The tables below represents a system of two linear equations in two variables, What is the solution to the system of equations?
Answers
x = 3, y = 4
Explanations:Let us find the equations represented by each of the tables
Calculate the slope for table 1 selecting the points (2, 5) and (3, 4)
\(\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ m\text{ = }\frac{4-5}{3-2} \\ \text{m = }\frac{-1}{1} \\ m\text{ = -1} \end{gathered}\)The equation of the line is given as:
\(\begin{gathered} y-y_1=m(x-_{}x_1) \\ y\text{ - 5 = -1(x - 2)} \\ y\text{ - 5 = -x + 2} \\ y\text{ = -x + 2 + 5} \\ y\text{ = -x + 7} \end{gathered}\)The equation represented by the first table is y = -x + 7
Calculate the slope for table 2 by selecting the points (0, 1) and (1, 2)
\(\begin{gathered} m\text{ = }\frac{2-1}{1-0} \\ m\text{ = 1} \end{gathered}\)\(\begin{gathered} y-y_1=m(x-x_1) \\ y\text{ - 1 = 1 (x - 0)} \\ y\text{ - 1 = x} \\ y\text{ = x + 1} \end{gathered}\)The equation represented by the second table is y = x + 1
The system of equations is:
y = -x + 7..........(1)
y = x + 1...........(2)
Equating equations (1) and (2)
-x + 7 = x + 1
x + x = 7 - 1
2x = 6
x = 6/2
x = 3
Substitute the value of x into equation (2)
y = 3 + 1
y = 4
The solution to the system of equations is x = 3, y = 4
Related Questions
A spherical balloon is being filled with air at the constant rate of 8 cm? sec How fast is the radius increasing when the radius is 6 cm? Submit an exact answer in terms of T. Provide your answer below: cm sec
Answers
A spherical balloon is being filled with air at the constant rate of 8 cm³/sec How fast is the radius increasing when the radius is 6 cm?
Rate of change of radius of sphere 0.0176 cm/sec.
A spherical balloon is filled with air at the constant rate of 8 cm³/sec.
Formula used: Volume of sphere = (4/3)πr³
Differentiating both sides with respect to time 't', we get: dV/dt = 4πr²dr/dt, where dV/dt is the rate of change of volume of a sphere, and dr/dt is the rate of change of radius of the sphere.
We know that the radius of the balloon is increasing at the constant rate of 8 cm³/sec. When the radius is 6 cm, then we can find the rate of change of the volume of the sphere at this instant. Using the formula of volume of a sphere, we get: V = (4/3)πr³
Substitute r = 6 cm, we get: V = (4/3)π(6)³ => V = 288π cm³ Differentiating both sides with respect to time 't', we get: dV/dt = 4πr²dr/dt, where dV/dt is the rate of change of volume of sphere, and dr/dt is the rate of change of radius of the sphere. Substitute dV/dt = 8 cm³/sec, and r = 6 cm,
we get:8 = 4π(6)²(dr/dt)
=>dr/dt = 8/144π
=>dr/dt = 1/(18π) cm/sec
Therefore, the radius is increasing at the rate of 1/(18π) cm/sec when the radius is 6 cm.
Rate of change of radius of sphere = 1/(18π) cm/sec= 0.0176 cm/sec.
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Evaluate: 128{1/7}
a:2
b:4
c:8
d:not a real number
Answers
None of the given answers are correct, The value of 128{1/7} will be a fraction number.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given a number 128{1/7}
Simplification of this number
=> 128(1/7)
=> 18.28
therefore, the Given number is a fraction number or a real number.
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in a study of the function of pectoral fins in fish, a graduate student examined 7 fish with the given lengths (in centimeters, cm). 30 28 29 27 31 25 29what is the variance of these 7 fish lengths?
Answers
The variance of the 7 fish lengths is 15.14.
To find the variance of a set of data, you need to find the mean of the data, subtract the mean from each value, square the differences, and average the squared differences. Here's how you can calculate the variance for the fish lengths:
Find the mean:
30 + 28 + 29 + 27 + 31 + 25 + 29 = 220
mean = 220 / 7 = 31.43
Subtract the mean from each value and square the differences:
(30 - 31.43)^2 = 1.43^2 = 2.04
(28 - 31.43)^2 = 3.43^2 = 11.86
(29 - 31.43)^2 = 2.43^2 = 5.95
(27 - 31.43)^2 = 4.43^2 = 19.68
(31 - 31.43)^2 = 0.43^2 = 0.18
(25 - 31.43)^2 = 6.43^2 = 41.17
(29 - 31.43)^2 = 2.43^2 = 5.95
Average the squared differences:
(2.04 + 11.86 + 5.95 + 19.68 + 0.18 + 41.17 + 5.95) / 7 = 15.14
So the variance of the 7 fish lengths is 15.14.
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find the lateral area and surface area of a triangular prism with a height of 6 inches and a right triangular base with legs of 9 inches and 12 inches. round to the nearest tenth, if necessary.
Answers
Answer:
Lateral surface area is 216 in²Total surface area is 324 in²----------------------
Find the hypotenuse c of the base using Pythagorean theorem:
\(c=\sqrt{a^2+b^2}\)\(c=\sqrt{9^2+12^2} =\sqrt{81+144}=\sqrt{225} =15\)Lateral surface area, three rectangular faces, is:
LSA = Ph = (9 + 12 + 15)*6 = 36*6 = 216Find base area, the area of two right triangles:
A = 2*(1/2)(9)(12) = 108Find total surface area:
TSA = LSA + Base areasTSA = 216 + 108TSA = 324In order to determine if there is a difference between the mean GPA of male and female scholarship athletes, a university administrator obtains a sample of the academic records of past and present scholarship athletes at the university. The administrator reports that the mean GPA (grade point average) of a random sample of 40 male scholarship athletes is 3.02 and the mean GPA of a random sample of 36 female scholarship athletes is 3.11. If there is no difference in the mean GPA of male and female athletes, the probability of obtaining this difference (3.11 – 3.02 = 0.09) or more extreme is approximately 0.287.1. In order to assess the evidence provided by the sample data, what is the appropriate question to ask?a. How likely is it to observe no difference in the mean GPA of male and female scholarship athletes?b. How likely is it to observe a mean GPA difference of 0.09 between male and female scholarship athletes?c. How likely is it to observe a difference of 0.09 or more extreme if there is no difference in the mean GPA for male and female scholarship athletes?d. How likely is it to observe a difference less than 0.09 in the mean GPA of male and female scholarship athletes?2. A university professor does not believe that there is really a difference between the GPA of male and female scholarship athletes, so he looks into how the sample was collected. His investigation shows that the study was given to all of the athletes on the basketball teams exclusively. Based on this information, should the university administration trust the results from this study?a. Yes, because the results were significantb. Yes, because a large enough sample was takenc. No, because not every scholarship athlete part of the studyd. No, because the study was not taken from a random sample of scholarship athletes
Answers
The university administration should not trust the results from this study as it did not take a random sample.
The appropriate question to ask in order to assess the evidence provided by the sample data is, "How likely is it to observe a difference of 0.09 or more extreme if there is no difference in the mean GPA for male and female scholarship athletes?"
This is because the sample data shows a difference of 0.09, so we want to find out how likely it is to observe a difference of this size or greater, given that there is no actual difference between the GPA of male and female scholarship athletes.
Based on the investigation that the professor conducted which revealed that the study was given to all of the athletes on the basketball teams exclusively, the university administration should not trust the results from this study.
This is because the study was not taken from a random sample of scholarship athletes, meaning that the sample did not accurately reflect the population. If the sample does not accurately reflect the population, then the results may be biased and should not be trusted.
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What expression would be easier to simplify if you use the associative property to change the grouping?
A.[(-0.2)+(-0.6)]+1.7
B.(2+5/2)+(-1/2)
C.(60+40)+(-27)
D.6+[4/9+(-2/9)]
Answers
Answer:
B
Step-by-step explanation:
2+5/2 is hard to add since first you have to make 2 into a fraction with the denominator 2. If you use the associative property, you can just easily combine -1/2 and 5/2 without any converting into fractions
Help me i don’t remember how to do this
Answers
help me please i will really appreciate it
Answers
Answer:
84 square cm
Step-by-step explanation:
Step-by-step explanation:
You should not photograph where unless you have permission?
A public park
Your backyard
A parade
Into someone's window
what is y- intercept of y=-3x+5?
Answers
And there’s this app called Cymath you can download
Answer:
y=−1/3 y+5/3
Step-by-step explanation:
PLS BRAINLIEST
ill tell you all the 4 math algebra calculators if you do
solve the literal equation for y
4x+1=9+4y show steps please i am confused
Answers
The solution to the literal equation is y = x - 2.
What is the solution to inequality?To solve inequality in y, we need a number such that the assertion holds if we replace y with that number. Isolating the variable on one side of the inequality and leaving the other terms constant is the first step in resolving the inequality.
From the given information:
4x + 1 = 9 + 4y
To solve for y, we have to switch the sides:
9 + 4y = 4x + 1
Subtract 9 from both sides
9 - 9 + 4y = 4x + 1 - 9
4y = 4x - 8
Divide both sides by 4
\(\dfrac{4y}{4}= \dfrac{4x}{4}-\dfrac{8}{4}\)
y = x - 2
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Select the correct answer.
Simplify the following radical expression.
√48
16√3
4√3
4√2
6√2
Answers
Step-by-step explanation:
\( = \sqrt{48} \)
\( = \sqrt{16 \times 3} \)
\( = \sqrt{ {4}^{2} \times 3 } \)
\( = \sqrt{ {4}^{2} } \times \sqrt{3} \)
\( = 4 \times \sqrt{3} \)
\( = 4 \sqrt{3} \)
The answer is B.
how would I answer this? I've been stuck on this for a while.
Answers
Answer:
a^2+a-6
Step-by-step explanation:
I don't know the full context of what your question is asking for, but I provided the full answer for when you multiply the two together.
________ determines how two sets of data from a sample vary simultaneously.
STDEV. P
COVARIANCE. S
CORREL
STDEV. S
Answers
CORREL determines how two sets of data from a sample vary simultaneously. Option 3, "CORREL", is the correct answer.
What is CORREL?The correlation coefficient between two cell ranges is returned by the CORREL function. To ascertain the connection between two properties, use the correlation coefficient.
The measure that determines how two sets of data from a sample vary simultaneously is called correlation.
Option 3, "CORREL", is the correct answer. Correlation measures the strength and direction of the linear relationship between two variables. It indicates how much one variable changes when the other variable changes, and is typically measured using a correlation coefficient, such as Pearson's correlation coefficient.
The other options listed are also measures of the relationship between two variables, but they measure different aspects of this relationship:
- STDEV.P is the population standard deviation, which measures the spread of a population of values around its mean.
- COVARIANCE.S is the sample covariance, which measures how two variables vary together in a sample.
- STDEV.S is the sample standard deviation, which measures the spread of a sample of values around its mean.
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What is the product of radical 5 and 10 radical 30 in simplest radical form
Answers
The product of radical 5 and 10 radical 30 in simplest radical form is 50√6
What is Expression?An expression is combination of variables, numbers and operators.
We need to find the product of radical 5 and 10 radical 30 in simplest radical form
It can be written as √5×10√30
√a.√b=√ab
√5×10√30
10√5×30
10√150
10√25×6
10.5√6
50√6
Hence, the product of radical 5 and 10 radical 30 in simplest radical form is 50√6
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Answer:
What the other dude said:
The product of radical 5 and 10 radical 30 in simplest radical form is 50√6
Step-by-step explanation:
Consider the pth percentile of a continuous random variable. Which of the following statements are always true? Select all that apply. The area under the curve to the left of the pth percentile is equal to (1-p). The area under the curve to the right of the pth percentile is equal to p. The area under the curve to the left of the pth percentile is equal to p. The area under the curve to the right of the ph percentile is equal to (1-p). The pth percentile is positive.
Answers
The correct statements regarding the pth percentile of a continuous random variable are: the area under the curve to the left of the pth percentile is equal to p, and the area under the curve to the right of the pth percentile is equal to (1-p).
In general, when considering the pth percentile of a continuous random variable, the following statements are always true:
1. The area under the curve to the left of the pth percentile is equal to p: This statement is correct. The pth percentile is the value below which p percent of the data falls. Therefore, the area under the curve to the left of the pth percentile represents p percent of the total area.
2. The area under the curve to the right of the pth percentile is equal to (1-p): This statement is also correct. Since the total area under the curve is equal to 1, the remaining area to the right of the pth percentile is (1 - p).
3. The pth percentile is positive: This statement is not necessarily true. The pth percentile can be positive, zero, or negative depending on the distribution of the random variable. It is possible for a significant portion of the data to fall below zero, resulting in a negative pth percentile.
Therefore, the correct statements are:
- The area under the curve to the left of the pth percentile is equal to p.
- The area under the curve to the right of the pth percentile is equal to (1-p).
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Pentagon ABCDE is reflected across the line shown and then rotated
72 clockwise about its center to create congruent pentagon FGHIJ.
Label the vertices of FGHU in the correct positions on the image.
Answers
Answer:
rotate it once to the right and you will get the vertices
Step-by-step explanation:
\(\left \{ {{y=24} \atop {x=2}} \right.\)
Answers
Please post your question fully !!
Answer:
huh?.............
Step-by-step explanation:
im not smart
an upright cylindrical tank with radius 7m is being filled with water at a rate of 4m3/mm how fast is the height of water increasing round the answer to four decimal places
Answers
The exact rate at which the height of the water is increasing, and we can use it to predict how much the height will increase in any given time interval.
The height of water how fast will increasing?
Let's start by finding the formula for the volume of the cylindrical tank. The volume of a cylinder is given by:
V = πr^2hwhere V is the volume, r is the radius, and h is the height.
To find how fast the height of the water is increasing, we need to take the derivative of the volume with respect to time (t) using the chain rule:
dV/dt = dV/dh * dh/dtwhere dV/dt is the rate of change of volume with respect to time, dV/dh is the rate of change of volume with respect to height, and dh/dt is the rate of change of height with respect to time.
We know that the rate of change of volume is 4 m^3/mm, so:
dV/dt = 4 m^3/mmTo find dV/dh, we take the derivative of the volume formula with respect to h:
dV/dh = πr^2Substituting these values into the chain rule formula, we get:
4 = π(7^2) * dh/dtSimplifying, we get:
dh/dt = 4 / (49π)To explain the result, we have found that the height of the water is increasing at a rate of 4 / (49π) mm/s (rounded to four decimal places).
This means that for every second, the height of the water is increasing by 4 / (49π) mm. As the volume of the cylindrical tank is increasing at a constant rate, the height of the water is also increasing at a constant rate.
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In 146 students in a high school, 56 play football, 49 play soccer and 67 play hockey. From those, 21 play football and hockey, and 14 play soccer and hockey. 3 students only play soccer and football, and 5 students play all. How many students do not participate any those sports? O a. 14 O b. 18 О с. 0 O d. 8 O e. i4
Answers
In a high school with 146 students, the number of students who do not participate in any of the sports mentioned is 8.
To find the number of students who do not participate in any of the sports, we can use the principle of inclusion-exclusion. First, we add up the number of students playing each sport: 56 play football, 49 play soccer, and 67 play hockey.
Next, we subtract the number of students who play two sports. From the given information, we know that 21 play football and hockey, 14 play soccer and hockey, and 3 play soccer and football. However, we need to subtract 5 students who play all three sports (football, soccer, and hockey) only once since we counted them twice when considering each sport individually.
So, the total number of students participating in at least one of the three sports is (56 + 49 + 67) - (21 + 14 + 3) + 5 = 139.
Finally, to determine the number of students who do not participate in any of the sports, we subtract the number of students who play at least one sport from the total number of students in the high school: 146 - 139 = 7.
Therefore, the correct answer is option D: 8.
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If x and y are jointly continuous with joint density function fx,y(x, y), show that X + Y is continuous with density function fx+Y(t) = Lºfx.y(x,1 – x) dx
Answers
The sum of X +Y follows a continuous distribution with a density function given by fx+Y(t) = Lºfx.y(x,1 – x) dx.
We have given a function of two continuous random variables. We need to prove that the sum of two random variables is continuous. Given that x and y are jointly continuous with joint density function fx,y(x, y) and need to show that X + Y is continuous with density function
fx+Y(t) = Lºfx. y(x,1 – x) dx.
In order to prove it, we need to find the marginal distribution of X+Y.
The marginal distribution of X:
fx(x)=∫∞−∞fy(x,y)dy
The marginal distribution of Y:
fy(y)=∫∞−∞fx(x,y)dx
The density of the sum:
fx+Y(t)=∫∞−∞fx(y,t−y)dy
So, the density function of X+Y is as follows:
fx+Y(t)=∫∞−∞fx.y(x, t−x)dx
Hence, X+Y is continuous with density function
fx+Y(t) = Lºfx. y(x,1 – x) dx.
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which is greater, f(2)=81 or g(2)=83? explain and show work please
Answers
f=81/2
81/2=40.5
f=40.5
g(2)=83
g=83/2
83/2=41.5
g>f
g is greater
What is DM?
22 cm
30 cm
38 cm
76 cm
Answers
Answer:
38cm
Step-by-step explanation:
38 is the answer . hope it helps.
Answer:
c. 38 cm
Step-by-step explanation:
Fill in the table using this function rule.
y=25-2x
Answers
Answer:(1,23)(2,21)(4,17)(6,13)
Step-by-step explanation:
Plug in the x values in the graph to the function. For example plug in 2 to it and you get 25-2(2) which transfers to 25-4. 25-4 equals 21
5+14a=9a - 5
Please help
Answers
Answer:
a=2
Step-by-step explanation:
5+14a=9a-5 subtract 9a from both sides
5+5a=-5 subtract 5 from both sides
5a=-10 divide by 5 on both sides
a=-2
hope you do well :)
the normal model n(58,21) describes the distribution of weights of chicken eggs in grams. suppose that the weight of a randomly selected chicken egg has a z-score of -1.41. what is the weight of this egg in grams? round to the nearest hundredth of a gram.
Answers
By using normal distribution, it is obtained that weight of a randomly selected chicken egg is 28.39 grams
What is normal distribution?
Normal distribution is a continuous type probability distribution whose probability density function is
\(\frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{z^2}{2}\)
where, z = \(\frac{x - \mu}{\sigma}\)
\(\mu\) is the mean and \(\sigma\) is the standard deviation
In case of normal distribution
Formula for z = \(\frac{x - \mu}{\sigma}\)
\(\mu\) is the mean and \(\sigma\) is the standard deviation
Let the weight of the egg be x grams
Here, z = -1.41, \(\mu\) = 58 and \(\sigma\) = 21
\(-1.41 = \frac{x - 58}{21}\\\)
x = -1.41 \(\times\) 21 + 58
x = 28.39 grams
Weight of a randomly selected chicken egg is 28.39 grams
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Evaluate. 3/4+(1/2+1/4)^2x2
Answers
Answer:
107/4
Step-by-step explanation:
Answer:
The answer is 1.875
Step-by-step explanation:
Just solved it.
13. Suppose there are 1.5 misprints on a page of a daily newspaper. Find the probability to observe 11 misprints on the first ten pages of this magazine. A 0.000 B 0.066 C 0.101 D None of them
Answers
The probability of observing 11 misprints on the first ten pages of this magazine is given as follows:
B. 0.066.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following mass probability function:
\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)
The parameters are listed and explained as follows:
x is the number of successes that we want to find the probability of.e = 2.71828 is the Euler number\(\mu\) is the mean in the given interval or range of values of the input parameter.Suppose there are 1.5 misprints on a page of a daily newspaper, hence the mean for the first 10 pages is given as follows:
\(\mu = 10 \times 1.5 = 15\)
Hence the probability of 11 misprints is given as follows:
\(P(X = 11) = \frac{e^{-15}(15)^{11}}{(11)!} = 0.066\)
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Help me please I forgot how to do this
Answers
Jeremy has a table with a glass centerpiece. he wants to repaint the wood part black and leave the glass as it is. if the table is 8 ft by 7 ft and the glass centerpiece is 4 ft across, how much paint will jeremy need?
Answers
Jeremy will need enough paint to cover an area of 56 square feet, which corresponds to the wood part of the table.
To determine the amount of paint Jeremy will need to repaint the wood part of the table black, we need to calculate the area of the wood surface.
The table has dimensions of 8 ft by 7 ft, which means the wood surface area is 8 ft multiplied by 7 ft, equaling 56 square feet.
Since Jeremy wants to repaint only the wood part, he does not need to paint the glass centerpiece. Therefore, he will not need any paint for the glass.
Thus, Jeremy will need enough paint to cover an area of 56 square feet, which corresponds to the wood part of the table. The specific amount of paint required will depend on the type of paint and the manufacturer's instructions for coverage per square foot.
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simplify assume that no denominator is equal to zero!! please help!!
Answers
-40 h^3 i^4 j^7