The 90% confidence interval for the proportion of air-conditioners from the population that pass all the tests is (0.94, 1.01).
Confidence Interval: A confidence interval is a range of values used to estimate a population parameter with a certain level of confidence. For example, a 90 percent confidence interval implies that 90 percent of the time, the true population parameter lies within the interval.
To find the confidence interval, we need to first calculate the sample proportion of air-conditioners that pass all the tests. The sample proportion is given as follows:
p = (Number of air-conditioners that passed the tests) / (Total number of air conditioners)
Therefore, the sample proportion is given by: p = (200 - 5) / 200 = 195 / 200 = 0.975
We are given that we need to find the 90% confidence interval for the proportion of air-conditioners from the population that pass all the tests. We can use the standard normal distribution to find the confidence interval.The standard normal distribution has a mean of 0 and a standard deviation of 1. The Z-score corresponding to a 90% confidence level is 1.645.
The formula for calculating the confidence interval is given as follows:
Lower Limit = Sample proportion - Z * (Standard Error)Upper Limit = Sample proportion + Z * (Standard Error), where Z = 1.645 for a 90% confidence levelStandard Error = √(p(1 - p) / n), where p is the sample proportion and n is the sample size.
Substituting the given values, we get:
Standard Error = √(0.975 * 0.025 / 200) = 0.022Lower Limit = 0.975 - 1.645 * 0.022 = 0.94Upper Limit = 0.975 + 1.645 * 0.022 = 1.01Therefore, the 90% confidence interval for the proportion of air-conditioners from the population that pass all the tests is (0.94, 1.01).
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15. JAGUARUNDI A jaguarundi springs from a fence post to swat at a low flying bird.
Her height h in feet can be modeled by the equation h = -161? + 22.31 + 2,
where t is time in seconds. Use the discriminant to determine if the jaguarundi
will reach the bird if the bird is flying at a height of 10 feet. Explain.
Answer:
The discriminant, -14.71 < 0, shows that there is no solution of the equation, h = -16·t² + 22.3·t + 2, at the line 'h = 10' feet, therefore, the Jaguarundi height as she springs will not be up to 10 feet and therefore she will not reach the bird
Step-by-step explanation:
From the question, the equation that models the Jaguarundi's height, 'h', ma be written approximately as follows;
h = -16·t² + 22.3·t + 2
Where;
t = The time (duration) in seconds
The discriminant of the equation a·x² + b·x + c = 0 is b² - 4·a·c
When h = 10, we have;
10 = -16·t² + 22.3·t + 2
∴ 0 = -16·t² + 22.3·t + 2 - 10 = -16·t² + 22.3·t - 8
The discriminant of the given quadratic equation is given as follows;
The discriminant = 22.3² - 4 × (-16 × (-8)) = -14.71 < 0
Therefore, the function, h = -16·t² + 22.3·t + 2 has no real root at h = 10
The parabola does not reach or pass through the line h = 10 which is the height at which the bird is flying.
The Jaguarundi will not reach the bird flying at the height of 10 feet.
Answer:
No, the Jaguarundi will not reach the bird
Step-by-step explanation:
The equation is
[tex]h=-16t^2+22.3t+2[/tex]
When h = 10 feet
[tex]10=-16t^2+22.3t+2[/tex]
[tex]\Rightarrow -16t^2+22.3t-8=0[/tex]
[tex]a=-16[/tex]
[tex]b=22.3[/tex]
[tex]c=-8[/tex]
Discriminant is given by
[tex]b^2-4ac=22.3^2-4(-16)(-8)[/tex]
[tex]\Rightarrow b^2-4ac=-14.71[/tex]
[tex]\Rightarrow b^2-4ac<0[/tex]
So, the Jaguanrundi will not reach the bird as the roots will be imaginary.
Estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints. (Round your answers to four decimal places.)
R4 =
R4 ≈ 1.5535. The given function is f(x) = 5 cos(x).
We have to estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints.
(Round your answers to four decimal places.)
Here is the given function graphically and the approximating rectangles: [tex]\text{graph}\left(5\cos\left(x\right),\ \left(0,\ \frac{\pi}{2}\right)\right)[/tex]
Now, let's find the value of ∆x:∆x = [b-a]/n, here n is the number of rectangles.
∆x = [π/2 - 0]/4= π/8
First, we will find the right endpoints of four approximating rectangles: x1 = ∆x+x0 = π/8+0 = π/8x2 = ∆x+x1 = π/8+π/8 = π/4x3 = ∆x+x2 = π/8+π/4 = 3π/8x4 = ∆x+x3 = π/8+3π/8 = π/2
Now, we will find the height of each rectangle: For rectangle 1: f(x1) = 5 cos(π/8) ≈ 4.8729
For rectangle 2: f(x2) = 5 cos(π/4) ≈ 3.5355For rectangle 3: f(x3) = 5 cos(3π/8) ≈ 1.4645
For rectangle 4: f(x4) = 5 cos(π/2) = 0
Therefore, the area under the curve using four approximating rectangles and right endpoints is:R4 = ∆x (f(x1) + f(x2) + f(x3) + f(x4))R4 = π/8(4.8729 + 3.5355 + 1.4645 + 0)≈ 1.5535 (rounded to four decimal places)
Hence, R4 ≈ 1.5535.
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38. The vertices of a trapezoid are points (0, a), (0,0), (6,0), and (c, a). Find the area in terms
of a, b, and c.
Answer:
(0,6), (6,0)
Step-by-step explanation:
Answer:
Whatttttttttttttttttt
Determine the value of x in the triangle shown.
Question 3 options:
132°
228°
42°
48°
Answer:
x = 132°
Just add the opposite interior angles
Deon wants to replace a glass window in his restaurant. The window is in the shape of a square. Its side lengths are 8 feet. Suppose glass costs $6 for each square foot. How much will the glass cost to replace the window?
Answer:
is 84 dollars
Step-by-step explanation:
Teresa wants to replace a glass window in her restaurant. The window is in the shape of a square. Its side lengths are 6 feet. Suppose glass costs $7 for each square foot. How much will the glass cost to replace the window? Please I really need help ASAP!!!
how many different four-digit ID tags can be made if repeats are allowed
Answer:
4!Explanation:
4! = 4×3×2×1 = 24
here's an example:
123412431324134214231432213421432314234124132431312431423214324134123421412341324213423143124321Which way will the parabola open? Explain.
You randomly choose a marble from a jar. The jar contains 4 red marbles, 10 blue marbles, 7 green marbles, and 6 yellow marbles. Find the probability of the event. Not choosing a blue marble.
Answer:
17/27
Step-by-step explanation:
Since there are 10 blue marbles, and 27 total marbles, the probability of not choosing a blue marble is 17/27 because you subtract the amount of blue marbles (10) from the amount of total marbles (27).
The probability of not choosing a blue marble is 17/27.
What is probability?
Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.
For the given situation,
Number of red marbles = 4
Number of blue marbles = 10
Number of green marbles = 7
Number of yellow marbles = 6
The event is the probability of not choosing a blue marble is
⇒ [tex]\frac{red+green+yellow}{Total marbles}[/tex]
⇒ [tex]\frac{4+7+6}{27}[/tex]
⇒ [tex]\frac{17}{27}[/tex]
Hence we can conclude that the the probability of not choosing a blue marble is 17/27.
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Please help!!
A school is constructing a rectangular play area against an exterior wall of the school
building. It uses 120 feet of fencing material to enclose three sides of the play area.
Answer:
Step-by-step explanation:
Question says that it uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides. Putting this into equation, we have something like this.
120 = L + 2W
Where
LW = area.
Again, in order to maximize the area with the given fencing, from the equation written above, then Width, w must be = 30 feet and length, l must be = 60
On substituting, we have
A = LW = (120 - 2W) W
From the first equation, making L the subject of the formula, we have this
L = 120 - 2W, which then we substituted above.
On simplification, we have
L = 120W -2W²
Differentiating, we have
A' = 120 - 4W = 0
Remember that W = 30
So therefore, L = 120 - 2(30) = 60 feet
The required length of the rectangular garden is 60 feet
Area of rectangular shapeAccording to the question, the school uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides.
Substitute into the perimeter of the rectangle will give:
120 = L + 2W
Area = LW
In order to maximize the area with the given fencing, from the equation written above, then w = 30 feet and l = 60
On substituting, we have;
A = LW = (120 - 2W) W
L = 120 - 2W,
On simplification, we have
L = 120W -2W²
Differentiating, we have
A' = 120 - 4W = 0
Remember that W = 30
So therefore, L = 120 - 2(30) = 60 feet
Hence the required length of the rectangular garden is 60 feet
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HELP PLS YALL HDHDGDUSHSHXHHXXHHXHXBXBXXHDBBDBDBDBDD
Answer:
with what?
Step-by-step explanation:
Answer this question to get marked as barinliest!!!!
3.14 × 16 = 50.24
C is ur answer
now gimme brainliest
Answer:
B or the second one i did my math
Step-by-step explanation:
Help, I don't want to lose my answer streak.
Answer:
[tex]4\frac{5}{12}[/tex]
Step-by-step explanation:
[tex]4\frac{3}{4} -\frac{1}{3} \\\\\frac{19}{4} -\frac{1}{3} \\\\\frac{57}{12} -\frac{4}{12} \\\\\frac{53}{12} \\\\4\frac{5}{12}[/tex]
Answer:
leon's older brother is 4 5/12 feet tall
Step-by-step explanation:
4 3/4 - 1/3
= 4 5/12
provide the missing information. the function f : = {(1, 5), (-2, 3), (-4, 2), (2, 5)} (is/is not) a one-to-one function. please respond only with: is or is not answer:
The function f: {(1, 5), (-2, 3), (-4, 2), (2, 5)} is a one-to-one function. It satisfies condition where each input value maps to unique output value, ensuring no repetition or multiple inputs leading to the same output.
A one-to-one function, also known as an injective function, is a type of function where each input value is uniquely mapped to an output value. In the given function f: {(1, 5), (-2, 3), (-4, 2), (2, 5)}, we can observe that each input value corresponds to a distinct output value. For example, the input 1 is mapped to the output 5, and no other input has the same output. Similarly, the inputs -2, -4, and 2 are associated with the outputs 3, 2, and 5 respectively, without any repetition.
This lack of repetition or duplication in the outputs demonstrates that the function is one-to-one. Each input has a unique correspondence with its output, and no two different inputs yield the same output value. Therefore, based on the provided set of mappings, we can conclude that the function f is indeed a one-to-one function.
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Find the slope of the line:
A health psychologist wants to test the effectiveness of a new stress-reduction method. In the general population, stress level is normally distributed with μ = 40 and σ = 10. 40 randomly selected people are trained in the method; the mean score afterward is 36.
6. Restate question as a research hypothesis and a null hypothesis about the populations.
Population 1:
Population 2:
Research hypothesis:
Null hypothesis:
7. Determine the characteristics of the comparison distribution.
8. Determine the cutoff sample score (or Z score) on the comparison distribution at which the null hypothesis should be rejected at p < .01.
The cutoff sample score is therefore:40 - 2.326(1.5811) ≈ 36.59
The research hypothesis and null hypothesis about the populations can be restated as follows:Population 1: The population of people who have not received the new stress-reduction method training.Population 2: The population of people who have received the new stress-reduction method training.Research hypothesis: The new stress-reduction method training has reduced stress levels in the population that has received it compared to the population that has not.Null hypothesis: The new stress-reduction method training has not reduced stress levels in the population that has received it compared to the population that has not.7. The comparison distribution in this case is the distribution of means from samples of the population that has not received the new stress-reduction method training. This distribution has a mean (μ) equal to the population mean of 40 and a standard deviation (σ) equal to the population standard deviation divided by the square root of the sample size, which is σ/√n = 10/√40 = 1.5811.8. To determine the cutoff sample score (or Z score) on the comparison distribution at which the null hypothesis should be rejected at p < .01, we need to find the z-score corresponding to a probability of .01 in the right tail of the distribution. This is given by:z = invNorm(0.99) ≈ 2.326Therefore, if the sample mean of the population that has received the new stress-reduction method training is more than 2.326 standard errors below the mean of the comparison distribution (which is 40), the null hypothesis can be rejected at the 0.01 level of significance.
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6. Restate question as a research hypothesis and a null hypothesis about the populations.
Population 1: The population of people who do not follow the stress-reduction method.
Population 2: The population of people who are trained in the stress-reduction method.
Research hypothesis: The mean score of population 2 is significantly less than the mean score of population 1, indicating that the stress-reduction method is effective in reducing stress levels.
Null hypothesis: There is no significant difference between the mean score of population 1 and population 2, indicating that the stress-reduction method is not effective in reducing stress levels.
7. The mean of the comparison distribution will be equal to the mean of the population of people who follow the stress-reduction method (which is 40), and the standard deviation of the comparison distribution will be equal to the standard deviation of the population of people who follow the stress-reduction method (which is 10 / sqrt(40) = 1.58).
8. The Z score of the sample mean is less than -2.33, we can reject the null hypothesis at p < .01. Since the Z score of the sample mean is -2.52, we can reject the null hypothesis at p < .01.
6. Restate question as a research hypothesis and a null hypothesis about the populations.
Population 1: The population of people who do not follow the stress-reduction method.
Population 2: The population of people who are trained in the stress-reduction method.
Research hypothesis: The mean score of population 2 is significantly less than the mean score of population 1, indicating that the stress-reduction method is effective in reducing stress levels.
Null hypothesis: There is no significant difference between the mean score of population 1 and population 2, indicating that the stress-reduction method is not effective in reducing stress levels.
7. To determine the characteristics of the comparison distribution.
The comparison distribution is the distribution of sample means if we drew all possible samples of the same size from the population of interest.
In this case, we have a sample of 40 people who were trained in the stress-reduction method, so the comparison distribution will be a distribution of sample means of size 40 from the population of people who follow the stress-reduction method.
The mean of the comparison distribution will be equal to the mean of the population of people who follow the stress-reduction method (which is 40), and the standard deviation of the comparison distribution will be equal to the standard deviation of the population of people who follow the stress-reduction method (which is 10 / sqrt(40) = 1.58).
8. To determine the cutoff sample score (or Z score) on the comparison distribution at which the null hypothesis should be rejected at p < .01.
To find the cutoff sample score (or Z score), we need to calculate the Z score of the sample mean (36) using the formula:
Z = (X - μ) / (σ / sqrt(n))
Z = (36 - 40) / (10 / sqrt(40))
Z = -2.52
The cutoff sample score (or Z score) on the comparison distribution at which the null hypothesis should be rejected at p < .01 is the Z score that corresponds to a probability of .01 in the upper tail of the distribution, which is equal to 2.33.
Therefore, if the Z score of the sample mean is less than -2.33, we can reject the null hypothesis at p < .01. Since the Z score of the sample mean is -2.52, we can reject the null hypothesis at p < .01.
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Use the z -score formula, z=x−μσ z = x − μ σ , and the information below to find the mean, μ . Round your answer to one decimal place, if necessary.
z = 2.25 x = 14.6 0 =3.6
The mean value is 6.5.
Given, z = 2.25, x = 14.6, σ = 3.6
The formula to calculate the z-score is,
z-score, z = (x - μ) / σOn
substituting the given values in the above formula, we get
2.25 = (14.6 - μ) / 3.6
Multiplying both sides by 3.6, we get,
2.25 * 3.6 = 14.6 - μ8.1 = 14.6 - μ
Subtracting 14.6 from both sides, we get,
-6.5 = -μOn multiplying both sides by -1, we get,
μ = 6.5
Hence, the mean value is 6.5.
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The decimal place z -score formula, z=x−μσ z = x − μ σ the mean (μ) is 6.5.
To find the mean (μ) using the z-score formula the Solve for μ
z = (x - μ) / σ
substitute the given values into the equation
2.25 = (14.6 - μ) / 3.6
solve for μ:
2.25 × 3.6 = 14.6 - μ
8.1 = 14.6 - μ
To isolate μ, subtract 14.6 from both sides:
8.1 - 14.6 = -μ
-6.5 = -μ
multiplying both sides by -1 gives
6.5 = μ
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Determine the p-value for the two-tailed t-test with df = 19 (remember, H_1: µ ≠ µo) and sample t = -0.36. At a significance level of α = .01 do you reject or retain the null hypothesis?
The p-value for the two-tailed t-test with degrees of freedom (df) = 19 and a sample t-value of -0.36 is greater than the significance level of α = 0.01. Therefore, we retain the null hypothesis.
In a two-tailed t-test, the null hypothesis (H₀) states that there is no significant difference between the population mean (µ) and a hypothesized mean (µo). The alternative hypothesis (H₁) states that the population mean is not equal to the hypothesized mean.
To determine the p-value, we compare the absolute value of the sample t-value (-0.36 in this case) with the critical t-value for the given degrees of freedom (df = 19). Since the sample t-value falls within the acceptance region, we find the probability of obtaining a t-value as extreme as -0.36 (or more extreme) assuming the null hypothesis is true.
If the p-value is less than the significance level (α = 0.01), we reject the null hypothesis. However, if the p-value is greater than the significance level, we retain the null hypothesis. In this case, since the p-value is greater than 0.01, we do not have sufficient evidence to reject the null hypothesis. Therefore, we retain it.
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it is now twenty-one minutes to ten. what time will it be in 5 hours and 17 minutes? write your answer using numbers and a colon (for example, 11:58).
The time after 21 minutes from 9:39 is 2:56am.
Given that it is now twenty-one minutes to ten, we need to determine the time in 5 hours and 17 minutes.
To find the answer, we can add 5 hours and 17 minutes to the current time, which is 9:39 PM. Let's first convert the hours to minutes:5 hours = 5 x 60 = 300 minutes.
Then, add 300 minutes and 17 minutes:300 minutes + 17 minutes = 317 minutes.
Since there are 60 minutes in an hour, we need to divide 317 by 60 to determine the number of hours:317 / 60 = 5 with a remainder of 17.
Therefore, the time in 5 hours and 17 minutes will be 2:56 AM.
To check our answer, we can work backward:
Start with 2:56 AM and subtract 5 hours and 17 minutes:2:56 AM - 5 hours = 9:56 PM9:56 PM - 17 minutes = 9:39 PMAs expected, we arrived back at the original time of 9:39 PM. Therefore, the final answer is 2:56.
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please answer the question
Answer:
I think it is 25÷8
Step-by-step explanation:
this is because the circumference is found by π multiplied by the diameter. So the inverse would be the circumference divided by the diameter.
Question 5 Multiple Choice Worth 5 por 03 01 LC) The social studies teacher wants to know whether the students in the entire school prefera model United Nations random sample from the following groups Al teachers in the school . Al boys in each grado • A students in each grado All students in the social studies club Which group best represents the population he should take a random sample from to get the best for ham O Al teachers in the school O All boys in each grade O All students in each grade O AB students in the social studios club
Answer:
D
Step-by-step explanation:
For 1-4, a line has the points (-2,-9),
(3, 1), and (6, 7). Find the polnts for the
translation described.
1. 6 units to the left
2. 3 units down
3. 5 units to the right
4 2 units up
Answer:
3 units down
Step-by-step explanation:
got it right on edg
During a blind taste test of 8 different sodas, some people were asked to choose a favorite. Each dot represents one person. If the ratio of people choosing B to people choosing H stays the same, he many people will choose H if the number of people who choose B increases to 20
Answer:
20:5
Step-by-step explanation:
1. What is the ratio for B and H?
Ratio = 4 to 1 or 4:1
2. What is the question asking?
The question is increasing 5 to 20. What is the quotient of 20 and 5? 4! The question is basically multiplying B by 5. Now, since math is a very jealous subject, it needs to be done on the other side too! So you need to multiply the B, which is 1, by 5.
3. 1 x 5?
5
4. Answer
So, since B is 20 and H is 5, the ratio would be 20:5!
Hiii, so I REALLY want to rank up, and I just need 4 more Branliests, so if you liked my answer, can you please give me one? Thank you so much, and thanks for the points!!
Answer:
Step-by-step explanation:
J
y=(2.5)^x graph and match function
Answer:
Step-by-step explanation:
a graph represents the perimeter y in units for an equilateral triangle
If the graph represents the perimeter (y) in units for an equilateral triangle, we can determine the relationship between the perimeter and the side length of the triangle.
In an equilateral triangle, all three sides are equal in length. Let's denote the side length of the equilateral triangle as x.
The perimeter (P) of an equilateral triangle is given by the formula:
P = 3 * x
Therefore, the relationship between the perimeter (y) and the side length (x) of the equilateral triangle is:
y = 3x
So, if the graph represents the perimeter (y) in units for an equilateral triangle, it would be a linear function with a slope of 3 and the side length (x) as the independent variable.
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What is the percent of change? Round to the nearest whole percent if necessary. State whether the percent of change is an increase or decrease. $99 to $74
Marcus asked 10 people at a juggling festival what age they were when they started to juggle
Question
Marcus asked 10 people at a juggling festival what age they were when they started to juggle. Which interval contains the median age?
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]n = 10[/tex]
Required
The median interval
The question is incomplete, as the required data is not given.
To solve this question, I will use the following assumed dataset.
[tex]Age:17\ 17\ 18\ 20\ 21\ 22\ 22\ 24\ 28\ 28[/tex]
First, calculate the median position.
[tex]Median = \frac{n+1}{2}\ th[/tex]
[tex]Median = \frac{10+1}{2}\ th[/tex]
[tex]Median = 5.5\ th[/tex]
This implies that the median is the mean of the 5th and 6th data
So, we have the interval to be.
[tex]Median = [5th, 6th][/tex]
[tex]Median=[21,22][/tex]
Generally, the median of 10 data set is located at interval 5 to 6
if h(x)=3^x then h (-4) =
Answer:
1/81
Step-by-step explanation:
In h(x)=3^x, replace each instance of x with -4:
h(-4) = 3^(-4), or
1
h(-4) = ----------- = 1/81
3^4
[tex]\huge{\mathbb{\tt { PROBLEM:}}}[/tex]
if h(x)=3^x then h (-4) =
[tex]\huge{\mathbb{\tt { ANSWER:}}}[/tex]
[tex] \frac{1}{81} [/tex]
[tex]\huge{\mathbb{\tt { EXPLANATION:}}}[/tex]
In h(x) = 3^x , you must replace each instance of with -4:
h(-4)=3^(-4)
[tex]h(4)= \frac{1}{3^4} = \frac{1}{81} [/tex]
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→X x K i m 0 2 x XTwo ovens have measurements as shown. Which oven has a greater volume? How much greater is
its volume?
The question is incomplete:
Two ovens have measurements as shown. Which oven has a greater volume? How much greater is its volume?
The image with the information is below.
Answer:
-Oven B has a greater volume.
-Its volume is greater by 768 in³.
Step-by-step explanation:
First, you have to calculate the volume of each oven by multiplying the area of the base by the height:
Oven A: 576 in²*15 in= 8640 in³
Oven B: 672 in²*14 in= 9408 in³
Now, you have to calculate the difference between the volumes:
9408-8640=768
According to this, the answer is that oven B has a greater volume. Its volume is greater by 768 in³.
What is the area of the triangle?
24
7
25
units2
PLZ HELP I WILL GIVE BRAINLIEST Question 3
What are three different types of solutions you can get when you solve a system of
linear equations?
Answer:
Answer:
one solution
infinite number of solutions
no solutions
Step-by-step explanation:
i hope this helps :)