The correct option is (A) f(x)=1+e+² since the value of y is obtained as et + 1, which is equal to 1+e^x 2. The other options do not satisfy the initial condition.
Given that, y = f(x) is a solution to the differential equation y' = et with the initial condition f(0) = 2. To find the correct option among the given options.
Therefore, let's solve this using the integration method. Let's integrate both sides with respect to x,y'=etdy/dx =etdy = etdx Integrating both sides, we get∫dy = ∫et dxy = ∫et dx + c ....(1) where c is the constant of integration. To find the constant c, we need to use the initial condition f(0) = 2.
Substituting x = 0 and y = f(0) = 2 in equation (1),2 = ∫e0 dx + c2 = 1 + c => c = 1. Therefore, the solution is y = ∫et dx + 1= et + 1
Therefore, the correct option is (A) f(x)=1+e+² since the value of y is obtained as et + 1, which is equal to 1+e^x 2. The other options do not satisfy the initial condition.
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9. a) Why does every pair of whole
a
numbers have a GCF of 1 or greater?
Answer:
A whole number is any positive integer greater than zero and is not a fraction or a decimal. Any whole number can be divided by itself and one so therefor all pairs of whole numbers have a GCF of one. However the bigger the number the more factors it can have so the GCF of a pair of whole numbers may have a greater GCF than 1.
Step-by-step explanation:
Helpoopooo please !!!!!!
Answer:
I believe the answer is 2/3
Step-by-step explanation:
find the mean median mode, round to the neaerest tenth. 60,70,75,78,80,80,83,85,87,90.90,90,90,93,95,95,98,100.
Answer:
Mean: 84.6
median:85
mode:90,80
range:40
minimum:60
maximum:100
Step-by-step explanation:
Answer:
mean = 85.5
median = 88.5
mode = 90
Step-by-step explanation:
Okay, so the mean is the sum of the terms divided by the total number of term so basically:
60 + 70 + 75 + 78 + 80 + 80 + 83 + 85 + 87 + 90 + 90 + 90 + 90 + 93 + 95 + 95 + 98 + 100 = 1,539
1,539 ÷ 17 = 85.5
Now, the median is just the number in the middle so we already have our numbers in order so the middle numbers are 87 and 90, so we just have to add them together and then divide by 2:
87 + 90 ÷ 2 = 88.5
and the mode is just the number that's repeated most, and that number is 90
hope this helps:)
Sombody please help ASAP!
Answer:
a translation down 9 unit
Step-by-step explanation:
Is it possible or impossible for a graph to have exactly one vertex of odd degree. If so, describe the graph by giving its degree sequence. If not, explain why not.
It is impossible for a graph to have exactly one vertex of odd degree.
What is a vertex?Vertex is described as a point on a polygon where the sides or edges of the object meet or where two rays or line segments meet.
The total of all vertices' degrees in any graph is always even. This is so because each edge adds two degrees—one for each endpoint—to the overall number of degrees.
The total number of degrees at all vertices must therefore be an even number.
If a graph had exactly one vertex of odd degree, the sum of the degrees of all other vertices would be even.
if we add an odd degree to an even sum, the result would be in an odd total degree count, which contradicts the fact that the sum of all degrees in a graph is always even.
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No image, Find the volume of a garden
seat in the shape of a
triangular prism with a height
of 30 inches and a base area
of 72 in^2 *Hint* Base
area means
they have
already
calculated
the area of
the base for
you!
Answer:
volume = 720 in³
Step-by-step explanation:
volume = 1/3Bh = 1/3 x 72 x 30 = 720 in³
What is the simple interest of $1500.00 for 4 months at 6 3/4%
annual interest?
A) $222.22
B)$101.25
C)$50.63
D)$33.75
The simple interest of $1500.00 for 4 months at 6 3/4% annual interest is $101.25. Thus, the correct answer is B) $101.25.
To calculate simple interest, we use the formula: Interest = Principal x Rate x Time. In this case, the principal (P) is $1500.00, the rate (R) is 6 3/4% (or 0.0675 as a decimal), and the time (T) is 4 months.
First, we need to convert the rate from a percentage to a decimal by dividing it by 100: 6 3/4% = 6.75/100 = 0.0675.
Next, we plug these values into the formula: Interest = $1500.00 x 0.0675 x 4 = $101.25.
Therefore, the simple interest on $1500.00 for 4 months at 6 3/4% annual interest is $101.25. Thus, the correct answer is B) $101.25.
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Omar rented a truck for one day. There was a base fee of $17.95, and there was an additional charge of 98 cents for each mile driven. Omar had to pay when he returned the truck. For how many mile did he drive the truck?
The given question is incomplete. The complete question is:
Omar rented a truck for one day. There was a base fee of $17.95, and there was an additional charge of 98 cents for each mile driven. Omar had to pay $23 when he returned the truck. For how many mile did he drive the truck?
Answer: Omar drove the truck for 5.15 miles
Step-by-step explanation:
Base fee = 17.95 $
Additional charge per mile = 98 cents = 0.98 $ ( 100cents = 1$)
Now Omar payed = 22 $
Let the miles he travelled = x
Now , [tex]17.95+0.98\times x=23[/tex]
Solvimg for x :
[tex]x=5.15miles[/tex]
Thus Omar drove the truck for 5.15 miles
Jeremiah and his children went into a bakery and he bought $20 worth of cupcakes and cookies. Each cupcake costs $5 and each cookie costs $1.25. He bought 4 times as many cookies as cupcakes. Graphically solve a system of equations in order to determine the number of cupcakes, x,x, and the number of cookies, y,y, that Jeremiah bought.
Answer: (2,8)
Step-by-step explanation:
5x+1.25=20
y=4x
5x+1.25y=20 y=4x
1.25y=-5x+20
1.25y/1.25=-5x+20/1.25
y=-4x+16
A cone has a volume of 100[tex]\pi[/tex] Cubic units and a diameter of 10 units. What is the height of the cone?
Answer:
12 units
Step-by-step explanation:
The formula for the volume of a cone is given as:
πr²h/3
The volume = 100π cubic units
Diameter = 10 units.
Radius = Diameter/2
= 10 units/2 = 5 units
Hence:
Formula to find the height of a cone
h = 3V/πr²
We substitute
h = 3 × 100π/π × 5²
h = 300π/25π
h = 12 units
The height = 12 units
Write the number in 2 equivalent forms as a fraction, decimal, or percent.
23%
Answer:
23%, 23/100, 0.23
Step-by-step explanation:
23%
= 23/100
= 0.23
Solve for v and put your answer in simplest radical form. Show steps plz!
r = stu/v^2
Answer:
V= √( r/Stu)
Step-by-step explanation:
r = stu/v^2
Let us cross multiply , we have
r. v^2 = (s. t. u)
Let us make v ^2 the subject of the formula, we have
v^2 = (s t u)/ r
Find the square of both sides we have
V= √( r/Stu)
A town has a population of 14000 and grows at 3% every year. What will be the population after 6 years, to the nearest whole number?
Answer:
Step-by-step explanation:
3x6= 18 then 14000 x 18 = 252,000
Which angles!!! Need answers 40% of my grade please and thank you
Answer:
alternate interior angle
Bamboo plants can grow 91 centimeters per day. what is the approximate growth of the plant inches per hour?
Answer:
roughly 1.5
Step-by-step explanation:
Finish the song:
Good little girl....
Always picking a fight with me~
You know that I'm bad!
But you're spending the night with me....
What do you want from my world?
You're a good little girl♪♪♪
Answer:
Bad little boy
That's what you're acting like
I really don't buy
That you're that kind of guy
And if you are
Why do you want to hang out with me?
Step-by-step explanation:
i had to look in the internet hehe click the ❤️
please
Classify the hypothesis test as left-tailed, right-tailed, or two-tailed. Circle your answer. Below your circle answer, state the null hypothesis, the alternative hypothesis, and label the claim. In the past, the mean running time for a certain type of manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has changed as a result. A) Right-tailed B) Two-tailed C) Left-tailed
The appropriate classification for the hypothesis test in this scenario is a two-tailed test.
A two-tailed test is used when we are interested in determining whether the mean running time has changed as a result of the introduced change in the production method, without specifying a specific direction of the change. We want to consider the possibility of both an increase and a decrease in the mean running time.
The null hypothesis (H0) for a two-tailed test states that there is no change in the mean running time. In this case, it would be stated as: H0: μ = μ0, where μ represents the population mean running time and μ0 represents the hypothesized mean running time under the previous production method.
The alternative hypothesis (Ha) for a two-tailed test states that there is a change in the mean running time, either an increase or a decrease. In this case, it would be stated as: Ha: μ ≠ μ0, indicating that the mean running time is not equal to the hypothesized mean running time.
The claim being tested is that the mean running time has changed as a result of the introduced change in the production method. This claim is not specific to whether the mean running time has increased or decreased, but rather focuses on the existence of a change.
By classifying the hypothesis test as two-tailed, we are considering the possibility of both an increase and a decrease in the mean running time. This allows for a more comprehensive evaluation of the effects of the introduced change in the production method.
In summary, the hypothesis test is classified as a two-tailed test. The null hypothesis states that there is no change in the mean running time, while the alternative hypothesis states that there is a change, whether it is an increase or a decrease. The claim being tested is that the mean running time has changed as a result of the introduced change in the production method.
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lily wants to put a bird food mix in her bird feeder.Her bird feeder can hold 8 cups of bird food.The bird food is a mix of 20% corn and the rest is sunflowers seeds how many cups of corn will lily need to fill the 8 cup bird feeder.If the rest of the mix is sunflower seed,what percent of the bird food is sunflower seed.
Answer:
80%
Step-by-step explanation:
100% is full so you do 100%-20%=80% so thats the answer
Determine The Sum Of - -5-8-11--------269 b)1-3+9----243
Given expression are:
a) -5 - 8 - 11 -... - 269 = -11823.
b) 1 - 3 + 9 - ... + 243 = 364.
a) To find the sum of the given expressions, we first have to identify the type of the sequence.
The first expression is an arithmetic sequence with common difference -3.
Using the formula of the sum of arithmetic sequence, we can find the sum of the sequence.
Formula to find sum of n terms in an arithmetic sequence:
Sn = (n/2) [2a + (n-1)d]
where n is the number of terms in the sequence, a is the first term and d is the common difference)
To find the sum of the first expression, we need to calculate the number of terms in the sequence.
Given, First term, a = -5 Common difference, d = -3 Last term, l = -269
Using the formula for finding nth term in an arithmetic sequence:
l = a + (n-1)d-269
= -5 + (n-1) (-3)-269
= -5 -3n + 3-3n
= -267n = 89
Therefore, there are 89 terms in the sequence.
Now, using the formula of the sum of the arithmetic sequence:
Sn = (n/2) [2a + (n-1)d]S89
= (89/2) [2(-5) + (89-1) (-3)]S89
= (89/2) [-10 - 264]S89
= -11823
The sum of the
is -11823.
b)The second expression is a geometric sequence with common ratio 3.
Using the formula of the sum of geometric sequence, we can find the sum of the sequence.
Formula to find sum of n terms in a geometric sequence:
S = [a(1-r^n)] / [1-r]where n is the number of terms in the sequence, a is the first term and r is the common ratio
To find the sum of the second expression, we need to calculate the number of terms in the sequence.
Given, First term, a = 1 Common ratio, r = 3 Last term, l = 243
Using the formula for finding nth term in a geometric sequence:
l = ar^(n-1)243
= 1 x 3^(n-1)3^(n-1)
= 243n-1 = 5n = 6
Therefore, there are 6 terms in the sequence.
Now, using the formula of the sum of the geometric sequence:
S = [a(1-r^n)] / [1-r]S
= [1(1-3^6)] / [1-3]S
= [1-729] / (-2)S
= 364
The sum of the geometric sequence is 364.
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Calculate Determine the amount of recoverable materials for an urban area in a recycling program if an MRF exists for separating and processing paper,cardboard,aluminum cans,metal tins,glass and mixed plastics.Assume the material distribution and percentage recoverable are as shown in example in class Component %MSW by weight Weight before recycling (suot) Food 46 5129 Paper ,cardboard 11 1226 Plastics 9 1003 Glass 7 780 Metals 5 558 Clothing/textiles 1 111 Ashes ,dust 19 2118 Unclassified 2 223
By considering the material distribution and recoverable percentages, we can calculate the amount of recoverable materials for the urban area's recycling program.
To determine the amount of recoverable materials in an urban area's recycling program, we need to consider the material distribution and the percentage of each component that is recoverable. Based on the provided data, let's calculate the recoverable weight for each component:
Food: 46% of municipal solid waste (MSW) weighs 5129 tons, so the recoverable weight is 46% of 5129 tons.
Paper and cardboard: 11% of MSW weighs 1226 tons, and assuming a certain percentage of paper and cardboard is recoverable, we multiply this percentage by 1226 tons to obtain the recoverable weight.
Plastics: 9% of MSW weighs 1003 tons, and the recoverable weight is determined similarly to paper and cardboard.
Glass: 7% of MSW weighs 780 tons, and the recoverable weight is calculated based on the recoverable percentage.
Metals: 5% of MSW weighs 558 tons, and the recoverable weight is determined using the recoverable percentage.
Clothing/textiles, ashes/dust, and unclassified materials: The recoverable weight for each component is calculated based on the respective percentages.
By summing up the recoverable weights of all components, we can determine the total amount of recoverable materials for the urban area's recycling program.
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Given f(x)=3x^2+kx+9, and the remainder when f(x) is divided by x-3 is 6, then what is the value of k?
Answer:
k = - 10
Step-by-step explanation:
6=9+3(k+9)
3(k+9)=-3
k+9= -1
k= -10
The value of k is -10.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Given a function 3x² + kx + 9.
Divide the function with x - 3.
Do the long division process.
After doing the long division,
(3x² + kx + 9) / (x - 3), we get the quotient as 3x + (k + 9) and the remainder as 9 + 3(k + 9).
9 + 3(k + 9) = 6
3(k + 9) = -3
k + 9 = -1
k = -1 - 9
k = -10
Hence the number k has the value -10.
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Jenny sleeps for 8 hours every day. How many days does she spend over the course
Answer:
56 Hours A Week... how long is the course though?
Step-by-step explanation:
Anna owns a small business selling used books. She knows that in the last week 29 customers paid cash, 26 customers used a debit card, and 62 customers used a credit card.
Based on these results, express the probability that the next customer will pay with cash as a percent to the nearest whole number.
The probability that the next customer will pay with cash, expressed as a percent to the nearest whole number, is 25%.
To calculate the probability that the next customer will pay with cash, we need to use the total number of customers in the last week (29 + 26 + 62 = 117) and the number of customers who paid with cash (29).
The probability that the next customer will pay with cash can be expressed as: P(cash) = 29/117
To express this probability as a percentage, we can multiply by 100:
P(cash) = 29/117 × 100 ≈ 24.79%
Therefore, the probability that the next customer will pay with cash is approximately 24.79%. To round this to the nearest whole number, we need to look at the decimal part of the percentage. If it's less than 0.5, we round down, and if it's 0.5 or greater, we round up. In this case, the decimal part is 0.79, which is greater than 0.5, so we round up:
P(cash) ≈ 25%
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Can someone help me with this. Will Mark brainliest.
Answer:
B (3, -4)
Step-by-step explanation:
A( -7, 2)
midpt ( -2, -1)
Equation:
(x + 5, y - 3)
Solve for B:
( -2, -1)
(x + 5, y - 3)
(3, -4)
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!
Answer:
a no b yes c no d no e yes
Step-by-step explanation:
Graph on a coordinate plane P(-3,-5)
Answer:
Answer is in the image below
Answer:
P is simply the mark or letter that the point will be called. In this case we have -3,-5. You will move left 3 spaces from the origin and down 5 places from the spot you marked -3. After that will be point P
Choose the best term from the box.
The ?
of an object is how heavy the object is.
?
weight
length
capacity
15
The equation of line s is y = __13 x − 3. The equation of line t is y = –x + 5. The equations of lines s and t form a system of equations. The solution to the system of equations is located at point P. Draw a line to represent line s and another line to represent line t. Then plot point P.
Answer:
They cross at point (0.571, 4.429)
Step-by-step explanation:
I just did it and got it correct
Please mark me Brainliest
Write an equation of the line that passes through point (-1, 5) and has the slope m = 4.
Answer:
y=4x+5
Step-by-step explanation:
y=mx+c
gradient =m
y intercept=c
m=4
c=5
so
y=4x+5
Answer:
y=4x+9
Step-by-step explanation:
y=mx+b
y=4x+b
5=4(-1)+b
5=-4+b
b=9
y=4x+9
Need to help to find the slope pls helppp
Answer:
Step-by-step explanation:
easy
Answer:
it is 2
Step-by-step explanation:
rise over run
it goes up 2 points and
moves right 1 point
2/1 =2