Given the points:
C = (10, -1) → x = 10; y = -1;
D = (-6, 3) → x = -6; y = 3.
To find the distance CD, follow the steps below.
Step 1: Substitute the values in the distance formula.
\(\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(-6-10_{})^2+(3_{}-(-1))^2} \end{gathered}\)Step 2: Solve the values inside the parentheses.
\(\begin{gathered} d=\sqrt[]{(-16)^2+(4)^2} \\ d=\sqrt[]{256+16} \\ d=\sqrt[]{272} \end{gathered}\)Step 3: Solve the square root and find d.
\(\begin{gathered} d=\sqrt[]{272} \\ d=16.5 \end{gathered}\)Answer: The distance CD is 16.5.
List the values in ascending order: -94%, -8/9, -.925, and -9/10
Answer:
-94%, -.925, -9/10, -8/9
Step-by-step explanation:
-.94, -.8, -.925, -.9
-.94, −0.925, −0.9, -0.8
is the model a good fit for the data? explain. a. no; the data are too far from the line of fit. b. no; the data are too close to the line of fit. c. yes; the data are distributed evenly around the line of fit. d. yes; the line of fit touches at least one point in the data set.
According to the statement the correct answer is option C - yes, the data are distributed evenly around the line of fit.
To determine if a model is a good fit for a data set, one needs to evaluate how closely the data points align with the line of fit. The line of fit represents the best possible straight line that can be drawn through the data points. If the data points are too far from the line of fit or too close to the line of fit, then it is an indication that the model is not a good fit for the data.
Option A states that the data points are too far from the line of fit, indicating that the model is not a good fit for the data. Option B states that the data points are too close to the line of fit, which is not necessarily a good or bad thing as it depends on the level of accuracy required for the analysis. Option C states that the data points are evenly distributed around the line of fit, which indicates that the model is a good fit for the data. Lastly, option D states that the line of fit touches at least one point in the data set, which is not sufficient to determine if the model is a good fit for the entire data set.
Therefore, the correct answer is option C - yes, the data are distributed evenly around the line of fit.
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Pls do this for me asap
What are the coordinates of the point?
(6, −3)
(−3, −6)
(3, 6)
(−3, 6)
Answer:
(-3,6)
Step-by-step explanation:
As graph shows x=-3 and y=6
Answer:
-3 to +6 is the answer to the question
There are 11 pens in a box : 5 pens are red , 4 pens are blue and 2 pens are green. One pen is selected at random from the box. What is the probability that pen is green?
Answer: 18.2%
Step-by-step explanation:
Using the color of the pen/the total pen amount you can get 18.1818181818181818... which rounded up to the tenth is 18.2%
An albatross is a large bird that can fly 400 kilometers in 8 hours at a constant speed. Using d for distance in kilometers and t for number of hours, an equation that represents this situation is d=50t. What are two constants of proportionality for the relationship between distance in kilometers and number of hours? Enter the larger of the two constants of proportionality.
Distance (d): 400 km
Time (t)= 8 hours
Direct relation formula: y=kx
Where k is the constant of proportionality.
d=50t
k=50
Constant of proportionality is
Find the midpoint of the line segment with end coordinates of:
(
−
4
,
−
2
)
and
(
−
2
,
−
10
)
Answer:
this is the answer (-3,-6)
There are four inequalities that define the region R.
One of these is y
Find the other three inequalities,
Answer:
\(y\geq 0\\y\geq \frac{3}{2}x-3\\ y\leq -x+3\)
Step-by-step explanation:
The region R is surrounded by 4 lines, the first one is y=x+1, the second one is y=0 or the axis x, and the third and fourth one need to be calcualted.
To find the equation of a line through the points (x1,y1) and (x2, y2) we can use the following equation:
\(y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)
Then, our third line is going to be the line that passes through the points (2,0) and (4,3), so the equation is:
\(y=\frac{3-0}{4-2}(x-2)\\y=\frac{3}{2}x-3\)
Our fourth line is the line that passes through the points (3,0) and (0,3), so the equation is:
\(y=\frac{3-0}{0-3}(x-3)\\y=-x+3\)
Then we can say that the other three inequalities are:
\(y\geq 0\\y\geq \frac{3}{2}x-3\\ y\leq -x+3\)
Beverly is making peanut butter-banana bread. She always doubles the amount of nuts and peanut butter chips. The total amount of chips and nuts after doubling is 4 1/2 cups. The recipe says one and a half cups of peanut butter chips, an unknown number of cups of nuts, and three very ripe bananas. Write and solve an equation to find the original amount of nuts, x, in the recipe.
Answer:
0.75 or three-fourth of a cup of nuts.
Step-by-step explanation:
Given that:
Original recipe has
1. One and half cups of peanut butter
2. Unknown number of cups of nuts, let this amount be \(x\) cups.
3. Three very ripe bananas.
Total amount of chips and nuts after doubling = \(4\frac{1}{2}\) cups
Before doubling, total amount of chips and nuts = \(4\frac{1}{2} \div 2 = 2.25\)
Now, as per given question statement:
\(2.25=x+1.5\)
Subtracting the number 1.5 from both the sides to find the value of \(x\):
\(2.25-1.5=x\\\Rightarrow x = \bold{0.75}\)
Therefore, 0.75 or three-fourth of a cup of nuts is the original amount in the recipe.
Bianca can run 5 miles in 41 minutes. Assuming she runs at a constant rate, write the linear equation that represents the situation.
Answer:
y=5/41x
Step-by-step explanation:
Alright, so we can get imagine two points. Imagine that the y axis is miles and the x axis is minutes. When bianca runs 0 miles, she would have run for 0 minutes, and we know that when Bianca runs 5 miles, she would have run for 41 minutes.
We can use slope formula using the change in y over change in x
\((y1 -y2)/(x1-x2)\\\)
So substituting values, we would get (5-0)/(41-0) or 5/41
slope is the letter m in the formula y=mx+b
so our equation would be \(y=\frac{5}{41}x+b\), b being the y intercept, which would be 0 as you cant run anything when no time has passed
Knowing all of this. the final equation is
\(y=\frac{5}{41}x\)
if your target number of calories is 1,703 per day to lose weight, but you are consuming 2,399 calories per day, then your target is to consume what percent of the calories you are consuming? round to the nearest whole number.
If your target number of calories to lose weight is 1,703 per day, but you are consuming 2,399 calories per day, then your target is to consume approximately 70% of the calories you are currently consuming.
To find the percentage of the target calories in relation to the current calories, we can divide the target calories by the current calories and multiply by 100. So, the calculation would be:
Percentage = (Target Calories / Current Calories) * 100
Substituting the values, we get:
Percentage = (1,703 / 2,399) * 100 ≈ 70%
Therefore, your target is to consume approximately 70% of the calories you are currently consuming in order to meet your weight loss goal.
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A car travels 120 mi on 6 gal of gasoline.
What is the car's unit rate and what does it mean?
Enter your answers in the boxes.
The unit rate is
This means the car travels
mi on 1 gal of gas.
Answer:
The unit rate is: 20 miles/gallon
This means the car travels 20 miles on 1 gal of gas.
Step-by-step explanation:
120 miles/ 6gallons
This means that for every gallon of gasoline, the car travels 20 miles
What is the equation of the line that passes through the point (-6,5)(−6,5) and has a slope of 1/2?
Answer: y=0.5x+8
Step-by-step explanation:
Question 38.
Write the first six terms of the arithmetic sequence with the first term, a1 = 240, and common difference, d= 24.
The first six terms are a1 = ,a3= , a4= ,a5= , and a6= .
\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)
Let f(x) = x² (ln x - 1). (a) Find the critical numbers of f. (b) Find the open interval(s) on which f is increasing and the open interval(s) on which f is decreasing. (c) Find the local minimum value(s) and local maximum value(s) of f, if any. (d) Find the open interval(s) where f is concave upward and the open interval(s) where f is concave downward. (e) Find the inflection point(s) of the graph of f, if any.
Then (a) x = 0 and x = e(1/2) are f's crucial numbers.
(b) To pinpoint the locations where f is rising and falling, we need
(a) To find the critical numbers of f, we need to find where its derivative is equal to zero or undefined. We have:
f(x) = x² (ln x - 1)
f'(x) = 2x (ln x - 1) + x
Setting f'(x) equal to zero and solving for x, we get:
2x (ln x - 1) + x = 0
x (2ln x - 1) = 0
x = 0 or x = e^(1/2)
To check whether f'(x) is undefined at any point, we look for values of x where ln x is undefined. However, ln x is defined for all x greater than 0, so f'(x) is defined for all x greater than 0.
Therefore, the critical numbers of f are x = 0 and x = e^(1/2).
(b) To determine where f is increasing and decreasing, we need to examine the sign of f'(x) on different intervals. We have:
f'(x) = 2x (ln x - 1) + x
f'(x) = x (2ln x + 1) - 2x
f'(x) = x (2ln x + 1 - 2)
f'(x) = x (2ln x - 1)
f'(x) is positive when 2ln x - 1 > 0 or ln x > 1/2, which means x > e^(1/2). Therefore, f is increasing on the interval (e^(1/2), infinity).
f'(x) is negative when 2ln x - 1 < 0 or ln x < 1/2, which means 0 < x < e^(1/2). Therefore, f is decreasing on the interval (0, e^(1/2)).
(c) To find the local minimum and maximum values of f, we need to examine the sign of f'(x) around the critical numbers. We have:
At x = 0, f'(x) = 0 + 0 = 0.
At x = e^(1/2), f'(x) = 2e^(1/2) (ln e^(1/2) - 1) + e^(1/2) = 0.
Therefore, both x = 0 and x = e^(1/2) are critical points of f.
To determine whether they are local minimum or maximum points, we need to examine the sign of f''(x) at these points. We have:
f''(x) = 2(ln x - 1) + 2 + x/x
f''(0) = 2(ln 0 - 1) + 2 + 0/0 = undefined
Therefore, x = 0 is not a local minimum or maximum point.
f''(x) = 2(ln x - 1) + 2 + x/x
f''(e^(1/2)) = 2(ln e^(1/2) - 1) + 2 + e^(1/2)/e^(1/2) = 1/e^(1/2) > 0
Therefore, x = e^(1/2) is a local minimum point of f.
(d) To find where f is concave upward and concave downward, we need to examine the sign of f''(x) on different intervals. We have:
f''(x) = 2(ln x - 1) + 2 + x/x
f''(x) is positive when ln x -
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Which one is correct ; BODMAS , BOMDAS, BIDMAS or PIDMAS?
Answer:
BODMAS
Step-by-step explanation:
BODMAS is correct.
Brackets
Of
Division
Multiplication
Addition
Subtraction
*Mathematics - Worth 20 Points* Kareem cannot decide which of two washing machines to buy. The selling price of each is $720. The first is marked down by 50%. The second is marked down by 30% with an additional 20% off. Find the sale price of each washing machine.
Answer:
see explantion
Step-by-step explanation:
The selling price is $495.
The first washing machine:
- is marked down by 30%
$495 - 100%
$x - 100% - 30% = 70%
Find the value of x:
The second washing machine:
- is marked down by 20% with an additional 10% off
$495 - 100%
$y - 100% - 20% = 80%
Find y:
Now,
$396 - 100%
$z - 100% - 10% = 90%
Find z:
Thus, the sale price of the first washing machine is $347 and the sale price of the second washing machine is $356. The second machine is more expensive.
Data obtained from a number of women clothing stores show that there is a (linear) relationship between sales (y, in dollars) and advertising budget (x, in dollars). The regression equation was found to be
y = 5000+ 7.25x
where y is the predicted sales value (in dollars). If the advertising budgets of two women clothing stores differ by $30,000, what will be the predicted difference in their sales?
Select one:
a. $150,000,000
b. $222,500
c. $5,000
d. $7250
e. $217,500
Therefore, the predicted difference in sales between two women's clothing stores differing by $30,000 is $217,500, which is option E.
Given a regression equation is y = 5000 + 7.25x, where y is the predicted sales value (in dollars) and x is advertising budget (in dollars).To find the predicted difference in sales of two stores which differ by $30,000 in advertising budget. Here, the slope of the line is 7.25. This means that for every dollar increase in advertising budget, sales will increase by $7.25. Therefore, a $30,000 difference in advertising budget will lead to a difference in sales of:7.25 × 30,000 = 217,500Therefore, the predicted difference in sales between two women's clothing stores differing by $30,000 is $217,500, which is option E.
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plzz solve this question
Answer:
cosecA
Step-by-step explanation:
sinA+2cosA/sin^2A+2sinAsinA+2cosA/sin^2A+2sinA.cosAsinA+2cosA/sinA×(sinA+2cosA)1/sinAcosecAWhat is the mode of the following set of numbers: 1, 2, 3, 2, 1, 5, 6, 1?#
PLS ANSWER I WILL MARK AS BRAINLIST
Answer:
5579183747482837371828282
The American Academy of Pediatrics recommends that parents begin reading to their children soon after birth and that parents set limits on screen time. A new study reinforces these recommendations. In the study, 27 four-year-olds were presented with stories in three different formats: audio (sound only), illustrated (sound and pictures), and animated (sound and animation). During the presentations, a magnetic resonance imaging (MRI) machine measured each child’s brain connectivity. The researches found a "Goldilocks effect," in which audio was too cold (with low brain connectivity as the children strained to understand) and animation was too hot (with low brain connectivity as the animation did all the work for the children). The highest connectivity (just right!) was found with the illustrated format, which simulates reading a book to a child.
a)What is the explanatory variable? Is it categorical or quantitative?
b)What is the response variable? Is it categorical or quantitative?
c)How many observational units (or individuals) are there?
a) The explanatory variable in the study is the format of the stories presented to the four-year-olds: audio, illustrated, and animated. This variable is categorical because it involves distinct categories or formats.
b) The response variable in the study is the brain connectivity measured by the magnetic resonance imaging (MRI) machine. This variable is quantitative as it represents a numerical measurement of brain connectivity.
c) The study includes 27 four-year-olds as the observational units or individuals.
Determine the different story format?The study aimed to investigate the impact of different story formats on brain connectivity in four-year-olds. The explanatory variable, format, was categorized into three groups: audio, illustrated, and animated.
The response variable, brain connectivity, was measured using an MRI machine. The researchers found a "Goldilocks effect" in the brain connectivity, indicating that the audio format was associated with low brain connectivity, possibly due to the children straining to understand.
On the other hand, the animated format also resulted in low brain connectivity, suggesting that the animation did all the work for the children.
The highest brain connectivity, considered optimal, was observed with the illustrated format, which simulated the experience of reading a book to a child.
The study included 27 four-year-olds as the observational units, providing insights into the relationship between story format and brain connectivity in young children.
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Complete the square
x^2 - 2x - 14 = 0
What is the standard form of the equation of a quadratic function with roots of 2 and −5 that passes through (1, −3)?
The standard form of the equation of a quadratic function is y = 1/2x² + 3x/2 - 5.
What is a quadratic function?
A polynomial of degree two in one or more variables is referred to as a quadratic polynomial. The polynomial function that a quadratic polynomial defines is known as a quadratic function.
Here, we have
Given: a quadratic function with roots of 2 and −5 that passes through (1, −3).
The required equation has the form:
y = a(x-2)(x+5)
because each root value will force y to be zero. To find a, substitute the point given, (1,-3), into this equation and then solve for a:
-3 = a(1-2)(1+5)
-3 = a(-1)(6)
-3 = -6a
a = 1/2
So, the required equation is:
y = 1/2(x-2)(x+5)
Next, expand and simplify:
y = 1/2(x²+3x-10)
y = 1/2x² + 3x/2 - 5
Hence, the standard form of the equation of a quadratic function is y = 1/2x² + 3x/2 - 5.
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An car can hold gallons of fuel . It contains gallons of fuel . How much more fuel is needed to fill the car?
The amount of gas a car holds depends on the size of the car. Smaller cars generally have gas tanks that hold 12 gallons worth of gas, while larger cars can hold 15 or 16 gallons.
Please helppp.there are 3 green, i purple,
and 2 orange markers in a bag
once a marker is selected, it
is not replaced. find the
probability of selecting two
orange markers
The probability of selecting two orange markers is 2/6 * 1/5 = 1/15.
What is non-replacement event?
Components that have not been altered typically have content that is present within the document, whereas elements that have been replaced typically have content that is present outside of the document.
Given that there are 3 green, 1 purple, and 2 orange markers.
Total number of markers is (3 + 1 + 2) = 6.
The probability of an event is the ratio of the number of outcomes of a favorable event to the total number of outcomes.
The probability that the first marker is orange is 2/6 = 1/3.
After picking the number of markers that left is (6 - 1) = 5.
The number of orange marker that left is 2 - 1 = 1.
The probability that the second marker is orange is 1/5.
The probability of selecting two orange markers is (1/3) × ( 1/5) = 1/15.
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Andrew is home one winter day studying for an exam. It is lunchtime and he is hungry. Instead of making a sandwich from roast beef in the fridge, he drives to taco bell and spends $5 for 2 tacos, a burrito, and a dr. Pepper. He reasons that he can make $10 per hour cutting lawns so he really saves $5 by going to taco bell rather than preparing his own meal. What's wrong with andrews argument?.
Answer:
He cannot save $5 when he is buying something instead of making it himself.
Step-by-step explanation:
He makes $10 from lawn mowing and spends $5 on Taco Bell. He has $5 left.
If he made is lunch, He would have had $10 dollars.
Andrew's argument is flawed because he is not considering all of the costs and benefits associated with his decision to go to Taco Bell instead of preparing his own meal.
What is the argument?An argument is a collection of claims, the premises of which are provided in support of another statement, the conclusion.
There are a few problems with Andrew's argument.
First, he is assuming that the only cost of preparing his own meal is the price of the ingredients. However, there are also opportunity costs associated with preparing his own meal, such as the time he spends making it and the opportunity to do something else during that time (such as study for his exam).
Second, Andrew is assuming that he would have spent the same amount of money on ingredients as he did on his meal at Taco Bell. However, it is possible that the ingredients he would have used to make his own meal would have cost less than $5, in which case he would not have saved as much money as he thinks.
Finally, Andrew is assuming that he would have spent the same amount of time preparing his own meal as he did going to Taco Bell. However, it is possible that it would have taken him longer to prepare his own meal, in which case the opportunity cost of his time would have been even higher.
Overall, Andrew's argument is flawed because he does not evaluate all of the expenses and advantages of his decision to eat at Taco Bell instead of cooking his own dinner.
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John jogged 4.5 miles on Thursday, 7 2/5 miles on Friday, and 10.4 miles on Saturday. How many miles does John have to run in order to run 25 miles for the week
im giving 20 points
Answer:
2.7 miles
Step-by-step explanation:
25 - 10.4 - 4.5 - 7 2/5 will give you 2.7
Answer:
8 miles
Step-by-step explanation:
If we divide 70 by 50, we get the unit rate for the ratio 70 minutes for every 50 miles.
70÷50=1.4
So the runner is running 1.4 minutes per mile. We can multiply this unit rate by the number of miles:
1.4 minutes mile × 5 miles = 7 minutes
Thus it will take her 7 minutes to run 5 miles at this pace.
If it takes her 7 minutes to run 5 miles, it will take her 7÷5 = 1.4 minutes to run 6÷3=2 miles at the same pace.
If it takes her 1.4 minutes to run 5 miles, it will take her 1.4×5=7 minutes to run 4×2=8 miles at the same pace. Since 60 minutes is 1 hour, she is running at a speed of 8 miles per hour.
We found her pace in minutes per miles in part (a).
Problem 1 Emma lives and works in Oberlin earning a salary of y dollars. She consumes two products and has the following utility function: U(x 1 ,x 2 )=2lnx 1 +3lnx 2 Prices of both products in Oberlin are equal to 1. The company she works for is planning to transfer her to Wellington where the price of the second product is two times higher than in Oberlin, while the first product has the same price. Emma argues that she should receive a pay raise of A dollars to not be worse off. If her company rejects her pay raise request, what is the maximum pay cut ( B dollars) she is willing to accept at another job in Oberlin in order to stay in town? a) Find A. b) Find B.
The maximum pay cut (B dollars) Emma is willing to accept at another job in Oberlin in order to stay in town is -y dollars.
a) To find the value of A, we need to compare Emma's utility before and after the transfer.
Before the transfer, Emma's utility function is U(x1, x2) = 2ln(x1) + 3ln(x2).
After the transfer, the price of the second product in Wellington is two times higher.
Let's denote the price of the second product in Oberlin as p, then the price of the second product in Wellington is 2p. The price of the first product remains the same in both cities.
To maintain the same level of utility, Emma needs to spend the same amount of money on each product in Wellington as she did in Oberlin.
Let's assume she spends x dollars on the first product and y dollars on the second product in Oberlin. Therefore, her total expenditure in Oberlin is \(p*x + p*y = p*(x + y).\)
In Wellington, she would need to spend the same amount on the first product (x dollars), but since the price of the second product is two times higher, she would need to spend 2p*y dollars on the second product. Therefore, her total expenditure in Wellington is p*x + 2p*y = p*(x + 2y).
Since she argues that she should receive a pay raise of A dollars to not be worse off, her total expenditure in Oberlin should be equal to her total expenditure in Wellington with the pay raise:
p*(x + y + A) = p*(x + 2y)
Simplifying the equation, we get:
x + y + A = x + 2y
Cancelling out the x terms:
y + A = 2y
Subtracting y from both sides:
A = y
Therefore, A = y dollars.
b) To find the value of B, we need to determine the maximum pay cut Emma is willing to accept at another job in Oberlin in order to stay in town.
Let's assume Emma's salary at her new job in Oberlin is y - B dollars. We want to find the maximum value of B.
Using the same logic as before, her total expenditure in Oberlin with the pay cut should be equal to her total expenditure in Wellington:
p*(x + y - B) = p*(x + 2y)
Simplifying the equation, we get:
x + y - B = x + 2y
Cancelling out the x terms:
y - B = 2y
Subtracting y from both sides:
-B = y
Therefore, B = -y dollars.
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You wish to test the following claim ( H a ) at a significance level of α = 0.005 . H o : p = 0.8 H a : p > 0.8 You obtain a sample of size n = 177 in which there are 154 successful observations. For this test, you should use the (cumulative) binomial distribution to obtain an exact p-value. (Do not use the normal distribution as an approximation for the binomial distribution.) The p-value for this test is (assuming H o is true) the probability of observing... at most 154 successful observations at least 154 successful observations What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.8. There is not sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.8. The sample data support the claim that the population proportion is greater than 0.8. There is not sufficient sample evidence to support the claim that the population proportion is greater than 0.8.
To find the p-value for this test, we need to calculate the probability of observing at least 154 successful observations (assuming H0 is true) using the cumulative binomial distribution.
Given:
H0: p = 0.8
Ha: p > 0.8
Sample size (n) = 177
Number of successful observations = 154
We will use the binomial distribution to calculate the probability of observing at most 154 successful observations and subtract it from 1 to get the probability of observing at least 154 successful observations.
Using a statistical software or calculator, the p-value is found to be 0.0002 (rounded to four decimal places).
Since the p-value (0.0002) is less than the significance level (α = 0.005), we reject the null hypothesis (H0).
Therefore, the final conclusion is that there is sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.8.
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some help would be nice.
Answer:
(х + 1)(х - 2)
Step-by-step explanation:
х²-х-2=(х + 1)(х - 2)