By answering the given question, we may state that Therefore, the equivalent inequality is: x < 2
What is inequality?A relationship between two terms or values which is not equal is known as an inequality in mathematics. Inequality follows imbalances, therefore. In mathematics, an inequality makes a link among two quantities that are not equal. Egality and inequality are different. Use the not similar symbol most frequently when two components are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two parts until only the variables are left, one can solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left & right.
inequality using basic algebraic operations:
5(2x-6)+6(3-x)<2x+4
10x-30+18-6x < 2x+4
4x - 8 < 0
4x < 8
x < 2
Therefore, the equivalent inequality is:
x < 2
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(d) (4 points) suppose it takes a half hour for a red truck to pass through the tunnel. if there are no red trucks in the tunnel when it enters the tunnel at 7:35am on a monday, what is the probability it will be the only red truck in the tunnel the whole time it spends in the tunnel? state the appropriate distribution and any parameter values for any random variable(s) you use to model the situation. write the probability statment and show your work to receive full credit. (e) (5 points) let w represent the amount of time in hours it takes for the 9th red truck to arrive at the tunnel on a monday morning. what time do you expect the 9th red truck to arrive at the tunnel on a monday morning (to the nearest 10 minutes)? recall the tunnel opens at 7am. your final answer should be a time.
(d) The appropriate distribution to use in this situation is the Poisson distribution. We can let X be the number of red trucks that enter the tunnel during the half hour that the first red truck is in the tunnel. The parameter value for the Poisson distribution is λ, which is the average number of red trucks that enter the tunnel in a half hour. We can use the given information to calculate λ:
λ = (average number of red trucks per hour) × (length of time in hours) = (18 red trucks per hour) × (0.5 hours) = 9 red trucks
Therefore, the probability that the first red truck is the only red truck in the tunnel during the half hour it spends in the tunnel is:
P(X = 0) = (λ^0 × e^-λ) / 0! = (9^0 × e^-9) / 0! = (1 × e^-9) / 1 = e^-9 ≈ 0.0001234
So the probability is approximately 0.0001234.
(e) The appropriate distribution to use in this situation is also the Poisson distribution. We can let W be the amount of time in hours it takes for the 9th red truck to arrive at the tunnel on a Monday morning. The parameter value for the Poisson distribution is still λ, which is the average number of red trucks that enter the tunnel per hour. We can use the given information to calculate λ:
λ = (average number of red trucks per hour) = (18 red trucks per hour) = 18 red trucks
The expected value of W is 1/λ = 1/18 hours = 0.0556 hours ≈ 3.33 minutes. Since the tunnel opens at 7am, we can add this expected value to the opening time to find the expected time that the 9th red truck will arrive at the tunnel:
Expected time = 7:00am + 3.33 minutes = 7:03am
So we expect the 9th red truck to arrive at the tunnel at 7:03am on a Monday morning.
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what is the lcm of 14 and 18
DUE TODAY PLEASE HELP NOW!!!!!!!!!!!!! 20 POINTS
Here is another triangle similar to DEF found in the lesson section labeled “Shrinking Triangles”.
• Label the triangle D”E”F”.
• What is the scale factor from triangle DEF to triangle D”E”F”?
• What are the coordinates of F”? Explain how you know.
• What are cos(D”), sin(D”), and tan(D”)?
The scale factor of dilation is 1/40 and the coordinates of F" are (1440, 600)
Labelling the image of the triangleThe image of the label is attached
The scale factor of the dilationGiven that
D'E' = 36 units
Then, we have
D"E" = 0.9 units
The scale factor is calculated as
Scale factor = D"E"/D'E'
So, we have
Scale factor = 0.9/36
Evaluate
Scale factor = 1/40
So, the scale factor of dilation is 1/40
The coordinates of F"This is calculated as
F = F'/Scale factor
So, we have
F = (36, 15)/(1/40)
F = (1440, 600)
The trigonometry ratiosThe trigonometry ratios are calculated as
sin(D") = EF/DF
cos(D") = DE/DF
tan(D") = EF/DE
So, we have the following approximated values
sin(D") = 15/39 = 0.36
cos(D") = 36/39 = 0.92
tan(D") = 0.36/0.92 = 0.39
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Demonstrate the property listed in the first column of the table by filling in the box in the second column of the table with an equivalent expression. Commutative Property of Addition Commutative Property of Multiplication gx h= Additive Identity Property of Zero n + 34 = Multiplicative Identity Property of One S+0= bx1 =
The property listed in the first column of the table by filling in the box in the second column of the table with an equivalent expression are: 1. Commutative Property of Addition 2. Additive Identity Property of Zero 3. Multiplicative Identity Property of One.
What is expression?An expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. It represents a value or quantity and can be evaluated or simplified to a single value or another expression. Expressions can contain constants, which are fixed values, such as the number 5 or the symbol π, or variables, which are symbols that represent varying values, such as x or y.
Here,
Commutative Property of Addition: The order in which two numbers are added does not change the result.
For example:
g + h = h + g
Additive Identity Property of Zero: Adding zero to any number does not change the value of the number.
For example:
n + 34 = n
Multiplicative Identity Property of One: Multiplying any number by one does not change the value of the number.
For example:
S * 1 = S
Commutative Property of Multiplication: The order in which two numbers are multiplied does not change the result.
For example:
b * x * 1 = x * b * 1
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a dvd rental company charges $10 per month plus $0.75 per rental. Andy wants to spend no more than 25.00 per month on DVD rentals. Select the inequality that represents how many DVDs Andy can rent in one month that satisfies this condition. The number of rentals in a month is represented by n. A. 10.75n < 25
The answer of the question based on the inequality the answer is Andy can rent up to 20 DVDs in a month and spend no more than $25.
What is Inequality equations?An inequality equation is mathematical statement that compares the two values or expressions using inequality symbol such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).
The total cost, C, for renting n DVDs in a month is given by:
C = 10 + 0.75n
The question tells us that Andy wants to spend no more than $25 per month on DVD rentals. Therefore, we can write an inequality:
C ≤ 25
Substituting the expression for C from above, we get:
10 + 0.75n ≤ 25
Simplifying the inequality, we can subtract 10 from both sides:
0.75n ≤ 15
Finally, we can divide both sides by 0.75:
n ≤ 20
Therefore, the inequality that represents how many DVDs Andy can rent in one month that satisfies the condition of spending no more than $25 per month is:
n ≤ 20
So, Andy can rent up to 20 DVDs in a month and spend no more than $25.
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What fraction times 4 1/3 is equal to 6 1/2?
Answer:
3/2
Step-by-step explanation:
4 1/3 = 13/3
6 1/2 = 13/2
fraction x 13/3 = 13/2
=> fraction = 13/2 / 13/3 = 13/2 x 3/13 = 3/2
GET 30 POINTS
1) Coordinate point B is at (4,3). What will the coordinates be for B' after a translation of (x-2,y+3)?
*
B' (5,4)
B' (2,6)
B' (6,2)
B' (-2,3)
What is the coordinate for G(3,-2) after it is reflected across the x-axis?
*
(2,3)
(-2,3)
(3,2)
(-3,-3)
What is the translation rule that describes the result of the composition of
(x, y) --> (x+4, y-1) and (x, y) --> (x-5, y-5)?
*
(x, y) --> (x-1, y-6)
(x, y) --> (x+1, y-3)
(x, y) --> (x+9, y+6)
(x, y) --> (x+1, y+6)
thank you so mcuh
After translatiοn, the cοrrect answer is B' (x+2, y+6).
The cοοrdinate after reflectiοn is (3,2).
The translatiοn rule that describes the result οf cοmpοsitiοn is (x, y) →(x-1, y-6).
What are transfοrmatiοns?Transfοrmatiοns in a triangle refer tο changes that can be made tο the shape, size, pοsitiοn, οr οrientatiοn οf the triangle οn a cοοrdinate plane. The three main types οf transfοrmatiοns that can be applied tο a triangle are:
Translatiοn: This transfοrmatiοn invοlves mοving the entire triangle tο a new pοsitiοn οn the cοοrdinate plane withοut changing its size οr shape.
Rοtatiοn: This transfοrmatiοn invοlves rοtating the entire triangle arοund a fixed pοint οn the cοοrdinate plane. The fixed pοint is called the center οf rοtatiοn, and the angle οf rοtatiοn determines the amοunt οf turn.
Scaling: This transfοrmatiοn invοlves changing the size οf the triangle by multiplying the x and y cοοrdinates οf each vertex by a fixed factοr.
1) Applying the translatiοn οf (x-2, y+3) tο pοint B(4,3) wοuld result in: B' = (4 + (x-2), 3 + (y+3)) = (x+2, y+6)
Therefοre, the cοrrect answer is B' (x+2, y+6)
2) Reflecting pοint G(3,-2) acrοss the x-axis results in the y-cοοrdinate being negated, and the x-cοοrdinate remains the same. Therefοre, the cοοrdinates οf the reflected pοint wοuld be G(3, 2).
The cοrrect answer is (3,2).
3) Tο determine the cοmpοsitiοn οf (x, y) → (x+4, y⁻¹) and (x, y) →(x-5, y⁻⁵), we need tο apply them in οrder. Firstly, (x, y) → (x+4, y-1) is applied tο pοint (x,y), which results in:(x, y)→ (x+4, y-1)
Next, (x, y) → (x-5, y-5) is applied tο the result frοm the previοus transfοrmatiοn (x+4, y-1), which results in:(x+4, y-1)→(x-1, y-6)
Therefore, the correct answer is (x, y) →(x-1, y-6).
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Please ASAP Help
Will mark brainlest due at 12:00
Answer:
plot the point at 1
Step-by-step explanation:
Answer:
(1,0)
Step-by-step explanation:
S = (-7,0)
T = (3,0)
W = (x,0)
Please ASAP Help
Will mark brainlest due at 12:00
Answer:
plot the point at -5
Step-by-step explanation:
Three friends participate in the loyalty program at a local coffee shop. A participant in the program earns points for each visit that can be used to get drinks and food for free. The graph below shows the point balances of the three friends over several weeks?
help me it's the 23 and the 24 please.
Answer:
On the graph, the point balances for the three friends on the 23rd week are:
- Friend A: 60 points
- Friend B: 80 points
- Friend C: 40 points
On the 24th week, the point balances are:
- Friend A: 80 points
- Friend B: 100 points
- Friend C: 60 points
It looks like all three friends are earning points and increasing their balances over time. Friend B seems to be earning points at a faster rate than the other two friends, as their balance is consistently higher. Friend C has the lowest balance, but is still earning points and increasing their balance.
PLEASE HELP !!!!!!! i really need help!
Answer: Ans b.
Vol_total
= 7800 yd^3
Step-by-step explanation:
The bottom part of your shape is a box, basically (rectangular prism) and the volume is:
V=
length×width×height
Those numbers are all given. Because it is a box shape, it doesn't matter which number is which.
V = 22 × 15 × 16
= 5280 yd^3
Now the "roof" part on top is a little bit different. It is a triangular prism. So the side that needs to be the Base of the prism is the front (or back) triangle.
The volume is:
V
= BaseArea×height
= Area_triangle× ht
= 1/2 bh × height
= 1/2•21•16 × 15
The key to understanding is knowing the triangle must be the base. And the roof line running front to back will be the height. And also understanding the difference between the height of just a triangle (21) and the height of the prism(15). They are different.
Vol_roof = 2520
Then add them together.
Vol_total
= 5280 + 2520
= 7800 yards cubed
A streaming service charges $200 to download a digital song as well as a $4.99
membership fee. Which expression below gives the total cost in dollars to join the
streaming service and download games. Remember the charge is $2.00 per game plus
a membership fee of $4.99.
A.4.99n
B.n+4.99
C.2n +4.99
D.I don't know how to
do this.
The expressiοn calculates the tοtal cοst οf membership and game dοwnlοads. Sο, the cοrrect οptiοn is (C) 2n + 4.99.
Describe Algebraic Expressiοn?Algebraic expressiοns can include οne οr mοre variables, which are typically represented by letters, such as x, y, οr z. These variables can be used tο represent unknοwn quantities οr tο express relatiοnships between different quantities in a prοblem.
Algebraic expressiοns can alsο include cοnstants, which are fixed numbers, and cοefficients, which are the numbers that multiply the variables in the expressiοn. Fοr example, in the algebraic expressiοn 3x + 2y, the cοnstants are 3 and 2, and the cοefficients are 3 and 2, respectively.
The given prοblem describes twο different charges: a οne-time charge οf $200 tο dοwnlοad a digital sοng, and a membership fee οf $4.99 that must be paid regardless οf hοw many sοngs οr games are dοwnlοaded. Additiοnally, fοr dοwnlοading games, there is a charge οf $2.00 per game.
Therefοre, the tοtal cοst in dοllars tο jοin the streaming service and dοwnlοad games can be represented by the expressiοn:
2n + 200 + 4.99
Here, "n" represents the number οf games dοwnlοaded, and the expressiοn calculates the tοtal cοst οf membership and game dοwnlοads.
Sο, the cοrrect οptiοn is (C) 2n + 4.99.
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Help please !!
WHAT does this mean
The probability that the coin shows heads and the number is two is 0.05.
What is probability?
A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Here, we have
Given: you flip a coin and use a random number generator to generate a number from 1 to 10.
To find the probability, we need to use that we have two independent events. First, flip a coin, and second, generate a number from 1 to 10. They are independent events because their occurrence is not dependent on any other event.
P(A∩B) = P(A).P(B)
Where A represents the event of flipping a coin
B represents the event of generating a number from 1 to 10.
P(A) = 1/2, P(B) = 1/10
P(A) = 0.5 and P(B) = 0.1 we need to replace their values in the initial formula
P(A∩B) = 0.5× 0.1
P(A∩B) = 0.05
Hence, The probability that the coin shows heads and the number is two is 0.05.
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PLEASE HELP IMMA DIE IF I GET THIS WRONG (im over exaggerating
)
In the given triangle, The value of x will be 6.
What exactly is a triangle?
A triangle is a closed two-dimensional geometric shape that is formed by three straight line segments that connect three non-collinear points. The three line segments that form a triangle are called sides, and the three points where the sides intersect are called vertices.
Triangles can be classified into six types. A triangle with all three sides of equal length is called an equilateral triangle, while a triangle with two sides of equal length is called an isosceles triangle. A triangle with all three angles measuring less than 90 degrees is called an acute triangle, while a triangle with one angle measuring exactly 90 degrees is called a right triangle. A triangle with one angle measuring more than 90 degrees is called an obtuse triangle.
Now,
For given triangle,
The angle bisector is perpendicular to the line having x.
As it divided angle into same ratio then the ratio
[tex]x/5[/tex]=[tex]12/10[/tex]
then x=6/5*5
x=6
Hence,
The measurement of side x will be 6.
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can you please help
Solve 3X+1
Answer: The answer is 3
Step-by-step explanation:
3x+1 take one minus one.
3x1-1 1-1 for exponents value becomes 0
3x0 for every term 0 is = to one in a exponent value so it become 3x1
3x1 = 3
So the answer is 3..
Step-by-step explanation:
In the 3x+1 problem, no matter what number you start with, you will always eventually reach 1. The problemproblm has been shown to be a computationally unsolvable problem.
Laila needs a new bike mirror. Her old mirror was a square with a side length of 7 cm. She wants
the new mirror to have approximately the same area as her old bike mirror.
Which circular bike mirror should Laila buy?
4 cm
7 cm
8 cm
Answer:
Approximately 4 cm
Step-by-step explanation:
Old mirror's area = S X S = 7 x 7 = 49cm2
Area of old mirror = Area of new mirror
49 = πr2
49 = 22/7 * r2
[tex]\frac{49 * 7}{22}[/tex] = r2
[tex]\frac{343}{22}[/tex] = r2
15.5909 = r2
r = [tex]\sqrt{15.5909}[/tex]
r = 3.948 cm = approx. 4cm
Hope it helps.
4. 2. 4Practice:Modeling: Slope-Intercept Equation of a Line
The slope-intercept form of the equation of a line is: y = mx + b
Where: y is the dependent variable (usually represented on the vertical axis of a graph). x is the independent variable (usually represented on the horizontal axis of a graph). m is the slope of the line (which represents the rate of change of y with respect to x). b is the y-intercept (which represents the value of y when x is equal to 0). To use this equation, you need to know the slope (m) and the y-intercept (b) of the line. You can find the slope of a line by taking any two points on the line and using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are any two points on the line. Once you know the slope, you can substitute it and the y-intercept into the slope-intercept form of the equation of the line to get the equation in its final form.
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Solve the system of equations. − 4 � + 3 � = − 2 � = � − 1 −4x+3y=−2 y=x−1 � = x=x, equals � = y=y, equals
The solution to the system of equations is: x = -1 and y = -2.
What is system of equations?A system of equations is the set of two or more equations with the same variables.
An example is: 2x + 3y = 10 and 4x - 5y = -8
To solve the system of equations:
-4x + 3y = -2
y = x - 1
We can substitute the second equation into the first to eliminate y:
-4x + 3(x - 1) = -2
Simplifying and solving for x:
-4x + 3x - 3 = -2
-x = 1
x = -1
Now that we know x = -1, we can use the second equation to find y:
y = -1 - 1
y = -2
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an ant is about to climb a 50-meter tree. in 2 hours, it can climb 5 meters, but it then slips down 1 meter. how long does it take the ant to reach the top
The ant will reach the top in 16.67 hours, or approximately 16 hours and 40 minutes
An ant is about to climb a 50-meter tree. In 2 hours, it can climb 5 meters, but it then slips down 1 meter. How long does it take the ant to reach the top?An ant can climb 4 meters in 1 hour since it climbs 5 meters but then slides down 1 meter in 2 hours. Let us assume that it takes the ant n hours to get to the tree's top. We don't understand the precise number of hours, thus we'll use 'n' to represent the number of hours it takes the ant to reach the top of the tree.
The ant climbs 4 meters per hour, thus it climbs 4n meters after n hours.The ant slips down 1 meter each hour, therefore, it slides down 1n meters after n hours.If the ant climbs 4n meters but slips down 1n meters, it is actually at 3n meters after n hours. Therefore, 3n = 50 since the ant should reach the top of a 50-meter tree.Since 3n = 50, n = 50/3 ≈ 16.67 (to two decimal places). As a result, the ant will reach the top in 16.67 hours, or approximately 16 hours and 40 minutes.
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A farmer has 2400 sheep, he loses 32,5% due to the drought. After that he loses 15% due to sickness. How many sheep does he have now?
The farmer now has 1377 sheep. If the farmer loses 32.5% of his 2400 sheep due to the drought, then he will have: 2400 * (1 - 0.325) = 1620 sheep left after the drought.
The farmer had 2400 sheep, but he lost 32.5% of them due to drought. Using the formula for finding percentages, we can calculate that 32.5% of 2400 is 780. So, the farmer had 2400 - 780 = 1620 sheep left after the drought. However, he then lost 15% of those remaining sheep due to sickness. Using the same formula, we can calculate that 15% of 1620 is 243. Therefore, the farmer had 1620 - 243 = 1377 sheep left after the sickness. So, the final number of sheep the farmer has now is 1377.
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Is 0.06 bigger than 0.066
Answer:
Yes, 0.06 is bigger than 0.066, because 0.06 is greater than 0.066 when they are written in decimal form. This is due to the fact that 0.06 has 6 tenths, while 0.066 has 66 hundredths.
Answer:
no
Step-by-step explanation:
that is because 0.6 = 0.6000000
and 0.066 = 0.6600000
write an equation in slope-intercept form of the line that passes through the given points
[tex]\left[\begin{array}{ccc}x&y\\-2&2\\0&1\\2&0\\4&-1\end{array}\right][/tex]
We can find the slope between the first two points (-2, 2) and (0, 1):
m = (1 - 2) / (0 - (-2))
m = -1 / 2
Now that we have the slope (m), we can use the point-slope form of the equation of a line to find the y-intercept (b). Using the point (0, 1):
y - y1 = m(x - x1)
y - 1 = (-1/2)(x - 0)
y = (-1/2)x + 1
Therefore, the equation of the line in slope-intercept form that passes through the given points is:
y = (-1/2)x + 1
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A store imploys 11 woman and 12 men
What percentage of the employees are men?
Nancy has twice as many apples as jay. Jay has 3 more apples than Ava. Nancy has 22 apples. How many apples dose Ava have?
Answer: 8
Step-by-step explanation: Nancy has 22 apples, it was previously stated that Nancy has TWICE as many apples than Jay meaning Jay has 11 apples. Jay has 3 more apples than Ava meaning Ava has 8.
A sample of students is taken from the school's A honor roll. The school estimates there are 360 students on the A honor roll. How many students on the A honor roll are 7th graders?
ou have learned that given a sample of size n from a normal distribution, the CL=95% confidence interval for the mean can be calculated by Sample mean +/- z((1-CL)/2)*Sample std/sqrt(n). Where z((1-cl)/2)=z(.025) is the z score.
a. help(qnorm) function. Use qnorm(1-.025) to find z(.025).
b. Create a vector x by generating n=50 numbers from N(mean=30,sd=2) distribution. Calculate the confidence interval from this data using the CI formula. Check whether the interval covers the true mean=30 or not.
c. Repeat the above experiments for 200 times to obtain 200 such intervals. Calculate the percentage of intervals that cover the true mean=30. This is the empirical coverage probability. In theory, it should be very close to your CL.
d. Write a function using CL as an input argument, and the percentage calculated from question c as an output. Use this function to create a 5 by 2 matrix with one column showing the theoretical CL and the other showing the empirical coverage probability, for CL=.8, .85, .9, .95,.99.
a. To find the z score for a given confidence level, you can use the `qnorm()` function in R. The `qnorm()` function takes a probability as an argument and returns the corresponding z score. To find the z score for a 95% confidence level, you can use `qnorm(1-.025)`:
```R
z <- qnorm(1-.025)
```
This will give you the z score for a 95% confidence level, which is approximately 1.96.
b. To create a vector `x` with 50 numbers from a normal distribution with mean 30 and standard deviation 2, you can use the `rnorm()` function:
```R
x <- rnorm(50, mean = 30, sd = 2)
```
To calculate the confidence interval for this data, you can use the formula:
```R
CI <- mean(x) + c(-1, 1) * z * sd(x) / sqrt(length(x))
```
This will give you the lower and upper bounds of the 95% confidence interval. You can check whether the interval covers the true mean of 30 by seeing if 30 is between the lower and upper bounds:
```R
lower <- CI[1]
upper <- CI[2]
if (lower <= 30 && upper >= 30) {
print("The interval covers the true mean.")
} else {
print("The interval does not cover the true mean.")
}
```
c. To repeat the above experiment 200 times and calculate the percentage of intervals that cover the true mean, you can use a for loop:
```R
count <- 0
for (i in 1:200) {
x <- rnorm(50, mean = 30, sd = 2)
CI <- mean(x) + c(-1, 1) * z * sd(x) / sqrt(length(x))
lower <- CI[1]
upper <- CI[2]
if (lower <= 30 && upper >= 30) {
count <- count + 1
}
}
percentage <- count / 200
```
This will give you the percentage of intervals that cover the true mean.
d. To write a function that takes a confidence level as an input and returns the percentage of intervals that cover the true mean, you can use the following code:
```R
calculate_percentage <- function(CL) {
z <- qnorm(1-(1-CL)/2)
count <- 0
for (i in 1:200) {
x <- rnorm(50, mean = 30, sd = 2)
CI <- mean(x) + c(-1, 1) * z * sd(x) / sqrt(length(x))
lower <- CI[1]
upper <- CI[2]
if (lower <= 30 && upper >= 30) {
count <- count + 1
}
}
percentage <- count / 200
return(percentage)
}
```
You can then use this function to create a 5 by 2 matrix with one column showing the theoretical CL and the other showing the empirical coverage probability:
```R
CL <- c(.8, .85, .9, .95, .99)
percentage <- sapply(CL, calculate_percentage)
matrix <- cbind(CL, percentage)
```
This will give you a matrix with the theoretical CL in the first column and the empirical coverage probability in the second column.
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E) Let y = g(x) be the particular solution to the differential equation dy/dx= 3sin(pix)/2y with initial condition
g(1/2)=3. Then g(x)= sqare root of a+bcos(pix) where a and b areconstants. Find a
Answer:
9
Step-by-step explanation:
You want the value of the constant 'a' in the solution y=√(a+b·cos(πx)) to the differential equation y'=3sin(πx)/(2y) with initial condition y(1/2) = 3.
Initial conditionSubstitute the initial condition into the equation for y:
y = 3 . . . . when x = 1/2
y = √(a +b·cos(πx))
3 = √(a +b·cos(π/2)) = √a
3² = a = 9
The value of a is 9.
__
Additional comment
The value of 'b' is -3/π.
It can be found by putting the equation for y in the original differential equation, and solving for b.
Determine a series of transformations that would map polygon ABCDE onto polygon A'B'C'D'E'?
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Answer:
Step-by-step explanation:
16. Since the angle between the two values is 90, that is already half of 180, which is the total of all of the angles. So you make the equation, 3n+3+2n+7+90=180, which simplifies down to 5n+100=180, and after solving you get n = 16.
Here is the answer to your question
[tex] = 16[/tex]
The band students at Brookshaw Junior High School got to choose between ordering a hoodie or a T-shirt to wear on spirit day this year. In the seventh grade band, 7 students ordered the hoodie and 18 students ordered the T-shirt. In the eighth grade band, 12 students ordered the hoodie and 15 students ordered the T-shirt. The hoodies cost h dollars each, and the T-shirts cost t dollars each.
Pick all the expressions that represent how much the band students spent on hoodies and T-shirts.
Answer:
[tex]19h + 33t[/tex]
[tex]7h + 18t +12h + 15t[/tex]
Step-by-step explanation:
The two expressions above are equal and both represent the total spent on hoodies and t-shirts.
[tex]25(h+t) + 27(h + t)[/tex] is incorrect because this implies that the cost of t-shirts and hoodies are interchangeable. The choice in the bottom right is incorrect also because it is equivalent to the aforementioned expression.