If m = 3/2, the two equations in the system are dependent and have an infinite number of solutions.
To do this, we can set the coefficients of x and y in the two equations equal to each other:
6 - 4m = 2k(2m - 1)
2n - 7 = 3k
Simplifying these equations, we get:
8m - 6 = 4km
2n - 7 = 3k
We can solve the first equation for k:
k = (8m - 6)/(4m)
Substituting this into the second equation and solving for n, we get:
n = (16m - 29)/(8m - 12)
Now we need to check if there are any values of m for which the equations are proportional. We can do this by checking if the expressions for k and n are the same for all values of m.
We find that the expressions for k and n are the same for m = 3/2.
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Complete Question:
Determine the values of m and n so that the following system of linear equations have infinite number of solutions:
(2m−1)x+3y−5=0
3x+(n−1)y−2=0
A snow making machine priced at $1800 is on sale for 25% off. The sales tax rate is 6. 25%. What is the sale price including tax? If necessary, round your answer to the nearest cent
The sale price including tax is $ 2390.625.
Given that,
The price of the snow machine= $ 1800
Discount percentage= 25%
Sales tax rate = 6.25%
Hence, Sale price = Price + Discount percentage of price
= 1800 + 25/100 × 1800
= 1800 + 450
= 2250.
Sale price including tax = Sale price + Tax rate
= 2250 + 6.25/100
= 2250 + 140.625
= $ 2390.625.
Hence, the sale price including tax is $ 2390.625.
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cathy's heart beats 12 times in 1/6 minute.how many times does her heart beats in 60 minutes.
Answer:
4,320 times
Step-by-step explanation:
12 x 6 = 72 beats per minute
72 x 60 = 4320 beats in 60 minutes
Answer: 840 in 30 minuets
Step-by-step explanation:
For Blake's lemonade recipe, 12 lemons are required to make 16 cups of lemonade. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
Answer: To fill out a table of equivalent ratios for Blake's lemonade recipe, we can use the ratio of lemons to cups of lemonade:
Lemons Cups of Lemonade
3 4
6 8
9 12
12 16
15 20
18 24
To plot the points on a coordinate axes, we can use the Lemons as the x-coordinate and the Cups of Lemonade as the y-coordinate. The points would lie on a line that passes through the origin (0,0) and the point (12,16).
| *
Cups of | * *
Lemonade | * *
|________________
Lemons
0 12
The line represents the proportional relationship between the number of lemons and the amount of lemonade produced. As the number of lemons increases, the amount of lemonade produced increases proportionally.
Step-by-step explanation:
solve and graph 4<4(k+3) also check please
Answer:
-8 < k
Step-by-step explanation:
4 < 4(k+3)
4 < 4k + 12
-8 < k
Sadio starts with savings of £15
Thomas starts with no savings.
Each week from now,
Sadio will save £3.50 and Thomas will save £3
In how many weeks will Sadio and Thomas have savings in the ratio 2 : 1?
Thomas and Sadio have a 15:8 savings ratio that will be ready in five weeks.
What is the ratio?In mathematics, a ratio shows how frequently one number appears in another.
For instance, the proportion of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons.
Oranges make up 8:14 of the total fruit, whereas lemons make up 6:8 of the total fruit.
So, the number of weeks would be:
Considering that Sadio savings = 15 + 4.50 times
Thomas = x4
Where the number of weeks is x.
Sadio : Thomas = 15 : 8
15 + 4.50x : 4x = 15 : 8
(15+ 4.50x ) / 4x = 15 / 8
Now, perform cross multiplication as follows:
8 (15+ 4.50x) = 15 (4x)
120 + 36x = 60x
60x - 36x = 120
24x = 120
x = 120 / 24 = 5 weeks
Therefore, Thomas and Sadio have a 15:8 savings ratio that will be ready in five weeks.
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Correct question:
Sadio starts with savings of £15. Thomas starts with no savings. Each week from now, Sadio will save £4.50 and Thomas will save £4. In how many weeks will Sadio and Thomas have savings in the ratio 15:8 ?
Complete the table for each function. Then answer the questions that follow. A=
; b =
; c =
; d =
;
e =
; f =
; g =
The values of a=4, b=4, c=8, d=16, e=12, f=36 and g = 64
The first step is to evaluate the function for each value of x given in the table, which gives us the values of y1, y2, and y3 for x=0, 1, 2, and 3.
For example, to find the value of y3 for x=1, we use the function y3=4^x and substitute x=1, which gives us y3=4^1=4. Similarly, we can find the values of y1 and y2 for each value of x using the given functions.
a = y3(x=1) = 4^1 = 4
a = y3(x=2) = 4^1 = 4
c = y1(x=2) = 4(2) = 8
d = y3(x=3) = 4^2 = 16
e = y1(x=3) = 4(3) = 12
f = y2(x=3) = 4(3)^2 = 36
g = y3(x=3)= 4^3 = 64
Complete, the table
x y1=4x y2=4x^2 y3=4^x
0 0 0 1
1 4 4 4
2 8 16 16
3 12 36 64
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The given question is incomplete, the complete question is:
Complete the table for each function. Then answer the questions that follow.
a = ?, b= ?, c= ?, d= ?, e= ?, f= ?, g= ?
The Anderson’s travelled for 880 km from St. John’s to Halifax via Argentia. Part of the trip was by car at 80 km/h, and the rest by ferry at 16 km/h. If the total travelling time for the entire trip was 27 h, how many hours were spent by car, and how many by ferry? (Answer: car = 7 h; ferry = 20 h)
The car travelled at 80km/h for 7 hours and travelled a distance of 560km whereas the ferry travelled at 16km/h for 20 hours and travelled a distance of 320km.
We know that the Anderson’s travelled for 880 km from St. Johns to Halifax via Argentia and that part of the trip was by car at 80 km/h and the rest by ferry at 16 km/h.
we need to find how much time did it take the Anderson’s to travel by car and by ferry
as part of the journey was done by car and the other by ferry
560km was travelled by car therefore now we need to find time travelled by car = distance = speed x time
we get time travelled by car = 7 hours
similarly we need to find the time take by ferry we have:
320km travelled by ferry at 16km/h we get the time travelled by ferry = 20hours
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Each section of the graphic organizer contains a vocabulary term or the possible
solution type for the system shown. Use the list below to complete the graphic
organizer. Some terms may be used more than once.
slope y-intercept linear equations
infinitely many solutions no solution one solution
System of
y= 3x+ 2
y= - 4x+ 2
Different
y= 2x+ 7
y= 2x- 4
Same
y= 6x+ 3
y= - x- 4
Number of solutions:
y= 4x+ 3
y= 4x- 1
Different
y= 3x+ 6
y= 3x+ 6
Same
y= 4x+ 3
y= 4x- 1
Number of solutions:
y= 3x+ 6
y= 3x+ 6
Number of solutions:
For the first equation with y = 3x + 2 and y = -4x + 2, the lines have the same slope, but a different y-intercept. This means that the lines are parallel and they will never intersect. Therefore, the system of equations has no solution.
For the second equation with y = 2x + 7 and y = 2x - 4, the lines have the same slope and the same y-intercept. This means that the lines are coincident and they will intersect at one point. Therefore, the system of equations has one solution.
For the third equation with y = 6x + 3 and y = -x - 4, the lines have a different slope and a different y-intercept. This means that the lines are not parallel and they will intersect at one point. Therefore, the system of equations has one solution.
For the fourth equation with y = 4x + 3 and y = 4x - 1, the lines have the same slope and the same y-intercept. This means that the lines are coincident and they will intersect at one point. Therefore, the system of equations has one solution.
For the fifth equation with y = 3x + 6 and y = 3x + 6, the lines have the same slope and the same y-intercept. This means that the lines are coincident and they will intersect at one point. Therefore, the system of equations
What is the measure of ∠Y?
According to the inscribed angle theorem the measure of angle Y is 43 degrees.
What is inscribed angle theorem?As the inscribed angle equals half of the central angle, the inscribed angle theorem is also known as the angle at the centre theorem. The centre angle is always the same since the endpoints are fixed, regardless of where it is on the same arc between the ends. The measure of the central angle is equal to double the measure of the inscribed angle occupied by the same arc, according to this theorem. OR. Half of a central angle that subtends the same arc is an inscribed angle. OR. The angle in a circle's centre is twice as large as any angle at its perimeter that the same arc occupies.
We know that, an inscribed angle is half of a central angle that subtends the same arc.
Here the given arc = 86 degrees.
The inscribed angle is half the arc of the circle thus,
angle Y = 1/2(86)
angle Y = 43 degrees.
Hence, according to the inscribed angle theorem the measure of angle Y is 43 degrees.
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Aamena buys a business costing $23000
She pays part of this cost with $12000 of her own money
Calculate what percentage of the $23000 this is
Show your calculations
Answer:
52.17%
Step-by-step explanation
[tex]\frac{12000}{23000}[/tex] ×100%
[tex]\frac{1200}{23}[/tex]
52.17
A restaurant at the food court in a mall is offering a lunch special. The table shows the relationship between the number of side dishes and the total cost of the special.
Restaurant
Number of Side Dishes Total Cost
2 $6.75
4 $8.25
5 $9.00
8 $11.25
Which of the following graphs shows the relationship given in the table?
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 6 and 75 hundredths through the point 3 comma 9
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 25 hundredths through the point 5 comma 9
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 6 and 75 hundredths through the point 1 comma 8 and 25 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 75 hundredths through the point 1 comma 7 and 25 hundredths
The correct answer is graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 6 and 75 hundredths through the point 3 comma 9.
What is axis?Axis refers to the number of dimensions in a graph, chart, or plot. It is an imaginary line that is used to measure and plot values in a graph. In a line graph, the x-axis is the horizontal line and the y-axis is the vertical line.
The first graph shows a relationship between the number of side dishes and the total cost of the special that does not match the data given in the table.
The second graph does not reflect the data given in the table, as the total cost of the special increases from $5.25 to $9.00 when the number of side dishes increases from 0 to 5.
The third graph also does not reflect the data given in the table, as the total cost of the special increases from $6.75 to $8.25 when the number of side dishes increases from 0 to 4.
The fourth graph also does not reflect the data given in the table, as the total cost of the special increases from $5.75 to $7.25 when the number of side dishes increases from 0 to 1.
Therefore, the correct answer is mentioned above. This graph accurately reflects the relationship between the number of side dishes and the total cost of the special.
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The correct answer is "graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0,6 and 75 hundredths through the point 3,9".
What is axis?Axis refers to the number of dimensions in a graph, chart, or plot. It is an imaginary line that is used to measure and plot values in a graph.
This graph correctly illustrates the relationship between the number of side dishes and the total cost of the special as shown in the table.
The line starts at 0 side dishes and $6.75
and ends at 4 side dishes and $8.25, both of which are in the table.
The graph accurately reflects this by having a line that starts at 2 side dishes and $6.75 and ends at 5 side dishes and $9.00.
This shows that as the number of side dishes increases, the cost also increases.
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The 1948 and 2018 temperatures at 197 random locations across the globe were compared and the mean difference for the number of days above 90 degrees was found to be
2.9
days with a standard deviation of
17.2
days. The difference in days at each location was found by subtracting 1948 days above 90 degrees from 2018 days above 90 degrees. A) What is the lower limit of a
90%
confidence interval for the average difference in number of days the temperature was above 90 degrees between 1948 and 2018 ? Rounded to nearest whole number. B) What is the upper limit of a
90%
confidence interval for the average difference in number of days the temperature was above 90 degrees between 1948 and 2018 ? Rounded to nearest whole number. C) What is the margin of error for the
90%
confidence interval? Rounded to nearest whole number. D) Does the
90%
confidence interval provide evidence that number of 90 degree days increased globally comparing 1948 to 2018? Why? E) Does the
99%
confidence interval provide evidence that number of 90 degree days increased globally comparing 1948 to 2018? Why? F) If the mean difference and standard deviation stays relatively constant would decreasing the degrees of freedom make it easier or harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally. G) If the mean difference and standard deviation stays relatively constant does lowering the confidence level make it easier or harder to conclude that there are more days above 90 degrees Choose...
∨1
4 No, not all values in confidence interval are positive 6 Yes, all values in confidence interval are positive harder
−1
5 easier 2
This means that, by lowering the confidence level, it is easier to reach the desired level of statistical significance and thus easier to conclude that the number of days above 90 degrees has increased.
F) Lowering the degrees of freedom would make it easier to conclude that there are more days above 90 degrees in 2018 compared to 1948 globally. The reason for this is that reducing the degrees of freedom makes it easier to achieve the desired statistical significance. By reducing the degrees of freedom, you are essentially decreasing the number of observations needed in order to reach the desired confidence level. This makes it easier to conclude that the number of days above 90 degrees has increased since 1948, as it requires fewer observations to reach the desired significance level.
G) Lowering the confidence level would make it easier to conclude that there are more days above 90 degrees in 2018 compared to 1948 globally. This is because a lower confidence level requires less data in order to achieve the desired statistical significance. By reducing the confidence level, fewer observations are needed in order to prove that the number of days above 90 degrees has increased since 1948. This means that, by lowering the confidence level, it is easier to reach the desired level of statistical significance and thus easier to conclude that the number of days above 90 degrees has increased.
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Sarun is thrice as old as his sister Anita. If five years is subtracted from Anita’s age and seven years added to Sarun’s age , then
Sarun will be five times Anita’s age. How old were they three years ago?
Answer:
Anita is 11 years old and sarun 55 years old( not so sure about this answer... what do you think)
Step-by-step explanation:
let Anita's age be x
and sarun's age be 3x
if, x-5 = 3x+7
3x+7 = 5(x-5)
3x+7=5x-25
32=2x
x=16
their ages 3 years ago,
Anita= 16-5=11yrs
sarun= 3*16+7 = 55yrs
Solve the inequality for u.
48<5u+8
Simplify the answer as much as possible
Answer:
U=8
Step-by-step explanation:
48<5U+8
-5U<8-48
-5U<-40
-5U/-5<-40/+5
U>8
what type of population growth will show a population reaching it's carrying capacity
Answer:
logistic growth
Step-by-step explanation:
In logistic growth, a population's per capita growth rate gets smaller and smaller as population size approaches a maximum imposed by limited resources in the environment, known as the carrying capacity ( K).
Need help to solve this please!!
Answer:
0.999
Step-by-step explanation:
If the driver wore a seat belt, that is the only column we have to look at.
The chance the driver survived is number survived / number total.
Plugging in, we get 412,042/412,493, or about 0.999.
Hope this helps!
a pizza parlor offers a choice of 16 different toppings. how many 6-topping pizzas are possible? (no double-orders of toppings are allowed) in this situation, does the order of the toppings matter? input yes or no. there are possible 6-topping pizzas.
By combinations, we get that there are 20,020 possible 6-topping pizzas.
Given that a pizza parlor offers a choice of 16 different toppings, we need to find the number of 6-topping pizzas that are possible. No double-orders of toppings are allowed. What is the number of 6-topping pizzas that are possible?
The formula for combinations is as follows:
ncr = (n!)/(r! * (n - r)!) where n = 16 (total number of toppings available)
r = 6 (number of toppings required for a pizza)
ncr = (16!)/(6! * (16 - 6)!)
⇒ ncr = (16!)/(6! * 10!)
⇒ ncr = (16 * 15 * 14 * 13 * 12 * 11)/(6 * 5 * 4 * 3 * 2 * 1)
⇒ ncr = (16 * 3 * 5 * 7 * 13 * 11)/(3 * 2 * 2)
⇒ ncr = 20,021
In this situation, the order of the toppings does not matter. Therefore, we cannot have a repeat of the same toppings, as mentioned. Hence the answer to the question is no. Thus, there are 20,020 possible 6-topping pizzas.
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I need the steps to how I got the answer for this question but I don’t know the answer! please help!
Thank you!!
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
$20 dollars needs to be split between Jack and Jill. Jill gets to make an initial offer. Jack can respond by either accepting Jill’s initial offer or offering a counter offer. Finally, Jill can respond by either accepting Jacks offer or making a final offer. If Jake does not accept Jill’s final offer both Jack and Jill get nothing. Jack discounts the future at 10% i. E. Future earnings are with 10% less than current earnings while Jill discounts the future at 20%. Calculate the best deal of this problem
The best deal for Jack and Jill would be for Jill to offer Jack $10, and for Jack to accept this offer. This would give Jack $9.09 in the future after discounting, and it would give Jill $10 in the future after discounting.
Jack will accept anything positive.
Jill offers: $20 to herself, $0 to JackJill is indifferent between $20 in one year and $16 today (she discounts the future at 20%).
Jack offers: $16 to Jill and $4 to HimselfJack is indifferent between $4 in one year and $3.60 today (he discounts the future at 10%). Note that $16.40 is preferred by Jill to $16 in one year.
Jill offers: $16.40 to herself, $3.60 to JackDiscount refers to the process of reducing the value of future benefits or costs, based on the assumption that people generally prefer immediate benefits to delayed ones. This means that the further into the future a benefit or cost occurs, the less valuable it is considered to be in the present.
Discounting is commonly used in economics, finance, and environmental analysis, where it plays a significant role in determining the present value of future cash flows, investments, and environmental damages. The concept is also used in decision-making, as individuals and organizations often make choices based on their perception of the present value of future outcomes.
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if you flipped a fair coin 40 times, what is the heoretical proportion of heads? in other words, what percent do you expect to come up heads> based on your confidence interval, do yuou think thje copi used was fair? wy or why not
A fair coin is flipped 40 times. The probability of getting a head when the coin is tossed is 0.5. If the same coin is flipped 40 times, the probability will remain 0.5. That is, there are equal chances of getting heads and tails when a fair coin is flipped.
Based on the confidence interval, if the actual proportion of heads falls within the range of the confidence interval, it can be said that the coin used was fair. If the actual proportion is outside the confidence interval, it may be an indication that the coin was not fair.
The level of confidence is typically 95% or 99%. If a confidence interval is constructed for the proportion of heads based on a sample of 40 flips and the interval includes the expected proportion of 50%, it can be said that the coin used was fair. If the interval does not include 50%, there is evidence that the coin may not be fair.
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A 64-ounce container of juice costs $5.76. What is the cost per ounce?
The cost per ounce of the juice is $0.0.9 using unitary method.
What is unitary method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unitary method, in its most basic form, is used to calculate the value of a single unit from a specified multiple. The unitary technique can be used to complete it. Additionally, after determining the value of a single unit, we can increase that value by the number of units needed to determine the value of the additional units. What is division?One of the four fundamental arithmetic processes, or how numbers are combined to create new numbers, is division. The other processes are addition, subtraction, and multiplication. The reverse of multiplying is division.
In this question,
64-ounce container of juice costs $5.76. I
ounce of juice costs = 5.76/64= $0.09
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AMOUNT ALREADY APPROVED R9 000,00 Cash already approved YOUR LOAN OFFER 1. EXPIRY DATE: 28 February 2023 . Payable over 48 months Monthly instalments = R 318,92 R 9 000,00 Calculate the TOTAL amount that Theo has to payback if s the loan. Why, do you think, do banks and other financial institutions cash loans to people that did not apply for it? Theo decides to take the loan and wants to invest the mon. he following options. Option 1: The R9 000 invested at 8% p.a. simple interest f Option 2: The R9 000 invested at 7% p.a. compound interest
The R9,000 loan offer can be analyzed as follows;
The total amount Theo pays is R15,308.16Banks offer loans as a marketing strategy and based on a customers credit profileOption 1 is the better investment as the total value of the investment after 4 years is higher than the total value of the investment in Option 2.What is a loan?A loan is a financial agreement that is made between a lender and a borrower, such that the borrower accepts a certain amount of money provided by the lender, which is to be paid back after a specified period of time, with an interest.
The total amount which has to be paid as repayment for the loan can be obtained by finding the product of the monthly installment and the total number of months to repay the loan:
Total amount Theo pays = R318.92 × 48 = R15308.16
Therefore; The amount Theo will have to pay back for the loan in 48 months is R15,308.16The reasons banks and other financial institutions offer loans to people that did not apply for loans includes;
Marketing; As a marketing, banks may offer loans to attract new customers. Pre-approved Loans; A banks may offer loans based on the credit history and financial profile of a customer.Theo's investment options can be analyzed as follows;
Option 1: Investment with simple interest calculation
Interest earned = R9,000 × 8% × 4 years = R2,880
The total value of the investment after 4 years = R9,000 + R2,880 = R11,880
Option 2: Investment with compound interest calculation
The total value of the investment after 4 years = R9,000 × (1 + 7%)⁴ = R11,797.16409
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Prove the triangles are congruent. Include all steps of proof.
As a result of demonstrating that two pairs of corresponding sides and their included angles are congruent in both triangles
What precisely is a triangle?A triangle is a closed, double-symmetrical object composed of three line segments known as sides that intersect at three points known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are less than 90 degrees), okay (one angle is equal to 90 degrees), or orbicular (all angles are greater than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.
Triangle ABC with AB, BC, and AC sides.
Triangle DEF with DE, EF, and DF sides.
Angle ABC and angle DEF are vertical angles, which means they are congruent, as shown in the diagram. As a result, angle ABC = angle DEF.
We can see from the diagram that BC and EF are both vertical, so they must be congruent because they are opposite sides of a parallelogram. As a result, BC = EF.
Because they are opposite sides of a parallelogram, they must be congruent. As a result, AC = DF.
As a result of demonstrating that two pairs of corresponding sides and their included angles are congruent in both triangles, we can conclude that Triangle ABC and Triangle DEF are congruent using the Side-Angle-Side (SAS) criterion.
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The third term of a geometric sequence is 32 and the fourth term is -108. Find the common ratio.
-3.375
-1.61
3.375
-1.43
Answer:
-3.375
Step-by-step explanation:
the point of a geometric sequence is that every new term is created by multiplying the previous term by a constant factor that is the same across the whole sequence.
that factor is called the common ratio.
so, 32 was multiplied by the common ratio, and we get -108 as result.
32 × cr = -108
cr = -108/32 = -27/8 = -3.375 = -3 3/8
A manufacturer of compact fluorescent light bulbs advertises that the distribution of the lifespans of these light bulbs is nearly normal with a mean of 9,000 hours and a standard deviation of 1,000 hours.
(a) What is the probability that a randomly chosen light bulb lasts more than 10,500 hours?
(b) Describe the distribution of the mean lifespan of 15 light bulbs.
(c) What is the probability that the mean lifespan of 15 randomly chosen light bulbs is more than 10,500 hours?
(d) Sketch the two distributions (population and sampling) on the same scale.
(e) Could you estimate the probabilities from parts (a) and (c) if the lifespans of light bulbs had a skewed distribution?
A manufacturer of compact fluorescent light bulbs advertises have a standard deviation of 1,000 hours so the values are:
A normal distribution with,
μ = 9000
σ = 1000
a) The standardized score is the value x decreased by the mean and then divided by the standard deviation.
x = 105000 - 9000 / 1000 ≈ 1.50
Determine the corresponding probability using the normal probability table in appendix,
P(X>10500) = P(Z>1.50) = 1 - P(Z<1.50)
= 1 - 0.9332 = 0.0668.
b) n = 15
The sampling distribution of the mean weight is approximately normal, because the population distribution is approximately normal.
The sampling distribution of the sample mean has mean μ and standard deviation σ/√n
μ = 1000/√15 = 258.19
c) The sampling distribution of the sample mean has mean μ and standard deviation σ/√n
The z-value is the sample mean decreased by the population mean, divided by the standard deviation:
z = x-u/σ/√n = 10500-9000/1000√15 = 5.81
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Leo has a number of toy soldiers between 27 and 54. If he wants to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation
please help it’s due today(midnight right now), I will mark brainliest
The answer is 45 toy soldiers which can be solved by applying the fundamentals of algebra.
What is algebra?Algebra is a branch of mathematics which uses symbols to represent numbers and variables in equations and formulas to solve problems. Algebra is used to understand the relationships between different values, to find unknown values, and to solve equations.
To represent the two scenarios provided in the question, we must first build up two equations.
If Leo arranges the toy troops in the first scenario four by four, then the equation is 4x = 27, where x is the total number of toy soldiers.
If Leo arranges the toy troops seven times out of seven in the second scenario, the equation is 7x = 54, where x is the total number of toy soldiers.
The equations must then be solved in order to determine the value of x in each equation.
We multiply both sides of the equation by 4 to get x = 6.75 for the first equation.
To get x = 7.71428 we multiply both sides of the second equation by 7.
We settle on 6, the lowest whole number between 6.75 and 7.7142, because there must be an even number of toy soldiers. In the first situation, Leo has a total of 24 toy soldiers, while in the second, he has 42, or 4 x 6 and 7 x 6, respectively.
Since the question specifies that there should be between 27 and 54 toy soldiers, we choose the higher value of 42 to arrive at the correct response, which is 45 toy soldiers.
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लगाउनुहोस् । The capacity of a closed cylindrical tank of height 2 m. is 3080 liters. Find the base area of the tank.
11.87 m² metal sheet would be needed to make the base area of tank.
Volume of the cylinderVolume of cylinder, determines how much material it can carry, is determined by the cylinder's volume. A cylinder is a three-dimensional structure having two parallel, identical bases that are congruent.
It is given that capacity of a closed cylindrical vessel of height 2 m is 3080 liters
Let us assume that Radius of cylinder = r
Then Volume of cylinder = π ×r² ×h
= 2π ×r²× m³
1 m³ = 1000 liters
= 2000 π r² liters
Volume of tank = Capacity
2000 π r² = 3080
=> 2000 × (22/7) × r² = 3080
=> r² = 49/100
=> r = 7/10 m
=> r = 0.7 m
Base Area of tank = TSA = 2πrh + 2πr²
= 2×(22/7)(0.7)×2 + 2×(22/7)×(0.7)²
= 3.0772 +8.792
= 111.87 m²
Hence, 11.87 m² metal sheet would be needed to make it.
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The diagram shows parts of three regular polygons, A, B and C, meeting at a point.
B
Polygon B has n sides.
Work out the value of n.
7x°
8x°
A
3.xº
C
Diagram NOT
accurately drawn
The value of n, which represents the number of sides in polygon B, is 160.
What is geometry?Geometry is a branch of mathematics that deals with the study of shapes, sizes, positions, and properties of objects in space.
The given diagram shows parts of three regular polygons, labeled as A, B, and C, meeting at a point. Angles within the polygons are labeled with their respective measures in degrees.
According to the diagram:
Angle at the meeting point of polygons A, B, and C is labeled as 7x°.Angle within polygon A is labeled as 3x°.Angle within polygon B is labeled as 8x°.Since polygons A, B, and C are regular polygons, all their interior angles are equal. Let's denote the measure of each interior angle in polygon B as n°.
Now, we can set up an equation based on the angle measures in the diagram:
3x + 8x + 7x = 360
Simplifying the equation:
18x = 360
Dividing both sides by 18 to solve for x:
x = 360 / 18
x = 20
Now, substituting the value of x back into the equation for n° in polygon B:
8x = 8 * 20 = 160
Hence, the value of n, which represents the number of sides in polygon B, is 160.
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Complete question:
The distance in miles of a motorist from her destination
The motorist has been traveling for approximately 2.6 hours when she is 299 miles from her destination.
To find how long the motorist has been traveling when she is 299 miles from her destination, we need to solve for t in the equation d(t) = 299.
Substituting 299 for d(t) in the given equation, we get:
299 = 468 - 65t
Subtracting 468 from both sides, we get:
-169 = -65t
Dividing both sides by -65, we get:
t ≈ 2.6
The given equation d(t) = 468 - 65t is an example of a linear function, where the distance traveled is a linear function of the time spent traveling. The slope of this function is -65, which means that the distance traveled decreases at a rate of 65 miles per hour.
The y-intercept of the function is 468, which represents the initial distance from the destination when the motorist starts traveling. The x-intercept of the function is found by setting d(t) = 0, which gives t = 7.2. This represents the time at which the motorist reaches her destination if she maintains a constant speed.
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Complete question is:
The distance in miles of a motorist from her destination is given by the function d(t)=468-65t,, where d(t) is the distance and t is the time she has been traveling, in hours. How long has the motorist been traveling when she is 299 miles from her destination?
Y= 1/3x-9
Write the equation of a line PERPENDICULAR to
point (-6, 10).
that passes through the
The equation of the line perpendicular to y = 1/3x - 9 that passes through the point (-6, 10) is y = -3x - 8.
The given equation is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
So, we can see that the slope of the given line is 1/3.
A line perpendicular to this line will have a slope that is the negative reciprocal of the slope of the given line.
The negative reciprocal of 1/3 is -3.
Now, we have the slope of the perpendicular line and a point that it passes through. We can use point-slope form to find the equation of the line.
Point-slope form, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Substituting the values we have
y - 10 = -3(x - (-6))
y - 10 = -3(x + 6)
y - 10 = -3x - 18
y = -3x - 8
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The given question is incomplete, the complete question is:
Write the equation of a line perpendicular to y = 1/3x - 9 that passes through the point (-6, 10)