Answer: $1,071.54
Step-by-step explanation:
To find the interest refund, first we need to calculate the total interest charged on the loan. We can do this by multiplying the monthly interest by the number of months in the loan:
Monthly interest = Total interest / Number of months
Monthly interest = $2,802 / 35
Monthly interest = $80.06
Total interest charged on the loan = Monthly interest x Number of months
Total interest charged on the loan = $80.06 x 35
Total interest charged on the loan = $2,802.10
Now we need to calculate the interest that would have been charged for the remaining 13 months of the loan:
Interest for remaining 13 months = Monthly interest x Remaining months
Interest for remaining 13 months = $80.06 x 13
Interest for remaining 13 months = $1,040.78
Finally, we can find the interest refund by subtracting the interest for the remaining 13 months from the total interest charged on the loan:
Interest refund = Total interest charged - Interest for remaining months
Interest refund = $2,802.10 - $1,040.78
Interest refund = $1,074.32
Therefore, the interest refund on the loan is $1,074.30.
The number of bacteria in a culture is growing at a rate of 3,000e^(2t/5) per unit of time t. At t=0, the number of bacteria present was 7,500. Find the number present at t=5.a. 1.200 e^2b. 3,000 e^2c. 7,500 e^2d. 7,500 e^5e. 15.000/7 e^7
The number of bacteria present with the given growth rate at t=5 is [tex]N(5) = 7,500 * e^2[/tex] and option x is the correct answer.
What is exponential growth?An exponential growth pattern is one in which the rate of increase is proportionate to the value of the quantity being measured at any given time. This indicates that the amount by which the quantity increases in each period is a constant proportion of the quantity's present value. Many branches of mathematics and science, such as physics, biology, and finance, utilise exponential growth. Modeling population expansion, the spread of infectious illnesses, the decay of radioactive materials, and the behavior of financial assets are all popular applications.
Given that, the number of bacteria present was 7,500.
The exponential growth is given by the formula:
[tex]N(t) = N(0) * e^{(kt)}[/tex]
Substituting the values N(0) = 7,500 and the growth rate is k = 2/5 we have:
[tex]N(5) = 7,500 * e^{(2/5 * 5)}\\N(5) = 7,500 * e^2[/tex]
Hence, the number of bacteria present at t=5 is [tex]N(5) = 7,500 * e^2[/tex] and option x is the correct answer.
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find the standard form of the parabola equation: 2x^(2)-8x-3y+11=0
The standard form of the parabola with the equation 2x² - 8x - 3y + 11 = 0 is y = 2/3x² - 8/3x + 11/3
Calculating the standard form of the parabola
Given that
2x² - 8x - 3y + 11 = 0
To put the given equation in standard form, we need to isolate the y term on one side of the equation.
Here's how to do it:
2x² - 8x - 3y + 11 = 0
Isolate 3y
This gives
3y = 2x² - 8x + 11
Divide through by 3
y = 2/3x² - 8/3x + 11/3
Hence, the standard form is y = 2/3x² - 8/3x + 11/3
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What is the meaning of logarithm in math?
In mathematics, a logarithm is a mathematical operation that determines how many times a given number (known as the base) must be multiplied by itself to produce another given number.
Logarithms are used to simplify complex calculations involving exponents and to convert between exponential and logarithmic expressions.
The logarithm of a number x to a given base b is represented as logb(x). For example, log10(100) = 2 because 10 multiplied by itself twice equals 100.
Logarithms have a wide range of applications in various fields, including mathematics, physics, engineering, finance, and computer science. They are particularly useful in scientific calculations involving large numbers, where working with exponents can become cumbersome. Logarithms are also used in the study of exponential growth and decay, as well as in the analysis of data sets with a wide range of values.
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1.3. The Dow Jones average (a stock market share index) dropped from 12 837 to 12 503 in one week in July 2012. 1.3.1. Calculate the drop in the share index. 1.3.2. If the price continued to drop at the same rate, calculate the Dow Jones average after 4 more weeks.
The Dow Jones average after 4 more weeks of the same rate of drop would be 11,167.
What is average?
Average, also known as mean, is a measure of central tendency that represents the typical or common value in a set of data. It is calculated by adding up all the values in a data set and then dividing the sum by the total number of values.
To calculate the drop in the Dow Jones average, we subtract the initial value from the final value:
Drop = Final Value - Initial Value
Drop = 12,503 - 12,837
Drop = -334
So the Dow Jones average dropped by 334 points in one week.
If the price continued to drop at the same rate for 4 more weeks, then the total drop after 5 weeks would be:
Total Drop = 5 x Drop
Total Drop = 5 x (-334)
Total Drop = -1670
To calculate the Dow Jones average after 4 more weeks, we need to subtract the total drop from the initial value:
New Dow Jones Average = Initial Value - Total Drop
New Dow Jones Average = 12,837 - 1,670
New Dow Jones Average = 11,167
Therefore, the Dow Jones average after 4 more weeks of the same rate of drop would be 11,167.
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In a candy factory, each bag of candy contains 300 pieces. The bag can be off by 10 pieces.
Write an absolute value inequality that displays the possible number of candy pieces that a bag contains.
Answer:
[tex] |x - 300| \leqslant 10[/tex]
Help me help me help me help me help me
Answer: cab
Step-by-step explanation:
you start with the last point and move up
I NEED HELP BADLY PLEASE HELP
Answer: 0.11
Step-by-step explanation:
5/45=0.11
Problem 13.3 Use the power method to determine the lowest eigenvalue and corresponding eigenvector for the system from Prob. 13.2. Problem 13.2 Use the power method to determine the highest eigenvalue and corresponding eigenvector for |2-x 8 10|
|8 4-x 5 |
|10 5 7-x|
In problem 13.2, we can use the power method to determine the highest eigenvalue and corresponding eigenvector for the matrix:
|2-x 8 10|
| 8 4-x 5 |
|10 5 7-x|
We start by assuming a random initial vector, say v0, and then repeatedly multiplying it by the matrix A and normalizing the resulting vector, until the vector converges to the eigenvector corresponding to the highest eigenvalue.
For problem 13.3, we can use a similar approach to determine the lowest eigenvalue and corresponding eigenvector. However, instead of multiplying by A, we multiply by A^-1. This is because the lowest eigenvalue is the reciprocal of the highest eigenvalue, and the corresponding eigenvector remains the same.
Both problems require us to perform the power method until the resulting vector converges to the desired eigenvector. The number of iterations required for convergence depends on the matrix A and the initial vector v0.
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A circle with radius of 2 cm sits inside a circle with radius of 4 cm. What is the area of the shaded region? Round your final answer to the nearest hundredth. 2 cm CH 4 cm
the area of the shaded region is approximately 37.68 cm².
define area of circleThe area of a circle is the amount of space that is enclosed by the circle in a two-dimensional plane. It is defined as the product of the square of the radius (r) of the circle and the mathematical constant pi (π), which is approximately equal to 3.14159.
The area of the larger circle is:
A1 = π(4 cm)² = 16π cm²
The area of the smaller circle is:
A2 = π(2 cm)² = 4π cm²
To find the area of the shaded region, we subtract A2 from A1:
A1 - A2 = 16π cm²- 4π cm² = 12π cm²
To round the final answer to the nearest hundredth, we can use the approximation π ≈ 3.14:
12π cm² ≈ 12 × 3.14 cm² ≈ 37.68 cm²
Therefore, the area of the shaded region is approximately 37.68 square centimeters.
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simplest form please
hmmm what we do is firstly make the recurring part a variable, then we multiply it such that, the recurring digits move over from the decimal point to the left, so we'd multiply it by some power of 10, in this case power of 3, because we have three digits to move, 246, so let's do all that
[tex]0.\overline{246}\hspace{5em}x=0.\overline{246}\hspace{5em} \begin{array}{llll} 1000x&=&246.\overline{246}\\\\ &&246+0.\overline{246}\\\\ &&246+x \end{array} \\\\[-0.35em] ~\dotfill\\\\ 1000x=246+x\implies 999x=246\implies x=\cfrac{246}{999}\implies x=\cfrac{82}{333}[/tex]
the following data represent the number of songs downloaded per month by people of various ages. a researcher wants to determine whether the age of the person downloading songs helps predict the number of songs downloaded. age 15 17 18 19 23 27 48 number of songs downloaded 34 33 38 27 21 16 6 the calculated correlation coefficient is r= -0.898. Would you say the correlation is weak, moderate, or strong?
The correlation coefficient r=-0.898. From this, we can conclude that the correlation is strong.
The researcher wants to determine whether the age of the person downloading songs helps predict the number of songs downloaded. The age and the number of songs downloaded per month data are as follows:
Age Number of Songs Downloaded153433183827192116486
The researcher can use the correlation coefficient to measure the correlation between the two variables. The correlation coefficient is denoted by r. It lies between -1 and +1. Here's what it means: If r is close to -1, then there is a strong negative correlation between the two variables. If r is close to +1, then there is a strong positive correlation between the two variables. If r is close to 0, then there is no correlation between the two variables.
The calculated correlation coefficient is r=-0.898. This indicates that there is a strong negative correlation between the age of the person downloading songs and the number of songs downloaded. Therefore, we can say that the correlation is strong.
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At the age of 30, Jasmine started a retirement account with $50,000 which compounded interest semi-annually with an interest rate of 1. 75%. She made no further deposits. After 25 years, she decided to withdraw 50% of what had accumulated in the account so that she could con- tribute towards her grandchild's college education. She had to pay a 10% penalty on the early withdrawal. What was her penalty?
Jasmine's penalty for the early withdrawal from her retirement account was approximately $3,702.50.
The formula to calculate the compound interest is:
[tex]A = P(1 + r/n)^{n \times t}[/tex]
Where:
A = the final amount after t years
P = the principal amount (initial investment) ($50,000 in this case)
r = the annual interest rate (1.75% in decimal form, so 0.0175)
n = the number of times interest is compounded per year (semi-annually, so 2)
t = the number of years (25 years in this case)
Let's calculate the final amount accumulated in the account:
[tex]A = 50000 \times (1 + 0.0175/2)^{2\times 25}[/tex]
[tex]A = 50000 \times (1.00875)^{50}[/tex]
A = 50000 × 1.481
A = $74,050
After 25 years, Jasmine has approximately $74,050 in her retirement account.
Now, she decides to withdraw 50% of that amount:
Withdrawal Amount = 0.5 × $74,050
Withdrawal Amount = $37,025
Finally, she had to pay a 10% penalty on the early withdrawal:
Penalty = 0.10×$37,025
Penalty = $3,702.50
So, Jasmine's penalty for the early withdrawal from her retirement account was approximately $3,702.50.
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A grocer has two kinds of candy: one sells for 90 cents per pound, and the other sells for 40 cents per pound. How many pounds of each kind must he use to make 50 pounds that he can sell of 85 cents per pound?
The grocer must use 45 pounds of each kind of candy
How to calculate the number of pounds that the grocer requires?A grocer has two kinds of candy
The first type of candy sells for 90 cents per pound
The second type of candy sells for 40 cents per pound
The number of pounds needed to make each kind of candy if he uses 50 pounds can be calculated as follows
The first step is to multiply 50 by 85%
50(85/100)
= 50(0.85)
= 42.5
Let y represent the unknown
y(90/100) + (50-y)(40/100)
0.9y + 0.4(50-y)
0.9y + 20-0.4y
0.9y-0.4y+20
0.5y+20(equate this value with 42.5)
0.5y+20= 42.5
collect the like terms
0.5y= 42.5-20
0.5y= 22.5
y= 22.5/0.5
y= 45
Hence the grocer needs 45 pounds for each kind of candy
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the six trigonometric functions are not invertible what has to be done make them invertible
Can you post the image in your question.
ling makes bracelets and necklaces and salesman a different crafts fairs the table shows how much is string is used to make each item
bracelet 7 1/2
small necklace 15
large necklace 19 1/4
ling plans to make at least 20 bracelets
write and solve an inequality to determine the minimum length of string that she needs to buy.
What is the least number of inches of string ling will need
According to the given information Ling has enough string to produce at least 20 bracelets.
What is a number and what are its many types?Numbers serve the purpose of counting, measuring, organising, indexing, and other purposes. Natural numbers, whole numbers, rational and irrational numbers, integers, actual values, complex numbers, even and odd numbers, and so on are all distinct forms of numbers.
What exactly is a number?A number is really a numerical value that is used to express quantity. As a consequence, a number seems to be a mathematical idea that may be used to count, measure, and name objects. As little more than a result, numbers are the foundation of mathematics. Here is one butterfly, and here are four butterflies.
Each bracelet requires 7 1/2 inches of string. So, the total length of string required to make 20 bracelets is:
20 × 7 1/2 = 150 inches
Therefore, Ling needs to buy at least 150 inches of string.
We can write the inequality to represent this situation as:
length of string ≥ 150
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The coefficient of variation is a better measure of risk than the standard deviation if the expected returns of the securities being compared differ significantly.
A. True
B. False
True. The coefficient of variation is a better measure of risk than the standard deviation if the expected returns of the securities being compared differ significantly.
The coefficient of variation (CV) is a relative measure of risk that takes into account the standard deviation and the mean of a distribution. It is a better measure of risk than the standard deviation when comparing securities with significantly different expected returns because it adjusts for the differences in the means.
The CV is calculated as the ratio of the standard deviation to the mean, and it allows for the comparison of the risk of investments with different expected returns on a standardized basis. Therefore, it is a useful tool for investors who want to compare the risk of investments that have different levels of expected returns. However, it should be noted that the CV has limitations and should not be the sole measure of risk used in investment analysis.
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Which scenario shows a value of 0. 4? select all that apply
Options B and C, Utilizing basic fractions, the qualities scenario displays a result of 0. 4 Jesse completed 40 out of 100 arithmetic problems and rode his bike for 4 of the 10 kilometers.
We are seeking a scenario that corresponds to a value of 0.4 or 40% among the possibilities mentioned, which represent various sections or fractions of a total.
Jesse rode his bike 4 out of the 10 miles in option B, which is equal to 0.4 or 40%.
Similarly, Jesse completed 40 of the 100 arithmetic problems in option C, which is likewise 0.4 or 40%. The other choices don't correspond to a 0.4 value.
A fraction of 2/3, or 0.666, is represented by choice A, a fraction of 4/100, or 0.04, by option D, and a fraction of 1/2, or 0.5, by option E.
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The question is -
Which of the following scenarios shows a value of 0.4? Select all that apply.
A. Jesse sold 40 out of 60 items at a garage sale.
B. Jesse rode 4 out of 10 miles on his bike.
C. Jesse finished 40 out of 100 math problems.
D. Jesse ate 4 out of 100 jellybeans.
E. Jesse returned 4 out of 8 library books.
3. The length of one leg of a 45-45-90 triangle is 7 m. What is the length of the other leg and the length of the hypotenuse?
The other leg is 7 m, and the hypotenuse is 7 m.
The other leg is 7 m, and the hypotenuse is 14 m.
O The other leg is 7√2 m, and the hypotenuse is 7 m.
The other leg is 7 m, and the hypotenuse is 7√2 m.
Answer: The other leg is 7 m, and the hypotenuse is 7√2 m.
Step-by-step explanation:
This is just a rule that in all cases, the two legs are equal and the hypotenuse is equal to the length of a leg times the square root of 2.
Hope this helps :)
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the liklihood that each baby will be a girl?
This method is designed to increase the likelihood that each baby will be a 15 girls is above 12.6 so it is significant high. It seems that method is effective.
Here we have
n=17, p=0.5
(a)
The mean is
np=17*0.5=8.5
The standard deviation is
[tex]\sigma=\sqrt{ np(1-p) } = 2.1[/tex]
(b)
Significantly low:
[tex]\mu[/tex] - 2[tex]\sigma[/tex] = 8.5 – 2* 2.1 = 4.4
Significantly high:
[tex]\mu[/tex] + 2[tex]\sigma[/tex] = 8.5+2 * 2.1 = 12.6
(c)
Since 15 girls is above 12.6 so it is significant high. It seems that method is effective.
Standard deviation is a statistical measure that describes the amount of variation or dispersion of a set of data from its mean or average value. In other words, it measures how much the data is spread out from the central tendency. It is calculated as the square root of the variance, which is the average of the squared differences between each data point and the mean.
The standard deviation is expressed in the same units as the data and is typically denoted by the symbol σ. A small standard deviation indicates that the data points are clustered around the mean, while a large standard deviation indicates that the data points are widely spread out from the mean.
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Complete Question: -
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 17 couples. Complete parts (a) through (c) below.
a. Find the mean and the standard deviation for the numbers of girls in groups of 17 births.
The value of the mean is μ=_____ (Type an integer or a decimal. Do not round.)
The value of the standard deviation is σ=____(Round to one decimal place as needed.)
b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.
Values of ___ girls or fewer are significantly low. (Round to one decimal place as needed.)
Values of ___ girls or greater are significantly high. (Round to one decimal place as needed.)
c. Is the result of 15 girls a result that is significantly high? What does it suggest about the effectiveness of the method?
The result ____ is not. is. significantly high, because 15 girls is greater than. less than. equal to _______ __ girls. A result of 15 girls would suggest that the method _______ is effective. is not effect.
3gh2x4g3h3 help me please
Answer:
Step-by-step explanation:
To find the product
Its gonna be
12g^4h^5
mathematics 3 and 4 grapgh mwehhh pleaseee
The answers of the question number 3 and 4 are given below respectively.
What is graph?A graph is a visual representation of data or mathematical relationships.
It typically involves plotting points on a coordinate plane and connecting them with lines or curves.
Graphs can help to illustrate patterns, trends, and relationships in data and make it easier to understand complex information.
3.Assuming that the sale of bracelets and necklaces are represented by the variables B and N respectively, the total sale would be represented by the mathematical statement:
Total sale = B + N
Graph of Total Sale = B + N
The x-axis represents the number of bracelets sold (B), and the y-axis represents the number of necklaces sold (N).
4.To represent Nimfa's goal of achieving a total sale of at least Php 15,000, we can use the inequality:
Total sale ≥ Php 15,000
or, using the expression from the previous question:
2B + N ≥ Php 15,000
Graph of Total Sale ≥ Php 15,000
The shaded area above the plane represents all the combinations of sales of bracelets and necklaces that result in a total sale of at least Php 15,000. Any point above the plane is a valid combination of sales that meet Nimfa's goal.
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3. The x-axis represents the number of bracelets sold (B), and the y-axis represents the number of necklaces sold (N).
4. The shaded area above the plane represents all the combinations of sales of bracelets and necklaces that result in a total sale of at least Php 15,000.
What is graph?A graph is a visual representation of data or mathematical relationships.
It typically involves plotting points on a coordinate plane and connecting them with lines or curves.
Graphs can help to illustrate patterns, trends, and relationships in data and make it easier to understand complex information.
3.Assuming that the sale of bracelets and necklaces are represented by the variables B and N respectively, the total sale would be represented by the mathematical statement:
Total sale = B + N
Graph of Total Sale = B + N
4.To represent Nimfa's goal of achieving a total sale of at least Php 15,000, we can use the inequality:
Total sale ≥ Php 15,000
or, using the expression from the previous question:
2B + N ≥ Php 15,000
Graph of Total Sale ≥ Php 15,000
The shaded area above the plane represents all the combinations of sales of bracelets and necklaces that result in a total sale of at least Php 15,000. Any point above the plane is a valid combination of sales that meet Nimfa's goal.
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The length of a rectangle is nine more than twice the width. If the perimeter is 120 inches, find the dimensions.
Answer:
Width = 17 inches
Length = 43 inches
Step-by-step explanation:
Framing and solving algebraic equation:Let the width of the rectangle = x inches
Length = 2*width +9
= (2x + 9) cm
[tex]\boxed{\bf Perimeter \ of \ rectangle = 2* (length + width)}[/tex]
2* (length + width) = 120 inches
2* (2x + 9 + x) = 120
2* (3x + 9) = 120
Use Distributive property,
2 * 3x + 2*9 = 120
6x + 18 = 120
Subtract 18 from both sides,
6x = 120 - 18
6x = 102
Divide both sides by 6,
x = 102 ÷ 6
x = 17
Width = 17 inches
Length = 2*17 +9
= 34 + 9
= 43 inches
sarah is trying to decide what combination of cups and plates to buy. her budget is $18. plates cost $6 each and cups cost $3 each. the numbers in the table represent total utility. given her budget, which combination will maximize total utility?
Answer:- Hence, the combination will maximize total utility is [tex]12.[/tex]
Step-By-Step-Explanation:-
What is cost?
Cost is the amount of money you spent to make the product or service. Price is what you will charge for it.
Here given that,
The cups and plates budget is [tex]$18 (3 plates x $6 each + 6 cups x $3 each)[/tex]
Then the utility for the combination is [tex]12 (3 plates x 4 utility each + 6 cups x 2 utility each).[/tex]
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are these equivalent
10-2x -2x10
find the values of a and b such that
x^2- +5=(x-a)^2+b
The value οf a = 1/2 and b = 19/4 in the equatiοn x² - x + 5 = (x-a)² + b.
What dο yοu mean by algebra?The part οf mathematics in which letters and οther general symbοls are used tο represent numbers and quantities in fοrmulae and equatiοn is called algebra.
x² - x + 5 = (x-a)² + b
x² - x + 5 = x² + a² - 2xa + b
-x + 5 = -2xa + a² + b
By matching cοrrespοnding terms,
2a = 1 and a²+ b = 5
a= 1/2 and a²+ b = 5
Substituting value οf "a"
(1/2)² + b = 5
1/4 + b = 5
b = 5- 1/4
b = 19/4
Thus, a = 1/2 and b = 19/4.
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The given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem. y = c1ex + c2e−x, (−[infinity], [infinity]); y'' − y = 0, y(0) = 0, y'(0) = 5
The given family of functions is y = c1ex + c2e−x which is the general solution of the differential equation y'' − y = 0 on the indicated interval which is (−∞, ∞).
Now, we are required to find a member of the family that is a solution to the initial-value problem which is
y(0) = 0 and y′(0) = 5.
The differential equation is y'' − y = 0
The characteristic equation is r2 − 1 = 0r2 = 1r1 = 1 and r2 = −1
The general solution of the differential equation is y = c1ex + c2e−x
Let us solve for the constants by using the given initial conditions:
At x = 0,y(0) = c1e0 + c2e0 = 0 + 0 = 0y(0) = 0
means c1 + c2 = 0or c1 = -c2At x = 0, y′(0) = c1ex |x=0 + c2e−x |x=0(d/dx)(c1ex + c2e−x) |x=0y′(0) = c1 - c2 = 5c1 - c2 = 5c1 - (-c1) = 5c1 + c1 = 5c1 = 5/2c1 = 5/2
Let's replace c1 = 5/2 in c1 = -c2, c2 = -5/2
The solution of the initial-value problem y = (5/2)ex − (5/2)e−x is a member of the family y = c1ex + c2e−x that is a solution of the initial-value problem y(0) = 0 and y′(0) = 5.
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Please look at the photo and let me know the three answers ASAP!! Thank you!
Answer:
(a) $ 67.1
(b) $98.60
(c) $ 1.26
Step-by-step explanation:
Given equation is
[tex]y\:=\:-1.26x\:+\:98.6[/tex]
where x is the temperature in °F and y is the heating cost in $
To find heating cost for a specific temperature just substitute the value of x (temperature) in the equation
Part (a)
For x = 25 we get
y = -1.26(25)+ 98.6 = $ 67.1
Part (b)
For x = 0 we get
y = -1.26(0) + 98.6 = 0 + 98.6 = $98.60
Part (c)
For a 1 degree increase in temperature, the predicted decrease is the slope of the line
Slope of line = coefficient of x = -1.26
So decrease in cost for 1 degree increase in temperature = $1.26
Use a triple integral to find the volume of the given solid The tetrahedronenclosed by the coordinate planes and the plane 10x y z 4
The volume of the tetrahedron is 1.0667 cubic units.
The tetrahedron is enclosed by the coordinate planes and the plane 10x + y + z = 4.
To find the volume of the tetrahedron using a triple integral, we can use the following bounds:
0 ≤ z ≤ 4 - 10x - y
0 ≤ y ≤ 4 - 10x
0 ≤ x ≤ 0.4
This is because the tetrahedron is bound by the coordinate planes, so x, y, and z all must be positive, and the plane 10x + y + z = 4 sets the upper bound for z and y, and the upper bound for x is simply where the plane intersects the x-axis (which can be found by setting y and z equal to 0 and solving for x).
The triple integral to find the volume of the tetrahedron is then:
V = ∫∫∫ dV = ∫0^0.4 ∫0^(4-10x) ∫0^(4-10x-y) dz dy dx
Evaluating this integral, we get:
V = ∫0^0.4 ∫0^(4-10x) (4-10x-y) dy dx
= ∫0^0.4 [4y - 10xy - (1/2)y^2]0^(4-10x) dx
= ∫0^0.4 [4(4-10x) - 10x(4-10x) - (1/2)(4-10x)^2] dx
= ∫0^0.4 (-25x^2 + 20x + 8) dx
= [-25/3 x^3 + 10 x^2 + 8x]0^0.4
= 1.0667
Therefore, the volume of the tetrahedron is approximately 1.0667 cubic units.
To find the "volume of the tetrahedron": https://brainly.com/question/19051909
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Write the equation of a line that is perpendicular to y=-2/7+9 and that passes through the point (4,-6)
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{7}}x+9\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-2}{7}} ~\hfill \stackrel{reciprocal}{\cfrac{7}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{7}{-2} \implies \cfrac{7}{ 2 }}}[/tex]
so we're really looking for the equation of a line whose slope is 7/2 and it passes through (4 , -6)
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{7}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{ \cfrac{7}{2}}(x-\stackrel{x_1}{4}) \implies y +6= \cfrac{7}{2} (x -4) \\\\\\ y+6=\cfrac{7}{2}x-14\implies {\Large \begin{array}{llll} y=\cfrac{7}{2}x-20 \end{array}}[/tex]
This shape is made up of one half-circle attached to an equilateral triangle with side lengths 20 inches. You can use 3. 14 as an approximation for π
If the shape is made up of one half-circle attached to an equilateral triangle with side lengths 20 inches then, the perimeter of the shape is 91.4 inches.
To find the perimeter of the shape, we need to know the length of the curved boundary (the circumference of the half-circle) and the length of the straight boundary (the perimeter of the equilateral triangle).
The radius of the half-circle is half the length of the side of the equilateral triangle, which is 10 inches. Therefore, the circumference of the half-circle is:
C = πr = π(10) = 31.4 inches.
The perimeter of the equilateral triangle is 3 times the length of one side, which is 20 inches. Therefore, the perimeter of the triangle is:
P = 3s = 3(20) = 60 inches
Finally, the perimeter of the entire shape is the sum of the lengths of the curved and straight boundaries:
Perimeter = C + P = 31.4 + 60 = 91.4 inches.
To know more about equilateral triangle
brainly.com/question/3461022
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Complete Question
This shape is made up of one half-circle attached to a square with side lengths 11 inches. Find the perimeter of the shape.
You can use 3.14 as an approximation for π. help i don't know it.