Answer:
We can use the formula for exponential growth:
A = P(1 + r)^t
where:
A = final amount
P = initial amount
r = annual growth rate (as a decimal)
t = time (in years)
Let's plug in the values:
P = 540
r = 0.039
t = 2035 - 2015 = 20
A = 540(1 + 0.039)^20
A ≈ 891
Therefore, the local government of Central Village can predict there will be approximately 891 houses in 2035.
Answer:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r)^n
where:
A = the final amount
P = the initial amount
r = the annual interest rate (as a decimal)
n = the number of years
In this case, we want to find the final amount (the number of houses in 2035), given the initial amount (540 houses in 2015), the annual interest rate (3.9%), and the number of years (20 years from 2015 to 2035).
So, we can plug in the values and solve for A:
A = 540(1 + 0.039)^20
A = 540(1.039)^20
A = 540(2.011)
A = 1086.54
Rounding to the nearest whole number, we get:
A ≈ 1087
Therefore, the local government of Central Village can predict there will be about 1087 houses in 2035.
I seriously cannot figure this out please help me :( IT'S SO LATE PLEASE
Tia's statement that the graph is a x^5 function is correct
How to determine who is correctThe statements from the question are:
Tia = x^5 functionMarcus = x^4 functionThe zeros and the multiplicities in the format (zero, multiplicity) from the question are (-3, 1), (-1, 2), (2, 1) and (3, 1)
The equation of the polynomial can be expressed as
P(x) = (x - zero)^multiplicity
When the zeros and the multiplicities are substituted, we have
P(x) = (x + 3)(x - 3)(x - 2)(x + 1)^2
Expand
P(x) = (x^2 - 9)(x - 2)(x + 1)^2
When evaluated, we have
P(x) = x^5 - 12x^3 - 2x^2 + 27x + 18
The above is a x^5 function
Hence, Tia is correct
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A gardener will use up to 250 square feet for planting flowers and vegetables. She wants the area used for vegetables to be at least four times the area used for
flowers. Let x denote the area (in square feet) used for flowers. Let y denote the area (in square feet) used for vegetables. Shade the region corresponding to all
values of x and y that satisfy these requirements.
The inequality equation that can be used to solve this problem is x + y ≤ 250 and y ≥ 4x
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.
Let x denote the area (in square feet) used for flowers and y denote the area (in square feet) used for vegetables.
A gardener will use up to 250 square feet for planting flowers and vegetables, hence:
x + y ≤ 250 (1)
She wants the area used for vegetables to be at least four times the area used for flowers. Hence:
y ≥ 4x (2)
Plotting both equations using geogebra, the solution is the darker region.
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Twelve students are going to listen to a talk. The group consists of 3 chemistry majors, 2 business majors, 3 political science majors and 4 journalism majors. In how many ways can these students sit in their twelve seats if they must be grouped by major?
There are 1,728 ways for the 12 students to sit in their assigned seats while maintaining the grouping by major.
How to find how many ways can these students sit in their twelve seats if they must be grouped by majorThere are four groups based on major: chemistry, business, political science, and journalism. We need to find the number of ways the 12 students can sit in their assigned seats while maintaining the grouping by major.
We can approach this problem by first considering the number of ways each group can be seated separately, and then multiply the results together to get the total number of arrangements.
For the chemistry group, there are 3 students who can be seated in any order.
For the business group, there are 2 students who can be seated in any order.
For the political science group, there are 3 students who can be seated in any order.
Finally, for the journalism group, there are 4 students who can be seated in any order.
Therefore, the total number of arrangements for the 12 students is:
3! * 2! * 3! * 4! = 6 * 2 * 6 * 24 = 1,728
Therefore, there are 1,728 ways for the 12 students to sit in their assigned seats while maintaining the grouping by major.
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can yall help me solve this please and thank you
Answer:
ANswer ig
Step-by-step explanation:
1/12+1/3=1/12+[4]/12=5/12
6\12. 1\2
I have to add mor but that is all so I’m writing this
please help there’s 3 different parts..a,b,and c.
The values of g(x) for the given values of x are g(0) = 4, g(-7) = 3, g(-4) = 0
Describe Function?Functions can be used to model a wide range of real-world phenomena, such as physical laws, economic relationships, or biological processes. They are a fundamental concept in mathematics and play a central role in many fields, including engineering, physics, computer science, and statistics.
Functions can be represented graphically, algebraically, or numerically, and can be manipulated and analyzed using a variety of mathematical tools and techniques. By understanding how functions work and how to use them, people can solve problems, make predictions, and gain insights into a wide range of mathematical and real-world phenomena.
To evaluate the piecewise function at each value of the independent variable, we need to substitute the given value of x into the appropriate expression for g(x):
a. To find g(0), we use the first expression since 0 is greater than or equal to -4:
g(0) = 0 + 4
g(0) = 4
b. To find g(-7), we use the second expression since -7 is less than -4:
g(-7) = -(-7 + 4)
g(-7) = -(-3)
g(-7) = 3
c. To find g(-4), we need to consider both expressions since -4 is exactly equal to -4:
g(-4) = -(-4 + 4) (using the second expression)
g(-4) = 0 (simplifying)
or
g(-4) = -4 + 4 (using the first expression)
g(-4) = 0 (simplifying)
So, g(-4) is equal to 0 using both expressions.
Therefore, the values of g(x) for the given values of x are:
g(0) = 4
g(-7) = 3
g(-4) = 0
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Which equation represents a line which is parallel to the line y = − 2/3x − 3
Answer:
Any line with a slope of -2/3 that doesnt have an intercept of -3
Step-by-step explanation:
y = − 2/3x − 3 is written in slope-intercept form y = mx + b, where m is the slope, and b is the y intercept
What your looking for is a line with the same -2/3 slope
Important! If a line has the same slope AND intercept, then they are identical, not parallel
The fine for an overdue library book is. 75 for the first day and. 50 for each additional day. Rewrite the expression. 75 +. 5(d-1) for the fine as a sum of two terms where d represents the number of days overdue
The expression can be written as the sum of two terms as 74.5 + 0.5d
Mathematical expressions:Mathematical expressions are combinations of numbers, variables, and operators (such as +, -, ×, ÷, =) that represent a mathematical relationship or computation.
To write the given expression as the sum of two terms simplify the expression by multiplying and adding or subtracting like terms.
Here we have
The expression 75 + 0.5(d - 1) represents the fine for an overdue library book, where d is the number of days overdue.
Simplify expression as shown below
=> 75 + 0.5(d - 1)
= 75 + 0.5d - 0.5
= 0.5d + 74.5
Now the expression is in the form of the sum of two terms
Therefore
The expression can be written as the sum of two terms as 74.5 + 0.5d
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The bar graph shows the results of rolling a number cube 300 times. How does the experimental probability of rolling a number greater than 1 compare with the theoretical probability?
The experimental probability of rolling a number greater than 1 is __%, which is close to the theoretical probability of __%
The experimental likelihood of rolling a number greater than 1 is 66.67%, which, according to the calculations above, is close to the theoretical probability of 83.33%.
What is probability?Calculating the likelihood that an event will occur or a statement will be true is the subject of probability theory, a branch of mathematics. A risk is a number between 0 and 1, where 1 denotes certainty and a probability of about 0 denotes the likelihood that an event will occur. The likelihood that an event will take place is mathematically expressed as probability. Probabilities can also be expressed as percentages ranging from 0% to 100% or as integers between 0 and 1. the proportion of equally plausible possibilities that actually happen in relation to all other outcomes when a specific event occurs.
The bar graph displays how many times a number cube was rolled along with the outcome. The graph shows that the number cube was rolled 300 times in total, yielding the number larger than 1 200 times.
Experimental probability is calculated as follows: 200/300 = 0.6667, or 66.67%, where experimental probability = (number of times greater than 1)/(total number of rolls)
Theoretical probability is calculated as follows: 5/6 = 0.8333 or 83.33% (number of possibilities greater than 1) / (total number of possible outcomes).
The experimental likelihood of rolling a number greater than 1 is 66.67%, which, according to the calculations above, is close to the theoretical probability of 83.33%.
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A shopkeeper buys 300 bicycles at Rs. 1500 per bicycle. He spends Rs 75 per bicycle on transportation. He spends Rs 7500 on advertising. Then he sell all the bicycles at Rs. 1700 per piece. Find he is profit or loss. Also calculate eat as a percentage
Therefore, the shopkeeper made a profit of Rs. 30,000 and the profit percentage is 6.25%.
What is percent?Percent is a way of expressing a fraction or a proportion as a quantity out of 100. The term "percent" means "per hundred". So, when we say that something is 50 percent, we mean that it is 50 out of 100 or 50/100, which can also be simplified to 1/2. The symbol used to represent percent is "%". For example, if a store is offering a discount of 20%, it means that the customer can buy the item for 20% less than the original price, or in other words, the customer will pay only 80% of the original price. Percentages are used in many different areas of life, such as finance, mathematics, science, and statistics. They are used to represent proportions, changes, growth rates, and many other types of data.
Here,
The total cost of 300 bicycles is:
Cost of 1 bicycle = Rs. 1500
Cost of 300 bicycles = 1500 x 300 = Rs. 4,50,000
Transportation cost per bicycle is Rs. 75, so the total transportation cost for 300 bicycles is:
Transportation cost of 1 bicycle = Rs. 75
Transportation cost of 300 bicycles = 75 x 300 = Rs. 22,500
The total cost of purchasing 300 bicycles including transportation cost is:
Total cost = Cost of bicycles + Transportation cost
Total cost = Rs. 4,50,000 + Rs. 22,500 = Rs. 4,72,500
The shopkeeper spent Rs. 7500 on advertising.
So, the total cost of the shopkeeper is:
Total cost = Cost of bicycles + Transportation cost + Advertising cost
Total cost = Rs. 4,72,500 + Rs. 7500 = Rs. 4,80,000
The selling price of 1 bicycle is Rs. 1700, so the selling price of 300 bicycles is:
Selling price of 1 bicycle = Rs. 1700
Selling price of 300 bicycles = 1700 x 300 = Rs. 5,10,000
The profit or loss is calculated by subtracting the total cost from the total selling price:
Profit/Loss = Selling price - Total cost
Profit/Loss = Rs. 5,10,000 - Rs. 4,80,000 = Rs. 30,000
Since the shopkeeper made a profit of Rs. 30,000, we can calculate the profit percentage as follows:
Profit percentage = (Profit / Total cost) x 100
Profit percentage = (30,000 / 4,80,000) x 100
Profit percentage = 6.25%
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Function F please help. I think that A can be one of em but I’m not sure about the rest
The true statement about the function notation are:
d(20) = d(40)d(0) = 0: Trued(80) = 60; Trued(92) = 0; TrueHow to determine the true function notationThe definition of the graph is given as
The distance vs time graph
This is represented by F = d(t)
The function notation would be determined to be true or false by observation
This is so because the graph is not drawn to scale
Using the above as a guide, we have the following:
d(20) = d(40): True, both equal 30d(0) = 0: Trued(t) = 10 when t = 20; Falsed(80) = 60; Trued(0) = 92; Falsed(92) = 0; Trued(80) < d(50); FalseRead more about function notations at
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Find d. Round to the nearest tenth.
Answer:
d=50.3
Step-by-step explanation:
cos(29)/1=44/d
cos29d/cos29=44/cos29
d=50.31
d=50.3
At the playground, the slide and its ladder form a right triangle with the ground. The distance from the bottom of the ladder to the base of the slide is 18 feet. The length of the slide is 20 feet. If b represents the height of the ladder, what is b?
The height of ladder is approximately 26.9 feet tall.
How can the hypotenuse of a right triangle with one side be determined?In order to get the length of the hypotenuse, divide the non-hypotenuse side that is close to the angle by cos(). If you prefer, you can multiply this length by tan() to obtain the length of the side that is perpendicular to the angle.
Let's tackle this issue using the Pythagorean theorem.
According to the Pythagorean theorem, the sum of the squares of the leg lengths in a right triangle equals
The length of the slide is the other leg, the distance from the ladder's bottom to its base is one leg, and the ladder itself is the hypotenuse.
b² = 18² + 20²
b² = 324 + 400
b² = 724
b = √(724)
b ≈ 26.9
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The right hexagonal pyramid has a base with equal length sides. The lateral faces of the pyramid are all triangles (that are exact copies of one another) with heights of 15 ft. Find the surface area of the pyramid
The surface area of the pyramid is 105.6 square feet.
To find the surface area of this pyramid, we need to calculate the area of all its faces and add them up.
Since all sides of our hexagon are equal, we can simplify this formula to:
Surface Area of Hexagon = 6 x (3√3 / 2) x (Side length)²
Total Surface Area = Surface Area of Base + Surface Area of Triangular Faces
Total Surface Area = 6 x (3√3 / 2) x (Side length)² + 6 x (Side length x 15) / 2
We can simplify this expression further by factoring out 6 x (Side length)² from both terms:
Total Surface Area = 6 x (Side length)² x [(3√3 / 2) + 15]
To find the surface area of a right hexagonal pyramid with equal-length sides and triangular faces of height 15 ft, we use the formula above:
Total Surface Area = 6 x (Side length)² x [(3√3 / 2) + 15]
When the value of side length is 1, then total surface area is
=> Total Surface Area = 6 x (1)² x [(3√3 / 2) + 15] = 105.6 square feet.
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i sell a car for £6502 making a 22% profit. how much did i buy it for originally
Answer:
£5329.51
Step-by-step explanation:
Knowing that £6502 is the price with 22% profit, we can understand that £6502 is 122% of the original price meaning that the individual would have had to multiply their original value by 1.22 to get £6502!
To find our answer we, therefore, have to do the inverse...
6502 ÷ 1.22 = 5329.5082Turning the value into money we round to 2d.p leaving our answer as...
£5329.51Hope this helps, have a lovely day! :)
Diego has 90 songs on his playlist. How many songs are there for each genre?
Answer: Diego's playlist has 36 songs in rock genre, 9 songs in Country genre, 27 songs in hip hop genre and 24 songs in electronica genre.
Based on the number of songs Diego has and the proportion of the genres, Diego's song classification is:
Rock = 36 songsCountry = 9 songsHip Hop = 27 songsElectronica = 18 songsThe number of songs from a particular genre is:
[tex]= \text{Total number of songs}\times\text{Percentage of genre}[/tex]
Rock:
[tex]= 40\% \times 90[/tex]
[tex]\bold{= 36 \ songs}[/tex]
Country:
[tex]= 10\% \times 90[/tex]
[tex]\bold{= 9 \ songs}[/tex]
Hip hop:
[tex]= 30\% \times 90[/tex]
[tex]\bold{= 27 \ songs}[/tex]
Electronica:
[tex]= (100\% - 40\% - 10\% - 30\%) \times 90[/tex]
[tex]\bold{= 18 \ songs}[/tex]
In conclusion, there are various genres on Diego's phone.
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Complete Question:
Diego has 90 songs on his playlist. How many songs are there for hip-hop?
40% rock
10% country
30% hip-hop
The rest is electronica
19. What is the length of side JN? (Round your answer to the nearest tenth.) 65 39 53
We οbtain JN 44.3 by rοunding tο the nearest tenth, Length οf side JN is rοughly 44.3 units lοng as a result. Therefοre 44.3 is the right respοnse.
What is the measurement οf a triangle's side?
The sides οf a triangle are straight lines that are jοined by the three vertices οf the triangle. In οther wοrds, we can say that the sides οf a triangle are line segments that meet each οther at the vertices οf the triangle.
The sides οf a right-angled triangle can be fοund οut by using variοus methοds like the Pythagοras theοrem οr by using the perimeter οf the triangle. In case sοme οf the angles and οther side lengths are given, we can use the law οf cοsines οr the law οf sines tο find the lengths οf the sides οf a triangle.
Law of sines
sin(∠A)/a = sin(∠B)/b = sin(∠C)/c
Therefore,
39/sin(53°) = JN/sin(65°)
JN = (39×sin(65°))/sin(53°)
JN = 44.3
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Matthew has an investment that is now worth $21 537.82. Find the original amount
he invested if he has had the money invested at 2.5% per month for 3 years.
I honestly don't know how to do this. Please explain it to me in the easiest way possible. Thank you.
The value of line segment AC is 8√2
What is Pythagoras theorem?Pythagoras theorem states that, in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
If the other two sides of the right triangle are a and b and the hypotenuse is c, then mathematically l, Pythagoras theorem can be written as:
c² = a²+b²
If CD = 4 and AD = 12, then AC will be
12² = (AC)² +4²
(AC)² = 12² - 4²
(AC)² = 144-16
(AC)² = 128
AC = √128
AC = 8√2
therefore the value of the line segment AC is 8√2
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A diet plan claims that women have a mean weight of 145 lbs. Assume that the weights of women have a standard deviation of 30. 86 lb. A sample of 40 weights of women has a mean weight of 153. 2 lb. Find the P-value and, using a 0. 05 significance level, state the conclusion about the null hypothesis
The null hypothesis is that the mean weight of women is 145 lbs.The P-value is 0.0145. At a 0.05 significance level, the null hypothesis can be rejected. This suggests that the mean weight of women is not 145 lbs.
The null hypothesis is that the mean weight of women is 145 lbs. To test the hypothesis, we need to calculate the P-value. The mean of the sample of 40 weights is 153.2 lbs, with a standard deviation of 30.86 lb. The P-value is calculated using a z-score formula which is (153.2-145)/(30.86/sqrt(40)) = 0.0145. Since the P-value is less than 0.05, this suggests that the mean weight of women is not 145 lbs. Therefore, at a 0.05 significance level, the null hypothesis can be rejected.
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How to do?
♀️♀️♀️♀️♀️
Can anyone give me the answer?!
x + 3x + 2x = 180°
Being straight angle...
6x = 180°
[tex]x = \frac{180}{6} \\ [/tex]
x = 30°
I dont know how to do this
pls answer if u know with simple working
Answer:
17,20,23...
Step-by-step explanation:
you just have to add 3 that's how the pattern works.
It is an arrangement of things in a definite order
A sequence is an ordered list of elements or objects that follows a specific pattern or rule, where the order of the terms is important.
A sequence is an ordered list of numbers, symbols, or other mathematical objects. The order in which the elements appear is important and determines the identity of the sequence. For example, consider the following two sequences:
1, 3, 5, 7, 9
3, 5, 1, 7, 9
The first sequence consists of odd numbers in ascending order, while the second sequence consists of the same numbers but in a different order. These two sequences are different because the order of the terms is different.
Sequences can have different patterns or rules that determine the order of the terms. For example, the sequence of Fibonacci numbers, which is a famous sequence in mathematics, has the following pattern:
1, 1, 2, 3, 5, 8, 13, 21, 34, ...
Each term in the sequence (starting with the third term) is the sum of the two preceding terms.
This pattern continues indefinitely, creating a sequence that has a distinct pattern and order.
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What is the arrangement of objects in a definite order called?
Can u please teach it step by step for me...
Step-by-step explanation:
ASA stands for angle, side, angle
How is triangle ABC congruent to DEF
If any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.
In the diagram you shared, side BC is equivalent to line FD
Angle B = angle F
Angle C = Angle D
(Compare the markings on both triangles)
The relationship between triangle ABC and triangle DEF are congruent only by 2 angles and one side.
A bag contains red, blue, and green tokens. Don randomly
chooses one token from the bag, records the color, and
replaces the token before choosing another token. He
performs the experiment 100 times. The final tally of the
results is shown in the table below.
Answer:
The correct probability is 16/100, or 4/25.
G
3
X
You are traveling by car to New York City. The map you will use for your journey is
below.
Seattle
• San Jose
• Los Angeles
1 unit
1 unit = 557 miles
Denver
El Paso
Chicago
Houston
a) What is the scale factor on the map? (1 point)
Memphis
New York
Jacksonville
grup
The scale factor given in the map to measure the distance is 1 unit = 557 miles.
What is scale factor?
The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.
The map is given for United States of America.
The map shows different states with their locations.
The maps say that 1 unit measures 557 miles.
The scale factor is the means to measure the distance on the map.
The scale factor mentioned in the map is 1 unit.
The value of 1 unit is given as 557 miles.
Therefore, the scale factor is 1 unit = 557 miles.
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The world population is now 8 billion people and growing at 2.2% per year. At that rate, how many people will there be in 25 years?
Using percentages we know that the population after 25 years would be 12.4 billion which is 12,40,00,00,000.
What is the percentage?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.
A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
The symbol "%" is frequently written after the number to indicate percentages.
Now, we know that:
The population is 8 billion.
The increasing percentage is 2.2%.
Then, the population after 25 years would be:
= 8000000000/100 * 2.2
= 17,60,00,000
Now, after 25 years:
= 17,60,00,000 * 25
= 4,40,00,00,000
Total population after 25 years:
4,40,00,00,000 + 8000000000 = 12,40,00,00,000
Therefore, using percentages we know that the population after 25 years would be 12.4 billion which is 12,40,00,00,000.
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(2x-3y)(x+5y)=0 where x>0 and y>0
find the ration x:y
Give your answer in its simplest form
The ratio of x:y is -9:5 or 3:-2.
The given equation is 2x-3y=0 and x+5y=0.
Since x is greater than 0 and y is greater than 0, we can solve the equations for x and y
2x = 3y
x = 3/2y
and
x = -5y
Substituting x = 3/2y in the second equation,
-5y = 3/2y
-10y = 3
y = -3/10
Substiuting y = -3/10 in the first equation,
2x = 3(-3/10)
x = -9/5
Therefore, the ratio of x:y is -9:5. In the simplest form, the ratio can be written as -9:5 or 3:-2.
2x - 3y = 0
x + 5y = 0
2x = 3y
x = 3/2y
-5y = 3/2y
-10y = 3
y = -3/10
2x = 3(-3/10)
x = -9/5
Therefore, x:y = -9:5 or 3:-2
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4.02 Lesson Check Arithmetic Sequences (9)
Answer:
a₉ = - 24
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
given a₁ = 8 and d = - 4 , then
a₉ = 8 + (8 × - 4) = 8 + (- 32) = 8 - 32 = - 24
Answer:
Tn = a + (n - 1)d
T9 = 8 + (9 - 1) × -4
T9 = (8 + 8) × -4
T9 = 16 × -4
T9 = -64
Question 2) Suppose you work for the Cheapo Coffee company and are tasked with studying their coffee shops around the country. You are interested in studying the number of cups of coffees sold per day at different cheapo coffee shops. To study this you randomly select 4 major cities from across the US. You visit each oh the cheapo coffee stores in these cities for a day and record the value is the number of customers they serve. You ultimately visit 17 shops and get the following data.
35, 43, 48, 52, 58, 67, 73, 85, 106, 125, 136, 174, 199, 213, 274, 351
a. What is the population in this question?
b. What is the sample in this question
a. The population in this question is all the Cheapo Coffee stores around the country.
b. The sample in this question is the 17 coffee shops that were visited and their daily sales data was recorded.
In statistics, a population is the entire group of individuals, items, or events that we are interested in studying. In this case, the population is all the Cheapo Coffee stores across the country, and we are interested in studying the number of cups of coffee sold per day at these stores.
However, it is often impractical or impossible to study the entire population, so we select a subset of the population, which is called a sample.
The sample is a representative subset of the population that we study to draw conclusions about the population as a whole. In this case, the sample consists of 17 Cheapo Coffee stores that were randomly selected from four major cities in the US, and the number of cups of coffee sold per day was recorded for each store.
We can use the data from the sample to estimate the average number of cups of coffee sold per day at all Cheapo Coffee stores across the country, which is the parameter of interest in this study.
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simplify the expression if m = -7 and n = 4: 5m + 9n
Answer:
If m = -7 and n = 4, then we can substitute these values into the expression:
5m + 9n = 5(-7) + 9(4)
= -35 + 36
= 1
Therefore, 5m + 9n simplifies to 1 when m = -7 and n = 4.
Step-by-step explanation: