6^-2x • 6^-x = 1/216
x=1 is the answer
Answer: x=1
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Step-by-step explanation: Negative power rule, quotient rule, then you'll simplify. After that use the negative power rule and multiply both sides by 6^3x. Then simplify 1/216 and multiply both sides by 216. Simplify 1*216=216, then finally you'll put both sides on the same base and cancel the base of six on both sides. Divide both sides by 3 and you'll get 1=x. Now just switch places so the x will be first (x=1).
Negative power rule x^-a=1/x^a
Quotient rule x^a/x^b=x^a-b
-----------------------------------------------------
P.S. if you want me to right out on paper how I did it if it would be easier for you to visually see the text to learn it then it would be my pleasure! Math is hard so I'm happy to help more with this problem!
HOPE THIS HELPS, HAVE A BLESSED DAY! :-) ;-)
꒰⑅•ᴗ•⑅꒱Select the correct answer. The number of scented candles packaged in a box can vary by at most two from an average of 80 candles per box. If the cost of producing a candle is two dollars, what is the range of the possible production costs, x, for 50 boxes of candles? A. 78 ≤ x ≤ 82 B. 156 ≤ x ≤ 164 C. 3,900 ≤ x ≤ 4,100 D. 7,800 ≤ x ≤ 8,200
Answer:
Step-by-step explanation:
From the problem statement, each box of candles has the following range of candles:
[tex]78 \leq x \leq 82[/tex]
We also know that we have 50 boxes of candles, so we multiply the above range by 50 to get the range of candles:
[tex]3900 \leq x \leq 4100[/tex]
Finally, each candle costs $2, so we have the final range of cost:
[tex]7800 \leq x \leq 8200[/tex]
By calculating the cost of producing the minimum and maximum number of candles that can be packaged in 50 boxes, we determine the range of possible production costs, x, is $7,800 to $8,200.
Explanation:The student needs to calculate the range of possible production costs for 50 boxes of candles, given that each box contains an average of 80 candles and the number of candles can vary by at most two from this average. Since each candle costs two dollars to produce, we can find the minimum and maximum number of candles in one box by subtracting and adding two to the average, respectively (78 and 82 candles). Multiplying these numbers by the cost per candle gives us the cost per box, and then multiplying by the number of boxes (50) gives us the total production cost range for all boxes.
To calculate the minimum cost, we use the minimum number of candles per box: 78 candles per box × $2 per candle × 50 boxes = $7,800. To calculate the maximum cost, we use the maximum number of candles per box: 82 candles per box × $2 per candle × 50 boxes = $8,200. Therefore, the range for the possible production costs, x, for 50 boxes of candles is $7,800 ≤ x ≤ $8,200, which corresponds to answer choice D.
x+2y=-5
y=x+2
solve x and y
Luis purchased a laptop computer that was marked down by 25 of the original price. What fractional part of the original price did Luis pay? A 15 B 45 C 35 D 25
Answer:
75%
Step-by-step explanation:
100%-25%= 75%
He would have paid 75% of the original price..
Answer:
C. [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
Let x be the original price of laptop computer.
We have been given that Luis purchased a laptop computer that was marked down by 2/5 of the original price.
The price of laptop computer after mark-down would be x minus 2/5 of x.
[tex]\text{The price of laptop computer after mark-down}=x-\frac{2}{5}x[/tex]
[tex]\text{The price of laptop computer after mark-down}=\frac{5}{5}x-\frac{2}{5}x[/tex]
[tex]\text{The price of laptop computer after mark-down}=\frac{5-2}{5}x[/tex]
[tex]\text{The price of laptop computer after mark-down}=\frac{3}{5}x[/tex]
Therefore, Luis paid [tex]\frac{3}{5}[/tex] of the original price.
A computer maker receives parts from three suppliers, S1, S2, and S3. Fifty percent come from S1, twenty percent from S2, and thirty percent from S3. Among all the parts supplied by S1, 5% are defective. For S2 and S3, the portion of defective parts is 3% and 6%, respectively. (a) What portion of all the parts is defective? (b) A customer complains that a certain part in her recently purchased computer is defective. What is the probability that it was supplied by S1?
Answer:
a) 4.9 % of all parts is defective or 0.049 of the total parts.
b) 0.5102 is the probability that the defective part was supplied by S1
Step-by-step explanation:
N is the total number of parts from supplier S1, S2 and S3.
N1 = 0.5*N is the total number of part supplied by S1
N2 = 0.2*N is the total number of part supplied by S2
N3 = 0.3*N is the total number of part supplied by S3
a) if Nd1 is the number of defective parts from supplier S1, Nd2 is the number of defective parts from supplier S2 and Nd3 is the number of defective parts from supplier S3, the the total defective parts Nd is:
Nd = Nd1 + Nd2 + Nd3, where
Nd1 = 0.05*N1 = 0.05*0.5*N = 0.025*N,
Nd2 = 0.03*N2 = 0.03*0.2*N = 0.006*N,
Nd3 = 0.06*N3 = 0.06*0.3*N = 0.018*N,
Then Nd = Nd1 + Nd2 + Nd3 = 0.049*N, so Nd/N = 0.049
b) [tex]P(S1 \vert d) = \frac{P(S1,d)}{P(d)} = \frac{P(d \vert S1)}{P(d)} = \frac{0.05*0.5}{0.049} \approx 0.5102[/tex]
for the last expression I used the Bayes tehorem.
[tex]P(S1 \vert d)[/tex] is the probability that occur S1 given that d (defective) is true. This a conditional probability.
see at https://en.wikipedia.org/wiki/Bayes%27_theorem
The overall defect portion from all suppliers is 4.9%. If a part is defective, the probability that it was supplied by S1 is approximately 51.02%.
Explanation:To determine what portion of all the parts is defective, we calculate a weighted average of the defect rates based on the supplier portion contributions. The calculation is as follows:
S1's contribution to the overall defect rate: 50% * 5% = 2.5%S2's contribution to the overall defect rate: 20% * 3% = 0.6%S3's contribution to the overall defect rate: 30% * 6% = 1.8%The overall defect rate is the sum of these contributions, which is [tex]2.5 + 0.6 + 1.8 = 4.9%.[/tex]
For part (b), the probability that the defective part was supplied by S1 can be found using Bayes' theorem:
If a part is defective, the probability of it being from S1 is the probability that S1 provided a defective part over the probability that any part is defective. This probability is ([tex]0.50 * 0.05) / 0.049 = 0.025 / 0.049 \approx 0.5102 or 51.02%.[/tex]
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A theater gives away one free ticket to every 10th customer and two free tickets to every 25th customer. The manager wants to give away four free tickets when the customer is both a 10th and a 25th customer. Who is the first customer that will recieve four free tickets
Answer:
The first customer that will get four free tickets is 50th customer
Step-by-step explanation:
Find the least common multiple of numbers 10 and 25. First, factorize these numbers:
[tex]10=2\cdot \underline{5}\\ \\25=\underline{5}\cdot 5\\ \\LCM(10,25)=\underline{5}\cdot 2\cdot 5=50[/tex]
When finding LCM, first write the all common multiples (underlined 5) and then multiply them by remaining multiples (2 and 5). You get 50 as LCM(10,25). This means that each 50th customer will get four free tickets.
Final answer:
The first customer who will receive four free tickets is the 100th customer.
Explanation:
To determine the first customer who will receive four free tickets, we need to find the smallest positive integer that is divisible by both 10 and 25. This is called the least common multiple (LCM). To find the LCM of 10 and 25, we can list the multiples of each number until we find a common multiple:
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
Multiples of 25: 25, 50, 75, 100
The LCM of 10 and 25 is 100. Therefore, the first customer who will receive four free tickets is the 100th customer.
Jill and Marcy go to an ice cream store where they have the option of getting a smoothie in either a cylindrical or rectangular container. The cylinder has a height of 8 cm and a radius of 8 cm. The rectangular container has a height of 8 cm, a length of 8 cm, and a width of 5 cm. Jill purchased the cylindrical container and Marcy purchased the rectangular container. Who got the larger smoothie, and what was its volume?
Answer: Jill got the larger smoothie and its volume is 1609.14 cubic cm.
Step-by-step explanation:
Since we have given that
Jill purchased the cylindrical container.
Height of container = 8 cm
Radius = 8 cm
So, volume of cylindrical container would be
[tex]\pi r^2h\\\\=\dfrac{22}{7}\times 8\times 8\times 8\\\\=1609.14\ cm^3[/tex]
Marcy purchased the rectangular container.
Height of container = 8 cm
Width = 8 cm
Length = 8 cm
so, volume of rectangular container would be
[tex]l\times b\times h\\\\=8\times 8\times 8\\\\=512\ cm^3[/tex]
Hence, Jill got the larger smoothie and its volume is 1609.14 cubic cm.
There were 2,605 people at the basketball game. A reporter rounded this number to the nearest hundred for a newpaper aticle. What number did the reporter use
Can you please answer this?
Part A: What is the solution to the pair of equations represented by g(x) and p(x)?
Part B: Write any two solutions for p(x).
Part C: What is the solution to the equation g(x) = f(x)? Justify your answer.
Answer:
A. (1, -1)
B. (1, -1), (2, 0)
C. x = 0
Step-by-step explanation:
A graph is a plot of all the points that are solutions to an equation.
Part A:
A point will be a solution to two equations if it is a point of intersection of their graphs. The one point that is a solution to both p(x) and g(x) is the one point where their graphs intersect: the red and blue lines cross at (1, -1).
__
Part B:
Any other point on the graph p(x) will be another solution of it. One that is near to the point of intersection with g(x) is the point where p(x) crosses the x-axis: (2, 0). Of course, the solution listed in Part A is also a solution to p(x).
__
Part C:
The point where the graph of g(x) crosses the graph of f(x) is (0, 3). The x-value that makes g(x) = f(x) is x=0. That is the solution to this equation. (We don't really care what the values of f(0) and g(0) are--just that they are equal.)
You have a 4 in. X 6in. family picture that you want to resize. You can choose from a 16 in. X 20 in. or an 18 in. X 24 in. Which size will keep more of the original picture?a 4 inch
Answer:
24/18=1.333
20/16=1.25
6/4=1.5 (the ratio to achieve9
1.333 is more close to 1.5 than 1.25 (11% difference compared to 17%)
Step-by-step explanation:
Answer:
16 in. X 20 in will keep more.
Step-by-step explanation:
Length of picture = 4 inches
Breadth of picture = 6 inches
Area of picture=[tex]length \times breadth[/tex]
=[tex]4 \times 6[/tex]
=[tex]24 inches^2[/tex]
Length of frame 1 = 16 inches
Breadth of frame 1 = 20 inches
Area of frame 1 = [tex]16 \times 20 = 320 inches^2[/tex]
So, % of picture can fit in frame 1= [tex]\frac{\text{original picture area }}{\text{Frame 1 area }} \times 100[/tex]
= [tex]\frac{24}{320} \times 100[/tex]
= [tex]7.5 %[/tex]
Length of frame 2 = 18 inches
Breadth of frame 2 = 24 inches
Area of frame 2 = [tex]18 \times 24 = 432 inches^2[/tex]
So, % of picture can fit in frame 2 = [tex]\frac{\text{original picture area }}{\text{Frame 1 area }} \times 100[/tex]
= [tex]\frac{24}{432} \times 100[/tex]
= [tex]5.56 %[/tex]
Since % of picture can fit in frame 1 is more than frame 2 .
So, 16 in. X 20 in will keep more.
Suppose that five ones and four zeros are arranged around a circle. Between any two equal bits you insert a 0 and between any two unequal bits you insert a 1 to produce nine new bits . Then you erase the nine original bits. Show that when you iterate this procedure , you can never get nine zeros . [Hint:work backward, assuming that you did end up with nine zeros.]
Answer:
Using backward reasoning we want to show that "We can never get nine 0's".
Step-by-step explanation:
Basically in order to create nine 0's, the previous step had to have all 0's or all 1's. There is no other way possible, because between any two equal bits you insert a 0.
If we consider two cases for the second-to-last step:
There were 9 0's:
We obtain nine 0's if all bits in the previous step were the same, thus all bit were 0's or all bits were 1's. If the previous step contained all 0's, then we have the same case as the current iteration step. Since initially the circle did not contain only 0's, the circle had to contain something else than only 0's at some point and thus there exists a point where the circle contained only 1's.
There were 9 1's:
A circle contains only 1's, if every pair of the consecutive nine digits is different. However this is impossible, because there are five 1's and four 0's (we have an odd number of bits!), thus if the 1's and 0's alternate, then we obtain that 1's that will be next to each other (which would result in a 1 in the next step). Thus, we obtained a contradiction and thus assumption that the circle contains nine 0's after iteratins the procedure is false. This then means that you can never get nine 0's.
To summarize, in order to create nine 0's, the previous step had to have all 0's or al 1's. As we didn't start the arrange with all 0's, the only way is having all 1's, but having all 1's will not be possible in our case since we have an odd number of bits.
Which is the range of the function f(x) =One-seventh(9)x?
a: all real numbers
b: all real numbers less than 0
c:all real numbers greater than 0
d: all real numbers less than or equal to 0
Answer:
Option c: all real numbers greater than 0
Step-by-step explanation:
we have
[tex]f(x)=\frac{1}{7}(9^{x})[/tex]
This is a exponential function of the form
[tex]f(x)=a(b^{x})[/tex]
where
a is the initial value (y-intercept)
b is the base
r is the rate
b=(1+r)
In this problem we have
a=1/7
b=9
r=b-1 ----> r=9-1=8 -----> r=800%
using a graphing tool
see the attached figure
The domain is the interval ------> (-∞,∞)
The domain is all real numbers
The range is the interval ---------> (0,∞)
The range is all real numbers greater than zero
Answer: all real numbers greater than 0
Step-by-step explanation:
Range is the set of y values for which the function is defined using a graphing tool
The domain is the interval ----> (-∞,∞) All real numbers
For all positive and negative values for x the value of y is always positive
The range is the interval ---->(0,∞)
All real numbers greater than 0
Given triangle ABC with coordinates A(−4, 4), B(−4, 1), and C(−6, 0), and its image A′B′C′ with A′(0, 0), B′(−3, 0), and C′(−4, −2), find the line of reflection.
The line of reflection is at y=
Answer:
y = x + 4
Step-by-step explanation:
The line of reflection is the perpendicular bisector of segment AA', so passes through point (A+A')/2 = (-2, 2) and is perpendicular to the line through A and A'. That line is y = -x, so the point-slope equation of the line of reflection is ...
y = 1(x -(-2)) +2
y = x +4
The line of reflection between triangle ABC and its image A'B'C' is y = -x. The point-slope equation of the line of reflection is y = x+4.
Explanation:To find the line of reflection between triangle ABC and its image A'B'C', we can observe that the corresponding points have the same x-coordinates and their y-coordinates are negatives of each other. Since the line of reflection is the perpendicular bisector of the segment joining each original point and its image, we can use the coordinates of two corresponding points to find the equation of the line. In this case, we can use points A and A', and points B and B' to determine the line of reflection.
Using the coordinates A(-4, 4) and A'(0, 0), we can calculate the slope of the line as (0 - 4) / (0 - (-4)) = -1. The midpoint between A and A' is (-2, 2), which lies on the line. So, the equation of the line is y = -x.
Similarly, using the coordinates B(-4, 1) and B'(-3, 0), we can calculate the slope as (0 - 1) / (-3 - (-4)) = 1. The midpoint between B and B' is (-3.5, 0.5), which also lies on the line y = x. Therefore, the line of reflection is y = -x.
So, the point-slope equation of the line of reflection is:
y = 1(x -(-2)) +2
y = x +4
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The graph for reflection is given below:
What is the volume of a right rectangular prism when the height is 11 m and the area of the square base is 9m 2 ?
Answer:
The answer to your question is: 99 m²
Step-by-step explanation:
Data
height = 11 m
area of the square base = 9 m²
Formula
Volume of a right rectangular prism = area of the base x height
= 11 x 9 substitution
= 99 m²
Solve for d. 6(d+1)−2d=54 Enter your answer in the box. d =
Answer:
The answer to your question is: d = 12
Step-by-step explanation:
6(d+1)−2d=54
Expand 6d + 6 -2d = 54
6d - 2d = 54 - 6
Simplify 4d = 48
d = 48 / 4
Result d = 12
A customer service survey was conducted of 500 customers: 250 men and 250 women. The data on one of the questions show that 175 men and 160 women rate the customer service as excellent. What percentage of men gave an excellent rating? What percentage of women gave an excellent rating? What was the total percentage of customers giving an excellent rating?
The percentage of men who gave an excellent rating is 70%. The percentage of women who gave an excellent rating is 64%. The total percentage of customers giving an excellent rating is 67%.
Explanation:To find the percentage of men who gave an excellent rating, we divide the number of men who gave an excellent rating (175) by the total number of men surveyed (250) and multiply by 100.
So the percentage of men who gave an excellent rating is 70%.
To find the percentage of women who gave an excellent rating, we divide the number of women who gave an excellent rating (160) by the total number of women surveyed (250) and multiply by 100.
So the percentage of women who gave an excellent rating is 64%.
To find the total percentage of customers who gave an excellent rating, we divide the total number of customers who gave an excellent rating (175 + 160 = 335) by the total number of customers surveyed (500) and multiply by 100. So the total percentage of customers who gave an excellent rating is 67%.
The percentage of men who gave an excellent rating is 70%, the percentage of women who gave an excellent rating is 80%, and the total percentage of customers giving an excellent rating is 67%.
First, let's calculate the percentage of men who gave an excellent rating:
- There are 250 men surveyed.
- Out of these, 175 men rated the customer service as excellent.
- To find the percentage, we use the formula: (Number of men who rated excellent / Total number of men) × 100.
- Plugging in the numbers, we get: (175 / 250) × 100.
- Simplifying this, we divide both the numerator and the denominator by 25 to get: (7 / 10) × 100.
- This simplifies to 70%.
Next, we calculate the percentage of women who gave an excellent rating:
- There are 250 women surveyed.
- Out of these, 160 women rated the customer service as excellent.
- Using the same formula as before: (Number of women who rated excellent / Total number of women) × 100.
- Plugging in the numbers, we get: (160 / 250) × 100.
- Simplifying this, we divide both the numerator and the denominator by 40 to get: (4 / 5) × 100.
- This simplifies to 80%.
Finally, we calculate the total percentage of customers who gave an excellent rating:
- The total number of customers surveyed is 500 (250 men + 250 women).
- The total number of excellent ratings is 175 from men and 160 from women, which sums up to 335.
- Using the formula: (Total number of excellent ratings / Total number of customers) × 100.
- Plugging in the numbers, we get: (335 / 500) × 100.
- Simplifying this, we divide both the numerator and the denominator by 5 to get: (67 / 100) × 100.
- This simplifies to 67%.
- Percentage of men giving an excellent rating: 70%
- Percentage of women giving an excellent rating: 80%
- Total percentage of customers giving an excellent rating: 67%
A discrete mathematics class contains 1 mathematics major who is a freshman, 12 mathematics majors who are sophomores, 15 computer science majors who are sophomores, 2 mathematics majors who are juniors, 2 computer science majors who are juniors, and 1 computer science major who is a senior. Express each of these statements in terms of quantifiers and then determine its truth value.
a) There is a student in the class who is a junior.
b) Every student in the class is a computer science major.
c) There is a student in the class who is neither a mathematics major nor a junior.
d) Every student in the class is either a sophomore or a computer science major.
e) There is a major such that there is a student
Answer and Step-by-step explanation:
As quantifiers, we can settle:
x is a student
M(x) is a math major student
C(x) is a computer science major student
F(x) is a freshman student
S(x) is a sophomore student
J(x) is a junior student
N(x) is a senior student
∃ exists
∀ every
¬ negation
∧ and
∨ or
a) There is a student in the class who is a junior.
∃xJ(x) value: True. There are 4 juniors
b) Every student in the class is a computer science major.
∀xC(x) value: False. There are math students
c) There is a student in the class who is neither a mathematics major nor a junior.
∃x¬M(x)∨¬C(x) value: False. All students are math ou computer science majors
d) Every student in the class is either a sophomore or a computer science major.
∀xS(x)∨C(x) value: False. There are some students who are neither, for example mathematics majors who are juniors
e) There is a major such that there is a student*
∃M(x)C(x)x value: True. All majors have students.
*This one seems incomplete, but I answered the way it is writen.
The expression of the statement based on the quantifiers show that the truth value will be:
True FalseTrue False FalseWhat is a quantifier?It should be noted that quantifies are the words or expressions that indicate the number of elements which a statement pertains to.
From the information, there is a student in the class who is a junior. It can also be deduced that not every student in the class is a computer science major. This is because there are mathematics majors too.
Furthermore, there is a student in the class who is neither a mathematics major not a junior but not every student in the class is either a sophomore or a computer science major.
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Todd wants to make a snack of a number of grapes and slices of cheese. He knows that each grape has 2 calories. The slice of cheese is 155 calories. Todd wants calorie snack using both grape and cheese. What equation could he use to determine the number of grapes he can eat? Part 2: how many grapes can he eat for his 205 calorie snack? Part 3: Todd's friend Francis brings more slices of cheese. How many total slices of cheese are required to make a 515 calories snack if the number of grapes remain the same?
Answer:
The answer to your question is:
a) C = 2g + 155c
b) g = 25 grapes
c) c = 3
Step-by-step explanation:
Data
grapes = g = 2 calories
cheese = c = 155 calories
a) Equation, we consider the amount of grapes and the calores given.
Total calories = C = 2g + 155c
b) We consider that the slices of cheese stays the same
2g + 155 = 205
2g = 205 -155
2g = 50
g = 50/2 = 25 grapes
c) Then the number of grapes stays the same
2(25) + 155c = 515
50 + 155c = 515
155c = 515 - 50
155c = 465
c = 465/155
c = 3 slices of cheese
According to Greg, perfect cherry pies have a ratio of 240240240 cherries to 333 pies. How many cherries does Greg need to make 999 perfect cherry pies?
999 is 3 times 333, so the ratio will have to be multiplied by three.
No of cherries needed = 240240240 * 3 = 720720720 cherries
The width of a singles tennis court is 75% of the width of a doubles court. A doubles court Is 36 feet wide. How wide is a singles court Is 36 feet wide. How wide is a singles court
Answer:
width of a singles court = 27 feet
Step-by-step explanation:
Width of a doubles tennis court = 36 feet
Width of a singles tennis court = 75% of 36
[tex]width = 75\% \times 36 \\ width = \frac{75}{100} \times 36 \\ width = \frac{3} {4} \times 36 \\ width = \frac{108}{4} = 27[/tex]
The perimeterof a parralelagram is 60 meters. The width of the parralelgram is 6 meters less than its length. Find the length and width of the paralelogram
Answer:
The answer to your question is:
length = 12
width = 6
Step-by-step explanation:
Perimeter of a parallelogram = 2 length + 2 width
We know that width = length - 6
So
60 = 2 length + 2(length -6)
60 = 2 length + 2 length - 12
60 - 12 = 4 length
48 = 4 length
length = 48/4 = 12 meters
width = length - 12
= 12 - 6
= 6
Answer:
12
6
Step-by-step explanation:
solve the equation -36 = -6(2x - 14)
Answer:
x = 10
Step-by-step explanation:
-36 = -6(2x-14)
6 = 2x-14
20 =2x
10 = x
Answer:
-x = -10
Step-by-step explanation:
-36 = -12x + 84
-120 = -12x
-10 = -x
State whether each function is a linear function. Explain.
1. y = 3x
2. y =- 2+5x
3. 2x + y= 10
4. f(x) = 4x^2
5. -3/x + y = 15
6. x + y + 8
Answer:
The answer is below
Step-by-step explanation:
1. y = 3x is a linear function because it doesn't have any power
2. y =- 2+5x is a linear function because it doesn't have any power
3. 2x + y= 10 is a linear function because it doesn't have any power
4. f(x) = 4x^2 it isn't a linear function because x is elevated to a power
5. -3/x + y = 15 is a linear function because it doesn't have any power
6. x + y + 8 is a linear function because it doesn't have any power
The first, second, third and sixth functions are linear functions, as they comply with the standard linear function format, y = mx + c. The fourth and fifth functions are not linear because they do not follow this standard format.
Explanation:A linear function is a function whose graph is a straight line. The general form of a linear function is y = mx + c, where m is the slope of the line, and c is the y-intercept.
y = 3x is a linear function, as it can be rewritten in the general form y = mx + c by considering m as 3 and c as 0. y =- 2+5x is also a linear function. Here, the slope m is 5 and the y-intercept c is -2. 2x + y= 10 can be rearranged as y = -2x + 10, which is a linear function with m = -2 and c = 10. f(x) = 4x^2 is not a linear function as the x term is raised to the power of 2, making it a quadratic function. -3/x + y = 15 is not a linear function as it includes an x term in the denominator. x + y + 8 is a linear equation. If this equation is rearranged in the format y = mx + c, it becomes y = -x - 8. Here, m = -1 and c = -8.Learn more about linear function here:
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An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. The standard deviation of completion times is 1.6 minutes. It is claimed that, under new management, the mean completion time has decreased. To test this claim, a random sample of 33 completion times under new management was taken. The sample had a mean of 11.2 minutes. Assume that the population is normally distributed. Can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? Assume that the standard deviation of completion times has not changed.
Let [tex]\mu[/tex] be the population mean.
Null hypothesis : [tex]\mu=12[/tex]
Alternative hypothesis : [tex]\mu<12[/tex]
Since Alternative hypothesis is left tailed so , the test is a left tailed test.
Given : n=33 > 30 , so we use z-test.
Test statistic : [tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
i.e. [tex]z=\dfrac{11.2-12}{\dfrac{1.6}{\sqrt{33}}}\approx-2.87[/tex]
Using z-value table,
P-value for left tailed test =[tex]P(z<-2.87)=0.0020524[/tex]
Since , the p-value (0.0020524) is less than the 0.05 level of significance, it means we reject the null hypothesis.
Therefore, we have enough evidence to support the claim that the mean completion time has decreased under new management.
Consider the following information.
1 hour = 3.6 · 103 seconds
1 day = 24 hours
1 year = 3.65 · 102 days
Use scientific notation to calculate the number of seconds in 3 days.
Answer:
2.592×10^5 seconds
Step-by-step explanation:
[tex]3\,days\cdot\dfrac{24\,h}{1\,day}\cdot\dfrac{3.6\cdot 10^3\,s}{1\,h}=3\cdot 24\cdot 3.6\cdot 10^3\,s=2.592\cdot 10^5\,s[/tex]
Answer:
Corrected answer is 8.64 x 10^4 seconds in one day
Step-by-step explanation:
A 12-cm-long thin rod has the nonuniform charge density λ(x)=(2.0 nC/cm)e−|x|/(6.0 cm), where x is measured from the center of the rod. What is the total charge on the rod? Hint: This exercise requires an integration. Think about how to handle the absolute value sign
Answer:
the total charge is
[tex]Q=24(1-\exp(-1))nC\approx15.171nC[/tex]
Step-by-step explanation:
Since x is measured from the center, that means that x=0 is the center so the edges of the rod correspond to x=-6 and x=6. that meas that the total charge can be calculated as
[tex]Q=\int^{6}_{-6}2\exp\left(\frac{-|x|}{6}\right)dx[/tex]
separating the integral from -6 to 0 and from 0 to 6, taking into account that |x|=-x for x<0 and |x|=x for x >=0, we get[tex]Q=\int^{0}_{-6}2\exp\left(\frac{x}{6}\right)dx+\int^{6}_{0}2\exp\left(\frac{-x}{6}\right)dx[/tex]
using the substitution x=-u in the first integral we get[tex]\int^{0}_{-6}2\exp\left(\frac{x}{6}\right)dx=-\int^{0}_{6}2\exp\left(\frac{-u}{6}\right)du=\int^{6}_{0}2\exp\left(\frac{-u}{6}\right)du[/tex]
which is the same as the first integral. Thus, the total charge is given by
[tex]Q=2\int^{6}_{0}2\exp\left(\frac{-x}{6}\right)dx[/tex]
integrating we get
[tex]Q=4(-6\exp\left(\frac{-x}{6}\right))\big|^{6}_{0}=-24(\exp(-6/6)-\exp(0))=24(1-\exp(-1))[/tex]
The total charge is Q= 15.171nC.
Calculations and Parameters:Since x is measured from the center, that means that x=0 is the center.
So, the edges of the rod correspond to
x=-6 and x=6.
That means that the total charge can be calculated as
[tex]Q= \int\limits^6_ 6 2 exp(-|x|/6)dx[/tex]
separating the integral from -6 to 0 and from 0 to 6,
Taking into account that
|x|=-x for x<0
and |x|=x for x >=0
Thus, the total charge is given by:
[tex]Q= 2\int\limits^6_0 2exp (-x/6), dx[/tex]
When we integrate, we get:
Q= 24(1- exp(-1))nC ≈
15.171nC
Read more about integration here:
https://brainly.com/question/20158587
A bathtub can hold a maximum of 50 gallons of water. Water can be drained out of the tub at a rate of 2 gallons per minute. If the tub is initially completely filled by a faucet at a rate of 1 gallon per minute, how long will it take to drain the full tub if the drain is opened but the faucet is kept on?
Answer:
50 minutes
Step-by-step explanation:
Given,
Water can be drained out of the tub at a rate of 2 gallons per minute,
So, the drained water in 1 minute = 2 gallon,
That is, change in 1 minute = -2 gallon
( negative sign shows losing water)
Also, it is filled by a faucet at a rate of 1 gallon per minute,
So, the filled water in 1 minute = 1 gallon,
That is, change in 1 minute = + 1 gallon
( Positive sign shows additional water ),
Thus, total change in 1 minute = -2 + 1 = -1 gallon,
Let x be the time after which the bathtub will be emptied completely,
Total change in x minutes = -x gallon,
Bathtub will be emptied, if,
Initial volume of water + total change in water = 0
50 - x = 0 ( given volume of tub is 50 gallon )
[tex]\implies x = 50[/tex]
Hence, it will take 50 minutes to drain the full tub.
Final answer:
To drain a bathtub initially filled with 50 gallons, with an incoming rate of 1 gallon per minute and a draining rate of 2 gallons per minute, it takes 50 minutes.
Explanation:
The question involves calculating the time it takes to drain a bathtub that is being filled and drained simultaneously. Initially, the bathtub is completely filled with 50 gallons of water. The faucet fills the tub at a rate of 1 gallon per minute, while the drain can remove water at a rate of 2 gallons per minute. Therefore, the net rate at which water is being drained is 1 gallon per minute (2 gallons out - 1 gallon in). To completely drain the tub of its initial 50 gallons, at a net rate of 1 gallon per minute, it would take 50 minutes.
Therefore, as per the above explaination, the correct answer is 50 min.
Hailey paid \$13$13dollar sign, 13 for 1\dfrac3{7} \text{ kg}1 7 3 kg1, start fraction, 3, divided by, 7, end fraction, space, k, g of sliced salami. What was the cost per kilogram of salami? \$
Answer:
The answer is 9.10, ($9.10).
Step-by-step explanation:
Oh just to let you know that other answer (joke) was such a loser joke.
For the following situation determine what type of sampling was used. A research company believes teens today are getting less than the recommended hours of sleep. The company takes a list of 2000 teen volunteers and assigns each volunteer a number. A random number generator is used to select 350 individuals to take part in a sleep survey.
Answer: Simple random sampling.
Step-by-step explanation:
A simple random sample is basically a subset (with size n) from the entire population, where the chance of getting selected for each element is equal.
Given :A research company believes teens today are getting less than the recommended hours of sleep. The company takes a list of 2000 teen volunteers and assigns each volunteer a number. A
A random number generator is used to select 350 individuals to take part in a sleep survey.
It is a simple random sampling because the researcher selected participants randomly such that the chance to get selected for each of them remains same.
Please please help me
Answer: 180
Step-by-step explanation:
divide 45 by 7.5 to get the amount of dollars earned per hour
45/7.5 = 6
6(x)= 30hours, = 6(30) = $180
Answer:
$180
Step-by-step explanation:
let pay be p and hours worked be h
Given p varies directly as h then the equation relating them is
p = kh ← k is the constant of variation
To find k use the condition p = 45 when h = 7.5, then
k = [tex]\frac{p}{h}[/tex] = [tex]\frac{45}{7.5}[/tex] = 6, thus
p = 6h ← equation of variation
When h = 30, then
p = 6 × 30 = $180
A researcher conducts a repeated-measures study to evaluate a treatment with a sample of n = 16 participants and obtains a t statistic of t = 1.94. The treatment is expected to increase scores and the sample mean shows an increase. Which of the following is the correct decision for a hypothesis test using α = .05.
- Reject the null hypothesis with either a one-tailed or a two-tailed test
- Fail to reject the null hypothesis with a one-tailed test but reject with two tails
- Reject the null hypothesis with a one-tailed test but fail to reject with two tails
- Fail to reject the null hypothesis with either a one-tailed or a two-tailed test
Answer:
Option 3) We reject the null hypothesis with one tail test and accept the null hypothesis with two tail test.
Step-by-step explanation:
We are given the following information:
n = 16
[tex]t_{statistic} = 1.94[/tex]
[tex]\alpha = 0.05[/tex]
Now,
Right One-tail Test
[tex]t_{critical} \text{ at 0.05 level of significance, 15 degree of freedom } = 1.753[/tex]
[tex]t_{stat} > t_{critical}[/tex]
We reject the null hypothesis in this case.
Two-tail Test
Now, [tex]t_{critical} \text{ at 0.05 level of significance, 9 degree of freedom } = \pm 2.131[/tex]
[tex]-2.131 < t_{stat} < 2.131[/tex]
We accept the null hypothesis in this case.
Option 3) We reject the null hypothesis with one tail test and accept the null hypothesis with two tail test.
The correct decision for this hypothesis test is to reject the null hypothesis with a one-tailed test but fail to reject with two tails.
Explanation:To make a decision in a hypothesis test, we compare the t statistic to the critical value. In this case, the t statistic is 1.94. Since the treatment is expected to increase scores and the sample mean shows an increase, we are conducting a one-tailed test. Looking at the critical value for a = 0.05 for a one-tailed test using the t15 distribution, we find that it is 1.753. Since the t statistic (1.94) is greater than the critical value (1.753), we reject the null hypothesis. Therefore, the correct decision for this hypothesis test is to reject the null hypothesis with a one-tailed test but fail to reject with two tails.
Learn more about Hypothesis testing here:https://brainly.com/question/34171008
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