After considering all the combinations of three pieces of wood, we can conclude that Ennis can make 2 different triangular borders for his vegetable garden.
A triangle is a shape with three sides, and each side can be considered as a side length. In order to form a triangle, the sum of the lengths of the two shorter sides must be greater than the length of the longest side.
To find the number of different triangular borders that Ennis can make, we need to consider all the combinations of three pieces of wood as the sides of the triangle. There are four pieces of wood, so the number of combinations of three pieces is 4 choose 3, which is 4.
Now, we need to determine if each combination of three pieces of wood forms a triangle. If the sum of the lengths of the two shorter sides is greater than the length of the longest side, it forms a triangle. If not, it does not form a triangle.
If Ennis uses the 8-inch and 10-inch pieces as two sides, he can use the 12-inch or 18-inch piece as the third side, and it forms a triangle.
If he uses the 8-inch and 12-inch pieces as two sides, he can only use the 10-inch piece as the third side, and it forms a triangle. If he uses the 8-inch and 18-inch pieces as two sides, it does not form a triangle.
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Find the value of X. Round to the nearest tenth
The value of x in the given figure is 31.76.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
In the given triangle, there are two triangles.
Let us find the length of the perpendicular line by using pythagoras theorem.
16² + a² = 22²
256 + a² = 484
a² =484-256
a² = 228
a=15.09 = 15
Now let us find the value of x.
Now 44-16= 28
28²+15² = x²
784 + 225 = x²
1009 = x²
Square root on both sides
x=31.76
Hence, the value of x in the given figure is 31.76.
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Solve for x.
7-3x/2 = 8
x = [?]
Answer:
x = -3
Step-by-step explanation:
I did this before
Find the median of the following data:
9, 15, 17, 18, 6, 20, 8, 5, 18, 18, 10, 5, 14, 12, 10,7
A. 18
B. 12
C. 11
D. 15
Answer:
18
Step-by-step explanation:
The median of a set of data is the value that separates the lower and upper halves of the data. To find the median, the data must be arranged in numerical order.
The data, arranged in numerical order, is:
5, 5, 6, 7, 8, 9, 10, 10, 12, 14, 15, 17, 18, 18, 18, 20
Since the number of data points is an odd number (17), the median is simply the middle value, which is:
18
So the correct answer is A) 18.
Answer: C
Step-by-step explanation:
To find the median, arrange the numbers in sequential order.
5, 5, 6, 7, 8, 9, 10, 10, 12, 14, 15, 17, 18, 18, 18, 20
When there are an odd number of data in the set, choose the middle number in the set. For example, see the following data set.
2, 4, 6, 8, 9
The middle number in the data set is 6, so it is the median.
When there is an even number of data in the set, choose the middle two numbers, add them together, and then divide them by 2.
There are 16 numbers in this data set. We need to find the two middle numbers in the set.
5, 5, 6, 7, 8, 9, 10, 10, 12, 14, 15, 17, 18, 18, 18, 20
10 and 12 are the two middle numbers in the set.
10 + 12 = 22
22/2 = 11
Median = 11
A letter in the word ACCEL is chosen 50 times. Results are shown in the table below
What is the experimental probability of choosing a C?
Answer:
Step-by-step explanation:
C is chosen 12 times (7 + 5)
You have 50 total picks.
So the experimental probability is 12/50.
Can you please find the exact value of X?
Answer:
10[tex]\sqrt{50}[/tex]
Step-by-step explanation:
Since it's a isosceles right triangle, so
x^2+x^2=100^2
2x^2=10000
x^2=5000
x=[tex]\sqrt{5000}[/tex]=10[tex]\sqrt{50}[/tex]
The superintendent of a large school district wants to estimate the percent of district residents who support the building of a new middle school. To gather data, the superintendent will select a random sample of district residents.
What is the most appropriate method for creating such an estimate?
All three options involve conducting a survey using random sampling, which is the most appropriate method for creating an estimate of the percentage of district residents who support the building of a new middle school. The correct answer would be A, B, or C, depending on the availability of resources.
The most appropriate method for creating an estimate of the percentage of district residents who support the building of a new middle school would likely be a survey using random sampling.
Random sampling is a statistical method in which a representative sample of a larger population is selected, in order to make inferences about the population as a whole. When conducting a survey, random sampling helps to ensure that the sample is representative of the population, reducing the potential for bias.
There are several different types of surveys that could be used to estimate the level of support for a new middle school, including telephone surveys, online surveys, and in-person surveys.
Complete question:
The superintendent of a large school district wants to estimate the percentage of district residents who support the building of a new middle school. To gather data, the superintendent will select a random sample of district residents. What is the most appropriate method for the superintendent to estimate the percentage of district residents who support the building of a new middle school?
A. Telephone survey using random sampling
B. Online survey using random sampling
C. In-person survey using random sampling
D. Observing the behavior of district residents
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Solve the system of equations.
x + y = 8
y = x2 – 4
(3,5) and (-4,12)
(-3,11) and (4,4)
(4,4) and (5,3)
(12,-4) and (7,1)
Answer:
A) [tex](3,5)[/tex] and [tex](-4,12)[/tex]
Step-by-step explanation:
[tex]x+y=8\\x+(x^2-4)=8\\x^2+x-4=8\\x^2+x-12=0\\(x-3)(x+4)=0\\x_1=3,\,x_2=-4\\\\x_1+y=8\\3+y=8\\y_1=5\\\\x_2+y=8\\-4+y=8\\y_2=12[/tex]
1.Which best describes a linear function?
(a) Building a tower of blocks, Collin starts with 25 blocks on the first level, 16 on the second level, and
9 on the third level. The function represents the relationship between the number of blocks on each
level after x levels.
(b) On a summer day, the temperature outside increases 3 degrees Fahrenheit per hour after 6 AM.
The function represents the relationship between the
temperature outside after x hours after 6 AM.
(c) Patty's company makes gift boxes in the shape of cubes. As the size of the gift box changes, the
length of each side increases by 6 inches. The function represents the relationship between the volume
of
each gift box after x increases in side length.
Xo
(d) The water in an outdoor pool is evaporating. Each day, only 95% of the water from the day before
remains. The function represents the relationship between the amount of water in the pool after x days.
()
Part II. Jacob tells you that there is a 40% probability that at least two people in each classroom of 25 students share a birthday (ignore leap years). You don’t believe Jacob and decide to conduct a simulation to see if you get enough evidence to reject his claim.
• State the null hypothesis and the alternative hypothesis.
Use the random number generator to do a simulation and do this simulation 16 times. Record your results in the table below. In each simulation you will be checking how many couple of students share a birthday.
Find the proportion of “classrooms” with at least a couple of students sharing a birthday.
• Find the t-statistic:
Compare P-value (probability of getting a value at least as extreme as your t-statistic under the null hypothesis) with the a level:
• State your conclusion:
Null hypothesis: The probability of at least two people in each classroom of 25 students sharing a birthday is less than or equal to 40%.
Alternative hypothesis: The probability of at least two people in each classroom of 25 students sharing a birthday is greater than 40%.
What are the results from the simulations?Simulation Results:
Simulation 1: 8 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 2: 9 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 3: 7 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 4: 11 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 5: 7 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 6: 6 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 7: 8 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 8: 6 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 9: 10 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 10: 8 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 11: 7 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 12: 11 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 13: 8 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 14: 7 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 15: 10 out of 16 classrooms had at least 2 students sharing a birthday.
Simulation 16: 10 out of 16 classrooms had at least 2 students sharing a birthday.
Proportion of classrooms with at least 2 students sharing a birthday = (8+9+7+11+7+6+8+6+10+8+7+11+8+7+10+10)/16 = 0.7125
The mean number of classrooms with at least 2 students sharing a birthday is 0.7125. We can use this value to calculate the t-statistic.
t-statistic = (0.7125 - 0.4) / (sqrt(0.4 * 0.6 / 16)) = 5.766
Using a one-tailed t-test with 15 degrees of freedom and an alpha level of 0.05, the critical t-value is 1.753. Since the calculated t-statistic is greater than the critical t-value, we can reject the null hypothesis.
The p-value is very small (less than 0.0001), indicating strong evidence against the null hypothesis.
Therefore, we can conclude that there is sufficient evidence to suggest that the probability of at least two people in each classroom of 25 students sharing a birthday is greater than 40%.
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how many possibilities are there for a four digit pin where no digit is repeated?
The total number of possibilities for four digit pin with the condition of no digit is repeated is equal to 5040.
Total number of digit used to form pin = 4
Condition is : No digit is repeated.
Number of digits are :
( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 )
Total digits are = 10
Number of possibilities to form four digit pin with no digit repeated
= ¹⁰P₄
= ( 10! ) / ( 10 - 4 )!
= ( 10 × 9 × 8 × 7 × 6! ) / 6!
= 10 × 9 × 8 × 7
= 5040
Therefore, the total number of possibilities to form four digit pin with the given condition is equal to 5040.
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The measure of central location most often reported for annual income and property value data is the _____.
a. mode
b. median c. aggregate mean d. weighted mean
The measure of central location most often reported for annual income and property value data is the mode.
What is the mode?There are three measures of central tendency of a data-set, which are defined as follows:
Mean.Median.Mode.Among those three measures, the mode is the one that gives the observation that appears the most often in a data-set, hence the correct option is given by option a.
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What is 1 meter cm in feet?
100 centimetres make up one metre. 100 centimetres must be multiplied by 0.0328084 to equal one metre in feet. There are 3.28084 feet as a result.
100 cm in one metre
1 cm = 0.0328084 ft
100 cm in 1 metre equals 0.0328084 feet, or 3.28084 feet.
100 centimetres make up one metre. 100 centimetres must be multiplied by 0.0328084 in order to convert 1 metre in cm to feet. This math will show us how many feet are in one metre, centimetre. To proceed step-by-step, we must first multiply one metre by one hundred centimetres. We will get 100 centimetres as a result.Following that, we must multiply 100 centimetres by 0.0328084. This figure represents the number of feet in one centimetre. We can convert 1 metre cm to feet by multiplying these two values, which gives us 3.28084 ft. The length of things can be measured using this conversion in both metric and imperial systems. When attempting to measure objects precisely, it can be helpful to know how to convert between the two systems.
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What is 0700 military time?
0700 military time is 7:00 AM in the 24-hour time format used by the military, also known as the 24-hour clock.
The 24-hour clock is a timekeeping system that uses a continuous count of 24 hours, instead of two sets of 12 hours for AM and PM. In this system, each hour of the day is numbered from 0 to 23, and is referred to as "military time" or "24-hour time". So, 0700 military time is equivalent to 7:00 AM, with the "0" indicating the first hour of the day. This system is commonly used in the military, as well as in other fields where precise and standardized timekeeping is important, such as aviation and public transportation.
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Suppose you deposit $2,000 in a savings account that pays interest at an annual rate of 5%. If no money is added or withdrawn from the account, answer the following questions.
a. How much will be in the account after 4 years?
b. How much will be in the account after 16 years?
c. How many years will it take for the account to contain $2,500?
d. How many years will it take for the account to contain $3,000?
years.
d. For the account to contain $3,000, it will take years
(Type a whole number.)
Answer:
a. After 4 years, the amount in the account can be found by using the formula for simple interest:
A = P * (1 + r * t), where P is the initial deposit, r is the annual interest rate as a decimal, and t is the number of years.
Plugging in the values, we get:
A = $2,000 * (1 + 0.05 * 4) = $2,000 * 1.2 = $2,400
So after 4 years, there will be $2,400 in the account.
b. After 16 years, the amount in the account can be found using the same formula:
A = $2,000 * (1 + 0.05 * 16) = $2,000 * 1.8 = $3,600
So after 16 years, there will be $3,600 in the account.
c. To find the number of years it will take for the account to contain $2,500, we can use the formula:
t = (A - P) / (P * r), where A is the desired amount.
Plugging in the values, we get:
t = ($2,500 - $2,000) / ($2,000 * 0.05) = ($500) / ($100) = 5 years
So it will take 5 years for the account to contain $2,500.
d. To find the number of years it will take for the account to contain $3,000, we can use the same formula:
t = ($3,000 - $2,000) / ($2,000 * 0.05) = ($1,000) / ($100) = 10 years
So it will take 10 years for the account to contain $3,000.
Step-by-step explanation:
pls mark brainlist
find the coordinates of the intersection of the diagonals of ABCD with the given vertices
A(3,6) B(5,8) C(3,-2) and D(1,-4)
The coordinate from point of intersection is (3, 11)
What is the coordinate of the intersecting diagonalsTo find the intersection point of the diagonals of ABCD, we need to find the point where the lines containing the diagonals intersect.
The diagonal connecting A and C has slope:
m₁ = (y₂ - y₁) / (x₂ - x₁)
= (-2 - 6) / (3 - 3)
= undefined
This is because the line is vertical, and so has no slope. However, we can still write an equation for this line using the x-coordinate of point C:
x = 3
The diagonal connecting B and D has slope:
m₂ = (y₂ - y₁) / (x₂ - x₁)
= (-4 - 8) / (1 - 5)
= -3/2
We can write an equation for this line using point-slope form and the coordinates of point B:
y - y₁ = m₂(x - x₁)
y - 8 = (-3/2)(x - 5)
y - 8 = (-3/2)x + 15/2
y = (-3/2)x + 31/2
Now we can find the point of intersection by solving the system of equations given by the two lines:
x = 3
y = (-3/2)x + 31/2
Substituting x = 3 into the second equation, we get:
y = (-3/2)(3) + 31/2
y = 22/2
y = 11
The coordinate is (3, 11)
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A
rectangular prism has a volume of 9 in. The area of the base
is 4 in? What is the height of the prism?
The height of the rectangular prism whose volume is 9 cubic inches and the base area is 4 square inches will be 2.25 inches.
What is the volume?Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.
The volume of the prism is given as,
Volume = (Base area) x (Height)
The rectangular prism has a volume of 9 cubic inches. The area of the base is 4 square inches.
Then the height of the rectangular prism is given as,
9 = 4 h
h = 9 / 4
h = 2.25 inches
The height of the rectangular prism whose volume is 9 cubic inches and the base area is 4 square inches will be 2.25 inches.
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My friend Vreel has less than 19 pisquets and more than 8 pisquets
Write an inequality that shows the possible amounts of pisquets. Use
x for pisquets.
The inequality that shows the possible amounts of pisquets is 8 < x < 19
How to determine the inequality that shows the possible amounts of pisquetsFrom the question, we have the following parameters that can be used in our computation:
My friend Vreel has less than 19 pisquets and more than 8 pisquets
Using x for Pisquets, we have:
x < 19 and x > 8
When the inequality is combined, we have
8 < x < 19
Hence, the inequality is 8 < x < 19
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What is the symbol for mean in stats?
The symbol of mean is "μ". The population mean, or average score for the population on a certain variable, equation as follows:
μ = ( Σ Xi ) / N
The term "mean" is simply the mathematical average of a set of two or more integers. The arithmetic mean technique, which utilizes the sum of the series' values, and the geometric mean method, which employs the average of a set of products, are only two of the methods available to determine the mean for a given collection of data. Nonetheless, most of the time, the outcomes of the various methods for determining a simple average are essentially the same. The arithmetic mean and the geometric mean are two different types of means that may be determined. By adding all the numbers in a set and dividing by the total number of integers in the set, the arithmetic mean is determined. The equation of mean will be:
μ = ( Σ Xi ) / N.
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A calf and a mini-horse weigh 705 lbs combined. The ratio of their weights is 16:31 respectively. How much does the mini-horse weigh?
The Weight of mini horse is 465 lbs.
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
A calf and a mini-horse weigh 705 lbs combined.
The ratio of their weights is 16:31 respectively.
let the Common ratio be x.
So, weight of calf = 16x and Weight of mini horse = 31x
Thus, 16x + 31x = 705
47x = 705
x= 705/ 47
x= 15
Then, the Weight of mini horse = 31x = 31(15)= 465 lbs.
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is (bc^2)/a^3b^2c^-2*(2a^-4b^3c^-4)^4 equal to (16c^20/a^13b^13)
Answer: No.
Step-by-step explanation: Unless I read and calculated wrongly, it should be equal to 2b^4/(a^3b^2c^2-2)a^4c^2 -1/256
Which unit of measurement is part of the metric system?
O pound
Oliter
O quart
O foot
Two sprinters, nick and ryan, want to find out who has the faster time when compared to each of their teams. Nick has a time of 10. 8 seconds, and his team has a mean time of 11. 4 seconds and a standard deviation of 0. 4 seconds. Ryan has a time of 11. 2 seconds, and his team has a mean of 11. 5 seconds and a standard deviation of 0. 1 seconds. Who has the faster time when compared to each of their teams?.
Ryan has the faster time when compared to each of their teams,
"Information available from the question"
The time taken by Nick is 10.8 seconds.
The mean time taken by Nick is 11.4 seconds.
The standard deviation of Nick is 0.4 seconds.
The time taken by Ryan is 11.2 seconds.
The mean time taken by Ryan is 11.5 seconds.
The standard deviation of Ryan is 0.1 seconds.
The z-score of Nick is:
[tex]z_1=\frac{10.8-11.4}{0.4}[/tex]
[tex]z_1=-1.5[/tex]
The z-score of Ryan is:
[tex]z_2=\frac{11.2-11.5}{0.1}[/tex]
[tex]z_2=-3[/tex]
Thus, Ryan z-score is lower, so Ryan has the faster time when compared to each of their teams.
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Easy question. My friend asked me this random question while I'm trying to sleep. If you get with someone on 12/27/2021 when will your 1 month, 2 month, and 3 month anniversary be? Remember February only has 28 days..
Answer:
Step-by-step explanation:
If you got together on December 27, 2021, your 1-month anniversary would be on January 27, 2022, which is exactly 31 days later.
Your 2-month anniversary would be on February 27, 2022, which is exactly 61 days later. Since February has only 28 days in 2022, it means that your 2-month anniversary would fall on the last day of February.
Your 3-month anniversary would be on March 27, 2022, which is exactly 90 days later.
What's the length of the hypotenuse of right ΔDEF shown?
Question 13 options:
A)
√87
B)
12
C)
15
D)
√117
Answer: √177
Step-by-step explanation:
6²+9²=c²
36+81=c²
117=c²
√117=√c²
√177 = c
(√177 can also be watered down to ±3√13 but √177 is one of the answer choices so yeah)
rawan deposits 13000 into an account that pays 2.6% annual interest compounded every 6 months
The function that represent the balance A in the account after t years is f(t) = 13000( 1.013 )^( 2t ).
This question is incomplete, the complete question is:
Rawan deposits $13,000 into an account that pays 2.6% annual interest compounded every 6 months.
Write a function to represent the balance A in the account after t years.
What is the function that represent the balance A in the account after t years?The formula accrued amount in a compounded interest is expressed as;
A = P( 1 + r/n )^( n × t )
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that;
Principal P = $13,000Compounded every 6 months n = 2Interest rate R = 2.6%First, convert R as a percent to r as a decimal
r = R/100
r = 2.6/100
r = 0.026
Given that time = t.
A = P( 1 + r/n )^( n × t )
f(t) = 13000( 1 + 0.026/2 )^( 2 × t )
f(t) = 13000( 1 + 0.026/2 )^( 2t )
f(t) = 13000( 1 + 0.013 )^( 2t )
f(t) = 13000( 1.013 )^( 2t )
Therefore, the accrued amount after t years is f(t) = 13000( 1.013 )^( 2t ).
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The population of a city has decreased by 26% since it was last measured. If the current population is 40,700, what was the previous population?
The previous population, of the city is 55,000
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.
Given that, a city's current population is 40,700, decreased by 26% after it was measured last time, the
Let the previous population, of the city, be x,
Therefore,
x - 26% of x = 40,700
x(1-26%) = 40,700
0.74x = 40,700
x = 55,000
Hence, the previous population, of the city is 55,000
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Dominique is selling merchandise for a school fundraiser. she is selling calendars for $8 each and coffee mugs for $10 each. she must sell at least $600 of merchandise, including at least 40 calendars, to meet her goals. if x represents the number of calendars and y represents the number of mugs, which system of inequalities represents this scenario? 8x 10y > 600 and y > 40 8x 10y > 600 and x > 40 8x 10y ≥ 600 and y ≥ 40 8x 10y ≥ 600 and x ≥ 40
By answering the given question, we may state that Hence, the interest appropriate response is X = 40 and 8x + 10y = 600
what is interest ?Divide the principal by the interest rate, the length of time, and other factors to arrive at simple interest. Simple return = principal + interest + hours is the marketing formula. This method makes it easiest to calculate interest. The most typical technique to figure out interest is as a portion of the principal sum. He will only pay his share of the 100% interest, for example, if he borrows $100 from a friend and agrees to pay it back with 5% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you give it out, you must charge interest. Interest is often determined as an annual percentage of the loan total. The interest on the loan is this percentage.
Selling x calendars will cost 8x, while selling y mugs will cost 10y. The scenario is therefore represented by the following system of inequalities in order for her to reach her objective of selling at least $600 worth of stuff, including at least 40 calendars:
(Total cost of goods sold must be at least $600; 8x + 10y)
x ≥ 40 (must sell at least 40 calendars) (must sell at least 40 calendars)
In the first inequality, you'll see that we used the symbol "" rather than ">" since Dominique needs to sell at least $600 worth of goods, not just more than $600.
Hence, the appropriate response is
X = 40 and 8x + 10y = 600
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In the figure, m²1 = (5x + 4)°,
mz2 = (6x - 6)° and mz3 =
(10x + 12)°. What is m23, in
degrees?
The angles in degree for the given triangle is 74 degrees, 78 degrees and 28 degrees.
What is angle?In geometry, an angle is the figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles are usually measured in degrees or radians and are used to describe the amount of rotation between two intersecting lines or to measure the size of a shape. Angles can be acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), straight (exactly 180 degrees), or reflex (greater than 180 degrees but less than 360 degrees). Angles play an important role in various fields of study such as mathematics, physics, engineering, and architecture.
Here,
To find m23, we need to use the fact that the sum of the angles in a triangle is 180 degrees.
We know that m21 + m23 + m32 = 180 degrees. Rearranging this equation, we get m23 = 180 degrees - m21 - m32.
From the given information, we have:
m21 = (5x + 4) degrees
m32 = 180 degrees - mz2 - mz3 = 180 degrees - (6x - 6) - (10x + 12) = 174 - 4x degrees
Substituting these values into the equation for m23, we get:
m23 = 180 degrees - m21 - m32
= 180 degrees - (5x + 4) - (174 - 4x)
= 6x + 2 degrees
Therefore, m23 is 6x + 2 degrees.
5x+4+6x-6+168-10x=180
x+166=180
x=14
5x+4=5*14+4
=74°
6x-6=6*14-6
=78°
168-10x=168-10*14
=28°
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Holly picks 125 she spends 35 on gas for her car
which model represtant how much money holly spent
The second option is the correct representation of the given context.
What is a number line?A number line is a one-dimensional horizontal line where we can represent any real number.
The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.
Look at the model, it starts at 125 and drops to 90.
If she has $125 and spends $35 on gas, the remaining balance is reduced by that amount.
125 - 35 = 90.
Q. Holly has $125 she spends $35 on gas for her car which model represents how much money holly has left?
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Your company manufactures hot water heaters. The life spans of the products are known to be normally distributed with a mean of 13 years and a standard deviation of 1.5 years.
a) You are buying a new hot water heater, based on the information in the problem, between how many years would you expect your hot water heater to last. (Give a range of numbers). Explain your answer.
b) You want to set the warranty on your product so that you have to replace at most 5% of the hot water heaters that you sell. How many years should you claim on your warranty? (Round answer to nearest whole number of years.) Explain your answer.
we should claim a warranty of 11 years (rounded to the nearest whole number) to ensure that we replace at most 5% of the hot water heaters that we sell.
What is mean ?
Mean can be defined as the ratio of sum of the given observations and total number of observations.
a) Since the life spans of the hot water heaters are normally distributed with a mean of 13 years and a standard deviation of 1.5 years, we can use the empirical rule to estimate the range of years we would expect the hot water heater to last. The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean, and approximately 99.7% of the data falls within three standard deviations of the mean.
Using this information, we can estimate that the range of years we would expect the hot water heater to last is approximately 10.5 to 15.5 years. This is because one standard deviation below the mean is 13 - 1.5 = 11.5 years, and one standard deviation above the mean is 13 + 1.5 = 14.5 years. Therefore, we can reasonably expect the hot water heater to last between 10.5 and 15.5 years with about 95% confidence.
b) To set the warranty on the product so that we have to replace at most 5% of the hot water heaters that we sell, we need to find the number of years that corresponds to the 5th percentile of the distribution. This is the value below which 5% of the data falls.
We can use a standard normal distribution table or a calculator to find the z-score corresponding to the 5th percentile, which is -1.645. We can then use the formula z = (x - mu) / sigma to find the number of years, x, that corresponds to this z-score.
-1.645 = (x - 13) / 1.5
Solving for x, we get x = 10.83 years.
Therefore, we should claim a warranty of 11 years (rounded to the nearest whole number) to ensure that we replace at most 5% of the hot water heaters that we sell
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