The definite integral of the given function will be \(\pi(\dfrac{1304}{27})\).
What is integration?Integration is defined as the summing up of the small parts to find the total value.The given function y = -x +2 will be integrated as follows:-
The limits are given as a = 0 and b = 2.
The integration will be done as:-
\(V = \pi\int_0^2\pi(y^2)dx\\\\\\V = \pi\int _0^2(\pi(-x+2)^2dx\\\\\\V = \pi\int _0^2(x^2+16+8x)dx\\\\\\V=\pi [ (\dfrac{x^3}{3}+16x+\dfrac{8x^2}{2}]_0^2\\\\\\V = \pi[(\dfrac{2^3}{3^3}+(16\times 2) + 8\dfrac{2)^2}{2}]-0\\\\\\V = \dfrac{1304}{27}\pi\)
Therefore definite integral of the given function will be \(\pi(\dfrac{1304}{27})\).
To know more about integration follow
https://brainly.com/question/15993715
#SPJ1
Helppp!! Malcolm is training for a marathon. He runs 3 miles in
hour. What is Malcolm's rate in miles per hour?
A)5.85
B)4.75
C)6.23
D)5.42
Answer:
Malcolm would logically be running at 4.75 and since he is running at 3, it would be the lowest possible therefore its B
Step-by-step explanation:
two marbles are randomly selected without replacement from a bag containing blue and green marbles. the probability they are both blue is . if three marbles are randomly selected without replacement, the probability that all three are blue is . what is the fewest number of marbles that must have been in the bag before any were drawn? (2000 mathcounts national target)
The probability of selecting two blue marbles without replacement is 1/6, and the probability of selecting three blue marbles without replacement is 1/35. The fewest number of marbles that must have been in the bag before any were drawn is 36.
Let's assume there are x marbles in the bag. The probability of selecting two blue marbles without replacement can be calculated using the following equation: (x - 1)/(x) * (x - 2)/(x - 1) = 1/6. Simplifying this equation gives (x - 2)/(x) = 1/6. Solving for x, we find x = 12.
Similarly, the probability of selecting three blue marbles without replacement can be calculated using the equation: (x - 1)/(x) * (x - 2)/(x - 1) * (x - 3)/(x - 2) = 1/35. Simplifying this equation gives (x - 3)/(x) = 1/35. Solving for x, we find x = 36.
Therefore, the fewest number of marbles that must have been in the bag before any were drawn is 36.
Learn more about probability here: https://brainly.com/question/31828911
#SPJ11
During the month of January George worked a total of 21 days, 8 hours each day. He did not work any overtime hours during October. Henry earns $29 per hour. What was his earned wages for the month of January ?
A) $232.00
B) $4,872.00
C) $4,640.00
D) $609.00
Answer:
B
Step-by-step explanation:
21*8=168
29*168=$4,872.00
A series of formulas that describe technical aspects of a system is a(n) _______ model.
a) textual
b) descriptive
c) graphical
d) mathematical
The correct option is d) mathematical
What is a technical system model?
A mathematical model is a set of equations or algorithms that represent technical aspects of a system. These equations or algorithms are used to predict or simulate system behavior and performance. Mathematical models are often used in engineering, science, economics, and other fields where complex systems need to be analyzed and optimized. For example, a mathematical model could be used to analyze how a communication network would perform with different levels of traffic or to predict how a chemical reaction would proceed under various conditions. Mathematical models are often represented graphically to provide a clear visualization of the complex relationships between variables within a system. Overall, mathematical models are an essential tool for designing, optimizing, and managing complex systems.
Learn more about algorithm
brainly.com/question/21172316
#SPJ11
Monique is planning the locations for three exhibit areas at the festival. She drew a model of one of the exhibit areas as shown on the coordinate grid below. To determine the location of the second exhibit area, she will reflect the first area across the dashed line. To determine the location of the third exhibit area, she will translate the second area (x,y)→(x+1,y+6)
The second area was translated 1 unit right and 6 units down to form the third exhibit area.
TransformationTransformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, dilation and rotation.
Translation is the movement of a point either up, down, left or right.
Given the translation (x,y)→(x+1,y+6). Hence:
The second area was translated 1 unit right and 6 units down to form the third exhibit area.
Find out more on Transformation at: https://brainly.com/question/1462871
Rearrange the formula m² = 5n³ + 4k to make n the subject.
Answer:
3√2-4k/5 = n
Step-by-step explanation:
m2-4k=5n^3
2-4k/5 = n^3
3√2-4k/5 = n
how many different functions are there from a set with 10elements to sets with the following numbers of elements?
Using the same logic, we can find the number of different functions from A to B2, B3, and so on. The number of possible mappings for each element in A remains the same, but the number of elements in B changes.
Let's denote the set with 10 elements as A, and the sets we are mapping to as B1, B2, B3, and so on.
To determine the number of different functions from set A to set B1, we need to consider that each element in A has to be mapped to an element in B1. There are no restrictions on which element can be mapped to which, so for each of the 10 elements in A, we have |B1| possible choices. Therefore, the total number of different functions from A to B1 is |B1|^10.
So, the total number of different functions from A to B2 is |B2|^10, and so on.
In summary, the number of different functions from A to sets with the following numbers of elements are:
- B1: |B1|^10
- B2: |B2|^10
- B3: |B3|^10
- and so on.
To determine the number of different functions from a set with 10 elements (the domain) to sets with varying numbers of elements (the range), we'll use the formula:
Number of functions = range size ^ domain size
For example, let's assume the range has 'n' elements. Then, the number of different functions from a set with 10 elements to a set with 'n' elements would be:
Number of functions = n^10
To find the number of functions for a specific range size, replace 'n' with the number of elements in that set.
To know more about Elements click here.
brainly.com/question/13025901
#SPJ11
If something was sold for $270 after it was reduced by 1/3 of the original price, what was the original price
Answer:
$810
Step-by-step explanation:
you can multiply 210 by 3
How do I know how to determine whether a relation is a function? What is a function?
Input: Output:
-3 11
0 5
3 -1
6 -7
9 -13
Answer:
all are functions
Step-by-step explanation:
a function is when each x has a y
a relation is when 1 x has more than 1 y which makes it invalid therefore not a function
Simplify The Following - c^5xc
if a + b is equal to 2 find the value of a cube plus b cube + 6ab
Multiply.
2x^4 (3x³ − x² + 4x)
Answer: A
Step-by-step explanation:
When multiplying: Numbers multiply with numbers and for the x's, add the exponents
If there is no exponent, you can assume an imaginary 1 is the exponent
2x⁴ (3x³ − x² + 4x)
= 6x⁷ -2x⁶ + 8x⁵
Answer:
A. \(6x^{7} - 2x^{6} + 8x^{5}\)
Step-by-StepLabel the parts of the expression:
Outside the parentheses = \(2x^{4}\)
Inside parentheses = \(3x^{3} -x^{2} + 4x\)
You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses
\(2x^{4}\) × \(3x^{3}\)
\(2x^{4}\) × \(-x^{2}\)
\(2x^{4}\) × \(4x\)
First, multiply the whole numbers of each value before the variables
2 x 3 = 6
2 x -1 = -2
2 x 4 = 8
Now you have:
6\(x^{4}x^{3}\)
-2\(x^{4}x^{2}\)
8\(x^{4} x\)
When you multiply exponents together, you multiply the bases as normal and add the exponents together
\(6x^{4+3}\) = \(6x^{7}\)
\(-2x^{4+2}\) = \(-2x^{6}\)
\(8x^{4+1}\) = \(8x^{5}\)
Put the numbers given above into an expression:
\(6x^{7} -2x^{6} +8x^{5}\)
Key Wordsdistribution
variable
like exponents
Who is in more debt a person with a balance of $-30 or a person with $-40? why
Answer:
A person with $-40 is in more debt
Step-by-step explanation:
The person with $-40 has borrowed or spent money from their credit card more than the person who is in debt for $-30.
Answer:$-40
Step-by-step explanation:
A person with negative 40 dollars has 40 dollars missing, a person with -30 dollars only has 30 dollars missing. So the person with -$40 is missing more money and therefore, is in more debt.
Help Fast. Choose the system of inequalities that best matches the graph below.
Answer:
D
Step-by-step explanation:
Solve through logic and brain rather than lengthy calculations
Trick to be used
See
the red line is solid and that denotes to the fact that the symbol must be ≤ or ≥ .It is parallel to x axis at y=4Rest values of y are less than 4 So y≤4Only option D contains y≤4
Option D is correct
PLS HELP, WILL GIVE BRAINLIEST!!
Answer: D = (- ∞, -1) ∪ (-1, ∞) R = (- ∞,3) U [5,5]
Step-by-step explanation:
Charles is going to purchase a new car that has a list price of $21,450. He is planning on trading in his good-condition 2004 Dodge Neon and financing the rest of the cost over three years, paying monthly. His finance plan has an interest rate of 12. 28%, compounded monthly. Charles will also be responsible for 6. 88% sales tax, a $1,089 vehicle registration fee, and a $124 documentation fee. If the dealer gives Charles 80% of the listed trade-in price on his car, once the financing is paid off, what percent of the total amount paid will the interest be? (Consider the trade-in to be a reduction in the amount paid. ) Dodge Cars in Good Condition Model/Year 2004 2005 2006 2007 2008 Viper $7,068 $7,225 $7,626 $7,901 $8,116 Neon $6,591 $6,777 $6,822 $7,191 $7,440 Intrepid $8,285 $8,579 $8,699 $9,030 $9,121 Dakota $7,578 $7,763 $7,945 $8,313 $8,581 a. 17. 64% b. 15. 67% c. 16. 70% d. 12. 86% Please select the best answer from the choices provided A B C D
Percent of the total amount a per the given list price, documentation fee , registration fee and other payment paid by Charles is given by :
Option c. 16.70%
Cost of his old 2004 Dodge Neon = $6591
Sales tax = 6.88%
Dealer gives 80% trade in price on hos car
After tax selling price of the car
= 6,591 × (80/100) × [ 1 - (6.88/100) ]
= $4910.03
= $4,910
Vehicle registration amount = $1,089
List price of car = $21,450
Documentation fee = $124
Total cost of the car
= $21,450 + $1,089 + $124
= $22,663
Net amount Charles needs to pay
= $22,663 - $4,910
= $17,753
Monthly payment at the rate of 12.28% compounded monthly for 3 years
= 17753 [ 12.28%( 1+ 12.28%)^3 / [( 1+ 12.28%)^3 -1 ]
= $592
Total amount paid by Charles
= $592 × 36
= $21,312
Total interest paid by Charles
= $21,312 - $17,753
= $3,559
Percent of the total amount
= ( $3,559 / $21,312 ) × 100
= 16.699%
= 16.70%
Therefore, the percent of the total amount paid by Charles is equal to Option c. 16.70%.
Learn more about percent here
brainly.com/question/29085726
#SPJ4
to find the height of a pole, a surveyor moves 150 feet away from The base of the pole and then, with a transit 4 feet tall, measures the angle of elevation to the top of the pool to be 42°. To the nearest foot, what is the height of the pole?
ANSWER :
139 feet
EXPLANATION :
The surveyor is 150 feet away from the base of the pole.
The transit is 4 feet tall and the angle of elevation to the top of the pole is 42 degrees.
The illustration will be :
We have a right triangle with an angle of 42 degrees.
The side opposite to the angle is x and the side adjacent to the angle is 150
Using Tangent function :
\(\begin{gathered} \tan\theta=\frac{\text{ opposite}}{\text{ adjacent}} \\ \\ \tan42=\frac{x}{150} \\ x=150\tan42 \\ x=135.06\sim135\text{ ft} \end{gathered}\)The height of the pole is x + 4
That will be 135 + 4 = 139 ft
from year to year, monthly data on the number of flu cases seen in a hospital emergency department would likely show consistent increases during certain months, and decreases during others. this is an example of group of answer choices exponential smoothing seasonality holt's method none of the above
The given scenario of monthly data on the number of flu cases seen in a hospital emergency department that shows consistent increases during certain months and decreases during others is an example of seasonality.
Seasonality refers to the predictable pattern of fluctuations in a time series data that occurs at regular intervals over a period of time. In this case, the seasonal pattern is related to the occurrence of the flu virus, which typically peaks during the winter months and decreases in the summer months.
Exponential smoothing is a statistical method used to forecast time series data, which involves assigning weights to past observations that decline exponentially over time. Holt's method is an extension of exponential smoothing that includes a trend component in addition to the level and seasonality components.
However, neither exponential smoothing nor Holt's method directly address seasonality in time series data. Therefore, the correct answer to the given question is "seasonality".
Know more about seasonality here:
https://brainly.com/question/19009677
#SPJ11
A recent conference had 875 people in attendance. In one exhibit room of 60 people, there were 46 teachers and 14 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 204 principals in attendance.
There were about 266 principals in attendance.
There were about 671 principals in attendance.
There were about 815 principals in attendance.
There were about 204 principals in attendance.
The correct option is (A).
What is Arithmetic?The mathematical branch known as arithmetic deals with the study and application of numbers, their relationships, and mathematical observations.
As per the given data:
The total number of people in the recent conference = 875
The total number of people in one exhibit room = 60
Number of teachers in one exhibit room = 46
Number of principals in one exhibit room = 14
To find out the total number of exhibit rooms:
= Total number of people in the conference / total people in one room
= 875 ÷ 60
= 14.58 = 15 {rounding off to the nearest integer}
Number of principals in one exhibit room = 14
Total number of principals in the conference:
= Number of rooms × Principals in one room
= 15 × 14 = 210 which is equal to 204 {approximate answer}
There were about 204 principals in attendance.
Hence, There were about 204 principals in attendance.
To learn more about arithmetic, click:
brainly.com/question/23848329
anyone know the answer? its algrebra
Does the equation represent an exponential function?
y = 4 • 5x
Yes
No
Answer:
yes is rhe anwers that was that i put
Carlos bought 6.5 pounds of bananas for $5.20.
● What is the price per pound of the bananas that Carlos bought?
What quantity of bananas would one dollar buy?
)A spinner is divided into sections of equal size, of which some are red, some are blue, and the remaining are green. The probability of the arrow landing on a section colored red is 50%. The probability of the arrow landing on a section colored blue is 10%. What is the probability of the arrow landing on a section colored green? I need help
Answer:
40%
Step-by-step explanation:
The probability of the arrow landing on the green section is a 40% chance
This is because there are only 3 sections where one is 50 and the other is 10
To find the green we can create an equation, where x = green section
50 + 10 + x = 100
The equation equals 100 because that's the highest the percentage will go in probability, unless we were told otherwise
60 + x = 100
x = 100 - 60
x = 40
The diameter of Jacob's circular tabletop is 6 feet. What is the area, in square feet, of Jacob's tabletop? A 6 B. 9 С. 12 D 36
Answer:
B. 9
Step-by-step explanation:
the area = π × 3² = 9π ft²
Area of a circle = pi x R^2
R is the radius which is 1/2 the diameter.
R = 6/2 = 3 feet
Area = pi x3^2
Area = 9pi
The answer is B
For the standard normal random variable z, find z for each situation. If required, round your answers to two decimal places. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300)'
a. The area to the left of z is 0.1827. z =
b. The area between −z and z is 0.9830. z =
c. The area between −z and z is 0.2148. z =
d. The area to the left of z is 0.9997. z =
e. The area to the right of z is 0.6847. z=
The z-values for the given situations are approximate:
a. The area to the left of z is 0.1827. z = -0.90
b. The area between −z and z is 0.9830. z = 2.17
c. The area between −z and z is 0.2148. z = 0.85
d. The area to the left of z is 0.9997. z = 3.49
e. The area to the right of z is 0.6847. z= -0.48
a. For an area of 0.1827 to the left of z, the corresponding z-value can be found using a standard normal distribution table or a statistical calculator. The z-value is approximately -0.90.
b. To find the z-value for an area between -z and z equal to 0.9830, we need to find the value that corresponds to (1 - 0.9830)/2 = 0.0085 in the upper tail of the standard normal distribution. Using the table or calculator, the z-value is approximately 2.17.
c. Similarly, for an area between -z and z equal to 0.2148, we find the value that corresponds to (1 - 0.2148)/2 = 0.3926 in the upper tail. The z-value is approximately 0.85.
d. For an area of 0.9997 to the left of z, we find the value that corresponds to 0.9997 in the upper tail. The z-value is approximately 3.49.
e. To find the z-value for an area to the right of z equal to 0.6847, we find the value that corresponds to 1 - 0.6847 = 0.3153 in the upper tail. The z-value is approximately -0.48.
In summary, the z-values for the given situations are approximate:
a. -0.90
b. 2.17
c. 0.85
d. 3.49
e. -0.48
These values can be used to determine the corresponding percentiles or probabilities for the standard normal distribution. The values are typically found using standard normal distribution tables or statistical calculators that provide the cumulative probability distribution function (CDF) for the standard normal distribution.
For more such answers on z-values
https://brainly.com/question/28000192
#SPJ8
Bonds that do not have any assets of the issuer pledged as collateral, sometimes named junk bonds, are known as: Select one: a. Secured bonds b. Callable bonds c. Convertible bonds d. Unsecured bonds
Bonds that do not have any assets of the issuer pledged as collateral and are often referred to as junk bonds are known as unsecured bonds.
Unsecured bonds, also known as non-collateralized bonds or debentures, are debt securities issued by companies or governments that do not have any specific assets pledged as collateral. These bonds rely solely on the creditworthiness and reputation of the issuer for repayment. They are considered riskier investments compared to secured bonds because in the event of default, there are no specific assets backing the bondholders' claims.
The term "junk bonds" is often used to describe high-yield bonds that carry a higher risk of default. These bonds are typically issued by companies with below-price-grade credit ratings. The term "junk" refers to the perceived low quality or higher risk associated with these bonds.
Learn more about price here:
https://brainly.com/question/19091385
#SPJ11
Scores on an exam follow an approximately normal distribution with a mean of 76. 4 and a standard deviation of 6. 1 points. What is the minimum score you would need to be in the top 7%?.
If the scores on an exam follow an approximately normal distribution with a mean of 76.4 and a standard deviation of 6.1 points, then the minimum score needed to be in the top 7% is calculated to be 85.404.
This type of normal distribution problem can be solved by using the z-score.
Considering Z to be the standard score, μ to be the mean, and σ to be the standard deviation, the z-score formula to find the minimum score to be in the top 7% can be given as,
Z = x - μ / σ
z-score can be determined using a standard table if the p-value is known.
As the minimum score to be in the top 7% is required to be found, p-value = 0.07
In the standard table, the z-score corresponding to the p-value of 0.07 is found to be 1.476
Therefore,
1.476 = x - 76.4 / 6.1
1.476 (6.1) = x - 76.4
9.004 = x - 76.4
x = 9.004 + 76.4
x = 85.404
Hence, the minimum score required to be in the top 7% is equal to 85.404
To learn more about normal distribution, click here:
https://brainly.com/question/4079902
#SPJ4
anemia for the study of jordanian children in exercise 4, the sample mean hemoglobin level was 11.3 g/dl and the sample standard deviation was 1.6 g/dl. a significance test yields a p-value of 0.0016. (a) interpret the p-value in context. (b) what conclusion would you make if a 0.05? a 0.01? justify your answer.
(a) The interpret the p-value in context of 0.0016 indicates that the probability of obtaining a sample mean hemoglobin level of 11.3 g/dl or lower.
(b) The conclusion would make if a 0.05 is rejected because the p-value (0.0016) is less than the significance level.
If using a significance level of 0.01, the null hypothesis would still be rejected because the p-value is less than 0.01.
Anemia Study Results(a) The p-value of 0.0016 indicates that the probability of obtaining a sample mean hemoglobin level of 11.3 g/dl or lower, assuming that the true population mean is 12 g/dl (or higher), is only 0.0016. This suggests that the observed difference between the sample mean and the hypothesized population mean is statistically significant and unlikely to be due to chance alone.
(b) If using a significance level of 0.05, the null hypothesis (that the true population mean is 12 g/dl or higher) would be rejected because the p-value (0.0016) is less than the significance level. Therefore, it can be concluded that the sample provides evidence that the true population mean hemoglobin level is lower than 12 g/dl.
If using a significance level of 0.01, the null hypothesis would still be rejected because the p-value is less than 0.01. In this case, the evidence is even stronger, and the conclusion that the true population mean is lower than 12 g/dl would be even more robust.
Learn more about Anemia Study Results here:
https://brainly.com/question/28200198
#SPJ4
What is the scale factor applied to Figure A to produce Figure B.
O
A 9
B 6
C 3
D 12
The scale factor applied to Figure A with one side's length of 6 inches to produce Figure B with one side's length of 18 inches is C. 3.
What is the scale factor?The scale factor refers to the ratio of one scale or object compared to another.
The scale factor can increase or decrease the measurement of the object.
The first side length of Figure A = 3 inches
The second side length of Figure A = 6 inches
The first side length of Figure B = 9 inches (3 x 3)
The second side length of Figure B = 18 inches (6 x 3)
Thus, the scale factor used on Figure A to produce Figure B is C. 3.
Learn more about the scale factor at https://brainly.com/question/28339205.
#SPJ1
A culture of bacteria triples by the end of each hour. If there were initially 40 bacteria in a culture, how many bacteria should be there after 3 hours.
Answer: 360 bacteria
Step-by-step explanation: if it triples every hour, you would need to triple the amount of hours, and multiply that by 40 since 40 was the initial bacterial count. Hope this helps:)
The critical value, or z*, that is used to construct a confidence interval for a proportion depends upon? A. the confidence level. B. the sample size.C. the confidence level and the sample size. D. the sample size and the sample proportion. E. the confidence level, the sample size, and the sample proportion.
The critical value that is used to construct a confidence interval for a proportion depends upon C. the confidence level and the sample size.
The critical value used to construct the confidence interval for proportion depends on:
1) The sample size:
The probability changes as the sample size changes as the distribution of the test statistics is dependent on sample size, thus the critical value will depend on sample size.
2) The confidence level:
The critical value is always calculated by using the confidence level, so it is dependent on it.
The sample proportion is the observed value which is used to perform the test, but not to construct the critical value.
Thus the correct option is:
Option C: The confidence level and sample size.
To learn more about probability check the link below:
https://brainly.com/question/13604758
#SPJ4
The
The table shows the average daily number of hours sleep of 10 children.
Age (years)
6 1 3 8 4 5 2 7 9 7
Number of hours sleep 12.5 15 13.2 11 14 12 14 11.69.8 11
The first eight results have been plotted.
a) Plot the next two points.
x
Number of hours sleep
b) What type of correlation is shown
by the graph? Negative
10
c) Draw a line of best fit.
2
4
6
8
10
Age (years)
Please help.
Answer:
C: about 10 Hours
Step-by-step explanation:
i was on the assignment and i got C correct
The missing points are (7, 11), and (9, 9.8) and the type of correlation is negative.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
\(\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\\\\\\\rm c = \dfrac{\sum y -m \sum x}{n}\)
Let the line of best fit is:
y = mx + c
The missing points are:
(7, 11), and (9, 9.8)
The correlation will be negative.
The line of best fit is shown in the picture.
Thus, the missing points are (7, 11), and (9, 9.8) and the type of correlation is negative.
Learn more about the line of best fit here:
brainly.com/question/14279419
#SPJ5