Calculate ∫ x3 dx. A. 3x2 + C B. x4/4 + C C. x2 D. x4 + C
Given random variable x is normally distributed, with a mean of 10 and standard deviation of 5, what is the probability that x is less than 11?
Order each set of values from least to greatest. 0.4,5/8,38%
What is the completely factored form of f(x)=x3+5x2+4x−6?
f(x)=(x−3)(x−(−1+i3√))(x−(−1−i3√))
f(x)=(x+3)(x−(−1+i3√))(x−(−1−i3√))
f(x)=(x+3)(x−(−1+3√))(x−(−1−3√))
f(x)=(x−3)(x−(−1+3√))(x−(−1−3√))
The factored type is the product of constants and two-dimensional terms, that is the root of a function as well as the graph's x-intercepts, and the further calculation can be defined as follows:
Given:
[tex]\bold{f(x)=x^3+5x^2+4x-6}[/tex]
To find:
factored form=?
Solution:
[tex]\bold{f(x)=x^3+5x^2+4x-6}[/tex]
putting the value x=-1,-2,-3...... to find the function value 0.
[tex]\to \bold{f(-1)=-1^3+5(-1)^2+4(-1)-6}\\\\[/tex]
[tex]\bold{=-1+5\times 1+4 \times (-1)-6}\\\\ \bold{= -1+5-4-6} \\\\ \bold{=-6}\\\\[/tex]
[tex]\to \bold{f(-2)=-2^3+5(-2)^2+4(-2)-6}[/tex]
[tex]\bold{=-8+5\times 4+4 \times(- 2)-6}\\\\\bold{= -8+20-8-6}\\\\\bold{=-2}\\\\[/tex]
[tex]\to \bold{f(-3)=-3^3+5(-3)^2+4(-3)-6}[/tex]
[tex]\bold{=-27+5\times 9+4 \times(- 3)-6}\\\\\bold{= -27+45-12-6}\\\\\bold{=0}\\\\[/tex]
Therefore, [tex]\bold{(x+3)}[/tex] is the factor of the function.
Let [tex]\bold{(x+3)}[/tex] divide by the function:
[tex]\to \bold{\frac{x^3+5x^2+4x-6}{(x+3)}= x^2+2x-2}[/tex]
compare the value [tex]\bold{x^2+2x-2}[/tex] by the standard equation [tex]\bold{ax^2+bx+c=0}[/tex] so,
[tex]\bold{a=1}\\\\\bold{b=2}\\\\\bold{c=-2}\\\\[/tex]
Putting value into the quadratic equation formula:
[tex]\bold{x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}}[/tex]
[tex]\bold{x=\frac{-(2) \pm \sqrt{(2)^2-4\times 1 \times -2}}{2\times 1}}\\\\\bold{x=\frac{-2 \pm \sqrt{4+8}}{2}}\\\\\bold{x=\frac{-2 \pm \sqrt{12}}{2}}\\\\\bold{x=\frac{-2 \pm 2\sqrt{3}}{2}}\\\\\bold{x=\frac{2(-1 \pm \sqrt{3})}{2}}\\\\\bold{x=(-1 \pm \sqrt{3})}\\\\\bold{x=(-1 + \sqrt{3}) (-1 -\sqrt{3})}\\\\[/tex]
Adding the factor value that is [tex]\bold{(x+3)}[/tex] so, the value is "[tex]\bold{(x+3)(-1+\sqrt{3})(-1-\sqrt{3}) }[/tex]"
So, the final answer is "[tex]\bold{f(x)=(x+3)(x-(-1+\sqrt{3}))(x-(-1-\sqrt{3}))}[/tex]"
Learn more:
brainly.com/question/16754415
witch set of numbers could represent the side lengths of a right triangle
The daily changes in the barometric pressure for four days are − − 0.05, 0.09, − − 0.04, and − − 0.08 inches. a. What is the mean change? Write your answer as a decimal. The mean change is inch. Question 2 b. The mean change after five days is − − 0.01 inch. What is the change on the fifth day? Write your answer as a decimal. The change on the fifth day is inch
A stereo system cost $275. It was on sale for 15% off. The sales person receives a 2% commission. How much of a commission do they receive?
Answer:
They receive $4.68 as a commission
Step-by-step explanation:
The cost of stereo system = $275
Price after discount of 15% = 275 - (15% × 275)
= 275 - ( 0.15 × 275)
= 275 - 41.25
= $233.75
2% commission of the sales person = 2% × 233.75
= 0.02 × 233.75
= $4.675 ≈ $4.68
They receive $4.68 as a commission
write a word problem that can be solved by ordering three decimals to thousandths. include a solution.
What is the estimate of 1/2% of 412
A student pays for 8.9 pounds of apples with a $10 bill. How much change does the student receive if the apples are .99 per pound
Answer:
[tex]\$\,1.19[/tex]
Step-by-step explanation:
Quantity of apples bought by the student = 8.9 pounds
Amount paid by the student for apples bought by the student = [tex]\$[/tex] 10
If cost of one pound of apples is [tex]\$[/tex] 0.99 then cost of 8.9 pounds = 0.99 × Quantity of apples bought by the student = [tex]8.9\times 0.99=8.811[/tex]
Therefore,
Amount of change that the student receive if the apples are .99 per pound = Amount previously paid by the student for apples bought by the student when the student pays [tex]\$[/tex] 10 - Amount paid by the student for apples if the apples are .99 per pound = [tex]\$ \,10-\$ \,8.811=\$\,1.19[/tex]
Select "Rational" or "Irrational" to classify each number.
Rational
Irrational
0.25
√0.25
√0.33
Answers
0.25 ⇒ It is rational
√0.25 ⇒ It is rational
√0.33 it is irrational
Explanation
a rational number is one that can be written as a ration. Or we can say that a rational number can be written as a/b where a and b are integers and b ≠0.
0.25 = 25/100
= 1/4
0.25 ⇒ It is rational.
√0.25 = 0.5
= 5/10
= 1/2
√0.25 ⇒ It is rational
√0.33 = 0.5744562664.......
This can not be written as a/b. So,√0.33 it is irrational
Final answer:
0.25 and √0.25 are rational numbers because they can be represented as ratios of integers, while √0.33 is an irrational number due to its inability to be precisely expressed as a fraction.
Explanation:
The question asks to classify each number (0.25, √0.25, √0.33) as either rational or irrational. The distinctions between rational and irrational numbers can be understood by recalling that rational numbers are those that can be expressed as a ratio of two integers, while irrational numbers cannot be exactly expressed as a fraction of two integers.
0.25: This can be expressed as the fraction 1/4, which is a ratio of two integers. Therefore, it is a rational number.
√0.25: The square root of 0.25 is 0.5, which can also be expressed as the fraction 1/2. Hence, this is also a rational number.
√0.33: This cannot be expressed as a precise fraction of two integers and its decimal representation is non-repeating and non-terminating. Therefore, it is an irrational number.
To classify, 0.25 and √0.25 are rational numbers because they can be represented as ratios of integers. √0.33 is considered an irrational number as it cannot be exactly expressed as a fraction.
Torrid had $20 to but a birthday present for her dad. She decided to buy a DVD for $18. The sales tax is 7%. Does she have enough money? Explain your reasoning.
Please Show Work Too
Identify two factors that have a product of 9/10.
"Please help"
Consider the following question:
What was the high temperature in Chicago yesterday?
Which BEST describes the question?
A) It is not a statistical question because the data is a single number.
B) It is a statistical question because the answer can be any number.
C) It is a statistical question because the answer is not known.
D) It is a statistical question because the answer is a measurement.
Answer:
A) It is not a statistical question because the data is a single number.
Step-by-step explanation:
A statistical question is a question that can be answered by collecting data that vary.
What was the high temperature in Chicago yesterday?
This is not statistical as its answer will not vary. It has been specifically asked that what was the HIGH temperature, so its answer will be a single value.
Rather, if it were to be a statistical question, it would have been - What was the temperature in Chicago throughout the day?
So, option A is correct.
A) It is not a statistical question because the data is a single number.
Understanding Statistical Questions
A statistical question is one that anticipates variability in the data and typically requires data collection and analysis. It often involves multiple observations or measurements that could vary.
Analysis of the Question
The question "What was the high temperature in Chicago yesterday?" is asking for a specific value — the high temperature on a particular day in a particular location.
Option A: It is not a statistical question because the data is a single number.
This seems correct because the question seeks one specific value rather than a range of values or a distribution.
Option B: It is a statistical question because the answer can be any number.
This is not quite accurate because, while the temperature could theoretically be any value, the question is asking for a specific single value.
Option C: It is a statistical question because the answer is not known.
The unknown nature of the answer doesn't necessarily make it a statistical question. Many non-statistical questions also have unknown answers that are single specific values.
Option D: It is a statistical question because the answer is a measurement.
Although the answer is a measurement, this alone does not make it a statistical question. It needs to involve data collected with variation.
what is the solution set of the equation x2 + 3x - 4 = 6
Sara notices that she double paid her gas bill. What online service should she use? reject payment service request a stop payment transfer transaction withdrawal tool
An equilateral triangle has a semiperimeter of 6 meters. What is the area of the triangle? Round to the nearest square meter. 2 square meters 7 square meters 20 square meters 78 square meters
Help me with those screen
Answer:
1. D. irrational
2. A. 5
3. A. 16 and 25
4. A. 3 and four
Step-by-step explanation:
Hope this helps
of the 24 students in gregs class, 3/8 ride the bus to school. how many students ride the bus?
Answer:
9 students ride the bus.
Step-by-step explanation:
Given: The total number of students in gregs class is 24 and [tex]\frac{3}{8}[/tex] ride the bus to school.
To find how many students ride the bus;
Let x be the number of student ride the bus.
Proportional is simply a statement that the two ratios are equal.
It can be written in two ways i.e, [tex]\frac{a}{b} = \frac{c}{d}[/tex] or
[tex]a : b :: c :d[/tex]
Then, as per the given conditions;
x : 24 = 3 : 8 or
[tex]\frac{x}{24} = \frac{3}{8}[/tex]
Multiply both sides by 24 we get;
[tex]\frac{x}{24} \times 24 =\frac{3}{8} \times 24[/tex]
Simplify:
x = 9
Therefore, the student ride the bus is, 9
Spreadsheet software can be used to determine the amount of simple interest owed on a 30 day note. what mathematical operations would be used?
Final answer:
Spreadsheet software can be used to determine the amount of simple interest owed on a 30-day note by using the formula for simple interest: Principal (P) × Interest Rate (R) × Time (T).
Explanation:
In spreadsheet software, you can determine the amount of simple interest owed on a 30-day note using mathematical operations. The mathematical operations involved are multiplication and addition.
The formula for simple interest is:
Simple Interest = Principal (P) × Interest Rate (R) × Time (T)
For example, if you have a principal of $100, an interest rate of 5%, and a time period of 30 days, you can calculate the simple interest as:
$100 × 0.05 × (30/365) = $1.23
Therefore, the amount of simple interest owed on the 30-day note would be $1.23.
at the library, you find 9 books on a certain topic. the librarian tells you that 55% of the books on this topic have been signed out. how many books does the library have a available on the topic?
To find the total number of books on a topic when 9 are available and 55% are signed out, set up a proportion and solve for 'x.' The calculation reveals there are a total of 20 books available on the topic.
Explanation:The student is asking how many books on a certain topic the library has available if 9 books are found and 55% of all the books on that topic have been signed out. To find the total number of books on the topic, we need to understand that the 9 books on the shelf represent 45% of the total books (100% - 55% = 45%). We can set up a proportion where 9 books is to 45% as the total number of books (let's call it 'x') is to 100% (the whole set of books on the topic).
Setting up the proportion, we have:
9 / 45% = x / 100%
To solve for 'x,' we cross-multiply and divide as follows:
9 * 100 = x * 45
900 = 45x
Now we divide both sides of the equation by 45 to find 'x':
x = 900 / 45
x = 20
Therefore, the library has a total of 20 books available on the topic.
Why am I wrong?
Picture attached.
Calculate the difference between the 1990-1997 average blue crab population and the 1998-2009 average blue crab population predict the average blue crab population for 2010-2020 and explain
To calculate the difference between the average populations, add the yearly populations and divide by the number of years for both periods, then subtract the first average from the second. To predict the 2010-2020 average, you could use trend analysis, a statistical method that identifies patterns in historical data.
Explanation:Before making any calculations, you need the blue crab population data for the specific years mentioned. To calculate the average, you sum up the individual yearly populations and then divide by the number of years. So, to calculate the average blue crab population from 1990-1997, you would add the population of each of these years and then divide by 8 (the number of years). For the period from 1998-2009, do the same but divide by 12. To determine the difference between these two averages, subtract the average for 1990-1997 from the average for 1998-2009.
To predict the average blue crab population for 2010-2020, you could use a statistical method known as trend analysis. This method involves identifying a pattern or trend in historical data and projecting this trend into the future. It’s important, though, to note that such methods can only predict based on the available data, and it may not account for unforeseen factors that could influence future populations.
Learn more about Average Calculation and Prediction here:https://brainly.com/question/31325885
#SPJ12
To calculate the difference between the average blue crab populations for the given time periods, add up the populations for each period and subtract them. However, predicting the average population for a future period requires additional data.
Explanation:To calculate the difference between the average blue crab populations for the given time periods, we need to find the average population for each period and then subtract them. Let's calculate:
1990-1997 average blue crab population: Add up the populations for each year (1990, 1991, ..., 1997) and divide by the number of years (8).1998-2009 average blue crab population: Add up the populations for each year (1998, 1999, ..., 2009) and divide by the number of years (12).To predict the average blue crab population for 2010-2020, we need more information about the population trends during that period. Without that information, we cannot accurately forecast the average population.Therefore, we can calculate the difference between the 1990-1997 average and the 1998-2009 average, but we cannot predict the average population for 2010-2020 without additional data.
Learn more about Calculating average populations and predicting future populations here:https://brainly.com/question/33654654
#SPJ12
A cab charges $1.50 for the first mile and $0.50 for each additional mile. Write and solve an inequality to determine how many miles Sharon can travel if she has $25 to spend.
A.$0.50 + $1.50x ≤ $25; x ≤ 16 miles
B.$0.50 + $1.50x ≥ $25; x ≥ 16 miles
C.$1.50 + $0.50x ≤ $25; x ≤ 47 miles
D.$1.50 + $0.50x ≥ $25; x ≥ 47miles
How many $10 bills are the same as ten $1 bills
Find the sum and product of the roots. 3x 2 - 4x - 7 = 0
Answer:
Part 1) The sum of the roots is [tex]4/3[/tex]
Part 2) The product of the roots is [tex]-7/3[/tex]
Step-by-step explanation:
Step 1
Find the roots
we have
[tex]3x^{2}-4x-7=0[/tex]
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]3x^{2}-4x-7=0[/tex]
so
[tex]a=3\\b=-4\\c=-7[/tex]
substitute in the formula
[tex]x=\frac{-(-4)(+/-)\sqrt{-4^{2}-4(3)(-7)}} {2(3)}[/tex]
[tex]x=\frac{4(+/-)\sqrt{16^{2}+84}} {6}[/tex]
[tex]x=\frac{4(+/-)10} {6}[/tex]
[tex]x1=\frac{4+10} {6}=7/3[/tex]
[tex]x2=\frac{4-10} {6}=-1[/tex]
Step 2
Find the sum of the roots
[tex]x1+x2=(7/3)-1=4/3[/tex]
Step 3
Find the product of the roots
[tex]x1*x2=(7/3)*(-1)=-7/3[/tex]
When I double my number and add seven, I get what number?
If a man can run p miles in x minutes, how long will it take him to run q miles at the same rate?
It will take the man [tex]\( \frac{qx}{p} \)[/tex] minutes to run q miles at the same rate he runs p miles in x minutes.
Rate of running: The rate at which the man runs is given by the ratio of miles to minutes, which is [tex]\( \frac{p}{x} \)[/tex] miles per minute. This means he runs p miles in x minutes.Finding the time to run q miles: To find out how long it will take him to run q miles at the same rate, we use the formula:Time = [tex]\frac{\text{Distance}}{\text{Rate}}[/tex]
where Time is the time taken, Distance is the distance traveled, and Rate is the rate of running.
Substituting values: Substituting the given values, we have:Distance = q miles
Rate = [tex]\( \frac{p}{x} \)[/tex] miles per minute.
Therefore,
Time = [tex]\frac{q}{\frac{p}{x}}[/tex]
Simplify the expression: To simplify the expression, we can multiply the numerator and denominator by x to get rid of the fraction in the denominator:Time = [tex]\frac{qx}{p}[/tex]
Which of the following are exterior angles?
Answer:
B,C, D ) angle 2, ,3,4 are exterior angles.
Step-by-step explanation:
Given : A figure .
To find : Which of the following are exterior angles.
Solution : We have given a figure of triangle
Exterior angle : An angle which are formed outside the closed figure,
We can see from the given figure angle 6 angle 5 , angle 1 are lies inside the triangle .
But Angle 2 , 4 ,3 are outside the triangle .
Therefore, B,C, D ) angle 2, ,3,4 are exterior angles.
How do you solve the literal equation for g=6x solve for x