A rational function does not have any factors in the denominator that can be equal to 0, then it will not have a vertical asymptote.
An even degree must be an even function is true. This is because a polynomial with an even degree has an even-numbered power, such as f(x)=x^2. This means that the function is symmetrical when its graph is reflected over the y-axis. This means that the graph will look the same if the x-values are reflected over the y-axis. For example, if f(3)=9, then f(-3)=9 as well.
Every polynomial of odd degree has at least one zero is true. This is because a polynomial with an odd degree will always have at least one x-value for which the equation is equal to 0. This is because the highest power of the equation must be odd, and the equation must cross the x-axis at least once. For example, f(x)=x^3 will have at least one x-value, such as x=0, where f(x)=0.
Every rational function that is not a polynomial has a vertical asymptote is false. A rational function that is not a polynomial may have a vertical asymptote, but it is not guaranteed. A vertical asymptote is created when the denominator of a rational equation has a factor that is equal to 0. This means that when this factor is equal to 0, the equation has an undefined value. If a rational function does not have any factors in the denominator that can be equal to 0, then it will not have a vertical asymptote.
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You measure narrow-sense heritability for three traits and find that it is 0.1 for trait A, 0.5 for trait B, and 0.8 for trait C. Which of the following can you conclude from your data?A. A parent-offspring regression for trait C will have the highest slope.B. Selection of trait A will have no effect on the population mean for this trait.C. A parent-offspring regression for trait B will be a flat line.D. Selection on each behavior will result in similar changes in the population mean for each trait.E. A parent-offspring regression on trait A will have a slope of 0.9.
You can deduce from your facts that assertion A is correct. Statement B is not conclusive. Statement C is incorrect. Statement D is not conclusive. statement E is false.
What is probability?The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms.
Here,
From your data, you can conclude that:
A. A parent-offspring regression for trait C will have the highest slope.
Heritability is the proportion of variation in a trait that can be explained by genetic variation. A higher heritability indicates that more of the variation in a trait is due to genetic differences, and less is due to environmental differences. If the heritability of a trait is 0.8, this means that 80% of the variation in the trait is due to genetic differences, and a parent-offspring regression would have a steeper slope than if the heritability was lower.
B. Selection of trait A will have no effect on the population mean for this trait.
This statement cannot be concluded from the data. Heritability of a trait does not dictate the responsiveness of a trait to selection. Even if the heritability of a trait is low, it can still respond to selection, and even if the heritability of a trait is high, it may not respond much to selection, depending on the presence of other factors such as the distribution of the trait in the population, the presence of linkage disequilibrium, and the presence of genetic constraints.
C. A parent-offspring regression for trait B will be a flat line.
This statement is false. If the heritability of a trait is 0.5, this means that half of the variation in the trait is due to genetic differences, and half is due to environmental differences. A parent-offspring regression would not be a flat line, but would still have a slope, albeit not as steep as if the heritability was higher.
D. Selection on each behavior will result in similar changes in the population mean for each trait.
This statement cannot be concluded from the data. Heritability is only one of many factors that affects the responsiveness of a trait to selection, and the responsiveness of each trait will depend on other factors as well.
E. A parent-offspring regression on trait A will have a slope of 0.9.
This statement is false. Heritability is the proportion of variation in a trait that can be explained by genetic differences, not the slope of a regression. The slope of a parent-offspring regression would depend on other factors such as the distribution of the trait in the population and the presence of environmental factors.
From your data, you can conclude that: statement A is true. statement B cannot be concluded. statement C is false. statement D cannot be concluded. statement E is false.
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How do I Solve for x
Answer: x = -22/7
Step-by-step explanation: Basically, all angles are the same as indicated in the image, this means that the triangle is equilateral and that all sidelengths will be the same lengths
we can now set up an equation that equals both side lengths to find x
4x+16 = -3x -6
4x+16-16= -3x -6 -16
4x = -3x - 22
4x +3x= -3x + 3x -22
7x/7 = -22/7
x = -22/7
1. Edgar measures the temperature of a solution at the beginning of an experiment to be . He monitors the temperature of the solution every minute for 10 minutes. He records the change in temperature from his previous reading. His data show a decrease of four times, a decrease of three times, no temperature change two times, and an increase of once.
A: The expression to represent the average change in temperature is -11/10 °F per minute.
B: The average change in temperature is -1.1 °F per minute,
C: For the second attempt average change is -0.1 per minute.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:
Expression: (Math Operator, Number/Variable, Math Operator)
Given temp. at beginning = 23°F
He monitors the temperature of the solution every minute for 10 minutes, and
He records the change in temperature from his previous reading. His data show a decrease of 2 degrees Fahrenheit four times, a decrease of 3 degrees Fahrenheit three times, no temperature change two times, and an increase of 6 degrees Fahrenheit
A) The expression to represent the average change in temperature each minute is given as follows:
The observations are given as follows:
-2, -2, -2, -2, -3, -3, -3, 0, 0, 6.
Mean = (4 x (-2) + 3 x (-3) + 0(2) + 6)/10.
Mean = -11/10
B) The average change in temperature for the first trial is given as follows:
The observations are given as follows:
-2, -2, -2, -2, -3, -3, -3, 0, 0, 6.
The average change = -11/10
The average change = -1.1ºF per minute.
C) In the second attempt of the experiment, the average change in temperature per minute,
A data set's mean is computed as the total number of observations divided by the total number of observations in the data set.
There are 10 observations in total in this problem.
The observations are given as follows:
-2, -2, -2, -2, -3, -3, -3, 0, 0, 6.
Hence, the mean is calculated as follows:
Mean = (4 x (-2) + 3 x (-3) + 6)/10
Mean = -1.1ºF per minute
1ºF greater than this for the second trial is given as follows:
-1.1 + 1 = -0.1 ºF per minute.
Hence the average change in temperature is -1.1 °F per minute,
C: For the second attempt average change is -0.1 per minute.
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The question is incomplete. The complete question is 'Edgar measures the temperature of a solution at the beginning of an experiment to be 23 degrees Fahrenheit . He monitors the temperature of the solution every minute for 10 minutes. He records the change in temperature from his previous reading. His data show a decrease of 2 degrees Fahrenheit four times, a decrease of 3 degrees Fahrenheit three times, no temperature change two times, and an increase of 6 degrees Fahrenheit once. (a) Write an expression to represent the average change in temperature each minute. (b) Using your expression from Part (a), determine the average change in temperature for the first trial(c) Edgar repeats the experiment and finds the average change in temperature each minute is 1 degrees Fahrenheit greater in the second trial than in the first trial. What is the average change in temperature each minute in the second trial of the experiment?'
NEED HELP!!
You want to put a 6-inch thick layer of topsoil for a new 35 feet by 14 feet garden. The dirt store only sells topsoil by the cubic yard. How many cubic yards of topsoil will you need to order to fill this garden?
Answer:
Therefore, you will need to order approximately 9.07 cubic yards of topsoil to fill the garden to a depth of 6 inches.
Step-by-step explanation:
To calculate the amount of topsoil needed, we need to find the volume of the garden in cubic yards, since topsoil is sold by the cubic yard.
The garden is 35 feet by 14 feet and 6 inches (or 0.5 feet) deep.
Volume of the garden = length x width x depth
= 35 feet x 14 feet x 0.5 feet
= 245 cubic feet
To convert cubic feet to cubic yards, we divide by 27 (since 1 cubic yard = 27 cubic feet):
Volume in cubic yards = 245 cubic feet / 27
= 9.07 cubic yards (rounded to two decimal places)
Therefore, you will need to order approximately 9.07 cubic yards of topsoil to fill the garden to a depth of 6 inches.
enrollment in a french class at a high school is 0.72 of enrollment in a spanish class. what is enrollment compared to spanish class as a fraction and as a percent?
Answer:
Step-by-step explanation:
Let's say the enrollment in the Spanish class is x.
According to the information given, the enrollment in the French class is 0.72 of the enrollment in the Spanish class, which means the enrollment in the French class is 0.72x.
The enrollment compared to Spanish class as a fraction is 0.72x / x = 0.72.
The enrollment compared to Spanish class as a percent is 0.72 x 100% = 72%.
The solution is, The enrollment compared to Spanish class as a percent is
72%.
Here, we have,
Let's say the enrollment in the Spanish class is x.
According to the information given, the enrollment in the French class is 0.72 of the enrollment in the Spanish class, which means the enrollment in the French class is 0.72x.
The enrollment compared to Spanish class as a fraction is,
0.72x / x = 0.72.
The enrollment compared to Spanish class as a percent is,
0.72 x 100% = 72%.
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A room addition requires 320 sq ft of wood floor Hardwood costs $5.59 per sq ft, while laminate costs $2.89 per sq ft. What is the total difference in cost between the
two types of flooring?
The difference in cost is $
(Round to the nearest dollar as needed.)
On solving the provided question, we can say that by bodmas, Hardwood cost = 5.59*320 = $1788.8 ; laminate cost = 2.89*320 = $924.8 and difference = 1788.8-924.8 = $864
what is bodmas?The abbreviation BODMAS aids kids in recalling the hierarchy of mathematical operations (the correct order for solving math problems). The acronym BODMAS is made up of the following terms: B Bracket, O Degree (Power/Exponent or Root), D Division, M Multiplication, A Addition, and S Subtraction. BODMAS is also referred to as PEDMAS in some locales. This symbolizes exponents, division, multiplication, addition, and subtraction. It also represents parentheses. The BODMAS rule states that parentheses must be handled first, followed by powers or roots (i.e., of), divisions, multiplications, additions, and lastly subtractions. While he is known as BODMAS in India and the UK, PEMDAS is primarily utilized in the US. However, they are identical to one another. The parentheses, order, and order of the operations of addition, subtraction, multiplication, and division are the same for the two rules.
A room addition requires 320 sq ft
Hardwood costs $5.59 per sq ft.
laminate costs $2.89 per sq ft.
Hardwood cost = 5.59*320 = $1788.8
laminate cost = 2.89*320 = $924.8
difference = 1788.8-924.8 = $864
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$580 is invested for two years at a rate of 9% per year, compounding annually. complete the table below to determine the final value of the investment, roudning your answers to the nearest cent.
Answer:
Year | Rate | Interest (9%) | Principal Invested | Final Value
1 | 9% | 52.20 | 580.00 | 632.20
2 | 9% | 56.94 | 580.00 | 688.14
Mhlaba is planning on doing a baking course.she,therefore,decided to buy a food processor while browsing the internet,she came across the following special promotions
Based on the information, it can be inferred that Mhlaba food processor on offer is the right choice for Mhlaba due to its quality product.
Which food processor should Mhlaba buy?According to the information, Mhlaba should buy a home food processor because he only needs to make small portions for himself and his family.
Therefore, there is no need for Mhlaba to look for another more professional food processor since he will not work as a cook nor will he require a large-capacity machine. Then he should choose the one on offer.
Note: This question is incomplete. Here is the complete information:
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pls help overdue!!
DIG DEEPER Two boats travel at the same speed to different destinations. Boat A reaches its destination in 12
minutes. Boat B reaches its destination in 18 minutes. Boat B travels 3 miles farther than Boat A. How fast do the
boats travel?
The boats travel
Justify your answer.
mile(s) per minute.
Answer:
0.5
Step-by-step explanation:
6 mins & travelled 3 miles farther
so miles/min = 3/6 = 0.5 mile(s) per minute.
If you increase the price of a product by 105%, you have to multiply the original price by the factor
Answer: Sorry ching cong ling long aoa
Step-by-step explanation:
Jack Fitzgerald wishes to purchase a used car that has a cash price of $11,000. The installment terms include a down payment of $2,000 and 48 monthly payments of $219.
a) What finance charge will Jack pay?
b) What is the APR to the nearest half percent?
The finance charge is $______?
The APR is_____%?
finance charge Jack will pay is $1,512.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, Jack Fitzgerald wishes to purchase a used car that has a cash price of $11,000. The installment terms include a down payment of $2,000 and 48 monthly payments of $219.
a)
The amount that needs to be financed is = 11,000 - 2,000 = $9,000.
Amount repayment = 219 x 48 = $8,100.
=> Finance charge = Amount repayment - Amount needs to be financed
Finance charge = 10512 - 9000
Finance charge = 1,512$
b)
We apply the PV for annuity formula to find the interest rate per one month denoted as i:
Amount needs to be finance = (equal monthly installment x i) / [ 1 - (1+i)^-36 ]
or 9,000 = (219/i) x [1 - (1+i)^-48 ] <=> i = 0.911%.
APR = 12 x i
APR = 10.932% .
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50PTS. NEED HELP ASAP WILL MARK IF CORRECT!!!!!
Answer:
Step-by-step explanation:
PART A: No, the trinomial 4x^3 + 28x + 49 is not a perfect square trinomial. To be a perfect square trinomial, the first and last terms must be perfect squares and the middle term must be twice the product of the square roots of the first and last terms. In this case, the first and last terms are not perfect squares, and the middle term is not twice the product of the square roots of the first and last terms.
PART B: To factor the expression 6x^2 + 5x - 4, we need to find two binomials whose product is equal to this expression.
First, we can break down the coefficient of x into two numbers whose product is 6 * (-4) = -24 and whose sum is 5. These numbers are 8 and -3.
Next, we use these two numbers to split the middle term 5x into two terms:
6x^2 + 8x - 3x - 4
We can now factor the expression by grouping:
(6x^2 + 8x) - (3x + 4)
2x(3x + 4) - 1(3x + 4)
(2x - 1)(3x + 4)
Therefore, the area of the rectangle can be factored as (2x - 1)(3x + 4).
To determine the dimensions of the rectangle, we set each factor equal to one of the dimensions and solve for the other dimension:
2x - 1 = length
3x + 4 = width
Alternatively, we could switch the factors and get the same answer:
2x - 1 = width
3x + 4 = length
Either way, these are the dimensions of the rectangle, expressed in terms of x.
which of the following statements about alpha is true? a. rows of alpha are numbered 0...24 and columns are numbered 0...9 b. rows of alpha are numbered 0...24 and columns are numbered 1...10 c. rows of alpha are numbered 1...24 and columns are numbered 0...9 d. rows of alpha are numbered 1...25 and columns are numbered 1...10
Rows of alpha are numbered 0...24 and columns are numbered 0...9 is the true statement about alpha.
What is alpha?
The first letter of the Greek alphabet is known as alpha. Alpha is typically used to signify an unidentified angle. Gamma, alpha, and beta are utilized as variables just as x, y, and z in mathematics. Mainly in quadratic problems, it is employed.
Since symbols are only meant for communication, you can create whatever you choose with them. It may take the form of a real number, vector, tensor, or index.
The rows of the alpha have to start from 0 so, the true statement lies in option a and option b.
Also, the columns are to be numbered till 9. So, the true statement lies in option a.
Hence, the true statement is that rows of alpha are numbered 0...24 and columns are numbered 0...9.
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Im so confused could someone help me here:(
For the function y=f(x), the domain is (-2,2] and the range is (-2,3).
The corresponding values are -
f(-1) = -6, f(0) = -5, f(1) = 6, f(2) = 3.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The graph for function y = f(x) is given.
The collection of input or argument values for which a function is actual and defined is known as its domain.
In the graph it can be seen that the graph is intersecting x-axis at x = -2 and at x = 2.
So, the domain is (-2,2]. The ( symbol denotes empty circle whereas the ] symbol denotes a filled circle.
A function's range is the collection of values for which the dependent variable is defined.
The coordinates for the ending of the graph is (2,3). So, the range of the function is [-2,3].
The value for f(-1) as seen in the graph is -
x = -1, then y = -6.
The value for f(0) as seen in the graph is -
x = 0, then y = -5.
The value for f(0) as seen in the graph is -
x = 1, then y = 6.
The value for f(2) as seen in the graph is -
x = 2, then y = 3.
Therefore, the domain and range is (-2,2] and (-2,3) respectively.
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Let theta equals negative 11 times pi over 4 period
Part A: What is a coterminal angle of θ such that 0 ≤ θ ≤ 2π? (5 points)
Part B: What are the exact values of all six trigonometric functions evaluated at θ? (10 points)
A coterminal angle of θ such that 0 ≤ θ ≤ 2π is 3π/4
How to find the coterminal angleA. A coterminal angle of θ such that 0 ≤ theta ≤ 2π is
= theta + 2π
= -11π/4 + 2π
= 3π/4.
B. The exact values of the six trigonometric functions evaluated at θ are as follows:
sin(θ) = sin(-11π/4) = -√2/2
cosec (θ) = cosec (-11π/4) = -2/√2
cos(θ) = cos(-11π/4) = -√2/2
sec (θ) = sec (-11π/4) = -√2/2
tan(θ) = tan(-11π) = 1
cotan (θ) = cotan (-11π) = 1
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To solve x-25 = 2, add
to each side.
The solution to the equation x - 25 = 2 is x = 27.
What is the equation?
An equation is a mathematical statement that asserts the equality of two expressions. In other words, it is a statement that states that two values are equal.
To solve the equation x - 25 = 2, we first add 25 to each side of the equation:
x - 25 + 25 = 2 + 25
Simplifying the right side of the equation, we get:
x = 27
Hence, The solution to the equation x - 25 = 2 is x = 27.
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Another pond has an algae bloom that is also decreasing exponentially. The area of this
bloom in square meters is given by the function B(d) = 100 27, where d is days since
the first measurement of the bloom. Which of the two algae blooms was larger initially?
Which is decreasing more quickly? Explain how you know.
1. The algae blooms was larger initially is the first algae.
2. The first algae bloom is decreasing more quickly than the second algae bloom.
Math problems errors1. To determine which algae bloom was larger initially, we can compare the values of the functions at d=0.
For the first algae bloom, we have A(0) = 200.
For the second algae bloom, we have B(0) = 100*27⁰ = 100.
Therefore, the first algae bloom was larger initially.
2. To determine which algae bloom is decreasing more quickly, we can compare the rates of decrease of the two functions. The rate of decrease is given by the derivative of the function, which tells us how fast the area is changing with respect to time.
For the first algae bloom, we have A'(t) = -20e^(-0.2t).
For the second algae bloom, we have B'(d) = -100*27^(-1)d.
To compare these rates of decrease, we can evaluate them at the same point in time or days. Let's evaluate them at d=1, which means one day has passed since the first measurement.
For the first algae bloom, we have A'(1) = -20e^(-0.2) ≈ -15.24.
For the second algae bloom, we have B'(1) = -100*27^(-1) ≈ -3.70.
Therefore, we can see that the first algae bloom is decreasing more quickly than the second algae bloom. This is because the rate of decrease of the first bloom is more negative than the rate of decrease of the second bloom.
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The tables show functions representing the growth of
two types of bacteria on certain days within an
experiment that lasted a total of 10 days.
Bacteria A
Time (days)
Bacteria Count
Bacteria B
Time (days)
Bacteria Count
Mark this and return
0
60
2 4
240
960
0
1
3
90 180 720
6
3,840
5
2,880
How do the functions in the table compare?
Since x-intercepts indicate the amount of each
bacteria at the start of the experiment, there was
more of bacteria B than bacteria A at the start.
Since y-intercepts indicate the amount of each
bacteria at the start of the experiment, there was
more of bacteria B than bacteria A at the start.
Since the maximum value in the table for bacteria A
is greater than the maximum value in the table for
bacteria B, bacteria A has a faster growth rate than
bacteria B.
Since the minimum value in the table for bacteria A
is less than the minimum value in the table for
bacteria B, bacteria A has a slower growth rate than
bacteria B.
Save and Exit
Next
Submit
The correct statement regarding the exponential functions is given as follows:
Since y-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.
How to model the situation?An exponential function is defined as follows:
y = ab^(x/n).
In which the parameters are defined as follows:
a is the initial value.b is the rate of change.n is the time needed for the rate of change.For Bacteria A, we have that:
The initial amount is of 60. (y-intercept).The amount doubles every 2 days.For Bacteria B, we have that:
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The triangle shown below has an area
of 75 units²
what is the area of the triangle?
The triangle has an area of 75 units² then the area of triangle be 15 units.
What is meant by area of the triangle?The space bounded by a triangle's three sides is known as the area of a triangle. The total area that is bounded by a triangle's three sides is referred to as the triangle's area.
Area of triangle = 1/2 (b h), where b is the base and h is the height, is the fundamental formula for calculating a triangle's area. The type of the triangle and the known dimensions can affect other formulas that are used to calculate the area of a triangle.
Let x be base of triangle
height = 19 units
Area of triangle = 1/2 base × height
substitute the values in the above equation, we get
75 = 1/2 × x × 10
simplifying the equation, we get
75 = x × 5
x = 75/5
x = 15 units
Therefore, the area of triangle be 15 units.
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An environmentalist wants to find out the fraction of oil tankers that have spills each month. Step 1 of 2 : Suppose a sample of 563 tankers is drawn. Of these ships, 445 did not have spills. Using the data, estimate the proportion of oil tankers that had spills. Enter your answer as a fraction or a decimal number rounded to three decimal places.
The proportion of oil tankers that had spills is:
1 - (445/563) = 0.208
Rounded to three decimal places, the answer is 0.208. Alternatively, this can be expressed as the fraction 52/253.
assume total units produced equals total units sold. if the company prepares a gross margin income statement and a contribution margin income statement,
Correct answer to the question is: operating profit will be the same on both statements; marketing and administrative costs will be the same on both statements.
A gross margin income statement focuses on the difference between the cost of goods sold (COGS) and the selling price of the products. It shows the gross profit as a percentage of sales, which can be used to evaluate the company's ability to generate revenue and cover its costs.
Both the gross margin and the contribution margin income statements provide important information to the company, but they offer different perspectives on the company's profitability. The gross margin income statement is useful for evaluating the overall efficiency of the company's sales and production processes, while the contribution margin income statement is useful for evaluating the potential profit from selling additional units.
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The complete question is :
Assume total units produced equals total units sold. If the company prepares a gross margin income statement and a contribution margin income statement, _____.
You construct a tangent to circle O at point X on the circle, as shown below. Suppose you choose point
X so that it is in a different position on the circle. Does the measure of ∠OXY change? Complete the
explanation.
The measure of <OXY is 90 degree.
What is Tangent?Tangents to circles are lines that cross the circle at a single point. Point of tangency refers to the location where a tangent and a circle converge. The circle's radius, where the tangent intersects it, is perpendicular to the tangent.
Given:
As, A line that crosses a circle at precisely one point, known as the point of tangency or tangency point, is said to be tangent to the circle.
The fact that the radius is perpendicular to the tangent line from the circle's center to the point of tangency is a significant outcome.
So, according to this tangent XY toucehes the circle at point X.
Thus, <OXY is perpendicular i.e., <OXY = 90
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Tony and Bobby each calculate the population of bacteria when t=5/2 hours.
Tony says that when t=5/2 hours, f(5/2) = (sqrt2)^5 bacteria.
Bobby says that f(5/2) = 4sqrt2 bacteria.
Who's correct?
Use definitions and rules to justify your reasoning. Then use the graph to estimate the value of f(5/2) as a decimal on a graph
None of them is correct and the value of f(5/2) is 1.6 to 1 decimal place
How to determine who is correctFrom the question, we have the following parameters that can be used in our computation:
f(x) = √x
Substitute 5/2 for x
So, we have
f(5/2) = √5/2
When the above is compared to their functions, we have no equivalent expression
This means that none of the notations is correct
Next. we have
f(5/2) = 1.6
Hence, the value is 1.6
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1. Write and solve a system of equations that represents the situation. Interpret the
solution. Harper is starting a new T-shirt printing business. She purchases plain T-shirts for $5 each and spends $150 for printing equipment. She decides to sell printed shirts
for $10 each. How many T-shirts does Harper need to sell so that the amount of
money she spends to start her business and the amount of money she earns are
the same?
The equation for Harper's situation is 10x = 150 + 5x. The number of t-shirts Harper needs to sell so that the amount of money she spends to start her business and the amount of money she earns are the same is 30 t-shirts.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The price of one plane t-shirt is = $5
The money spent on printing equipment is = $150
The price for printed t-shirt is = $10
Let the number of t-shirts to be sold be x.
The expression for earning money is 10x
The amount she spends on starting the business is -
150 + 5x
So, according to question the equation is -
10x = 150 + 5x
10x - 5x = 150
5x = 150
x = 150 / 5
x = 30
Therefore, 30 t-shirts needs to be sold.
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A block wall 100 feet long and 7 feet high will be constructed using blocks that are 1 foot high and either 2 feet long or 1 foot long (no blocks may be cut). The vertical joins in the blocks must be staggered as shown, and the wall must be even on the ends. What is the smallest number of blocks needed to build this wall?
The smallest number of blocks needed to build the wall is 350 blocks which are 1 foot high and either 2 feet long.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
Dimension of the wall.
Length = 100 feet
Height = 7 feet
Area = 100 x 7 = 700 ft²
Dimension of the larger block.
Length = 2 feet
Height = 1 feet
Area = 2 x 1 = 2 ft²
Dimension of the smaller block.
Length = 1 feet
Height = 1 feet
Area = 1 x 1 = 1 ft²
Now,
The number of smaller blocks needed to build the wall.
= 700
The number of larger blocks needed to build the wall.
= 700 / 2
= 350
Thus,
The smallest number of blocks needed is 350 blocks which are 1 foot high and either 2 feet long.
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a wheelbarrow can can carry up to 300 lbs of weight. a bag of soil weighs 20 lbs. write a multiplication inequality to show the number of bags (b) the wheelbarrow can carry
The multiplication inequality that shows the number of bags (b) the wheelbarrow can carry is 20b ≤ 300.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
The wheelbarrow can carry upto = 300 lbs
The bag of soil weighs = 20 lbs.
Now,
Number of bags of soil = b
We can write an inequality for the number of bags of soil the wheelbarrow can carry.
20b ≤ 300
Thus,
20b ≤ 300 is the multiplication inequality to show the number of bags (b) the wheelbarrow can carry.
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1700/49 + 1700/49 + 1700/49 + 1700/49 + 1700/49 + 33/5
Answer:
44117/245 or 180 17/245
Answer:
1700/49×5 + 33/5
173.45 + 6.6
180
I. f(x) = f (x) = StartFraction 1 minus x squared Over x minus 1 EndFraction
II. f(x) = f (x) = StartFraction x squared minus x cubed Over x squared minus 1 EndFraction
III. f(x) = g (x) = StartLayout Enlarged left-brace First row StartFraction x squared minus 5 x + 6 Over x minus 3 EndFraction, x not-equals 3 Second row 5, x = 3 EndLayout
IV. f(x) = f (x) = StartLayout First Row StartFraction x squared minus 3 x + 2 Over x minus 1 EndFraction, x not-equals 1 Second Row negative 1, x = 1 EndLayout
For which function does the Limit of f(x) as x approaches 1 not exist?
For the function, [tex]f(x) = \frac{1 - x^2}{x - 1}[/tex] the Limit of f(x) as x approaches 1 does not exist.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, [tex]f(x) = \frac{1 - x^2}{x - 1}[/tex], [tex]g(x) = \frac{x^2 - 5x + 6}{x - 3}[/tex].
We know, In a rational expression (p/q), q ≠ 0 as the expression would be undefined.
Therefore, The function for which the Limit of f(x) as x approaches 1 does not exist is [tex]f(x) = \frac{1 - x^2}{x - 1}[/tex], as at x = 1, f(x) is undefined.
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Could someone help me thank you
f⁻¹(x) = 4x + 7
This can be solved using the concept of function.
What is functions?Function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). A function is described as a relationship between a group of inputs and one output each. In simple terms, a function is a connection between inputs, with each input corresponding to exactly one output. Every function has its own domain and codomain, as well as a range. f(x), where x is the input, is a common way to refer to a function.
Given that,
f(x) = x -7/4
f⁻¹(x) = 4x + 7
Now, f (f⁻¹(x)) = f (4x + 7)
= [{(x - 7) / 4} ÷ 4] + 7
= x [Proved]
Next, f⁻¹(f(x))
= f⁻¹ (x -7/4)
= 4 × [(x -7/4)] + 7
= x [Proved]
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Thomas has $59 in his bank account and deposits $57 per month into his account. Christian has $15 and deposits $79 per month into his account.
Enter the number of months it will take for both Thomas and Christian to have the same amount of money in their accounts.
Let's start by setting up an equation to represent the situation:
59 + 57x = 15 + 79x
where x is the number of months it will take for both Thomas and Christian to have the same amount of money in their accounts.
Simplifying this equation, we get:
64x = 44
Dividing both sides by 64, we get:
x = 0.6875
So it will take approximately 0.6875 months for Thomas and Christian to have the same amount of money in their accounts. However, since time is measured in months, we cannot have a fraction of a month. Therefore, we round up the result to the nearest whole month and conclude that it will take 1 month for both Thomas and Christian to have the same amount of money in their accounts.