Answer:
It is True that all concepts rely on ratios meaning to provide a type of measurement because ratio compares one quantity to another
Step-by-step explanation:
Ratio shows how many times one quantity is to another
Answer:
it's division.
Step-by-step explanation:
Leon and Marisol biked the Brookside Trail to the end and back. Then they biked the Forest Glen Trail to the end and back before stopping to eat. How far did they bike before they stopped to eat?
The question is incomplete because you haven't attached the map with it. I am attaching the photo of the map here and answering according to it.
Answer:
Before stopping to eat, Leon and Marisol biked a total distance of 12 [tex]\frac{1}{3}[/tex] miles.
Step-by-step explanation:
Leon and Marisol first biked the Brookside Trail to the end an back. According to the map, this trail is 3 [tex]\frac{2}{3}[/tex] miles long and the distance from the trail to the end and back can be calculating by adding this distance twice. The distance is a mixed fraction and we need to convert it into a simple fraction to add it.
To convert the mixed fraction, we will first multiply the denominator with the whole number, i.e. 3x3 = 9 and then add the numerator to it i.e. 9 + 2 = 11. The new denominator will be the same as the previous denominator.
The fraction can now be written as [tex]\frac{11}{3}[/tex]. The distance of Brookside trail to the end and back is
[tex]\frac{11}{3}[/tex] +
Then, they biked the Forest Glen Trail to the end and back. The distance of this trail is 2 [tex]\frac{1}{2}[/tex] miles. We will add this distance twice as well to obtain the total distance traveled for this trail.
To convert the mixed fraction into a simple fraction, multiply the denominator with the whole number i.e. 2 x 2 = 4. Then add the numerator to this answer i.e. 4 + 1 = 5. This is the new numerator and the denominator stays the same. The fraction is [tex]\frac{5}{2}[/tex].
The distance of Forest Glen Trail to the end and back is:
[tex]\frac{5}{2}[/tex] +
The total distance traveled can be calculated by adding both the distances traveled in the individual trails. i.e.
[tex]\frac{22}{3}[/tex] + 5
This can be written as:
[tex]\frac{22}{3}[/tex] + [tex]\frac{5}{1}[/tex]
The denominators are different so we will find out the L.C.M (Lowest Common Multiple) of 3 and 1 which is 3.
We will multiply the numerator and denominator of second fraction with 3 to make the denominator equal to 3.
[tex]\frac{22}{3} + \frac{5 X 3}{1 X 3}[/tex]
= [tex]\frac{22}{3} + \frac{15}{3}[/tex]
= [tex]\frac{22+15}{3}[/tex]
= [tex]\frac{37}{3}[/tex]
To convert [tex]\frac{37}{3}[/tex] miles into a mixed fraction, divide 37 by 3 and write down the answer as a whole number, the remainder as the numerator and the previous denominator i.e. 3 as the new denominator.
3 x 12 = 36. So dividing 37 by 3 will yield 12 as the whole number. The remainder is 37-36 = 1. So, the mixed fraction will be 12 [tex]\frac{1}{3}[/tex]
Before stopping to eat, Leon and Marisol biked a total distance of 12 [tex]\frac{1}{3}[/tex] miles.
Answer:
Step-by-step explanation:
The question is incomplete because you haven't attached the map with it. I am attaching the photo of the map here and answering according to it.
Answer:
Before stopping to eat, Leon and Marisol biked a total distance of 12 miles.
Step-by-step explanation:
Leon and Marisol first biked the Brookside Trail to the end an back. According to the map, this trail is 3 miles long and the distance from the trail to the end and back can be calculating by adding this distance twice. The distance is a mixed fraction and we need to convert it into a simple fraction to add it.
To convert the mixed fraction, we will first multiply the denominator with the whole number, i.e. 3x3 = 9 and then add the numerator to it i.e. 9 + 2 = 11. The new denominator will be the same as the previous denominator.
The fraction can now be written as . The distance of Brookside trail to the end and back is
+
Then, they biked the Forest Glen Trail to the end and back. The distance of this trail is 2 miles. We will add this distance twice as well to obtain the total distance traveled for this trail.
To convert the mixed fraction into a simple fraction, multiply the denominator with the whole number i.e. 2 x 2 = 4. Then add the numerator to this answer i.e. 4 + 1 = 5. This is the new numerator and the denominator stays the same. The fraction is .
The distance of Forest Glen Trail to the end and back is:
+
The total distance traveled can be calculated by adding both the distances traveled in the individual trails. i.e.
+ 5
This can be written as:
+
The denominators are different so we will find out the L.C.M (Lowest Common Multiple) of 3 and 1 which is 3.
We will multiply the numerator and denominator of second fraction with 3 to make the denominator equal to 3.
=
=
=
To convert miles into a mixed fraction, divide 37 by 3 and write down the answer as a whole number, the remainder as the numerator and the previous denominator i.e. 3 as the new denominator.
3 x 12 = 36. So dividing 37 by 3 will yield 12 as the whole number. The remainder is 37-36 = 1. So, the mixed fraction will be 12
Before stopping to eat, Leon and Marisol biked a total distance of 12 miles.
Determine the 3-day simple moving averages for the ten consecutive day closing
prices.
7.78,7.90, 8.00, 7.97,7.86,7.67,7,60, 7.65,7.65, 7.70
:6
on
Final answer:
3-day Simple Moving Averages are computed by taking the average of three consecutive closing prices. The process is repeated for each set of three days within the ten-day period, resulting in a smoothed series of averages.
Explanation:
The 3-day simple moving average (SMA) of a series of stock prices is calculated by taking the sum of three consecutive closing prices and dividing by three. For the input series 7.78, 7.90, 8.00, 7.97, 7.86, 7.67, 7.60, 7.65, 7.65, 7.70, we perform the following steps:
For days 1, 2, and 3, the SMA would be (7.78 + 7.90 + 8.00) / 3.
For days 2, 3, and 4, the SMA would be (7.90 + 8.00 + 7.97) / 3.
Continue this process until you calculate the SMA for the last three days in the series.
Here is how they are actually calculated:
Day 1-3: (7.78 + 7.90 + 8.00) / 3 = 7.8933
Day 2-4: (7.90 + 8.00 + 7.97) / 3 = 7.9567
Day 3-5: (8.00 + 7.97 + 7.86) / 3 = 7.9433
Day 4-6: (7.97 + 7.86 + 7.67) / 3 = 7.8333
Day 5-7: (7.86 + 7.67 + 7.60) / 3 = 7.7100
Day 6-8: (7.67 + 7.60 + 7.65) / 3 = 7.6400
Day 7-9: (7.60 + 7.65 + 7.65) / 3 = 7.6333
Day 8-10: (7.65 + 7.65 + 7.70) / 3 = 7.6667
These averages help show the trend by smoothing out fluctuations in the data.
Discrete or Continous?
A) the number of passengers in a passenger vehicle on a highway at rush hour
B) the air pressure of a tire on an automobile
C) the weight of refuse on a truck arriving at a landfill
Final answer:
Data can be categorized as discrete or continuous. Discrete data consist of countable values, while continuous data can take on any value within a range and are measurable. Examples include the number of passengers (discrete) and air pressure of a tire (continuous).
Explanation:
When categorizing data, it's important to determine whether the data are discrete or continuous. A discrete variable is one that can only take on certain, typically countable, values. Continuous variables, on the other hand, can take on any value within a range and are measurable.
Examples:
The number of passengers in a passenger vehicle on a highway at rush hour is discrete, as you can count passengers.The air pressure of a tire on an automobile is continuous, as pressure can be measured and can vary along a continuum within a range.The weight of refuse on a truck arriving at a landfill is continuous because weight can take on any value within a range and is not countable.Further examples:
The number of gallons of gasoline necessary to fill an automobile gas tank is discrete.The number of cm in 2 m is discrete, as centimeters can be counted and there is a fixed number of them in 2 meters.The mass of a textbook is continuous, as mass can vary along a continuum and is measured.The time required to drive from San Francisco to Kansas City at an average speed of 53 mi/h is continuous, because time can take any value and is measured.The temperature outside is 15 degrees Fahrenheit . If the temperature drops 20 degrees , will the outside temperature be represented by a positive integer or negative integer?Explain your reasoning
Answer:
The temperature would be -5 degrees Fahrenheit
Step-by-step explanation: It's represented by a negative integer because 15 - 20 = -5. This means the temperature outside would be -5 degrees Fahrenheit.
Hope this helps! (:
The temperature would be -5 degrees Fahrenheit if The temperature outside is 15 degrees Fahrenheit . If the temperature drops 20 degrees,
What is unit conversion?It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, multiplication by a conversion factor.
It is given that:
The temperature outside is 15 degrees Fahrenheit . If the temperature drops 20 degrees
=15 - 20
= -5.
A negative sign means the temperature outside would be -5 degrees Fahrenheit.
Thus, the temperature would be -5 degrees Fahrenheit if The temperature outside is 15 degrees Fahrenheit. If the temperature drops 20 degrees,
Learn more about the unit conversion here:
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100 points , please help. I am not sure if I did this correct if anyone can double-check me thanks!
my answer:
2. In order to find the definite integral of the riemann sum given to us. We need to label everything out. We know that our delta x = 3/n , a=1 and that b=4. We found B by subtracting
b-a=delta x
b-1=3
b=4.
Then now we plug everything in giving us our final answer, ⎰^4 and 1 on the bottom (sqrt 1 + 3/n) dx.
Step-by-step explanation:
[tex]\lim_{n \to \infty} \sum\limits_{k=1}^{n}f(x_{k}) \Delta x = \int\limits^a_b {f(x)} \, dx \\where\ \Delta x = \frac{b-a}{n} \ and\ x_{k}=a+\Delta x \times k[/tex]
In this case we have:
Δx = 3/n
b − a = 3
a = 1
b = 4
So the integral is:
∫₁⁴ √x dx
To evaluate the integral, we write the radical as an exponent.
∫₁⁴ x^½ dx
= ⅔ x^³/₂ + C |₁⁴
= (⅔ 4^³/₂ + C) − (⅔ 1^³/₂ + C)
= ⅔ (8) + C − ⅔ − C
= 14/3
If ∫₁⁴ f(x) dx = e⁴ − e, then:
∫₁⁴ (2f(x) − 1) dx
= 2 ∫₁⁴ f(x) dx − ∫₁⁴ dx
= 2 (e⁴ − e) − (x + C) |₁⁴
= 2e⁴ − 2e − 3
∫ sec²(x/k) dx
k ∫ 1/k sec²(x/k) dx
k tan(x/k) + C
Evaluating between x=0 and x=π/2:
k tan(π/(2k)) + C − (k tan(0) + C)
k tan(π/(2k))
Setting this equal to k:
k tan(π/(2k)) = k
tan(π/(2k)) = 1
π/(2k) = π/4
1/(2k) = 1/4
2k = 4
k = 2
A swimming pool has to be drained for maintenance. The pool is shaped like a cylinder with a diameter of 5 m and a depth of 1.7 m. Suppose water is pumped out of the pool at a rate of 12 m3 per hour. If the pool starts completely full, how many hours will it take to empty the pool?
Answer:
2.78hrs
Step-by-step explanation:
Volume of water in the pool =πr2h
V = 3.142 * 2.5² *1.7
V = 33.38m³
Emptying the pool out at 12m³ per hour
= 33.38/12
= 2.78hrs
If anna is 11 years older than Robert and robert is 2 years younger than sara david is 8 years older than Sara how old is everyone else
Answer:
The information given is not enough to determine their ages explicitly, so, here their ages are given in terms of Anna's age, which is the best that could be determined.
Anna's age = x years
Robert's age = (x - 11) years
Sara's age = (x - 9) years
David's age = (x - 1) years
Step-by-step explanation:
Let Anna be x years old.
Anna's age = x
Because Anna is 11 years older than Robert, we can say Robert's age is Anna's age minus 11.
Robert = x - 11
But Robert is 2 years younger than Sara, we can say Sara's age is Robert's age plus 2
Sara = (x - 11) + 2
= x - 9
David is 8 years older than Sara, we can say David's age is Sara's age plus 8.
David = (x - 9) + 8
= x - 1
A bus left new york city and arrived in Philadelphia after 2 1/3 hours. From there, it took 1 3/4 hours to travel Baltimore. It took another 5/6 hour to go from baltimore to washington. If the bus arrived in washington at 10:05 pm, at what time did it leave New York city
Answer:
The bus left New York city at 5:10pm
Step-by-step explanation:
First, we need to calculate the total number of hours the bus used to travel from New York to Washington.
Total number of hours traveled
= 2 1/3hr + 1 3/4hr + 5/6hr
= 7/3+7/4+5/6
=28+21+10/12
=59/12
= 4 11/12hours
Converting 11/12hours to minutes we will have 11/12×60 = 55minutes
Therefore the bus traveled for 4hours 55minutes.
If the bus arrived in Washington at 10:05 pm and the bus left New York 4hours 55minutes ago, this means that the bus did left New York at (10.05-4.55)pm i.e 5:10pm
4hours past 10:05pm will be 6:05pm
55minutes past 6:05pm will be 5:10pm
This means that the bus left New York city at 5:10pm
Marcus sold brownies at a bake sale. He sold d dollars worth of brownies he spent a total of $5.50 on materials, so his total profit p in dollars can be found by subtracting $5.50 from his earnings. Write an equation that represents this situation
Answer:
d = $5.50 - p
Step-by-step explanation:
Answer: d = $5.50 - p
Step-by-step explanation:
Vote me Brainlets pls!
Choco Dream is a firm that produces both dark chocolates as well as liquor chocolates. During a given month, the firm uses its resources to produce both varieties. Initially, the firm produced 5,000 bars of dark chocolates and 4,000 bars of liquor chocolates in a month. In order to increase production of the latter to 4,500, they had to reduce production of dark chocolates by 800 bars. When demand for liquor chocolates increased further, Choco Dream produced 5,000 bars of liquor chocolates and 3,200 bars of dark chocolates per month. Which of the following inferences can be drawn from the given information? A. Choco Dream's production possibilities frontier is linear. B. Both types of chocolates sold by Choco Dream are equally popular among consumers. C. Resources are equally productive in the production of both types of chocolates. D. The company is operating at one end of the PPF. E. Choco Dream faces increasing marginal opportunity cost in the production of liquor chocolates.
Answer:
E) Choco Dream faces increasing marginal opportunity cost in the production of liquor chocolates.
Step-by-step explanation:
When Choco Dream increased their production of liquor chocolates by 500 units (to 4,500 bars per month), their opportunity was 800 units of dark chocolate. But when they needed to increase liquor chocolates by 500 more units (to 5,000 bars per month), then the opportunity cost increased to 1,000 units of dark chocolate.
That means that for the first 500 extra liquor bars, the opportunity cost = 800 dark chocolate bars / 500 liquor bars = 1.6 dark chocolate bars for every extra liquor bar.
The second increased required a higher opportunity cost = 1,000 dark chocolate bars / 500 liquor bars = 2 dark chocolate bars for every extra liquor bar.
One number exceeds another by 4. The sum of the number is 68. What are the numbers?
A - B = 4
A + B = 64
__________ +
A - B + A + B = 64 + 4
2A = 68
A = 34
B = 34 - 4
B = 30
A college has a 30% completion rate, meaning that 30% of all students who start at the college complete the goal they set. The president of the college sets a goal of increasing this number by 50%. What will the completion rate goal be as a percentage.
Answer:
45%
Step-by-step explanation:
For simplicity, let use assume there are 100 students in the school.
No. of students to complete college = (30/100) x 100 = 30 Students
President wants to increase by 50% = (50/100) x 30 = 15 Students
New set goal = 30 + 15 = 45 students.
Total number of students = 100 students
Therefore;
Rate goal % = (45/100) x 100% = 45%
Write the standard form of the line that passes through the given points. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution. (6, 1) and (5, 4)
Answer:
STANDARD FORM PEOPLE Ax + By =C
so
find slope
m=-3
then plug that and one of the two points into the equation
y - y1 = m(x - x1)
y-1= -3(x-6)
y-1=-3x + 18
y + 3x = 19
so your answer is
3x + y = 19
what does 124.06=2.35h+72.36
a.16
b.22
c.2.2
d.none of these
Answer:
B. 22
Step-by-step explanation:
124.06 = 2.35h + 72.36
124.06 - 72.36 = 2.35h
51.7 = 2.35h
51.7/2.35 = h
22 = h
The school store sells erasers. If Mrs. McBryde purchases 1000 erasers for $70.00, how much does 1 eraser cost? (Hint: Do not try to solve this with a long division problem!)
Answer:
The cost of 1 eraser is $0.07.
Step-by-step explanation:
Given:
The school store sells erasers. If Mrs. McBryde purchases 1000 erasers for $70.00,
Now, to find the cost of 1 eraser.
Let the cost of 1 eraser be [tex]x.[/tex]
The cost of 1000 erasers is $70.00.
So, 1000 is equivalent to $70.00.
Thus, 1 is equivalent to [tex]x.[/tex]
Now, to solve by using cross multiplication method:
[tex]\frac{1000}{70} =\frac{1}{x}[/tex]
By cross multiplying we get:
[tex]1000x=70[/tex]
Dividing both sides by 1000 we get:
[tex]x=\$0.07.[/tex]
Therefore, the cost of 1 eraser is $0.07.
Final answer:
The cost of one eraser is found by dividing the total cost of $70.00 by the number of erasers purchased, which is 1000, resulting in a cost of $0.07 per eraser.
Explanation:
To find the cost of one eraser, we divide the total cost by the number of erasers Mrs. McBryde purchased. She bought 1000 erasers for $70.00. So, we need to perform the division $70.00 ÷ 1000 erasers = $0.07 per eraser. This means each eraser costs 7 cents.
Peter takes16 minutes longer to mow the lawn by himself than Charles . Together they can mow the lawn in 18 minutes. How long will it take Charles to do it alone?
Answer:
about 29.7 minutes
Step-by-step explanation:
If it take c minutes for Charles to mow the lawn by himself, it takes c+16 minutes for Peter. The two of them working together can mow in one minute this fraction of the entire lawn:
1/c + 1/(c+16) = 1/18
Multiplying by 18c(c+16), we get ...
18(c +16) + 18(c) = c(c+16)/18
36c +288 = c^2 +16c
c^2 -20c = 288 . . . . . subtract 36c
c^2 -20c +100 = 388 . . . . . add (20/2)^2 = 100 to complete the square
(c -10)^2 = 388
c = 10 +√388 ≈ 29.6977 . . . . . take the positive square root
It takes Charles about 29.7 minutes to mow the lawn by himself.
HELP ASAP FOR BRAINLIEST: The time required to finish a test in normally distributed with a mean of 60 minutes and a standard deviation of 10 minutes. What is the z-score for a student who finishes the test in 23 minutes? Show work please :)
Answer:
The z-score = -3.7 and p (-3.7) = 0.00011 or 0.011%
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Mean of time to finish a test = 60 minutes
Standard deviation of time to finish a test = 10 minutes
Time that a student finishes the test = 23 minutes
2. What is the z-score for the student?
z-score = (Time that a student finishes the test - Mean of time to finish a test)/Standard deviation of time to finish a test
Replacing with the real values:
z-score = (23 -60)/10 = -37/10 = -3.7
z-score = -3.7 and p (-3.7) = 0.00011 or 0.011%
Biologists tagged 103 fish in a lake january 1. On feburary 1, they returned and collected a random sample of 24 fish, 12 of which had been previously tagged. How many fish does the lake have
Answer:
206
Step-by-step explanation:
We have been given that Biologists tagged 103 fish in a lake January 1. On February 1, they returned and collected a random sample of 24 fish, 12 of which had been previously tagged.
To find the number of fish in the lake, we will use proportions because ratio of tagged fish and collected fish on February 1 will be equal to ratio of tagged fish and total fish on January 1.
[tex]\frac{\text{Tagged fish}}{\text{Collected fish}}=\frac{12}{24}[/tex]
Upon substituting the number of tagged fish in our proportion, we will get:
[tex]\frac{103}{\text{Total fish}}=\frac{12}{24}\\\\\frac{103}{\text{Total fish}}=\frac{1}{2}[/tex]
Cross multiply:
[tex]1\cdot \text{Total fish}=103\cdot 2\\\\\text{Total fish}=206[/tex]
Therefore, there are approximately 206 fishes in the lake.
Jeff sold the pumpkins he grew for $7 each at the farmers market. If Jeff sold 30 pumpkins how much money did he make. Write an expression to the amount of money in dollars Jeff made.
Jeff made $210 by selling 30 pumpkins.
Step-by-step explanation:
Given,
Selling price of each Pumpkin = $7
Number of pumpkins sold by Jeff = 30
We will multiply number of pumpkins sold by selling price per pumpkin.
Amount made by Jeff = Price per pumpkin * Number of pumpkins
Amount made by Jeff = 7 * 30 = $210
Therefore;
Jeff made $210 by selling 30 pumpkins.
Keywords: multiplication
Learn more about multiplication at:
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Need help doing this questions, all help is appreciated thanks.
Answer:
The answer to your question is the third option
Step-by-step explanation:
To know if two lines are parallel we must get their slopes if the slopes are equal, the lines are parallel.
Data
A (2,2)
B (3,6)
C(0,5)
D(1,9)
Formula
slope = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
Process
1.- Calculate the slope of line 1
slope 1 = [tex]\frac{6 - 2}{3 - 2}[/tex]
slope 1 = [tex]\frac{4}{1}[/tex]
slope 1 = 4
2.- Calculate slope 2
slope 2 = [tex]\frac{9 - 5}{1 - 0}[/tex]
slope 2 = [tex]\frac{4}{1}[/tex]
slope 2 = 4
3.- Compare the slope
slope 1 = 4 and slope 2 = 4, both slope are equals, then the lines are parallel.
The population of grand island, nebraska, grew by 600,000 people between 1995 and 2005, one fifth more than the town council originally predicted the city's population would grow by ?
Answer:
500000 people
Step-by-step explanation:
The population grew by 600,000 which is 120% the earlier prediction by the town council.
Using direct proportion
600,000 -------- 120%
X --------- 100%
X = (600000 × 100) ÷ 120 = 500000
Therefore the earlier prediction by the town council is 500000 people
The student's question is a mathematical problem calculating population growth predictions. The town council of Grand Island originally predicted a growth of 500,000 people, which is 20% less than the actual growth of 600,000 people.
To determine the prediction made by the town council, we can use the fact that the actual growth exceeded the prediction by one fifth (or 20%). If the actual growth was 600,000 people, the predicted growth can be calculated by dividing 600,000 by 1.2, as the actual growth represents 120% of the predicted value (100% original prediction + 20% excess).
Calculating the Predicted Population Growth
To find the town council's predicted growth, we can set up the equation:
Actual Growth = Predicted Growth + (Predicted Growth × 0.20)600,000 = Predicted Growth × 1.20Predicted Growth = 600,000 / 1.20Predicted Growth = 500,000Therefore, the town council had originally predicted that the population of Grand Island, Nebraska, would increase by 500,000 people between 1995 and 2005.
please hurry
Which situations can represent the expression Check all that apply. Naomi gives some of her six pencils away. Sydney increased her collection of coins by six. Benjamin lost six of his stickers. Six servings of dinner were decreased by a number. Westville has 6 fewer schools than Eastville. Gabrielle decreased her 6-minute mile by an unknown amount of time.
Step-by-step explanation:
Hi,
Since there are multiple scenarios, lets first discuss the rules of developing expressions.
Any unknown value can be assumed as a variable.An increase means addition and decrease means subtraction.Using these rules we can develop the following expressions:
[tex]x - 6[/tex], where [tex]x[/tex] indicates the total number of pencils Naomi had.[tex]y + 6[/tex], where [tex]y[/tex] represents the number of coins Sydney had initially. [tex]z - 6[/tex], where [tex]z[/tex] refers to the total number of stickers Benjamin had.[tex]6 - a[/tex], where a is the number of servings decreased.[tex]b + 6,[/tex] where b is the number of schools in Eastville.[tex]6 - c[/tex], where c indicates the amount of time Gabrielle reduces.Tip:
In addition, the order of number doesn't matter however this is not the case in subtraction.
Alexa took out a $42,000 loan to remodel a house. The loan rate is 8.3% simple interest per year and will be repaid in six months. What is the maturity value that is paid back ?
Answer: The maturity value is $43743
Step-by-step explanation:
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the loan.
P represents the principal or amount that was taken as loan.
R represents interest rate.
T represents the duration of the loan in years.
From the information given,
P = 42000
R = 8.3
T = 6 months = 6/12 = 0.5 years
I = (42000 × 8.3 × 0.5)/100 = $1743
The maturity value is the total amount paid after the duration of the loan. It becomes
42000 + 1743 = $43743
The distribution of scores on the SAT is approximately normal with a mean of mu = 500 and a standard deviation of sigma = 100. For the population of students who have taken the SAT, a.What proportion have SAT scores greater than 700? b.What proportion have SAT scores greater than 550? c.What is the minimum SAT score needed to be in the highest 10% of the population? d.If the state college only accepts students from the top 60% of the SAT distribution, what is the minimum SAT score needed to be accepted ?
Answer:
a. 2.28%
b. 30.85%
c. 628.16
d. 474.67
Step-by-step explanation:
For a given value x, the related z-score is computed as z = (x-500)/100.
a. The z-score related to 700 is (700-500)/100 = 2, and P(Z > 2) = 0.0228 (2.28%)
b. The z-score related to 550 is (550-500)/100 = 0.5, and P(Z > 0.5) = 0.3085 (30.85%)
c. We are looking for a value b such that P(Z > b) = 0.1, i.e., b is the 90th quantile of the standard normal distribution, so, b = 1.281552. Therefore, P((X-500)/100 > 1.281552) = 0.1, equivalently P(X > 500 + 100(1.281552)) = 0.1 and the minimun SAT score needed to be in the highest 10% of the population is 628.1552
d. We are looking for a value c such that P(Z > c) = 0.6, i.e., c is the 40th quantile of the standard normal distribution, so, c = -0.2533471. Therefore, P((X-500)/100 > -0.2533471) = 0.6, equivalently P(X > 500 + 100(-0.2533471)), and the minimun SAT score needed to be accepted is 474.6653
Using the normal distribution, it is found that:
a) 0.0228 = 2.28% of students have SAT scores greater than 700.
b) 0.3085 = 30.85% of students have SAT scores greater than 550.
c) The minimum SAT score needed to be in the highest 10% of the population is 628.
d) The minimum SAT score needed to be accepted is 475.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
The mean is [tex]\mu = 500[/tex]The standard deviation is [tex]\sigma = 100[/tex].Item a:
This proportion is 1 subtracted by the p-value of Z when X = 700, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{700 - 500}{100}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772.
1 - 0.9772 = 0.0228.
0.0228 = 2.28% of students have SAT scores greater than 700.
Item b:
This proportion is 1 subtracted by the p-value of Z when X = 550, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{550 - 500}{100}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a p-value of 0.6915.
1 - 0.6915 = 0.3085.
0.3085 = 30.85% of students have SAT scores greater than 550.
Item c:
This is the 100 - 10 = 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 500}{100}[/tex]
[tex]X - 500 = 1.28(100)[/tex]
[tex]X = 628[/tex]
The minimum SAT score needed to be in the highest 10% of the population is 628.
Item d:
This is the 100 - 60 = 40th percentile, which is X when Z has a p-value of 0.4, so X when Z = -0.25.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.25 = \frac{X - 500}{100}[/tex]
[tex]X - 500 = -0.25(100)[/tex]
[tex]X = 475[/tex]
The minimum SAT score needed to be accepted is 475.
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In a particular hospital, 5 newborn babies were delivered. here are their weights (in ounces): 119, 104, 92, 97, 103 Assuming these weights constitute an entire population find the standard deviation of the population, round answers to at least two decimal places.
Answer: standard deviation is 6.96
Step-by-step explanation:
Let m be mean
M=mean=sum/n
M=525/5
M=103
The standard deviation formula is :
S.D = sqrt( Summation of |x-m|^2 / n-1)
Let start finding:
|x-m|^2
For 1st: |119-103|^2=36
For 2nd: |104-103|^2=1
For 3rd: |92-103|^2=121
For 4th: |97-103|^2=36
For 5th: |103-103|^2=0
Summation of |x-m|^2 = 194
The standard deviation formula is :
S.D = sqrt( Summation of |x-m|^2 / n-1)
S.D= sqrt(194 / 4)
S.D=sqrt(48.5)
S.D= 6.96
The standard deviation is approximately 9.1 ounces.
Calculating the Population Standard Deviation
To find the standard deviation of the population of newborn babies' weights in a hospital, we need to follow several steps. The weights of the babies (in ounces) are 119, 104, 92, 97, and 103.
Calculate the mean (average) weight: (119 + 104 + 92 + 97 + 103) / 5 = 103
Determine the squared deviations from the mean for each weight: ((119 - 103)²), ((104 - 103)²), ((92 - 103)²), ((97 - 103)²), ((103 - 103)²).
Sum the squared deviations: 256 + 1 + 121 + 36 + 0 = 414.
Since we have the entire population, divide by the number of data points, which is 5: (414 / 5 = 82.8).
Take the square root of 82.8 to find the population standard deviation: √82.8} =approximately 9.1 ounces.
The population standard deviation of the babies' weights is approximately 9.1 ounces, rounded to two decimal places.
Having trouble with this and 3 others
Answer:
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Step-by-step explanation:
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What do you know to be true about the values of a and b?
A. a = b
B. a < b
C. a > b
D. Can't be determined.
Answer:
A
Step-by-step explanation:
The triangles are the same size but in a different form. Y= 50 and a and b equal eachother.
The option (D) Can't be determined is correct because we cannot determine the value of b because there are two unknowns b and y.
What is the triangle?The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
We have a triangle shown in the picture.
From the triangle first we can find the value of a:
a = 180 - (50 + 45)
a = 85 degree
We cannot determine the value of b because there are two unknowns b and y.
Thus, the option (D) Can't be determined is correct because we cannot determine the value of b because there are two unknowns b and y.
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In one U.S. city, the quadratic function f (x )equals 0.0039 x squared minus 0.42 x plus 36.79 models the median, or average, age, y, at which men were first married x years after 1900. In which year was this average age at a minimum (round to the nearest year)? What was the average age at first marriage for that year (round to the nearest tenth)?
Answer:
The average age was minimum at 1954 and the average age is 25.5.
Step-by-step explanation:
The given quadratic function is
[tex]f(x)=0.0039x^2-0.42x+36.79[/tex]
It models the median, or average, age, y, at which men were first married x years after 1900.
In the above equation leading coefficient is positive, so it is an upward parabola and vertex of an upward parabola, is point of minima.
We need to find the year in which the average age was at a minimum.
If a quadratic polynomial is [tex]f(x)=ax^2+bx+c[/tex], then vertex is
[tex]Vertex=(-\dfrac{b}{2a},f(-\dfrac{b}{2a}))[/tex]
[tex]-\dfrac{b}{2a}=-\dfrac{(-0.42)}{2(0.0039)}=53.846153\approx 54[/tex]
54 years after 1900 is
[tex]1900+54=1954[/tex]
Substitute x=54 in the given function.
[tex]f(54)=0.0039(54)^2-0.42(54)+36.79=25.4824\approx 25.5[/tex]
Therefore, the average age was minimum at 1954 and the average age is 25.5.
The year when the average age at first marriage was at a minimum in a specific U.S. city was approximately 1954. The average age at first marriage for that year was approximately 28.4 years.
Explanation:To find the year when the average age at first marriage was at a minimum, we need to determine the x-value at the vertex of the quadratic function. The x-value at the vertex can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic function. For the given function f(x) = 0.0039x2 - 0.42x + 36.79, the x-value at the vertex is x = -(-0.42)/(2*0.0039) = 53.85. Since the x-value represents years after 1900, we add 1900 to get the year: 1900 + 53.85 ≈ 1954.
To find the average age at first marriage for that year, we substitute x = 53.85 into the quadratic function. f(53.85) = 0.0039(53.85)2 - 0.42(53.85) + 36.79 ≈ 28.4. Therefore, the average age at first marriage for the year 1954 was approximately 28.4 years.
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Jamaica is considering buying either a car which goes 25 miles on 1 gallon of gas, or a truck that goes 10 miles on a gallon of gas. If gasoline costs $2.50 per gallon and Jamaica drives 1000 miles per month, how much less would it cost to drive the car each month than it would to drive the truck?
Answer: if he drives the car each month, he would spend $150 lesser than when he drives the truck.
Step-by-step explanation:
The car goes 25 miles on 1 gallon of gas. Jamaica drives 1000 miles per month, it means that the number of gallons of gas that he would use in a month is
1000/25 = 40 gallons of gas
If gasoline costs $2.50 per gallon and Jamaica chooses to buy a car, the cost of gas per month would be
2.5 × 40 = $100
The truck goes 10 miles on 1 gallon of gas. Jamaica drives 1000 miles per month, it means that the number of gallons of gas that he would use in a month is
1000/10 = 100 gallons of gas
If gasoline costs $2.50 per gallon and Jamaica chooses to buy a truck, the cost of gas per month would be
2.5 × 100 = $250
The difference between both costs is
250 - 100 = $150
Let x1, x2, and x3 be 0 - 1 variables whose values indicate whether the projects are not done (0) or are done (1). Which answer below indicates that at least two of the projects must be done?a.x1+ x2+ x3>2b.x1+ x2+ x3<2c.x1+ x2+ x3= 2d.x1- x2= 0
Answer:
Correct statement: a. x₁ + x₂ + x₃ > 2
Step-by-step explanation:
The variables x₁, x₂ and x₃ takes value 0 if the projects are not done and 1 if the projects are done.
Consider that at least two projects are done, i.e. 2 or more projects are done.
This can happen in:
x₁ = 0, x₂ = 1 and x₃ = 1
x₁ = 1, x₂ = 0 and x₃ = 1
x₁ = 1, x₂ = 1 and x₃ = 0
x₁ = 1, x₂ = 1 and x₃ = 1
The statement (x₁ + x₂ + x₃ > 2) will be true only when all the variables takes the value 1.
This statement implies that 2 projects are definitely done.
Thus, the correct statement is (a).