Answers
Answer: 5
Step-by-step explanation:
They are the points
There are 5 points so answer is 5
Related Questions
Write a polynomial function in standard form with real coefficients whose zeros include 1,4i, and -4i
Answers
(x - 1)(x - 4i)(x + 4i)
To write this polynomial in standard form, we need to multiply out the factors and simplify:
(x - 1)(x - 4i)(x + 4i)
= (x - 1)(x^2 - (4i)^2)
= (x - 1)(x^2 - 16i^2)
= (x - 1)(x^2 + 16)
Expanding the product, we get:
x^3 + 16x - x^2 - 16
So the polynomial function with real coefficients whose zeros include 1, 4i, and -4i is:
f(x) = x^3 - x^2 + 16x - 16
:))
Answer:
f(x) = x^3 - x^2 + 16x - 16
Step-by-step explanation:
If a polynomial has the zeros 1, 4i, and -4i, then it must have the factors (x - 1), (x - 4i), and (x + 4i). This is because a factor of (x - a) produces a root of x = a.
To find the polynomial, we can multiply these factors together:
(x - 1)(x - 4i)(x + 4i)
= (x - 1)(x^2 - (4i)^2)
= (x - 1)(x^2 + 16)
= x^3 + 16x - x^2 - 16
So the polynomial function in standard form with real coefficients whose zeros include 1, 4i, and -4i is:
f(x) = x^3 - x^2 + 16x - 16
Raman is watching the movie 4 times and he fislokw s the value wirh
Answers
Answer:learn how to spell :)
Step-by-step explanation:
Joe bought a house for $370,000. The assessed value of
the house is $280,000. The property tax rate is 2.9%. What
is Joe's annual property tax bill for this house?
Answers
Answer: Joe's property tax bill is based on the assessed value of the house, not the purchase price.
To calculate his annual property tax bill, we first need to calculate the assessed value of the house that will be used to determine the tax. The assessed value is given as $280,000.
The annual property tax bill is then calculated as follows:
Tax bill = assessed value x tax rate
Tax bill = $280,000 x 0.029
Tax bill = $8,120
Therefore, Joe's annual property tax bill for this house is $8,120.
What is the area of Rectangle A?
Answers
Answer:
30 square units
Step-by-step explanation:
The area of a rectangle is its length multiplied by its width.
We can see that the length of Rectangle A is 6 units, and its width is 5 units.
Multiplying these together to get the rectangle's area:
6 units × 5 units = 30 square units
Let $a_1, a_2, a_3,\dots$ be an arithmetic sequence.
If $a_1 + a_3 + a_5 = -12$ and $a_1a_3a_5 = 80$, find all possible values of $a_{10}$.
(There are multiple)
Answers
The possible values of [tex]$a_{10}$[/tex] are [tex]$-\frac{263}{4}$[/tex]and [tex]$-\frac{13}{5}$[/tex].
Since [tex]$a_1, a_2, a_3,\dots$[/tex] is an arithmetic sequence, we can write[tex]$a_3 = a_1 + d$[/tex] and [tex]$a_5 = a_1 + 2d$[/tex] where [tex]$d$[/tex] is the common difference between consecutive terms. Then the given equations become[tex]$3a_1 + 4d = -12$ and $a_1(a_1 + d)(a_1 + 2d) = 80$.[/tex] Simplifying the second equation gives $a_[tex]1^3 + 3da_1^2 + 2d^2a_1 - 80 = 0$.[/tex]
We can solve for [tex]$d$[/tex] in the first equation: [tex]$d = \frac{-3a_1-12}{4} = -\frac{3}{4}a_1 - 3$[/tex]. Substituting this into the second equation yields a cubic equation in terms of[tex]$a_1$[/tex]:
[tex]a\frac{3}{1}-[/tex] [tex]\frac{9}{4} a\frac{2}{1} -[/tex] [tex]\frac{15}{4} a_{1}- 80=0[/tex]
Using synthetic division or another method, we can find that [tex]$a_1 = -5$[/tex] is a root of this equation. Dividing by [tex]$a_1 + 5$[/tex] yields the quadratic [tex]$a_1^2 - \frac{1}{4}a_1 - 16 = 0$[/tex], which has roots [tex]$a_1 = -4$[/tex] and [tex]$a_1 = 4/5$[/tex].Therefore, the possible values of the common difference [tex]$d$[/tex] are [tex]$-\frac{27}{4}$[/tex] and [tex]\frac{4}{5}$[/tex]
Using [tex]$a_1 = -5$[/tex] and [tex]$d = -\frac{27}{4}$[/tex], we find that [tex]$a_{10} = a_1 + 9d = -5 - \frac{243}{4} = -\frac{263}{4}$.[/tex]
Using [tex]$a_1 = -5$[/tex] and [tex]$d = \frac{4}{5}$[/tex], we find that [tex]$a_{10} = a_1 + 9d = -5 + \frac{36}{5} = -\frac{13}{5}$.[/tex]
Therefore, the possible values of [tex]$a_{10}$[/tex] are [tex]$-\frac{263}{4}$[/tex]and [tex]$-\frac{13}{5}$[/tex].
For more questions like Arithmetic sequence click the link below:
brainly.com/question/15412619
#SPJ1
Please help, It's a statistics question, I need the answer ASAP
A particular variable measured on the US population is approximately normally distributed with a mean of 112 and a standard deviation of 22. Consider the sampling distribution of the sample mean for samples of size 16.
Answers
Answer:
Step-by-step explanation:
The sampling distribution of the sample mean for samples of size n is approximately normal with mean μ and standard deviation σ/sqrt(n), where μ is the mean of the population, σ is the standard deviation of the population, and sqrt(n) is the square root of the sample size.
In this case, the population mean is μ = 112 and the population standard deviation is σ = 22. We are interested in the sampling distribution of the sample mean for samples of size n = 16.
The mean of the sampling distribution of the sample mean is the same as the population mean, which is μ = 112.
The standard deviation of the sampling distribution of the sample mean is σ/sqrt(n) = 22/sqrt(16) = 5.5.
Therefore, the sampling distribution of the sample mean for samples of size 16 is approximately normal with mean 112 and standard deviation 5.5.
PLSSS HELP ITS DUE TOMMROW I WILL GIVE U MORE POINTS WHEN I GET MORE PLSSS
Answers
Answer:
[tex]A_{\text{red}} = 1766.25 \text{ in}^2[/tex]
Step-by-step explanation:
We can see that there are four bands total on the target, two of which are red bands. With this information, we can solve for the radius of the circle within each band, since we know that each band is the same width:
[tex]r_1 = \dfrac{1}{4} \cdot 30 = 7.5\\[/tex]
[tex]r_2 = \dfrac{2}{4} \cdot 30 = 15\\[/tex]
[tex]r_3 = \dfrac{3}{4} \cdot 30 = 22.5\\[/tex]
[tex]r_4 = 30[/tex]
We can now find the area of each red band by subtracting:
the area of the circle within the white band just inward of the red band
-- from --
the area of the circle within the red band.
Finding the area of the outer red band:
[tex]A_{\text{outer red}} = A(\text{circle within outer red}) - A(\text{circle within outer white})[/tex]
[tex]A_{\text{outer red}} = A(\odot \text{ with radius }r_4) - A(\odot \text{ with radius } r_3)[/tex]
↓ substituting the radius values into the circle area formula ([tex]\pi r^2[/tex])
[tex]A_{\text{outer red}} = (\pi \cdot 30^2) - (\pi \cdot 22.5^2)[/tex]
↓ using 3.14 for [tex]\pi[/tex]
[tex]A_{\text{outer red}} = (3.14 \cdot 30^2) - (3.14 \cdot 22.5^2)[/tex]
↓ evaluating the right side
[tex]A_{\text{outer red}} = 2826 - 1589.625[/tex]
[tex]A_{\text{outer red}} = 1236.375 \text{ in}^2[/tex]
Finding the area of the inner red band:
[tex]A_{\text{inner red}} = A(\text{circle within inner red}) - A(\text{circle within inner white})[/tex]
[tex]A_{\text{inner red}} = A(\odot \text{ with radius }r_2) - A(\odot \text{ with radius } r_1)[/tex]
↓ substituting the radius values into the circle area formula ([tex]\pi r^2[/tex])
[tex]A_{\text{inner red}} = (\pi \cdot 15^2) - (\pi \cdot 7.5^2)[/tex]
↓ using 3.14 for π
[tex]A_{\text{inner red}} = (3.14 \cdot 15^2) - (3.14 \cdot 7.5^2)[/tex]
↓ evaluating the right side
[tex]A_{\text{inner red}} = 706.5 - 176.625[/tex]
[tex]A_{\text{inner red}} = 529.875 \text{ in}^2[/tex]
Finally, we can find the area of all of the red on the target by adding the area of the outer and inner red bands.
[tex]A_{\text{red}} = A_{\text{outer red}} + A_{\text{inner red}}[/tex]
[tex]A_{\text{red}} = 1236.375 \text{ in}^2 + 529.875 \text{ in}^2[/tex]
[tex]\boxed{A_{\text{red}} = 1766.25 \text{ in}^2}[/tex]
algebra please help quickly, you don't have to explain anything just straight up state the answers true or false
Answers
Answer:
they are correct
Step-by-step explanation:
The scatter plot shows the amount of money, y, Sally was paid in each of her jobs versus the number of hours x she worked in each job.
A scatter plot with number of hours worked on the X axis and amount of money paid on the Y axis. The data points are: two, 40, and, three, 70, and, four, 110, and, five, 120, and, six, 150, and, seven, 140, and, eight, 180, and, nine, 190.
Part A
Which equation best models a line of fit for the data?
A. y = 24x + 10
B. y = 21x + 11
C. y = −18x + 15
D. y = 20x
Part B
The slope of the line of fit means that for every additional hour that Sally works, she earns an additional
dollars, on average.
Answers
Using the given data, the equation that best models a line of fit for the data is y = 20x. The slope of the line of fit indicates that for each additional hour that Sally works, she earns an additional $20, on average. So, the correct option is D).
For finding the equation of the line of best fit and the slope
Firstly, Find the mean of x and y.
Mean of x = (2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) / 8 = 5.5
Mean of y = (40 + 70 + 110 + 120 + 150 + 140 + 180 + 190) / 8 = 127.5
Calculate the deviations from the mean for x and y.
Deviation from mean of x = x - mean of x
= [2 - 5.5, 3 - 5.5, 4 - 5.5, 5 - 5.5, 6 - 5.5, 7 - 5.5, 8 - 5.5, 9 - 5.5]
= [-3.5, -2.5, -1.5, -0.5, 0.5, 1.5, 2.5, 3.5]
Deviation from mean of y = y - mean of y
= [40 - 127.5, 70 - 127.5, 110 - 127.5, 120 - 127.5, 150 - 127.5, 140 - 127.5, 180 - 127.5, 190 - 127.5]
= [-87.5, -57.5, -17.5, -7.5, 22.5, 12.5, 52.5, 62.5]
Calculate the product of the deviations for each data point.
Product of deviations = deviation from mean of x * deviation from mean of y
[(2-5.5) * (40-127.5)] + [(3-5.5) * (70-127.5)] + [(4-5.5) * (110-127.5)] + [(5-5.5) * (120-127.5)] + [(6-5.5) * (150-127.5)] + [(7-5.5) * (140-127.5)] + [(8-5.5) * (180-127.5)] + [(9-5.5) * (190-127.5)]
= [-135.625, -51.875, 32.625, 28.125, 17.8125, 26.25, 137.8125, 229.0625]
Calculate the sum of the deviations of x squared.
Sum of deviations of x squared = (deviation from mean of x)²
= (-3.5)² + (-2.5)² + (-1.5)² + (-0.5)² + 0.5² + 1.5² + 2.5² + 3.5²
= 70
Calculate the slope of the line of best fit.
slope = sum of products of deviations / sum of deviations of x squared
= (−135.625 + (−51.875) + 32.625 + 28.125 + 17.8125 + 26.25 + 137.8125 + 229.0625) / 70
= 20
Calculate the y-intercept of the line of best fit.
y-intercept = mean of y - slope * mean of x
= 127.5 - 20 * 5.5
= 10
The equation of the line of best fit in slope-intercept form.
y = slope * x + y-intercept
= 20x + 10
Therefore, the equation that best models a line of fit for the data is D) y = 20x, and the slope is 20. So, the correct answer is D).
To know more about slope-intercept form:
https://brainly.com/question/29146348
#SPJ1
A principal of $3900 is invested at 4.25% interest, compounded annually. How much will the investment be worth after 5 years?
Answers
If principal of $3900 is invested at 4.25% interest, compounded annually, the investment will be worth approximately $4,756.89 after 5 years.
To calculate the future value of the investment, we use the formula for compound interest:
A = [tex]P(1 + r/n)^{(n*t)[/tex]
where A is the future value, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, P = $3900, r = 4.25%, n = 1 (compounded annually), and t = 5. Plugging these values into the formula, we get:
A = 3900(1 + 0.0425/1)⁵
A = 3900(1.0425)⁵
A ≈ $4,756.89
To learn more about investment click on,
https://brainly.com/question/31784776
#SPJ1
HELP ITS AN EMERGENCY
Given the expression: 4x2 + 18x − 10
Part A: What is the greatest common factor? Explain how to find it. (3 points)
Part B: Factor the expression completely. Show all necessary steps. (5 points)
Part C: Check your factoring from Part B by multiplying. Show all necessary steps. (2 points)
Answers
Answer:
Part A ----> 2
Part B ----> 2 (2x - 1) (x + 5)
Part C -----> See explanation below
Step-by-step explanation:
Given expression is
4x² + 18x - 10
Part A
The greatest common factor (GCF) of the terms 4x², 18x and 10 is the largest number that divides into all three numbers without a remainder
To find this
Find the prime factors of each of the terms
4x² = 2 · 2 · x · x
18x = 2 · 3 · 3 · x
10 = 2 · 5
The prime factor common to all 3 is 2
Therefore the GCF of the expression is 2
Part B
The factored expression can be obtained by factoring out the GCF
4x² + 18x - 10 = 2(2x² + 9x - 5)
We can further factor the term in parentheses:
2x² + 9x - 5
To do this,
Break the expression into groups:
= (2x² - x) + (10x - 5)
Factor x from 2x² - x: x(2x - 1)
Factor 5 from 10x - 5: 5(2x - 1)
Therefore
(2x² - x) + (10x - 5) = x(2x - 1) + 5(2x - 1)
Factor out the common term 2x -1 to get
(2x - 1)(x + 5)
Therefore
4x² + 18x + 10 = 2 (2x - 1) (x + 5)
Part C
Checking if factorization is correct
Multiply (2x - 1)(x + 5) using the FOIL method
= 2x ·x + 2x · 5 + (-1) · x + (-1) · 5
= 2x² + 10x -1x -5
= 2x² + 9x - 5
Multiply the whole expression by 2
2 · 2x² + ² · 9x - 2 · 5
= 4x² + 18x + 10
which is the original expression
So the factorization is correct
Which of the following pairs consists of equivalent fractions? 3/9 and 5/15 ,12/20 and 20/25,5/6 and 6/5,6/12 and3/4
Answers
Answer:
[tex]The[/tex] [tex]Answer[/tex] [tex]Is:[/tex] [tex]\frac{3}{9}[/tex] [tex]&[/tex]& [tex]\frac{5}{15}[/tex]
Step-by-step explanation:
Divide by 4 , 2nd fraction Divide by 5:
3/4 ≠ 4/5
5/6 ≠ 6/5 We can already see it.
Divide by 3. . .
2/4 ≠ 3/4
Divide by 3 , 2nd fraction Divide by 5:
1/3 = 1/3 [tex]Perfect![/tex]
The answer is, [tex]\frac{3}{9}[/tex] & [tex]\frac{5}{15}[/tex]
Bob has saved $600 each month for the last 3 years
to make a down payment on a house. The account
earned an interest rate of 0.50 percent per month.
How much money is in Bob's account?
Answers
Answer:
300
Step-by-step explanation:
determine whether the sample may be biased. a company randomly selects 500 customers from its computer database and then surveys those customers to find out how they like their service.
Answers
Answer:
Step-by-step explanation:
Based on the information given, it is not possible to determine whether the sample may be biased or not.
However, there is a possibility that the sample may be biased if the company's computer database does not accurately represent its entire customer base. For example, if the database contains only a specific type of customers, such as those who frequently make large purchases, then the sample may not be representative of the company's entire customer base. In this case, the survey results may not accurately reflect the opinions of all the company's customers.
It is also important to consider other factors such as how the survey was conducted and how the questions were framed, as these can also affect the validity of the survey results
Beth has three as much money as Dennis. Dennis has $20 more than Will. If all of them had a total of $1260, how much money does Beth have?
Answers
- Let x be the amount of money that Will has.
- Then, Dennis has $20 more than Will, so Dennis has x + $20.
- Beth has three times as much money as Dennis, so Beth has 3(x + $20).
We know that the total amount of money that all three have is $1260, so we can write an equation:
x + (x + $20) + 3(x + $20) = $1260
Simplifying and solving for x:
x + x + $20 + 3x + $60 = $1260
5x + $80 = $1260
5x = $1180
x = $236
So Will has $236, Dennis has x + $20 = $256 + $20 = $276, and Beth has 3(x + $20) = 3($256) = $768.
Therefore, Beth has $768.
Answer:
Beth has $752
Step-by-step explanation:
First we lay out what we know:
Beth: 3x+20
Will: x
Dennis: x+20
Next we write the equation:
3x+20+20+x+x=1260
Then we add any numbers that can be added to each other:
5x+40=1260
Then we solve,
We first minus 40 from both sides of the equation,
5x+40=1260
-40 -40
---------------------
5x=. 1220
Last we divide 1220 by 5,
5x=1220
÷5. ÷ 5
----------------
x=244
Now that we know that x is 244 we fill in the blanks,
Beth: 732+20
Will: 244
Dennis: 244+20
Then we just solve the equations,
Beth: 732+20=752
Will: 244
Dennis: 244+20=264
That's it,
if you want to check your work you can add them all up and if they equal 1260 it's correct.
752+244+264=1260
Your welcome, have a good day/night.
Frank spends $90 on his $1800 monthly income what percent of monthly check does not go toward food
Answers
To find the answer we hav ego do these steps:
1800/100 = 18 - 18 dollars is 1%
90/18 = 5 - 90/18 = 5%
5% of his income is spent on food
If Frank spends $90 on his $1800 monthly income, then 95 percent of monthly check does not go toward food.
Let's say Frank spends $90 on food and has a monthly income of $1800. We can calculate the percentage of his monthly check that does not go towards food as follows:
Percentage = (Total Income - Food Expenses) / Total Income
Percentage = (1800 - 90) / 1800
Percentage = 0.95 = 95%
Therefore, 95% of Frank's monthly check does not go towards food.
Here are the steps in detail:
Subtract the food expenses from the total income to get the amount of money that is not spent on food.
Divide the amount of money that is not spent on food by the total income to get the percentage.
In this case, the amount of money that is not spent on food is $1800 - $90 = $1710. The percentage of the monthly check that is not spent on food is $1710 / $1800 = 0.95 = 95%.
To learn more about percent here:
https://brainly.com/question/31323953
#SPJ2
A number cube with faces labeled 1 to 6 is rolled once.
The number rolled will be recorded as the outcome.
Consider the following events.
Event A: The number rolled is odd.
Event B: The number rolled is greater than 3.
Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.
Answers
The possible outcomes for each of the given events are:
A --> {1, 3, 5}
B --> {4, 5, 6}
How to find the outcomes for each event?For a regular number cube, the sample space (possible outcomes) is:
S = {1, 2, 3, 4, 5, 6}
Now we have two events.
A = rolling an odd number
Here the outcomes can be any of the odd numbers in the sample space, so the possible outcomes are:
A --> {1, 3, 5}
The second event is:
B = the number rolled is greater than 3. Again, the outcomes are thevalues in the sample space that are larger than 3, these are:
B --> {4, 5, 6}
Learn more about sample spaces at:
https://brainly.com/question/2117233
#SPJ1
solve for x image attached please help x, 3 ,7 set up the proportion x/3=?
Answers
The proportion relation obtained from the similar triangles indicates that the x/3 = 10/x
What are similar triangles?Similar triangles are triangles that have the same shape but their sizes may vary.
The proportion equation from the image based on the ratio of the corresponding sides of the similar right triangles can be found as follows;
The side x is the hypotenuse side of the smallest right triangle
The ratio x/3, is equivalent to the ratio of the hypotenuse side to the shortest side of the right triangle
The corresponding ratio in the medium triangle is ((x² - 3²) + 7²)/(x² - 3²)
((x² - 3²) + 7²)/(x² - 3²) = (x² + 40)/(x² - 3²)
The corresponding ratio in the large similar right triangle is (7 + 4)/x = 10/x
Therefore, the corresponding ratio is; x/3 = 10/x
The proportion is; x/3 = 10/x
Learn more on similar triangles here: https://brainly.com/question/30850803
#SPJ1
Select each angle of rotation about the origin, (0, 0) that maps WXYZ TO W’ X’ Y’Z
Answers
The angle of rotation about the origin, (0, 0) that maps WXYZ TO W’ X’ Y’Z are
180 degrees
540 degrees
900 degrees
How to find the angle of rotationThe transformation rule for an angle of 180 degrees is simply a reflection or a flip. This means that any object or figure that undergoes this transformation will be flipped over a line or axis.
The rule is (x, y) will become (-x, -y)
Where 540 degrees = 360 + 180
where 900 degrees = 360 + 360 + 180
Learn more about angle of rotation at
https://brainly.com/question/28672446
#SPJ1
Please help!!!
Natalie gathered a random sample of flower bouquets at the florist. She calculated data on different variables. For one data that she collected, she constructed a bar graph
Which of the following variables did she use?
O Type of flowers in each bouquet
O Amount of water needed for each bouquet
O Number of flowers in each bouquet
O Price for each bouquet
Answers
The variables that Natalie used in the data collected was C. Number of flowers in each bouquet.
How to find the variable ?The bar graph that Natalie crafted utilized the variable "number of flowers in each bouquet." This particular type of graph reveals the frequency or count associated with every number of flowers contained within a single bouquet.
As an illustration, let us suppose there were 20 bouquets holding 5 flowers, 30 bouquets possessing 10 flowers, and 15 bouquets that had 15 flowers each; consequently, the bar chart would exhibit exactly three bars symbolizing the count for all three categories as outlined above.
Find out more on variables at https://brainly.com/question/29884403
#SPJ1
The list below gives the number of people who made the trip for a selection of nine summer days 2756 64 36 40 29 2756 and 30 find the range of the data set
Answers
Answer:
The range is 37
Step-by-step explanation:
highest - lowest = range
64-27= 37
Hope it helped! :)
Transactions on Furnell's credit card are shown for the month of June. The interest rate is 1.4% per month.
June 1 Balance $352.12
June 4 Sears $331.89
June 8 eBay $81.58
June 15 Outback $30
June 18 Payment $200
Find the average daily balance $
184.89
Find the interest for the month $
Find the balance for the following month $
Answers
The balance for the following month is $598.18.
How to solveThe average daily balance for June is $184.89.
To calculate the interest for the month, multiply the average daily balance by the interest rate: $184.89 * 1.4% = $2.59.
To find the balance for the following month, add the initial balance, transactions, and interest, then subtract the payment: $352.12 + $331.89 + $81.58 + $30 + $2.59 - $200 = $598.18.
The balance for the following month is $598.18.
Read more about interest rates here:
https://brainly.com/question/25793394
#SPJ1
If the dealership you are buying the car from is offering 6.3% interest on a 5 year loan, what will your monthly payment be? How am I able to solve this when the selling price is $56,937.
Answers
Answer:
Step-by-step explanation:
To calculate the monthly payment on a loan, you can use the formula for the monthly payment on an annuity: P = (r * PV) / (1 - (1 + r)^(-n)), where P is the monthly payment, r is the monthly interest rate, PV is the present value of the loan (i.e., the amount borrowed), and n is the total number of monthly payments.
In this case, the amount borrowed is $56,937 and the interest rate is 6.3% per year. To convert this to a monthly interest rate, we divide by 12: r = 0.063 / 12 = 0.00525. The loan term is 5 years, so the total number of monthly payments is n = 5 * 12 = 60.
Substituting these values into our formula for the monthly payment, we get: P = (0.00525 * 56937) / (1 - (1 + 0.00525)^(-60)) ≈ $1102.53. So, the monthly payment on this loan would be approximately $1102.53.
What is ? Complete the statement.
is the ratio of the circumference to the ?
rence of a Circle-Instruction-Level G
area
circumference
radius
diameter
of a circle.
Answers
The ratio of the circumference of a circle with radius r to its area is 2:r or 2 to r.
Define circleA circle is a two-dimensional shape that is defined as the set of all points in a plane that are at a fixed distance, called the radius, from a given point, called the center. The distance around the circle is called the circumference, and the distance across the circle passing through the center is called the diameter.
The circumference of a circle with radius r is given by the formula:
C = 2πr
The area of a circle with radius r is given by the formula:
A = π×r²
Therefore, the ratio of the circumference of a circle with radius r to its area is:
C/A = (2πr) / (πr²)
Simplifying the expression by canceling out π and r from the numerator and denominator, we get:
C/A = 2/r
Therefore, the ratio of the circumference of a circle with radius r to its area is 2:r or 2 to r.
To know more about diameter, visit:
https://brainly.com/question/5501950
#SPJ1
The complete question is:
Find the following ratio.
The ratio of circumference of circle with radius r to its area.
Water is leaking out of an inverted conical tank at a rate of 11500.0 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 9.0 m and the the diameter at the top is 4.5 m. If the water level is rising at a rate of 21.0 cm/min when the height of the water is 2.0 m, find the rate at which water is being pumped into the tank in cubic centimeters per minute.
Answers
water is being pumped into the tank at a rate of 23.7 cm³/min.we can take the derivative of the volume formula with respect to time and solve it
what is derivative ?
In mathematics, a derivative is a measure of how much a function changes as its input value changes. More specifically, the derivative of a function is defined as the rate of change of the function at a particular point.
In the given question,
We can solve this problem using related rates, where we relate the rate of change of one variable to the rate of change of another variable.
Let's denote the height of the water in the tank by h, and the radius of the water surface by r. Then, we can use the formula for the volume of a cone to relate these variables:
V = (1/3)πr²h
We are given that the tank has height 9.0 m and diameter (and thus radius) 4.5 m at the top. We can use this information to find the relationship between h and r:
r = (1/2) × diameter = 2.25 m
h = 9.0 m - 2.0 m = 7.0 m
Now, we can take the derivative of the volume formula with respect to time:
dV/dt = (1/3)π(2r(dr/dt) + r²(dh/dt))
We want to find the rate at which water is being pumped into the tank, which is the rate of change of the volume with respect to time when the water level is rising at a rate of 21.0 cm/min. We are also given that water is leaking out of the tank at a rate of 11500.0 cm^3/min, so we can set these rates of change equal to each other:
dV/dt = (21.0 cm/min) × (1 m/100 cm)³ = 0.021 m³/min
11500.0 cm³/min = 11.5 × (1 m/100 cm)³ m³/min
Substituting these values and the values we found for r and h into the derivative formula, we get:
0.021 m³/min = (1/3)π(2(2.25 m)(dr/dt) + (2.25 m)²(11500.0 cm³/min)/(100 cm/m)³)
Simplifying and solving for dr/dt, we get:
dr/dt = [(0.021 m³/min) - (1/3)π(2(2.25 m)(11500.0 cm³/min)/(100 cm/m)³)] ÷ [(1/3)π(2(2.25 m))]
= 0.0237 m/min = 23.7 cm/min
Therefore, water is being pumped into the tank at a rate of 23.7 cm³/min.
To know more about derivative , visit:
https://brainly.com/question/25324584
#SPJ1
Elaina is trying to fit the longest stick she can into her pet lizard’s tank. She knows running it diagonally from the front corner to the back will give her the most room but she is uncertain what size she should buy. What is the biggest length stick that will fit into her 12 by 8 by 8 tank?
Answers
The biggest length stick that will fit is 16.49 units long.
What is the biggest length stick for the tank?The length stick which will fit into Elaina's 12* 8*8 tank can be found using the Pythagorean theorem.
The diagonal length, of tank will be equal to square root of the sum of the squares of its length, width and height.
So, the diagonal length of the tank, using Pythagorean theorem, is
= √(12² + 8² + 8²)
= √(144 + 64 + 64)
= √272
≈ 16.49.
Read more about tank lenght
brainly.com/question/27196379
#SPJ1
The standard deviation of test scores on a certain achievement test is 11.4. A random sample of 50 scores on this test had a mean of 75.3. Based on this
sample, find a 95% confidence interval for the true mean of all scores. Then give its lower limit and upper limit.
Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)
Lower limit:
Upper limit:
X
Ś
Answers
The lower limit is 72.1 and the upper limit is 78.5.
The sample mean is 75.3, and the standard error is 1.613.
What is standard deviation?The standard deviation is a measurement of how differently distributed a set of data values are from their mean or average. Finding the square root of the variance, which is the sum of the squared deviations between each data point and the mean, is how it is determined.
To find the confidence interval, we can use the formula:
Confidence interval = sample mean ± (critical value) x (standard error)
where the standard error is the standard deviation of the sample mean and the critical value is based on the desired confidence level and the sample size.
Since we want a 95% confidence interval and the sample size is 50, we can find the critical value from a t-distribution with 49 degrees of freedom (n-1). Using a t-distribution instead of a normal distribution is appropriate here because the population standard deviation is not known.
From a t-distribution table or calculator, the critical value for a 95% confidence interval with 49 degrees of freedom is approximately 2.009.
The standard error can be found using the formula:
standard error = standard deviation / sqrt(sample size)
Substituting the given values, we get:
standard error = 11.4 / sqrt(50) = 1.613
Now we can plug in the values into the formula for the confidence interval:
Confidence interval = 75.3 ± 2.009 x 1.613 = (72.14, 78.46)
Therefore, the lower limit is 72.1 and the upper limit is 78.5. The sample mean is 75.3, denoted by X-bar and the standard error is 1.613, denoted by Ś.
To know about standard deviation:
https://brainly.com/question/29808998
#SPJ1
Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(-4) = -11 B. g(0) = 2 C. g(7) = -1 D. g(-13) = 20
Answers
Answer:
Based on the information given, we know that the domain of g is -20 ≤ x ≤ 5 and the range is -5 ≤ g(x) ≤ 45. We also know that g(0) = -2 and g(-9) = 6.
A. g(-4) = -11: This statement could be true or false, as there is not enough information to determine its validity.
B. g(0) = 2: This statement is false, since we know that g(0) = -2.
C. g(7) = -1: This statement could be true or false, as there is not enough information to determine its validity.
D. g(-13) = 20: This statement is false, since -13 is outside the domain of g (-20 ≤ x ≤ 5).
Step-by-step explanation:Therefore, the statement that could be true for g is A. g(-4) = -11 or C. g(7) = -1.
Find the approximate area of the shaded region below, consisting of a right triangle with a circle cut out of it. Use 3.14 as an
approximation for pi.
a. 1.254 square meters
b. 312 square meters
c. 2, 822 square meters
d. 314 square meters
Answers
Answer:
(a) 1.254 square metersStep-by-step explanation:
We are given a figure, consisting of a right triangle with a circle cut out of it.
To Calculate : area of the shaded region below,
First Let's find the Area of the right triangle:
Area(triangle) = 1/2 × Base × Height
= 1/2 × 56 × 56
= 1/2 × 3136
= 3136/2
= 1568 m².
Now, We are diameter of the circle = 20 m
Radius of the circle = 20/2 = 10 m
Area of circle = πr²Acc. to question we have to use 3.14 as an
approximation for pi.
Area (circle) = 3.14 × 10 × 10
Area (circle) = 3.14 × 100
Area (circle) = 314 m²
Area of shaded region = Area of triangle - Area of circle =
= 1568 m² - 314 m²
= 1.254 square meters
Therefore, The approximate area of the shaded region is 1.254 square meters.
Option (a) is the required answer.
Joey wants to buy a $3,000 vehicle with 20 percent down for three years at 12 percent interest. What will his monthly payment be?
Monthly Payment per $1,000 Finance
A. $72.82
B. $89.67
C. $79.70
D. $119.56
Answers
Joey’s monthly payment is solved to be
C. $79.70
How to find the monthly payment20% down 600 to calculate the monthly payment on a 3 000 car we would pay 2 400.
the interest rate is 12% per annum which equates to 1% per month the term of the loan is three years which equates to 36 months we can use a formula to calculate the monthly payments
[tex]Monthly salary = (P * r * (1 + r)^n) / ((1 + r)^n - 1) .[/tex]
where
P is the principal (premium),
r is the monthly interest rate, and
n is the number of months.
Plug in the prices and we have:
[tex]Monthly salary = (2400 * 0.01 * (1 + 0.01)^{36} ) / ((1 + 0.01)^{36} - 1)[/tex]
= $79.65 per square foot
So Joey’s monthly payment would be $79.65.
Learn more about percent interest at
https://brainly.com/question/25793394
#SPJ1