Answer:
Using the Pythagorean theorem we can first put the points into x and y
x1 = 7
y1 = 9
x2 = 1
y2 = 1
The distance between the two points can be found as follows:
d = √((x2 - x1)² + (y2 - y1)²)
= √((1 - 7)² + (1 - 9)²)
= √((-6)² + (-8)²)
= √(36 + 64)
= √100
= 10
Therefore, the distance between the points (7, 9) and (1, 1) is 10 units.
Please help!! Factor the equation and show your work.
x^2 - 4
Answer:
(x-2)( x+2 )
Step-by-step explanation:
Answer:
(x+2)(x-2)
Step-by-step explanation:
x²-4
we going to rewrite 4 as in power so x²-2²
then we going to apply the difference of two squares formula since we have the same format which is x²-y²=(x+y)(x-y) , so x²-2² = (x+2)(x-2)
and that's the answer.
Which two angles are complementary?
Angle A and Angle D
Angle C and Angle E
Angle B and Angle C
Angle A and Angle C
The angles A and C are complementary angles.
How to determine a pair of complementary angles
In this problem we find six possible angles, from which we must determine two angles that are complementary angles. Two angles are complementary when the total measure is equal to 90°. The algebraic formula representing the situation is shown below:
α + β = 90°
Where α, β are angles.
If we know that α = 61° and β = 29°, then the result is:
m = α + β
m = 61° + 29°
m = 90°
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Answer:
A and C
Step-by-step explanation:
a complementary angle is when 2 angles add up to 90 degrees
As for A and C, A’s degree is 29 when C’s 61
29+61 is 90
Use the theorem given below to show that if two rows of a square matrix are equal, then det A=0. The same is true for two columns. Why?
Let A be a square matrix.
a. If a multiple of one row of A is added to another row to produce a matrix B, then det B = det A.
b. If two rows of A are interchanged to produce B, then det B = - det A.
c. If one row of A is multiplied by k to produce B, then det B = k det A.
PLEASE HELP ME I WILL GIVE 43 POINTS HELP ME PLEASE AND FIRST CORRECT ANSWER GETS BRAINLIEST
Answer:
864
Step-by-step explanation:
12x12=144
144x6 because of all the sides
Subtract 1/8 minus 3/4
Answer: 5/8
Step-by-step explanation:
Find the probability that a student scored less than 600 or took less than 4 years of math. SHOW ALL WORK.
The probability that a student scored is 0.8.
How to find the probability?To find the probability that a student scored less than 600 or took less than 4 years of math.
We need to add the probabilities of each of these events occurring separately, and then subtract the probability of both events occurring together.
Let P(L) be the probability that a student scored less than 600 and P(M) be the probability that a student took less than 4 years of math.
We are not given the joint probability of both events, so we need to calculate it using the formula:
P(L and M) = P(L) + P(M) - P(L or M)
where P(L or M) is the probability that a student scored less than 600 or took less than 4 years of math.
Assuming that the events of scoring less than 600 and taking less than 4 years of math are independent, we can calculate their probabilities separately:
P(L) = 0.35 (given)
P(M) = 0.25 (given)
To calculate P(L or M), we add the probability of scoring less than 600 to the probability of taking less than 4 years of math, and then subtract the probability of both events occurring together:
P(L or M) = P(L) + P(M) - P(L and M)
We don't have the value of P(L and M), so we cannot directly calculate P(L or M). However, we know that the sum of probabilities of all possible events is equal to 1.
Therefore, we can use the formula:
P(not L and not M) = 1 - P(L or M)
where P(not L and not M) is the probability that a student scored 600 or more and took 4 or more years of math.
Since we know that the events of not scoring less than 600 and taking 4 or more years of math are complementary to scoring less than 600 or taking less than 4 years of math.
We can use the complement rule to calculate P(not L and not M):
P(not L and not M) = 1 - P(L or M)
= 1 - (P(L) + P(M) - P(L and M))
= 1 - (0.35 + 0.25 - P(L and M))
= 0.4 - P(L and M)
Now we need to find P(L and M) to calculate P(not L and not M). We are not given this probability directly, so we cannot use the product rule.
However, we know that the number of students who scored less than 600 and took less than 4 years of math is 80, and the total number of students is 400. Therefore, we can use the formula:
P(L and M) = number of students who scored less than 600 and took less than 4 years of math / total number of students
= 80 / 400
= 0.2
Substituting this value in the formula for P(not L and not M), we get:
P(not L and not M) = 0.4 - P(L and M)
= 0.4 - 0.2
= 0.2
Therefore, the probability that a student scored less than 600 or took less than 4 years of math is:
P(L or M) = 1 - P(not L and not M)
= 1 - 0.2
= 0.8
So the probability that a student scored less than 600 or took less than 4 years of math is 0.8.
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Tyree is ordering drink coasters with the school logo printed on the top. The coasters are circular with a radius of 1.75 inches. What is the area of each coaster? (Use 3.14 for π)
FILL IN THE BLANK. "Test Yourself
If a and b are positive integers and a | b, then ________ is less than or equal to _______."
If a and b are positive integers and a | b, then a is less than or equal to b.
The notation a | b means that a is a divisor of b, or in other words, b is a multiple of a. Since a is a positive integer and a is a factor of b, it follows that a must be less than or equal to b. This is because b is composed of a and some multiple of a, and so it must be greater than or equal to a.
For example, if a = 3 and b = 15, we know that 3 | 15 since 15 is a multiple of 3. In this case, a is equal to 3 and b is equal to 15, and we can see that a is less than b.
This property is important in number theory and is often used in proofs involving divisibility and prime numbers.
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4b. Jenna went on a 140-mile road trip. When it was not raining, she drove 50 miles per hour. When it was raining, she drove 40 miles per hour. The rest of her trip it did not rain. How much time did it take Jenna to drive the rest of her road trip?
The time Jenna spent driving the rest of her road trip was 2/3 hours.
Let the time Jenna spent driving at 50 mph be t1 and the time spent driving at 40 mph be t2. Also, let the distance covered while it was not raining be d.
We know that t1 + t2 = total time, and d + 2t2 + 2t1 = 140 miles.
Since we know that Jenna drove 50 mph while it was not raining, we can find the distance she covered during that time as d = 50t1.
Similarly, we know that Jenna drove 40 mph while it was raining, so the distance covered during that time can be found as 80t2, since Jenna's speed relative to the road was only 10 mph (50 mph - 40 mph).
Substituting the above values in the second equation, we get:
50t1 + 80t2 = 60
Dividing by 10, we get:
5t1 + 8t2 = 6
Multiplying the above equation by 2, we get:
10t1 + 16t2 = 12
Now, substituting t1 + t2 = total time = 140/50 + t2, we get:
10t1 + 16t2 = 14
Subtracting the above equation from the previous one, we get:
6t2 = 2
Therefore, t2 = 1/3 hours.
Thus, the time Jenna spent driving at 50 mph was t1 = 1.4 - 2t2 = 1.4 - 2/3 = 2/3 hours.
So, the time Jenna spent driving the rest of her road trip was 2/3 hours.
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Edna is finding the volume of a cone and the volume of a cylinder. Both the cone and the cylinder have a radius of 4 inches and a height of 8 inches.
What is the volume of the cone?
Use ≈3.14 and round your answer to the nearest whole number.
and whats the ratios of the cone's volume to the cylinder's volume
The volume of the cone is 58.875 cubic inches. The volume of the cylinder is 176.625 cubic inches. The volume of the cylinder is three (3) times the volume of the cone.
We have,
The volume of a cone is equal to one-third (1/3) of the area of the circular base as well as the height product.
Mathematically, the volume of a cone can be expressed as:
where;
radius = 2.5 inches
height = 9 inches
V = 58.875 in^3
The volume of a cylinder implies the amount of quantity of material being carried in the cylinder. The volume of the cylinder can be expressed as:
V = πr²h
V = π(2.5)² × 9
V = 3.14 × (2.5)² × 9
V = 176.625 inches³
The volume of the cylinder is three times the volume of the cone because:
= 3
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complete question:
1. In ceramics class, Robert made a cone with a radius of 2.5 inches and a height of 9 inches. What was the volume of the cone?
Use ≈3.14 and round your answer to the nearest whole number.
2. Later, Robert made a cylinder with the same radius and height as the cone. What is the volume of the cylinder?
Use ≈3.14 and round your answer to the nearest whole number.
3. Complete the sentence below that describes the relationship between the volumes of the cone and cylinder. Use a whole number.
The cone and cylinder have the same height and radius, so the volume of the cylinder is
____ times the volume of the cone.
It is appropriate to approximate the Poisson distribution with the normal distribution when ....
It is appropriate to approximate the Poisson distribution with the normal distribution when the mean of the Poisson distribution is large (typically, greater than 20).
This is known as the Poisson approximation to the normal distribution or the Poisson limit theorem. As the mean of the Poisson distribution increases, the Poisson distribution becomes more and more like a normal distribution.
The normal distribution is easier to work with mathematically than the Poisson distribution, which is discrete in nature. The normal distribution has a continuous probability density function, which makes it easier to calculate probabilities and work with statistical models. Additionally, the normal distribution has well-known properties, such as the 68-95-99.7 rule, which makes it a useful tool for statistical inference.
However, it is important to note that the approximation may not be accurate for small means. Therefore, if the mean of the Poisson distribution is small, it is better to use the Poisson distribution directly rather than approximating it with the normal distribution.
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If a = 8x + 4 and b = 8x - 4, what is the value of a - b ?
Answer: 8
Step-by-step explanation:
Substitute a-b for the equations given:
8x+4 - (8x-4) = 8x+4-8x+4 = 8
Julia observa en una tienda comercial los precios de una lavadora y las promociones que ofrecen. Las promociones indican descuentos por campaña del 10% y por el día de la madre un descuento adicional del 12%. Si julia compra la lavadora que cuesta 1200 soles haciendo uso de los descuentos ¿ cuanto pagara por todo ??
Por lo tanto, si Julia compra la lavadora haciendo uso de los descuentos, pagaría 950.4 soles por todo.
Si la lavadora cuesta 1200 soles y se ofrece un descuento del 10% por campaña, entonces el precio de la lavadora después del primer descuento sería:
Precio después del primer descuento = 1200 - (10% * 1200) = 1200 - 120 = 1080 soles
Luego, si se ofrece un descuento adicional del 12% por el día de la madre, entonces el precio de la lavadora después de ambos descuentos sería:
Precio después de ambos descuentos = 1080 - (12% * 1080) = 1080 - 129.6 = 950.4 soles
Por lo tanto, si Julia compra la lavadora haciendo uso de los descuentos, pagaría 950.4 soles por todo.
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3). Joshua is playing a video game. The more time Joshua spends on the game, the more levels of the
game he passes. Which of these is the independent variable in this situation?
A. The levels Joshua passes
B. The time Joshua plays
C. The number of levels the game has
D. The number of points he scores
The time Joshua plays the video game is the independent variable. Option B
What is an independent variable?In scientific research, an independent variable is a variable that is manipulated or controlled by the experimenter. It is also known as the predictor variable because it is used to predict changes in the dependent variable.
In the given scenario, the level of the game passed by Joshua is dependent on the time he spends playing the game. The more time he spends playing the game, the more levels he is likely to pass.
Therefore, the time spent playing the game is the independent variable as it is being manipulated and is expected to cause a change in the dependent variable.
The other options such as the number of levels the game has or the points scored by Joshua are not being manipulated in the scenario and do not have a direct effect on the number of levels passed.
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Assuming that a 280-foot tall giant redwood grows vertically, if I walk a certain distance from the tree and measure the angle of elevation to the top of the tree to be 60°, how far from the base of the tree am I? (Round your answer to four decimal places. )
You are approximately 161.5566 feet away from the base of the tree.
To determine the distance from the base of the tree, we can use trigonometry and the concept of tangent.
Let's denote the distance from the base of the tree as "x."
We have a right triangle formed by the tree, the distance from the base, and the angle of elevation. The opposite side of the triangle is the height of the tree, which is 280 feet, and the adjacent side is the distance from the base, denoted as "x."
Using the tangent function, we have:
tan(60°) = opposite/adjacent
tan(60°) = 280/x
To solve for x, we can rearrange the equation:
x = 280 / tan(60°)
Using a calculator, we can evaluate the expression:
x ≈ 280 / 1.7321 ≈ 161.5566
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An ice cream store sells 20 flavors of ice cream. Determine the number of 5 dip sundaes.
How many 5 dip sundaes are possible if order is not considered and no flavor is​ repeated?
There are 15,504 possible 5 dip sundaes that can be made from the 20 flavors of ice cream available at the store.
To find the number of 5 dip sundaes that are possible if order is not considered and no flavor is repeated, we can use the combination formula:
nCr = n! / r!(n-r)!
where n is the total number of flavors (20 in this case), and r is the number of dips in the sundae (5 in this case).
So the number of 5 dip sundaes that are possible is:
20C5 = 20! / 5!(20-5)! = (20 x 19 x 18 x 17 x 16) / (5 x 4 x 3 x 2 x 1) = 15,504
Therefore, there are 15,504 possible 5 dip sundaes that can be made from the 20 flavors of ice cream available at the store.
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If c varies jointly as b and the square root of m,
and c = 168 when b = 10 and m = 36,
find c
when b = 11 and m = 196
The value of c when b = 11 and m = 196 is 954.8.
We have,
c varies jointly as b and the square root of m.
So, c = kbm
Now, put c= 168, b=10 and m= 36
168 = k (10)(36)
168 = k (360)
k = 168/360
k = 21 /45
k = 7/15
Now, we get the equation
c = 7/15 mb
Again, put b = 11 and m =196
c = 7/15 x 11 x 186
c = 14332/15
c= 954.8
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Place the correct function type in the table to show whether the situation could be modeled with a linear or an exponential function. Response area with 5 blank spaces Situation Linear or Exponential? A competition eliminates one-fourth of the participants per round. Blank space 1 empty A pizzeria charges a base price for pizza and then $1.50 for each additional topping. Blank space 2 empty A tutor charges $40 per hour of tutoring. Blank space 3 empty An animal population doubles every 3 months. Blank space 4 empty An electrician charges $125 per house call and then $65 per hour of work. Blank space 5 empty Answer options with 2 options. Answer Options Linear Exponential
The correct function type for each situation:
1) A competition eliminates one-fourth of the participants per round. - exponential
2) A pizzeria charges a base price for pizza and then $1.50 for each additional topping. - linear
3) A tutor charges $40 per hour of tutoring. - linear
4) An animal population doubles every 3 months. - exponential
5) An electrician charges $125 per house call and then $65 per hour of work. - linear
We know that, in order to determine whether fundtion is linear or exponential we chaeck the relationships in the way the y-values change when the x-values increase by a constant amount:
In case of a linear function, the y-values have equal differences.
And in an exponential function, the y-values have equal ratios.
1) A competition eliminates one-fourth of the participants per round.
This is an exponential function.
2) A pizzeria charges a base price for pizza and then $1.50 for each additional topping.
This situation could be modeled with a linear function.
3) A tutor charges $40 per hour of tutoring.
This situation could be modeled with a linear function.
4) An animal population doubles every 3 months.
This situation could be modeled with an exponential function.
5) An electrician charges $125 per house call and then $65 per hour of work.
This situation could be modeled with a linear function.
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Find the complete question below.
Suppose an office manager hopes to establish that a new electronic reporting system decreases the time employees spend filling out travel forms. If they spent an average of 20 minutes filling out travel forms in the past, what hypotheses should the manager test?
The hypotheses that the office manager should test to establish that the new electronic reporting system decreases the time employees spend filling out travel forms are:
Null hypothesis: The average time employees spend filling out travel forms with the new electronic reporting system is equal to or greater than 20 minutes (no significant difference).
Alternative hypothesis: The average time employees spend filling out travel forms with the new electronic reporting system is less than 20 minutes (a significant decrease).
What hypotheses to test to determine if a new electronic reporting system reduces the time employees spend filling out travel forms if they previously spent an average of 20 minutes? The office manager can collect a sample of data on the time it takes employees to fill out travel forms using the new electronic reporting system and calculate the sample mean. They can then use a one-sample t-test to determine if the sample mean is significantly different from 20 minutes at a certain level of significance (usually 5%). If the p-value (the probability of obtaining a result as extreme or more extreme than the observed result if the null hypothesis were true) is less than the level of significance, the null hypothesis can be rejected in favor of the alternative hypothesis, indicating that the new electronic reporting system has significantly decreased the time employees spend filling out travel forms.
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Rita just got a babysitting job. She will work about 10 hours each week and make $9 an hour. Her parents say she needs to save half, but she can spend the other half. Rita estimates she'll have around $50 of spending money each week. Is that a good estimate?
Rita's estimate of $50 is a good estimate, but it's not precise. If she works 10 hours a week and makes $9 an hour, her total will be $90. Half of 90 is 45. This means her spending money each week is $45.
which is read as 'for all x, if x is an apple then x is red or green', or summarised as
'apples are red or green'
The statement "for all x, if x is an apple then x is red or green" can be summarized as "apples are red or green." This means that every apple is either red or green in color.
This can be interpreted as asking for a statement that includes the terms "for all x", "x is red or green", and "apples are red or green". The statement can be phrased as follows:
For all x, if x is an apple, then x is red or green. This can be summarized as "apples are red or green."
Here's a step-by-step explanation:
1. "For all x" means that the statement applies to every element x in a given set or context.
2. "If x is an apple" is the condition that needs to be satisfied for the next part of the statement to be applicable.
3. "Then x is red or green" describes the property that x has if the condition in step 2 is met.
4. Summarizing the entire statement, we can say that "apples are red or green," which implies that if something is an apple, it must be either red or green.
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Graph the function f(x) = 2 (1/2) ^x-7 on the axes below. You must plot the asymptote and any two points with integer coordinates
The vertical line at x = infinity represents the vertical asymptote.
The graph approaches the asymptote but never touches it.
We have,
To graph the function f(x) = 2(1/2)^x - 7, we first need to find the coordinates of the asymptote and two points with integer coordinates.
The function has an asymptote at x = infinity, since as x approaches infinity, the value of 2(1/2)^x approaches 0.
So the line x = infinity is a vertical asymptote for the graph.
To find two points with integer coordinates, we can simply choose two integer values of x and evaluate the function at those values.
Let's choose x = 0 and x = 3.
When x = 0, we have f(0) = 2(1/2)^0 - 7 = -5, so one point on the graph is
(0, -5).
When x = 3, we have f(3) = 2(1/2)^3 - 7 = -6, so another point on the graph is (3, -6).
And,
The dot at (0, -5) represents the point where the graph crosses the y-axis.
The dot at (3, -6) represents another point on the graph.
Thus,
The vertical line at x = infinity represents the vertical asymptote.
The graph approaches the asymptote but never touches it.
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the area of a rectangle is 16/1-3 sq inches.The width is 4 2/3 in.Find the length
If the area of a rectangle is[tex]16\frac{1}{3}[/tex], the width is [tex]4\frac{2}{3}[/tex] in then length of rectangle is 49/14 inches.
Area of rectangle is length time width
Area = Length ×width
[tex]16\frac{1}{3}[/tex]=Length × [tex]4\frac{2}{3}[/tex]
Convert mixed fractions to improper
49/3 = Length × 14/3
Divide both sides by 14/3
length=49/3×3/14
Length=49/14
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What is the x coordinate for the patch (and any other patch on the left face)?
The x coordinate for the patch (and any other patch) on the left face of an object is the smallest x value within the object's domain, as it corresponds to the position of the left face in relation to the coordinate system. All patches on the left face share this same x coordinate value, regardless of their location on the face.
To answer this question about the x coordinate for the patch on the left face, let's break it down:
1. Identify the left face: First, we need to recognize which face of the object is the left face. This is typically the side that faces left when looking at the object in its standard orientation.
2. Find the x coordinate: Since the left face of an object is perpendicular to the x-axis, the x coordinate for any point (or patch) on that face will be the same. This means that all patches on the left face share the same x coordinate value.
3. Determine the specific x coordinate value: To find the actual value of the x coordinate, examine the object's dimensions and/or coordinate system. The x coordinate for the left face will be the smallest x value within the object's domain.
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What conditions must be satisfied to make the probabilities from a binomial probability distribution approximated well by using a normal distribution with a mean μ = np, and a standard deviation σ = √(npq)?
The conditions are: a large enough sample size, probability of success between 0.1 and 0.9, and number of successes and failures both ≥ 10.
How to find the mean and standard deviation for a binomial distribution?The binomial probability must be satisfied to make the probabilities from a binomial probability distribution approximated well by using a normal distribution are:
The sample size, n, must be large enough. A general rule of thumb is that n should be greater than or equal to 20. This ensures that there are enough data points to create a normal distribution.
The probability of success, p, must be between 0.1 and 0.9. If p is too close to 0 or 1, the distribution becomes too skewed and the normal approximation is not accurate.
The number of successes, np, and the number of failures, nq, must both be greater than or equal to 10. This ensures that the normal approximation is accurate enough to be useful.
If these conditions are met, then the probabilities from a binomial probability distribution can be approximated well by using a normal distribution with a mean μ = np, and a standard deviation σ = √(npq). This approximation can be useful in calculating probabilities and making statistical inferences.
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In the analysis of variance procedure (ANOVA), "factor" refers to
a. the dependent variable
b. the independent variable
c. different levels of a treatment
d. the critical value of F
In the analysis of variance procedure (ANOVA), "factor" refers to the independent variable(b).
In the analysis of variance procedure (ANOVA), "factor" refers to the independent variable. ANOVA is used to determine if there is a significant difference between the means of two or more groups, and the factor is the variable being studied that is believed to have an effect on the outcome. Variance is a measure of the variability or spread of the data, and ANOVA compares the variance between groups to the variance within groups to determine if there is a significant difference. The different levels of a treatment are also referred to as levels of the factor.
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The quotient of a rational number by an irrational number is _____ irrational.
Answer:
The quotient of a rational number by an irrational number is generally irrational.
In 2010, the population of a city was 167,000. From 2010 to 2015, the population grew by 8%. From 2015 to 2020, it fell by 3%. How much did the population decrease from 2015 to 2020, to the nearest 100 people?
The population decreased by 5,400 people from 2015 to 2020.
By how much did the population decrease?Also known as population decline, means the reduction in a human population size
Population in 2015 = Population in 2010 + Growth from 2010 to 2015
Population in 2015 = 167,000 + (8% of 167,000)
Population in 2015 = 167,000 + 13,360
Population in 2015 = 180,360
Population in 2020 = Population in 2015 - Decrease from 2015 to 2020
Population in 2020 = 180,360 - (3% of 180,360)
Population in 2020 = 180,360 - 5,411.8
Population in 2020 = 174,948.2
The population decrease from 2015 to 2020 is:
= Population in 2015 - Population in 2020
= 180,360 - 174,948.2
= 5,411.8
= 5,400 to nearest 100 people.
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Find g(x), where g(x) is the translation 9 units up of f(x)= –3x–8.
Write your answer in the form mx+b, where m and b are integers.
g(x)=
To translate a function 9 units up, we need to add 9 to the output (y) of the original function.
So, we can start with the function f(x) = -3x - 8 and add 9 to it:
g(x) = f(x) + 9
g(x) = -3x - 8 + 9
g(x) = -3x + 1
Therefore, g(x) = -3x + 1 is the translation 9 units up of f(x) = -3x - 8.
We can write this in the form mx + b, where m = -3 and b = 1.
So, g(x) = -3x + 1 can be written as g(x) = mx + b, where m = -3 and b = 1.
If a sample of parts is measured and the mean of the measurements is outside the control limits, the process is:
If a sample of parts is measured and the mean of the measurements is outside the control limits, the process is considered to be out of control.
This means that there may be an issue with the process that is causing the measurements to vary significantly from the expected range, and corrective action may be necessary to bring the process back into control.
It is important to investigate the cause of the out-of-control condition and make any necessary adjustments to ensure that the process is producing parts that meet the desired specifications.
If a sample of parts is measured and the mean of the measurements is outside the control limits, it indicates that the process is out of control.
The control limits are the boundaries that are established based on the process's historical data to determine whether the process is in control or out of control.
When a process is in control, its output is predictable and stable within the control limits. However, when the process is out of control, its output is unpredictable and varies beyond the control limits, indicating that there is a problem with the process.
In such a situation, the next step is to identify the source of the problem and take corrective action to bring the process back into control.
This could involve identifying and correcting any issues with the equipment, materials, or methods used in the process.
Additionally, it may involve retraining or revising the procedures followed by the personnel involved in the process.
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