In the year 2010, the population of a city was 600,000 citizens. The population increases at a rate of 1.8% per year.
a. Create a function and table to model the population y (in thousands), in terms of x years (form 2010 to 2020). (or the expression "with x being years from 2010 to 2020")
In complete sentences, interpret the table and its function. include if the data is linear or exponential and how that conclusion was reached.
b. Predict the population of the city in the year 2025.
In your final answer, be sure to include the table, interpretation, and prediction of the function.
Answers
a. The population of the city can be modeled using the exponential growth function:
y = 600(1 + 0.018)^x
with x being years from 0 to 10, where x = 0 corresponds to the year 2010. We can create a table to show the population for each year from 2010 to 2020:
(you can see above)
We can see from the table that the population of the city is increasing each year, and the rate of increase is accelerating. This is because the growth function is exponential, not linear. We know it is exponential because the function has a power of x in the exponent, which causes the rate of growth to increase over time. If the function were linear, the rate of growth would be constant.
b. To predict the population in 2025, we can use the same function with x = 15 (since 2025 is 15 years after 2010):
y = 600(1 + 0.018)^15
y ≈ 846.5 (in thousands)
Therefore, we can predict that the population of the city in 2025 will be approximately 846,500 citizens.
Related Questions
Standard Appliances obtains refrigerators for $1,620 less 26% and 6%. Standard's overhead is 17% of the selling price of $1,690. A scratched demonstrator unit from their floor display was cleared out for $1,345. a. What is the regular rate of markup on cost? % Round to two decimal places b. What is the rate of markdown on the demonstrator unit? % Round to two decimal places c. What is the operating profit or loss on the demostrator unit? Round to the nearest cent d. What is the rate of markup on cost that was actually realized? % Round to two decimal places
Answers
a. The regular rate of markup on cost is approximately 26%.
b. The rate of markdown on the demonstrator unit is approximately 20%.
c. The operating profit on the demonstrator unit is approximately $3.73.
d. The rate of markup on cost that was actually realized is approximately 0.28%.
a. To calculate the regular rate of markup on cost, we need to find the difference between the selling price and the cost, and then calculate the percentage markup based on the cost.
Let's denote the cost as C.
Selling price = Cost + Markup
$1,690 = C + (26% of C)
To find the cost:
$1,690 = C + 0.26C
$1,690 = 1.26C
C = $1,690 / 1.26
C ≈ $1,341.27
Markup on cost = Selling price - Cost
Markup on cost = $1,690 - $1,341.27
Markup on cost ≈ $348.73
Rate of markup on cost = (Markup on cost / Cost) * 100
Rate of markup on cost = ($348.73 / $1,341.27) * 100
Rate of markup on cost ≈ 26%
The regular rate of markup on cost is approximately 26%.
b. The rate of markdown on the demonstrator unit can be calculated by finding the difference between the original selling price and the clearance price, and then calculating the percentage markdown based on the original selling price.
Original selling price = $1,690
Clearance price = $1,345
Markdown = Original selling price - Clearance price
Markdown = $1,690 - $1,345
Markdown = $345
Rate of markdown on the demonstrator unit = (Markdown / Original selling price) * 100
Rate of markdown on the demonstrator unit = ($345 / $1,690) * 100
Rate of markdown on the demonstrator unit ≈ 20%
The rate of markdown on the demonstrator unit is approximately 20%.
c. Operating profit or loss on the demonstrator unit can be calculated by finding the difference between the clearance price and the cost.
Cost = $1,341.27
Clearance price = $1,345
Operating profit or loss = Clearance price - Cost
Operating profit or loss = $1,345 - $1,341.27
Operating profit or loss ≈ $3.73
The operating profit on the demonstrator unit is approximately $3.73.
d. The rate of markup on cost that was actually realized can be calculated by finding the difference between the actual selling price (clearance price) and the cost, and then calculating the percentage markup based on the cost.
Actual selling price (clearance price) = $1,345
Cost = $1,341.27
Markup on cost that was actually realized = Actual selling price - Cost
Markup on cost that was actually realized = $1,345 - $1,341.27
Markup on cost that was actually realized ≈ $3.73
Rate of markup on cost that was actually realized = (Markup on cost that was actually realized / Cost) * 100
Rate of markup on cost that was actually realized = ($3.73 / $1,341.27) * 100
Rate of markup on cost that was actually realized ≈ 0.2781% ≈ 0.28%
The rate of markup on cost that was actually realized is approximately 0.28%.
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the amusement park charges $20 to get in plus $1.50 per ride which linear equation represents this relationship y=1.5+20x,y=21.5x,y=1.5x+20,y=20x+1.5
Answers
Step-by-step explanation:
1.50 per ride tones X number of rides plus a 20 entrance fee
y= 1.5x + 20
WHOEVER ANSWERS FIRST WITH A SERIOUS QUESTION WILL GET BRAINLIEST
While at a Mets game, Jose got thirsty and decided to buy a soda. The food stands sold sodas in three different sizes:
Sorta Swig: 12 ounces for $1.35
Big Swig: 20 ounces for $2.10
Super Swig: 32 ounces for $3.60
Which size soda should Jose buy to get the best deal? Justify your answer with mathematical reasoning (show your work).
Answers
Answer: See Explanation
Step-by-step explanation:
Take the amount of money and divide by the ounces for how much it costs per ounce
1.35 / 12 = 0.1125 per ounce
2.10 / 20 = 0.105 per ounce
3.60 / 32 = 0.1125 per ounce
The Big Swig would be the best deal because the cost per ounce is the lowest, getting you the cheaper price for a good size. I believe I did this right, hope I could help.
Please do a explanation:’)
Answers
Answer:
3x-3xy-2xy-5x+6. ( multiply the number that were outside the bracket)
By BODMAS rule...
= 3x-5x-3xy-2xy+6
= -2x-5xy+6
hope you understood...
Answer and Step-by-step explanation:
We are given an expression to simplify. According to PEMDAS
(Parenthesis, Exponents, Multiplication, Division, Addition, and Subtract [in that order]), we need to start with the parentheses first.
With what we are given, we need to multiply the value outside of the parenthesis to the values inside the parenthesis.
Start with the first set of terms in the expression.
3(x - xy)
We need to multiply 3 to the x and negative xy.
3x - 3xy
Now we go to the next set of terms in the expression.
-x(2y + 5)
Distribute the x (multiply) to the 2y and 5.
-2xy - 5x
Now, we combine like terms within the entire expression.
Combining like terms is essentially saying to combine the terms that have similar properties/values. We have values that have an x with it, and xy with it, and no variables with it. We can combine only the values with the x variable together, and the values with the xy variable can only be combined together. The values without the variables (if you have more than one), will combine only with each other.
3x - 3xy - 2xy - 5x + 6
____________________________________________
-5xy - 2x + 6 <- This is the final answer; the simplified version of the expression.
#teamtrees #PAW (Plant And Water)
Select the number of the punctuation error.on february 23,1992___1. the committee presented its agenda;2. call the meeting to order, approve minutes of the bylaws change,3. hold discussion,4. vote on the bylaws change, and adjourn.
Answers
There is a punctuation error in the sentence "call the meeting to order, approve minutes of the bylaws change,3. hold discussion,4. vote on the bylaws change, and adjourn." The correct answer is sentence 2.
The error is the missing punctuation after "bylaws change." To correct this, you should insert a comma after "bylaws change," like this: "call the meeting to order, approve minutes of the bylaws change, hold discussion, vote on the bylaws change, and adjourn."
Here's a breakdown of the corrected sentence:
1. "call the meeting to order": This is the first action to be taken.
2. "approve minutes of the bylaws change": This means that the committee will review and agree upon the minutes related to the bylaws change.
3. "hold discussion": This refers to engaging in a conversation or debate.
4. "vote on the bylaws change": This means that the committee will cast votes regarding the proposed bylaws change.
5. "adjourn": This indicates the end of the meeting.
By including the missing comma, the sentence becomes grammatically correct and clearer to understand. Thus, the correct option is (2), call the meeting to order, approve minutes of the bylaws change,
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the standard error of the regression, se, is calculated by taking the square root of divided by .
Answers
The standard error of the regression (se) is calculated by taking the square root of the mean squared error (MSE) divided by the degrees of freedom (df).
The mean squared error (MSE) is calculated by summing the squared residuals (the differences between the actual observed values and the predicted values) and dividing by the number of observations minus the number of predictors (variables) in the regression model.
The formula for the mean squared error is:
MSE = Σ(residuals^2) / (n - k)
where Σ denotes the sum, residuals^2 represents the squared residuals, n is the number of observations, and k is the number of predictors in the regression model.
To calculate the standard error of the regression, se, we take the square root of the mean squared error divided by the degrees of freedom:
se = √(MSE / df)
The degrees of freedom (df) in a regression model is equal to the number of observations minus the number of predictors (k).
Therefore, the standard error of the regression, se, is calculated by taking the square root of the mean squared error divided by the degrees of freedom (df).
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1) At the supermarket you can fill your own honey bear container. A customer buys 12 oz of honey for $5.40.
Answers
From the problem, the cost of 12 oz honey is $5.40
a. the cost of honey per ounce will be :
\(\frac{\$5.40}{12oz}=\$0.45\text{per oz}\)The answer is $0.45 per ounce.
b. the amount of honey per dollar will be :
\(\frac{12oz}{\$5.40}=2.22\)The answer is 2.22 oz per dollar
c. when h = ounces of honey and c = cost in dollar
The equation will be :
For the cost of honey per ounce :
\(c=0.45h\)For the amount of honey per dollar :
\(h=0.22c\)d. Graphing one equation, we will graph c = 0.45h
A line with points (0, 0) and (12, 5.40)
x-axis will be the amount of honey
y-axis will be the cost in dollar.
Problem Description: An example of arithmetic progression would be a series of integers (which we will call terms) like: 3, 7, 11, 15, 19, 23, 27, 31, ... Note that 3 is the first term, 7 is the second term, 11 is the 3rd term, etc. 4 is the common difference between any two consecutive terms. Now, if we know that the progression has 100 terms, we would be interested in calculating the 100th term as well as the sum and the float average of all 100 terms. The following formulas can be used to calculate these items: LastTerm = FirstTerm + (NumberOfTerms - 1) x CommonDifference Sum of all terms = NumberOfTerms x (FirstTerm + LastTerm) / 2 Average of all terms = (Sum of all terms) / NumberOf Terms The program should adhere to the following pseudocode: 1. Prompt for and read the first term 2. 3. Prompt for and read the common difference Prompt for and read the number of terms Calculate the last term (see formula above) 4. 5. Calculate the sum of all the terms (see formula above) Calculate the average of all the terms (see formula above) 7. Display the results 6. Your program must match the following sample run (between the lines of dashes). Note that the 3, 3, and 100 on the first three lines were entered by the user. You should also check results for other set of inputs as well. Enter first term: 3 Enter common difference: 3 Enter number of terms: 100 The last term is 300 The sum of all the terms is 15150 The average of all the terms is 151.5
Answers
The last term is 300
The sum of all the terms is 15150.0
The average of all the terms is 151.5
Here is an example solution in Python that follows the given pseudocode:
# Prompt for and read the first term
first_term = int(input("Enter first term: "))
# Prompt for and read the common difference
common_difference = int(input("Enter common difference: "))
# Prompt for and read the number of terms
number_of_terms = int(input("Enter number of terms: "))
# Calculate the last term
last_term = first_term + (number_of_terms - 1) * common_difference
# Calculate the sum of all the terms
sum_of_terms = number_of_terms * (first_term + last_term) / 2
# Calculate the average of all the terms
average_of_terms = sum_of_terms / number_of_terms
# Display the results
print("The last term is", last_term)
print("The sum of all the terms is", sum_of_terms)
print("The average of all the terms is", average_of_terms)
If you run this code and enter the values from the sample run (first term: 3, common difference: 3, number of terms: 100), it will produce the following output:
The last term is 300
The sum of all the terms is 15150.0
The average of all the terms is 151.5
The program prompts the user for the first term, common difference, and number of terms. Then it calculates the last term using the given formula. Next, it calculates the sum of all the terms and the average of all the terms using the provided formulas. Finally, it displays the calculated results.
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Could someone please help me and show work
Answers
Step-by-step explanation:
remember, the sum of all angles in a triangle is always 180°.
and the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
with a, b, c being the sides opposite of their associated angles (A, B, C).
1)
17/sin(26) = 12/sin(C)
sin(C) = 12×sin(26)/17 = 0.309438457...
C = 18.02539254...° ≈ 18°
3)
180 = 27 + 115 + C
C = 38°
19/sin(38) = AC/sin(27)
AC = 19×sin(27)/sin(38) = 14.01065332... in ≈ 14 in
In first triangle side angle m∠C is 18° and in first triangle side AC is 14 in. This can be obtained by using the law of sine.
Find the required angle and side:We know the law of sine which is,
If in a triangle, Δ ABC,
\(\frac{sin A}{a} =\frac{sin B}{b}= \frac{sinC}{c}\), where a is the side opposite to the angle m∠A, b is the side opposite to the angle m∠B and c is the side opposite to the angle m∠C.
sine of the angle scan be found using calculator.
From the question,
1) In first triangle side,
AB = 12ft, BC = 17 ft and m∠A=26°
⇒By using the law of sine,
\(\frac{sin A}{a} =\frac{sin B}{b}= \frac{sinC}{c}\)
sin 26°/17 = sin B/AC = sin C/12
sin 26°/17 = sin C/12
12×sin 26° = 17×sin C
sin C = 5.26/17 = 0.3091
C = 18.023° ≈ 18°
3) In second triangle side,
m∠B = 27°, AB = 19 in and m∠A = 115°
m∠A + m∠B +m∠C = 180°
115° + 27° + m∠C = 180°
142° + m∠C = 180°
m∠C = 38°
⇒By using the law of sine,
\(\frac{sin A}{a} =\frac{sin B}{b}= \frac{sinC}{c}\)
sin 115°/BC = sin 27°/AC = sin 38°/19
sin 27°/AC = sin 38°/19
sin 27° × 19 = sin 38° × AC
8.63 = 0.62 × AC
AC = 13.91 in ≈ 14 in.
Hence in first triangle side angle m∠C is 18° and in first triangle side AC is 14 in.
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i need some help please
Answers
Answer:
1)3 2)24 3)-6 4)8 5)-2 6)18 7)-10 8)4
Step-by-step explanation:
easyyyyyy
Find the solution to the equation.
30=−5n+16+3n
Enter only a number. Do NOT enter an equation. If the number is not an integer, enter it as a fraction in simplest form. If there is no solution, “no solution” should be entered.
Answers
Answer:
-7
Step-by-step explanation:
30-16= -5n +3n
14 = -2n
multiplying both by half,u have -
7 = -n
multiply both by -1
7 = n
A mother tracks the duration of her baby's three daily naps for a few weeks. The mean time, in minutes, and the standard deviation, SD, for each nap are recorded in the table below. 1st Nap 2nd Nap 3rd Nap Mean = 83 SD = 9 Mean = 52 SD = 6 Mean = 39 SD = 11 Use the information in the table to select the true statement. A. The 3rd nap is the least consistent in duration because its mean is the lowest. B. The 2nd nap is the least consistent in duration because its standard deviation is the lowest. C. The 1st nap is the least consistent in duration because its mean is the highest. D. The 3rd nap is the least consistent in duration because its standard deviation is the highest.
Answers
UPDATED:
Plato users: answer is now A:
"The 3rd nap is the least consistent in duration because its
standard deviation is the highest."
they just shuffled the answers, the answer choice itself is still the same, just a dif letter choice
< 26 / Jan / 2022 >
The correct answer is the last one, that the 3rd nap is the least consistent in duration because its standard deviation is the highest.
What is the standard deviation?Standard deviation is a measure of variation from the mean; it tells how different values are from the mean.
We have given that,
A mother tracks the duration of her baby's three daily naps for a few weeks. The mean time, in minutes, and the standard deviation, SD, for each nap are recorded in the table below.
Now, For that nap to have a higher standard deviation means that its values were on average more different from the mean than the others.
Thus, The correct answer is the last one, that the 3rd nap is the least consistent in duration because its standard deviation is the highest.
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. Importance of hydrologic cycle The role of water is central to most natural processes - Transport - Weathering, contaminant transport - Energy balance - transport of heat, high heat capacity - Greenhouse gas - 80% of the atmospheric greenhouse effect is caused by water vapor - Life - for most terrestrial life forms, water determines where they may live; man is exception
Answers
The hydrologic cycle, also known as the water cycle, plays a crucial role in the Earth's natural processes. It involves the continuous movement of water between the Earth's surface, atmosphere, and underground reservoirs.
The importance of the hydrologic cycle can be understood by considering its various functions:
Transport: The hydrologic cycle facilitates the transport of water across the Earth's surface, including rivers, lakes, and oceans. This movement of water is vital for the distribution of nutrients, sediments, and organic matter, which are essential for the functioning of ecosystems.
Weathering and Contaminant Transport: Water plays a significant role in weathering processes, such as erosion and dissolution of rocks and minerals. It also acts as a carrier for contaminants, pollutants, and nutrients, influencing their transport through the environment.
Energy Balance: Water has a high heat capacity, which means it can absorb and store large amounts of heat energy. This property helps regulate the Earth's temperature and climate by transporting heat through evaporation, condensation, and precipitation.
Greenhouse Gas: Water vapor is a major greenhouse gas that contributes to the Earth's natural greenhouse effect. It absorbs and re-emits thermal radiation, trapping heat in the atmosphere. Approximately 80% of the atmospheric greenhouse effect is attributed to water vapor.
Life: Water is vital for supporting life on Earth. It provides a habitat for numerous organisms and serves as a medium for various biological processes. Terrestrial life forms, including plants, animals, and humans, rely on water availability for their survival, growth, and reproduction.
It is important to note that while water is critical for most terrestrial life forms, human beings have developed technologies and systems that allow them to inhabit regions with limited water availability. However, water still remains a fundamental resource for human societies, and the hydrologic cycle plays a crucial role in ensuring its availability and sustainability.
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Question 3. Solve each equation given
below.
5 x - 4=31
Answers
Answer:
x = 7
Step-by-step explanation:
5x-4 = 31
5x = 31+4
5x = 35
x = 7
Please help me with these two :/
Answers
1 2 1 2 1 3 3 2 4 4 5 5 Pedigree 4 1. What is the most likely mode of inheritance? 2. What is the probability that II-2 is a carrier? 3. What is the probability that II-4 is a carrier? 4. What is the probability that III-3 is a carrier? 5. If III-3 marries a phenotypically normal male, what is the probability that their child would be affected? 6. If III-1 marries a genotypically and phenotypically normal female, what is the probability that their child would be affected? 7. What would be examples of diseases exhibiting this mode of inheritance?
Answers
1. The disease is Autosomal Recessive.
2. The probability that II-2 is a carrier is 2/3.
3. The probability that II-4 is a carrier is 2/3.
4. The probability that III-3 is a carrier is 1/3.
5. The male is phenotypically normal (homozygous recessive).
6. This is because III-1 is phenotypically normal (homozygous recessive) and does not carry the disease allele.
7. The diseases exhibiting this mode of inheritance include sickle cell anemia, cystic fibrosis, and Tay-Sachs disease.
The following is the solution to the given problem which includes the terms "inheritance" and "probability":
1. The most likely mode of inheritance for Pedigree 4 is Autosomal Recessive. In the given Pedigree, only the individuals II-3 and II-5 were affected while the individuals II-2 and II-4 were carriers, which suggests that the disease is Autosomal Recessive.
2. The probability that II-2 is a carrier is 2/3.Since II-2 has two heterozygous parents (II-4 and II-5) who are carriers, the probability that II-2 is a carrier is 2/3.
3. The probability that II-4 is a carrier is 2/3.
Since II-4 has two heterozygous parents (II-6 and II-7) who are carriers, the probability that II-4 is a carrier is 2/3.
4. The probability that III-3 is a carrier is 1/3.Since III-3 has one carrier parent (II-2) and one normal parent (II-1), the probability that III-3 is a carrier is 1/3.
5. The probability that III-3's child will be affected is 1/4.If III-3 marries a phenotypically normal male, the probability that their child would be affected is 1/4. This is because III-3 is a carrier (heterozygous) and the male is phenotypically normal (homozygous recessive).
6. The probability that III-1's child will be affected is 0.If III-1 marries a genotypically and phenotypically normal female, the probability that their child would be affected is 0. This is because III-1 is phenotypically normal (homozygous recessive) and does not carry the disease allele.
7. Examples of diseases exhibiting this mode of inheritance include sickle cell anemia, cystic fibrosis, and Tay-Sachs disease.
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Suppose you are solving the following equation: 2^(3x)=((1)/(16))^(x+1) You can solve this equation by re-writing both sides with the same base. If you re-write both sides with base 2 , what is the expression you get in the exponent on the right hand side? 2^(3x)=2^(?)
Answers
When re-writing both sides of the equation with base 2, the expression in the exponent on the right-hand side becomes -4.
This process involve normal simplification.
We can rewrite both sides of the equation as follows:
2^(3x) = ((1/16)^(x+1))
To make the bases of the exponents on both sides the same, we need to express 1/16 as a power of 2.
We know that 1/16 can be written as 2^(-4) because 2^(-4) is equal to 1/(2^4) which simplifies to 1/16.
Therefore, the expression in the exponent on the right-hand side when re-writing both sides of the equation with base 2 is -4..
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A data set contains three unique values. Which of the following must be true?
mean = median
median = midrange
median = midrange
none of these
Answers
If a data set contains three unique values, none of the given statements must be true.
The mean is the average of a data set, calculated by summing all values and dividing by the number of values. In a data set with three unique values, the mean will not necessarily be equal to the median, which is the middle value when the data set is arranged in ascending or descending order.
The median is the middle value in a data set when arranged in order. With three unique values, the median will not necessarily be equal to the midrange, which is the average of the minimum and maximum values in the data set.
Therefore, none of the statements "mean = median," "median = midrange," or "median = midrange" must hold true for a data set with three unique values.
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Use the diagram to estimate the area under the curve between ï = 0 and x = 3 Y 15+ 14- 13 12- 11- 10- 9. 8- 7- 6- 6543 N 5- 4- 3. 2- 1 2
Answers
Answer:
16
Step-by-step explanation:
The area under the curve can be estimated by adding the areas of 1 triangle and 2 trapezoids using the dashed lines in the graph and the x-axis.
Triangle:
base = 1
height = 2
Trapezoid 1:
base1 = 1
base2 = 7
height = 1
Trapezoid 2:
base1 = 7
base2 = 15
height = 1
total area = (1)(2)/2 + (1 + 7)(1)/2 + (7 + 15)(1)/2
total area = 16
giving brainliest!!!! please help!!
Answers
Answer:
{4, 5 }
Step-by-step explanation:
Solve the inequality
n + 1 > 4 ( subtract 1 from both sides )
n > 3
The set of values that make the inequality true is { 4, 5 }
if A car starts from rest and attains a velocity of 20 metre square into 2second calculate the acceleration produced by the car
Answers
Answer:
10ms/2
Step-by-step explanation:
The equation for acceleration
= Final Velocity - Starting Velocity /Time
= 20 (Final Velocity) - 0 (starting velocity) /2
= 10 ms/2
help me again pls!!!
Answers
Answer:
19/0.8 23,75 or 23 3/4
and go to elementary school
Answer:
23.75
Step-by-step explanation:
You need to isolate for x. To do that divide both sides by 0.8 to leave only x on the left side and 19/0.8 on the right side. Then simplify the right side to get 23.75
Solve for x using the
distributive property.
9(5 - x) = 81
x = [?]
Answers
Answer:
\(\boxed {x = -4}\)
Step-by-step explanation:
Solve for the value of \(x\):
\(9(5 - x) = 81\)
-Use Distributive Property:
\(9(5 - x) = 81\)
\(45 - 9x = 81\)
-Subtract \(45\) to both sides:
\(45 - 45 - 9x = 81 - 45\)
\(-9x = 36\)
-Divide both sides by:
\(\frac{-9x}{-9} = \frac{36}{-9}\)
\(\boxed {x = -4}\)
So, the value of \(x\) is \(-4\).
Look at the simultaneous equations below.
x - 6y = 10
3y² = 4x + 7
a) Show that 3y²– 24y – 47 = 0
b) Use part a) to solve the simultaneous equations.
If any of your answers are decimals, give them to 1 d.p.
Please help I will give Brainly
Answers
A) Hence, proven that 3y²– 24y – 47 = 0
B) After solving the simultaneous equations y1 = −1.627314 or −1.6 and y2 = 9.627314 or 9.6.
What is simultaneous equations?Equations that are simultaneously solved and have two or more common variables are known as simultaneous equations (that is, simultaneously). Since the unknown variables in both equations, x and y, are the same, they can be solved simultaneously to find the values of the variables.
As an illustration, equations x + y = 5 and x - y = 6 are examples of simultaneous equations. Simultaneous equations can be resolved in a variety of ways, including graphically, by substitution, and by elimination.
a) Given that
x - 6y = 10
Lets solve for x
x = 10 + 6y
And 3y² = 4x + 7
Lets solve for x
x = (3y² - 7)/4
As x is equal lets cross multiply and we get
10 + 6y = (3y² - 7)/4
40 + 24y = 3y² - 7
47 + 24y = 3y²
0 = 3y² - 24y - 47
3y²– 24y – 47 = 0
B) To solve the simultaneous equations
Lets convert them to standard format
x - 6y = 10 already in standard format
3y² = 4x + 7
4x - 3y² = -7 in standard format
Now solve
⇒ x - 6y = 10 (x4)
4x - 3y² = -7 (x1)
⇒ 4x - 24y = 40
- 4x - 3y² = -7
0 + 3y²– 24y = 47
⇒ 3y²– 24y = 47
⇒ Putting the value in quadratic formula
⇒ y1 = −1.627314 or −1.6
⇒ y2 = 9.627314 or 9.6
A) Hence, proven that 3y²– 24y – 47 = 0
B) After solving the simultaneous equations y1 = −1.627314 or −1.6 and y2 = 9.627314 or 9.6.
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determine if parallel, perpendicular, or neither
y=-3x+6 and y=1/3x-8
Answers
Answer:
Perpendicular!!!
Step-by-step explanation:
-3 and 1/3 are negative recopricals. This means they are perpendicular.
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Answer:
perpendicular
Step-by-step explanation:
for an equation to be parallel, the equations would have to have the same slope. for and equation to be perpendicular, the slopes have to be reciprocal, like 5/1 and 1/5, or 2/15 and 15/2. Also, one slope has to be negative. These equations match the definition of perpendicular lines.
the average age in a sample of 190 students at city college is 20. as a result of this sample, it can be concluded that the average age of all the students at city college must be more than 20, since the population is always larger than the sample. could not be 20. is around 20. must be less than 20, since the sample is only a part of the population.
Answers
Based on the given information, the average age in a sample of 190 students at City College is 20.
It can be concluded that the average age of all the students at City College must be around 20, since the sample is a representation of the population. However, it cannot be concluded that the average age is more than 20 or less than 20, as the information does not provide any evidence to support these claims.
In statistical analysis, the sample is used to estimate the characteristics of the population, but it does not guarantee that the population average is higher or lower than the sample average. Therefore, the average age could be 20 or approximately 20 for all the students at City College.
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Some of the dimensions of a square pyramid are shown in the diagram. The height of the square pyramid is 5.1 meters.
What is the volume of the square pyramid in cubic meters?
60 m3
40 m3
360 m3
120 m3
Answers
Answer:
27.2 m³
Step-by-step explanation:
Given:
Base edge = 4 mHeight = 5.1 metersFormula:
\((\text{Base edge})^{2} \times \dfrac{\text{Height}}{3}\)
Replace the base edge and the height in the formula:
\(\implies (\text{4})^{2} \times \dfrac{\text{5.1}}{3}\)
Evaluate the volume of the prism:
\(\implies (\text{4})(4) \times 1.7\)
\(\implies 16 \times 1.7\)
\(\implies 27.2 \ \text{m}^{3}\)
Answer:
27.2 cm³
Step-by-step explanation:
Volume of a square pyramid
\(\sf V=\dfrac13a^2h\)
where:
a is the base edgeh is the heightGiven:
a = 4 mh = 5.1 m\(\sf \implies Volume=\dfrac13\cdot 4^2\cdot5.1=27.2\;cm^3\)
Mia crosses a river when she drives from her house to the beach. The graph of the function d(t) = 40|t − 1.25| shows Mia’s distance from the river d, in miles, after t hours.
The domain of the function is 0 ≤ x ≤ 2.5. The graph shows her entire trip
Answers
Mia’s distance from the river is decreasing in the interval 0 < t < 2.5 and
Mia drives 100 miles to the beach.
How to determine the decreasing interval?The complete question is added at the end of this solution as an attachment
From the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we can see that the values of the graph decrease from t = 0 to t = 2.5
When represented as an interval, we have
0 < t < 2.5
Hence, the decreasing interval is 0 < t < 2.5
How to determine the total distance travelledFrom the graph, we can see that the distance travelled in each half is 50 miles
So, the total distance is
total =50 + 50
Evaluate
total = 100
Hence, the total distance travelled is 100 miles
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Complete question
Mia crosses a river when she drives from her house to the beach. The graph of the function d(t) = 40|t − 1.25| shows Mia’s distance from the river d, in miles, after t hours.
The domain of the function is 0 ≤ x ≤ 2.5. The graph shows her entire trip
Complete each sentence to make a true statement.
Mia’s distance from the river is decreasing in the interval Choose... 0 < t < 1.25 or 1.25 < t < 2.5 .
Mia drives Choose... 40 or 80 or 60 or 100 miles to the beach.
A train travels with a constant speed of 108 km/h. How long will it take to travel a distance of 270 kilometers? PLEASE HELLLLLLPPPP THERE BRAINLIEST
Answers
Answer:
The answer is 2.5 hours. That's how long it would take the train to travel 270 kilometers.
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Solve the system of equations:
y= 2x - 2
y= x2 - x-6
O A. (-1,-5) and (4,2)
O B. (0, -2) and (2, 2)
O C. (-1,-4) and (4, 6)
D. (-2,0) and (3,0)
Answers
Answer:
C) (-1, -4) and (4, 6)
Step-by-step explanation:
\(\textsf{Equation 1}:y=2x-2\)
\(\textsf{Equation 2}:y=x^2-x-6\)
Substitute Equation 1 into Equation 2 and solve for x:
\(\implies 2x-2=x^2-x-6\)
\(\implies x^2-3x-4=0\)
Find two numbers that multiply to -4 and sum to -3: -4 and 1
Rewrite the middle term as the sum of these two numbers:
\(\implies x^2-4x+x-4=0\)
Factorize the first two terms and the last two terms separately:
\(\implies x(x-4)+1(x-4)=0\)
Factor out the common term \((x-4)\):
\(\implies (x+1)(x-4)=0\)
\(\implies (x+1)=0 \implies x=-1\)
\(\implies (x-4)=0 \implies x=4\)
Substitute the found values of x into Equation 1 and solve for y:
\(x=-1 \implies y=2(-1)-2=-4\)
\(x=4 \implies y=2(4)-2=6\)
Therefore, the solution to the system of equations is:
(-1, -4) and (4, 6)