pi, approximately 3.14
r = radius of the base of the cone
h = height of the cone
2 x V = 2 * (1/3) * 3.14 * 2.8² * 3.5
The volume of the cone is 57.44 cubic cm
2.
Volume = volume of cone + volume of sphere
= (4/3)πr³ + (1/3)πr²h
= (4/3) * 3.14 * 3.4³ + (1/3) * 3.14 * 3.4² * 5.4
= 229.88 cubic cm
3. Volume of square pyramid
= base area * h/3
when base is 230
= 230² * 147/3 = 2592100
when base is 260
260² * h/3 = 2592100
h/3 = 2592100 / 260²
h = 115.03 cm
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(×) = 2×- 5ײ+3
Ayudenmeeeee Porfavor siiiiiiiiiiii
The expression (×) = 2× - 5ײ + 3 is a quadratic function. It represents a parabola that opens downward with a vertex at (0,3). The x-intercepts are (-1,0) and (3/5,0), and the y-intercept is (0,3).
The given expression (×) = 2× - 5ײ + 3 is a quadratic function in standard form, where the coefficient of the x² term is negative, indicating that the parabola opens downward. The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.
To find the vertex of the parabola, we can use the formula x = -b/2a, which gives the x-coordinate of the vertex. In this case, a = -5 and b = 2, so x = -2/(2*(-5)) = 0. The y-coordinate of the vertex can be found by substituting x = 0 into the expression, which gives f(0) = 2(0) - 5(0)² + 3 = 3. Therefore, the vertex of the parabola is at (0,3).
To find the x-intercepts of the parabola, we can set the expression equal to zero and solve for x. This gives the quadratic equation 5x² - 2x - 3 = 0. Factoring this equation, we get (5x + 3)(x - 1) = 0, so the x-intercepts are -3/5 and 1. However, we can discard the negative value because it is not within the domain of the problem. Therefore, the x-intercept is (3/5,0).
To find the y-intercept of the parabola, we can set x = 0 in the expression, which gives f(0) = 3. Therefore, the y-intercept is (0,3).
In conclusion, the expression (×) = 2× - 5ײ + 3 represents a downward-opening parabola with a vertex at (0,3), x-intercept at (3/5,0), and y-intercept at (0,3).
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if the saving rate is 1 (i.e., s = 1), we know that
If the saving rate is 1, it means that an individual or an economy saves their entire income and spends nothing. This implies that the consumption rate is 0, and all income is being saved.
In this scenario, the investment rate is equal to the saving rate, as there is no consumption spending. Therefore, the economy is investing all of its income in capital goods and not in consumption goods. This approach may result in high economic growth in the future due to the increased production capacity of the economy. However, in the short term, it may lead to a decrease in consumer demand and a decrease in output and employment in sectors producing consumer goods.
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Use the interactive graph below to sketch a graph of y = 310g, (-X) - 9.
The graph of the logaritmic function is on the image at the end.
How to graph the function?So here we want to graph the function:
y = 3log₂(-x) - 9
To graph this, we can evaluate it in some values and then find some points. We can graph these points and then connect them.
if x = -1 then:
y = 3*log₂(1) - 9 = -9
So we have the point (-1, 9)
if x = -2 then:
y = 3*log₂(2) - 9 = -6
We have the point (-2, -6)
And so on, when you have enough points, you can graph them and connect them, you should get something like the graph in the image at the end.
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lowest common multiple of 5,10and 12
Answer: 60
Step-by-step explanation:
Lowest common multiple is the smallest number that 5 10 and 12 can all multiply too
Multiples of 10 are easy, any number ending in 0
So you need to find a number that 5 and 12 go into that ends in 0
We can do this by doing 5*12 which gives us 60 which is divisible by 10
What is the missing ratios of the values below
The missing values from the ratio table are underlined:
Peppermints: 14, 2, 2/7.
Chocolates: 21, 21, 189.
How to find the missing value of the ratio table?To fill in the missing values in the ratio table, we need to find the common ratio between the given values.
For the Peppermints row:
Common ratio = (2nd value) / (1st value) = 2 / 14 = 1/7
So, the missing value can be found by multiplying the 2nd value (2) by the common ratio:
Missing value = (2nd value) * (common ratio) = 2 * (1/7) = 2/7
Therefore, the missing value in the Peppermints row is 2/7.
For the Chocolates row:
Common ratio = (3rd value) / (2nd value) = 189 / 21 = 9
The missing value in the Chocolates row can be found by dividing the 3rd value (189) by the common ratio:
Missing value = (3rd value) / (common ratio) = 189 / 9 = 21
Therefore, the missing value in the Chocolates row is 21.
The completed ratio table is as follows:
Peppermints - 14, 2, 2/7
Chocolates - 21, 21, 189
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In 1-3 find the diagonal distance between the two points to the nearest tenth
1. point A is 2Y 1X point B is 9Y 9X
2. point A is 4Y -1X point B is -15Y 3X
3. point A is 7Y 1X point B is 5Y 9X
The Diagonal distance between point A and point B is approximately 8.2 units.
1. To find the diagonal distance between point A (2Y, 1X) and point B (9Y, 9X), we can use the distance formula:
distance = √((y2 - y1)^2 + (x2 - x1)^2)
distance = √((9 - 2)^2 + (9 - 1)^2)
distance = √(49 + 64)
distance = √113
distance ≈ 10.6
Therefore, the diagonal distance between point A and point B is approximately 10.6 units.
2. To find the diagonal distance between point A (4Y, -1X) and point B (-15Y, 3X), we can use the distance formula:
distance = √((y2 - y1)^2 + (x2 - x1)^2)
distance = √((-15 - 4)^2 + (3 - (-1))^2)
distance = √(361 + 16)
distance = √377
distance ≈ 19.4
Therefore, the diagonal distance between point A and point B is approximately 19.4 units.
3. To find the diagonal distance between point A (7Y, 1X) and point B (5Y, 9X), we can use the distance formula:
distance = √((y2 - y1)^2 + (x2 - x1)^2)
distance = √((5 - 7)^2 + (9 - 1)^2)
distance = √4 + 64
distance = √68
distance ≈ 8.2
Therefore, the diagonal distance between point A and point B is approximately 8.2 units.
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true/false: one or two extreme data points (outliers) can have a dramatic effect on the strength of a correlation
a professor asks the first 5 55 students who arrive to class to participate in a research study about young adult sleep patterns. what type of sample
Based on the information provided, the type of sample used in the research study would be a convenience sample.
A convenience sample is a non-probability sampling technique where participants are selected based on their availability and willingness to participate. In this case, the professor selected the first 55 students who arrived in class, which means the sample was not selected randomly or systematically. It is important to note that convenience samples may not represent the entire population accurately, and therefore, the results obtained from such samples may not be generalizable to the larger population. As such, caution should be taken when interpreting the findings of this research study.
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the solution set for 3 => x-4/2 + x/3 => 2, x belongs to an integer
Answer:
To solve the inequality 3 ≤ (x - 4)/2 + x/3 < 2, we can start by simplifying the expression on the right-hand side:
(x - 4)/2 + x/3 = (3(x - 4) + 2x)/6 = (5x - 12)/6
Substituting this back into the inequality, we have:
3 ≤ (5x - 12)/6 < 2
Multiplying both sides by 6, we get:
18 ≤ 5x - 12 < 12
Adding 12 to all sides, we get:
30 ≤ 5x < 24
Dividing all sides by 5, we get:
6 ≤ x < 4.8
Since x is an integer, the only integer that satisfies this inequality is x = 6. Therefore, the solution set for the inequality 3 ≤ (x - 4)/2 + x/3 < 2, where x belongs to an integer, is {6}.
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Which has reflectional symmetry but not rotational symmetry?
The shape that has reflectional symmetry but not rotational symmetry is the water bottle and
bulb
What is reflectional symmetry?A shape or object that exhibits reflectional symmetry but not rotational symmetry is one that can be reflected acros a line or axis to create a mirror image but it cannot be rotated by any angle and still maintain the same appearance. In other words, it does not possess any rotational symmetry
Along the vertical axis, the water bottle has reflectional symmetry. Th bulb can possess reflectional symmetry when kept symmetrical to a particular axis.
Both lacks rotational symmetry
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Find the measure of < A C B :
< A C B = °
The measure of the angle m∠ACB subtended by the arc AB at the center is equal to 140°
What is angle subtended by an arc at the centerThe angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.
The arc AB completes the circumference of the circle, with the other arc ADB
So since;
arc AB = 360° - 220°
arc AB = 140°
so;
m∠ACB = 140°
Therefore, the measure of the angle m∠ACB subtended by the arc AB at the center is equal to 140°
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Given vector
�
=
<
−
2
,
−
3
>
u=⟨−2,−3⟩ and
�
=
<
−
1
,
3
>
,
v=⟨−1,3⟩, find a linear combination of the vectors
�
u and
�
v of the form
�
�
+
�
�
au+bv that would result in the vector
<
−
10
,
−
6
>
.
⟨−10,−6⟩.
The linear combination of u and v that gives us the vector ⟨−10,−6⟩ is (−22,−6)
How did we get the value?To find a linear combination of the vectors u and v that results in the vector ⟨−10,−6⟩, solve the system of linear equations:
a u + b v = ⟨−10,−6⟩
where a and b are scalars.
Expanding the left-hand side using the given vectors:
a ⟨−2,−3⟩ + b ⟨−1,3⟩ = ⟨−10,−6⟩
Simplify:
⟨−2a − b, −3a + 3b⟩ = ⟨−10,−6⟩
The following system of equations is derived:
-2a - b = -10
-3a + 3b = -6
Solve for a and b by substitution. Rearrange the first equation to solve for b:
b = -10 + 2a
Substitute this expression for b into the second equation:
-3a + 3(-10 + 2a) = -6
Simplify:
-3a - 30 + 6a = -6
3a = 24
a = 8
Substitute the value for a into the expression for b:
b = -10 + 2a = -10 + 2(8) = 6
Therefore, the linear combination of u and v that gives us the vector ⟨−10,−6⟩ is:
8u + 6v = 8⟨−2,−3⟩ + 6⟨−1,3⟩ = ⟨−16,−24⟩ + ⟨−6,18⟩ = ⟨−22,−6⟩
So, 8u + 6v = ⟨−22,−6⟩ which is the desired linear combination of the vectors u and v.
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The complete question in ideal form is given as thus:
Given vector u = (-2,-3 and v (-1,3) , find a linear combination of the vectors U and v of the form au + bv that would result in the - vector (-10, -6).
Question in the picture below
The best estimate of the random sample in the survey that support the proposal is the option; 4.1
What is a random sample?A random sample is a collection of data selected from a population such that each member of the population have the same chance of being selected.
The best estimate can be obtained from the mean value of the result from the poll, which can be obtained as follows;
The mean response = The sum of the response ÷ The count or the number of responses
The responses are; 7, 2, 6, 7, 3, 5, 5, 3, 2, 1
The sum of the response = 7 + 2 + 6 + 7 + 3 + 5 + 5 + 3 + 2 + 1 = 41
The number of response = 10
The mean of the response = (7 + 2 + 6 + 7 + 3 + 5 + 5 + 3 + 2 + 1)/10 = 4.1
The best estimate of the state citizens that support the proposal, therefore is; 4.1, which indicates that the citizens in the sample are slightly in support of the proposal.
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the diamtery of a standard basketball is 9.5 inches. if there basketballs are covered in rubber, what is the minimum amount of rubber needed to manufacture a set of four basketballs?
Therefore, the minimum amount of rubber needed to manufacture a set of four basketballs is 1130.96 square inches.
To determine the minimum amount of rubber needed to manufacture a set of four basketballs, we need to calculate the total surface area of one basketball. The formula to calculate the surface area of a sphere is 4πr², where r is the radius of the sphere. The diameter of a standard basketball is 9.5 inches, so the radius is half of that, which is 4.75 inches.
Using the formula, we can calculate the surface area of one basketball as 4π(4.75)² = 282.74 square inches. To manufacture a set of four basketballs, we need to multiply the surface area of one basketball by four, which gives us 1130.96 square inches.
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a recent personalized information sheet from your wireless phone carrier claims that the mean duration of all your phone calls was μ = 2.4 minutes with a standard deviation of o = 1.8 minutes. complete parts a through c below.
a. is the population distribution of the duration of your phone calls likely to be bell shaped, right, or left skewed?
b. You are on a shared wireless plan with your parents, who are statisticians. They look at some of your recent monthly statements that list each call and its duration and randomly sample 45 calls from the thousands listed there. They construct a histogram of the duration to look at the data distribution. Is this distribution likely to be bell shaped, right-, or left-skewed?
c. From the sample of n = 45 calls, your parents compute the mean duration. Is the sampling distribution of the sample mean likely to be bell shaped, right-, or left-skewed, or is it impossible to tell?
Answer:
a. The population distribution of the duration of your phone calls is likely to be bell shaped. This is because the mean, median, and mode are all equal to 2.4 minutes. This means that the data is evenly distributed around the mean.
b. The distribution of the 45 calls is likely to be bell shaped as well. This is because the sample size is large enough to be representative of the population. Additionally, the sample was randomly selected, so it is unlikely to be biased.
c. The sampling distribution of the sample mean is also likely to be bell shaped. This is because the central limit theorem states that the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is large enough. In this case, the sample size is 45, which is large enough to satisfy the requirements of the central limit theorem.
It is important to note that the sampling distribution of the sample mean will only be exactly normal if the population distribution is normal. However, in most cases, the sampling distribution will be approximately normal, even if the population distribution is not.
Step-by-step explanation:
true or false: the steps in a two sample hypothesis test are twice the number of steps in a one sample hypothesis test.
False. The number of steps involved in each type of hypothesis test depends on the specific details of the problem and the statistical method used.
what is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
False. The steps in a two-sample hypothesis test are not necessarily twice the number of steps in a one-sample hypothesis test.
Both one-sample and two-sample hypothesis tests involve similar basic steps such as stating the null and alternative hypotheses, selecting a significance level, calculating a test statistic, and making a decision to reject or fail to reject the null hypothesis based on the calculated p-value.
However, in a two-sample hypothesis test, there are additional steps required to compare the means or proportions of two different groups or samples. These additional steps involve checking the assumptions of equal variances and independence, calculating a pooled standard error or degrees of freedom, and performing a two-sample t-test or z-test depending on the sample size and distribution.
Therefore, False. the number of steps involved in each type of hypothesis test depends on the specific details of the problem and the statistical method used.
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Choose the INCORRECT statement below.
Answer: #4
Step-by-step explanation:
I haven't done anything like this in years but I think it is the 4th answer :)
Sorry if I'm wrong. I am a year ahead in math and in an honors class so i would think I'm pretty smart
(b)Find the area of square whose its diagonals have length of 12.5cm.
156.25cm
Step-by-step explanation:
The area of a square is L×L
12.5×12.5=156.25cm
Find all positive interger x, y, z so that 2x^5 + y^5 = 3z^5 and 2x + y + 2z is a prime number.
The solution to the system of equations is
x = 3
y = 2
z = 2
Here, we have,
To solve for x, y, and z, we can use the elimination method or substitution method. Here, we will use the elimination method.
First, we will eliminate y from the equations by multiplying the first equation by 3 and the second equation by 1, and then adding them:
(3) (2x – y + 3z = 10)
6x – 3y + 9z = 30
(1) (x + 3y – 2z = 5)
x + 3y – 2z = 5
Adding the two equations gives:
7x + 7z = 35
Simplifying, we get
x + z = 5 (Equation 1)
Next, we will eliminate y again by multiplying the second equation by 2 and the third equation by 3, and then adding them:
(2) (x + 3y – 2z = 5)
2x + 6y – 4z = 10
(3) (3x – 2y + 4z = 12)
9x – 6y + 12z = 36
Adding the two equations gives:
11x + 8z = 46
Substituting x + z = 5 from Equation 1 into the above equation, we get:
11(x + z) + 8z = 46
11x + 19z = 46
Solving for z, we get:
z = 2
Substituting z = 2 into x + z = 5 from Equation 1, we get:
x + 2 = 5
x = 3
Finally, substituting x = 3 and z = 2 into any of the original equations, we can solve for y:
2x – y + 3z = 10
2(3) – y + 3(2) = 10
6 – y + 6 = 10
y = 2
Therefore, the solution to the system of equations is:
x = 3
y = 2
z = 2
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complete question:
Solve for x, y and z
2x – y + 3z = 10
x + 3y – 2z = 5
3x – 2y + 4z = 12
there are seven nickels and six dimes in your pocket. you randomly pick a coin out of your pocket and then return it to your pocket. then you randomly pick another coin. find the probability that both coins are nickels.
Step-by-step explanation:
a probability is airways the ratio
number of desired cases / number of totally possible cases
so, we have 7 nickels and 6 dimes. together that means we have 7+6 = 13 coins in total in the pocket.
since we return the coin from the first pull, we have the exact same probabilities for the second pull.
the 2 pulls are to be considered one combined event, so we need to combine the individual probabilities for the overall event probability.
the probabilty to pull a nickel in a pull is
7/13
7 desired possible outcomes over 13 total possible outcomes.
the combination of the probabilities of both pulls is simply their product.
so, the probability to pull 2 nickels is
7/13 × 7/13 = 49/169 = 0.289940828...