We can reject the null hypothesis and conclude that there is a significant difference in the average customer satisfaction ratings between Home Depot and Lowe's.
What is hypothesis?
A hypothesis is a proposed explanation or prediction that can be tested through empirical investigation.
To test the difference in the average customer satisfaction rating for Home Depot and Lowe's, we can perform a two-sample t-test. Let's go through the steps of conducting the hypothesis test:
Step 1: State the hypotheses:
Null Hypothesis (H₀): The average customer satisfaction rating for Home Depot is equal to the average customer satisfaction rating for Lowe's.
Alternative Hypothesis (H₁): The average customer satisfaction rating for Home Depot is different from the average customer satisfaction rating for Lowe's.
Step 2: Set the significance level (α):
Let's assume a significance level of α = 0.05. This means we want to have strong evidence to reject the null hypothesis if the p-value is less than 0.05.
Step 3: Collect the data and calculate the sample statistics:
We have the following customer satisfaction ratings:
Home Depot: 79, 81
Lowe's: 72, 78, 79, 76, 72
To calculate the sample statistics, we need to find the sample means and sample standard deviations for Home Depot and Lowe's.
Sample mean of Home Depot [tex](\bar x_1)[/tex] = (79 + 81) / 2 = 80
Sample mean of Lowe's [tex](\bar x_2)[/tex] = (72 + 78 + 79 + 76 + 72) / 5 = 75.4
To calculate the sample standard deviations, we need to find the differences between each rating and the respective sample mean, square the differences, sum them up, divide by n-1, and then take the square root.
Home Depot: [(79-80)² + (81-80)²] / (2-1) = 1 / 1 = 1
Lowe's: [(72-75.4)² + (78-75.4)² + (79-75.4)² + (76-75.4)² + (72-75.4)²] / (5-1) = 16.8 / 4 = 4.2
Step 4: Calculate the test statistic:
To calculate the test statistic, we use the formula:
[tex]t = (\bar x_1 - \bar x_2) / \sqrt((s_1^2/n_1) + (s_2^2/n_2))[/tex]
Substituting the values:
[tex]t = (80 - 75.4) / \sqrt{((1^2/2) + (4.2^2/5))}\\\\t = 4.6 / \sqrt(0.5 + 1.68)[/tex]
t ≈ [tex]4.6 / \sqrt(2.18)[/tex]
t ≈ 4.6 / 1.476
t ≈ 3.116
Step 5: Determine the p-value:
We need to find the p-value associated with the calculated test statistic. Since this is a two-sided test, we need to find the probability of observing a test statistic as extreme as t = 3.116 or more extreme in either tail of the t-distribution.
Using a t-distribution table or statistical software, the p-value is found to be p ≈ 0.021.
Step 6: Make a decision:
Compare the p-value to the significance level. Since the p-value (0.021) is less than the significance level (0.05), we have enough evidence to reject the null hypothesis.
Step 7: State the conclusion:
Based on the sample data, there is sufficient evidence to conclude that the average customer satisfaction rating for Home Depot is different from the average customer satisfaction rating for Lowe's at a significance level of 0.05.
Therefore, we can reject the null hypothesis and conclude that there is a significant difference in the average customer satisfaction ratings between Home Depot and Lowe's.
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Represent Real-World Problems: Rob is making the kite shown in the figure.
a. Can Rob conclude that △ABD≅△ACD? Why or why not?
b. Rob says AB = AC and BD = CD. Do you agree? Explain.
c. Given that BD = x + 15cm and AB = x cm, write an expression for the distance around the kite in centimeters.
A) Yes, we can conclude that △ABD≅△ACD .
B) Rob says AB = AC and BD = CD. I agree.
C) The expression for the distance around the kite (perimeter) in centimeters is 4x + 30.
How is this so?A) According to the principles of geometry, when two angles are marked alike, it means that they are equal.
Thus, ∠BAD ≅ ∠CAD; and
∠BDA ≅∠ADC
Since ∠BDA ≅∠ADC and
AD = DA (Based on the Reflexive postulate,
Then on the basis of the Angle - Side - Angle theorem, △ABD≅△ACD.
B) AB = AC and BD = CD
This is because we have already proven that △ABD≅△ACD on the basis of A-S-A theorem.
C) Since both triangles are equal, the expression for their perimeter =
x + 15 + x + x + 15 + x
= 4x + 30
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the typical american adult eats an average of 48.5 hamburgers in a year. assume the number of hamburgers eaten is normally distributed with a standard deviation of 8.3 pounds. find the probability that a randomly selected adult eats more than 40.0 hamburgers in a year.
The probability that a randomly selected adult consumes more than 40.0 hamburgers in a year is approximately 0.85.
In order to find the probability that randomly selected adult eats more than 40.0 hamburgers in a year, we use the normal distribution and z-scores.
First, we need to standardize the value of 40.0 using the formula : z = (x - μ)/σ,
Where : x = value we want to standardize (40.0 hamburgers), μ = mean number of hamburgers eaten (48.5 hamburgers), σ = standard-deviation (8.3 hamburgers),
Substituting the values,
We get:
z = (40.0 - 48.5)/8.3,
z = -1.024
Next, we find the area under the normal-curve to the right of z = -1.024. This represents the probability of randomly selecting an adult who eats more than 40.0 hamburgers.
We know that area to left of z = -1.024 is approximately 0.15. We need the area to right, so, we subtract this value from 1,
P(x > 40.0) = 1 - P(x ≤ 40.0)
P(x > 40.0) = 1 - 0.15
P(x > 40.0) ≈ 0.85,
Therefore, the required probability is 0.85.
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The table below shows the number of customers served in a restaurant each week. Based on the information, how many customers should the restaurant expect to serve during week ten?
Answer:
150
Step-by-step explanation:
The restaurant should expect to serve 180 customers in week 10.
How to explain the valueThe number of customers served in the restaurant follows a repeating pattern of 180, 170, 200, 180, 210, 180, 210, 170, 200, 180. Therefore, the number of customers served in week 10 will be 180.
The number of customers served in the restaurant follows a repeating pattern of 180, 170, 200, 180, 210, 180, 210, 170, 200, 180. This means that after 10 weeks, the number of customers served will be the same as it was in week 1. Since week 1 had 180 customers served, week 10 will also have 180 customers served.
As you can see, the number of customers served in week 10 is the same as the number of customers served in week 1. Therefore, the restaurant should expect to serve 180 customers in week 10.
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The table shows the possible outcomes of spinning a fair spinner twice with sections labeled A, B, C, and D.
The probabilities are given as follows:
Spinner landing on at least one A: 7/16.Spinner landing on C and D in any order: 1/8.Spinner landing on two B's: 1/16.Spinner landing on C on the second spin: 1/4.How to calculate a probability?The parameters that are needed to calculate a probability are given as follows:
Number of desired outcomes in the context of a problem/experiment.Number of total outcomes in the context of a problem/experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
Out of 16 trials, in 7 of them, which are the first row and the first column, the spinner lands on at least one A, hence the probability is given as follows:
p = 7/16.
For C and D, there are two outcomes, (C, D) and (D, C), hence the probability is given as follows:
p = 2/16 = 1/18.
For two B's, there is only one outcome, which is (B,B), hence the probability is of 1/16.
For C on the second spin, we consider the third column, which has four outcomes, hence the probability is given as follows:
p = 4/16 = 1/4.
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Which graph represents the function p(x) = |x-1|?
-8
24
72+3
24
4₁
-2
3.
ITX
O
--2-4
4.
23
The graph of the absolute function, p(x) = |x - 1|, has a minimum point (1, 0), and the points (-6, 7), and (6, 5), on the graph
Please find attached the graph of the absolute function created with MS Excel.
What is an absolute function?An absolute function is a function that nests an algebraic expression within an absolute value symbol.
The specified absolute function, p(x) = |x - 1|, indicates that the minimum value of the function, occurs where; p(x) = 0 = |x - 1|
Therefore; |x - 1| = 0, x = 1
When x = -6, we get; p(-6) = |(-6) - 1| = 7
When x = 6, we get; p(6) = |6 - 1| = 5
Therefore, the points on the graph are;
(-6, 7), (1, 0), and (6, 5)
Please find attached the graph of the absolute function created with MS Excel
The possible question, includes graph with the attached four options
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what is the claim that he is testing? the mean height of the 102 12 -year-old boys in the sample is greater than 59.2 in. the mean height of all 12 -year-old boys is 59.2 in. the mean height of 12 -year-old boys from high-income families is 59.2 in. the mean height of 12 -year-old boys from high-income families is 59.5 in. the mean height of 12 -year-old boys from high-income families is greater tha
The claim that is being tested is: "the mean height of 12-year-old boys from high-income families is greater than 59.2 inches."
In order to test this claim, one could follow these steps:
1. Gather data: Collect a sample of 12-year-old boys from high-income families. 2. Calculate the sample mean: Compute the mean height of the boys in the sample. 3. Formulate a null hypothesis (H0): The mean height of 12-year-old boys from high-income families is equal to 59.2 inches.
4. Formulate an alternative hypothesis (H1): The mean height of 12-year-old boys from high-income families is greater than 59.2 inches. 5. Perform a hypothesis test: Using the appropriate statistical test, compare the sample mean to the population mean of 59.2 inches. 6. Draw conclusions: Based on the results of the hypothesis test, either reject the null hypothesis (supporting the alternative hypothesis) or fail to reject the null hypothesis (not enough evidence to support the alternative hypothesis).
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The claim that their mean height is greater than 59.2 in is the alternative hypothesis, which will be accepted or rejected based on the results of the data analysis.
The claim that he is testing is that the mean height of 12-year-old boys from high-income families is greater than 59.2 in. This claim is being tested by collecting data from a sample of 102 12-year-old boys and calculating their mean height. The hypothesis is that this mean height will be greater than 59.2 in, which is the assumed population mean height for all 12-year-old boys. The researcher is specifically interested in the height of boys from high-income families, so this is the subgroup that is being tested. The claim that their mean height is greater than 59.2 in is the alternative hypothesis, which will be accepted or rejected based on the results of the data analysis.
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A gumball machine contains 12 red, 13 green, and 8 yellow gumballs. What is the least number of gumballs jack has to buy to be certain he gets 6 gumballs of the same color?
Answer: What is the least number of gumballs jack has to buy to be certain he gets 6 gumballs of the same color?
Step-by-step explanation:
To be certain he gets 6 gumballs of the same color, Jack must buy at least 16 gumballs.
This is because he could buy 5 gumballs of each color (for a total of 15 gumballs) and still not have 6 gumballs of the same color. However, if he buys one more gumball, he will have at least 6 gumballs of one color.
Therefore, the least number of gumballs Jack has to buy to be certain he gets 6 gumballs of the same color is 16.
{Hope This Helps! :)}
NEED HELP ASAP WITH WORK
so I can use the work for the questions later on
The width of the rectangular garden is 21 feet.
What is a rectangle?A rectangle is a plane shape that have pair of opposite sides equal and parallel.
To calculate the width of the rectangle, we use the formula below
Formula:
w = 3P/20...................... Equation 1Where:
w = Width of the rectangleP = Perimeter of the rectangleFrom the question,
Given:
P = 140 feetSubstitute into equation 1
w = 3×140/20w = 21 feetHence, the right option is D. 21 feet.
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If 1kg of margarine costs R34.99 how much would 250g be
evaluate the line integral where c is the given curve
∫c x sinyds C is line segment from (0 3) to (4 6)
Consider the line integral,
∫c x sin yds; C is the line segment from (0 3) to (4 6)
The value of the line integral is (-16/3)cos(6) + (16/9)sin(6). Evaluating this integral, you will get the value of the line integral for the given curve.
To evaluate the line integral ∫c x sin yds, where C is the line segment from (0,3) to (4,6), we first need to parameterize the curve. We can do this by letting x = t and y = 3 + (3/4)t, where t goes from 0 to 4. This gives us the parametric equations x = t and y = (3/4)t + 3.
Next, we need to find ds, the length of the curve element. We can use the formula ds = sqrt(dx^2 + dy^2) to get ds = sqrt(1 + (3/4)^2)dt = sqrt(25/16)dt = (5/4)dt.
Now we can substitute in our parameterization and ds into the line integral to get ∫c x sin yds = ∫0^4 t sin((3/4)t + 3) (5/4)dt.
We can evaluate this integral using integration by parts. Let u = t and dv = sin((3/4)t + 3) (5/4)dt, then du/dt = 1 and v = (-4/3)cos((3/4)t + 3). The integral becomes:
∫0^4 t sin((3/4)t + 3) (5/4)dt = uv|0^4 - ∫0^4 v du/dt dt
= (-4/3)t cos((3/4)t + 3)|0^4 - ∫0^4 (-4/3)cos((3/4)t + 3) dt
= (-4/3)t cos((3/4)t + 3) + (16/9)sin((3/4)t + 3)|0^4
= (-16/3)cos(6) + (16/9)sin(6)
Therefore, the value of the line integral is (-16/3)cos(6) + (16/9)sin(6).
To evaluate the line integral ∫c x sin y ds, where C is the line segment from (0, 3) to (4, 6), you first need to parameterize the curve C.
A possible parameterization is r(t) = (1-t)(0, 3) + t(4, 6) = (4t, 3+3t), with t ∈ [0, 1]. Then, compute the derivative dr/dt = (4, 3).
Now, find the integrand by replacing x and y with the parameterized curve components: x sin y = (4t) sin(3 + 3t).
Next, find the magnitude of the derivative: |dr/dt| = √(4² + 3²) = 5.
Finally, compute the integral:
∫[0, 1] (4t sin(3 + 3t))(5) dt.
Evaluating this integral, you will get the value of the line integral for the given curve.
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2x+3y= -4
x+9y=13
find the solution of the system of equations.
Answer:
(-5, 2)
Step-by-step explanation:
2x + 3y = -4
x + 9y = 13
We can solve this by substituting or using elimination.
Substituting:
2x + 3y = -4
-2x = -2x Subtract 2 from both sides.
3y = -2x - 4
3 = 3 Divide both sides by 3.
y = -2/3x - 4/3
x + 9(-2/3x - 4/3) = 13 Replace the y with -2/3x - 4/3.
x - 6x - 12 = 13 use the distributive property.
-5x - 12 = 13
+12 = + 12 Add 12 to both sides.
-5x = 25
-5 = -5 Divide both sides by -5.
x = -5
Now that we know what x is, we substitute -5 for the variable x in any of the two equations.
x + 9y = 13
-5 + 9y = 13 Replaced x with -5
+5 = +5 Add 5 to both sides.
9y = 18
Divide both sides by 9 to get:
y = 2
The other way to solve:
Elimination:
2x + 3y = -4
x + 9y = 13
Make the variable y cancel out.
-3(2x + 3y = -4) use the distributive property.
-6x - 9y = 12
-6x - 9y = 12
x + 9y = 13
Add the equation.
-5x = 25
Divide both sides by -5.
x = -5
Plug in -5 for x.
2(-5) + 3y = -4
-10 + 3y = -4
+10 = +10 Add 10 to both sides.
3y = 6
Divide both sides by 3:
y = 2
We get the same answer in both strategies, you could use either one.
PLEASEEE!! Help me, will give brainliest :)
Which statement correctly compares the shapes of the distributions?
A. Team A's scores are positively skewed, and team B's are
symmetric.
B. Team A's scores are symmetric, and team B's are positively skewed.
C.Team A's scores are negatively skewed, and team B's are
symmetric.
D. Team A's scores are symmetric, and team B's are negatively skewed.
Answer: D
Step-by-step explanation:
Team A has symmetric scores because the upper quartile (right part of the rectangle) is equal to lower quartile (left part of rectangle) in terms of size, so median (middle line in the rectangle) is equal to the mean. Team B has negative skewed scores because the upper quartile is smaller than lower quartile, so the median is greater than the mean.
Thus, the answer is D.
Use the information given in the figure to find the length R U.
The lengths on the figure are not drawn accurately.
The length of RU in triangle is,
⇒ RU = 16
We have o given that;
In triangle;
ST = 37
UT = 35
RS = 20
Hence, By using definition of Pythagoras theorem we get;
In triangle STU;
⇒ ST² = SU² + UT²
⇒ 37² = SU² + 35²
⇒ 1369 = SU² + 1225
⇒ SU² = 144
⇒ SU = 12
Hence, In triangle RSU;
⇒ RS² = SU² + RU²
⇒ 20² = 12² + RU²
⇒ 400 - 144 = RU²
⇒ RU² = 256
⇒ RU = 16
Thus, The length of RU in triangle is,
⇒ RU = 16
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determine whether the mean, median, or mode would be the best choice to describe the center of the following set of data. an elementary school has 92 first graders. depending on when their birthday falls, the first graders might be six, seven, or eight on the last day of the school year. would it be best to use the mean, median, or mode to describe the typical age of the first-graders?
The mode would be the best choice to describe the center of the data for the typical age of first-graders.
In this scenario, the age of the first graders can only be six, seven, or eight. Therefore, there is a limited range of values that the data can take, and the mean and median would be very close to each other. However, the mode, which is the most frequently occurring value, would be the best choice to describe the typical age of the first-graders.
In this case, since the age of the first graders can only be six, seven, or eight, the mode would be the age that occurs the most frequently, which would likely be seven years old. Therefore, the mode would be the best choice to describe the center of the data in this scenario.
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Choose the INCORRECT statement below.
#3, the transformation can be represented by (x, -y)
Why are we here what is the purpose?
Answer:
We are here because we need help with a particular course or question
Step-by-step explanation:
Our goal is to try our best and explain to others to their understanding (and win titles)
BOOM!!!
a coin is tossed and an equally divided spinner (as shown) is spun. what is the probability of a head on the coin or a prime number on the spinner?
The probability of getting a head on the coin or a prime number on the spinner is 2/3.
The probability of getting a head on the coin toss is 1/2, and the probability of landing on a prime number on the spinner is 1/6. By adding up the probabilities in the column corresponding to a head or any prime number, we find the overall probability.
Overall probability:
P(head or prime) = P(H) + P(2) + P(3) + P(5)
= 1/2 + 1/6 + 1/6 + 1/6
= 1/2 + 3/6
= 4/6
= 2/3
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14 The people working for a company work in Team A or in Team B. number of people in Team A: number of people in Team B = 3/4; 4/5 of Team A work full time. 24% of Team B work full time. Work out what fraction of the people working for the company work full time. Give your fraction in its simplest form.
Answer:
Let's denote the number of people in Team A as a, and the number of people in Team B as b. From the problem, we know that:
a/b = 3/4
Now, we also know that 4/5 of Team A and 24% (or 24/100 = 6/25) of Team B work full time. So, the number of people working full time from Team A is 4a/5 and from Team B is 6b/25.
The total number of people working for the company is a + b, and the total number of people working full time is 4a/5 + 6b/25.
We are asked to find the fraction of people working full time, which can be represented as:
(4a/5 + 6b/25) / (a + b)
Firstly, we need to have a common denominator for the fractions, so we can express 4a/5 as 20a/25:
[tex](20a/25 + 6b/25) / (a + b)[/tex]
Simplifying, we can write this as:
[tex](20a + 6b) / (25(a + b))[/tex]
Now, since we know a/b = 3/4, we can substitute a = 3b/4 in the above expression:
[tex](20*(3b/4) + 6b) / (25((3b/4) + b))[/tex]
Simplifying the above, we get:
[tex](15b + 6b) / (25((3b/4) + b)) = 21b / 25b[/tex]
So, the fraction of people working full time is 21/25.
Directions: Find the prime factors of the polynomials.
1. 2a2 - 2b2
2. 6x2 - 6y2
3. 4x2 - 4
4. ax2 - ay2
5. cm2 - cn2
6. st2 - s
7. 2x2 - 18
8. 2x2 - 32
9. 3x2 - 27y2
10. 18m2 - 8
11. 12a2 - 27b2
12. 63c2 - 7
13. x3 - 4x
14. y3 - 25y
15. z3 - z
16. 4c3 - 49c
17. 9db2 - d
18. 4a3 - ab2
19. 4a2 - 36
20. x4 - 1
21. 3x2+ 6x
22. 4r2 - 4r - 48
23. x3 - 7x2 + 10x
24. 4x2 -6 x - 8
25. 16x2 - x2 v 4
The factors of the given polynomial 18m²-8 are 2, (3m+2) and (3m-2).
The factors are the polynomials which are multiplied to produce the original polynomial.
Use the identity (a²-b²)=(a+b)(a-b)
1) 2a²-2b²
= 2(a²-b²)
= 2(a+b)(a-b)
2) 6x²-6y²
= 6(x²-y²)
= 6(x+y)(x-y)
3) 4x² - 4
= 4(x²-1)
= 4(x+1)(x-1)
4) ax²-ay²
= a(x²-y²)
= a(x+y)(x-y)
5) cm²-cn²
= c(m²-n²)
= c(m+n)(m-n)
6) st²-s
= s(t²-1)
= s(t+1)(t-1)
7) 2x²-18
= 2(x²-9)
= 2(x²-3²)
= 2(x+3)(x-3)
8) 2x²-32
= 2(x²-16)
= 2(x²-4²)
= 2(x-4)(x+4)
9) 3x²-27y²
= 3(x²-9y²)
= 3(x²-(3y)²)
= 3(x+3y)(x-3y)
10) 18m²-8
= 2(9m²-4)
= 2((3m)²-(2)²)
= 2(3m+2)(3m-2)
Therefore, the factors of the given polynomial 18m²-8 are 2, (3m+2) and (3m-2).
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HELP ME OR ELSE I WILL EAT U >:3
he ray has been lined up with the baseline and origin on the protractor. What is the next step in drawing a 40° angle? (1 point)
a protractor showing a ray lined up with the base line
a
Line up the ray with the baseline and origin on the protractor
b
Draw a ray
c
Draw a ray connecting the vertex and the mark
d
Draw a mark on the paper at 40°
This process will give you a ray originating from the vertex and extending at a 40° angle.
To draw a ray connecting the vertex and the mark at a 40° angle, please follow these steps:
1. Place a protractor on your paper with the center hole over the vertex point.
2. Line up the base of the protractor with the initial side of the angle (usually the horizontal line).
3. Find the 40° mark on the protractor and make a small mark on the paper.
4. Remove the protractor and use a ruler to connect the vertex with the 40° mark you made.
5. Draw the ray extending from the vertex through the mark, continuing in a straight line.
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sally's algebra grade depends on three unit tests and a final exam. the grade for the final exam is weighted to equal the grade of two unit tests. what is the minimum grade that sally must get on her final exam in order to have a class average of 90 or above for the course, if her unit test scores are 95, 88, and 85
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What is the solution to x2 – 9x < –18?
x < –6 or x > 3
–6 < x < 3
x < 3 or x > 6
3 < x < 6
The correct solution to the inequality x^2 - 9x < -18 is x < 3 or x > 6.
To solve the inequality x^2 - 9x < -18, you can follow these steps:
Move all terms to one side of the inequality to form a quadratic expression: x^2 - 9x + 18 < 0.
Factorize the quadratic expression: (x - 6)(x - 3) < 0.
Determine the sign of the expression for different intervals of x. To do this, you can create a sign chart:
Interval | (x - 6) | (x - 3) | (x - 6)(x - 3) |
x < 3 | - | - | + |
3 < x < 6 | - | + | - |
x > 6 | + | + | + |
Analyze the sign chart to determine when the expression (x - 6)(x - 3) is less than zero (negative).
The expression is negative when x is between 3 and 6, i.e., 3 < x < 6.
Write the solution in interval notation:
x < 3 or x > 6
Therefore, the correct solution to the inequality x^2 - 9x < -18 is x < 3 or x > 6.
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convert 4315425quinary number into decimal number
Converting 4315425 quinary number into a decimal number results in 73,240.
What is a quinary number?A quinary number is a number that is in base 5.
A decimal number is a number in base 10.
The powers of 5 include (1, 5, 25, 125, 625, and so on). We write these powers of 5 beside the quinary digits written from bottom to top and then multiply each digit by its associated power.
The sum of the products gives the decimal number of the quinary number.
Digit Power Multiplication
5 1 5 (5 x 1)
2 5 10 (2 x 5)
4 25 100 (4 x 25)
1 125 125 (1 x 125)
5 625 3,125 (5 x 625)
3 3,125 9,375 (3 x 3,125)
4 15,625 62,500 (4 x 15,625)
Total 73,240
Thus, 4315425 quinary is equal to 73,240 decimal.
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Solve for x. Round to the nearest tenth, if necessary. 56 Z 43° x M
The length of side x in the right triangle is approximately 38.2 units.
It looks like you have a right triangle problem where you need to solve for side x. The given information is the hypotenuse (Z) with a length of 56 units, an angle (M) of 43°, and side x which is opposite to angle M.
To solve for x, we can use the sine function in the context of the right triangle. The sine function is defined as:
sin(M) = opposite side (x) / hypotenuse (Z)
We are given the values for angle M (43°) and the hypotenuse (Z = 56 units). Plugging these values into the equation, we get:
sin(43°) = x / 56
Now, to solve for x, we will multiply both sides of the equation by 56:
x = 56 * sin(43°)
Next, use a calculator or trigonometric table to find the sine of 43°:
sin(43°) ≈ 0.682
Now, multiply this value by 56:
x ≈ 56 * 0.682
x ≈ 38.192
Finally, round your answer to the nearest tenth:
x ≈ 38.2
So, the length of side x in the right triangle is approximately 38.2 units.
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compute 4.659×10^4−2.14×10^4. round the answer appropriately.
An amusement park charges an entrance fee plus a charge for each ride. If you go on 7 rides, the total cost would be $51.25. If you go on 12 rides, the total cost would be $70. What is the slope of the line that represents this relationship?
The slope of the line that represent this relationship is 3.75.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.Based on the information provided about the charges by this amusement park, we have the following system of equations;
51.25 = 7m + c ....equation 1.
70 = 12m + c ......equation 2.
By solving equation 1 and equation 2 simultaneously, we have the following:
70 = 12m + 51.25 - 7m
70 - 51.25 = 5m
18.75 = 5m
Slope, m = 18.75/5
Slope, m = 3.75
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Which type of compound event is generally associated with​ multiplication? Which is generally associated with​ addition?
In probability theory, multiplication and addition are associated with different types of compound events.
Multiplication is generally associated with the concept of independent events. When two events are independent, the probability of both events occurring is calculated by multiplying their individual probabilities. This is known as the multiplication rule of probability. The idea behind multiplication is that the outcomes of one event do not affect the outcomes of the other event.
On the other hand, addition is generally associated with the concept of mutually exclusive events. Mutually exclusive events are events that cannot occur at the same time. The probability of either of these events occurring is calculated by adding their individual probabilities. This is known as the addition rule of probability. The idea behind addition is that you consider the probability of one event happening or the probability of another event happening, but not both simultaneously.
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Suppose that data collected from police reports of motor vehicle crashes show a moderate positive correlation between the speed of the motor vehicle at the time of the crash and the severity of injuries to the driver. Answer the following question based only on this information. True or false: It can be concluded that the faster a motor vehicle is traveling at the time of a crash, the more severe the injuries to the driver are. Select the correct answer below: True or False?
False. It can be concluded that the faster a motor vehicle is traveling at the time of a crash, the more severe the injuries to the driver are
While the information states that there is a moderate positive correlation between the speed of the motor vehicle and the severity of injuries, correlation does not imply causation. Therefore, it cannot be concluded that the faster a motor vehicle is traveling at the time of a crash, the more severe the injuries to the driver are. Correlation simply indicates that there is a relationship between the two variables, but other factors may also be influencing the severity of injuries.
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10 points.
What is the circumference of the circle? Use 3.14 for π.
157.75 inches
50.24 inches
25.12 inches
12.56 inches
The circumference of the circle is 25.12 inches. The Option C.
What is the circumference of the circle?
The Circumference, also perimeter of circle means the ratio of circumference to diameter of any circle.
The length of the segment represents radius of the circle which half length of diameter. So, the diameter is:
= 2 * 4 inches
= 8 inches.
The circumference is found using C = πd.
C = π*d
C = 3.14 * 8 inches
C = 25.12 inches.
Full question:
What is the circumference of the circle? Use 3.14 for π.
circle with a segment drawn from the center of the circle to a point on the circle labeled 4 inches
A. 157.75 inches
B. 50.24 inches
C. 25.12 inches
D. 12.56 inches.
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hey im back and i need help answers?
The value of x in the triangle is,
x = 9.4 cm
We have to given that;
A triangle is shown in figure.
Now, By trigonometry formula we get;
cos 20° = Base / Hypotenuse
cos 20° = x / 10
0.94 = x / 10
x = 0.94 × 10
x = 9.4 cm
Thus, The value of x in the triangle is,
x = 9.4 cm
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