Answers
The average rate of change of function \(g(x)=5(2)^{x}\) from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.
The correct option is (A).
What is the average rate of change of a function?
The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function.
Using function notation, we can define the Average Rate of Change of a function f from a to b as:
\(rate(m) = \frac{f(b)-f(a)}{b-a}\)
The given function is \(g(x) = 5(2)^{x}\),
Now calculating the average rate of change of function from x = 1 to x = 2.
\(m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(2)-g(1)}{2-1}\\\\m=\frac{5(2)^{2}-5(2)^1}{2-1}\\ m=\frac{10}{1} \\m=10\)
Now, calculate the average rate of change of function from x = 3 to x = 4.
\(m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(4)-g(3)}{4-3}\\\\m=\frac{5(2)^{4}-5(2)^3}{4-3}\\ m=\frac{40}{1} \\m=40\)
The jump from m = 10 to m = 40 is "times 4".
So option (A) is correct.
Hence, The average rate of change of function \(g(x)=5(2)^{x}\) from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.
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Related Questions
£410 is divided between Gordon, Malachy & Paul so that Gordon gets twice as much as Malachy, and Malachy gets three times as much as Paul. How much does Malachy get?
Answers
The amount of money that Malachy get is £123 .
In the question ,
it is given that ,
£410 is divided between Gordon, Malachy and Paul .
also given that Malachy gets three times as much as Paul ,
let the amount that Paul get = x .
So , the amount that Malachy get = 3x
it is given that Gordon gets twice as much as Malachy ,
that means , the amount that Gordon get = 2(3x) = 6x
given the total amount is £410 ,
So, equation representing the total amount is
x + 3x + 6x = 410
4x + 6x = 410
10x = 410
x = 410/10
x = 41
So , the amount that Paul get = £41 ,
amount that Malachy get = 3(41) = £123
amount that Gordon get = 6(41) = £246
Therefore , The amount of money that Malachy get is £123 .
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Electric utility poles in the form of right cylinders are made out of wood that costs $25.37 per cubic foot. Calculate the cost of a utility pole with a diameter of 1.5 ft and a height of 45 ft. Round your answer to the nearest cent.
Answers
The cost of the utility pole is approximately $593.96.
What is volume?Volume is a measure of the amount of space occupied by a three-dimensional object. It is usually measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), or cubic feet (ft³). The volume of an object can be found by measuring its length, width, and height and using a formula that relates these dimensions to the amount of space the object occupies. In geometry, the most common shapes for which volume is calculated include cubes, spheres, cylinders, pyramids, and cones.
The volume of a right cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height.
In this case, the diameter of the utility pole is 1.5 ft, so the radius is 0.75 ft. The height is 45 ft. Therefore, the volume of the utility pole is:
V = π(0.75 ft)²(45 ft) = 23.3826... cubic feet
Rounding to the nearest hundredth, we get:
V ≈ 23.38 cubic feet
The cost of wood per cubic foot is $25.37. Therefore, the cost of the utility pole is:
$25.37/cubic foot × 23.38 cubic feet ≈ $593.96
So the cost of the utility pole is approximately $593.96.
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could you graph the function f(x)=5x using itercepts? explain you reasoning
Answers
Answer:
The xxx-intercept is the point where a line crosses the xxx-axis, and the yyy-intercept is the point where a line crosses the yyy-axis.
Step-by-step explanation:
Find the area of the trapezoid. The median is equal to 25cm and the height is 8cm. (btw if you explained how to find the base would help a lot) :)
Answers
The area of trapezium with a median of 25 cm and height of 8 cm = 200 cm².
What is the Area of a Trapezium?Area of trapezium = 1/2(a + b)h, where a and b are the parallel bases of the trapezium, and h is the height.
Note, median of a trapezium = half of the sum of the length of the two bases of a trapezium = 1/2(a + b). Therefore, the area of a trapezium with a given median would be:
A = median length × height
Given the following:
Median = 25 cmHeight = 8 cm.Area of trapezium = 25 × 8 = 200 cm².
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if the growth rate r of a population is positive and remains constant, the number of people added to the population:
Answers
The number of persons added to the population rises annually if the population's growth rate, r, is positive and stable.
Given statement,
If the growth rate r of a population is positive and remains constant, the number of people added to the population,
In the given case the solution will be the number of people added to the population " increases each year ".
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can someone help me. this is geo. if you could help that would mean to me
Answers
Answer:
1.) x = 37
2.) m<SVW = 74 deg
3.) m<TWV = 106 deg
Step-by-step explanation:
Linea SY and TZ are shown to be parallel.
Angles SVW and TWV are same-side interior angles.
Theorem:
If parallel lines are cut by a transversal, then same-side interior angles are supplementary.
m<SVW + m<TWV = 180 (by the definition of supplementary angles)
2x + 3x - 5 = 180
5x - 5 = 180
5x = 185
x = 37
m<SVW = 2x = 2(37) = 74
m<TWV = 3x - 5 = 3(37) - 5 = 111 - 5 = 106
Answer:
1.) x = 37
2.) m<SVW = 74 deg
3.) m<TWV = 106 deg
if you write this number in standard notation (or decimal notation), how many zeros would you include? 8.47 x 1012
Answers
In standard or decimal notation, the number 8.47 x 10^12 is written as 847 x 10^10. So there are 10 zeroes included in the standard or decimal notation of 8.47 x 10^12.
To convert from scientific notation to standard notation, we move the decimal point to the right or left by the number of places specified by the exponent . The exponent tells us how many places the decimal point should be moved.
The number 8.47 x 10^12 is written in scientific notation. In scientific notation, a number is expressed as a product of a coefficient and a power of 10. The coefficient is 8.47 in this case, and the power of 10 is 12.
The power of 10 indicates the number of zeros that are included in the number. In this case, 10^12 means 10 multiplied by itself 12 times, which is equal to 10,000,000,000,000.
Therefore, the number 8.47 x 10^12 is equal to 8.47 x 10,000,000,000,000.
= 847 x 10^10
So there are 10 zeroes included in the standard or decimal notation of 8.47 x 10^12.
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Help me with this pls
Answers
Answer:
x=65
Step-by-step explanation:
90 degree angle
90-25= 65
It is a straight line with angle measures of 90°, x° and 25° opposite to the angle marked 180°.
Hence, their sum is 180°.
➛\(90 \degree + x + 25 \degree = 180 \degree\)
➛\(115 \degree + x = 180 \degree\)
Then,
➛\( x = 180 \degree - 115 \degree\)
➛\(x = 65 \degree\)
Hence:-The measure of the angle will be 65° (Ans)
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Which Of The Following Statements Are Correct In The Simple CLRM Of One Variable And An Intercept Y=Β1+Β2X+U ? (Choose All Correct Answers) If We Know That Β2^<0 Then Also Β^1≪0. The Sample Correlation Of X And U^ Is Always Zero. The OLS Estimators Of The Regression Coefficients Are Unbiased. The Estimator Of Β2 Is Efficient Because It Has Lower Variance
Answers
The correct statements in the simple classical linear regression model (CLRM) with one variable and an intercept (Y = β1 + β2X + U) are:
1. If we know that β2 < 0, then also β1 < 0.
2. The OLS estimators of the regression coefficients are unbiased.
Let's analyze each statement:
1. If we know that β2 < 0, then also β1 < 0.
This statement is correct. In the simple CLRM, β1 represents the intercept, and β2 represents the slope coefficient. If the slope coefficient (β2) is negative, it implies that there is a negative relationship between X and Y. Consequently, the intercept (β1) needs to be negative to account for the starting point of the regression line.
2. The OLS estimators of the regression coefficients are unbiased.
This statement is correct. In the ordinary least squares (OLS) estimation method used in the simple CLRM, the estimators of β1 and β2 are unbiased. This means that, on average, the OLS estimators will be equal to the true population values of the coefficients. The unbiasedness property is a desirable characteristic of the OLS estimators.
The other two statements are incorrect:
3. The sample correlation of X and U^ is always zero.
This statement is not necessarily true. The error term (U) in the simple CLRM represents the part of the dependent variable (Y) that is not explained by the independent variable (X). The sample correlation between X and the estimated error term (U^) can be different from zero if there is a relationship between X and the unexplained variation in Y.
4. The estimator of β2 is efficient because it has lower variance.
This statement is incorrect. The efficiency of an estimator refers to its ability to achieve the lowest possible variance among all unbiased estimators. In the simple CLRM, the OLS estimator of β2 is indeed unbiased, but it is not necessarily efficient. Other estimation methods or assumptions may yield more efficient estimators depending on the characteristics of the data and the model.
To summarize, the correct statements are:
- If we know that β2 < 0, then also β1 < 0.
- The OLS estimators of the regression coefficients are unbiased.
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HELP ASAP!!! THANK YOUUUUU :)
Jeffery surveyed 50 randomly selected workers at a factory. He collected data about the individual output of a worker on an average day. The results are shown using the box-and-whisker plot. What percent of workers have output more than 70 units?
50%
30%
15%
25%
Answers
Answer:
25%
Step-by-step explanation:
In which of the following cases is the construction of triangle ABC possible?
Answers
Triangle with sides AB = 8cm , CA = 5cm , BC = 7cm and AB = 7cm , BC = 10cm , CA = 8cm can construct a Triangle.
What are cases for construction of triangle?Condition : For forming the triangle, the sum of two sides must be greater than the third side.
a. AB = 4cm, CA = 3cm, BC = 10cm
CA+BC=AB
3+1=4
4=4
Therefore, it cannot form a triangle because it is not satisfying the condition.
b. AB = 8cm , CA = 5cm , BC = 7cm
AB+CA>BC
AB+BC>CA
CA+BC>AB
Therefore, it can form a triangle because it satisfies the condition.
c. AB = 7cm, BC = 10cm, CA = 8cm
AB+BC>CA
AB+CA>BC
BC+BC>AB
Therefore, it can form triangle because it satisfies the condition.
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In a horse race, how many different finishes among the first 3 places are possible if 10 horses are running?
Answers
There are 720 possible horse combinations for the first 3 places in the race.
To solve this problem, let us break this down one by one.
There are 10 possible horses that could win in first place.
Therefore, this means that for each of these possibilities, there are now 9 horses that could come in second.
So there are 10 x 9 possible combinations for the first 2 places.
10 x 9 = 90.
And for each of those combinations, there are also 8 possible horses that could come in the third place. So
10 x 9 x 8 = 720
There are 720 possible horse combinations for the first 3 places in the race.
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Help!! Find m
this is geometry btw
Answers
The measure of angle ABD as required to be determined from the task content is; 32°.
What is the measure of angle ABD?As evident in the task content;
m<ABD + m<CBD = m<ABC = 90°.
This follows from the fact that the angle ABC is a right angle.
4x - 4 + 2x + 40 = 90
6x = 54
x = 54 / 6 = 9
Ultimately, the measure of angle ABD is; 4(9) - 4 = 36 - 4 = 32.
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Help help help help please please thank
Answers
Answer:
it's the 2nd answer.....
Answer:
(7×7×7×7×7)(7×7×7×7×7)(7×7×7×7×7)
Step-by-step explanation:
Properties of exponents state that in this case, the exponents multiply together. So, 5×3 is 15. Now it is \(7^{15}\)
A machine stamps 330 parts in 11 minutes. Find the unit rate in parts per hour.
Answers
Answer:
1,800 parts per hour
Step-by-step explanation:
330 parts = 11 min
330/11=30
30 parts = 1 min
60 min = 1 hour
30x60min=1,800
1,800 parts per hour
100 points!
The slope of a line is - 1/3 . Find the slope of a line that is perpendicular to this line.
-3
1/3
3
Answers
Answer:
3
Step-by-step explanation:
The equation of a perpendicular line to m = - \(\frac{x}{3}\) must have a slope that is the negative reciprocal of the original slope.
m perpendicular = - \(\frac{1}{\frac{-1}{3} }\)
Simplify the result.
m perpendicular = 3
The answer is:
3
Work/explanation:
If two lines are perpendicular to each other, their slopes will be negative inverses.
The slope of the given line is \(\sf{-\dfrac{1}{3}}\).
The negative inverse of that is 3; so I changed the sign from negative to positive, and flipped the number.
Hence, the slope is 3.using a rank size rule equation, if the population of the 4th largest city in country a is 8 million, what is the population of the largest city in that country? 16 million 24 million 32 million 64 million
Answers
The city at 1st position with the largest population, have a population of 64 million.
Given, the population of the 4th largest city in country a is 8 million.
we have to find the population of the largest city in that country and
we have options : 16 million, 24 million, 32 million and 64 million
As, the given city with 8 million population is at 4th position in the country.
then, the city at 3rd position will be having a population of 2×8 million i.e. 16 million
similarly, the city at 2nd position will be having a population of 2×16 million i.e. 32 million
and the city at 1st position will be having a population of 2×32 million i.e. 64 million.
So, the city at 1st position have a population of 64 million.
Hence, the city at 1st position have a population of 64 million.
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3 coins what is the probability of flipping all tails
Answers
To determine the probability of flipping all tails with 3 coins, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Each coin flip has two possible outcomes: heads or tails. Since we have 3 coins, the total number of possible outcomes is 2^3 = 8, as each coin can independently have two outcomes.
Out of these 8 possible outcomes, there is only one outcome where all three coins land on tails. Therefore, the number of favorable outcomes is 1.
The probability of flipping all tails is calculated by dividing the number of favorable outcomes by the total number of possible outcomes: 1/8.
Thus, the probability of flipping all tails with 3 coins is 1/8 or 0.125, which can also be expressed as a percentage of 12.5%.
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there were 40 questions on Roberts test. How many problems did Robert get right if he received an 87.5% oh his test?
Answers
Answer:
Robert got 35 problems right if he received an 87.5% oh his test.
Step-by-step explanation:
Total questions = 40As Robert got right 87.5% on his test.
so the expression becomes
87.5% × 40
= 87.5/100 × 40
= 0.875 × 40
= 35
Therefore, Robert got 35 problems right if he received an 87.5% oh his test.
What is the product?
Answers
Answer:
Step-by-step explanation:
[ 5x2=10 5x3=15 5x4=20]
[5x9= 45 5x(-1)=-5 5x(-7)= -35]
[5x11=55 5x5=25 5x(-3)= -15]
answer is A
The logarithmic expression \(log_{b}(\frac{1}{b^{-b}} )\) where b > 0, is equal to
a) \(b^{-b}\)
b) \(b^{b}\)
c) \(-b\)
d) \(b\)
Answers
\(\log_b \left(\dfrac 1{b^{-b}}\right)\\\\=\log_b (b^{-b})^{-1}\\\\=\log_b b^b\\\\=b \log_b b\\\\=b \cdot 1\\\\=b\)
20 out of 45 students attended the concert; 12 out of 25 students attend the concert is it equivalent or not
Answers
Answer:
Step-by-step explanation:
No
If the equation ax = b is consistent, then its solution set is obtained by translating the solution set of ax = 0. true or false?
Answers
True, ax=b requires only one solution to be homogeneous. If ax=b is consistent, the ax=b solution set is acquired by translating the ax=0 solution set.
What is consistent?A two-linear equation system can have one solution, an infinite number of solutions, or even no solution. The number of solutions distinguishes equation systems.
Some key features regarding the consistent are-
A system is said to be consistent if it has at least one solution.A consistent system is independent if it has exactly one solution.It is dependent if a consistent system does have an infinite number of solutions. When the equations are graphed, they constitute the same line.A system is considered to be inconsistent if it has no solution. Because the line graphs do not intersect, the graphs are parallel, and that there is no solution.Therefore, if the equation ax=0 has a trivial solution, the columns of the a matrix A are linearly independent.
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Select the correct answer.
An image of two lines m and n parallel to each other. Lines p and q are parallel to each other. Line p and n for a hundred degrees angle. The angle formed by lines q and m is marked x.In the figure, lines m and n are parallel to each other. Lines p and q are also parallel to each other. What is the value of x?
A.
40°
B.
80°
C.
100°
D.
180°
Answers
if Lines p and q are also parallel to each other then value of x is 100, option C is correct.
What are Parallel lines?Parallel lines are coplanar infinite straight lines that do not intersect at any point.
The known angle is supplementary with angle A (Look at the attachment), that means that the sum of the known angle and A is 180°, therefore the value of angle A is 80°
Angle A and B are corresponding angles, which means that they have the same value, that happens because p and q are parallels and both cut line n in the same way. the value of the angles B is 80°
Angles B and C are corresponding too, so the value of the angle C is 80°.
Angles C and X are supplementary too for which the sum of X and C is 180°, so the value of X is 100°
Hence, if Lines p and q are also parallel to each other then value of x is 100, option C is correct.
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. if you owned this stock, would you want a positive or negative slope? why?
Answers
Answer:
positive slope
Step-by-step explanation:
You want a positive slope so you get more money, positive slopes grow from left to right. Which, starting from the origin means your stock value would increase. This is unless you want to lose money.
A coffee shop is running a promotion where a number of free coffee samples are given away each day. The equation above can be used to model the number of free coffee samples, y, that remain to be given away x days after the promotion began. What does it mean that (11, 0) is a solution to this equation?
110xy = 1,210
A) During the promotion, 11 samples are given away each day.
B) It takes 11 days during the promotion to see 1,210 customers.
C) It takes 11 days during the promotion until none of the samples are remaining.
D) There are 11 samples available at the start of the promotion
Answers
Answer:
C
Step-by-step explanation:
First, let us clarify what (11, 0) represent
(x, y) ---> (11, 0)
The values are as followed:
x = 11
y = 0
If the problem states that x is the number of days after the promotion started, then it will be 11 days.
When we assert that it has been 11 days, we rule answers A and D.
If the problem states that y is the number of free coffee samples that remain after 11 days (because x is included in this statement), then it will be 0 samples.
Therefore, the answer will be C. After 11 days of the promotion, there will be 0 samples that are left.
THIS IS STATEMENT AND REASON PLSS HELP!
Answers
Answer:
Line FH is the same as FK
Step-by-step explanation:
The triangle on the left is the same on the right, but inverted. This is proved because lines eh equals gk and angle e and g are the same.
Answer:
line fh is the same as fk
Please help me with this homework
Answers
The equation for slope is rise over run. Y is the rise and X is the run. The point equation is (y2-y1)/(x2-x-1) = slope.
Plugging in the numbers: (-4-1)/(-4-0) = 1.25
Answer:
5/4
Step-by-step explanation:
Slope = Rise↕/Run↔
In other words, from coordinates (-4,-4) go up 5 units then go right 4 units, to get to coordinates (0,1).
Hope this makes sense :)
Can someone help me ASAP? It’s due today
Answers
The only option that represents an independent event is: Option C: "Spinning a Spinner with eight evenly spaced sections, then spinning it again.".
How to Identify Independent Events?Independent events are defined as those events whose occurrence is not dependent on any other event. For example, if we flip a coin in the air and get the outcome as Head, then again if we flip the coin but this time we get the outcome as Tail. In both cases, the occurrence of both events is independent of each other.
Looking at the given options, the only one that represents an independent event is "Spinning a Spinner with eight evenly spaced sections, then spinning it again.".
This is because each event does not depend on another one of the events being described.
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solve 15 2x = 36. round to the nearest ten-thousandth.
Answers
To solve the equation 15 + 2x = 36, we can start by subtracting 15 from both sides of the equation to get 2x = 21. Then, we can divide both sides by 2 to get x = 10.5. Rounded to the nearest ten-thousandth, the solution is x = 10.5000.