Option D is correct the answer. The average rate of change over the interval 1 < x < 5 is greater than the average rate of change over the same interval for the function g(x) = 1. 8x2 is k(x) = 2x^2
The average rate of change:
Given a function y, the average rate of change S of y=f(x) in an interval (xs,xf) will be given by the following equation:
[tex]S=\frac{f(xf)-f(xo)}{xf-xo}[/tex]
In this problem, we have that:
Interval (1,5), so xf=5,xo=1
Then
[tex]S=\frac{f(5)-f(1)}{4}[/tex]
All options are compared to g(x).
[tex]g(x)=1.8x^{2}[/tex]
g(5) = 1.8*(5)^2 = 45
g(1) = 1.8*(1)^2 = 1.8
[tex]S=\frac{45-1.8}{4} =10.8[/tex]
A.=f(x) = x^2
f(5) = 5^2 = 25
f(1) = 1^2 = 1
[tex]S=\frac{25-1}{4} =6.25[/tex]
Smaller than 10.8, so this is not the answer.
B.=g(x) = 1.2x^2
g(5) = 1.2*(5)^2 = 30
g(1) = 1.2*(1)^2 = 1.2
[tex]S=\frac{30-1.2}{4} =7.2[/tex]
Smaller than 10.8, so this is not the answer.
C.=h(x) = 1.5x^2
h(5) = 1.5*(5)^2 = 37.5
h(1) = 1.5*(1)^2 = 1.5
[tex]S=\frac{37.5-1.5}{4}= 9[/tex]
Smaller than 10.8, so this is not the answer.
D.=k(x) = 2x^2
k(5) = 2*(5)^2 = 50
k(1) = 2*(1)^2 = 2
[tex]S=\frac{50-2}{4} =12[/tex]
Greater than 10.8, this is the answer.
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What i the denity of an object that ha ma of 73,430 kilogram and a volume of 7m exponent 3
The Density of object is 10,490 kg/m³
What is Density, Mass and Volume ?
Measurement of the amount of matter (or stuff) in an object is MassMeasurement of the amount of space an object takes object up is VolumeDensity is defined as mass per unit volume.Given,
Mass = 73,430 Kg
Volume = 7 m³
We know,
Density = Mass / volume
Now, plug in the values
Density = 73430/7
= 10, 490 kg/m³
Hence, the Density of object is 10,490 kg/m³
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Lulu the Lucky puts chests of gems into her treasure vault. Each chest holds the same number of
gems. The table below shows the number of gems Lulu received from three different adventures
and the number of chests she needed to hold the gems.
Number of gems
Number of chests
Adventure A
600
2
Adventure B
1500
5
Adventure C
4800
16
Write an equation to describe the relationship between g, the number of gems, and c, the
number of chests.
Answer:
The relationship between the number of gems and the number of chests can be represented by an equation in the form of g = kc, where g is the number of gems, c is the number of chests, and k is a constant.
To find the value of the constant k, we can substitute the values from one of the adventures into the equation and solve for k. For example, using the values from Adventure A:
g = 600
c = 2
Substituting these values into the equation, we get:
600 = k * 2
Solving for k, we get:
k = 600 / 2 = 300
Therefore, the equation that describes the relationship between the number of gems and the number of chests is:
g = 300c
Using the information provided in the table, we know that for Adventure B, Lulu received 1500 gems and needed 5 chests to hold them. Substituting these values into the equation, we get:
g = 1500
c = 5
Substituting these values into the equation g = 300c, we get:
1500 = 300 * 5
This equation can be used to determine the number of chests needed to hold a given number of gems, or vice versa. For example, to find the number of chests needed to hold 1200 gems, we can substitute 1200 for g and solve for c:
g = 1200
c = 1200 / 300 = 4
Thus, 4 chests would be needed to hold 1200 gems.
use scenario 6-9. what is the probability that the total weight of three randomly selected grapefruits is more than 3.4 pounds?
Answer:
What is scenario 6-9?
Step-by-step explanation:
Gives brainliest for best answer and easy to understand!
Answer: the right answer is D
Step-by-step explanation:
If you multiply 4 by 2 you get 8. If this goes on the answers are aways the same and it’s going to be proportional
A man is considering two companies from which to rent a truck. Triangle Truck Rental charges $20 per day and 35 cents a mile. Circle Rent-A-Truck charges $35 a day and 30 cents a mile. How far would need to drive in one day for the both companies to have the same total cost?
Answer: 300 miles
Step-by-step explanation:
Let x be the number of miles
We have the equation below
20 + 0.35x = 35 + 0.30x
Subtract 20 from both sides
0.35x = 15 + 0.30x
Then subtract 0.30x from both sides
0.05x = 15
Then divide by 0.05 from both sides
x = 300 miles
35. Performance Task A manufacturer can save
money by making a can that maximizes volume
and minimizes the amount of metal used. For
a can with radius r and height h, this goal is
reached when 2 πr^3= πr^2h.
Part A Solve the equation for h. How is the height to the radius for a can that meets the manufacturers goal?
Part B The area of a label for a can is A=2 πrh. Use your result from Part A to write a formula giving the area of a label for a Can that meets the manufacturers goals.
A) The value of h, h = 2r.
The height of the can is two times of the radius.
B) The formula for the Can Area is 4πr².
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
For a can with radius r and height h, this goal is reached when
2 πr³= πr²h
a) 2 πr³= πr²h
Solve for 'h'
h= 2 πr³ / πr²
h = 2r
So, the height of the can is two times of the radius.
b) Now, The area of a label for a can is A=2 πrh.
So, putting h= 2r
Area, A = 2 πrh
= 2πr(2r)
= 4πr²
So, the formula for the Can Area is 4πr².
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What i the lope of the line that pae through the point (1, -9)(1,−9) and (4, -7)(4,−7)?
The slope of the line is 2/3.
What is a line?
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.
Given coordinates of the points are A(1,-9) and (4,-7).
The formula of slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).
Here x₁ = 1, y₁ = -9, x₂ = 4, and y₂ = -7
m = (-7 - (-9))/(4 - 1)
m = 2/3
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Fluffy Stuffy Stuffed Animals wants to sell their stuffed animals in a local toy store. In which store should they sell their products if they hope to make the most money?
HELP ME PLEASE
Drag the tiles to the correct locations on the table. Not all tiles will be used.
Match each quadratic function with the attributes of its parabolic graph.
The quadratic functions given are matched with the parameters as follows
f(x) = -0.3(x - 2)² + 5 f(x) = 0.2(x + 2)² - 5
vertex (-2, 5)
axis of symmetry, x = -2 axis of symmetry, x = 2
focus f (-2, 4 1/6) focus f (2, -3 3/4)
How to find the axis of symmetry of parabolic functionBoth the vertex form and the standard form of the quadratic equation are used in the axis of symmetry formula. Any geometric shape is divided into two equal halves by the symmetry.
Parabolic equation in vertex form is written as
f(x) = a (x - h)² + k
the vertex is v (h, k)
f(x) = -0.3(x - 2)² + 5, v (-2, 5)
f(x) = 0.2(x + 2)² - 5, v ( 2, -5)
The axis of symmetry formula is given as, x = h
f(x) = -0.3(x - 2)² + 5, x = -2
f(x) = 0.2(x + 2)² - 5, x = 2
the focus, f (h, k + 1/4a)
f(x) = -0.3(x - 2)² + 5, f (-2, 5 + 1/(4 * -0.3)) = f(-2, 5 - 5/6) = f (-2, 4 1/6)
f(x) = 0.2(x + 2)² - 5, f (2, -5 + 1/(4 * 0.2)) = f(2, -5 + 1/0.8) = f (2, -3 3/4)
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Please help I’m giving brainlyest
Answer:
A. Eight-four percent of 6th grade girls surveyed prefer cereal A
Step-by-step explanation:
Out of 100 6th grade students, 50 were girls and 50 were boys.
42% of the 100 students i. e. 42 were girls who preferred cereal A
Percentage of girls who liked cereal A = (42/50)x100%
= 84%
Answer:
A
Step-by-step explanation:
42% of entire 6th grade girls were surveyed
it means that 84% of ONLY the 6th grade girls liked Cereal A
If f(x) is a third degree polynomial function and g(x) = f(2x), which of the following must be true?
A f(x) and g(x) have the same x-intercepts.
B f(x) and g(x)have the same y-intercepts.
Option A is the correct answer
what is a polynomial?
A polynomial function is made up of terms called monomials; If the expression has exactly two monomials it’s called a binomial. A third-degree polynomial is of the form f(x) = ax³ + bx²+ cx + d where is not equal to zero. It is also called a cubic polynomial as it has a degree of 3.
Given here the polynomial as g(x) = f(2x)
=8ax³ + 4bx²+2cx + d
Both the polynomial have the same constant d and therefore the same y-intercept.
Hence, the correct option is B
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The cuboid-shaped cake below has a total height of 7 cm. The top layer, the cream, and the jam have a combined height of 2 cm. Work out the volume of the bottom layer of the cake. Give your answer in cm³.
Answer:
360 cm³
Step-by-step explanation:
height of bottom layer = 7 - 2 = 5cm
Volume = 9 · 8 · 5 = 360 cm³
How much work have you done if you lift a 5 newton box 1.5 meters off the ground?
Answer:
7.5 joules
Step-by-step explanation:
The amount of work done on an object is equal to the force applied to the object times the distance over which the force is applied. In this case, the force applied to the box is 5 newtons and the distance over which the force is applied is 1.5 meters.
The amount of work done on the box is therefore 5 newtons * 1.5 meters = 7.5 joules. This is the amount of energy that has been transferred to or from the box as a result of the force applied to it.
Which of the following is a linear function? a.f(x)=2x-3 b.f(x)=x²+3 c.f(x)=2x³ d.x=3-2x?
Answer: A
Step-by-step explanation:
:D
the answer is A. because x² is quardatic function and x³ is cubic function
Complete the two-column proof.
Given: <1 and <6 are supplementary
Prove: a//b
The lines a and b are parallel. The proof is given.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Given:
Statement 1:
∠1 and ∠6 are supplementary.
Justification:
If two angles sum up to 180 degrees, they are referred to as supplementary angles.
That means,
∠1 + ∠6 = 180°
∠1 = 180°- ∠6
∠1 =∠5, given that the angles are made by intersecting lines.
Statement 2:
∠1 ≅∠4
Justification:
Vertical angles are also congruent angles, meaning they are equal or have the same measurement.
Two crossing lines actually create two sets of opposite angles that, when the measures of their angles, are added all together.
Since, ∠1 ≅∠4
That means, ∠4 and ∠6 are supplementary.
Statement 3:
∠4 and ∠6 are supplementary.
Justification:
If two angles sum up to 180 degrees, they are referred to as supplementary angles.
Statement 4:
a and b are parallel lines.
Justification:
This means that lines a and b make the same angle with the intersecting line, meaning they don't intersect each other at any point.
a and b are parallel lines.
Therefore, the all statements are true.
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The ratio of cars to pickup trucks in a parking lot is 4 to 1. There are
252 cars in the parking lot. How many pickup trucks are in the lot?
HELP
Answer:
63
Step-by-step explanation:
using the ratio
[tex] \frac{4}{1} = \frac{252}{x} [/tex]
cross multiply
[tex]4x = 252[/tex]
divide both sides by (4)
[tex] \frac{4x}{4} = \frac{252}{4} [/tex]
x = 63
i hope this helps
The correct answer is x = 63
How did we figure this out?[tex]\boxed{\frac{4}{1}=\frac{252}{x}4x=252\frac{4x}{4} =\frac{252}{4}x=63 }\\\huge\boxed{\underline_ So, \frac{4}{1}=\frac{252}{\bold{63}} }[/tex]
Therefore, the correct answer is x = 63
a statistics instructor wants to use the number of hours studied to predict exam scores in his class. he wants to use a linear regression model. data from previous years shows that the average number of hours studying for a final exam in statistics is 8.5, with a standard deviation of 1.5, and the average exam score is 75, with a standard deviation of 15. the correlation is .76. should the instructor use linear regression to predict exam scores for a student who studied 10 hours for the final? write the letter of the correct answer.
Yes, the instructor should use linear regression to predict exam scores for a student who studied 10 hours for the final.
What is meant by linear regression?A variable's value can be predicted using linear regression analysis based on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.
What is linear regression vs non-linear?Nonlinear regression uses a curve to associate the variables, whereas linear regression uses a straight line.
If a clear linear relationship can be shown on the scatterplot, linear regression may be useful. The use of linear regression is appropriate because there is a high correlation. So, it is concluded that it is beneficial for instructor to use linear regression.
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the researcher will conduct a chi-square test of independence. which pair of variables can the researcher use?
The researcher can use two categorical variables or two values from a contingency table to perform chi - squared test.
A standard hypothesis test used to analyze contingency tables with large sample sizes is the chi-squared approach. This test is designed to examine if two categorical factors influence the test statistic independently. Pearson's chi-squared test and its variants are true when the test statistic equals chi-squared under the null hypothesis.
Pearson's chi-squared test is used to determine whether there is a statistically significant difference between expected and observed frequencies for one or more contingency table categories. For contingency tables with fewer samples, a Fisher's exact test is employed instead.
In the traditional application of this exam, observations are classified into mutually exclusive kinds. If the null hypothesis is correct and there are no variations in the population between classes, the test statistic generated by the data has a two-frequency distribution.
The test's purpose is to estimate how likely observed observed frequencies are if the null hypothesis is true.
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a quantity with an initial value of 800 grows exponentially at a rate of 5.5% every 10 minutes. what is the value of the quantity after 30 minutes, to the nearest hundredth?
940 is the initial value, to the closest hundredth, after 30 minutes when amount that starts out at 800 increases exponentially at a rate of 5.5% every 10 minutes.
Given that,
An amount that starts out at 800 increases exponentially at a rate of 5.5% every 10 minutes.
We have to find what is the quantity's value, to the closest hundredth, after 30 minutes.
We know that,
Formula is
S=a(r+1)ⁿ
Here,
S is initial value
a is 800
r is 5.5%
n is time 30/10
800×(5.5%+1[tex])^{30\div10}[/tex]
=939.3931
Therefore, 940 is the quantity's value, to the closest hundredth, after 30 minutes when amount that starts out at 800 increases exponentially at a rate of 5.5% every 10 minutes.
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Answer:
939.39
Step-by-step explanation:
what is the average rate of change of the number of chevy car sales from 1990 to 1992? model year color sales chevy 1990 red 5 chevy 1990 white 87 chevy 1990 blue 62 chevy 1991 red 54 chevy 1991 white 95 chevy 1991 blue 49 chevy 1992 red 31 chevy 1992 white 54 chevy 1992 blue 71 ford 1990 red 64 ford 1990 white 62 ford 1990 blue 63 ford 1991 red 52 ford 1991 white 9 ford 1991 blue 55 ford 1992 red 27 ford 1992 white 62 ford 1992 blue 39
The average rate of change of the number of chevy car sales from 1990 to 1992 is 1
What is the average change rate?
The average rate of change is the rate at which one value in a function changes in relation to another. Usually, the average rate of change is used to calculate the slope of a graphed function.
The average rate of change of a function is determined by the slope of the line connecting the two endpoints of a specific interval (known as the secant line).
According to the given question:
The average rate of change of the number of chevy car sales from 1990 to 1992 is (total chevy car sold in 1992- total chevy car sold in 1990)/ Total difference in no. of years
That gives (156-154)/2
So, the average rate of change of the number of chevy car sales from 1990 to 1992 is 1
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A train travels from City A to City B. The table below shows the distance and the amount of time it takes on the train.
Answer:
The train does not go the same distance each minute.Approximately 6 minutes.--------------------------------------------
The distance traveled in each minute is a speed.
Find the speed per min for each distance:
9/3 = 3 km/min,12/4 = 3 km/min,18/9 = 2 km/min.Since the speed is not same over the total distance, the first choice is correct.
Find the average speed over the given distance:
(9 + 12 + 18)/(3 + 3 + 2) = 39/8 = 4.875 km/minFind the predicted time to travel 30 km:
30 / 4.875 ≈ 6.15 min
how can graphics and/or statistics be used to misrepresent data? where have you seen this done?
(1) We incorrectly interpret the beta number, compare the two, and draw the inference that because the beta for years is greater than the beta for income, the beta for years of experience is stronger.
(2) The ANOVA will reveal who consistently does better in terms of the typical amount of time needed to finish a job.
1) Assume you predicted the variable "Number of Promotion Earned" by regressing it against just two other variables, "Income in $s" and "Years of Experience."
When compared to the beta for years of experience, the income beta is quite modest. You incorrectly interpret the beta number, compare the two, and draw the inference that because the beta for years is greater than the beta for income, the beta for years of experience is stronger.
But until we standardize the variables, this is incorrect. Then they can be put side by side.
2) As HR, I was questioned about whether employees who earn more money perform better. Do those with higher salaries complete the same task more quickly? I've been given data with two columns: "HIGH" salary people's income, and "LOW" salary people's income.
I conduct an ANOVA method test on two groups of individuals and track their typical completion time. The ANOVA will reveal who consistently does better in terms of the typical amount of time needed to finish a job.
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The complete question is:
First, how can graphics and/or statistics be used to misrepresent data? Where have you seen this done? Second, image that you are a human resources (HR) analyst reporting to a recently hired supervisor. Your supervisor has asked you to provide an example of data processed by HR. Describe one type of data that an HR department may process, and discuss a corresponding statistical method that may be used to summarize the data.
If CD=9 and DE= 15. AB = 20, what is the length of AD?
Answer:
12
Step-by-step explanation:
4) A 2-gallon container of laundry detergent costs $22.00. What is the price per quart?
Submit
4 quarts in a gallon, 8 quarts in 2 gallons, so 32.40 divided by 8 is $4.05..
each quart cost 4 dollars and 5 cents
Step-by-step explanation:
The price per quart will be $4.05.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
It should be noted that 4 quarts are in a gallon. Therefore, since the 2-gallon container of laundry detergent costs $22.00. The price per quart will be:
= $22.00 / (4 × 2)
= $4.05
The price is $4.05.
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Can someone help me with Question 2b of this assignment? I'd deeply appreciate it! :)
Value of x is -6
According to question
(x/2)-6 = 2+(2x+1)
⇒x-12/2 = 3+2x
⇒x-12=2(3+2x)
⇒x-12=6+4x
⇒-3x=18
⇒x=18/-3
∴x=-6
The value of x is -6.
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Answer:
x = - 6
Step-by-step explanation:
(b)
[tex]\frac{1}{2}[/tex] x - 6 = 2 + (2x + 1) ← remove parenthesis
[tex]\frac{1}{2}[/tex] x - 6 = 2 + 2x + 1
[tex]\frac{1}{2}[/tex] x - 6 = 2x + 3 ( add 6 to both sides )
[tex]\frac{1}{2}[/tex] x = 2x + 9 ( multiply through by 2 to clear the fraction )
x = 4x + 18 ( subtract 4x from both sides )
- 3x = 18 ( divide both sides by - 3 )
x = - 6
Amadou bought a pair of sunglasses online for $60. He used a coupon code to get a 40% discount. The website also applied a 15% processing fee to the price after the discount. How much was the discount, in dollars and cents?
A total discount of $18.6 and 1860 cents is availed by Amadou in buying pair of sunglasses after the final step of processing charge.
Given the intital price as $60 i.e cost price
given he had a coupon code to get discount of 40%
so after apply discount the price of pair of sunglasses is [tex]\frac{100-40}{100} *60[/tex]
=> 0.6 *60
=>36
so the current price of pair of sunglasses is $36
now we need to apply 15% processing fee after the discount so the current price of pair of sunglasses will increase from previous value and is given by:
[tex]36 + \frac{15}{100} *36[/tex]
=>36 + 5.4
=> 41.4
so the final price of pair of sunglasses is $ 41.4
Total discount = initial price - final price
=> 60- 41.4
=> $18.6
$1 = 100 cents
so total discount = 18.6 *100 = 1860 cents
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consider the function below. f(x) = x2e−x (a) find the exact value of the minimum of f for x ≥ 0.
The exact value of the minimum of function f(x) = x^2 e^−x for x ≥ 0 is f(x) = 0
In this question we have been given a function f(x) = x^2 e^−x
We need to find the exact value of the minimum of function for x ≥ 0.
Consider the first derivative of the function
f'(x) = x^2 f/dx(e^−x) + e^−xd/dx(x^2)
f'(x) = -x^2 e^(-x) + e^-x (2x)
f'(x) = xe^-x (2 - x)
To find the critical points., consider f'(x) = 0
xe^-x (2 - x) = 0
xe^-x = 0, (2 - x) = 0
x = 0, x = 2
Substitute the value of critical point into the function.
f(0) = 0^2 e^(0)
f(0) = 0
and f(2) = 2^2 e^-2
f(2) = 0.5413
This means, the minimum of the function occurs at x = 0
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Prove that the difference between quare of conecutive even number i alway a multiple of 4
let n tand for any integer in your working
It is proved that the difference between squares of consecutive even numbers is always a multiple of 4.
Let's consider two consecutive even numbers.
If n = a positive integer
Then the 1st even number would be = 2n
Let the next consecutive even number = 2(n+1)
The consecutive even numbers would be:
2n, 2(n+1)
The square of each consecutive even number is given by -
(2n)² = 2n ×2n = 4n²
[2(n+1)]² = (2n+2)² =(2n+2)(2n+2)
Expanding, we get,
= 4n² +4n +4n+4
[2(n+1)]² = 4n²+8n+4
To determine if the difference between squares of consecutive even numbers is always a multiple of 4, we would substitute values for ' n ' to find the differences between the squares of each consecutive even number.
Let n = 1, 2, 3
For n= 1,
4n² = 4(1)² = 4×1 = 4
4n²+8n+4 = 4(1)² + 8(1) + 4
= 4+8+4 = 16
Thus, the difference between the squares of consecutive even numbers = 16-4 = 12
For n= 2,
4n² = 4(2)² = 4×4 = 16
4n²+8n+4 = 4(2)² + 8(2) + 4
= 16+16+4 = 36
Thus, the difference between the squares of consecutive even numbers = 36-16 = 20
For n= 3
4n² = 4(3)² = 4×9 = 36
4n²+8n+4 = 4(3)² + 8(3) + 4
= 36+24+4 = 64
Thus, the difference between the squares of consecutive even numbers = 64-36 = 28
Clearly, we can see that 12, 20, and 28 are multiples of 4.
Therefore, the difference between squares of consecutive even numbers is always a multiple of 4.
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(Attached image) PLEASE HELP!!!!
Answer:
So the answer is A and D
Step-by-step explanation:
I think it is A and D cause it is 3 and -3 its a bigger number and smaller number
or
A school needs 6,062 slices of pizza for a pizza party. If each pizza has 14 slices, how many pizzas should the school buy?
Answer:
433 pizzas
Step-by-step explanation:
6062 / 14 = 433