For each conjecture below, you are to describe in words what the Null Hypothesis and Alternative Hypothesis are. Consider the decision that you have to make based upon your conjectures. Explain in words or with a chart what the Type I and Type II errors mean in context. Finally, describe the ramifications of making these errors within the context of the problem and describe which of the 2 errors are worse (in your opinion).
1. It is believed that a new drug can cure a cold.
2. The teacher will never check homework today.
3. In a big store like Wal-Mart, they will never catch me if I shoplift.
4. If I try to learn to ski, I will end up hurting myself.

Answers

Answer 1

Type I error is generally worse than a Type II error in all of these scenarios, as it can have more severe consequences.

The Null Hypothesis is a statement that assumes that there is no significant difference or effect between two groups or variables. The Alternative Hypothesis is a statement that assumes that there is a significant difference or effect between two groups or variables.

Conjecture: It is believed that a new drug can cure a cold.

Null Hypothesis: The new drug does not cure a cold.

Alternative Hypothesis: The new drug does cure a cold.

Type I error: We conclude that the drug cures a cold, but it does not.

Type II error: We conclude that the drug does not cure a cold, but it actually does.

Ramifications: If we make a Type I error, we may give the drug to people who do not need it, which can have negative side effects. If we make a Type II error, people who could have benefited from the drug will not receive it.

Conjecture: The teacher will never check homework today.

Null Hypothesis: The teacher will check homework today.

Alternative Hypothesis: The teacher will not check homework today.

Type I error: We conclude that the teacher will not check homework today, but they actually do.

Type II error: We conclude that the teacher will check homework today, but they actually do not.

Ramifications: If we make a Type I error, we may not do our homework and receive a lower grade. If we make a Type II error, we may waste time doing homework that will not be checked.

Conjecture: In a big store like Wal-Mart, they will never catch me if I shoplift.

Null Hypothesis: Wal-Mart will catch me if I shoplift.

Alternative Hypothesis: Wal-Mart will not catch me if I shoplift.

Type I error: We conclude that Wal-Mart will not catch us if we shoplift, but they actually do.

Type II error: We conclude that Wal-Mart will catch us if we shoplift, but they actually do not.

Ramifications: If we make a Type I error, we may shoplift and get caught, which can have legal consequences. If we make a Type II error, we may shoplift and get away with it, which can encourage further illegal behavior.

Conjecture: If I try to learn to ski, I will end up hurting myself.

Null Hypothesis: Trying to learn to ski does not result in injury.

Alternative Hypothesis: Trying to learn to ski does result in injury.

Type I error: We conclude that trying to learn to ski results in injury, but it actually does not.

Type II error: We conclude that trying to learn to ski does not result in injury, but it actually does.

Ramifications: If we make a Type I error, we may avoid skiing altogether and miss out on the experience. If we make a Type II error, we may attempt skiing and get injured, which can have physical and financial consequences

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Related Questions

Is the theoretical probability that the coin lands head up all three times is the same value as the theoretical probability that the coin lands tails up all three times? Explain.

Answers

Yes, the theoretical probability of getting three heads in a row is the same as the theoretical probability of getting three tails in a row. This is because each flip of a fair coin is an independent event and has an equal chance of landing on either heads or tails.

What is  theoretical probability about?

The probability of getting heads on a single coin flip is 0.5 (or 1/2), and the same is true for getting tails on a single coin flip. The probability of getting three heads in a row is calculated by multiplying the probability of getting heads on each of the three flips together, which is"

(1/2) x (1/2) x (1/2) = 1/8.

Similarly, the probability of getting three tails in a row is also:

(1/2) x (1/2) x (1/2) = 1/8.

Therefore, the theoretical probability of getting three heads in a row is the same as the theoretical probability of getting three tails in a row, both of which are 1/8.

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What is the area of the polygon?

Answers

The area of the polygon is 42 metres squared.

How to find the area of a figure?

The figure is a composite figure. The area of the figure is the sum of the area of the individual shapes.

Therefore,

area of the figure = area of the rectangle + area of trapezium

Hence,

area of the rectangle = lw

where

l = lengthw = width

Therefore,

area of the rectangle = 6 × 4

area of the rectangle = 24 m²

area of trapezium = 1  /2 (a + b)h

area of trapezium = 1 / 2 (4 + 8)3

area of trapezium = 1 / 2 (36)

area of trapezium = 18 m²

Therefore,

area of the figure = 18 + 24

area of the figure = 42 m²

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A function f is said to have a removable discontinuity at a if:
1. f is either not defined or not continuous at a.
2. f(a) could either be defined or redefined so that the new function is continuous at a.
Let f(x)=2x²+4x-6/x-1
Show that f has a removable discontinuity at 1 and determine the value for f(1) that would make f continuous at 1.Need to redefine f(1)=

Answers

The discontinuity of the function is removed and the value of the function at 1 after removing the discontinuity is 8.

What is meant by a discontinuity in a function?

In algebra, a discontinuous function is one that has a point at which the function is not defined, at which the left-hand limit and right-hand limit are equal but not equal to the value of the function at that point, or at which the limit of the function does not exist. If a function in algebra is not continuous, it is referred to as a discontinuous function. A discontinuous function has a discontinuous curve, just like a continuous function does.

Given f(x) = 2x²+4x-6 / (x-1)  

This function has a  discontinuity at 1 because when we substitute x =1, the denominator becomes 0 and the function becomes undefined.

But this discontinuity is removable and can be done as shown:

We can factorize the numerator as below:

2x²+4x-6 = 2x²+6x - 2x -6 = 2x(x+3) -2(x+3) = (2x - 2)(x+3) = 2(x-1)(x+3)

Now when we substitute the factorized form of the numerator in the function. Then,

 

f(x) =  2(x-1)(x+3) / (x-1)

(x-1) can be cancelled from both the numerator and denominator. So the discontinuity is removed.

f(x) = 2(x+3)

Now f(1) = 2 * (1+3) = 8

Now the function is continuous at 1.

Therefore the value of the function at 1 after removing the discontinuity is 8.

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Prove that if x is a non-empty set of real numbers which is bounded above, then there is a sequence of real numbers in x converging to sup(x).

Answers

For all sufficiently large n, which shows that (xn) converges to sup(x) as desired. Therefore, if x is a non-empty set of real numbers that is bounded above, then there is a sequence of real numbers in x converging to sup(x).

Let x be a non-empty set of real numbers that is bounded above. Then, by the least upper bound property of the real numbers, sup(x) exists and is a real number.

For each positive integer n,

let xn be an element of x such that sup(x) - 1/n < xn ≤ sup(x).

Such an element xn exists because sup(x) is the least upper bound of x, so there must be elements of x arbitrarily close to sup(x).

We claim that the sequence (xn) converges to sup(x).

To see this, let ε > 0 be arbitrary.

Since xn ≤ sup(x) for all n,

we have sup(x) - xn ≥ 0, and so sup(x) - xn < ε for all n such that 1/ε is an integer. Thus, we have

|sup(x) - xn| < ε

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What is the frequency range of the UHF broadcast station

Answers

The frequency range of UHF is band between 470 MHz and 608 MHz.

What is broadcast station?Radio broadcasting is the transmission of audio (sound), sometimes with related metadata, by radio waves to radio receivers belonging to a public audience. In terrestrial radio broadcasting the radio waves are broadcast by a land-based radio station, while in satellite radio the radio waves are broadcast by a satellite in Earth orbit.

Given is to find the frequency range of the UHF broadcast station

The frequency range of UHF band is between 470 MHz and 608 MHz.

Therefore, the frequency range of UHF is band between 470 MHz and 608 MHz.

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{Complete question -

What is the frequency range of the UHF broadcast station?}

The density of this a box of tissues is 1 g/cm3. The mass of the object is 728 grams.
The length is 20.8cm, the width is 7cm, what is the height?

Answers

The formula for the volume of a rectangular box is V = l × w × h, where l is the length, w is the width, and h is the height. Since the density is given as 1 g/cm³, the mass of the object is equal to its volume in cubic centimeters (cc):

mass = volume × density

728 g = V × 1 g/cm³

V = 728 cm³

We are given the length and width of the box, so we can substitute these values into the formula for volume:

V = l × w × h

728 cm³ = 20.8 cm × 7 cm × h

Simplifying the right-hand side:

728 cm³ = 145.6 cm² × h

Dividing both sides by 145.6 cm²:

h = 728 cm³ ÷ 145.6 cm²

h = 5 cm

Therefore, the height of the box is 5 cm.

According to the Rational Root Theorem, the following are potential roots of f(x) = 2x² + 2x - 24.
-4,-3, 2, 3, 4
Which are actual roots of f(x)?
O-4 and 3
O-4, 2, and 3
O-3 and 4
O-3, 2, and 4

Answers

Answer: The actual roots of f(x) = 2x² + 2x - 24 are -3 and 4.

Step-by-step explanation:

Write an inequality that represents the statement “x is at most –5 or at least 7.”

Answers

Answer:

x ≤ - 5 or x ≥ 7

or, in interval notation

[ - ∞, -5] ∪ [7, ∞]

Step-by-step explanation:

From the question we get the following two inequalities
x is at most -5 ==>     x ≤ -5

x is at least 7 ==>       x ≥ 7 which can be rewritten as 7 ≤ x

This can be written as
x ≤ - 5 or x ≥ 7

In interval notation this would be
[ - ∞, -5] ∪ [7, ∞]

On the number line this would be represented as shown in the figure

Una empresa minera compra un terreno en
Perú. Los estudios determinaron las siguientes
probabilidades previas:
a.
P(encontrar oro de buena calidad)=0.50
b. P(encontrar oro de mala calidad)=0.30
C. P(no encontrar oro)=0.20
Calcular la probabilidad de encontrar oro en dicho

Answers

The probability of finding gold in that land is 0.8.

What is Probability?Probability of a event measures the chances of that event to happen. The only difference is that probability gives a mathematical explanation of the event. Probability of a event lie between zero and one.

Given is that a mining company buys a piece of land in Peru. The studies determined the following prior probabilities -

P(find good quality gold)=0.50P(find poor quality gold)=0.30P(find no gold)=0.20

We can write the probability of finding gold in that land as -

P{E} = P(find good quality gold) + P(find poor quality gold)=0.30

P{E} = 0.5 + 0.3

P{E} = 0.8

Therefore, the probability of finding gold in that land is 0.8.

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{QUESTION IN ENGLISH -

A mining company buys a piece of land in

Peru. The studies determined the following

prior probabilities:

to.

P(find good quality gold)=0.50

b. P(find poor quality gold)=0.30

C. P(find no gold)=0.20

Calculate the probability of finding gold in that}

Determine all zeros for the function () = (2 + 2 − 8) ( − 6). Show all work.

Answers

The function's two zeros are: x = -1 and x = 6.

What is function?

In mathematics, a function is a set of ordered pairs (input, output), where each input is associated with exactly one output. The input is commonly referred to as the independent variable, and the output is referred to as the dependent variable. A function can be represented algebraically, graphically, or verbally. Algebraically, a function is often represented by an equation that defines the relationship between the independent variable and the dependent variable. For example, the equation y = 2x + 1 defines a linear function, where x is the independent variable and y is the dependent variable.

Here,

The zeros of a function are the values of the independent variable for which the function equals zero. To determine all zeros for the function f(x) = (2x + 2)(x - 6), we need to find the solutions to the equation f(x) = 0.

To do this, we can set the two factors equal to zero and solve for x:

2x + 2 = 0

x = -1

x - 6 = 0

x = 6

These are the two zeros of the function: x = -1 and x = 6.

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There are 2 green marbles, 7 blue marbles, 3 white marbles, and 4 purple marbles in a bag. Once a marble is drawn, it is NOT replaced. Find the probability of white then purple P(white, purple). Write your answer as a simplified fraction.

Answers

Answer:

P(a purple marble then a white marble) is 6/105 ⇒ 1st answer

Step-by-step explanation:

* Lets explain how to solve the problem

- There are 2 green marbles

- There are 7 blue marbles

- There are 3 white marbles

- There are 4 purple marbles

- Once a marble is drawn, it is NOT replaced

- We need to find P(a purple marble then a white marble)

* At first lets find the total number of marbles by adding all color

∵ There are 2 green , 4 purple , 3 white and 7 blue

∴ The total number of marbles = 2 + 4 + 3 + 7 = 16

There are  16 marbles in the bag

∵ Probability = number of events/number of all outcomes

∵ There are 4 purple marbles

∴ The probability of chosen a purple marble is P(purple) = 4/15

∵ Once a marble is drawn, it is NOT replaced

∴ The total number of marbles = 15 - 1 = 14 marbles

∵ The number of white marbles is 3

∴ The probability of chosen a white marble is P(white) = 3/14

∵ P(a purple marble then a white marble) = P(purple) . P(white)

∵ P(purple) = 4/15

∵ P(white) = 3/14

∴ P(a purple marble then a white marble) = (4/15)(3/14) = 6/105

* P(a purple marble then a white marble) is 6/105

4(x - 1)(3x - 1) = 0 answer?

Answers

Answer:

[tex]x = 1 \ \ \ \text{OR} \ \ \ x = \dfrac{1}{3}[/tex]

Step-by-step explanation:

First, multiply out the set of parentheses and simplify the resulting quadratic expression.

[tex]4(x - 1)(3x - 1) = 0[/tex]

[tex]4(3x^2-x-3x+1) = 0[/tex]

[tex]4(3x^2-4x+1) = 0[/tex]

Then, factor out a 3 from the parentheses to get rid of the coefficient on the quadratic's first term.

[tex]4(3(x^2-\dfrac{4}{3}x+\dfrac{1}{3})) = 0[/tex]

[tex]12(x^2-\dfrac{4}{3}x+\dfrac{1}{3}) = 0[/tex]

Finally, complete the square.

[tex]12\left(x^2-\dfrac{4}{3}x + \left(\dfrac{-\dfrac{4}{3}}{2}\right)^2\right) = 12\left(-\dfrac{1}{3}\right) + 12\left(\dfrac{-\dfrac{4}{3}}{2}\right)^2[/tex]

[tex]12\left(x^2-\dfrac{4}{3}x + \dfrac{4}{9}\right) = -4 + \dfrac{16}{3}[/tex]

[tex]12\left(x - \dfrac{2}{3}\right)^2 = \dfrac{4}{3}[/tex]

[tex]\left(x - \dfrac{2}{3}\right)^2 = \dfrac{1}{9}[/tex]

↓ take the square root of both sides

[tex]x - \dfrac{2}{3}\right = \pm \sqrt{\dfrac{1}{9}}[/tex]

[tex]x = \dfrac{2}{3} \pm \sqrt{\dfrac{1}{9}}[/tex]

[tex]x = \dfrac{2}{3} \pm\dfrac{1}{3}[/tex]

↓ split into two equations

[tex]x = \dfrac{2}{3} + \dfrac{1}{3} \ \ \ \text{OR} \ \ \ x = \dfrac{2}{3} - \dfrac{1}{3}[/tex]

[tex]\boxed{x = 1 \ \ \ \text{OR} \ \ \ x = \dfrac{1}{3}}[/tex]

Rearrange for n
m = n² + 3

Answers

Answer:

Step-by-step explanation:

EVALUATE

n(m ^5+m−n) divided by

m(m−n)

EXPAND

m^2mn Divided by

mn-n^2+nm^5

3. Dimitri's car has a fuel efficiency of 21 miles per gallon. His tank is full with 12 gallons of gas. Does he have
enough gas to drive from Cincinnati to Toledo, a distance of 202.4 miles?
Show your calculations, including at least one use of dimensional analysis. You choose how to round.

Answers

Yes, Dimitri has enough gas to drive from Cincinnati to Toledo. To calculate this, we can multiply the fuel efficiency by the amount of gas in the tank.

What is multiplication?

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.

Fuel efficiency: 21 miles per gallon

Gas in the tank: 12 gallons

So, the total distance that Dimitri can drive is:

= 21 miles per gallon x 12 gallons

= 252 miles

Since the distance from Cincinnati to Toledo is 202.4 miles, and the total distance that Dimitri can drive is 252 miles, we can conclude that he has enough gas to make the trip.

Dimensional analysis:

= 21 miles/gallon x 12 gallons

= 252 miles (correct dimensions)

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Andy's two nephews want to travel to Philadelphia with him to see a show. Andy has two free plane tickets and three tickets to the show. Which of the following best describes the two plane tickets?
A scarce resource

Answers

The amount of two plane tickets are a scarce resource, meaning there are not enough to provide for all three people.

A scarce resource is something that is in limited supply. In this case, the two plane tickets are the scarce resource because there are not enough to provide for all three people. This means that if Andy wants to travel to Philadelphia with his two nephews, only two of them can go. This is because while they may have three tickets to the show, they still need to find a way to get there. The two plane tickets are a scarce resource, as they are not enough for all three of them. This means that Andy must make a difficult decision about who can go and who has to stay home. The two plane tickets are the only way for two of them to get to Philadelphia, so they are a scarce resource in this situation.

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What is the relative change in tuition? (Give your answer as a percent between 0 and 100, not a decimal between 0 and 1. Round to ONE decimal place and remember the absolute value).

The relative change in tuition tells us the tuition in 2016/17 decreased by — %

Answers

The relative change in tuition tells us the tuition in 2016/17 decreased by 9.99 %.

What is relative change?

The indicator's value in the earlier period is used to calculate the relative change, which expresses the absolute change as a percentage. Additionally, indicators that are expressed as percentages, such as the unemployment rate, are subject to the concepts of absolute and relative change.

Given:

The tuition in University if Washington in 2015-16 = 10,203

and, The tuition in University if Washington in 2016-17 = 9,183

so, the relative change is

= (10203 - 9183)/ 10203

= 1020/ 10203

= 0.0999

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Read the following excerpt from the Declaration of Independence, and read the question that follows."—Such has been the patient sufferance of these Colonies; and such isnow the necessity which constrains them to alter their former Systems of Government. The history of the present King of Great Britain is a history of repeated injuries and usurpations, all having in direct object the establishment of an absolute Tyranny over these States. Based on the Declaration of Independence, how would the patriots describe King George 111?
A. Out of touch with the colonies
B. Terrifying
C. As a tyrant
D. As an ally

Answers

Answer:

c

Step-by-step explanation:

The colonists thought of King George III as a tyrant, which is evident when looking at the founding documents of the United States and the political parties. The Constitution created separation of powers so nobody would be able to become a tyrant or dictator. There are checks and balances to keep people from gaining too much power and overtaking the government. When looking into the political parties later on, there were the Anti-federalists, who did not want a strong central government because they did not want another King George, who they just got out of a war with.

Osvoldo has a goal of getting at least 30% of his grams of carbohydrates each day from whole grains. Today, he ate 220 grams of carbohydrates, and 55 grams were from whole grains.

Answers

Answer: 25%

Step-by-step explanation:

The answer is 25%. This is calculated by dividing the number of grams of carbohydrates from whole grains (55 grams) by the total number of carbohydrates eaten (220 grams). This gives 0.25, which can be expressed as 25%. Therefore, Osvoldo consumed 25% of his carbohydrates from whole grains today.

Answer:

Osvoldo only got 25% of his grams of carbohydrates from whole grains today, which is below his goal of 30%

Step-by-step explanation:

To find the percentage of Osvoldo's carbohydrates that came from whole grains, we can use the formula:

percentage = (part/whole) x 100%

where "part" is the number of grams from whole grains, and "whole" is the total number of grams of carbohydrates. So we have:

percentage = (55/220) x 100%

percentage = 0.25 x 100%

percentage = 25%

Therefore, Osvoldo only got 25% of his grams of carbohydrates from whole grains today, which is below his goal of 30%.

A fitness club with 100 members offers one free training session per member in either running, swimming, or weightlifting. Thirty of the fitness center members sign up for the free session. The running and swimming sessions are each twice as popular as the weightlifting session. What is the probability that a randomly chosen fitness club member signs up for a free running session?

Answers

The probability that a randomly chosen fitness club member signs up for a free running session is 20%.

What is Probability?

Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of the likelihood of an event occurring divided by the number of possible outcomes. Probability is used to determine the chances of a particular outcome occurring and can range from 0 to 1.


This is because 30 members signed up for a free session, with 10 signing up for the running session, 10 signing up for the swimming session, and 10 signing up for the weightlifting session. Since the running and swimming sessions are each twice as popular as the weightlifting session, there is a 20% chance that any given member will choose the running session.

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I need the answer like now

Answers

Answer:

1.             0             10             20           30            40            50

             10             14             18            22            26            30

2. (the immage)

3. Yes this is a liner equation

Step-by-step explanation:

Admission to a baseball game is $2.00 for general admission and $3.50 for reserved seats. The receipts were $2716.00 for 1139 paid admissions. How many of each ticket were sold?

Answers

Let G be the number of general seats sold.

Let R be the number of reserved seats sold.

The total number of seats sold is G + R = 1139

Since general seats costs $2 each, 2G is the total receipts from general tickets sales.

Since reserve seats costs $3.50 each, 3.5R is the total receipts from reserved ticket sales.

The total receipts is 2G + 3.5R = 2716

We now have two equations in two unknowns and can solve for G and R.

Given the following list of values, is the mean or the median likely to be a better measure of the center of the data set? 25, 29, 23, 26, 25, 27. 10. 26. 23. 23. 26 Select the correct answer below: O Mean O Median

Answers

If we consider between mean and median in case of better measure of the center, median is likely to be the better measurement.

The list of values given here is 25, 29, 23, 26, 25, 27, 10, 26, 23, 23, 26.

First we are making or rearranging it in ascending/ descending order.

10, 23, 23, 23, 25, 25, 26, 26, 26, 27, 29.

Mean will be  the average of the given set.

Median will be the exact middle number or the average of the two middle entries.

Mean = 23.9

Median = 25

If we consider the range of data and how it is distributed, you can see it ranges from 10 to 29.

But the problem is that, after 10, the second least value is 23 and rest of the values are nearer also.

There is a clear gap between the values of other data points and the first data entry 10.

As mean is the average of every data, this 10 can directly influence the value of mean and cannot gave us an approximation of center.

Imagine that if the last entry is somewhat very big number, then the mean will surely slant to the higher number as it is the sum average of the given set of data.

But median is then also the exact middle number and not influenced by the range of the given data.

Mean and median can be the same in certain cases but when we approximate the measurement of center more than mean, median will likely to give better answer.

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PLEASE HELP!!!

Which angles are supplementary to each other?

A) ∠5 and ∠3
B) ∠5 and ∠11
C) ∠4 and ∠2
D) ∠11 and ∠10

PLEASE LOOK AT PICTURE!!!

Answers

Answer:

Angles 11 and 10 both make a 180-degree angle, but so do 5 and 3. I would go with 11 and 10

Answer:

D, <11 and <10

Step-by-step explanation:

Supplementary angles are angles that sum to 180°

Please help me answer this question ASAP!!

Answers

The total distance driven by Ryan is given as follows:

20.5 miles.

What is the relation between velocity, distance and time?

Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:

v = d/t.

Considering that 12 minutes = 12/60 = 0.2 hours, the distance for the first customer was of:

40 = d/0.2

d = 40 x 0.2

d = 8 miles.

Considering that 15 minutes = 15/60 = 0.25 hours, the distance for the second customer was of:

50 = d/0.25

d = 0.25 x 50

d = 12.5 miles.

Hence the total distance was of:

8 + 12.5 = 20.5 miles.

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Find the value of k so that the given differential equation is exact. (y3 + kxy4 − 2x) dx + (3xy2 + 24x2y3) dy = 0

Answers

The value of k for the given differential equation is exact is,

⇒ k = 12

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The given differential equation is,

⇒ (y³ + kxy⁴ - 2x) dx + (3xy² + 24x²y³) dy = 0

And, The given differential equation is exact.

Now, We know that;

For the differential equation M dx + N dy = 0;

The condition of exactness is,

⇒ dM / dy = dN / dx  .. (i)

Here, We have;

M = y³ + kxy⁴ - 2x

N = 3xy² + 24x²y³

Hence, We get;

M = y³ + kxy⁴ - 2x

dM / dy = 3y² + 4kxy³

N = 3xy² + 24x²y³

dN / dx = 3y² + 48xy³

From (i);

⇒ dM / dy = dN / dx

⇒ 3y² + 4kxy³ = 3y² + 48xy³

⇒ 4kxy³ = 48xy³

⇒ 4k = 48

⇒ k = 48/4

⇒ k = 12

Thus, The value of k = 12

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Differentiate y=x4 -x

Answers

Answer:

Step-by-step explanation:

To differentiate the function y = x^4 - x, we will use the power rule of differentiation. The power rule states that if f(x) = x^n, then the derivative of f(x) is f'(x) = nx^(n-1).

So, for y = x^4 - x, we can find the derivative as follows:

y' = 4x^3 - 1

So, the derivative of the function y = x^4 - x is y' = 4x^3 - 1.

Convert 3.5 kilograms to grams

Answers

3.5 kilograms is 3500 grams

Answer: 3500

Step-by-step explanation: one kilogram is 1000 gram so multiply 3.5 x 1000

Candidate A makes 48 speeches. Candidate B makes 16 speeches. a. Write the ratio of speeches by candidate A to candidate B b. Simplify the ratio so the second quantity is 1. Show your work.

Answers

Answer:

a. 48:16

b. 3:1

Step-by-step explanation:

Part a asks for a ratio of the two speeches. You simply separate the two numbers with a colon to show that it's a ratio.

Part b asks that the second quantity (which is the speeches made by B) be 1. To do this, divide 16 on both sides. 48 divided by 16 is 3, and 16 divided by 16 is 1. Thus, 3:1

Simplify fully 48 seconds 1 minute

Answers

Answer:

1.48

1 minute and 48 seconds

The population of a large US city is 1,703,210. Show how you could express this in Scientific Notation.

Answers

The population of a large US city is 1.70321 × 10⁶ in Scientific Notation.

What is Scientific Notation?

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It may be referred to as scientific form or standard index form.

Given that, the population of a large US city is 1,703,210. we need to show this number in Scientific Notation.

We know that, a number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

The number is written in two parts:

The digits, with the decimal point placed after the first digit, followed by × 10 to a power that puts the decimal point where it should be

Therefore,

1,703,210 = 1.70321 × 10⁶

Hence, the population of a large US city is 1.70321 × 10⁶ in Scientific Notation.

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