The volume of the largest right circular cone that can be inscribed in a sphere of radius 18 cm is approximately 11622.85 cubic centimeters.
To find the largest right circular cone that can be inscribed in a sphere of radius 18 cm, we need to find the cone with the largest possible volume that can fit inside the sphere.
Let's assume that the apex of the cone is at the center of the sphere. Since the cone is a right circular cone, the base of the cone will lie on the surface of the sphere, forming a circle with radius equal to the radius of the sphere, which is 18 cm.
Let's call the height of the cone "h" and the radius of the base of the cone "r". Then we can use the Pythagorean theorem to relate the height, radius, and slant height (which is equal to the radius of the sphere):
r^2 + h^2 = (18 cm)^2
The volume of a cone can be expressed as V = (1/3)πr^2h. We want to maximize this expression subject to the constraint above. We can use the constraint to eliminate one of the variables in the volume expression, then differentiate with respect to the remaining variable and set the derivative equal to zero to find the maximum.
From the constraint, we can solve for h^2:
h^2 = (18 cm)^2 - r^2
Substituting into the volume expression, we get:
V = (1/3)πr^2(18 cm - sqrt(r^2 + h^2))
Simplifying this expression, we get:
V = (1/3)πr^2(18 cm - sqrt((18 cm)^2 - r^2))
Differentiating with respect to r, we get:
dV/dr = (1/3)π(36 cm)r - (1/3)πr^3/sqrt((18 cm)^2 - r^2)
Setting this equal to zero and solving for r, we get:
r = (18 cm)/sqrt(2)
Substituting this value of r back into the expression for h, we get:
h = (18 cm)/sqrt(2)
Finally, substituting these values of r and h into the expression for the volume, we get:
V = (1/3)π((18 cm)/sqrt(2))^2((18 cm) - sqrt(((18 cm)/sqrt(2))^2 + ((18 cm)/sqrt(2))^2))
Simplifying this expression, we get:
V ≈ 11622.85 cubic centimeters
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Plot the points (-3, 8) and (5, -8) on the plane below. Determine the slope-intercept form of the equation of the line
through these points.
A graph of the points (-3, 8) and (5, -8) is shown on the plane below.
The slope-intercept form of the equation of the line through these points is y = -2x + 2.
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At data point (-3, 8), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:
y - 8 = (-8 - 8)/(5 + 3)(x + 3)
y - 8 = -16/8(x + 3)
y = -2(x + 3) + 8
y = -2x - 6 + 8
y = -2x + 2
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Examine the coordinate grid below. What are the coordinates of the point A’ when point A is reflected across the x-axis?
Answer:
The rule for reflection along the x axis (x;y) to (x; -y)
A' (x ; -(y) )
A' (4 ; -(5) )
A' (4 ; -5 )
A right triangle has a base, b
, that is 6
inches. The area of the triangle, with h
representing the height, is given by the expression
The height of the triangle is h = 2A/6.
What is height?Height is the measure of vertical distance, either how "tall" something or someone is, or how "high" the point is. For example, a person's height is typically measured using a stadiometer and is recorded in centimeters or feet and inches. The height of a mountain is usually measured in meters or feet. In aviation, height is measured from the surface of the earth, either above ground level (AGL) or above mean sea level (AMSL).
To find the height of a right triangle given the base, we can use the area formula A = 1/2bh. Rearranging this equation gives us the height: h = 2A/b. In this case, the base is 6 inches and the area is given as A. Therefore, the height of the triangle is h = 2A/6.
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procedures that help organize or describe data collected from a sample or a population are called . group of answer choices a. inferential statistics b. analytical variables c. dependent variables d. descriptive statistics
Procedures that help organize or describe data collected from a sample or a population are called Descriptive statistics.
Hence, option D is correct answer.
Descriptive statistics and examples: what are they?Data can be meaningfully and effectively described or summarised using descriptive statistics. For instance, knowing that everyone in our scenario wore blue shoes wouldn't be helpful. It would be helpful to know how evenly distributed their anxiety scores were. Measures of central tendency and measurements of variability make up descriptive statistics (spread).
The mean, median, and mode are measurements of central tendency, while the standard deviation, variance, minimum and maximum variables, kurtosis, and skewness are measures of variability.
Why do we utilise descriptive statistics?
In order to emphasise potential correlations between variables and to give basic information about the variables in a dataset, descriptive statistics can be helpful for both of these aims. The three most used descriptive statistics, which represent the following three variables: graphical/illustrative techniques.
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What is the frequency of the function f(x)? f(x)=14cos(2x)+5 express the answer in fraction form. Enter your answer in the box.
The frequency of the function f(x) is 1/π.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable. In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
We need to find the frequency of given function;
f(x)=1/4 cos(2x)+5
To finding the period and then use the general relation frequency
frequency = 1/period
In the given function f(x)=1/4 cos(2x)+5 here, only the constant 2 which will multiply with x effects the period.
As we know that 2π is the period of cosx then the period of cos(2x) is
2x=2π
x=π
So, the period of cos(2x) is π
Now the frequency is F=1/π
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jo needs to estimate the cost, icluding tax, of a pair of jeans originally priced at $30, they are on sale for 40% off.
which is the best plan for determining the sale price ?
Therefore , the solution of the given problem of percentage comes out to be $18 is the original price.
What is a percentage?In mathematics, a percentage is any value that can be represented as a fraction of 100. There are also sporadic uses of the abbreviations "pct.," "pct," or "pc." Nonetheless, it is typically denoted by the "%" symbol. The proportional amount is flat and lacks any dimensions. As percentages have a numerator of 100, they can be thought of as fractions. The percent symbol (%) must come after a number to denote that it is a percentage.
Here,
To determine the sale price of the jeans including tax, Jo should follow these steps:
Find the sale price of the jeans before tax:
Sale price = Original price - Discount
= $30 - 40%($30)
= $30 - $12
= $18
Find the tax amount by multiplying the sale price by the tax rate (which varies depending on the location):
Tax amount = Sale price x Tax rate
Add the sale price and the tax amount to get the total cost:
Total cost = Sale price + Tax amount
So the best plan for Jo to determine the sale price including tax would be to follow the above steps using the applicable tax rate in their location.
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Yesterday, a movie theater sold 289 bags of popcorn. A large bag of popcorn costs $4. A small bag of popcorn costs $1. In all, the movie theater made $544 from popcorn sales. Write and solve a system of equations to find how many bags of each side of popcorn were sold.
The movie theater sold __ large bags of popcorn.
The movie theater sold __ small bags of popcorn.
(MARKING BRAINLIEST FOR RIGHT ANSWER)
Answer:
The movie theater sold 85 large bags of popcorn and 204 small bags of popcorn.
Step-by-step explanation:
Let's use the following variables to represent the number of large and small bags of popcorn sold:
L: the number of large bags of popcorn sold
S: the number of small bags of popcorn sold
We can then write a system of equations based on the information given in the problem:
L + S = 289 (the total number of bags sold is 289)
4L + S = 544 (the total revenue from popcorn sales is $544)
To solve for L and S, we can use the method of substitution. Rearrange the first equation to solve for one variable in terms of the other:
L = 289 - S
Substitute this expression for L in the second equation and solve for S:
4(289 - S) + S = 544
1156 - 4S + S = 544
3S = 612
S = 204
Now that we know that 204 small bags of popcorn were sold, we can use the first equation to solve for L:
L + S = 289
L + 204 = 289
L = 85
Therefore, the movie theater sold 85 large bags of popcorn and 204 small bags of popcorn.
Find domain Range Y-intercept X- intercept Vertical asymptote Horizontal asymptote Pic attached below note write domain and range in interval notation Find domain Range Y-intercept X intercept Vertical asymptote Horizontal asymptote Pic attached below
The domain of the function is (-∞, -2) ∪(-2, ∞) and it's range is (-∞, 1) ∪ (1, ∞). The function has vertical and horizontal asymptotes as x = -2 and y = 1
What is the domain and range of a functionIn mathematics, the domain of a function is the set of all possible input values (also known as the independent variable) for which the function is defined. The range of a function is the set of all possible output values (also known as the dependent variable) that the function can produce.
To determine the domain and range of a function, it's important to consider the nature of the function, its graph or formula, and any restrictions that may apply.
The function f(x) = - (2/ x + 2) + 1
The domain of the function is (-∞, -2) ∪(-2, ∞)
The range of the function is (-∞, 1) ∪ (1, ∞)
The vertical asymptote is x = -2
The horizontal asymptotes y = 1
The y-intercept is (0, 0)
The x - intercept is (0, 0)
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A circular grassy plot of land of diameter 42 metre has a path wide 3.5 m running around it on outside find the cost of gravelling the path ₹ 4 per square metre
Answer:
₹ 2,001.20
Step-by-step explanation:
We can consider the grassy plot as a circle with radius = 42/2 = 21 m
The grassy plot and the path together form another circle with radius = 21 + 3.5 = 24.5 m
Area of a circle = πr² where r is the radius
Area of grassy plot = π x 21² = 441π m²
Area of outer circle (grassy plot + path) = π x (24.5)² = 600.25π m²
Area of the outer path alone = 600.25π - 441π = 159.25π = 500.30 sq meters
Cost of paving 1 square meter = ₹ 4
Cost of paving 500.3 sq m = 500.3 x 4 = ₹ 2,001.20
A researcher calculated sample proportions from two independent random samples. Assuming all conditions for inference are met, which of the following is the best method for the researcher to use to estimate the true difference between the population proportions?Construct a two-sample z-interval for the difference between population proportions.Answer A: Construct a two-sample z -interval for the difference between population proportions.AConstruct a two-sample z-interval for the difference between sample proportions.Answer B: Construct a two-sample z -interval for the difference between sample proportions.BPerform a z-test for the difference in sample proportions.Answer C: Perform a z -test for the difference in sample proportions.CSubtract the proportions and construct a one-sample z-interval for a single population proportion.Answer D: Subtract the proportions and construct a one-sample z -interval for a single population proportion.DSubtract the proportions and construct a z-interval for a single sample proportion.
Answer A: Construct a two-sample z-interval for the difference between population proportions.
What is fraction?
A fraction is a mathematical expression that represents a part of a whole or a ratio between two quantities. It is written as a/b, where a is called the numerator and b is called the denominator. The numerator represents the number of parts or units being considered, while the denominator represents the total number of parts or units in the whole.
According to given conditions:
The best method for the researcher to use to estimate the true difference between the population proportions would be to:
Answer A: Construct a two-sample z-interval for the difference between population proportions.
This is the most appropriate method for estimating the difference between population proportions, as it takes into account the variability of the sample proportions and provides a confidence interval for the true difference between the two populations. The formula for calculating the two-sample z-interval for the difference between population proportions is:
(p₁−p₂) ± z x √[(p₁(1−p₁))/₁ + (p₂(1−p₂))/₂]
Therefore, Answer A: Construct a two-sample z-interval for the difference between population proportions.
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What is 5/8 equative to
Answer chooses
0.48
0.6
0.675
Answer: C
Step-by-step explanation:
given that f(x) =x^2 - 13x + 36 and g (x) = x -4, find f (x) -g (x) and express the result as a polynomial in simplest form.
Answer:
f(x)-g(x)
= [tex](x^{2} - 13x + 36) - ( x -4)[/tex]
= [tex]x^{2} -13x+36-x+4[/tex]
= [tex]x^{2} -14x-40[/tex]
A 4-yard dumpster cost $95.00 monthly how much would it cost for the year?
Answer options:
A) 190.00
B) 180.00
C) 170.00
D) 160.00
If a 4-yard dumpster cost $95.00 monthly, the total cost for the year is $1,140.
How is the total cost determined?The total cost for the year of the dumpster is the product of the multiplication of the monthly cost and 12.
Multiplication is one of the four basic mathematical operations, including addition, subtraction, and division.
In any multiplication, there must be the multiplicand (the number being multiplied), the multiplier (the number multiplying the multiplicand), and the product (or the result).
The monthly cost of the 4-yard dumpster = $95.00
1 year = 12 months
The total annual cost = $1,140 ($95 x 12)
Thus, using the multiplication operation, we can find that none of the options is correct as the total annual cost but $1,140.
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Regina and Abby both want to buy new shoes for their shoe collection.
Regina only has 500 dollars the shoes she wants is 600 dollars.
Her mom makes her work for 5 hours and she gets 120 dollars per hour.
Abby has 600 dollars and the shoes she wants is $870
Her mom makes her work for 5 hours and gets $320
Is the relationship between hours worked and money proportional? Who would buy their shoes first?
The relationship between hours worked and money is not proportional.
Regina would be able to buy her shoes first after working an additional 50 minutes.
What is proportion?
In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.
To determine if the relationship between hours worked and money is proportional, we need to calculate the hourly rate for each person and see if it is the same.
For Regina, she earned $120 per hour and worked for 5 hours, so she earned a total of 5 x 120 = $600.
This means her hourly rate is $120.
For Abby, she earned $320 for 5 hours of work, so her hourly rate is 320/5 = $64.
Since the hourly rates are different, the relationship between hours worked and money is not proportional.
Now let's see who would be able to buy their shoes first.
Regina needs $100 more to be able to buy her shoes, and she earned $600 from working 5 hours.
Therefore, she can buy the shoes after working for an additional $100/$120 = 0.83 hours, which is approximately 50 minutes.
On the other hand, Abby needs $270 more to buy her shoes, and she earned $320 from working 5 hours.
Therefore, she can buy the shoes after working for an additional $270/$64 = 4.22 hours, which is approximately 4 hours and 13 minutes.
Therefore, Regina would buy her shoes first.
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The multiplicative inverse of a number is also called its _______________.
Answer:
Step-by-step explanation:
I'll give brainliest
(-7, 4).
Step-by-step explanation:1. Write the given equations.[tex]x=-2y+1\\ \\3x+8y=11[/tex]
2. Solve one of the equations for one of the variables.Most of the times you solve a systems of equations, you'll have to solve one of the equations for one of the variables (x or y), since the first equation is already solved for "x", we may use that and skip this first solving step.
[tex]x=-2y+1[/tex]
3. Substitute the value of "x" on the second equation by the argument of "x" in the first equation.[tex]3(-2y+1)+8y=11[/tex]
4. Distribute and multiply on the left side of the equation.Chech attached image 1.
[tex](3)(-2y)+(3)(1)+8y=11\\ \\(-6y)+(3)+8y=11\\ \\-6y+3+8y=11[/tex]
5. Subtract "3" from both sides of the equation.[tex]-6y+3+8y-3=11-3\\ \\-6y+8y=8[/tex]
6. Work out like terms at the left hand side.[tex]2y=8[/tex]
7. Divide by "2" on both sides.[tex]\frac{2y}{2} =\frac{8}{2} \\ \\y=4[/tex]
8. Substitute "y" by the calculated value (4) on any of the equations to find the value of "x".[tex]x=-2(4)+1\\ \\x=-8+1\\ \\x=-7[/tex]
9. Express the final answer.Now that weëve found a value for both "x" and "y", write the solution as an ordered pair:
(x, y)
(-7, 4).
10. Verify your answer.To algebraically verify your answer, you must use the value of either "x" or "y" on both of the equations and it should return the other value of the missing variable.
Since we already checked with the first equation, go ahead and plug in any of the values on the second equation and check if it returns the correct value.
For example, if we use y=4 in equation 2, it should return an "x" value of -7. Let's test it!
[tex]3x+8(4)=11\\ \\3x+32=11\\ \\3x=11-32\\ \\3x=-21\\ \\\frac{3x}{3} =\frac{-21}{3} \\ \\x=-7[/tex]
That's correct! Answer is (-7, 4).
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Round 10.468 to the nearest hundredth
Answer:
Step-by-step explanation:
10.468 rounded to the nearest hundredth would be 10.47
4 = tenths place
6 = hundredths place
8 = thousandths place
8 >= 0.5 so 10.468 --> 10.47
Answer: 10.47
Step-by-step explanation: After the decimal, it goes tenths, hundredths, thousandths. So we're looking at the second place after the decimal, which is a 6, and the next number is 8. Think of it like 68, rounding up to the next ten, or 70. So that turns it into 10.470, and you get to drop the zero to make it 10.47.
Together, teammates Pedro and Ricky got 2685 base hits last season. Pedro had 285 more hits than Ricky. How many hits did each player have?
Answer:
Ricky has 1204 hits and Pedro has 1481 hits.
Step-by-step explanation:
Answer: pedro had 1,200 and ricky had 1,485
Step-by-step explanation: all i did was 2685 - 285 which equals 2,400. then i did 2,400 divided by 2 which was 1,200, pedro had 1.200 hits.
1,200 add 285 equals 1,485. ricky has 1,485. to double check add 1,200 and 1,485 and you should get 2,685
In formally proving that lim (x² + x) = 42, let e > 0 be arbitrary.
In formally proving that lim (x² + x) = 42
m = ⌈√ε⌉ - 1
How do we calculate?It is shown that for any ε > 0, there exists a δ > 0 such that if 0 < |x - c| < δ, then |(x^2 + x) - 42| < ε.
|(x^2 + x) - 42| = |x^2 + x - 42| = |(x - 6)(x + 7)|
Since |x - c| < δ, we have:
|x - 6| < δ + 6 < δ(m+2)
|x + 7| < δ + 7 < δ(m+2)
Since δ = ε/(m+1), we can solve for m:
m+1 = ε/δ
m+1 = ε/ (ε/(m+1) )
(m+1)^2 = ε
m^2 + 2m + 1 = ε
m^2 + 2m + (1-ε) = 0
Using the quadratic formula, we get:
m = (-2 ± ⌈√ε⌉ - 1 (4 - 4(1-ε)))/2 = -1 ± √(ε)
Therefore, in conclusion m = ⌈√ε⌉ - 1
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Determine whether descriptive or inferential statistics were used in the statement. in 2008, the average credit card debt for college students was $3173. (source: newser)
The collection, description, analysis, and drawing of conclusions from quantitative data are all included in the area of statistics, which is a branch of applied mathematics. Probability theory, linear algebra, and calculus of differential and integrals are some of the core mathematical concepts in statistics.
Descriptive statistics were used in the statement.
Descriptive statistics is a branch of statistics that deals with the collection, presentation, and summary of data. It is used to describe and summarize the main features of a data set, such as measures of central tendency (e.g., mean, median, mode) and measures of dispersion (e.g., range, variance, standard deviation).
In this case, the statement is simply reporting a single value, the average credit card debt for college students in 2008. This is an example of a descriptive statistic because it is a summary measure that describes a characteristic of the population or sample under study.
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Descriptive statistics were used in the statement.
What is descriptive statistics?Descriptive statistics is a branch οf statistics that deals with the analysis, descriptiοn, and summarizatiοn οf data. It invοlves the use οf variοus statistical measures, such as measures οf central tendency (mean, median, and mοde), measures οf dispersiοn (standard deviatiοn, variance, range), and graphical representatiοns (histοgrams, bοx plοts, scatter plοts, etc.) tο describe the features οf a dataset.
Descriptive statistics were used in the statement. The statement is simply describing the average credit card debt fοr cοllege students in 2008. Descriptive statistics are used tο describe οr summarize a dataset οr pοpulatiοn, while inferential statistics are used tο draw cοnclusiοns οr make predictiοns abοut a larger pοpulatiοn based οn a sample οf data. Since the statement οnly prοvides infοrmatiοn abοut a specific grοup οf cοllege students in 2008, it dοes nοt invοlve making any inferences οr predictiοns beyοnd this grοup.
Hence, Descriptive statistics were used in the statement.
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The diameter of a circle is 22 feet. What is the circle's area?
Use 3.14 for .
Answer: 3.14 ft
Step-by-step explanation:
★Given,→ Diameter = 2 feet → Circumference = 2/2 = 1 feet
★Now,→Area of a circle = πr²→ = 3.14 × 1 × 1→ = 3.14 feet
Hence , the circumference is 3.14 ft.
What is the equivalent expression to 4(9+3)
Answer:
4(9+3) = 48
Step-by-step explanation:
To simplify the expression 4(9+3), we need to perform the addition inside the parentheses first and then multiply the result by 4.
9+3 = 12, so we can substitute this into the expression as follows:
4(9+3) = 4(12)
Now we can perform the multiplication:
4(12) = 48
Therefore, the equivalent expression to 4(9+3) is simply 48.
show how the damping ratio for a mass-spring-damper system is defined by the ode for a mass-spring-damper system in terms of mass, m, stiffness, k, and damping, b?
The equation that shows the damping ratio for a mass-spring-damper system which is defined in terms of the mass, m, stiffness, k, and damping, b is ζ = b / (2sqrt(mk)).
What is damping ratio?The damping ratio ζ is defined as the ratio of the damping coefficient b to the critical damping coefficient b_c, which is the minimum damping required to prevent the system from oscillating.
The damping ratio is a dimensionless quantity that represents the amount of damping in the system relative to the critical damping needed to prevent oscillations. A higher damping ratio indicates a more heavily damped system, while a lower damping ratio indicates a less damped system that may oscillate more.
The motion of a mass-spring-damper system can be described by a second-order linear ordinary differential equation (ODE) of the form:
md²x/dt² + bdx/dt + kx = F(t)
where m is the mass of the system, b is the damping coefficient, k is the spring constant, x is the displacement of the mass from its equilibrium position, and the external force applied to the system is F(t).
The critical equation will be -
b_c = 2√(mk)
Therefore, the damping ratio can be expressed as:
ζ = b / b_c
Substituting the expression for b_c into the above equation, we get:
ζ = b / (2√(mk))
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Least Common Denominator
The required least common denominator for the given expression is 4x³(x + 3). Option C is correct.
What is a rational fraction?A rational expression is a mathematical expression that is the ratio of two polynomial expressions. That is, a rational expression is formed by dividing one polynomial expression by another polynomial expression.
Here,
The given rational expression,
= 1/x² - 1/4x² + 12x
In the question, we have been asked to determine the least common denominator for the given rational expression.
Since least common denominator is given expression,
= x² (4x² + 12x)
= 4x³(x + 3)
Thus, the required least common denominator for the given expression is 4x³(x + 3). Option C is correct.
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What is the volume of a cube with a side length of 1/4 inch?
Answer: 1/64 cubic inch
Step-by-step explanation:
Side of cube = 1/4
Volume = s^3 = 1/4^3
= 1/64
Hope this helps!!
Determine whether the following statement describes a population or a sample. The amount of money each person in your world history class spends renting movies in a week.
The statement describes a sample. Specifically, it is referring to the amount of money each person in your world history class spends renting movies in a week. The class is a subset of a larger population, and the statement is only referring to the sample within that population.
How can you tell if a sample is representative of the whole?By incorporating members of all demographic categories (gender, rural/urban, economic levels, etc.) and having them in the same proportions as the entire population, your sample must be representative of the general population. If there are excessive numbers of participants from rural areas, men, etc., it is not truly representative.
Is money a sampling or a population?Response and justification: A population is the sum of money each student in your global history class spends each week on movie rentals. Because each member of the group is included in the study, this is a population.
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Suppose that the quadratic function:
f (x) = (x − 3)² + 5
is transformed
into:
g(x) = (x − 6)² + 3.
How is the graph of the original function transformed?
A: left 2 units and down 3 units
B: right 3 units and down 2 units
C: right 3 units and up 2 units
D: right 2 units and down 3 units
E: left 3 units and up 2 units
F: left 3 units and down 2 units
Answer:B
Step-by-step explanation: I took the test
trust me :p
If the discriminant is negative, there are nο real sοlutiοns, but there are twο cοmplex sοlutiοns in the fοrm οf cοmplex cοnjugates.
What is the quadratic equatiοn?In algebra, a quadratic equatiοn is any equatiοn that can be rearranged in standard fοrm as where x represents an unknοwn value, and a, b, and c represent knοwn numbers, where a ≠ 0.
A quadratic equatiοn is a secοnd-degree pοlynοmial equatiοn in οne variable οf the fοrm:
ax² + bx + c = 0
where a, b, and c are cοnstants, and x is the variable. The quadratic equatiοn is used tο sοlve prοblems that can be represented by a secοnd-degree pοlynοmial functiοn.
The general fοrm οf the quadratic equatiοn can be sοlved using the quadratic fοrmula:
x = (-b ± √(b² - 4ac)) / 2a
where the "±" sign means that there are twο pοssible sοlutiοns, οne with the pοsitive square rοοt and the οther with the negative square rοοt.
The quadratic equatiοn can have οne, twο, οr nο real sοlutiοns depending οn the value οf the discriminant b² - 4ac. If the discriminant is pοsitive, there are twο distinct real sοlutiοns. If the discriminant is zerο, there is οne real sοlutiοn with a multiplicity οf 2.
If the discriminant is negative, there are nο real sοlutiοns, but there are twο cοmplex sοlutiοns in the fοrm οf cοmplex cοnjugates.
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In a controlled lab environment some organisms exhibit constant growth over a specific period.
Suppose a certain organism starts out weighing 16 mg and grows to 46 mg over a 5 hour period.
Find a linear model (equation of line) that describes the growth of the organism for the time period given.
Hint x is number of hours and y is the weight. Show work
So the linear model that describes the growth of the organism over the 5 hour period is: y = 6x + 16, where x is the number of hours and y is the weight of the organism in mg.
What is linear model?A linear model is a mathematical equation that describes a linear relationship between two or more variables. In other words, it is a model that assumes that the relationship between the variables can be represented by a straight line. Linear models are commonly used in various fields, including economics, finance, engineering, and science, to analyze and predict the relationship between variables. They are particularly useful when analyzing data that shows a linear trend, or when making predictions based on historical data. Linear models can be simple or multiple, depending on the number of independent variables involved. They can also be adjusted to fit nonlinear data by transforming the variables or using a different model altogether.
Here,
To find a linear model that describes the growth of the organism over time, we need to determine the rate of growth (change in weight per unit time) and the initial weight.
The rate of growth can be found by taking the difference between the final weight and the initial weight and dividing by the time period:
Rate of growth = (final weight - initial weight) / time period
= (46 mg - 16 mg) / 5 hours
= 6 mg/hour
So the organism is growing at a rate of 6 mg per hour.
The initial weight of the organism is given as 16 mg.
Now we can write the equation of the line as:
y = mx + b
where y is the weight of the organism in mg, x is the time in hours, m is the rate of growth in mg/hour, and b is the initial weight in mg.
Substituting the values we found, we get:
y = 6x + 16
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The vertices of a rectangle are at (-4,2),(3,2),(3,-2), and (-4,-2). What is the length of the longer side of the rectangle?
The longer side of the rectangle is the side that connects the points (-4,2) and (3,2), which have the same y-coordinate, so it is a horizontal line.
The length of this side is the distance between the x-coordinates of these two points, which is:
3 - (-4) = 7
Therefore, the length of the longer side of the rectangle is 7 units.
use the multiplier method to increase £258 by 43%
Answer:
43% * 258 = 110.94 (£110.94 is 43% of £258) 258 + 110.94 = 368.94
Step-by-step explanation: