The constants a and b can be found by ensuring the function is continuous and that the limits at each point match. This can be done by setting the values of a and b so that the function and its derivative are equal at each point.
To find the constants a and b for the given piece-wise cubic function, we must consider the definition of continuity and limits. Firstly, for the function to be continuous, the function and its derivative must be equal at each point. Thus, we need to set the values of a and b so that the function and its derivative are equal at the points x=1, x=2 and x=3. We can use this to create a system of equations to solve for a and b. Once we have determined the values of a and b, we can then check that the limits at each point match. This can be done by computing the left and right hand limits at each point, and ensuring they are equal. If the limits are equal, then the function is continuous and the constants a and b are correct.
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At a local pizza shop, the delivery person earns $2 for every pizza delivered, plus $70 per day. How many pizzas must the delivery person deliver to earn more than $100 in one day? Write an inequality to represent this situation.
70 + 2x > 100 is an inequality to represent this situation.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given, At a local pizza shop, the delivery person earns $2 for every pizza delivered, plus $70 per day.
Let "x" be the number of pizzas he delivers
Thus, the Total money he earns by delivering pizza = 70 + 2x
To earn more than 100$ inequality represents
70 + 2x > 100
So,
2x > 30
x > 15
Therefore, to earn more than 100$ every day he needs to deliver at least 15 pizzas.
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functions that aren't invertible can be made invertible by restricting their domains. for example, the function $x^2$ is invertible if we restrict $x$ to the interval $[0,\infty)$, or to any subset of that interval. in that case, the inverse function is $\sqrt x$. (we could also restrict $x^2$ to the domain $(-\infty,0]$, in which case the inverse function would be $-\sqrt{x}$.) similarly, by restricting the domain of the function $f(x).
When the domain of x is restricted, the function x2 becomes one-to-one, and the inverse function is x.
It is true that limiting a function's domain might cause it to become invertible. Because it is not one-to-one in the example, the function x2 is not invertible across its complete domain of real numbers (i.e., it assigns multiple outputs to some inputs). However, x2 becomes one-to-one and invertible when the domain of x is constrained to or any subset of that interval. The range of x2, which is, is used to define the inverse function in this situation, which is
The function x2 becomes one-to-one when the domain of x is constrained, and the inverse function is
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during a severe storm, electrical transformers that function independently are expected to operate 85 percent of the time. suppose 20 electrical transformers are randomly selected from the population. let the random variable t represent the number of electrical transformers operating during a severe storm. which of the following is the best interpretation of the random variable t ?
The binomial variable with mean 17 transformers and standard deviation √2.55 transformers.
In math standard deviation is defined as a measure of how dispersed the data is in relation to the mean.
Here we have know that the good electrical transformers operate at approximate 85% of the total time and 20 electrical transformers are chosen at random.
Here let us assuming the variable is a binomial variable.
Then we have written it as in the following form,
=> Mean = number of samples * probability
And the value of standard deviation is calculated as
=> Standard Deviation = √mean (1 − probability)
Here we know that the value of mean is calculated as,
=> 85% * 20 = 0.85*20 = 17 transformers
Then the value of Standard deviation is calculated as,
=> √mean * (1 − 0.85)
Apply the values on the formula, then we get,
=> √17 * 0.15 =√2.55 transformers.
Hence the random variable is a binomial variable.
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If you borrow $220,000 at an APR of 3.5% for 25 years, you will pay $1,101.37 per month. If you borrow the same amount at the same APR for 30 years, you will pay $987.90 per month.
a. What is the total interest paid on the 25-year mortgage?
b. What is the total interest paid on the 30-year mortgage?
a. The total interest paid on the 25-year mortgage is $110411.
b. The total interest paid on the 30-year mortgage is $135644.
What is the meaning of APR?
Annual percentage rate (APR) is the term used to describe the annual interest produced by a sum that is levied against borrowers or distributed to investors. APR is a percentage that expresses the actual yearly cost of borrowing money over the course of a loan or the income from an investment. This does not account for compounding and includes any fees or additional costs related to the transaction. Consumers can compare lenders, credit cards, or investment products using the APR as a benchmark figure.
Given that, the amount that is borrowed is $220,000.
If you borrow it for 25 years, you will pay $1,101.37 monthly.
The amount that you need to pay is (1,101.37×12×25) = 330411.
The total interest is = (330411 - 220,000) = $110411.
If you borrow it for 30 years, you will pay $987.90 monthly.
The amount that you need to pay is (987.90×12×30) = 355644.
The total interest is = (355644 - 220,000) = $135644
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An airplane travels 4466 kilometers against the wind in 7 hours and 5866 kilometers with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind? Note that the ALEKS graphing calculator can be used to make computations easier. Rate of the plane in still air: Rate of the wind: km h km h 010 S
The Rate of plane in still air and rate of wind is 738 , 100 respectively .
What is Linear equation ?
Linear equation can be defined as the equation in which the highest degree is one
Given ,
An airplane travels 4466 kilometers against the wind in 7 hours and 5866 kilometers with the wind in the same amount of time.
Let speed of plane be Vp and Va
Now,
Vp - Va = 4466 / 7
Vp+Va = 5866 / 7
So, Evaluating the equations,
we get,
2Vp = (4466+5866) / 7
Vp = 1476 / 2
Vp = 738
So substitute Vp =738 in Vp-Va = 4466/7
738 - Va = 638
Va = 738 - 638
Va = 100.
Hence, The Rate of plane in still air and rate of wind is 738 , 100 respectively .
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Find the midpoint between (-1, -5) and (-5, 9) by using the Midpoint Formula.
Answer: Midpoints (-3/2)
Step-by-step explanation:
Midpoint formula is (x1+x2)/2 , (y1+y2)/2
Plugin x values and solve
(-1 +-5)/2 = -3
Plugin y values and solve
(-5+9)/2 = 2
The midpoint is -3/2
I hope this helped you :D
Which set of numbers could be the side lengths that will form a triangle?
All u have to do is use the Traingle Inequality theorem, which states that the sum of two sides lenghts of a triangle is always greater than the third side. if this is true for all three combinations of added side lengths then you will have a triangle
Hope this helps :>
Answer:
3, 5, 7
Step-by-step explanation:
given 3 sides, for a triangle to be formed, then the sum of any 2 sides must be greater than the third side.
4 , 4 , 8
4 + 4 = 8 , not greater than 8, so does not form a triangle
1 , 2 , 3
1 + 2 = 3 , not greater than 3, so does not form a triangle
3 , 9 , 14
3 + 9 = 12 < 14 , so does not form a triangle
3 , 5 , 7
3 + 5 = 8 > 7
3 + 7 = 10 > 5
5 + 7 = 12 > 3
condition is satisfied , so will form a triangle
at westville high school there are 315 seniors and 389 juniors. 65% of the seniors have parkign passes and 42% of teh juior have parking passes. the statistics teacher selects a srs of 30 seniors and a seperate srs of 30 juniors.
a. The shape of the sampling distribution is normal by the Central Limit Theorem.
b. The mean is 0.23.
c. The standard error is 0.125, which means that the sample proportions differ by around 0.125 from the mean of 0.23.
d. The probability is 0.2877 = 28.77%.
By the Central Limit Theorem, each sample has at least 10 successes and at least 10 failures, and the shape of the distribution is normal.
For each sample, the mean and the standard error are specified as follows:
Seniors : [tex]p_{s} = 0.65, s_{s} =\sqrt{\frac{0.65(0.35)}{30} } = 0.087[/tex]Juniors : [tex]p_{j}= 0.42, s_{j} =\sqrt{\frac{0.42(0.58)}{30} } = 0.09[/tex]Hence, the distribution of differences, the mean, and the standard error are specified as follows:
Mean= 0.65 - 0.42 = 0.23.Standard error: [tex]s =\sqrt{0.087^{2}+0.09^{2} } = 0.125[/tex]Using the z-score formula, the probability that the difference is greater than 30 is 1 subtracted by the p-value of Z when X = 0.3, Therefore:
Z = (0.3 - 0.23)/0.125
Z = 0.56
Z = 0.56
1 - 0.7123 = 0.2877 = 28.77%.
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The complete question is:
At Westville High School there are 315 seniors and 389 juniors. 65% of the seniors have parking passes and 42% of the juniors have parking passes. The statistics teacher selects an SRS of 30 seniors and a separate SRS of 30 juniors. Let ^ps-^pj be the difference in the sample proportion of seniors and juniors that have parking passes.
a. What is the shape of the sampling distribution of ^ps-^pj? Why?
b. Find the mean of the sampling distribution.
c. Calculate and interpret the standard deviation of the sampling distribution.
d. What is the probability that the difference in sample proportions (senior-junior) of students with parking passes is greater than 30%?
Determine the slope of the linear relationship
The increase in the y-coordinatesis then calculated by dividing it by the change in the x-coordinates.
How can you determine a linear graph's slope?Locating Slope using a graphChoose two random spots on the line's graph (preferably with integer coordinates).Identify them as A and B. (in any order).The "rise" from A to B should be calculated. If necessary, when moving vertically from point A to point B.Determine the "run" distance from A to B.Apply the following equation: slope = rise/run.You need the coordinates for two points on a line in order to calculate its slope. The increase in the y-coordinates (also known as the slope) is then calculated by dividing it by the change in the x-coordinates (referred to as the run).-6 to 29-2 to 152 to 18 to -20To learn more about linear relationship refer to:
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if the pattern below contiunues which equation(s) is a recursive formula that reprsents the number of sequences in this sequence
The recursive formula that represents the number of sequences in this sequence is n(n-1)(n-2)/6, where n is the number of terms in the sequence.
This recursive formula is based on the pattern of the sequence. The sequence has three terms, a, b and c, and then three combinations of two terms, ab, ac and bc, and then one combination of all three terms, abc. This pattern of three terms, then three combinations of two terms, then one combination of all three terms continues as the sequence increases.
The recursive formula represents this pattern in a mathematical equation. The formula is n(n-1)(n-2)/6, where n is the number of terms in the sequence. This formula is derived from the fact that for each term there are two other terms that can combine with it to form a two-term combination, and one combination of all three terms. Therefore, for n terms, there are n(n-1)/2 two-term combinations and one combination of all three terms, for a total of n(n-1)(n-2)/6 sequences.
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The complete question is
if the pattern below contiunues which equation(s) is a recursive formula that reprsents the number of sequences in this sequence 5, 10, 20, 40.
delta airlines quotes a flight time of hours, minutes for its flights from cincinnati to tampa. suppose we believe that actual flight times are uniformly distributed between hours and hours, minutes.
The required probability for the given delta airlines is given by :
a. Probability of flight late no more than 5 minutes is 0.25.
b. Probability of flight late more than 10 minutes is 0.5
c. Expected flight time is equal to 130 minutes.
Flight time from Cincinnati to Tampa = 2 hours 5 minutes
Actual time distributed between 2 hours and 2 hours 20 minutes
2 hours = 120 minutes
2 hours 20 minutes = 140 minutes
f(x) = [tex]\left \{ {{\frac{1}{( 140 - 120)} , 120 \leq x\leq 140\atop {0 , x = 0 }} \right.[/tex]
a. Probability of flight no more than 5 minutes late
[tex]\int_{130}^{125} \frac{1}{20} dx[/tex]
= 1 / 4
= 0.25
b. Probability of flight more than 10 minutes late
[tex]\int_{135}^{125} \frac{1}{20} dx[/tex]
= 1/2
= 0.5
c. Expected flight time in minutes
= [tex]\int_{140}^{120} \frac{x}{20} dx[/tex]
= 130 minutes
Therefore, the required probability are given by :
a. Probability of flight late no more than 5 minutes is 0.25.
b. Probability of flight late more than 10 minutes is 0.5
c. Expected flight time is equal to 130 minutes.
The above question is incomplete , the complete question is :
Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes. What is the probability that the flight will be no more than 5 minutes late (to 2 decimals)? What is the probability that the flight will be more than 10 minutes late (to 2 decimals)? What is the expected flight time, in minutes?
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50 POINTS REWARD + BRAINLEST!! NEEDED ASAP!! PLEASE!!
15. The algebraic expression 25x - 1,500 can be used to describe the daily profit of a company that makes waffle irons.
A. What does the first term of the expression represent? What does the second term of the expression represent?
B. Explain what the algebraic expression represents if the company sells 350 waffle irons per day.
C. What is the company's profit for a 5-day week? Explain.
A). The first term represents the total cost of the waffle irons and the second term represents the expenses.
B). The algebraic expression represents if the company sells 350 waffle irons per day will be 350x - 1500
C). The company's profit for a 5-day week is $250.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the algebraic expression 25x - 1,500 can be used to describe the daily profit of a company that makes waffle irons.
A). The first term represents the total cost of the waffle irons and the second term represents the expenses. Here 25 is the number of the waffle iron and the x is the number of days.
B). The algebraic expression represents if the company sells 350 waffle irons per day will be written as:-
350x - 1500
C). The company's profit for a 5-day week will be;-
Profit = 350x - 1500
Profit = ( 350 x 5 ) + 1500
Profit = 1750 - 1500
Profit = 250
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12. The ratio of dolphins to penguins is 2:5. So, for every 2 dolphins, there are 5 penguins. If there are 30 penguins, how many dolphins would there be?
If the ratio of dolphins to penguins is 2:5, then for every 2 dolphins, there are 5 penguins. If there are 30 penguins, you can use this ratio to find out how many dolphins there are. To find out how many dolphins there are, you can set up a proportion:
(number of dolphins) / (number of penguins) = (2) / (5)
You know that the number of penguins is 30, so you can substitute that in and solve for the number of dolphins:
(number of dolphins) / 30 = 2 / 5
Multiply both sides by 30 to solve for the number of dolphins:
number of dolphins = (2/5) * 30 = 6
So, if there are 30 penguins, there would be 6 dolphins.
Solve the system of linear equations by elimination.
5x+6y=50
x-6y=-26
Answer:x=4, y=5
Step-by-step explanation:
Given the geometric sequence where a1 = 7 and the common ratio is 3, what is the domain for n?
All integers where n ≥ 1
All integers where n ≥ 0
All integers where n > 7
All integers
The domain for 'n' will be all integers where n ≥ 1. Then the correct option is A.
What is a geometric sequence?A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.
Let a₁ be the first term and r be the common ratio. Then the nth term of the geometric sequence is given as,
aₙ = a₁ · (r)ⁿ⁻¹
The geometric sequence where a₁ = 7 and the common ratio is 3. Then the formula is given as,
aₙ = 7 · (3)ⁿ⁻¹
In the geometric sequence, the value of the exponent should be greater than or equal to zero. Then we have
n - 1 ≥ 0
n ≥ 1
The domain for 'n' will be all integers where n ≥ 1. Then the correct option is A.
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His total bill, with tax, was $7.95. He paid 6 percent sales tax. How much did he pay for the cooler alone without the tax?
The amount that he pays for the cooler alone without the tax will be $7.37.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
His total bill, with tax, was $7.95. He paid 6 percent sales tax.
Let 'x' be the total bill without the sales tax. Then the equation is given as,
107.95% of x = $7.95
1.0795x = $7.95
x = $7.37
The amount that he pays for the cooler alone without the tax will be $7.37.
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Show that the quadrilateral, formed by joining the mid-points of the sides of a square is also a square.
Since the mid-points of opposite sides of a square are equal, the quadrilateral formed will also be a square.
A four-sided polygon whose all sides are equal is a square. This means that the opposite sides of a square are equal in length and the opposite angles are also equal. Furthermore, the diagonals of a square bisect each other at their mid-points. Therefore, if the mid-points of opposite sides of a square are joined, a quadrilateral is formed. Since the opposite sides and angles are equal, the quadrilateral formed is also a square. To prove this, we can draw a line from the mid-point of one side of the square to the mid-point of the opposite side. We can then draw a line from the mid-point of the other side of the square to the mid-point of the opposite side. This will form a quadrilateral, and due to the equal sides and equal angles, it will be a square.
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Points D, B, and E are collinear. Find the value of a so that points A, B, and C are
collinear.
Because x is 6, points A, B, and C are collinear.
What is intersecting lines?The intersection of two lines in Euclidean geometry can be the empty set, a point, or another line. Distinguishing these cases and locating the intersection have applications in computer graphics, motion planning, and collision detection, among others. The intersecting lines are two lines that share exactly one common point. The intersecting lines have a point in common. The point of intersection is the common point that exists on all intersecting lines. When two or more lines intersect in a plane, they are referred to as intersecting lines. The intersecting lines share a common point, which exists on all of them and is known as the point of intersection.
Here,
Since the opposite angle are equal in intersecting lines,
42=7x
x=6
The value of x is 6 so that points A, B, and C are collinear.
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HELP WANTED TYY!!! Charlie has two different-sized vases for flowers. The dimensions of his small vase with a diameter of 6 cm are shown below.
A vase shaped like a cylinder is shown. A dashed line drawn across the bottom of the vase is labeled six centimeters. The height of the vase is labeled twenty-one centimeters.
His large vase has the same height as the small vase, but its diameter is 2 times greater. How do the volumes of Charlie’s two flower vases compare? Use 3.14 for π.
Select the answers from the drop-down lists to correctly complete each sentence.
The volume of his large vase is ________ = A) 2,373.84 B) 593.46 C) 791.28
D) 1582.56 cm^3.
This is _______ = A) 4 B) 2 C) 3
times the volume of his small vase.
The volume of his large vase is 2,373.84cm^3 (option A)
The is 4 times the volume of the small verse. (option A)
What is the volume of the large verse?A cylinder is a three-dimensional object. It is a prism with a circular base.
volume of a cylinder = nr^2h
Where:
π = 3.14r = radius = diameter / 2 h = heightRadius of the small verse = 6/2 = 3 cm
Volume of the small verse = 3.14 x 3² x 21 = 593.46 cm³
Radius of the large verse = (2 x 6) / 2 = 6cm
Volume of the large verse = 3.14 x 6² x 21 = 2,373.84 cm³
Difference in volumes = 2,373.84 cm³/ 593.46 cm³ = 4
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Function Tables
Thank you!
The complete function tables are written above.
What is a function? What is a quadratic function?A function describes a relationship between a dependent and independent variable. Example -
y = f(x) = 5x + 9
A quadratic function is of the form -
f(x) = ax² + bx + c
Given are the function tables as shown in the image attached.
{ 4 } -
Rule : h = 8c
{c} 2 3 4 5 6 7
{h} 16 24 32 45 48 56
{5} -
Rule : k = 2r
{r} 6 7 8 9 12 11 14
{k} 12 14 16 18 24 22 28
{6} -
Rule : k = 2r
{r} 6 7 8 9 12 11 14
{k} 12 14 16 18 24 22 28
Therefore, the complete function tables are written above.
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please please please help
Answer:
[tex]\underline{x\quad \:\:\:\:\:\:-8\quad\quad\;\;-6\quad\quad0\quad\quad\quad\;\; \;\;2}\\y\quad\quad\;\;\;\boxed{\dfrac{1}{3}}\quad\quad\quad \boxed{0} \quad\;\boxed{-1} \quad\quad \boxed{\dfrac{4}{3}}[/tex]
Step-by-step explanation:
The strategy is to substitute the value of each of the given x values into the equation
[tex]y = -\dfrac{x}{6} - 1[/tex]
and find the corresponding value for [tex]y[/tex]
[tex]x\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{x}{6} - 1\\\line(1,0){180}\\\\[/tex]
[tex]-8\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{-8}{6} - 1 = \bf{{\dfrac{1}{3}[/tex]
[tex]-6\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{-6}{6}-1 = \bf{0}[/tex]
[tex]0\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{0}{6}-1 = \bf{-1}[/tex]
[tex]2\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{2}{6} -1 =\bf{-}\dfrac{4}{3}[/tex]
[tex]\line(1,0){180}\\\\[/tex][tex]\line(1,0){180}\\\\[/tex]
I need the answer as soon as possible!
3x + 4y^2 ; x = -3 and y = 5
Thank You!
The value of the expression 3x + 4y² when x = -3 and y = 5 is 91.
What is the value of the given expression?Given the expression in the question;
3x + 4y²
x = -3y = 5To determine the value of the expression when x = -3 and y = 5, plug in x = -3 and y = 5 for every x and values in the expression and simplify.
3x + 4y²
3( -3 ) + 4( 5 )²
Simplify
Take the square of 5
3( -3 ) + 4( 25 )
Multiply 3 and -3
-9 + 4( 25 )
Multiply 4 and 25
-9 + 100
Add -9 and 100
91
Therefore, the value of the expression is 91.
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Find the following for the given functions.
f(x): =
X/X + 9 ,
g(x) = x³
The results of operations between functions:
Case A: (f + g) (x) = x / (x + 9) + x³
Case B: (f - g) (x) = x / (x + 9) - x³
Case C: (f · g) (x) = x⁴ / (x + 9)
Case D: (f / g) (x) = 1 / [x² · (x + 9)]
Function (f / g) (x) has the following domain: x ∈ R - {- 9, 0}.
How to find the result of operations between two functions
According to function theory, we can obtain a function with more complexity by operations between two functions, the most common operations are listed below:
Addition: (f + g) (x) = f (x) + g (x)Subtraction: (f - g) (x) = f (x) - g (x)Multiplication: (f · g) (x) = f(x) · g(x)Division: (f / g) (x) = f (x) / g (x)Now we proceed to determine the resulting function:
Case A:
(f + g) (x) = f(x) + g(x)
(f + g) (x) = x / (x + 9) + x³
Case B:
(f - g) (x) = f(x) - g(x)
(f - g) (x) = x / (x + 9) - x³
Case C:
(f · g) (x) = f (x) · g (x)
(f · g) (x) = [x / (x + 9)] · x³
(f · g) (x) = x⁴ / (x + 9)
Case D:
(f / g) (x) = f(x) / g(x)
(f / g) (x) = [x / (x + 9)] / x³
(f / g) (x) = 1 / [x² · (x + 9)]
The domain of (f / g) (x) is the set of all values of x-values such that the function exists. In this case, we must determine the values of the denominator of (f / g) (x) such that it is not equal to zero.
x² · (x + 9) = 0
x = 0 or x = - 9
The domain of (f / g) (x) is: x ∈ R - {- 9, 0}.
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volumes (cm)^3 of 20 brains have a mean of 1120.6cm^3 and a standard deviation of 124.5cm^3. use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. would a brain volume of 1389.6^3 be significantly high ? is 1389.6^3 significantly high? what are the significantly low values or lower and what are the significantly higher values.
The significantly low values are:
Lower than 871.6 cm³.
The significantly high values are:
Higher than 1369.6 cm³.
Hence a volume of 1389.6 cm³ is significantly high, as it is more than 2 standard deviations from the mean.
What is the range rule of thumb?The range rule of thumb states that measures that are more than two standard deviations from the mean in a data-set are considered unusual.
Considering the mean and the standard deviation for this problem, the bounds are given as follows:
Significantly low: Lower than 1120.6 - 2 x 124.5 = 871.6 cm³.Significantly high: Higher than 1120.6 + 2 x 124.5 = 1369.6 cm³.More can be learned about the range rule of thumb at brainly.com/question/15825971
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NO LINKS!!!
Please help me #49 and 50
Answer:
49. a) A - C - 1
49. b) 1 - 2R
49. c) 2Q - P
50. x = 103
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5cm}\underline{Log laws}\\\\$\log_axy=\log_ax + \log_ay$\\\\$\log_a \left(\dfrac{x}{y}\right)=\log_ax - \log_ay$\\\\$\log_ax^n=n\log_ax$\\\\$\log_ab=c \iff b=a^c$\\\\&\log_aa=1$\\ \end{minipage}}[/tex]
Question 49Part a
Given:
[tex]\log_5 9=A[/tex]
[tex]\log_5 6=B[/tex]
[tex]\log_5 11=C[/tex]
[tex]\begin{aligned}\log_5 \dfrac{9}{55}&=\log_5 9 - \log_5 55\\&=\log_5 9 - \log_5 (11 \cdot 5)\\&=\log_5 9 - (\log_5 11 + \log_5 5)\\&=\log_5 9 - \log_5 11 - \log_5 5\\&=A-C-1\\\end{aligned}[/tex]
Part b
Given:
[tex]\log_3 10=R[/tex]
[tex]\log_3 4=S[/tex]
[tex]\log_3 11=T[/tex]
[tex]\begin{aligned}\log_3 \dfrac{3}{100}&=\log_3 3 - \log_3 100\\&=\log_3 3 - \log_3 (10 \cdot 10)\\&=\log_3 3 - \log_3 10^2\\&=\log_3 3 - 2\log_3 10\\&=1-2R\\\end{aligned}[/tex]
Part c
Given:
[tex]\log_3 4=P[/tex]
[tex]\log_3 10=Q[/tex]
[tex]\log_3 7=R[/tex]
[tex]\begin{aligned}\log_3 25&=\log_3 \dfrac{100}{4}\\&=\log_3 100 - \log_3 4\\&=\log_3 (10 \cdot 10) - \log_3 4\\&=\log_3 10^2 - \log_3 4\\&=2 \log_3 10 - \log_3 4\\&=2Q-P\end{aligned}[/tex]
Question 50The error was in line 4 of the calculation. The log law
[tex]\log_ab=c \iff b=a^c[/tex]was not applied correctly.
The correct solution is:
[tex]\begin{aligned}3 \log (x-3) + 1 & = 7\\3 \log (x-3) & = 6\\\log (x-3) & = 2\\x-3&=10^2\\x&=3+10^2\\x&=103\end{aligned}[/tex]
MAKING FAIR DECISIONS
2. A group of 6 students are in the school chess club. Their teacher has 2 tickets to a chess tournament She wants to make sure she has a fair way of deciding which 2 students will win the tickets. She decides that every time a student wins a chess match, that student's name will be put in a hat for a chance to win the tickets. She will choose two names from the hat at the end of the week
Part A: Is the teacher's method fair? Explain. If it is not fair, explain how you would change her method to make it fair. (5 points: 1 point for correctly deciding whether the method is fair or unfair, 4 points for the explanation and, if it is unfair, for a correction to the method)
Part B: Two new students join the chess club. The teacher wants to include them in the chance to win the tickets. How can she set up a fair way to make the decision that includes everyone? Explain why this method is fair (5 points)
Part A: The teacher's method is partially fair.
Part B: She can set up a fair way to make the decision that includes everyone by making it an open tournament for all such that all can participate.
How can she make the decision to be fair?Part A: The teacher's method is fair in terms of giving all students an equal opportunity to win the tickets by playing chess matches and having their names put into the hat.
However, it does not take into account the skill level of the students, which could result in a less skilled student winning the tickets over a more skilled student. To make the method more fair, the teacher could use a combination of wins and chess ratings to determine which students have the best chance to win the tickets.
Part B: To include the new students in the chance to win the tickets, the teacher could have them play chess matches against the current club members and use a combination of wins and chess ratings to determine the two students who will win the tickets.
This method is fair because it gives all students, including the new ones, the opportunity to compete and be recognized for their chess skills, rather than simply giving the tickets to the two students who have been in the club the longest. Additionally, using a combination of wins and ratings ensures that the most skilled players have a better chance of winning the tickets.
Therefore, the correct answer is as given above
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3.3x0.14 = ?
hazgxjklkkspkoxdh
Answer:
Step-by-step explanation:
0.462
Answer:
0.462 :) hope this helps and please put me as brainiest thankyou !!
Step-by-step explanation:
Which expression is equivalent to 64x - 16?
O 16(4x + 1)
O-16 (4x - 1)
16(4x - 1)
- 16(4x + 1)
whoever answers first will be brainlyist
what is the largest power of 10 that is a factor of the following numbers, i.e., how many zeroes are at the end of the decimal representation? a. 50! b. 1000!
In 50! will have 12 leading zeroes so the power of 10 will be 12 And for 1000! will have 249 Zeroes so here the power of 10 will be 249.
We calculate the leading zeroes by knowing the numbers 2 And 5 So
This number must end with 249 zeroes since there are 249 fives (and more than 249 twos) in its prime factorization. Thus 10 249 is the highest power of 10 that divides 1000!
To see why we have 249 powers of five:
there are 200 numbers ≤ 1000 that are multiples of 5there are 40 numbers ≤ 1000 that are multiples of 5^2 = 25there are 8 numbers ≤ 1000 that are multiples of 5^3 = 125there is 1 number ≤ 1000 is a multiple of 5^4 = 625200 + 48 + 8 + 1 = 249
And also we can do this with a formula n−σp(n)/(p−1) where σp(n) is the sum of the digits of n written in base-p
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.
Solve the equation
1
4
(4x − 24) + x = 14.
The solution to an equation is 10.Solving an equation refers to the process of determining its solution.
Which one provides an answer to the problem?A variable's value that, when substituted into the equation, results in a true assertion is known as the solution. Solving an equation refers to the process of determining its solution. Finding the value of the variable that causes an equation to hold true is referred to as finding the solution to an equation.Solving an equation refers to the process of determining its solution. Finding the value of the variable that causes an equation to hold true is referred to as finding the solution to an equation.Make the available
14to obtain the desired amount:
x – 6 + x = 14
Put similar phrases together to get:
2x – 6 = 14
Adding 6 to both sides yields:
2x = 20
x = 10.
The complete question is,
1 4 (4x 24) + x = 14 must be solved.
By dividing the 1 by 4, you can obtain:
Put similar phrases together to get:
Adding 6 to both sides yields:
x =
Consequently, is the necessary response.
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